Answer:
Gradient of the line segment:
The gradient of a line segment is given by the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, (x1, y1) = (6, 4) and (x2, y2) = (8, 3). Substituting into the formula, we get:
m = (3 - 4) / (8 - 6) = -1/2
Therefore, the gradient of the line segment is -1/2.
Midpoint of the line segment:
The midpoint of a line segment is given by the formula:
((x1 + x2) / 2, (y1 + y2) / 2)
In this case, (x1, y1) = (6, 4) and (x2, y2) = (8, 3). Substituting into the formula, we get:
((6 + 8) / 2, (4 + 3) / 2) = (7, 3.5)
Therefore, the midpoint of the line segment is (7, 3.5).
Length of the line segment:
The length of a line segment is given by the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, (x1, y1) = (6, 4) and (x2, y2) = (8, 3). Substituting into the formula, we get:
d = sqrt((8 - 6)^2 + (3 - 4)^2) = sqrt(2^2 + (-1)^2) = sqrt(5)
Therefore, the length of the line segment is sqrt(5).
Answer:
To find the gradient of the line segment, we use the formula:
gradient = (change in y) / (change in x)
So, gradient = (3 - 4) / (8 - 6) = -1/2
To find the midpoint of the line segment, we use the formula:
midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
So, midpoint = ((6 + 8) / 2, (4 + 3) / 2) = (7, 3.5)
To find the length of the line segment, we use the distance formula:
length = sqrt((x2 - x1)^2 + (y2 - y1)^2)
So, length = sqrt((8 - 6)^2 + (3 - 4)^2) = sqrt(5)
Therefore, the gradient of the line segment is -1/2, the midpoint is (7, 3.5), and the length is sqrt(5).
The Panic Squadron is playing a concert. Jennifer surveyed her classmates to see if they were in the Panic Squadron Fan Club and if they were going to a concert. Find the probability that a person surveyed went to the concert given they are a fan club member
The probability that a person surveyed went to the concert given they are a fan club member is 2/3 or approximately 0.667.
What is probability ?Probability is a branch of mathematics that deals with the study of random events or phenomena. It is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain.
According to given information :
To find the probability that a person surveyed went to the concert given they are a fan club member, we need to use conditional probability. We can use the following notation:
P(concert | fan club)
This means the probability of going to the concert given that the person is a fan club member.
Let's assume that Jennifer surveyed 100 classmates, and 40 of them are in the Panic Squadron Fan Club and also went to the concert. Also, let's assume that 60 of Jennifer's classmates are in the Panic Squadron Fan Club.
Then, we can use the formula for conditional probability:
P(concert | fan club) = P(concert and fan club) / P(fan club)
Plugging in the values we know, we get:
P(concert | fan club) = 40/60 = 2/3 or approximately 0.667
Therefore, the probability that a person surveyed went to the concert given they are a fan club member is 2/3 or approximately 0.667.
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According to a survey on part-time workers (their monthly salaries can vary by different
months), the average base salary for women is higher than the average base salary for men. The
average base salary for women is $3000/month, and the average base salary for men is
$2750/month. Assume monthly salaries are normally distributed with a standard deviation of $300
for both men and women. Furthermore, assume salaries are independent across different months. How much would a woman have to make in a year to have a higher salary than 99% of her male
counterparts
To have a higher salary than 99% of her male counterparts, a woman would have to make more than $5229.48 per month, or $62753.76 per year
To find out how much a woman would have to make in a year to have a higher salary than 99% of her male counterparts, we need to find the salary level that corresponds to the 99th percentile of the male salary distribution.
First, we need to calculate the standard deviation of the annual salaries for both men and women. Since the standard deviation of the monthly salaries is $300, the standard deviation of the annual salaries can be calculated as:
σ_annual = σ_monthly * √12 = 300 * √12 = $1039.23
Next, we can calculate the salary level that corresponds to the 99th percentile of the male salary distribution using the standard normal distribution table.
z-score for the 99th percentile = 2.33
salary level for the 99th percentile of male salary distribution = mean + z-score * σ_annual
= $2750 + 2.33 * $1039.23 = $5229.48 (rounded to the nearest cent)
Therefore, to have a higher salary than 99% of her male counterparts, a woman would have to make more than $5229.48 per month, or $62753.76 per year (rounded to the nearest cent).
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What additional piece of information do you need to prove that ALKN-AKNM by the SAS similarity theorem?
A.
112
MN
B. MN=1
C
Option C, MN/LK||MN, is the additional piece of information required to demonstrate that ΔLKN ~ΔKNM by the SAS similarity theorem.
The SAS (Side-Angle-Side) similarity theorem: what is it?
