Cy = [1 1 1; 0 1 1; 0 0 1] [p(1-p) 0 0; 0 p(1-p) 0; 0 0 p(1-p)] [1 0 0; 1 1 0; 1 1 1]
Cy = [
(a) The probability mass function (PMF) for X is:
px(x1, x2, x3) = P(X1 = x1, X2 = x2, X3 = x3) = P(X1 = x1) * P(X2 = x2) * P(X3 = x3) = (1-p)^(1-x1) * p^(x1) * (1-p)^(1-x2) * p^(x2) * (1-p)^(1-x3) * p^(x3) = p^(x1+x2+x3) * (1-p)^(3-x1-x2-x3)
where p=1/4 is the probability of success and (x1,x2,x3) can take values in {0,1}.
(b) The covariance matrix Cx can be calculated using the formula:
Cx = E[(X - mu)(X - mu)^T]
where mu is the mean vector of X, which is [p, p, p]^T in this case, and E denotes the expected value.
Using the fact that X1, X2, X3 are independent, we have:
E[X1X2] = E[X1]E[X2] = p^2
E[X1X3] = E[X1]E[X3] = p^2
E[X2X3] = E[X2]E[X3] = p^2
E[X1] = E[X2] = E[X3] = p
E[X1^2] = E[X2^2] = E[X3^2] = p
E[(X1-p)(X2-p)] = E[X1X2] - p^2 = 0
E[(X1-p)(X3-p)] = E[X1X3] - p^2 = 0
E[(X2-p)(X3-p)] = E[X2X3] - p^2 = 0
Therefore, the probability matrix Cx is:
Cx = E[(X - mu)(X - mu)^T] = E[X X^T] - mu mu^T
Cx = [p^2+p(1-p) p^2 p^2;
p^2 p^2+p(1-p) p^2;
p^2 p^2 p^2+p(1-p)]
- [p^2 p^2 p^2;
p^2 p^2 p^2;
p^2 p^2 p^2]
Cx = [p(1-p) 0 0;
0 p(1-p) 0;
0 0 p(1-p)]
(c) Y can be expressed as a linear combination of X:
Y = [1 0 0] X1 + [1 1 0] X2 + [1 1 1] X3
Therefore, the matrix A is:
A = [1 0 0;
1 1 0;
1 1 1]
(d) The covariance matrix Cy of Y can be calculated as:
Cy = A Cx A^T
Substituting the values of A and Cx, we get:
Cy = [1 1 1; 0 1 1; 0 0 1] [p(1-p) 0 0; 0 p(1-p) 0; 0 0 p(1-p)] [1 0 0; 1 1 0; 1 1 1]
Cy = [
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Darrien and his family are at a football game. Darrien’s dad gives him $22 to buy snacks. He finds that drinks cost $1.50 and a bowl of nachos cost $2.75. Write and graph an inequality that shows the amount of sodas and nachos that Darien can afford to buy.
Help me pls. 20 points.
Answer: 2/3 or 12/18
Step-by-step explanation:
A person's muscle mass is expected to decrease with age. To explore this relationship in women, a nutritionist randomly selected 6 women. The results follow: X is age, and Y is a measure of muscle mass. X Y
43 106 47 97
41 106
47 92 48 92
46 113 Answer the following questions: 1. Fit a quadratic regression model, interpret the meaning of the regression coefficient. (2 Marks) [use R program to solve (X'X)^-1] 2. Test whether the quadratic term can be dropped from the regression model use a = 0.05. (2 Marks) [Hint: MSE = 47.086, SSR(x,x^2) = 230.74 and SSR(x) = 135.03] 3. Express the fitted regression function obtained in (1) in terms of the original variable X (1 Mark)
1. The quadratic regression model is [tex]Y = b0 + b1X + b2X^2[/tex] . The regression coefficient b2 represents the rate of change in muscle mass with respect to age squared. 2. The quadratic term can not be dropped from the regression model, since the calculated F-value is less than the critical value. 3. The fitted regression function in terms of the original variable X is [tex]Y = 87.017 + 0.241X - 0.002X^2[/tex].
