If 3 is congruent to 4 then which statement must be true?

1)  The test statistic is 1.5

2) The p-value is  0.1544.

What is a hypothesis?

A hypothesis is a theory put up to explain a phenomenon. A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis. Scientific hypotheses are typically based on prior observations that cannot be adequately explained by the current body of knowledge.

Here, we have

Given: Students at a certain college claim that the average distance students commute to campus is 26 miles per day.

This will be a two-tailed test because the alternative hypothesis is showing a specific direction

This is the two-tailed test.

The null and alternative hypothesis is,

H₀ : μ = 26

Hₐ: μ ≠ 26

x = 29

s = 8

n = 16

1) Test statistic = t = (x-μ)/s/√n

= (29-26)/8/√16

= 3/8/4

= 1.5

degrees of freedom = n - 1 = 16 - 1 = 15

p(t > 1.5) = 1-P (t < 1.5) = 1 - 0.9228

= 0.0772

This is the two-tailed test.

2) p-value = 2 * p(t > 1.5)

p-value = 2 * 0.0772

p-value = 0.1544

Hence, 1)  The test statistic is 1.5

2) The p-value is  0.1544.

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According to a histogram that displays the percentage of replies over time, an April Gallup poll indicated that 55% of Americans think autonomous cars would be widely used in the next ten years.

Whether completely automated "driverless automobiles" would be widely deployed in the United States was the subject of a Gallup Poll conducted in April, which polled Americans ages 18 and older.

How soon, in your opinion, do you believe autonomous cars will be widely used in the US? According to the survey, 55% of Americans think autonomous cars will become commonplace over the next ten years.

The survey's results were displayed as a histogram, displaying the proportion of replies at various time intervals. This indicates how many respondents indicated that driverless cars will be widely utilised within a particular time period (e.g., within 5 years, within 10 years, etc.).

This survey reveals how people feel about autonomous cars in the future and how soon they believe they will be a common sight on the roads.

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The question is -

A Gallup Poll utilizing a random sample of adults ages or older was conducted in April. The survey indicated a majority of Americans () say driverless cars will be common in the next years (). The question asked was: Thinking about fully automated, "driverless cars," cars that use technology to drive and do not need a human driver, based on what you have heard or read, how soon do you think driverless cars will be commonly used in the [United States]? The figure below shows a summary of the results of the survey in a histogram indicating the percentage of the total responses in different time intervals.

Answer: -30

Step-by-step explanation:

My answer is correct because, All you have to do is subtract all the numbers by 11 and the one that has the sum -19 is the correct choice. In this case -30 does and we can make sure were orrect by subtracting 11 by -19 and that equals -30.

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The formula for finding the area of a triangle with an unknown height is: Area = (Base * Height) / 2. This formula uses the base length of the triangle, multiplied by the height of the triangle, then divided by 2.

The formula for finding the area of a triangle with an unknown height is: Area = (Base * Height) / 2. This formula uses the base length of the triangle, multiplied by the height of the triangle, then divided by 2. To use this formula, start by determining the base length of the triangle. This is the length of any one side of the triangle. Once the base is determined, use the formula to calculate the area. In the formula, the base is multiplied by the height of the triangle. Since the height is unknown, use the Pythagorean Theorem to calculate it. The Pythagorean Theorem states that the square of the hypotenuse (the longest side of the triangle) is equal to the sum of the squares of the other two sides. Once the hypotenuse is known, the height can be found by using the formula (Height = Hypotenuse - Base) / 2.

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first concert : 12 bodyguards

second concert : 15 bodyguards

12 x = 15

x = 15/12

x = 1.25

Multiply by 100 to obtain the percentage form

1.25 x 100 = 125

Subtract 100

125-100 = 25

It was a 25% increase change

Answer:

y - 1 = 4/5 (x + 2)

Step-by-step explanation:

the formula for point slope form is y - y = m (x - x)

if any of the number of the point is negative, then it would be a positive when in the equation. y - 1 = 4/5 (x - (+ x))

Answer:

C

Step-by-step explanation:

When the nuII hypοthesis is true, the expected vaIue οf the t statistic is 0.

The t-statistic in statistics measures hοw far an estimated vaIue οf a parameter deviates frοm its hypοthesised vaIue in reIatiοn tο its standard errοr.

T symbοI in statistics mean Test statistic fοr t-test ( t-scοre )

This is because the t statistic measures the difference between the sampIe mean and the nuII hypοthesis mean in units οf standard errοr, and when the nuII hypοthesis is true, there is nο difference between the sampIe mean and the nuII hypοthesis mean, resuIting in a t statistic οf 0.