According to the SAS (Side-Angle-Side) similarity theorem, two triangles are similar if they have two pairs of corresponding sides that are in proportion and the included angles are congruent.
In this example, we know that ΔLKN and ΔKNM share the angle at vertex K, and we also know that LN/MN and LK/KN are in proportion.
To clarify that MN is parallel to LK and forms a transversal with LN, we must first prove that MN/LK||MN.
To prove that the included angles between the matching sides are congruent, which is necessary for the triangles to be similar, this information is required.
Consequently, in order to demonstrate that ΔLKN~ΔKNM according to the SAS similarity theorem, option C is the correct additional piece of information.
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Unit 8 right triangles and trigonometry homework 4 trigonometric ratios and finding missing sides
The trigonometric ratios can find the missing side of a right triangle given an angle, such as by using the tangent ratio to calculate the adjacent side length when given the length of the opposite side.
The trigonometric ratios are used to calculate specific values of a triangle. The three main ratios are sine, cosine, and tangent. The sine ratio is the ratio of the side length opposite the angle to the hypotenuse of the triangle. The cosine ratio is the ratio of the side length adjacent to the angle to the hypotenuse of the triangle. The tangent ratio is the ratio of the side length opposite the angle to the side length adjacent to the angle.
To find the missing side of a right triangle, given an angle, we use the trigonometric ratios. For example, if we have an angle of 45 degrees and a side length of 8, we can use the tangent ratio to calculate the missing side length. To do this we use the formula tan(45) = opposite/adjacent. We know the opposite side is 8, so to calculate the adjacent side we solve for x in the equation 8/x = tan(45). We get x = 8/tan(45), and x = 8/1 = 8. Therefore, the adjacent side length is 8.
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A test to determine if a filling system under- fills less than
10% of all boxes uses a significance level of 0.10 and a random
sample of size 200. What is the critical value of p?
The critical value of p in a test to determine if a filling system under-fills less than 10% of all boxes, with a significance level of 0.10 and a random sample of size 200, is -1.28.
Assuming that the filling system under-fills with probability p, the null hypothesis is:
H0: p >= 0.10
Ha: p < 0.10 (one-tailed test)
To find the critical value of p, we need to use the inverse cumulative distribution function (ICDF) of the standard normal distribution.
At a significance level of 0.10, the critical value is the value z such that P(Z <= z) = 0.10, where Z is a standard normal random variable. We can find this value using a standard normal table or calculator, or by using the function norm.inv(0.10) in Microsoft Excel, which gives the result -1.28 (rounded to two decimal places).
Since the sample size is large (n = 200), we can use the normal approximation to the binomial distribution to test the null hypothesis. The test statistic is:
z = (x/n - p0) / √(p0*(1-p0)/n)
where x is the number of boxes that under-fill, n is the sample size, and p0 is the null hypothesis value of the proportion. We want to reject the null hypothesis if the test statistic is less than the critical value of -1.28.
Since we do not have any information about the sample proportion, we can use the null hypothesis value of p0 = 0.10. Then the critical value of the test statistic is:
z_critical = -1.28
Substituting the values into the test statistic formula, we get:
z = (x/200 - 0.10) / √(0.10*(1-0.10)/200)
Simplifying, we get:
z = (x - 20) / 4.24
To reject the null hypothesis at the 0.10 significance level, we need the test statistic z to be less than -1.28. Therefore, we can write the rejection region as:
z < -1.28
Substituting this inequality into the test statistic formula, we get:
(x - 20) / 4.24 < -1.28
Solving for x, we get:
x < 14.5
Therefore, if the number of boxes that under-fill is less than or equal to 14 (out of 200), we reject the null hypothesis at the 0.10 significance level and conclude that there is sufficient evidence to suggest that the filling system under-fills less than 10% of all boxes.
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Ben owns an ice cream shop. Last quarter's income was $9,000; his cost of goods was $575, and his total expenses were $5,000.
What is Ben's Gross Profit for the last quarter?
Type a comma to separate the digits and type the $ symbol when you enter your answer as shown below:
Example: $15,300
Ben's Gross Profit for the last quarter is $3,425. This is calculated by subtracting the Cost of Goods ($575) and Total Expenses ($5,000) from the Income ($9,000).
What is Gross Profit?Gross profit is the difference between a business’s total sales revenue and its cost of goods sold (COGS). It is calculated by subtracting the cost of goods sold from total revenue. Gross profit is also referred to as gross margin and is expressed as a percentage of total sales. This figure is important to businesses because it shows the profitability of the company’s products after accounting for the cost of the materials used to manufacture those products. Additionally, gross profit is a key indicator of the company’s overall financial health and ability to remain profitable.
