Which expression is equivalent to 5 EXPONENT 4 X5 EXPONENT NEGITIVE 4

Answer:

SSS

Step-by-step explanation:

They share one common side, and the two other sides are marked with single and double line identifiers, meaning they are the same. Therefore, SSS.

The proportion of those surveyed who chose basketball as their favorite sport is 34.149 (option a)

Let's denote the proportion of adults who chose basketball as their favorite sport as P(Basketball). To calculate P(Basketball), we need to divide the total number of adults who chose basketball by the total number of surveyed adults. Mathematically, it can be represented as:

P(Basketball) = (Number of adults who chose basketball) / (Total number of surveyed adults)

To calculate the number of adults who chose basketball, we sum up the values from the age range categories:

Number of adults who chose basketball = Number of adults (18-30) who chose basketball + Number of adults (31-50) who chose basketball + Number of adults (51 and above) who chose basketball

Looking at the table, we find that the number of adults (18-30) who chose basketball is 15, the number of adults (31-50) who chose basketball is 8, and the number of adults (51 and above) who chose basketball is 11. Adding these values together, we get:

Number of adults who chose basketball = 15 + 8 + 11 = 34

Now, let's calculate the total number of surveyed adults. We can sum up the values from the age range categories:

Total number of surveyed adults = Total number of adults (18-30) + Total number of adults (31-50) + Total number of adults (51 and above)

From the table, we find that the total number of adults (18-30) is 49, the total number of adults (31-50) is 48, and the total number of adults (51 and above) is 52. Adding these values together, we get:

Total number of surveyed adults = 49 + 48 + 52 = 149

Now, we have the values we need to calculate the proportion:

P(Basketball) = (Number of adults who chose basketball) / (Total number of surveyed adults)

= 34 / 149

Hence the correct option is (a).

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Given:

The arrow diagram of a relation.

To find:

Whether the given relation is a function or not.

Solution:

A relation is a called a function it there exist a unique y-value or unique output value for each x-value or input value.

From the given arrow diagram it is clear that y=2 and y=-1 for x=-1.

Since we have more than one value of y at x=-1, therefore, the given relation is not a function.

Hence, the correct option is B.

The given matrix A is diagonalizable, and the matrix P such that P⁻¹AP = D is:

P = [[1, 1],

    [0, 1]

D = [[2, 0],

    [0, 3]]

To determine whether a given matrix is diagonalizable, we need to check if it has a full set of linearly independent eigenvectors. If it does, then it is diagonalizable.
To determine if a matrix is diagonalizable and find the diagonal matrix D:
1. Compute the eigenvalues of matrix A by solving the characteristic equation det(A - λI) = 0, where λ is an eigenvalue and I is the identity matrix.
2. For each eigenvalue λ, find the corresponding eigenvectors by solving the equation (A - λI)X = 0, where X is a vector.
3. If the number of linearly independent eigenvectors is equal to the size of the matrix (i.e., the matrix has n linearly independent eigenvectors), then the matrix A is diagonalizable.
4. Once you have found a set of linearly independent eigenvectors, construct the matrix P using these eigenvectors as columns.
5. Find the inverse of matrix P, denoted as P⁻¹.
6. Compute the diagonal matrix D by using the equation D = P⁻¹AP.
If the matrix A is diagonalizable, then matrix P will be the matrix of eigenvectors, and D will be a diagonal matrix consisting of the corresponding eigenvalues on the diagonal.

Example:
Let's say we have a matrix A:
A = [[2, 1],
    [0, 3]]
1. Compute the eigenvalues:
  The characteristic equation is det(A - λI) = 0:
  |2-λ  1   |
  |0    3-λ |
  Setting this determinant equal to zero, we get:
  (2-λ)(3-λ) - 0 = 0
  Expanding and simplifying, we have:
  λ² - 5λ + 6 = 0
  Factoring, we get:
  (λ - 2)(λ - 3) = 0
  So, the eigenvalues are λ = 2 and λ = 3.

