100 points PLEASEEEEEEE HEEELLLLPPPPPPP

Step-by-step explanation:

The triangles are similar. Writing a proportion:

(3x − 5 + 10) / 28 = (3x − 5) / 20

Cross multiply:

20 (3x − 5 + 10) = 28 (3x − 5)

Simplify and solve:

20 (3x + 5) = 28 (3x − 5)

5 (3x + 5) = 7 (3x − 5)

15x + 25 = 21x − 35

60 = 6x

x = 10

If Harper divides 12 baby carrots evenly among her 3 pet hamsters, Harvey, Hammy, and Flo, then each hamster would get 4 baby carrots. However, since Flo ate 2 baby carrots right away, she would only have 2 baby carrots left.


When Harper divides a package of 12 baby carrots among her 3 pet hamsters, each hamster gets 4 baby carrots. But since Flo eats 2 baby carrots right away, she is left with only 2 baby carrots. This means that Harvey and Hammy also have 4 baby carrots each, as they did not eat any carrots. It's important to divide food equally among pets, as it ensures that every pet gets an equal share of nutrients.


In conclusion, Harper divided 12 baby carrots among her 3 pet hamsters equally, but Flo ate 2 baby carrots right away. Therefore, Flo was left with only 2 baby carrots, while Harvey and Hammy had 4 baby carrots each. Dividing food equally among pets is important to ensure that every pet gets a fair share of nutrients.

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There are 6,227,020,800 ways in which Aaron can arrange the 13 songs on the playlist.

To determine the number of ways Aaron can arrange the 13 songs on the playlist, we can use the concept of permutations. Since the order of the songs matters (i.e., each arrangement is different), we can use the formula for permutations.

The number of ways to arrange n items in a specific order is given by n factorial, denoted as n!. The factorial of a number n is the product of all positive integers less than or equal to n.

In this case, Aaron has 13 songs to arrange on the playlist, so the number of arrangements can be calculated as:

13! = 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

Calculating this expression, we find:

13! = 6,227,020,800

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False. The symbol x¯ represents the population mean of all possible sample means of size n.

The symbol x¯ (x-bar) represents the sample mean, not the population mean of all possible sample means of size n. The population mean of all possible sample means of size n is denoted by μ (mu). The sample mean, x¯, is calculated by taking the average of the observations in a specific sample.

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Answer: 54, 63, 72

Step-by-step explanation: Well let's multiply 9 till 75 so 9(1), 18(2), 27(3), 36(4), 45(5), 54(6), 63(7), 72(8). The underlined numbers are ones that are divisible by 3. Hope this helps! :)

Answer: C

Step-by-step explanation:

You are trying to find the number of muffins Nola started the day with.

When she baked 21 muffins she gained 21 muffins (addition)

When she gave away 30 muffins she lost 30 muffins (subtraction)

The third equation has her gaining 21 muffins and losing 30 muffins for a final amount of 44 so it must be C

The probability of selecting a P on the first draw and a V on the second draw is 2/4950

From the question, we are to determine the probability of selecting a P on the first draw and a V on the second draw.

From the formula for probability, we have that

P(A) = Number of favorable outcomes to A / Total number of possible outcomes

From the given tiles,

Number of favorable outcomes to P = 2

Total number of possible outcomes = 100

Thus,

Probability of selecting a P on the first draw = 2/100

On the second draw

Number of favorable outcomes to V = 2

Total number of possible outcomes = 99

Thus,

Probability of selecting a V on the second draw = 2/99

Now,

The probability of selecting a P on the first draw and a V on the second draw is

P(1st P and 2nd V) = 2/100 × 2/99

P(1st P and 2nd V) = 1/50 × 2/99

P(1st P and 2nd V) = 2/4950

Hence, the probability is 2/4950

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The statistic that indicates how much scores differ from each other is Standard deviation.

Standard deviation is the measure of dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

To calculate the standard deviation, you must first calculate the mean of the data set. This is done by adding up all the values in the data set and dividing by the number of values. Once you have the mean, you must subtract it from each value in the data set and square the result.

Then, you must add up all of the squared values, divide by the total number of values, and take the square root of that number. The result is the standard deviation.