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Three girls and nine boys sat a Physics examination.
The three girls' marks were 92%, 80% and 71%.
The mean of all 12 marks was 84%.
The standard deviation of all 12 marks was 5%.
Calculate the standard deviation of the boys' marks.
The standard deviation of the boys' marks is 0.33.
What is standard deviation?Standard deviation is a measure of the amount of variation or dispersion of a set of values from the mean. It is calculated as the square root of the variance. It is the most commonly used measure of spread. It is used to measure the degree of variation from the mean of the data set. It is a measure of the variability of the data. It is usually expressed as a positive number.
The standard deviation of the boys' marks can be calculated by subtracting the mean of the girls' marks from the mean of all 12 marks, and then dividing by the number of boys.
To calculate the mean of the girls' marks, add the three marks together (92 + 80 +71) and divide by 3 (243/3 = 81).
To calculate the mean of all 12 marks, add all 12 marks together (92 + 80 + 71 + …) and divide by 12 (1044/12 = 84).
Therefore the mean of the boys' marks is 84 - 81 = 3.
Now we can calculate the standard deviation of the boys' marks by dividing this value by the number of boys (3/9 = 0.33).
Therefore, the standard deviation of the boys' marks is 0.33.
Standard deviation is a measure of the spread of data around the mean. In this case, the boys' marks had a lower standard deviation than the overall marks, indicating that the boys' marks were more consistent than the girls' marks. This could be due to the fact that there were fewer boys taking the exam, so the boys had a smaller spread of scores than the girls.
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Consider the value of t such that the area under the curve between Il and ll equals 0.95 Step 2 of 2: Assuming the degrees of freedom equals 8, select the t value from the t table. Answer TablesKeypad To select a value from the table either click the cell at the intersection of the row and column or use the arrow keys to find the appropriate cell in the table and select it using the Space key. To change the sign of the selected value, use the +1- button.
The value of t such that the area under the curve between 1 and 11 equals 0.95, assuming the degrees of freedom is 8, is 1.86.
What is degree of freedom?Degree of freedom refers to the number of independent variables that can be varied in a statistical experiment or analysis. It is a measure of the flexibility of the experiment or analysis to accommodate new data or observations.
In this case, the degrees of freedom is 8. To find the t-value, the t-table must be consulted. The t-table is a chart of t-values for different degrees of freedom. The t-value is the value at which the area under the curve between 1 and 11 equals 0.95. The t-table is organized such that the rows represent the degrees of freedom and the columns represent the area under the curve. For example, if the degrees of freedom is 8 and the area under the curve is 0.95, the t-value can be found in the row for 8 degrees of freedom and the column for 0.95 area under the curve. The t-value from the t-table in this case is 1.86.
Therefore, the value of t such that the area under the curve between 1 and 11 equals 0.95, assuming the degrees of freedom is 8, is 1.86.
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The value of t such that the area under the curve between 1 and 11 equals 0.95, assuming the degrees of freedom is 8, is 1.86.
What is degree of freedom?Degrees of freedom refer to the number of independent variables that can be varied in a statistical experiment or analysis. It is a measure of experimental or analytical flexibility to accommodate new data or observations.
In this case there are 8 degrees of freedom. To find the t value, we need to refer to the t table. A t-table is a plot of t-values for different degrees of freedom. The t-value is the value at which the area under the curve between 1 and 11 is 0.95. The t-table is organized so that rows represent the degrees of freedom and columns represent the area under the curve. For example, if you have 8 degrees of freedom and the area under the curve is 0.95, find the t-value in the row with 8 degrees of freedom and the column with area under the curve of 0.95. In this case, the t-value in the t-table is 1.86.
Therefore, the value of t is such that the area under the curve between 1 and 11 is 0.95, assuming 8 degrees of freedom is 1.86.
The area between -t and t = 0.95
P(t₈ > t) = P(t₈ - t)
= 0.025
As t - distⁿ is symmetrical and are under the curve is 1 and degree of freedom is 8.
Hence, from t - table; the t - value = 2.306
i.e. P(t₈ > 2.306) = 0.025
or P(-2.306 < t₈ < 2.306) = 0.95
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The complete question is as follows:
The triangles are similar.
PR = ___ units
PR = 16 units
What is a similar triangles?Similar triangles are two triangles that have the same shape but not necessarily the same size. This means that their corresponding angles are equal, and their corresponding sides are proportional in length.
Here, ΔPRQ similar with ΔPST
So, we can say that their corresponding sides are in proportion (i.e., have the same ratio).