Hοwever, it is impοrtant tο nοte that the distributiοn οf t statistics varies depending οn the sampIe size and the IeveI οf significance chοsen. Therefοre, even when the nuII hypοthesis is true, the οbserved t statistic may deviate frοm 0 due tο randοm sampIing errοr. In practice, a t statistic that is cIοse tο 0 and nοt statisticaIIy significant (i.e., dοes nοt reject the nuII hypοthesis) prοvides evidence that the nuII hypοthesis is pIausibIe.

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Answer:4,200

Step-by-step explanation:

The probability of at least one of the next four randomly selected births being a boy can be calculated as approximately 0.992.

To find the probability of at least one boy, we can calculate the probability of the complementary event, which is the probability of all four births being girls.

The probability of a single birth being a girl is 0.473, so the probability of all four births being girls is :

\((0.473)^4 = 0.049\)

Therefore, the probability of at least one boy is 1 - 0.049 = 0.951. However, this probability represents the chance for any of the four births to be a boy. Since there are four opportunities for a boy to be born, we need to consider the complement of no boy being born in any of the four births, which is \((1 - 0.951)^4\)≈ \(0.992\\\). Hence, the probability that at least one of the next four births is a boy is approximately 0.992.

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A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = –16t² + 40t + 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0.2 s and 2.7 s.

the solution to be eliminated is -0.2s this is because time do not have negative values

ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a.

It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be real or complex.

Considering the given function, the answer is both real one is negative the other is positive.

The solution in this case represents time, and time of negative value do not apply in real life

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Answer:

≈ 15 ft

Step-by-step explanation:

There is a right triangle formed by the ground, the building and the ladder.

The ground and the height the ladder is up the wall are the legs and the ladder is the hypotenuse.

let x be the distance from the base of the building to the bottom of the ladder.

Using Pythagoras' identity in the right triangle

x² + 26² = 30²

x² + 676 = 900 ( subtract 676 from both sides )

x² = 224 ( take the square root of both sides )

x = \(\sqrt{224}\) ≈ 15 ft ( to the nearest foot )

By taking the quotient between the total volume of paint and the volume needed to fill a container we can see that 16 containers can be filled.

We know that the art teacher has 12 + 4/5 gallons of paint, and we know that it requires 4/5 gallons to fill a single container.

Then the number of containers that can be filled is equal to the quotient between the total volume of paint and the volume needed fill a single container, it gives:

(12 + 4/5)/(4/5) = 16

So 16 containers can be totally filled.

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Cindy spent a total of $128.09 on ingredients for pies. She will be able to make 18 slices of pie with this amount of ingredients.

1. Cindy spent $65.25 on ingredients for blueberry pies and $62.84 on ingredients for cherry pies.

2. Add the two amounts together: $65.25 + $62.84 = $128.09

3. Each slice of pie sells for $3.50.

4. Divide the total spent on ingredients by the cost of a slice of pie: $128.09 / $3.50 = 18 slices of pie.

the complete question is :

Cindy spent $65. 25 on ingredients for blueberry pies and $62. 84 on

ingredients for cherry pies. Each slice of pie sells for $3. 50.How much did Cindy spend on ingredients for blueberry and cherry pies, and how many pies can she make from that?

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Choosing a decision alternative that maximizes the minimum profit is a feature of the maximin approach.

The maximin approach is a decision-making strategy that aims to identify the decision alternative that provides the highest payoff for the worst-case scenario.

It is commonly used in situations where the decision-maker is risk-averse or where the consequences of making the wrong decision are severe.

By selecting the alternative that maximizes the minimum profit, the decision-maker can ensure that they are prepared for the worst-case scenario and can minimize potential losses.

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Question

Choosing a decision alternative that maximizes the minimum profit is a feature of the ____ the maximum profit is a feature of the ____

The expression that gives the distance, d, between the ships after t hours is d = 25t

From the question, we are to write an expression that gives the distance, d, between the ships after t hours

First, we will determine the distance the ships have traveled after t hours

Using the formula,

Distance = Speed × Time

Thus,

The first ship would have traveled

20 × t miles

= 20t miles

The second ship would have traveled

15 × t miles

= 15t miles

Using the Pythagorean theorem,

The distance, d, between the ships after t hours is

d² = (20t)² + (15t)²

d² = 400t² + 225t²

d² = 625t²

d = √(625t²)

d = 25t miles

Hence, the expression that gives the distance, d, between the ships after t hours is d = 25t

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Answer:

a. Function; every x-value corresponds to only 1 y-value

b. Not a function; doesn't pass the VLT

c. Function, passes the VLT

2.

a. -200

b. x= -22.5

Step-by-step explanation:

Here is the basic rule for a function:

Every input (x) value goes only to one output (y) value.

For example, an x-value of 4 cannot go to y-values of both 2 and 4. {(4,2), (4,4)

a.

In a, we see that every x value has only one line- no x-value goes to two different y values, therefore, a is a function.

b. Remember that every x-value can only have one matching y value. This definition allows us to do a special test called the vertical line test (VLT). If we pass a vertical line through a graph (|) and it doesn't pass through two points at the same x value, then that graph is a function.

However, in this graph we can clearly see that this function DOES NOT pass the VLT.

(-2, 2) and (-2,-3)

c.

We're going to use the VLT once again. If we put a vertical line through the observable graph does any x value appear to have two or more y-values? No, so this is the graph of a function

2.

g(x)= 16 -4x

g(54) is the same as saying input 54 in for x, so

16- 4(54)

16- 216 = -200

a. -200

b.

So, g(x) = 106 and they want you to determine x.

Set g(x) equal to 106 and solve:

106= 16-4x

90 = -4x

x= -22.5

Answer:

y=0.25x^2−2x

Step-by-step explanation:

You have to use the disruptive property.

"As x increases, y increases along entire the graph".

A cubic function is a polynomial function of degree 3.

According to the given question.

We have a cubic function

\(f(x) = x^{3} +x^{2}+x+1\)

To find the behavior of graph, we will draw the graph of the cubic function.  

For this we will find the values of f(x), for different values of x.

So,

At x = 0

\(f(0) = (0)^{3} +(0)^{2} +0+1=1\)

At  x = -1

\(f(-1) = (-1)^{3} +(-1)^{2} +(-1)+1\\\)

\(\implies f(-1) = -1+1-1+1=0\)

At x = 1

\(f(1) =(1)^{3} +(1)^{2} +1+1\)

\(\implies f(1) = 1+1+1+1=4\)

At x = -2

\(f(-2) = (-2)^{3} +(-2)^{2} +(-2)+1\)

\(f(-2) = -8+4-2+1= -5\)

If we draw a graph using these points (0, 1), (-1, 0), (1, 4) and (-2, -5).

We see that "as x increases, y increases along entire the graph".

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Answer: 13/25

Step-by-step explanation: it is equal to 52% which is greater than 50%

50% is greater than 13/25. To compare these two values, you can convert both of them to a common denominator, such as 50%. 50% is equal to 1/2, so 13/25 is equal to 52/50, which is less than 1/2 or 50%. Alternatively, you can also express both fractions as decimals and compare the two values that way. 50% is equal to 0.5, and 13/25 is equal to 0.52, so 50% is still greater than 13/25.

The trigonometric expression cos (π/2 + r) is equivalent to the negative of sin r. Then the correct option is C.

Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.

The trigonometric expression is given below.

\(\cos (\dfrac{\pi}{2} + r)\)

We know that the formula

\(\cos (\dfrac{\pi}{2} + r) = -\sin r\)

Thus, the cos (π/2 + r) is equivalent to the negative of sin r.

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Answer:

C?

Step-by-step explanation:

, someone confirm

Answer:

y = 3/2x + 7/2

Step-by-step explanation:

Slope-intercept form is when y is the subject. So we make y the subject:

Add 3x to both sides :

2y = 3x + 7

Now we divide both sides by 2 :

y = 3/2x + 7/2

This is our final answer.

Hope this helped and brainliest please

Hi student, let me help you out! :)

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

We are asked to write the equation -3x+2y=7 in slope-intercept form.

\(\triangle~\fbox{\bf{KEY:}}\)

So let's write this equation, -3x+2y=7, in slope-intercept form...

///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\\////\\\\///\\\////\\\///\\\///\\\////\\\\////\\\\

First, we add -3x to both sides of the equal sign:

\(\large\pmb{2y=7+3x}\)

We can switch the order of the terms:

\(\large\pmb{2y=3x+7}\)

This is starting to look like the slope-intercept equation. In fact, all we have to do is divide both sides by 2:

\(\large\pmb{y=(3x+7)\div2}\)

Which simplifies to...

\(\large\pmb{y=\cfrac{3}{2}x+\cfrac{7}{2}}\)

That's the equation in slope-intercept form.

Hope this helps you out! :D

Ask in comments if any queries arise.

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Answer:

In picture

Step-by-step explanation:

Brainliest please

When Myriam was flying in the plane at a cruising altitude of 10 km, she felt no different sitting in her seat than she had felt on the ground. This is because both the plane and its occupants, including Myriam, are moving at the same speed and direction relative to each other. In other words, there is no relative motion between Myriam and the plane's interior.

From the perspective of the passengers inside the plane, they are essentially moving together as a single unit. The air inside the cabin is also moving with the same velocity as the plane. Therefore, there is no noticeable change in sensation or feeling of motion. This is similar to how we don't feel the motion of being inside a moving car if we are not looking outside or feeling any external forces.

The sensation of motion primarily arises when there is a change in velocity or when there are external forces acting on our bodies. In the case of an airplane flying smoothly at a constant speed and altitude, there are no significant forces or changes in velocity experienced by the passengers, so they feel no different than if they were on the ground.

The magician's trick of pulling a tablecloth out from under a set of dishes on a table is explained by the principle of inertia, which is a fundamental concept of Newton's First Law of Motion. According to Newton's First Law, an object at rest tends to stay at rest, and an object in motion tends to stay in motion with the same speed and direction, unless acted upon by an external force.

When the magician pulls the tablecloth rapidly, the key is to apply a quick and forceful pull in a horizontal direction. By doing so, the frictional force between the tablecloth and the dishes is overcome, and the tablecloth slides out from underneath the dishes. Due to the inertia of the dishes, they tend to resist changes in their state of motion, so they remain relatively stationary even as the tablecloth is rapidly removed.

The magician's trick is more successful when the tablecloth is pulled rapidly rather than slowly. Pulling the tablecloth slowly would increase the time over which the frictional force acts, causing a greater chance for the dishes to be affected by the force and potentially get disturbed or toppled. A rapid pull reduces the duration of the force acting on the dishes, allowing them to maintain their state of motion (or rest) due to inertia and minimizing the likelihood of disruption.

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Step-by-step explanation:

a) To form a committee of 8 with 3 prefects, we need to choose 3 prefects from the 5 available prefects, and 5 non-prefects from the remaining 7 boys. We can do this by using the combination formula:

Number of ways = (Number of ways to choose 3 prefects) × (Number of ways to choose 5 non-prefects)

Number of ways to choose 3 prefects from 5 = C(5, 3) = 10

Number of ways to choose 5 non-prefects from 7 = C(7, 5) = 21

Therefore, the total number of committees of 8 with 3 prefects that can be formed is:

Number of ways = 10 × 21 = 210

b) To form a committee of 8 with at least 3 prefects, we need to consider two cases: one where we choose exactly 3 prefects, and one where we choose all 5 prefects. We can calculate the number of ways for each case using the combination formula:

Number of ways to choose exactly 3 prefects and 5 non-prefects = C(5, 3) × C(7, 5) = 210

Number of ways to choose all 5 prefects and 3 non-prefects = C(5, 5) × C(7, 3) = 35

Therefore, the total number of committees of 8 with at least 3 prefects that can be formed is:

Number of ways = (Number of ways to choose exactly 3 prefects and 5 non-prefects) + (Number of ways to choose all 5 prefects and 3 non-prefects)

Number of ways = 210 + 35 = 245

Answer:

y=3/2x-4

Step-by-step explanation:

3x-2y=8

-2y=-3x+8

y=3/2x-4

y=3/2x-4

3x-2y=8

-2y=3x+8

y=3/2x-4

Answer:

m=1

Step-by-step explanation:

calculate slope (m) with this formula: (y2-y1)/(x2-x1)

here are the given points: (0,0) and (3,3)

label the points

x1=0

y1=0

x2=3

y2=3

now substitute into the equation

m=(3-0)/(3-0)

m=3/3

m=1

the slope is therefore 1

hope this helps :)

Answer:

x = 135°

Step-by-step explanation:

x and y are supplementary angles, that is they sum to 180° , then

x + y = 180 ← substitute x = 3y into the equation

3y + y = 180

4y = 180 ( divide both sides by 4 )

y = 45

then

x = 3y = 3 × 45° = 135°

Answer:

c

Step-by-step explanation:

The lateral surface area of the frustum with a lower base radius of 6 inches, an upper base radius of 3 inches, and a height of 4 inches is 45π sq. inches is 45π sq. inches

The lateral surface area of the frustum is calculated using the given formula:

Lateral surface area of frustum = π × (sum of the radii) × √(difference of radii²  + height²)

Lower base radius of frustum = 6 inches

Upper base radius of frustum = 3 inches

Height of frustum = 4 inches

Lateral surface area of given frustum = π × (6 + 3) × √[(6 - 3)² + 4²]

                                                              = π × 9 × √[(9 + 16]

                                                              = 9π × 5

                                                              = 45π sq. inches

Hence, the lateral surface area of the given frustum is 45π sq. inches

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