a recent survey reported that in a sample of 300 students who attend 2-year colleges, 105 work at least 20 hours per week. additionally, in a sample of 225 students attending private 4-year universities, only 20 students work at least 20 hours per week. what is the test value for a test of the difference between these two population proportions?

The required value of the probability of P(0.3) is given as 0.10. Option B is correct.

Given that,
The equation of the curve is given as y = -2x, For the interval {0, 1}, To find the probability of point 0.3 on the line.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
Sample space = 10 [since there are 10 subpoints in interval {0, 1}]

Favorable outcome = 1 [since there is only on valve 0.3]
Probability of the point 0.3 = 1 / 10 = 0.1

Thus, the required value of the probability of P(0.3) is given as 0.10. Option B is correct.

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Answer:

for the tringle:

area=\(p^{2} -2p-3\)

for the frame:

area=\(8x+28\)

Step-by-step explanation:

For the tringle:-

Area=1/2bh

Area=1/2(2p-6)(p+1)

Area=1/2(\(2p^{2} -4p-6\))

Area=\(p^{2} -2p-3\)

For the picture frame:-

part 1:the area of the big frame

Area=lw

Area=(x+7)(x+4)

Area=\(x^{2} +11x+28\)

part 2:the area of the small frame

Area=lw

Area=(x+3)(x)

Area=\(x^{2} +3x\)

To find the area of the shaded regions:

Area of shaded region=area of the big frame-the area of the small frame

Area of shaded region=\((x^{2} +11x+28)-(x^{2} +3x)\)

Area of shaded region=\(8x+28\)

A Pearson correlation coefficient of +1.00 between two variables, X and Y, indicates a perfect positive correlation between them. This means that as the values of X increase, so do the values of Y, and vice versa.

In other words, the two variables are perfectly linearly related, and there is no variability in their relationship. A Pearson correlation coefficient of +1.00 is the strongest possible correlation coefficient, and it suggests that there is a direct and strong association between the two variables being measured.

For example, let's say we have data on the height and weight of a group of individuals. If we find a Pearson correlation coefficient of +1.00 between height and weight, it means that as a person's height increases, their weight will also increase perfectly in a linear fashion. This information can be useful in predicting weight based on height, or vice versa, and can help inform decisions related to health and fitness.

Overall, a Pearson correlation coefficient of +1.00 suggests that the two variables being measured have a strong and direct relationship, which can be useful in many different contexts.

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Answer:

c

Step-by-step explanation:

ive never been wrong

Answer: C

Step-by-step explanation:

Edge 1945

The null and alternative hypotheses for the above scenario are

H0: Their van has a miles/gallon (MPG) rating equal to 57.2 miles/gallon

Ha: Their van has a miles/gallon (MPG) rating that is different from 57.2 miles/gallon

Given that,

One automaker says that their van gets 57.2 miles per gallon (mpg). An impartial testing business has been hired to evaluate the mpg for this van. They tested 91 vans, and the results showed that the average mileage was 56.9 with a standard deviation of 1.8 mpg. Is there adequate proof that the vans don't meet their mpg rating at the 0.025 level

To find: state the null and alternative hypotheses for the above scenario.

The null and alternative hypotheses for the above scenario are

H0: Their van has a miles/gallon (MPG) rating equal to 57.2 miles/gallon

Ha: Their van has a miles/gallon (MPG) rating that is different from 57.2 miles/gallon

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SOLUTION

The formula for length of arc is given as

For the length of arc FEG

Therefore the length of arc FEG is

Calculate the value

Therefore, the length of arc FEG is 28.47 yards

Answer:

24

Step-by-step explanation:

A^2+b^2=c^2

In this case C^2 is solved and we have to solve for the remaining leg.

7^2+b^2=25^2

49+b^2=625

625-49=576

sqrt 576 = 24

The height is 24

The solution of the given problem of expression comes out to be  9x³.

There is a need for calculations like variable multiplying, splitting, joining, and currently removing. If they were combined, it would read: A mathematical formula, some data, and an equation. Values, elements, and mathematical operations like additions, subtractions, mistakes, subdivisions, but also arithmetic formulas all make up a declaration of truth. It is possible to assess and analyse words and sentences.

Here,

The following is the provided sentence's algebraic expression:

=> 9x³

where x is a numerical symbol.

Therefore , the solution of the given problem of expression comes out to be  9x³.

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Complete question:

Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify.

{Nine times the difference of 8 and a number.}

Nine times the difference of 8 and a number.

a) The amount of water in the pool after 2 hours can be calculated using the equation.

Water in pool = 10L/hour × 2 hours = 20L.

b) The pool will be 80L when the equation is satisfied: 80L = 10L/hour × Time.

Solving for Time, we find Time = 8 hours.

c) Part b) is linear.

a) To calculate the amount of water in the pool after 2 hours, we can use the equation:

Water in pool = Water filling rate × Time

Since the pool gets filled up with 10L of water per hour, we can substitute the values:

Water in pool = 10 L/hour × 2 hours = 20L

Therefore, after 2 hours, there will be 20 liters of water in the pool.

b) To determine the number of hours it takes for the pool to reach 80 liters, we can set up the equation:

Water in pool = Water filling rate × Time

We want the water in the pool to be 80 liters, so the equation becomes:

80L = 10 L/hour × Time

Dividing both sides by 10 L/hour, we get:

Time = 80L / 10 L/hour = 8 hours

Therefore, it will take 8 hours for the pool to contain 80 liters of water.

c) Part b) is linear.

The equation Water in pool = Water filling rate × Time represents a linear relationship because the amount of water in the pool increases linearly with respect to time.

Each hour, the pool fills up with a constant rate of 10 liters, leading to a proportional increase in the total volume of water in the pool.

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Answer:

D

Step-by-step explanation:

\(Tan \ 19 = \dfrac{Opposite \ side}{Adjacent \ side}\\\\0.3443 = \dfrac{x}{15}\\\\0.3443*15=x\)

x = 5.1645

x = 5.2

Answer:

Exterior alternate angles

x=5

Step-by-step explanation:

The relationship between these 2 angles is exterior alternate angles, which says that the alternating exterior angles that are made by a parallel line and a transversal are equal.

To solve for x, we can set up an equation:

24x=120

x=5

The probability that a car stops at the light for more than 30 seconds is approximately 0.714, or 71.4%.

To calculate the probability that a car stops at the light for more than 30 seconds, we need to first calculate the total time of the traffic light cycle, which is:

60 seconds (red) + 10 seconds (yellow) + 90 seconds (green) = 160 seconds

Next, we need to calculate the probability that a car arrives at the traffic light during each color phase. Since arrival times are uniformly distributed, the probability of a car arriving during any particular phase is simply the duration of that phase divided by the total cycle time. Therefore:

- Probability of arriving during red phase = 60/160 = 0.375
- Probability of arriving during yellow phase = 10/160 = 0.0625
- Probability of arriving during green phase = 90/160 = 0.5625

Now, to calculate the probability that a car stops at the light for more than 30 seconds, we need to consider two cases:

1. The car arrives during the red or yellow phase: In this case, the car will stop at the light for at least 60 seconds (the duration of the red phase) before the light turns green. Therefore, the probability of stopping for more than time 30 seconds in this case is:

Probability of arriving during red phase * Probability of stopping for more than 30 seconds during red phase = 0.375 * (60-30)/60 = 0.25

Probability of arriving during yellow phase * Probability of stopping for more than 30 seconds during yellow phase = 0.0625 * (90-30)/90 = 0.375

Total probability for this case = 0.25 + 0.375 = 0.625

2. The car arrives during the green phase: In this case, the car will not stop at the light if it arrives before the end of the green phase, which happens with probability:

Probability of arriving during green phase * Probability of arriving before end of green phase = 0.5625 * 90/160 = 0.315625

Therefore, the probability of stopping for more than 30 seconds in this case is:

Probability of arriving during green phase * Probability of stopping for more than 30 seconds during green phase = 0.5625 * 0.5 = 0.28125

Total probability for this case = 0.315625 * 0.28125 = 0.0888671875

Finally, we can add the probabilities from both cases to get the total probability of stopping for more than 30 seconds:

Total probability = Probability from case 1 + Probability from case 2 = 0.625 + 0.0888671875 = 0.7138671875

Therefore, the probability that a car stops at the light for more than 30 seconds is approximately 0.714, or 71.4%.

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Approximately 4.5 gallons of paint would be needed for one coat on the entire exterior of the barn, including the roof.

To determine the number of gallons of paint needed for one coat on the entire exterior of the barn, including the roof, we need to calculate the total surface area that needs to be painted.

Let's consider the dimensions of the barn:

Length: 30 feet

Width: 20 feet

Height: 10 feet

First, let's calculate the surface area of the four walls. Since a rectangular barn has opposite walls with equal dimensions, we can calculate the area of one wall and multiply it by 4:

Wall area = Length * Height

= 30 feet * 10 feet

= 300 square feet

Now, multiply the wall area by 4 to account for all four walls:

Total wall area = Wall area * 4

= 300 square feet * 4

= 1200 square feet

Next, let's calculate the surface area of the roof, which is a rectangle:

Roof area = Length * Width

= 30 feet * 20 feet

= 600 square feet

Finally, we calculate the total surface area that needs to be painted by adding the wall area and the roof area:

Total surface area = Total wall area + Roof area

= 1200 square feet + 600 square feet

= 1800 square feet

Given that one gallon of paint covers 400 square feet, we can divide the total surface area by 400 to determine the approximate number of gallons needed for one coat:

Number of gallons = Total surface area / Coverage per gallon

= 1800 square feet / 400 square feet

= 4.5 gallons

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The total area under a probability density function is always equal to 1.

This means that the probability of any possible outcome occurring in the given probability distribution is 1, or 100%. The area under the probability density function represents the likelihood of a random variable falling within a particular range of values, and the total area represents the probability of all possible outcomes.

The probability density function can be used to calculate the probability of a random variable taking on a specific value, as well as the probability of a random variable falling within a certain range of values. The area under the probability density function can be calculated using integration techniques.

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hello mai brou tenkuiusnriejqbe

Step-by-step explanation:

5x-4x =24

1x = 24

X = 24/1

X = 24 ans.there is no value of 1 then also I have written so u can understand.

Answer:

182.59

Step-by-step explanation:

46.80 + 0.79+ 135

The sum of the expression £46.80 + 79p + £135 will be £182.59.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The expression is given below.

⇒ £46.80 + 79p + £135

We know that £1 = 100p. Then the sum of the expression will be

⇒ 46.80 + 0.79 + 135

⇒ £182.59

The sum of the expression £46.80 + 79p + £135 will be £182.59.

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Answer:Ax + By = C

-ax -ax

-------------------

By = -Ax + C

--- ------------

B B

--------------------

y = -Ax + C

----------

B

Step-by-step explanation:

Answer:

y=c/b-ax/b

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

The Fourier series of the function f(x) on the interval -π < x < π is f(x) = (1/π) + ∑[(2/π) [1 - cos(nπ)] sin(nx)].

To find the Fourier series of the function f(x) on the given interval, we can use the formula for the Fourier coefficients.

Since f(x) is a piecewise function with different definitions on different intervals, we need to determine the coefficients for each interval separately.

For the interval -π < x < 0, f(x) is equal to 0. Therefore, all the Fourier coefficients for this interval will be 0.

For the interval 0 ≤ x < π, f(x) is equal to 1. To find the coefficients for this interval, we can use the formula:

a₀ = (1/π) ∫[0,π] f(x) dx = (1/π) ∫[0,π] 1 dx = 1/π

aₙ = (1/π) ∫[0,π] f(x) cos(nx) dx = (1/π) ∫[0,π] 1 cos(nx) dx = 0

bₙ = (1/π) ∫[0,π] f(x) sin(nx) dx = (1/π) ∫[0,π] 1 sin(nx) dx = (2/π) [1 - cos(nπ)]

Therefore, the Fourier series of f(x) on the given interval is:

f(x) = (1/π) + ∑[(2/π) [1 - cos(nπ)] sin(nx)]

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The degrees of freedom associated with a pooled-variance two-sample t-test or confidence interval in the given case would be 48.

When a pooled-variance two-sample t-test or confidence interval is to be conducted on two groups, the degrees of freedom is calculated using the following formula: df = n1 + n2 - 2, where n1 and n2 are the sample sizes of the two groups being compared.

In the given scenario, data is collected from 20 random luxury hotels in New York and 30 random luxury hotels in Los Angeles. Therefore, the degrees of freedom for a pooled-variance two-sample t-test or confidence interval would be:df = 20 + 30 - 2df = 48. Hence, the degrees of freedom associated with a pooled-variance two-sample t-test or confidence interval are 48.

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Answer:

10 Milk chocolates

8 dark chocolates

6 white chocolates

24 TOTAL

\frac{10}{24} Probability that Hanissa choose a milk chocolate

Now, since she has already eaten one chocolate, then what's left is 23 chocolates.

So, since the second one should be a white chocolate and there are 6 of them, then

\frac{6}{23} - probability of choosing a white chocolate.

Then, multiply,

( \frac{10}{24} )( \frac{6}{23} )= \frac{60}{552} or \frac{5}{46}

Answer: 5/46 or 10.87%

Step-by-step explanation: no explanation:

Dots in scatterplots that deviate conspicuously from the main dot cluster are viewed as potential outliers.

Outliers are observations that are significantly different from other observations in the dataset. They can occur due to measurement error, data entry errors, or simply due to the natural variability of the data. Outliers can have a significant impact on the results of statistical analyses, so it is important to identify and investigate them. In a scatterplot, outliers are often seen as individual data points that are located far away from the main cluster of data points. They may indicate a data point that is unusual or unexpected, or they may be the result of a data entry error. In any case, outliers should be examined closely to determine their cause and whether they should be included in the analysis or removed from the dataset.

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The mathematical proof is given below. Then the claims are correct.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The triangle ΔABC is a right-angle triangle. And line CD is perpendicular to line AB.

In triangles ΔABC, ΔACD, and ΔCDB, we have

∠ACB = ∠ADC = ∠BDC                     (Right angle)

∠ABC = ∠ACD = ∠CBD                     (Corresponding angles)

Then the triangles ΔABC, ΔACD, and ΔCDB will be similar to each other. And in triangle ΔABC by the Pythagoras theorem is written as,

AB² = AC² + BC²

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The main difference between everyday logic and mathematical logic is that everyday logic is based on general observations and opinions, while mathematical logic is based on precise statements and facts.

Differences:
- Everyday logic is based on common sense and intuition, while mathematical logic is based on strict rules and formulas.
- Everyday logic is often used to make decisions or solve problems in daily life, while mathematical logic is used to solve complex mathematical problems.
- Everyday logic can be subjective and influenced by personal beliefs or experiences, while mathematical logic is objective and follows a set of universally accepted principles.

Similarities:
- Both everyday logic and mathematical logic use reasoning to draw conclusions.
- Both everyday logic and mathematical logic rely on evidence and facts to support their conclusions.
- Both everyday logic and mathematical logic can be used to solve problems and make decisions.

In conclusion, while everyday logic and mathematical logic have some similarities in terms of their use of reasoning and evidence, they differ in their approach and application. Everyday logic is based on common sense and intuition, while mathematical logic is based on strict rules and formulas.

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The value of the angle m<QPS cannot be determined. Option D

To determine the value of the angle, we need to take note of the properties of a parallelogram

From the information given, we have that;

m<R = 6x -14

m<Q = 3x + 8

m< S= 5x + 4

The value of the angle , QPS cannot be determined because the angle is not represented with any variable for calculation

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Based on the triple scalar product, u, v, and w are not coplanar and based on the definition of linear combination, u, v, and w are not coplanar and u, v, and p are linearly independent.

To show that u, v, and w are coplanar using their triple scalar product, we calculate the scalar triple product (u x v) · w.

If the scalar triple product is equal to zero, then the vectors are coplanar.

Let's calculate:

(u x v) · w = [(2, -1, 4) x (0, -9, 18)] · (0, -9, 18)

= (36, 0, 18) · (0, -9, 18)

= 36(0) + 0(-9) + 18(18)

= 0 + 0 + 324

= 324

Since the scalar triple product is not zero, u, v, and w are not coplanar.

To show that u, v, and w are coplanar using the definition that there exist two nonzero real numbers α and β such that w = αu + βv, we can write down the equations and solve for α and β.

We have:

w = (0, -9, 18)

u = (2, -1, 4)

v = (0, -9, 17)

Let's set up the equations:

0 = α(2, -1, 4) + β(0, -9, 17)

From the equations, we can see that the x-component equation is 2α = 0, which implies α = 0.

However, the y-component equation is -α - 9β = -9, which is inconsistent with α = 0.

Therefore, there are no nonzero real numbers α and β that satisfy the equations, and thus u, v, and w are not coplanar.

To show that u, v, and p are linearly independent, we need to demonstrate that there are no real numbers α, β, and γ, not all zero, such that αu + βv + γp = 0.

We have:

u = (2, -1, 4)

v = (0, -9, 17)

p = (0, -9, 17)

Let's set up the equations:

α(2, -1, 4) + β(0, -9, 17) + γ(0, -9, 17) = (0, 0, 0)

From the equations, we can see that the x-component equation is 2α = 0, which implies α = 0. However, the y-component equation is -α - 9β - 9γ = 0, which is inconsistent with α = 0.

Therefore, there are no nonzero real numbers α, β, and γ that satisfy the equations, and thus u, v, and p are linearly independent.

In summary, based on the results of the calculations, we conclude that u, v, and w are not coplanar, u, v, and w are not coplanar based on the definition of linear combination, and u, v, and p are linearly independent.

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The amount of fuel needed for 600 km is 50 liters

From the question, we have the following parameters that can be used in our computation:

240Km on 20 liters of fuel.

This can be expressed as

Fuel : Distance = 20 liters : 240 km

For 600 km, we have

Fuel : 600 km = 20 liters : 240 km

Express as fraction

Fuel = 600 * 20/240

Evaluate

Fuel = 50

Hence, the amount of fuel is 50 liters

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Answer:

6/15

Step-by-step explanation:

3/5*2/3=6/15

a) A function that expresses f(x) is f(x) = 1.5x.

b) A graph of the function is shown in the image below.

c) The domain and range of the function are all real numbers or [-∞, ∞].

Assuming the variable x represent the amount of a transaction and the variable f(x) represent the amount Isabel is charged for the transaction, a linear function charges on each sale by the credit card company can be written as follows;

f(x) = 1.5x

Part b.

In this exercise, we would use an online graphing tool to plot the function f(x) = 1.5x as shown in the graph attached below.

Part c.

By critically observing the graph shown below, we can logically deduce the following domain and range:

Domain = [-∞, ∞] or all real numbers.

Range = [-∞, ∞] or all real numbers.

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Complete Question:

A transaction is positive if there is a sale and negative when there is a return. Each time a customer uses a credit card for a transaction, the credit company charges Isabel. The credit company charges 1.5% of each sale and a fee of 0.5% for returns.

a) Let x represent the amount of a transaction and let f(x) represent the amount Isabel is charged for the transaction. Write a function that expresses f(x).

b) Graph the function.

c) What are the domain and range of the function?