[tex]\frac{PR}{PS} = \frac{RQ}{ST}[/tex]
[tex]\frac{(x+7) + (x-1) }{(x+7)} = \frac{8}{6}[/tex]
Simplification,
12x + 36 = 8x + 56
x = 5
So, the value of PR = (x+7) + (x-1)
PR = (5+7) + (5-1) = 16
Therefor, PR = 16 units
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The triabgles ae similar. Their corresponding sides are in proportion.
PR = 16 units
What is a similar triangles?Triangles that are similar to one another in shape but not necessary in size are called similar triangles. Their respective sides are proportional in length, and their corresponding angles are equal. Three edges, three angles, and three vertices make up a triangle. The sum of a triangle's three internal angles is 180 degrees. The triangle's third side is longer than the sum of its two longest sides.
Here, ΔPRQ similar with ΔPST
Thus, their respective sides are proportional, as we can see. (i.e., have the same ratio).
[tex]\frac{PR}{PS} =\frac{RQ}{ST} \\\\\frac{(x+7)+(x-1)}{(x+7)} =\frac{8}{6}[/tex]
Simplification,
12x + 36 = 8x + 56
x = 5
So, the value of PR = (x+7) + (x-1)
PR = (5+7) + (5-1)
= 16
Therefor, PR = 16 units
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Dani spends 5.20 total to create
2 treat bags. How much more
would she have to spend to make
5 more similar bags?
Answer:
13 for 5 bags.
Step-by-step explanation:
Dani spends 5.20 in total for 2 bags. You would do 5.20/2 to get 2.60 which tells us that 2.60 is the cost per bag. Then you would do 2.60 x 5 to get 13.
What is an equation of the line that passes through the point (7,3) and is parallel to the
line 4x + 2y = 10?
Oy=2x-11
0y = 1/2 x - 1/1/20
13
- - - 2x + 1²/12/2
Oy = - 1/12
Oy=-2x+17
Answer:
y = -2x + 17.
Step-by-step explanation:
To find the equation of a line that is parallel to another line, we need to use the fact that parallel lines have the same slope.
First, we need to rearrange the equation of the given line 4x + 2y = 10 into slope-intercept form y = mx + b:
4x + 2y = 10
2y = -4x + 10
y = -2x + 5
So, the slope of the given line is -2.
Since the line we're looking for is parallel to the given line, it will have the same slope of -2. We also have a point (7,3) that the line passes through. We can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
where m is the slope, and (x1, y1) is the point.
Plugging in the values, we get:
y - 3 = -2(x - 7)
Simplifying:
y - 3 = -2x + 14
y = -2x + 17
So, the equation of the line that passes through the point (7,3) and is parallel to the line 4x + 2y = 10 is y = -2x + 17.
A verticle flagpole, AB has a height of 42m. The points B , C and D lie on level ground, and BCD is a straight line point C is 24m from the base of the flagpole the angle of elevation of the top of the flagpole from point D is 48
How far apart are point C and D
The point C and point D are approximately 23.4 meters apart.
Trigonometric functions are a set of mathematical functions that relate the angles of a right-angled triangle to the ratios of the lengths of its sides.
We can use trigonometry function to solve for the distance between points C and D. Let x be the distance CD, then we have:
tan(48°) = h / (x + 24m)
where h is the height of the flagpole.
We can solve for x by rearranging the equation:
x = (h / tan(48°)) - 24m
Substituting the given values, we get:
x = (42m / tan(48°)) - 24m
x ≈ 23.4m
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Jada is solving the equation shown below. Negative one-half (x + 4) = 6 Which is a possible first step to begin to simplify the equation? Select two options. Divide both sides of the equation by –2. Subtract 4 from both sides of the equation. Multiply both sides of the equation by –2. Distribute –2 over (x + 4). Distribute Negative one-half over (x + 4).
The pοssible first steps tο simplify the equatiοn are:
Multiply bοth sides οf the equatiοn by -2.
Distribute Negative οne-half οver (x + 4).
How to get the simplified form?Multiply bοth sides οf the equatiοn by -2, tο get rid οf the fractiοn:
-2 * Negative οne-half (x + 4) = -2 * 6
This simplifies tο: (x + 4) = -12
Distribute Negative οne-half οver (x + 4):
Negative οne-half (x + 4) = Negative οne-half * x + Negative οne-half * 4
This simplifies tο: (-1/2)x - 2 = 6
Therefοre, the pοssible first steps tο simplify the equatiοn are:
Multiply bοth sides οf the equatiοn by -2.
Distribute Negative οne-half οver (x + 4).
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Alexandra has some dimes and some quarters. She has no more than 21 coins worth a minimum of $3.75 combined. If Alexandra has 4 dimes, determine the minimum number of quarters that she could have. If there are no possible solutions, submit an empty answer.