2. Find the eigenvectors:
  For λ = 2, we solve the equation (A - 2I)X = 0:
  |0  1| |x1|   |0|
  |0  1| |x2| = |0|
  Solving this system of equations, we get one eigenvector:
  X1 = [1, 0]
  For λ = 3, we solve the equation (A - 3I)X = 0:
  |-1  1| |x1|   |0|
  |0   0| |x2| = |0|
  Solving this system of equations, we get one eigenvector:
  X2 = [1, 1]
3. Since we have found two linearly independent eigenvectors (X1 and X2) and the matrix A is a 2x2 matrix, it is diagonalizable.
4. Construct matrix P:
  P = [X1, X2] = [[1, 1],
                  [0, 1]]
5. Find the inverse of matrix P:
  P⁻¹ = [[1, -1],
          [0,  1]]
6. Compute the diagonal matrix D:
  D = P⁻¹AP = [[2, 0],
                [0, 3]]
Therefore, the given matrix A is diagonalizable, and the matrix P such that P⁻¹AP = D is:
P = [[1, 1],
    [0, 1]]
D = [[2, 0],
    [0, 3]]

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Since the p-value (0.0179) is less than the typical significance level of 0.05, we reject the null hypothesis. We have evidence to suggest that the true proportion of uninjured occupants in head-on collisions exceeds 0.25 based on the sample data.

To test whether the true proportion of uninjured occupants in head-on collisions exceeds 0.25, we can perform a hypothesis test using the given sample data.

Let's set up the null and alternative hypotheses:

Null Hypothesis (H₀):

The true proportion of uninjured occupants in head-on collisions is 0.25 or less.

Alternative Hypothesis (H₁):

The true proportion of uninjured occupants in head-on collisions exceeds 0.25.

To test these hypotheses, we can use the proportion test, assuming the conditions for the test are met (e.g., the sample can be considered random and independent, and the sample size is sufficiently large).

Let's calculate the test statistic (z-score) and p-value based on the sample data.

Sample proportion of uninjured occupants:

p = 95/319 = 0.2978

Sample size:

n = 319

Under the null hypothesis, assuming the true proportion is 0.25 or less, the expected proportion of uninjured occupants is 0.25.

The test statistic (z-score) can be calculated as:

z = (p - p₀) / sqrt((p₀ * (1 - p₀)) / n)

where p₀ is the assumed proportion under the null hypothesis (0.25), and n is the sample size.

Substituting the values:

z = (0.2978 - 0.25) / sqrt((0.25 * (1 - 0.25)) / 319)

z = 2.1185

To determine the p-value associated with this test statistic, we can use a standard normal distribution table or a calculator. The p-value is the probability of observing a test statistic as extreme as the calculated z-value, assuming the null hypothesis is true.

The p-value associated with a z-score of 2.1185 is approximately 0.0179.

Finally, we can compare the p-value to the significance level (α) to make a decision. If the p-value is less than α (typically 0.05), we reject the null hypothesis in favor of the alternative hypothesis. If the p-value is greater than or equal to α, we fail to reject the null hypothesis.

In this case, since the p-value (0.0179) is less than the typical significance level of 0.05, we reject the null hypothesis. We have evidence to suggest that the true proportion of uninjured occupants in head-on collisions exceeds 0.25 based on the sample data.

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Answer:

5

Step-by-step explanation:

Use the distance formula: \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

\(\sqrt{(-5-(-9))^2+(-5-(-2))^2} \\\\\sqrt{(4)^2+(-3)^2}\\\\\sqrt{16+9}\\\\\sqrt{25}\\\\5\)

Answer:

1/4 pound

Step-by-step explanation:

2 1/2 divided by 10

=

1/4

or

5/2 divided by 10

=

1/4

Answer: 1/4 lbs

Step-by-step explanation:

To find weight lost each day, you have to divide total weight lost 2 1/2 lbs by total number of days 10.

