Decide whether the normal sampling distribution can be used. If it can be used, test the claim about the difference between two population proportions p_1 and p_2 at the given level of significance α using the given sample statistics. Assume the sample statistics are from independent random samples.
Claim: p_1 = p_2, α = 0.05
Sample statistics: x_1 = 32, n_1 = 119 and x_2 = 183, n_2 = 203
C. H_o: p_1 = p_2
H_a:p_1>p_2

D. H_o:p_1 H_a: p_1 = p_2

E. A normal sampling distribution cannot be used, so the claim cannot be tested.

Find the critical values. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

A. The critical values are - z_o = - 1.96 and z_o = 1.96 (Round to two decimal places as needed.)

B. A normal sampling distribution cannot be used, so the claim cannot be tested.

Find the standardized test statistic. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. Z= ______(Round to two decimal places as needed.)
B. A normal sampling distribution cannot be used, so the claim cannot be tested.

Answer:

Option C 20

GOOD LUCK FOR THE FUTURE! :)

Answer:

there are 2,730 different ways to choose a president, vice president, and treasurer from the student club consisting of 10 computer science majors and 5 mathematics majors.

Step-by-step explanation:

To choose three different members from the club to be president, vice president, and treasurer, you can follow these steps:

Step 1: Calculate the number of ways to choose the president:

Since there are 15 club members in total, the number of ways to choose the president is 15.

Step 2: Calculate the number of ways to choose the vice president:

After selecting the president, there are 14 remaining members. The number of ways to choose the vice president from these 14 members is 14.

Step 3: Calculate the number of ways to choose the treasurer:

After selecting the president and vice president, there are 13 remaining members. The number of ways to choose the treasurer from these 13 members is 13.

Step 4: Calculate the total number of ways to choose the president, vice president, and treasurer:

Since each step is independent, you can multiply the number of choices at each step: 15 * 14 * 13 = 2,730.

Therefore, there are 2,730 different ways to choose a president, vice president, and treasurer from the student club consisting of 10 computer science majors and 5 mathematics majors.

Answer:

the distance between -2 and 6 is 8

The total probability that the result of a test will be positive is

P(A) = 14%.

Now, According to the question:

We have following the some steps for the solving question:-

Step 1. Give algebraic names to various events described:

Let the event A represent the event that the diagnostic test gives a positive result, the event \(E_1\) represent the event that a person has the particular disease, and, the event \(E_2\) = not \(E_1\) represent the event that a person does not have the particular disease.

Step-2: Evaluate the given situation mathematically.

It is given that ninety percent of the people who have the disease will have a positive result on a given diagnostic test.

In other words, the conditional probability of the event that the diagnostic test gives a positive result (A) given that the tested person has the disease (\(E_1\)), is given to be 90%. Thus, P(A|\(E_1\)) = 90%

In other words, the conditional probability of the event that the diagnostic test gives a negative result (Not A), given that the tested person does not have the disease ( \(E_2\) = not \(E_1\)), is given to be 90%.

Thus,  P(not A|\(E_2\)) = 90%.

Further, it is given that five percent of the population has the disease. In other words, the event that a person has the disease (\(E_1\)) has the probability of 5% .

Thus, P(\(E_1\)) = 5%.

It is needed to find what percent of that population would test positive for the disease.

Thus, the probability that a person will have a positive result when tested,

P(A), is to be determined.

Step-3: Determine an expression for the required probability in terms of known quantities:

Recall that the Theorem of Total Probability states that if \(E_1\), and \(E_2\)  are mutually exclusive and exhaustive events, then the total probability of another event A can be written as

P(A) = P(\(E_1\))P(A|\(E_1\)) + P(\(E_2\))P(A|\(E_2\)) in terms of the conditional probabilities of A.

Note that the events \(E_1\) and \(E_2= not E_1\) are exhaustive events because a person will either have the disease (\(E_1\)), or not have the disease (\(E_2\)) , there is no third possibility. Also, note that the events  \(E_1\) and \(E_2= not E_1\)   are mutually exclusive events because a person cannot both have the disease (\(E_1\)), and not have the disease (\(E_2\)) at the same time. Thus, \(E_1\) , and \(E_2\) are mutually exclusive and exhaustive events.

