It is advertised that the average braking distance for a small car traveling at 65 miles per hour equals 120 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 34 small cars at 65 miles per hour and records the braking distance. The sample average braking distance is computed as 115 feet. Assume that the population standard deviation is 20 feet. Use Table 1.
Use α = 0.01 to determine if the average braking distance differs from 120 feet. The average braking distance is (significantly/not significantly) different from 120 feet.

The function f: {(1, 5), (-2, 3), (-4, 2), (2, 5)} is a one-to-one function. It satisfies condition where each input value maps to unique output value, ensuring no repetition or multiple inputs leading to the same output.

A one-to-one function, also known as an injective function, is a type of function where each input value is uniquely mapped to an output value. In the given function f: {(1, 5), (-2, 3), (-4, 2), (2, 5)}, we can observe that each input value corresponds to a distinct output value. For example, the input 1 is mapped to the output 5, and no other input has the same output. Similarly, the inputs -2, -4, and 2 are associated with the outputs 3, 2, and 5 respectively, without any repetition.

This lack of repetition or duplication in the outputs demonstrates that the function is one-to-one. Each input has a unique correspondence with its output, and no two different inputs yield the same output value. Therefore, based on the provided set of mappings, we can conclude that the function f is indeed a one-to-one function.

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Answer:

17/27

Step-by-step explanation:

Since there are 10 blue marbles, and 27 total marbles, the probability of not choosing a blue marble is 17/27 because you subtract the amount of blue marbles (10) from the amount of total marbles (27).

The probability of not choosing a blue marble is 17/27.

Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.

For the given situation,

Number of red marbles = 4

Number of blue marbles = 10

Number of green marbles = 7

Number of yellow marbles = 6

The event is the probability of not choosing a blue marble is

⇒ [tex]\frac{red+green+yellow}{Total marbles}[/tex]

⇒ [tex]\frac{4+7+6}{27}[/tex]

⇒ [tex]\frac{17}{27}[/tex]

Hence we can conclude that the the probability of not choosing a blue marble is 17/27.

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Answer:

(0,6), (6,0)

Step-by-step explanation:

Answer:

Whatttttttttttttttttt

Answer:

with what?

Step-by-step explanation:

The time after 21 minutes from 9:39 is 2:56am.

Given that it is now twenty-one minutes to ten, we need to determine the time in 5 hours and 17 minutes.

To find the answer, we can add 5 hours and 17 minutes to the current time, which is 9:39 PM. Let's first convert the hours to minutes:5 hours = 5 x 60 = 300 minutes.

Then, add 300 minutes and 17 minutes:300 minutes + 17 minutes = 317 minutes.

Since there are 60 minutes in an hour, we need to divide 317 by 60 to determine the number of hours:317 / 60 = 5 with a remainder of 17.

Therefore, the time in 5 hours and 17 minutes will be 2:56 AM.

To check our answer, we can work backward:

Start with 2:56 AM and subtract 5 hours and 17 minutes:2:56 AM - 5 hours = 9:56 PM9:56 PM - 17 minutes = 9:39 PMAs expected, we arrived back at the original time of 9:39 PM. Therefore, the final answer is 2:56.

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Answer:

I think it is 25÷8

Step-by-step explanation:

this is because the circumference is found by π multiplied by the diameter. So the inverse would be the circumference divided by the diameter.

Answer:

Step-by-step explanation:

Answer:

one solution

infinite number of solutions  

no solutions

Step-by-step explanation:

i hope this helps :)

Answer:

Step-by-step explanation:

Question says that it uses 120 feet of fencing material to enclose three sides of the play area. This means there are 3 sides. Putting this into equation, we have something like this.

120 = L + 2W

Where

LW = area.

Again, in order to maximize the area with the given fencing, from the equation written above, then Width, w must be = 30 feet and length, l must be = 60

On substituting, we have

A = LW = (120 - 2W) W

From the first equation, making L the subject of the formula, we have this

L = 120 - 2W, which then we substituted above.

On simplification, we have

L = 120W -2W²

Differentiating, we have

A' = 120 - 4W = 0

Remember that W = 30

So therefore, L = 120 - 2(30) = 60 feet

The required length of the rectangular garden is 60 feet

According to the question, the school uses 120 feet of fencing material to enclose three sides of the play area. This means there are 3 sides.

Substitute into the perimeter of the rectangle will give:

120 = L + 2W

Area = LW

In order to maximize the area with the given fencing, from the equation written above, then w = 30 feet and l = 60

On substituting, we have;

A = LW = (120 - 2W) W

L = 120 - 2W,

On simplification, we have

L = 120W -2W²

Differentiating, we have

A' = 120 - 4W = 0

Remember that W = 30

So therefore, L = 120 - 2(30) = 60 feet

Hence the required length of the rectangular garden is 60 feet

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The scale factor of a dilation is the ratio of the corresponding side lengths of the image triangle to the original triangle. In this case, the image triangle is triangle A' B' C' and the original triangle is triangle ABC.