To determine the quadratic regression model follow these steps:
1. Using R program, the quadratic regression model:
[tex]Y = b0 + b1X + b2X^2[/tex]
where Y is the muscle mass, X is the age.
The regression coefficients are:
b0 = 283.962
b1 = -14.501
b2 = 0.162
The regression coefficient b2 (quadratic term) represents the rate of change in muscle mass with respect to age squared. It measures the acceleration or deceleration of the change in muscle mass as the age increases.
2. Using the F-test.
[tex]F = [SSR(x,x^2) - SSR(x)] / [(k - 1) * MSE][/tex]
where k = number of coefficients = 3 (b0, b1, b2).
MSE = Mean Squared Error = 47.086
[tex]SSR(x,x^2), SSR(x) =[/tex] Sum of Squares due to Regression with both X and [tex]X^2[/tex] as predictors = 230.74, due to Regression with only X as predictor = 135.03
Therefore,
[tex]F = [230.74 - 135.03] / [(3 - 1) * 47.086] = 2.214[/tex]
Using a significance level the critical value for F-test is 5.143.
Since the calculated F-value (2.214) is less than the critical value (5.143), we fail to reject the null hypothesis. Therefore, there is not enough evidence that quadratic term can be dropped from regression model.
3. The fitted regression function in terms of the original variables:
[tex]Y = 87.017 + 0.241X - 0.002X^2[/tex]
where X is the age and Y is the measure of muscle mass.
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a construction worker is using the coordinate grid to show the length of the wall inside a house one end of the wall will be at 5,6 the wall will be 4 units long which point could be the location of the other end of the wall.
The point that could be the location of the other end of the wall will be (0, 5).
How to explain the pointBy using one or more elements or coordinates, a reference frame can properly pinpoint location alongside other mathematical components on such space, including Euclidean space.
A point or object in a two-dimensional plane can be found by utilizing its coordinates, which appear to be sets of integers. The y and x vectors can be used to identify the position of a point on a double surface. a group of photos used to identify certain areas.
In conclusion, the point that could be the location of the other end of the wall will be (0, 5).
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Help fast pls Geometry
Answer:
64.141 cm ^2
Step-by-step explanation:
Formula for solving this is Pi(7^2) (170/360)
170 being the angle in degrees.
What is the equation of the following line written in general form (4,5) (1,2)
The equation of the line written in general form (4,5) (1,2) is y - x = 1.
The formula to find the line equation from two points is as follows -
(y - [tex] y_{1}[/tex])/(x - [tex] x_{1}[/tex]) = ([tex] y_{2}[/tex] - [tex] y_{1}[/tex])/([tex] x_{2}[/tex] - [tex] x_{1}[/tex]). In the formula, [tex] y_{1}[/tex] and [tex] y_{2}[/tex] are initial and final y-axis values and [tex] x_{1}[/tex] and [tex] x_{2}[/tex] are initial and final x-axis values.
Keep the values in formula to find the equation -
(y - 5)/(x - 4) = (2 - 5)/(1 - 4)
Simplifying the equation
(y - 5)/(x - 4) = -3/-3
Divide the values
(y - 5)/(x - 4) = 1
Rewriting the equation
(y - 5) = (x - 4)
Rearranging the equation
y - x = 5 - 4
y - x = 1
Hence, the equation of line is y - x = 1.
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an orange juice company sells a can of frozen orange juice that measures 9.4 centimeters in height and 8.5 centimeters in diameter. the company wants to design a new label for the can of juice. if the label will cover the area between the bases, what dimension will be available for the design?
The dimension available for the design is the lateral surface area of the can, which is approximately 251.33 square centimeters.
The area between the bases of the can is the lateral surface area of the can, which can be calculated using the formula:
Lateral surface area = 2 x π x r x h
where π is the mathematical constant pi (approximately 3.14159), r is the radius of the can (which is half of the diameter), and h is the height of the can.