(2 1/2) / 10 = 5/2 * 1/0 = 1/4 lbs lost each day

Answer:

yes

Step-by-step explanation:

there is a single x value for every y value

Answer:

136 \(m^{2}\)

Step-by-step explanation:

Well if you find the lateral area (the area of the rectangles on the sides) to get 112, so you just need to add that to the triangles and for those (they add up to 36) you can just use the formula for the area of a triangle,  which is \(b*h/2\).

Hope this helps :)

Answer:

2/5

Step-by-step explanation:

flip 5/6 to become 6/5 then cross reduce then cross multiply

The range of the function f(x) = 3x + 9 option is B: {y | y > 9}.

The range is the set of all values which the given function can output.

we have the function as

f(x) = 3x +9

The linear function has a range of all real numbers that is (-∞, ∞).

f(x) can take any real value.

x = -3

The correct option is B: {y | y > 9}.

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Answer:

n=-3.1

Step-by-step explanation:

To solve this, first subtract 3 from both sides of the equation to get 2n=-6.2. Next, divide both sides of the equation by 2 n order to get the final answer of n=-3.1

The 99% interval would be wider than a 90% interval and narrower than a 95% interval  and by increasing the number of observations by an appropriate amount we can obtain a narrower width of confidence level.

a. The correct answer is C. A 99% interval would be wider than a 90% interval and narrower than a 95% interval—the value of t* for a 99% interval is greater than that of a 90% interval but less than that of a 95% interval.

This is because as the confidence level increases, the interval width increases as well.

Since a 99% interval requires a larger t-value than a 90% interval, it will be wider.

However, since a 95% interval is wider than a 90% interval, but requires a smaller t-value than a 99% interval, the 99% interval will be narrower than the 95% interval but wider than the 90% interval.

b. The correct answer is: C. Increase the number of observations by an appropriate amount.

To obtain a narrower interval at a higher confidence level, firstly we need to increase the sample size.

This is because a larger sample size reduces the standard error of the mean, which leads to a narrower interval.

Therefore, increasing the number of observations by an appropriate amount is the best way to achieve this.

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The value of the midpoint between (1, 2) and (11,12) is,

⇒ (6, 7)\

We have to given that;

To find the midpoint between (1,2) and (11,12).

Since, A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Now, By definition of midpoint, we get;

The midpoint between (1,2) and (11,12) is,

⇒ (1 + 11)/2, (2 + 12) / 2

⇒ (12/2, 14/2)

⇒ (6, 7)

Thus, The value of the midpoint between (1, 2) and (11,12) is,

⇒ (6, 7)\

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Answer:

vertex (-3,-5) axis of symmetry x = -3

Step-by-step explanation:

Explanation

A function is a relation for which each value from the set the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair, let's check x=2

we have

2 is associated with two values from the set of second components(0 and 5), then

this is not a funcion of x

I hope this helps you

Option- d is correct that is [t > 1.4, RH₀] when there enough evidence in the data to draw the inference that, at the 0.01 level of significance.

Given that,

We have to find is there enough evidence in the data to draw the inference that, at the 0.01 level of significance, there are more errors in auditing approach A than in auditing technique B.

We know that,

The Alternative Hypothesis, Value of the Test Statistic.

D=Errors in A-Errors in B

H₀=β

β>0

Mean: H₀=average(d)

=4.444

Standard deviation H₁=stved(d)

=6.7474

n=9

Paried t-test:

​​​​​​​d>0

t=x-μ(d)/σ√n

t=1.9760

p-value:P(t>1.97)

=0.0421

P<α ---->Reject H₀

Therefore, Option- d is correct that is [t > 1.4, RH₀] when there enough evidence in the data to draw the inference that, at the 0.01 level of significance.

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Answer:

3√10

Step-by-step explanation:

√3 * √5 * √6

= √3 * √5 * √2 * √3                        (Split √6, as it will be easy)

= √9 * √5 * √2                                (Multiply √3 * √3 = √9 = 3)

= 3√10

Answer:

A

Step-by-step explanation:

5/44=0.11kg

Answer:

I think A

Step-by-step explanation:

I think A would be the answer.