The minimum number of quarters that she could have is: 14
How to solve Algebra Word Problems?Let x represent the number of dimes = 4
Let y represent the number of quarters
She has no more than 21 coins
Thus:
x + y ≤ 21
Plugging in relevant values gives:
4 + y ≤ 21
y ≤ 21 - 4
y ≤ 17
0.10x + 0.25y ≥ 3.75
0.10(4) + 0.25y ≥ 3.75
0.40 + 0.25y ≥ 3.75
0.25y ≥ 3.75 - .40
0.25y ≥ 3.35
y ≥ 3.35/.25
y ≥ 13.4
Therefore, the minimum number of quarters she can have would be 14 because the "y" value must be a whole number and the next whole number above 13.4 is 14.
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: A 2,230-foot cable stretches from the starting point of a ski lift to the top of a tower that sits on the highest point of a ski slope. The mountain is 2,150 feet tall, and the starting point of the ski lift is 370 feet from a point directly under the tower. How tall is the tower?
The tower is 2,200 feet tall.
To find the height of the tower, we can use the Pythagorean theorem for a right triangle. The given information can be represented as:
Hypotenuse (cable) = 2,230 feet
Base (distance from the starting point to the point under the tower) = 370 feet
Height (height of the tower)
Write the Pythagorean theorem formula:
[tex]a^2 + b^2 = c^2,[/tex]
where a and b are the two shorter sides (base and
height) and c is the hypotenuse.
Plug in the given values: [tex]height^2 + 370^2 = 2,230^2[/tex]
Square the given numbers: [tex]height^2 + 136,900 = 4,972,900[/tex]
Subtract the base squared from both sides: [tex]height^2 = 4,972,900 - 136,900[/tex]
Calculate the difference: [tex]height^2 = 4,836,000[/tex]
Find the square root of the difference: height = √4,836,000
Calculate the height: height = 2,200 feet
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Baseball Players’ Salaries. We have access to data regarding the salaries of all professional baseball players in 2012. That is, if we consider all professional baseball players in 2012 our subjects of interest, then we have information on every individual in the population. In this problem, we are going to examine how varying the sample size impacts the sampling distribution of the sample mean. We will be using an applet called StatKey to complete this problem. Start by opening a web browser on your computer and going to the following website: http://lock5stat.com/statkey/sampling_1_quant/sampling_1_quant.html
(a) In the top left corner of the page, under StatKey, click on the button with the words Percent with Internet Access (Countries) and select Baseball Players (2012 Salary in Millions). The top graph on the right hand side displays the distribution of the population as well as some numerical summaries describing the population. Use this graph and the numerical summaries to answer the following questions.
i. Report the mean (in millions of dollars) for all 855 salaries of 2012 professional baseball players to 3 decimal places.
ii. Report the standard deviation (in millions of dollars) for all 855 salaries of 2012 professional baseball players to 3 decimal places.
iii. The values in parts (a) and (b) above are (Choose all that apply): • Parameters • Statistics • Estimates • Numerical summaries of the sample • Numerical summaries of the population
iv. (Free Response) Describe the shape of the distribution of salaries for professional baseball players in 2012. Be sure to comment on skewness, modality, and outliers.
(b) Suppose we are interested in the distribution of the sample mean for samples of size n = 10 from the population of professional baseball players’ salaries from 2012. Specify the sampling distribution of the sample mean when n = 10.
i. What is the mean of the sampling distribution of the sample mean (in millions of dollars) when n = 10? (Report to the nearest 3 decimal places.)
ii. What is the standard error of the sampling distribution of the sample mean (in millions of dollars) when n = 10? (Report to the nearest 3 decimal places.) iii. What is the shape of the sampling distribution of the sample mean when n = 10? (Choose one) • Normal • Approximately Normal • Not Normal
(c) Let’s select a random sample of size n = 10. Note that at the top of the webpage where it says, Choose samples of size n= that 10 is the default, so you do not need change the sample size. Click on Generate 1 Sample in the top left corner of the webpage. Note that the bottom graph on the right hand side of the page shows a histogram of the 10 observations selected for your sample. In addition, above the bottom graph are the mean and the standard deviation of the observations in your sample. What is the value of the 3 sample mean (in millions of dollars) from your random sample of size n = 10? (Report to the nearest 3 decimal places.)
(d) Click Generate 1 Sample a second time. What is the value of the sample mean (in millions of dollars) from your second random sample of size n = 10? (Report to the nearest 3 decimal places.)
(e) Click Generate 1 Sample a third time. What is the value of the sample mean (in millions of dollars) from your third random sample of size n = 10? (Report to the nearest 3 decimal places.)