In this case, the height of the can is given as 9.4 centimeters, and the diameter (and hence the radius) is given as 8.5/2 = 4.25 centimeters.
Plugging in these values, we get:
Lateral surface area = 2 x π x 4.25 cm x 9.4 cm
= 251.327 square centimeters
Therefore, the dimension available for the design is the lateral surface area of the can, which is approximately 251.33 square centimeters.
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GEOMETRY PLEASE HELP!! FOR 30 POINTS!!
A dart hits the circular dartboard shown below at a random point. Find the probability that the dart lands in the shaded circular region. The radius of the dartboard is 9 in, and the radius of the shaded region is 4 in.
Use the value 3.14 for pie. Round your answer to the nearest hundredth.
Mr victor had 100 computers for sale he sold w computers in the morning and (2w+3) computers in the afternoon. He had 7computers left. How many computers did he sell in the morning?
From the addition arithematic operation, the total number of sold computers by Mr victor is equals to ninty-three out of hundard computers .
Addition, subtraction, multiplication, and division are four basic arithmetic operations used in mathematics.
Total number of computers Mr victor has
= 100
Number of computers sold by him in morning = w
Number of computers sold by him in afternoon = 2w + 3
Number of computers left after selling = 7
We have to determine the number of computers he had to sell. We have total counts of computers so we equate all sold and unsold computers to total and will determine value of variable w. Using addition, w + 2w + 3 + 7 = 100
Simplify, 3w + 10 = 100
=> 3w = 90
Dividing by 3 both sides,
=> w = 30
So, Number of computers sold in morning = 30
Number of computers sold in afternoon = 2×30 + 3 = 63
So, total sold computers = 63 + 30 = 93.
Hence, required value is 93.
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Pete, the skateboarding penguin, practices on a ramp in the shape of a right triangular prism
as shown below.
I need help ASAP!!! please
Of course! I'm here to help. Please provide me with the details or information you need assistance with regarding Pete, the skateboarding penguin and the right triangular prism ramp. I'll do my best to provide you with prompt and accurate help.
A drawing of William’s backyard is given.
If William plans to mow the yard, how much area will he have to mow?
Responses
48
yd2
48 yd, 2
96
yd2
96 yd, 2
112
yd2
112 yd, 2
144
yd2
Answer:48 yd2
Step-by-step explanation:
The area of the yard that William would have to mow would be C. 112 yards ²
How to find the area ?To find the area to be mowed, find the area of the entire yard including the porch, and then the area of the porch, and then subtract the area of the porch.
Area of yard :
= 12 x 12
= 144 yard ²
The area of the porch is:
= ( 12 - 8 ) x ( 12 - 4 )
= 4 x 8
= 32 yards ²
The area to be mowed is:
= 144 - 32
= 112 yards ²
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Pleas help me I will give 50
Answer:
Stem | Leaf
1| 9
2| 5 9
3| 0 3 3 8
4| 0 7 9
5| 4 5
6| 1 5
7| 2 7
8| 1
Step-by-step explanation:
Minimum: 19
Maximum: 81
Range: 62
Count: 17
Sum: 808
Mean: 47.53
Median: 47
Mode: 33
Standard Deviation: 18.9
Variance: 357.3
Suppose the trip take 3 hours and 15 minutes of driving time for the 124-mile round trip. What is the average speed of the buses in miles per hour?
The average speed of the buses is approximately 19.08 miles per hour.
We have,
If the trip takes 3 hours and 15 minutes of driving time, that's a total of 3.25 hours.
The distance traveled is 124 miles round trip, so the distance traveled in one direction is half of that or 62 miles.
To find the average speed of the buses in miles per hour, we can use the formula:
average speed = distance/time
where distance is in miles and time is in hours.
So, the average speed of the buses in miles per hour is:
Average speed
= 62 miles / 3.25 hours
= 19.0769 miles per hour (rounded to 4 decimal places)
Therefore,
The average speed of the buses is approximately 19.08 miles per hour.
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It is estimated that the average smartphone owner used 606 megabytes of data per month with a standard deviation of 240 megabytes per month. A random sample of 64 smartphone users was selected a. What is the mean of the sample mean, my? b. What is the standard deviation (standard error) of the sample mean? C. What is the probability that the average amount of data used in this sample was greater than 632 megabytes (P(X > 632))? Show your work! >
Previous question
The probability that the average amount of data used in this sample was greater than 632 megabytes is approximately 0.1922 or 19.22%.
a. The mean of the sample mean (my) can be calculated using the formula:
my = population mean = 606 megabytes per month
b. The standard deviation (standard error) of the sample mean can be calculated using the formula:
standard error = [tex]\frac{standard deviation}{\sqrt{sample size} }[/tex]
standard error = [tex]\frac{240}{\sqrt{64} }[/tex]
standard error = 30
Therefore, the standard error of the sample mean is 30 megabytes per month.
c. To find the probability that the average amount of data used in this sample was greater than 632 megabytes, we need to use the formula for the z-score:
z = [tex]\frac{(x - my) }{standard error}[/tex]
where x is the sample mean, my is the population mean, and standard error is the standard error of the sample mean.
z = [tex]\frac{(632 - 606) }{30}[/tex]
z = 0.87
Using a z-table or calculator, we can find that the probability of getting a z-score of 0.87 or higher is 0.1922. Therefore, the probability that the average amount of data used in this sample was greater than 632 megabytes is approximately 0.1922 or 19.22%.
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3. Convert the given Infix expression "A+B* C + D" to Postfix expression using Stack. (2 marks)
The postfix expression for the given infix expression is "A B C * + D +".
To convert the infix expression "A+B*C+D" to postfix expression using a stack, we can follow these steps:
Create an empty stack and an empty output queue.
Process each symbol in the infix expression from left to right.
If the symbol is an operand (e.g. A, B, C, D), add it to the output queue.
If the symbol is an operator (e.g. +, *), then do the following:
a. While the stack is not empty and the top of the stack has greater precedence than or equal precedence to the current operator, pop the top of the stack and add it to the output queue.
b. Push the current operator onto the stack.
After processing all the symbols in the infix expression, pop any remaining operators from the stack and add them to the output queue.
Using this algorithm, we can convert the infix expression "A+B*C+D" to postfix expression as follows:
Symbol: A + B * C + D
Action: Push A Push + Push B Push * Push C Pop * Pop + Push D
Output: A B C * + D +
Therefore, the postfix expression for the given infix expression is "A B C * + D +".
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Find the P-hate and E by using the given confidence
interval (0.444, 0.484)
p-hate=
E=
The true population proportion and the sample proportion, given the confidence level and sample size.
In statistics, P-hat represents the sample proportion and E represents the margin of error.
Given a confidence interval of (0.444, 0.484), we can find P-hat and E as follows:
P-hat = (lower limit + upper limit) / 2
P-hat = (0.444 + 0.484) / 2
P-hat = 0.464
Therefore, the sample proportion (P-hat) is 0.464.
To find E (the margin of error), we need to use the formula:
E = (upper limit - lower limit) / 2
E = (0.484 - 0.444) / 2
E = 0.02
Therefore, the margin of error (E) is 0.02.
Note that the margin of error indicates the maximum likely difference between the true population proportion and the sample proportion, given the confidence level and sample size.
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an incomplete table of values for an exponential function is shown. the exponential function is of the form y=a*b^x, where a is a real number such as a does not equal 0 and b is a positive number not equal to 1. complete the table with possible values for the exponential function
The table showing the exponential function is completed and presented below
x y
0 96
1 192
2 384
3 768
How to complete the tableThe expression for the table is given as
y = a * b^x,
Point (0, 96) is on the table.
a = 96,
when b = 2, we have that
for x = 1
y = 96 x 2^x = 96 x 2^1 = 192
for x = 2
y = 96 x 2^x = 96 x 2^2 = 384
for x = 3
y = 96 x 2^x = 96 x 2^3 = 768
Therefore, The required exponential function will be
x y
0 96
1 192
2 384
3 768
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In a random sample of 18 residents of the state of Montana, the mean waste recycled per person per day was 2.1 pounds with a standard deviation of 0.74 pounds. Determine the 80% confidence interval for the mean waste recycled per person per day for the population of Montana. Assume the population is approximately normal.
Construct the 80% confidence interval. Round to one decimal
Lower endpoint: ??
Upper endpoint: ??
The 80% confidence interval for the mean waste recycled per person per day for the population of Montana is given as follows:
(1.9, 2.3).
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 80% confidence interval, with 18 - 1 = 17 df, is t = 1.33.
The parameters are given as follows:
[tex]\overline{x} = 2.1, s = 0.74, n = 18[/tex]
The lower bound of the interval is given as follows:
2.1 - 1.33 x 0.74/sqrt(18) = 1.9.
The upper bound of the interval is given as follows:
2.1 + 1.33 x 0.74/sqrt(18) = 2.3.
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the figure below is reflected over x axis. what are the coordinates of the image of point v after this transformation
Note that the coordinates of V after it has been reflected over the x-axis will be: V' (3, -5)
The coordinates given are
V (3, 5)
W(5,8)
X (9, 6)
y (3, 3)
When point is reflected over the x- ais, it's y - coordinate takes on a polarized sign that is it goes from positive to negative of vice versa while the x-cordinte remains the same
So after the image on point v hs been reflected, the new coordinates for V = V' = (3, -5)
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b) Another larger triangle is made from smaller, similar triangles. The perimeter
of this larger triangle is 32 times larger than the perimeter of one of the smaller
triangles.
How many smaller triangles are used to form this larger triangle?
The number of smaller triangles used to fill the larger triangle is given as follows:
1024 triangles.
How to obtain the number of smaller triangles?The perimeter of the larger triangle is 32 times larger than the perimeter of one of the smaller triangles, which means that the ratio of the areas is given as follows:
32² = 1024.
The ratio of the areas is obtained squared as the perimeter is measured in units, while the area is measured in units squared.
This means that 1024 smaller triangles are needed to fill the larger triangle.
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Place point D where it partitions
the segment into a 1:2 ratio.
1
+
2
3
D
+
4
5
6
Answer: Partitioning a Segment in a Given Ratio ; Find the coordinates of the point that divides the directed line segment · with the coordinates of endpoints at M(−4,0) ...
Step-by-step explanation:
Jaxon bought two boxes of eggs at a market and recorded the mass of each egg
in the stem-and-leaf diagram below.
a) Which of the boxes has the smaller range of masses?
b) What is the value of this range? Give your answer in grams (g).
Box A
9865 4 39
2 5
84 6
65321 7
Box A
Box B
Box B
4679
157
258
Key
25 represents a mass of 52 g
5/4 represents a mass of 54 g
The range of Box A is 31 grams which is smaller.
Given that, Jaxon bought two boxes of eggs at a market and recorded the mass of each egg in the stem-and-leaf diagram,
So, the ranges are ;
Box A = 76 - 45 = 31 grams
Box B = 78 - 43 = 35 grams
Therefore, we see that the range of the box A is smaller than the range of the box B.
Hence, the range of Box A is 31 grams which is smaller.
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Any equation is given
40=x^2-3x
What is one solution to the equation?
The solution of the quadratic equation, 40 = x² - 3x is x = 8 or x = -5.
How to solve quadratic equation?Quadratic equation can be represented as follows:
ax²+ bx + c
where
a, b and c are constantTherefore, let's solve the quadratic equation as follows:
40 = x² - 3x
Hence,
x² - 3x - 40 = 0
x² + 5x - 8x - 40 = 0
x(x + 5) - 8(x + 5) = 0
(x - 8)(x + 5) = 0
x = 8 or x = -5
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T/FThe area of descriptive statistics was developed to provide further detail to statisticians about population inferences.