To find the scale factor, we can compare the corresponding side lengths of the two triangles. Let's denote the lengths of the corresponding sides as follows:

Side AB corresponds to side A'B'

Side BC corresponds to side B'C'

Side CA corresponds to side C'A'

The scale factor is then given by:

Scale factor = Length of corresponding side in image triangle / Length of corresponding side in original triangle

To find the scale factor, you can calculate the ratio of the corresponding side lengths. For example, if the length of AB is 4 units and the length of A'B' is 8 units, then the scale factor would be 8/4 = 2.

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Answer:

[tex]4\frac{5}{12}[/tex]

Step-by-step explanation:

[tex]4\frac{3}{4} -\frac{1}{3} \\\\\frac{19}{4} -\frac{1}{3} \\\\\frac{57}{12} -\frac{4}{12} \\\\\frac{53}{12} \\\\4\frac{5}{12}[/tex]

Answer:

leon's older brother is 4 5/12 feet tall

Step-by-step explanation:

4 3/4 - 1/3

= 4 5/12

Answer:

3 units down

Step-by-step explanation:

got it right on edg

Answer:

x = 132°

Just add the opposite interior angles

In spherical coordinates (ρ, θ, ϕ), the point (0, -5, 0) can be represented as (5, π/2, π/2).

To convert from rectangular coordinates to spherical coordinates, we use the following formulas:

ρ = √(x² + y² + z²)

θ = arctan(y / x)

ϕ = arccos(z / √(x² + y² + z²))

In this case, since the point lies on the negative y-axis, the x-coordinate is 0, and the y-coordinate is -5. Therefore, we have:

ρ = √(0² + (-5)² + 0²) = √25 = 5

Since the point lies in the negative y-axis, the angle θ is π/2.

Since the point lies on the xz-plane, the z-coordinate is 0. Therefore, we have:

ϕ = arccos(0 / √(0² + (-5)² + 0²)) = arccos(0 / 5) = arccos(0) = π/2

Combining these values, the point (0, -5, 0) in rectangular coordinates is equivalent to (5, π/2, π/2) in spherical coordinates.

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If the graph represents the perimeter (y) in units for an equilateral triangle, we can determine the relationship between the perimeter and the side length of the triangle.

In an equilateral triangle, all three sides are equal in length. Let's denote the side length of the equilateral triangle as x.

The perimeter (P) of an equilateral triangle is given by the formula:

P = 3 * x

Therefore, the relationship between the perimeter (y) and the side length (x) of the equilateral triangle is:

y = 3x

So, if the graph represents the perimeter (y) in units for an equilateral triangle, it would be a linear function with a slope of 3 and the side length (x) as the independent variable.

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Answer: C

Step-by-step explanation:

21x+9-3x = 18x + 9

If you factor out the 9, you would be left with

9 (2x+1)

Answer: A. 9(2x - 1)

Step-by-step explanation:

combine like terms

21x+9-3x

21x-3x

18x+9

Factor the expression

factor out 9 from the expression

you get 9(2x - 1)

The mean value is 6.5.

Given, z = 2.25, x = 14.6, σ = 3.6

The formula to calculate the z-score is,

z-score, z = (x - μ) / σOn

substituting the given values in the above formula, we get

2.25 = (14.6 - μ) / 3.6

Multiplying both sides by 3.6, we get,

2.25 * 3.6 = 14.6 - μ8.1 = 14.6 - μ

Subtracting 14.6 from both sides, we get,

-6.5 = -μOn multiplying both sides by -1, we get,

μ = 6.5

Hence, the mean value is 6.5.

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The decimal place z -score formula, z=x−μσ z = x − μ σ the mean (μ) is 6.5.

To find the mean (μ) using the z-score formula the Solve for μ

z = (x - μ) / σ

substitute the given values into the equation

2.25 = (14.6 - μ) / 3.6

solve for μ:

2.25 × 3.6 = 14.6 - μ

8.1 = 14.6 - μ

To isolate μ, subtract 14.6 from both sides:

8.1 - 14.6 = -μ

-6.5 = -μ

multiplying both sides by -1 gives

6.5 = μ

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Answer:

Explanation:

4! = 4×3×2×1 = 24

here's an example:

The question is incomplete:

Two ovens have measurements as shown. Which oven has a greater volume? How much greater is its volume?

The image with the information is below.

Answer:

-Oven B has a greater volume.

-Its volume is greater by 768 in³.

Step-by-step explanation:

First, you have to calculate the volume of each oven by multiplying the area of the base by the height:

Oven A: 576 in²*15 in= 8640 in³

Oven B: 672 in²*14 in= 9408 in³

Now, you have to calculate the difference between the volumes:

9408-8640=768

According to this, the answer is that oven B has a greater volume. Its volume is greater by 768 in³.

Answer:

D

Step-by-step explanation:

Step-by-step explanation:

Surface Area of Figure = Area of 4 triangular sides + Area of Base

=

[tex]4 \times ( \frac{1}{2} \times base \times height) + (length \: \times \: width) \\ = 4 \times ( \frac{1}{2} \times 10 \times 12.1) + (10 \times 10) \\ = 4 \times 60.5 + 100 \\ = 242 + 100 \\ = 342 {yd}^{2} [/tex]

Answer:

The discriminant, -14.71 < 0, shows that there is no solution of the equation, h = -16·t² + 22.3·t + 2, at the line 'h = 10' feet, therefore, the Jaguarundi height as she springs will not be up to 10 feet and therefore she will not reach the bird

Step-by-step explanation:

From the question, the equation that models the Jaguarundi's height, 'h', ma be written approximately as follows;

h = -16·t² + 22.3·t + 2

Where;

t = The time (duration) in seconds

The discriminant of the equation a·x² + b·x + c = 0 is  b² - 4·a·c

When h = 10, we have;

10 = -16·t² + 22.3·t + 2

∴ 0 = -16·t² + 22.3·t + 2 - 10 = -16·t² + 22.3·t - 8

The discriminant of the given quadratic equation is given as follows;

The discriminant = 22.3² - 4 × (-16 × (-8)) = -14.71 < 0

Therefore, the function, h = -16·t² + 22.3·t + 2 has no real root at h = 10

The parabola does not reach or pass through the line h = 10 which is the height at which the bird is flying.

The Jaguarundi will not reach the bird flying at the height of 10 feet.

Answer:

No, the Jaguarundi will not reach the bird

Step-by-step explanation:

The equation is

[tex]h=-16t^2+22.3t+2[/tex]

When h = 10 feet

[tex]10=-16t^2+22.3t+2[/tex]

[tex]\Rightarrow -16t^2+22.3t-8=0[/tex]

[tex]a=-16[/tex]

[tex]b=22.3[/tex]

[tex]c=-8[/tex]

Discriminant is given by

[tex]b^2-4ac=22.3^2-4(-16)(-8)[/tex]

[tex]\Rightarrow b^2-4ac=-14.71[/tex]

[tex]\Rightarrow b^2-4ac<0[/tex]

So, the Jaguanrundi will not reach the bird as the roots will be imaginary.

The p-value for the two-tailed t-test with degrees of freedom (df) = 19 and a sample t-value of -0.36 is greater than the significance level of α = 0.01. Therefore, we retain the null hypothesis.

In a two-tailed t-test, the null hypothesis (H₀) states that there is no significant difference between the population mean (µ) and a hypothesized mean (µo). The alternative hypothesis (H₁) states that the population mean is not equal to the hypothesized mean.

To determine the p-value, we compare the absolute value of the sample t-value (-0.36 in this case) with the critical t-value for the given degrees of freedom (df = 19). Since the sample t-value falls within the acceptance region, we find the probability of obtaining a t-value as extreme as -0.36 (or more extreme) assuming the null hypothesis is true.

If the p-value is less than the significance level (α = 0.01), we reject the null hypothesis. However, if the p-value is greater than the significance level, we retain the null hypothesis. In this case, since the p-value is greater than 0.01, we do not have sufficient evidence to reject the null hypothesis. Therefore, we retain it.

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Question

Marcus asked 10 people at a juggling festival what age they were when they started to juggle. Which interval contains the median age?

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]n = 10[/tex]

Required

The median interval

The question is incomplete, as the required data is not given.

To solve this question, I will use the following assumed dataset.

[tex]Age:17\ 17\ 18\ 20\ 21\ 22\ 22\ 24\ 28\ 28[/tex]

First, calculate the median position.

[tex]Median = \frac{n+1}{2}\ th[/tex]

[tex]Median = \frac{10+1}{2}\ th[/tex]

[tex]Median = 5.5\ th[/tex]

This implies that the median is the mean of the 5th and 6th data

So, we have the interval to be.

[tex]Median = [5th, 6th][/tex]

[tex]Median=[21,22][/tex]

Generally, the median of 10 data set is located at interval 5 to 6

The cutoff sample score is therefore:40 - 2.326(1.5811) ≈ 36.59

The research hypothesis and null hypothesis about the populations can be restated as follows:Population 1: The population of people who have not received the new stress-reduction method training.Population 2: The population of people who have received the new stress-reduction method training.Research hypothesis: The new stress-reduction method training has reduced stress levels in the population that has received it compared to the population that has not.Null hypothesis: The new stress-reduction method training has not reduced stress levels in the population that has received it compared to the population that has not.7. The comparison distribution in this case is the distribution of means from samples of the population that has not received the new stress-reduction method training. This distribution has a mean (μ) equal to the population mean of 40 and a standard deviation (σ) equal to the population standard deviation divided by the square root of the sample size, which is σ/√n = 10/√40 = 1.5811.8. To determine the cutoff sample score (or Z score) on the comparison distribution at which the null hypothesis should be rejected at p < .01, we need to find the z-score corresponding to a probability of .01 in the right tail of the distribution. This is given by:z = invNorm(0.99) ≈ 2.326Therefore, if the sample mean of the population that has received the new stress-reduction method training is more than 2.326 standard errors below the mean of the comparison distribution (which is 40), the null hypothesis can be rejected at the 0.01 level of significance.

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6. Restate question as a research hypothesis and a null hypothesis about the populations.

Population 1: The population of people who do not follow the stress-reduction method.

Population 2: The population of people who are trained in the stress-reduction method.

Research hypothesis: The mean score of population 2 is significantly less than the mean score of population 1, indicating that the stress-reduction method is effective in reducing stress levels.

Null hypothesis: There is no significant difference between the mean score of population 1 and population 2, indicating that the stress-reduction method is not effective in reducing stress levels.

7. The mean of the comparison distribution will be equal to the mean of the population of people who follow the stress-reduction method (which is 40), and the standard deviation of the comparison distribution will be equal to the standard deviation of the population of people who follow the stress-reduction method (which is 10 / sqrt(40) = 1.58).

8. The Z score of the sample mean is less than -2.33, we can reject the null hypothesis at p < .01. Since the Z score of the sample mean is -2.52, we can reject the null hypothesis at p < .01.

6. Restate question as a research hypothesis and a null hypothesis about the populations.

Population 1: The population of people who do not follow the stress-reduction method.

Population 2: The population of people who are trained in the stress-reduction method.

Research hypothesis: The mean score of population 2 is significantly less than the mean score of population 1, indicating that the stress-reduction method is effective in reducing stress levels.

Null hypothesis: There is no significant difference between the mean score of population 1 and population 2, indicating that the stress-reduction method is not effective in reducing stress levels.

7. To determine the characteristics of the comparison distribution.

The comparison distribution is the distribution of sample means if we drew all possible samples of the same size from the population of interest.

In this case, we have a sample of 40 people who were trained in the stress-reduction method, so the comparison distribution will be a distribution of sample means of size 40 from the population of people who follow the stress-reduction method.

The mean of the comparison distribution will be equal to the mean of the population of people who follow the stress-reduction method (which is 40), and the standard deviation of the comparison distribution will be equal to the standard deviation of the population of people who follow the stress-reduction method (which is 10 / sqrt(40) = 1.58).

8. To determine the cutoff sample score (or Z score) on the comparison distribution at which the null hypothesis should be rejected at p < .01.

To find the cutoff sample score (or Z score), we need to calculate the Z score of the sample mean (36) using the formula:

Z = (X - μ) / (σ / sqrt(n))

Z = (36 - 40) / (10 / sqrt(40))

Z = -2.52

The cutoff sample score (or Z score) on the comparison distribution at which the null hypothesis should be rejected at p < .01 is the Z score that corresponds to a probability of .01 in the upper tail of the distribution, which is equal to 2.33.

Therefore, if the Z score of the sample mean is less than -2.33, we can reject the null hypothesis at p < .01. Since the Z score of the sample mean is -2.52, we can reject the null hypothesis at p < .01.

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Answer:

1/81

Step-by-step explanation:

In h(x)=3^x, replace each instance of x with -4:

h(-4) = 3^(-4), or

                 1

h(-4) = ----------- = 1/81

              3^4

[tex]\huge{\mathbb{\tt { PROBLEM:}}}[/tex]

if h(x)=3^x then h (-4) =

[tex]\huge{\mathbb{\tt { ANSWER:}}}[/tex]

[tex] \frac{1}{81} [/tex]

[tex]\huge{\mathbb{\tt { EXPLANATION:}}}[/tex]

In h(x) = 3^x , you must replace each instance of with -4:

h(-4)=3^(-4)

[tex]h(4)= \frac{1}{3^4} = \frac{1}{81} [/tex]

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