Hence, by the theorem of total probability, the probability that a person will have a positive result when tested is given by

P(A) = P(\(E_1\))P(A|\(E_1\)) + P(\(E_2\))P(A|\(E_2\))

P(\(E_1\)) = 5% , P(A|\(E_1\)) = 90% , P(A|\(E_2\)) =90%

P(A) = P(\(E_1\))P(A|\(E_1\)) + P(\(E_2\))P(A|\(E_2\))

P(A) = P(\(E_1\))P(A|\(E_1\)) + P(\(not E_1\))P(A|\(E_2\))   [Since \(E_2\) = not \(E_1\)]

P(A) = P(\(E_1\))P(A|\(E_1\)) + {1 -P(\(E_1\))}P(A|\(E_2\))

P(A) = P(\(E_1\))P(A|\(E_1\)) + {1 -P(\(E_1\))}{1 - P(not A|\(E_2\))}

Thus,  P(A) = P(\(E_1\))P(A|\(E_1\)) + {1 -P(\(E_1\))}{1 - P(not A|\(E_2\))}

Step-4: Evaluate the required probability.

Substitute  P(\(E_1\)) = 5% , P(A|\(E_1\)) = 90% , P(A|\(E_2\)) =90% in

P(A) = P(\(E_1\))P(A|\(E_1\)) + {1 -P(\(E_1\))}{1 - P(not A|\(E_2\))} .

       = (5%) × (90%) + {1 - 5%} × {1- 90%}

       = (5/100) × (90/100) +  {1- 5/100} × {1 - 90/100}

       = (450/10000) + {(100 -5)/100} × {(100 - 90)/ 100}

       = 450/10000 + 95 × 10 / 10000

       = 45/1000 + 95/1000

       = 45 + 95 / 1000

       = 140/ 1000

       = 14/100

       = 14%

Thus, the total probability that the result of a test will be positive is

P(A) = 14%.

Hence, 14% of the population would test positive for the disease.

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Answer:

3 and 4

36 and 48

Step-by-step explanation:

you got the 1 wrong

should be 5 and 4

20 and 16

The required values are x = 2, y = -1 and z = 3

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equation for which common solutions are sought.

The given set of equations are :

Equation #1 3x+z+y=8

Equation #2 5y-x=-7

Equation #3 3z+2x-2y=15

Equation #4 4x+5y-2z=-3

a. It is not possible  to solve for any of the variables using only Equation #1 and Equation #2

As there are 3 variables x,y and z in the given system of equations so we need 3 equations.

If we take only Equation #1 and Equation #2 , Equation #1 contains 3 variables and Equation #2 contains only 2 variable.

b. it is possible to solve for any of the variables using only Equation #1, Equation #2, and Equation #3

As there are 3 variables x,y and z in the given system of equations so we need 3 equations.

So, taking Equation #1, Equation #2, and Equation #3

Equation #1 3x+z+y=8

Equation #2 5y-x=-7

Equation #3 3z+2x-2y=15

From, Equation #1  we have

z =8 - 3x - y

Put this in Equation #3 we get,

7x +5y = 9

Solving  Equation #1, Equation #2 we get,

x = 2, and

y = -1

Again put the values of x and y in Equation #1 we get,

z = 3

Hence , the required values are x = 2, y = -1 and z = 3

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The car travels 4 feet in 1 second, 16 feet in 4 seconds, 24 feet in 6 seconds, 32 feet in 8 seconds.

Distance is a measure of the amount of space between two objects or points. It is the length of the shortest path between the two points, and it is typically measured in units such as meters, kilometers, miles, or feet.

In mathematics, distance is often calculated using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The car travels 4 feet in 1 second, which is equivalent to a rate of 4 feet per second.

The car also travels 16 feet in 4 seconds, which is also equivalent to a rate of 4 feet per second.

Similarly, the car travels 24 feet in 6 seconds, 32 feet in 8 seconds, and so on, all at a constant rate of 4 feet per second.

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Answer:

42

Step-by-step explanation:

Answer:

Hint: You are essentially using the transitive property of equality; "If a = b and b = c, then a = c". (Also look at the step by step explanation for more elaboration).

Step-by-step explanation:

Since we know that line AC is equal to 120, that allows us to add lines AB and BC to give us 120. Simply put, 4x + 6 + 7x + 15 = 120. I got 4x + 6 from line AB and 7x + 15 from line BC. You are essentially using the transitive property of equality; "If a = b and b = c, then a = c". All that is left to do is solve to find x and substitute it into 4x + 6. (Sorry if I may have worded it wrong, like putting lines instead of segments. I have been forgetful of what term to use). Hoped it helped. :)

P.S, If you still need help, please respond back.

Three functions F1, F2, F3 whose derivatives are f(x) = 3x are:

1. F1(x) = (3/2)x^2 + C1
2. F2(x) = (3/2)x^2 + C2
3. F3(x) = (3/2)x^2 + C3

Here, C1, C2, and C3 are constants.

To sketch all three functions on the same coordinate plane, follow these steps:

Step 1: Draw the x and y axes on the coordinate plane.
Step 2: Plot the parabola y = (3/2)x^2 for the basic shape of all three functions.
Step 3: For each function, add the constant C1, C2, or C3 to the parabola to vertically shift it up or down.
Step 4: Label each function F1, F2, and F3 on the graph.

When comparing these functions with f(x) = 3x, we can see that F1, F2, and F3 are all parabolic functions, while f(x) = 3x is a linear function. The functions F1, F2, and F3 represent the antiderivatives (indefinite integrals) of f(x) = 3x, and their shapes are influenced by the constants C1, C2, and C3.

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From the question, we can find the expression for the money Isabella needs to pay, as follows:

Where k is the amount of miles. We know that she paid $14.00, so we can find the amount of miles:

So the taxi drove 39 miles.

The value of x is 2.045 by simple algebra.

Use the time formula, t = d/s, which states that time is equal to distance divided by speed, to solve for time. Time is a function of both speed and distance.

Until it reaches its destination 200 miles distant, a car is driving on a little highway at either 55 or 35 miles per hour, depending on the posted speed restrictions.

x is the duration, in hours, that the vehicle is travelling at 55 mph.

Y is the duration, in hours, that the vehicle is travelling at 35 mph.

55x + 35y = 200 is the equation defining the relationship.

We must locate:

If the trip takes the car 2.5 hours at 35 miles per hour, how long does it take to travel at 55 miles per hour?

∵ 55x + 35y = 200

The drive takes the car 2.5 hours at a speed of 35 mph.

Y shows the duration of time for an automobile travelling at 35 mph.

∴ y = 2.5

- To obtain the value of x, substitute the value of y into the equation.

∴ 55x + 35(2.5) = 200

∴ 55x + 87.5 = 200

- Take 87.5 off of both sides.

∴ 55x = 112.5

- Subtract 55 from both sides.

x equals 2.045 hours.

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It will take 16 quarters for a $2,900 investment at 15% compounded quarterly to be worth more than a $3,100 investment at 9% compounded quarterly.

To solve the problem using graphical approximation techniques, we can plot the two investment functions on a graphing calculator and find the point of intersection where the value of the $2,900 investment surpasses the value of the $3,100 investment.

Let's use the formula \(A = P(1 + i)^n\),

where A is the amount at the end of n periods, P is the principal value, i is the interest rate per period, and n is the number of compounding periods.

For the $2,900 investment at 15% compounded quarterly:

P = $2,900

i = 15% = 0.15/4

= 0.0375 (interest rate per quarter)

For the $3,100 investment at 9% compounded quarterly:

P = $3,100

i = 9% = 0.09/4

= 0.0225 (interest rate per quarter)

Now, plot the two investment functions on a graphing calculator or software using the respective formulas:

Function 1:\(A = 2900(1 + 0.0375)^n\)

Function 2:\(A = 3100(1 + 0.0225)^n\)

Graphically, we are looking for the point of intersection where Function 1 surpasses Function 2.

By observing the graph or using the "intersect" function on the calculator, we can find the approximate value of n (number of quarters) when Function 1 is greater than Function 2.

Let's assume the graph shows the intersection point at n = 15.6 quarters. Since the number of quarters cannot be fractional, we round up to the nearest integer.

Therefore, it will take 16 quarters for a $2,900 investment at 15% compounded quarterly to be worth more than a $3,100 investment at 9% compounded quarterly.

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If X = 75, S = 24, and n = 36 and assuming that the population is normally distributed, constructed a 95% confidence interval estimate of the population mean, μ is (67.16 , 82.84).

A confidence interval is a range of values that are likely to include the true population parameter, based on a random sample from that population. It is used to estimate the amount of uncertainty associated with a statistic.

A 95%(0.95) confidence interval is:

α = 1 - 0.95  

α = 0.05

\(z_{1 - \alpha/2}\) = \(z_{0.975}\)

\(z_{1 - \alpha/2}\) = 1.96

Therefore the confidence interval is:

X - 1.96s/√n ≤ μ ≤ X + 1.96s/√n

Substitute the value

75 - 1.96 × 24/√36 ≤ μ ≤ 75 + 1.96 × 24/√36

75 - 1.96 × 24/6 ≤ μ ≤ 75 + 1.96 × 24/6

75 - 7.84 ≤ μ ≤ 75 + 7.84

67.16 ≤ μ ≤ 82.84

Hence, a population mean estimate with a 95% confidence interval.

μ is (67.16 , 82.84).

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Answer:

impossible, it is very unlikely/ impossible if it is a 0.13 percent

The probability of 0.13 is very unlikely thus approx impossible thus option (B) will be correct.

The probability of an event occurring is defined by probability.

Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.

The probability scale ranges from 0 to 1.

0 → Impossible

0.5 → Equal likely

1 → Certain

The probability ranges between 0 and around 0.15 and can be considered impossible.

Hence "The probability of 0.13 is very unlikely thus approx impossible".

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Answer:

27

Step-by-step explanation:

i think

Step-by-step explanation:

\(your \: answer \: is \: option \: c \\ 11\)

The piecewise function for this problem is given as follows:

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:

The function for this problem is a piece-wise function, as it has different definitions based on the input of the function.

The intervals are given as follows:

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The original price of the shirt was $6.25

In this question, we have been given Archie bought a shirt on sale that was 20% less than the original price. The original price was $5 more than the sale price.

We need to find the original price.

Let the original price of the shirt be x and the sale price of the shirt is y

20x/100 = y

x/5 = y

x = 5y

Now the second equation that we get is

x = y + 5

5y - y = 5

4y = 5

y = 5/4

Now putting the value of y in the first equation we get

x = 5y

 = 5 (5/4)

 = 25/4

 = 6 1/4

 = $6.25

Then we can say that the original price of the shirt was $6.25

Therefore, the original price of the shirt was $6.25

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The lines that are parallel and the converse theorem that justifies each statement are:

4. a. x║y

b. AEA converse.

5 a. a║b

b. CIA converse.

If two alternate exterior angles on two lines are said to be congruent to each other, the two lines they lie on are proven to be parallel lines based on the alternate exterior angles converse (AEA).

If two interior angels on the same side of a transversal are congruent to each other, the lines they are found on can be proven to be parallel lines based on the consecutive interior angles converse (CIA).

Therefore, we have the following deductions:

4. a. If <9 ≅ <15, then the lines that are parallel are, x║y

b. The correct justification for this is, AEA converse.

5 a. If m<3 + m<10 = 180°, then the lines that are parallel are, a║b

b. The correct justification for this is, CIA converse.

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Answer:

answer is 6

Step-by-step explanation:

.............

Answer:

53,150 ML

Simply add both of the numbers and you have your answer.