Have a nice day !

Answer:

Step-by-step explanation:

You can write and equation for this problem.

as 20.27-2.01x= The left money for food.

x: is two.

SO applying the number to the equation:

20.27-4.02= Food money

$16.25 is the answer

Answer:

Step-by-step explanation:

-1/4(-8x+12y)

-1*(-8x+12y)/4

8x-12y/4

4(2x-3y)/4(4 and 4 gets cancel)

2x-3y

Answer : b: How many push-ups can a sixth grade girl do? and d:What are the weights of the sixth grade boys?

Answer:

How much do sixth grade boys weigh?

 How many push-ups can a sixth grade girl do?

Step-by-step explanation:

A statistical question is one that has a variable answer.

Determine which questions are statistical questions and can be answered with the data gathered in the fitness test.

The questions "How many sixth grade students are there?" and "What is the shortest height of the sixth grade students?" can be answered with the data gathered in the fitness test. However, they do not have variable answers, so they are not statistical questions.

The questions "What are the heights of the eighth grade girls?" and "How many chin-ups can a sixth grade boy do?" do have variable answers, so they are statistical questions. However, these questions cannot be answered with the data gathered in the fitness test.

The questions "How much do sixth grade boys weigh?" and "How many push-ups can a sixth grade girl do?" do have variable answers, so they are also statistical questions. These questions can be answered with the data gathered in the fitness test.

Hope I helped.

Answer:

They each got 10 each.

Step-by-step explanation:

2+1=3

30 divided by 3=10!

Given:

Required: To determine a more appropriate domain for Noah to use.

This is explained thus:

From the given graph, the domain of x is from 0 to 4 while the maximum height is at y = 15.

Since the volume of a box cannot be negative, the x-values to use must correspond to non-negative y-values.

Hence, the answer is:

The linear equation in slope intercept form  that models

the value "y" of the television in "x" years is y = 700 - 5.60x

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If  \(\theta\) is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m =  \(tan\theta\)

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

Here,

Original price of a 65 inches television today = $700

The TV's value is expected to decrease at a rate of $5.60 per

year

By the problem,

y = 700 - 5.60x

where y is the price of television after x years

This is the required equation of line in slope intercept form that models this situation.

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The pages read by Luis, Dayja and Michael read all together is 252.

What is Percentage?

A relative value indicating hundredth part of any quantity is called percentage.

Given that;

The conditions is,

Luis read 75% more pages than Dayja, and Dayja read 75% more pages than Michael.

Total pages read by Dayja = 84

Now,

Since,  Luis read 75% more pages than Dayja.

So, The pages for Luis = 75% of 84

                                   = 75/100 × 84

                                   = 6,300 / 100

                                   = 63

Thus, Pages for Luis = 84 + 63

                                 = 147

And, Number of pages read by Michael = 84 - 63

                                                              = 21

Thus,  Number of pages read by Michael = 21

So, Total number of pages read by Luis, Dayja and Michael all together is;

= 84 + 147 + 21

= 252

Therefore,

The pages read by Luis, Dayja and Michael read all together is 252.

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The transformations of the exponential function g(x) from the parent function f(x) are a vertical stretch by a factor of 4 and a vertical shift downward by 5 units.

The function g(x) = 4(f(x))^2 - 5 has the following transformations from the parent function f(x) = x^2:

Vertical stretch: The coefficient 4 in front of (f(x))^2 indicates a vertical stretch by a factor of 4 compared to the parent function.

Vertical shift: The constant term -5 at the end of the function indicates a vertical shift downward by 5 units compared to the parent function.

Therefore, the transformations of the exponential function g(x) from the parent function f(x) are a vertical stretch by a factor of 4 and a vertical shift downward by 5 units.

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Answer:

The answer is 8 The GCF of 24 and 32 is 8

Step-by-step explanation:

Hope this helps

Answer:

the answer is 8

Step-by-step explanation: