The value of test statistics z=1.04
First, state the null and alternative hypotheses:
[tex]H_o=u_1=u_2\\H_a=u_1 > u_2[/tex]
Use z-statistics:
[tex]z=\frac{x_1-x_2}{y} ------(1)[/tex]
where x₁ and x₂ are the means and:
[tex]y=\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2} }[/tex]
Calculating the value of test statistics:
[tex]y=\sqrt{\frac{(23.53)^2}{47}+\frac{(71.32)^2}{54} }[/tex]
[tex]y=\sqrt{\frac{533.6609}{47}+\frac{5086.542}{54} }[/tex]
[tex]y=\sqrt{11.780+7.460}[/tex]
[tex]y=\sqrt{19.24}[/tex]
y = 4.386
Now substitute the y value in equation (1)
[tex]z=\frac{75.57-71.32}{4.386}[/tex]
z = 1.04
The test statistics is z = 1.04
The decision rule for rejecting the null hypothesis is: α≤ test statistics
Using the z-score table, it is possible to determine the p-value, which is:
value = 0.877
Comparing the p-value with the level of significance (α = 0.05):
0.877 > 0.05
Therefore, we fail to reject the null hypothesis.
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Suppose that you first want to eliminate the fraction in the example equation. What would your first step be? is -2 still the solution when you start by eliminating the fraction first?
The first steps of the elimination of fraction is to take LCM for the denominators.
In math the term fraction is defined as represent the parts of a whole or collection of objects
Here we have know that first we want to eliminate the fraction in the example equation.
As we all know that the process of eliminating in fraction will follow the following steps, they are listed as follows:
First we have to take the LCM for the fractions and then we have to enter the equations.
Then we have to multiply each equation by a number to get the lowest common multiple for one of the variables.
And then we have to add or subtract the two equations to eliminate that variable .
Then we should substitute that variable into one of the equations and solve for the other variable.
Finally we have to check by substituting your answer into one of the equations,
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POINTS GIVEN!!! ASAP Alang was out at a restaurant for dinner when the bill came. His dinner came to $18. He wanted to leave a 10% tip. How much was his meal plus the tip, before tax, in dollars and cents? ASAP
Answer: $19.80
Step-by-step explanation:
Step 1:
Multiply to get tip:
18*0.1=1.8
Step 2:
Add:
18+1.8=19.8
Add the zero in the hundredths digit place since there are always two-digit places after the decimal point when dealing with money.
how to determine if a function is even or odd algebraically
If f(-x) = -f(x), the function is odd. and if f(-x) = f(x), the function is even.
What are functions?A function is defined as a relation between a set of inputs having one output each, a function is a relationship between inputs where each input is related to exactly one output.
We can decide algebraically if a function is even, odd or neither by replacing x by -x and computing f(-x).
If f(-x) = f(x), the function is even.
If f(-x) = -f(x), the function is odd.
In order to "determine algebraically" whether a function is even, odd, or neither, you take the function and plug − x in for x, simplify, and compare the results with what you'd started with.
If you end up with the exact same function that you started with (that is, if f (− x) = f (x), so all the signs are the same), then the function is even; if you end up with the exact opposite of what you started with (that is, if f (− x) = − f (x), so all the signs are switched), then the function is odd.
If the result is neither exactly the same nor exactly opposite (that is, nor having all the same terms but with all the signs reversed), then the function is neither even nor odd.
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(b) A workshop produces 360 chairs in
5 days.
The rate of production is ?
chairs/day.
Answer:
72
Step-by-step explanation:
just divide 360 by 5
ez
To find the rate of production, you have to divide the number of chairs produced by the amount of days.
Given:
Chairs produced - 360
Days - 5
[tex]360\div5[/tex]
[tex]\fbox{72 chairs per day}[/tex]
many television viewers express doubts about the validity of certain commercials. in an attempt to answer their critics, timex group usa wishes to estimate the true proportion p of all consumers who believe what is shown in timex television commercials. what is the smallest number of consumers that timex can survey to guarantee a margin of error of 0.05 or less at a 99% confidence level?
Timex can survey at least 384 consumers to guarantee a margin of error of 0.05 or less at a 99% confidence level.
What is proportion ?
A proportion is a way to express the relationship between two or more quantities or values. It is a statement that asserts that two ratios or fractions are equal, such as "2/5 is equal to 4/10".