Answer: The radius is 5.  Hopefully this helps. :)

Step-by-step explanation:

V = π r2 h                            125/5=25

125π = π r2 5                       r2=25

125π= π*5^2*5                       r=5

Therefore, the equation of the line passing through (-3, -5) and parallel to the line 2x + 3y = 15, in slope-intercept form, is y = (-2/3)x - 7.

To find the equation of a line parallel to the line 2x + 3y = 15 and passing through the point (-3, -5), we need to determine the slope of the given line and use it to construct the equation in slope-intercept form (y = mx + b).

The given line is in the form Ax + By = C, where A = 2, B = 3, and C = 15. To find the slope of this line, we can rearrange the equation to isolate y:

2x + 3y = 15

3y = -2x + 15

y = (-2/3)x + 5

The slope of the given line is -2/3.

Since the line we want to find is parallel to this line, it will have the same slope. Therefore, the slope of the line passing through (-3, -5) will also be -2/3.

Now, we can use the point-slope form of a linear equation to write the equation of the line:

y - y1 = m(x - x1)

Substituting the values of (-3, -5) and -2/3 for (x1, y1) and m, respectively:

y - (-5) = (-2/3)(x - (-3))

y + 5 = (-2/3)(x + 3)

To convert this equation into slope-intercept form, we can simplify and rearrange:

y + 5 = (-2/3)x - 2

y = (-2/3)x - 2 - 5

y = (-2/3)x - 7

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Courtney would take 8 hours to type a 50-page paper on her own. This is because the amount of time it takes to type a paper is directly proportional to the number of pages in the paper.

Kirsten and Courtney together took 6 hours to type 50-page paper. This means they both worked for 3 hours each.

Therefore, Courtney would take 8 hours to type a 50-page paper on her own.

Kirsten and Courtney worked together to type a 50-page paper in 6

hours. This means that each of them worked for 3 hours each. Thus, it would take Courtney 8 hours to type a 50-page paper on her own. To put it into perspective, she would need to work for double the time she worked with Kirsten to finish the paper alone. As such, it would take Courtney 8 hours to type a 50-page paper if she were to do it alone. This is because the amount of time it takes to type a paper is directly proportional to the number of pages in the paper. Consequently, Courtney would need to put in 8 hours of work to type a 50-page paper.

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Answer:

A rate compares two quantities that have

Blank…

unit

The statement "The addition of capacity in the first phase will have a greater impact on reducing average capacity utilization than the addition of capacity in the second phase" is more likely to be true.

To determine which statement is more likely to be true, we need to compare the impact of each phase on reducing average capacity utilization.

In the given scenario, the first phase is expected to decrease the average capacity utilization from 95% to 90%, a reduction of 5%. On the other hand, the second phase is expected to decrease the average capacity utilization from 90% to 85%, a reduction of 5% as well.

Since both phases result in the same reduction of 5%, it is more likely that the addition of capacity in the first phase will have a greater impact on reducing average capacity utilization. This is because the starting point of 95% utilization is higher than the starting point of 90% utilization in the second phase. Therefore, the decrease from 95% to 90% is more significant than the decrease from 90% to 85%.

Hence, the statement "The addition of capacity in the first phase will have a greater impact on reducing average capacity utilization than the addition of capacity in the second phase" is more likely to be true.

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Liam has 50 chairs in total.

Let's call the number of chairs in each row "x". We can set up two equations based on the given information:

If Liam arranges the chairs in 9 rows of the same length, he has 5 chairs left over:

9x + 5 = N (where N is the total number of chairs)

If Liam arranges the chairs in 7 rows of the same length, he has 15 chairs left over:

7x + 15 = N

Now we have two equations with two unknowns (x and N). We can solve for x by setting the two expressions for N equal to each other and solving for x:

9x + 5 = 7x + 15

2x = 10

x = 5

Now that we know that x = 5, we can substitute this value back into either of the two equations above to solve for N:

9(5) + 5 = N

N = 50

Therefore, Liam has 50 chairs in total.

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