Descriptive statistics is a branch of statistics that deals with the collection, analysis, interpretation, and presentation of data. It focuses on summarizing and describing the characteristics of a sample or population. The purpose of descriptive statistics is to provide a clear and concise summary of the data, including measures of central tendency, variability, and distribution.
True,This information can be used to make inferences about the population as a whole. Therefore, descriptive statistics helps statisticians to better understand and interpret the population data.
False, Descriptive statistics is a branch of statistics that focuses on summarizing and organizing data from a sample or population. It provides insights into the basic features of the data, such as the mean, median, and standard deviation, but does not make inferences about the population.
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Tam has $74. Then the following events happen, in order: Tam spends $5 on lunch. Tam's parents double the money she has left. Tam adds all the money to the $148 in her savings account. 2. Use the drop-down menus to answer the questions below. An expression that models this series of events is 148 + 2(74-5) C CLEAR Sarah also had some money. The amount she currently has is equal to 2 x 18 -9 + 50. A possible series of events that led to this amount would be: 1. starts with $18 O CHECK P
Answer:
Step-by-step explanation:
Tam's initial amount of money = $74
Tam spends $5 on lunch, so she has $74 - $5 = $69 left.
Tam's parents double the money she has left, so she now has $69 x 2 = $138.
Tam adds all the money to the $148 in her savings account, so her total amount of money becomes $138 + $148 = $286.Expression that models this series of events: 148 + 2(74-5)For Sarah:
Sarah starts with $18.
Sarah doubles her money, so she now has $18 x 2 = $36.
Sarah subtracts $9 from her current amount, so she now has $36 - $9 = $27.
Sarah adds $50 to her current amount, so she now has $27 + $50 = $77.A possible series of events that led to Sarah's current amount of money: Starts with $18, doubles it to $36, subtracts $9, and then adds $50.
A store sells 140 stainless steel thermal travel mugs per month at 24 dollars each. A survey indicates that for each $1. 50 decrease in price sales will increase by 5 travel mugs. A) Determine the demand function. B) Determine the revenue function c) Determine the marginal revenue d) Solve for R(x)=0. What does it mean? How can the store use this information? e) What price corresponds to value found in part d)
A) The demand function is [tex]y = 500 - 20x[/tex]
B) The revenue function [tex]R(x) = 500x - 20x^2[/tex]
C) The marginal revenue [tex]MR(x) = 500 - 40x[/tex]
D) This means that the store can maximize its revenue by setting the price at $25
E) The price corresponding to the value found in part d) is $25
To determine the demand function, we need to use the information given in the problem that for each $1.50 decrease in price, sales will increase by 5 travel mugs. Let x be the price in dollars and y be the number of travel mugs sold.
A) Then, we can write the demand function as:
[tex]y = 140 + 5((24-x)/1.5)[/tex]
Simplifying this expression, we get:
[tex]y = 140 + 20(16 - x)[/tex]
[tex]y = 500 - 20x[/tex]
Therefore, the demand function is[tex]y = 500 - 20x.[/tex]
B) The revenue function is given by the product of the price and the quantity sold:
[tex]R(x) = x(500 - 20x)[/tex]
[tex]R(x) = 500x - 20x^2[/tex]
C) The marginal revenue is the derivative of the revenue function with respect to x:
[tex]MR(x) = dR/dx[/tex]
[tex]= 500 - 40x[/tex]
D) To solve for R(x) = 0, we need to set the revenue function equal to zero and solve for x:
[tex]500x - 20x^2 = 0[/tex]
[tex]x(500 - 20x) = 0[/tex]
[tex]x = 0[/tex] or [tex]x = 25[/tex]
Since the price cannot be zero, the store can only set the price at $25 to achieve zero revenue. This means that the store can maximize its revenue by setting the price at $25.
E) The price corresponding to the value found in part d) is $25.
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PLEASE HELP ME TO SOLVE THIS QUESTION
3.Xavier's salary increases by 2% each year.
In 2010 , his salary was £40,100
i) Calculate his salary in 2015 and give your answer to the nearest pound.
ii) In which year did Xavier's salary first greater than £47,500
i) Based on exponential growth, Xavier's salary in 2015 is £44,274.
ii) The year that Xavier's salary first became greater than £47,500 would be 2019.
What is exponential function?Exponential functions show the relationship between two variables and a variable exponent with a periodic constant rate of growth or decay in the value of something
Annual increase in Xavier's salary = 2% or 0.02
Xavier's salary in 2010 = £40,100
The number of years between 2015 and 2010 = 5 years
Exponential Function:i) y = £40,100(1.02)^5
= £44,273.64
= £44,274
ii) £47,500 = £40,100(1.02)^t
t = 9 years
= 2019 (2010 + 9)
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Estimation (gcse maths)
Answer:
√(4.93 × 17.1) is about √(5 × 20) = √100 = 10. 0.209 is about 0.2, or 1/5.
So we have 10/0.2 = 100/2 = 50.
Find all real solutions of this equation to answer the question.
(6 – 2x)(3 – 2x)x = 40
Yes. Because 3/2 is a root, you can cut squares with sides of 3/2 in. to make the box
No. This equation has no real solutions.
No. The only real solution is x = 4. It is not possible to cut squares of this size.
Answer:
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Step-by-step explanation:
To solve the equation (6 – 2x)(3 – 2x)x = 40, we can start by simplifying the left-hand side:
(6 – 2x)(3 – 2x)x = 40
(18x – 12x^2 – 6x + 4x^2)x = 40
(2x^3 – 8x^2 + 18x)x = 40
2x^4 – 8x^3 + 18x^2 = 40
2x^4 – 8x^3 + 18x^2 – 40 = 0
We can try to factor this equation by grouping terms:
2x^4 – 8x^3 + 18x^2 – 40 = 0
2(x^4 – 4x^3 + 9x^2 – 20) = 0
2((x^2 – 2x + 1)(x^2 – 2x – 20)) = 0
2(x – 1)^2(x – 5)(x + 4) = 0
Therefore, the real solutions of the equation are x = 1 (with multiplicity 2), x = 5, and x = -4.
Now, to answer the question, we need to determine whether it is possible to cut squares with sides of 3/2 in. to make a box. We can use the value of x = 3/2 to find the dimensions of the box:
length = 6 – 2x = 6 – 2(3/2) = 3 in.
width = 3 – 2x = 3 – 2(3/2) = 0 in.
height = x = 3/2 in.
Since the width is 0, it is not possible to cut squares with sides of 3/2 in. to make a box. Therefore, the correct answer is:
No. It is not possible to cut squares of this size.
The following frequency table shows the observed high temperatures in Buffalo, New York, in May 2007. Which interval contains the median temperature? 50 - 59 60 - 69 70 - 79 80 - 89
The interval that contains the median temperature is 70-79 in the frequency table showing the observed high temperatures in Buffalo.
First, we need to calculate the total number of observations, which is 5+12+9+5=31.
The median is the middle value of the data set when arranged in ascending or descending order. Since there are 31 observations, the median will be the 16th value.
To determine which interval contains the median temperature, we need to calculate the cumulative frequency of each interval. The cumulative frequency for the first interval is 5, for the second interval it is 5+12=17, for the third interval it is 17+9=26, and for the fourth interval it is 26+5=31.
Since the median is the 16th value, it lies within the third interval, which is 70-79.
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The question is -
The following frequency table shows the observed high temperatures in Buffalo, New York, in May 2007. Which interval contains the median temperature?
temperature frequency
50-59 5
60-69 12
70-79 9
80-89 5