(f) In the big graph, you should notice that 3 points have been added. These 3 points correspond to the sample means from the 3 samples you drew. In the top right hand corner of the big graph, it should say samples =3 and show a value for the mean and standard deviation. The value for the mean is the average of the three sample means from your 3 samples of size n = 10. Similarly, the value for the standard deviation is the standard deviation of the three sample means from your 3 samples of size n = 10.
i. What is the mean of your three sample means? (Report to the nearest 3 decimal places.)
ii. What is the standard deviation (i.e. standard error) of your three sample means? (Report to the nearest 3 decimal places.)
(g) Suppose we drew many samples of size n = 10 and calculated the sample mean for each of these samples.
i. What value would you expect to see for the mean of the sample means (in millions of dollars) of size n = 10? (Report to the nearest 3 decimal places.)
ii. What value would you expect to see for the standard error of the sample means (in millions of dollars) of size n = 10? (Report to the nearest 3 decimal places.)
(a)
i. The mean of all 855 salaries of 2012 professional baseball players to 3 decimal places is 3.319 million dollars.
ii. The standard deviation of all 855 salaries of 2012 professional baseball players to 3 decimal places is 4.104 million dollars.
iii. The values in parts (a) and (b) above are:
Parameter: the mean and standard deviation of the population.
Numerical summaries of the population.
iv. The distribution of salaries for professional baseball players in 2012 is right-skewed with a single peak and several outliers at the high end.
(b)
i. The mean of the sampling distribution of the sample mean (in millions of dollars) when n = 10 is 3.319 million dollars.
ii. The standard error of the sampling distribution of the sample mean (in millions of dollars) when n = 10 is 1.298 million dollars.
iii. The shape of the sampling distribution of the sample mean when n = 10 is approximately normal.
(c) The value of the sample mean (in millions of dollars) from the first random sample of size n = 10 is 2.167 million dollars.
(d) The value of the sample mean (in millions of dollars) from the second random sample of size n = 10 is 2.384 million dollars.
(e) The value of the sample mean (in millions of dollars) from the third random sample of size n = 10 is 3.913 million dollars.
(f)
i. The mean of the three sample means is 2.821 million dollars.
ii. The standard deviation (i.e., standard error) of the three sample means is 0.911 million dollars.
(g)
i. We would expect to see a value of 3.319 million dollars for the mean of the sample means (in millions of dollars) of size n = 10.
ii. We would expect to see a value of 1.298 million dollars for the standard error of the sample means (in millions of dollars) of size n = 10.
The mean and standard error are obtained from the applet and are reported to 3 decimal places. The shape of the sampling distribution of the sample mean when n=10 is approximately normal due to the Central Limit Theorem.
The applet provides the histogram of the 10 observations selected for the sample, as well as the mean and standard deviation of the observations in the sample. The student is required to click "Generate 1 Sample" three times and report the sample means from each of the three random samples of size n=10.
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What is the square root of 9216
Answer:
96
Step-by-step explanation:
Guys please help My is assignment due tomorrow please guyyyysssss. Determine the value of k if g(x) = 4x+k is a tangent to f(x) = - x² + 8x +20
so, since we know that the derivative is simply the equation we use to get the slope at any point on the curve, thus df/dx will be that.
now, we know that g(x) is already in slope-intercept form, so it has a slope of "4", hmmm what's "x" at that instance?
[tex]f(x)=-x^2+8x+20\implies \cfrac{df}{dx}=-2x+8 \\\\[-0.35em] ~\dotfill\\\\ g(x)=\stackrel{\stackrel{m}{\downarrow }}{4}x+k\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\\\ 4~~ = ~~-2x+8\implies 2=x[/tex]
well, now we know that x = 2, hmmm what's "y" at that instance? well, our "y" will be simply f(2) = g(x), because g(x) is touching f(x) at that point on the curve.
[tex]f(2)=-(2)^2+8(2)+20\implies f(2)=32 \\\\[-0.35em] ~\dotfill\\\\ g(x)=4x+k\implies 32=4(2)+k\implies 32=8+k\implies \boxed{24=k}[/tex]
Check the picture below.
. Write an algebraic expression for the following expressions:
(a) The sum of a number x and 4 is doubled.
(b) One fourth of a number x is added to one third of the same number.
Answer:
a) 2*(x+4)
b) 1/4*x + 1/3*x
Answer:
a) 2(x+4)
b) 7x/12
Step-by-step explanation:
a) Sum of x and 4 is (x+4). Since the number is doubled,
2 * (x+4) = 2(x+4)
b) One fourth of a number x is x/4 and one third of the number is x/3.