To estimate the true proportion p of consumers who believe what is shown in Timex television commercials, Timex can use a sample proportion formula which is:
p = (number of positive responses) / (sample size)
To guarantee a margin of error of 0.05 or less at a 99% confidence level, Timex can use a sample size calculator. The sample size calculator takes into account the margin of error, confidence level, and the proportion of the population that is expected to be positive.
The sample size can be calculated using the formula :
n = (z^2 * p * (1-p)) / E^2
Where z is the z-score for the desired confidence level (z = 2.576 for 99% confidence level), p is the estimated proportion of the population that is expected to be positive (0.5 if the true proportion is unknown), and E is the desired margin of error (0.05).
Timex can survey at least 384 consumers to guarantee a margin of error of 0.05 or less at a 99% confidence level.
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Translate the following statements into equations and solve. Show your solution.
1. Two more than four times a number is -10.
2. One less than thrice a number is equal to 26.
3. Seven added to a certain number is 34.
Answer: 4x + 2 = -10
3x - 1 = 26
x + 7 = 34
Step-by-step explanation:
Please answer the question :)
An inequality represented by situation A is x < -4.
An inequality represented by situation B is x ≤ 3.
What is an inequality?In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two or more numerical values and variables in an algebraic equation based on any of the following inequality symbols:
Less than or equal to (≤).Greater than (>).Greater than or equal to (≥).Less than (<).In this exercise, we would use interpret each of the situations by using an inequality to model them. On the balance in situation A, the tray on the left is denoted with the variable (x) while the tray on the right is denoted with numerical values of "-1" in four places, therefore, we would write the inequality as follows:
x < 4(-1)
x < -4.
In situation B, the circle on the number line (graph) is closed because it represents the less than or equal to (≤) symbol and it decreases to the left of the number line;
x ≤ 3.
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A sculpture needs to lift a piece of marble.
It is a cuboid with dimensions 1 m by 0.6 m by 0.3 m.
Marble has a density of 2.7g/cm cubed.
What is the mass of the marble in kg?
The mass of the marble lifter by a sculpture is 0.0306 kg.
What is a cuboid?A cuboid is a three-dimensional closed figure which has volume along with surface area.
The volume of a cuboid is the product of its length, width, and height.
The total surface area of a cuboid is 2(lw + wh + wl) and the lateral surface area is 2(l + w)×h.
We know the volume of a cuboid is (length×width×height).
Therefore, The volume of this cuboid is (1×0.6×0.3) = 0.18 m³.
The marble has a density of 2.7g/cm which is equivalent to 0.17kg/meter.
We know Mass = volume×density.
Therefore, The mass of the marble is 0.17×10.18 kg.
= 0.0306 kg.
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Write the word sentence as an inequality.
A number y minus
is no more than
N100
The inequality is
A number y is no more than -8. So the expression as inequality is y ≤ -8.
We have to write the word sentence as an inequality.
A number y is no more than -8.
A relationship between two values in an algebraic statement that are not equal is shown by an inequality. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
The statement is saying that y is no more than means y is less that or equal to -8.
So we can write the expression as
y ≤ -8
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The complete question is:
Write the word sentence as an inequality. A number y is no more than -8.
Solve the quadratic inequality in terms of x 3x^2-8x+15>10x
The solution of the inequality in terms of x is x > 3 or x < 5/3.
What is quadratic inequality?
A quadratic inequality is simply a type of equation that does not have an equal sign and includes the highest degree of two. The wavy curve method is a method used to solve quadratic inequalities. Solving quadratic inequalities is the same as solving quadratic equations.
To solve the quadratic inequality 3x^2 - 8x + 15 > 10x, we first need to move all the terms to one side of the inequality sign to create a standard form of quadratic inequality.
3x^2 - 8x + 15 > 10x
3x^2 - 18x + 15 > 0
Now we can factor the left side of the inequality as (3x-5)(x-3) > 0
To solve the inequality, we need to find the values of x that make the expression (3x-5)(x-3) > 0 true. We can do this by setting each factor to zero and solving for x:
3x - 5 = 0, x = 5/3
x - 3 = 0, x = 3
Now we need to test these values of x in the original inequality to see if they make it true or false, and also we need to test values of x between and around these roots.
For x = 5/3, we have 3(5/3)^2 - 8(5/3) + 15 > 10(5/3)
Which is true.
For x = 3, we have 3(3)^2 - 8(3) + 15 > 10(3)
Which is also true.
So, we can conclude that the solution of the inequality is x > 3 or x < 5/3.