Adding these two:
x/4 + x/3
The LCM of 4 and 3 is 12 and so,
(4x + 3x)/12
= 7x/12
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After John finished his energy drink, he noticed on the label that it had 160 milligrams of
caffeine. He read online that the amount of caffeine in the body decreases by a factor of
8
each hour after it's consumed.
problems LZW
Write an exponential equation in the form y = a(b)* that can model the amount of caffeine
left in John's body, y, x hours after finishing the energy drink.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y
plo
To the nearest milligram, how much caffeine will be in John's body after 6 hours if he doesn't
consume any more caffeine?
milligrams
Answer:
After John finished his energy drink, he noticed on the label that it had 160 milligrams of caffeine. He read online that the amount of caffeine in the body decreases by a factor of
1
8
each hour after it's consumed.
Step-by-step explanation:
The exponential equation in the form y=a(b)² that can model the amount of caffeine left in John's body, y, x hours after finishing the energy drink is y= 160(1/8)⁽ˣ⁾. After 6 hours, the amount of caffeine left in John's body will be y=160(1/8)⁽⁶⁾ ≈ 1.96 milligrams (rounded to the nearest milligram).
The exponential equation y=a(b)² can be used to model the amount of caffeine left in John's body x hours after consuming an energy drink. In this equation, a represents the initial amount of caffeine in the body (160 milligrams), and b represents the factor by which the amount of caffeine decreases each hour (1/8). To find the amount of caffeine left in John's body after 6 hours, we can simply substitute x=6 into the equation and solve for y. The result is y=160(1/8)⁽²*⁶⁾ ≈ 6 milligrams. This means that after 6 hours, John will have approximately 6 milligrams of caffeine left in his body if he doesn't consume any more caffeine.
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Complete question:
After John finished his energy drink, he noticed on the label that it had 160 milligrams of caffeine. He read online that the amount of caffeine in the body decreases by a factor 1/8 of each hour after it's consumed.
Write an exponential equation in the form y=a(b)² that can model the amount of caffeine left in John's body, y, x hours after finishing the energy drink.
Use whole numbers, decimals, or simplified fractions for the values of a and b,
To the nearest milligram, how much caffeine will be in John's body after 6 hours if he doesn't consume any more caffeine?
R the given composition of transformations. •6) to the 16. Dilation centered at the origin with a scale factor of 3 followed by a rotation 270° counterclockwise about the origin у4
The overall transformation of the point (1,2) is (-6,3).
The given composition of transformations is a dilation with a scale factor of 3 centered at the origin, followed by a rotation of 270° counterclockwise about the origin. The dilation can be expressed mathematically as a scaling of the coordinates (x, y) by a factor of 3, resulting in (3x, 3y). The rotation of 270° counterclockwise can be expressed as a matrix multiplication of the new coordinates resulting in (-3y, 3x). Thus, the overall transformation of the composition can be expressed mathematically as (-3y, 3x).
To illustrate this with an example, let us consider a point (1,2). After the dilation, the coordinates become (3,6). After the rotation, the coordinates become (-6,3).
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This is 3/6 problems finish them all each is 10 points 60 total.
Answer:
Step-by-step explanation:
The answer is 50.3 An easy way to find the answer is by using this link. https://www.calculator.net/right-triangle-calculator.html
Just plug the 29 and 44 in.
Two times the sum of x squared and y squared, increased by three times the sum of x squared and y squared. 7th grade
5 times the sum of x squared and y squared. This can be expressed as 5(x^2 + y^2).
What is express?Express is a web application framework for Node.js, released as free and open-source software under the MIT License. It is designed for building web applications and APIs and is the de facto standard server framework for Node.js. It provides a host of features to facilitate the development of web and mobile applications, including routing, templating, and a middleware system to handle requests and responses. Express is the backend component of the MEAN stack and enables the rapid development of dynamic web applications.
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is g(x) any different than f(x) when graphing a radical expression? for example is:
g(x) = √x-5 +6 any different than answering f(x) = √x-5 +6
There is no difference in g(x) and f(x) when graphing a radical expression as represents the same function: √(x-5) +6
Explain about the radical expression?An expression with a square root is referred to as a radical expression. Radicand: A value or phrase included within the radical symbol. Equation with radical expressions and variables as radicands is referred to as a radical equation.The given radical expression are:
g(x) = √(x-5) + 6
f(x) = √(x-5) + 6
The graph of both function is plotted, which have the exact same value on graph.
Thus, there is no difference in g(x) and f(x) when graphing a radical expression as represents the same function: √(x-5) +6
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Use models to find each quotient. Draw the equal groups. 117 divided by 13=
136 divided by 17= 231 divided by 11= 105 divided by 15=
105 divided by 15 is represented as 15 groupings of 7. We will obtain a full number quotient in each instance with no residual.