Therefore, the solution of the inequality in terms of x is x > 3 or x < 5/3.
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Sandy sold her homemade strawberry jam for $5 per jar at the farmers’ market. She bought a basket of strawberries for $24 to make the jam. If x represents the number of jars of jam sold, which expression represents Sandy’s earnings?
The expression that represents Sandy’s earnings is 5x - 24
How to determine the earnings expressionFrom the question, we have the following parameters that can be used in our computation:
Cost price = $24
Selling price = 5 per jar
This means that the total sales is
Total = 5 * x
Evaluate
Total = 5x
The earnings is the difference between the total sales and the cost price
Sp, we have
Earnings = 5x - 24
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6) A container ship made a trip to
Madagascar and back. On the trip there it
traveled 16 km/h and on the return trip it
went 10 km/h. How long did the trip there
take if the return trip took eight hours?
The trip there take if the return trip took eight hours is 5hrs.
What is Distance?
Distance is the sum of an object's movements, regardless of direction. Regardless of an object's starting or ending position, distance can be defined as the amount of ground it has covered.
What is Rate?
A rate in mathematics is the comparison of two related values expressed in different units. The numerator of the ratio expresses the corresponding rate of change in the other (dependent) variable if the denominator of the ratio is written as a single unit of one of these quantities and it is assumed that this quantity may be modified systematically (i.e., is an independent variable).
We are given ;
A container ship made a trip to Madagascar and back
On the trip there it traveled 16 km/h.
the return trip it went 10 km/h.
if the return trip took eight hours;
then,
16x = 10 * 8
16x = 80
x = 80/16
x = 5
Therefore, he trip there take if the return trip took eight hours is 5hrs.
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A survey showed that 74% of adults need correction (eyeglasses, contacts, surgery, etc. ) for their eyesight. If 21 adults are randomly selected, find the probability no more than that of them need correction for their eyesight. Is a significantly number of adults requiring eyesight correction?
7.9 x 10⁻¹¹ is the probability of people who need correction for there eyesight.Yes, it is a significantly number of adults requiring eyesight.
The probability of no more than 21 out of 21 randomly selected adults needing correction for their eyesight would be calculated using the binomial probability formula:
(n choose k) × [tex]p^{k}* (1-p)^{n-k}[/tex]
where n is the total number of trail. k is the number of successful trials (the number of adults not needing correction), p is the probability of a successful trial (the probability of an adult not needing correction)which is:
1-0.74 =0.26)
(n choose k) is the binomial coefficient, which is calculated by:
n! / (k! × (n-k)!).
So, the probability of no more than 21 out of 21 randomly selected adults needing correction for their eyesight would be:
(21 choose 21) ×0.26²¹ ×0.74⁰= 0.26²¹ = 7.9 x 10⁻¹¹
This is a very low probability, indicating that it is highly unlikely that no more than 21 out of 21 randomly selected adults would not need correction for their eyesight.
Yes, it is a significantly number of adults requiring eyesight correction. 74% is a high percentage.
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Find an equation for the line through (0, -5) and parallel to y = 1/2x + 1
Answer:
y=1/2x-5
Step-by-step explanation:
Parallel lines always have the same slope. Thus, since you know y=1/2+1 is parallel you know the slope is 1/2 as in y=mx+b, m is the slope. In addition, you know the y-intercept as -5. So the equation is y=1/2x-5
Answer:
y=1/2x-5
Step-by-step explanation:
to be parallel it needs to have the same slope so the slope is the same
0,-5 is the y intercept so -5 is the y intercept
In the triangle ABC, AB = 6cm and BC = 9cm. Given that the area of the triangle is 18 cm², find the possible values of the angle B.
The angle, ∠B has 2 possible angles, one is 41.81° and the other will be 138.19°
In ΔABC we have been given that
AB = 6 cm
BC = 9 cm
A formula for the area of a triangle is
1/2 X one side X oth sde X sin(common angle)
Hence if we consider AB and BC with common angle, ∠B we get
1/2 X 6 X 9 X sinB = 18
or, sinB = 18/27
or, sinB = 2/3
Now since sin is positive in 2 quadrants, we will have 2 possible values for ∠B
one will be 41.81° and the other will be (180 - 41.81)° = 138.19°
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What’s the missing angles??
Try multiplying the 91 and 65 then that's an answer for one. Then try dividing them for another angle.
Question Down Below: (Please i really need to complete this right now)
The inequality to represent the constraints will be:
x + y ≥ 325
x + 2y = 600
How to calculate the inequality?Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.
Let x = number of vegetarian meals
Let y = number of meats.
The inequality to represent the constraints will be:
x + y ≥ 325
x + 2y = 600
In this case, the daily budget is 600.
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if the variance of a normal population is 5, what is the probability that the variance of a random sample of size 15 exceeds 9.329 (round off to third decimal place)?
If the variance of a normal population is 5, the probability that the variance of a random sample of size 15 exceeds 9.329 is 0.069.The variance of a sample from a normal population has a chi-squared distribution, which is the sum of the squares of the standard normal distribution.
The probability can be calculated by finding the area to the right of the chi-squared value of 9.329 on the chi-squared distribution. This area can be found by using the chi-squared cumulative distribution function, which is the integrated form of the chi-squared probability density function.
To find the probability, the chi-squared cumulative distribution function is used to calculate the area to the right of the chi-squared value of 9.329. This will give us the probability of the variance of the sample exceeding 9.329, which is 0.069.
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Fifth term of (x-3y)^6
The fifth term of the expression is 1215x²y⁴.
What is Binomial Theorem?Binomial theorem is the method of expanding an expression consisting of two terms raised to any power.
By binomial theorem,
(x - 3y)⁶ = 6C₀ x⁶ + 6C₁ x⁵ (3y) + 6C₂ x⁴ (3y)² + 6C₃ x³ (3y)³ + 6C₄ x² (3y)⁴ + 6C₅ x (3y)⁵ + 6C₆ (3y)⁶
Simplifying the combination part,
= x⁶ + 6x⁵(3y) + 15x⁴(3y)² + 20x³(3y)³ + 15x²(3y)⁴ + 6x(3y)⁵ + (3y)⁶
= x⁶ + 18x⁵y + 135x⁴y² + 540x³y³ + 1215x²y⁴ + 1458xy⁵ + 729y⁶
Hence the fifth term of the expression is 1215x²y⁴.
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the track of a bicycle tire that completes one revolution is 54 ft. what are the radius, diameter, and circumference of the wheel?
The radius is 8.59 ft, the diameter is 17.18 ft and the circumference is 54 ft.
How to find the radius, diameter, and circumference of the wheel?The circumference of the wheel will be 54 ft, since that's the distance the tire travels in one revolution.
The diameter of the wheel is twice the radius, so if we can find the radius we can find the diameter.
To find the radius (r), we can use the formula:
circumference = 2 × π × radius
54 = 2 × π × r
r = 54 /2 π = 8.59 ft
The diameter is twice the radius, so:
diameter = 2r
diameter = 2 × 8.59 = 17.18 ft
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a cook wants to know what happens to bacon when it is fried in a frying pan versus microwaving it. specifically, the cook wonders if the bacon ends up moister and more flavorful when fried or when microwaved. what are the dependent variables
The dependent variables in the following scenario are whether the bacon becomes moister and more flavorful and the independent variable is the cooking method.
In statistics, a dependent variable is one whose value is determined by another set of variables called independent variables. To put it simply, the dependent variable is the thing that is being tested or calculated. The dependent variable is sometimes known as the "outcome variable." In the given scenario, the chef was curious as to whether or not frying or microwaving the bacon would produce a moister and more flavorful final product. The bacon is the result of the experiment, hence it is a dependent variable.
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Several friends each want to buy new basketball shoes that cost $60. To earn money, they do yard work for $9 an hour. The table shows the number of hours each person did yard work for each day. Who earned enough money to buy the basketball shoes? What inequality can you write to represent this situation?
Indicate whether or not each friend earned enough money to buy the basketball shoes.
Answer:
Step-by-step explanation:
There's no table or image attached to your question, but they would have to work at least 7 hours in order to earn enough money. In 7 hours, they would earn $63.
You live and work in a country that tells you where to work and sets your wage. The goods you produce go to the government, which then sells them in government-run stores. What type of economy do you live in? A. Specialized B. Command C. Free market D. Mixed
The given situation represents the (B) command economy.
What is a command economy?In a planned economy, the production, distribution, and allocation of capital goods all occur in accordance with economic plans that may be economy-wide or specific to a particular class of products and services.
Centralized, decentralized, participative, or Soviet-style economic planning is all possible in a planned economy.
Depending on the precise kind of planning mechanism used, the degree of centralization or decentralization in decision-making and involvement will vary.
Central planning has been utilized in socialist regimes built on the Soviet model, however, some, like the former Socialist Federal Republic of Yugoslavia, have embraced some kind of market socialism.
Therefore, the given situation represents the (B) command economy.
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purple
black
green
5-110
The spinner shown to the left is spun twice. Make a
table and calculate the probability of each of the
following outcomes. Write your answers as simplified
fractions.
Probability Table: NEED HELP WITH THE PROBABILITY TABLE
P(getting green twice)
Step-by-step explanation:
give me a brainlist please
There are two blue marbles, 10 orange marbles, and 4 white marbles in a bag. What is the probability of picking a blue or white marble?
Answer: Blue: 12.5%
White: 25%
Orange: 62.5%
Blue or White: 37.5%
Step-by-step explanation:
Step 1: Add all the Marbles together: 2 blue + 10 Orange + 4 White = 16 Marbles
Step 2: Add Blue and White marbles together: 2 blue + 4 White = 6 Marbles
Step 3: Divide Blue and White Marbles with total Marbles: 6/16 = 0.375
Step 4: Convert to Percentage: 0.375 x 100 = 37.5%
An architect's model for a building is 1. 4 m long and 0. 8 m wide. The
actual building is 240 m wide. What is the length of the building?
Answer:
Based on the dimensions of architecture's model and width of the building, the length of actual building is 420 meters.
The question is based on scale concept. Here the ratio of length to width will be same between the actual building and architect's model. Using this information to find the length of the building. Let us assume the length of actual building be x.
The ratio will be -
length:width (architect's model) = length:width (actual building)
1.4 : 0.8 = x : 240
Representing it as fraction
1.4/0.8 = x/240
x = 1.4 × 240/ 0.8
Performing multiplication in numerator
x = 336/0.8
Performing division
x = 420 meters
Thus, the length of the building is 420 meters.
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solve for [tex]tan\frac{17\pi }{12}[/tex]
After calculating , The value of given expression is -3.73
What is Tanx in terms of sinx and cosx?
Tanx can be defined as the ratio of sinx and cosx or tanx also can be defined as the ratio opposite side and adjacent side.
Given
expression,
tan(17pi/12)
The value of pi = 180
so by putting the value we get,
tan(17*180 / 12 )
tan ( 3060 / 12 )
as we know the value of 3060/12 = 255.
tan(255)
= -3.73
so we got the value of tan(255) is -3.73 approximately
Hence, The value of given expression is -3.73
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Draw a tape diagram that represents 5÷2/3
The numerical answer is 5
How to draw a tape diagram that represents 5÷2/3?Start by drawing three unit tapes, and divide each one of them in 5 equal parts since we need to be dividing the quantity 3 by 3/5 (denominator 5)
In the second step, join the three tapes in one long one maintaining the original divisions.
In the third step, select groups of 3 divisions (recall you need to divide by 3/5) which will identify in your tape how many of these 3/5 groups you have.
Finally count the number of 3/5 groups you found in the collection of the three original tapes placed together. You should count a total of 5 of these 3/5 groups.
5 then tells you what is the quotient of 3 divided in 3/5
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HS
Population
1200
1450
900
1500
1400
1005
# of active band members
150
155
100
125
125
120
What is the correlation coefficient? Interpret what this means for the context of this
data.
Answer:
I'm trying to figure that out to
what is the probability of spinning a three on the first spinner, the color orange on the second spinner, and rolling an even number of the fair number cube?
A. 1/12
B. 1/16
C. 1/24
D. 1/48
Show your work please!!
Answer:
D. 1/48
Step-by-step explanation:
Each event (spinning a 3, spinning orange, rolling an even number) is an independent event, so the overall probability is the product of the three individual probabilities.
For each event,
p(event) = (number of desired outcomes)/(total number of possible outcomes)
p(spinning a 3) = 1/6
p(spinning orange) = 1/4
p(even number) = 3/6 = 1/2
p(spinning a 3 then spinning orange then rolling an even number) =
= 1/6 × 1/4 × 1/2
= 1/48
Answer: D. 1/48
Answer:
1/48
Step-by-step explanation:
First look at the spinner- there is only one three out of six, so the spinner is 1/6
Now looking at the second spinner- there are four spaces and one orange- giving us 1/4
And finally for the die there are six sides and three are even- which is 3/6
And in order to get our final answer we will multiply 1/6 * 1/4 * 3/6 which equals 1/48