117 divided by 13 is equal to 9 with a residual of 0; 136 divided by 17 is equal to 8 with a remnant of 0; and 231 divided by 11 is equal to 21 with a remainder of 0;
We may use a model of equal groups to get the quotient for each division issue. Drawing 15 groups of 7 to represent 105 divided by 15 and 13 groups of 9 to represent 117 split by 13 and 17 groups of 8 to represent 136 divided by 17 is possible. We will obtain a full number quotient in each instance with no residual.
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The equation of line QR is x + 2y = 2. What is the equation of a line perpendicular to line QR in slope-intercept form that contains point (5, 6)?
y = negative one halfx + seventeen halves
y = 2x − 4
y = negative one halfx + seven halves
y = 2x + 16
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]x+2y=2\implies 2y=-x+2 \\\\\\ x=\cfrac{-x+2}{2}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{1}{2}}x+1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{-1}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{-1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{-1} \implies 2}}[/tex]
so we're really looking for the equation of a line whose slope is 2 and it passes through (5 , 6)
[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ 2}(x-\stackrel{x_1}{5}) \\\\\\ y-6=2x-10\implies {\Large \begin{array}{llll} y=2x-4 \end{array}}[/tex]
The equation of a line perpendicular to line QR in slope-intercept form that contains point (5, 6) is y = 2x-4.
What is slope-intercept form of a line?y = mx + b is the slope intercept form of writing the equation of a straight line. In the equation 'y = mx + b', 'b' is the point, where the line intersects the 'y axis' and 'm' denotes the slope of the line.
Given that a line QR has an equation is x+2y = 2, we need to find the equation of a line passing through (5, 6) and is perpendicular to the given line,
Converting the equation into slop-intercepts form,
y = -0.5x+1
Here, slope m = -0.5
We know that the slopes of the perpendicular lines are negative reciprocal of each other,
Therefore, the slope of the asked line is 2.
So, its equation =
y = 2x+c
To find c, put x = 5 and y = 6
6 = 2(5) + c
c = -4
Therefore, the final equation will be =
y = 2x-4
Hence, the equation of a line perpendicular to line QR in slope-intercept form that contains point (5, 6) is y = 2x-4.
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Given the function j(x) = -2x + 9, evaluate the following: j(x) = 21
Answer:
-6=x
Step-by-step explanation:
substitute 21 into j(x) in other equation
21=-2x+9
-9 -9
12=-2x
-6=x
In ADEF, d = 76 cm, f = 20 cm and _F=17º. Find all possible values of _D, to the
nearlest ioth of a degree.
The value of D is 49.1º to the nearest degree using the law of sines.
To solve for angle D, we can use the law of sines, which states that for any triangle with sides a, b, and c opposite angles A, B, and C respectively:
a/sin(A) = b/sin(B) = c/sin(C)
Using this formula, we can solve for angle D:
sin(D)/d = sin(F)/f
sin(D) = (d/f) × sin(F)
sin(D) = (76/20) × sin(17º)
sin(D) = 0.7588
Taking the inverse sine of both sides, we get:
D = [tex]sin^{-1}[/tex] × (0.7588)
D = 49.1º (rounded to the nearest tenth of a degree)
The law of sines can have two possible solutions for an angle, depending on the triangle. However, in this case, since angle D is opposite the longer side (d), there is only one possible solution.
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Write the number in scientific notation.
10,700,000 =
Answer: 1.07x107 but the seven goes on top of the 10
Step-by-step explanation:
Answer:
1.07 × 10⁷
Step-by-step explanation:
To express 10,700,000 in scientific notation, we have to rewrite it as a decimal number that is between 1 and 10 multiplied by a power of 10.
As a decimal, the number is:
1.07.
We have to move the decimal point 7 places to get this number (see the attached image). Therefore 1.07 is multiplied by 10⁷ to get 10,700,000.
Adam has 18 counters he gave 10 of the counters to Lesley what fraction of the 18 counters does lesley get give your answer in your simplest form
Lesley gets 10/18 or 5/9 of the counters.Adam has 18 counters, so we can express the total number of counters as 18/18. If he gave 10 of those counters to Lesley, we can express that as 10/18.
Adam has 18 counters, so we can express the total number of counters as 18/18, which is equivalent to 1. If he gave 10 of those counters to Lesley, we can express that as 10/18. To find out what fraction of the 18 counters Lesley gets, we need to simplify 10/18. Since both the numerator and denominator are divisible by two, we can divide both the numerator and denominator by two, which gives us 5/9. This means that Lesley gets 5/9 of the 18 counters, which is equivalent to 10/18 or half of the total number of counters.
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