Standard deviation is important because it can be used to compare the data to its mean and can help determine the amount of risk associated with a particular data set. Standard deviation is a measure of how spread out a data set is from its mean or average. It is used to measure the amount of variability or dispersion for a given data set.

Thus, The statistic that indicates how much scores differ from each other is Standard deviation.

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Answer: C

Step-by-step explanation:

The standard deviation measures the amount of variation or dispersion of a set of scores from the mean. Therefore, the correct answer is C.

By finding the inverses we can see that:

Two functions g(x) and g⁻¹(x) are inverses if:

g⁻¹(g(x)) = x

Here we know that the function g is defined by:

g={(-8, -3), (-3, 2), (3, 0), (5, 6)}

And we want to find:

g⁻¹(-3)

On the table we can see that g(-8) = -3, then:

g⁻¹(-3) = -8

And we have:

h(x) = -2x + 13

Evaluating on the inverse we should get:

h(h⁻¹(x)) = x

            = -2*h⁻¹(x)   + 13 = x

Solving for the inverse:

h⁻¹(x) = (x - 13)/-2

Now we can get the product:

(h⁻¹*h)(3) = (-2*3 + 13)(3 - 13)/-2

              = 7*5 = 35

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Answer:

This graph is a negative linear association. C is the correct answer.

The function g(f(x)) is √(3x + 1).

We have,

This is a composite function.

To find g(f(x)), we need to substitute the function for f(x) into g(x) wherever we see x:

g(f(x)) = g(3x + 2)

Then, we substitute the function for g(x).

g(f(x)) = √(3x + 2 - 1)

Simplifying the expression inside the square root.

g(f(x)) = √(3x + 1)

Therefore,

g(f(x)) = √(3x + 1).

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Answer:

he correct answer is c. vD = -7 vs = 5.

The Doppler shift equation is:

f = f' (v - vD) / (v - vS)

Where:

f is the frequency detected

f' is the frequency emitted

v is the speed of sound

vD is the velocity of the detector

vs is the velocity of the source

In this case, the source is traveling at 5 m/s away from the detector, the detector is traveling at 7 m/s toward the source, and there is a 3 m/s wind blowing from the source toward the detector.

The velocity of the detector is negative because it is moving towards the source. The velocity of the source is positive because it is moving away from the detector.

Therefore, the values that should be substituted into the Doppler shift equation are:

vD = -7

vs = 5

Step-by-step explanation:

Answer:a

Step-by-step explanation:s

The center is (1,0), thus the center lies on the x-axis, the radius is 3 units and the radius of the circle is the same with x² + y² = 9.

The radius is half the diameter of a circle and the center of the circle is a point from which all distance to the edge of the circle is equal.

The equation that represents the center of the circle equation is (x - h)² + (y - k)² = r², where h,k represents the center and r is the radius.

Our circle in this form is: (x − 1)² +(y − 0)² = 3. Thus, h = 1, k = 0, r = 3. The standard form is y² + (x − 1)² = 9.

We can conclude that the center is (1,0), thus the center lies on the x-axis, the radius is 3 units and the radius of the circle is the same with x² + y² = 9.

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The length of Alice’s step is 0.6 m.

The length of Basil’s step is 0.8 m.

Since Basil takes 100 fewer steps than Alice to walk 240 m;

the number of steps Basil takes = (240/A) - 100.

Basil's step is 20 cm longer than Alice's step;

B = A + 0.2

The distance each person walks is calculated as;

A(240/A) = (A + 0.2) [(240/A) - 100]

240 = 240 - 100A + 48/A - 20

0 =  - 100A + 48/A - 20

100A - 48/A = -20

100A² - 48 = -20A

100A² + 20A - 48 = 0

Solve for A using formula method;

A = 0.6 m

Basil's step length:

B = 0.6 + 0.2

B = 0.8 m

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The dimensions of the deck are 26 meters by 16 meters and 84 meters of fencing will need to be purchased for the deck and pool area.

Let's denote the width of the deck as 'x'.

The length of the pool is 20 meters, and the width is 10 meters.

The combined area of the pool and the deck is 264 square meters.

The area of the pool is length times width: 20 × 10 = 200 square meters.

The area of the deck is (20 + 2x)(10 + 2x) - 200 square meters. We subtract 200 square meters to account for the area of the pool.

Therefore, the polynomial equation representing the given information is:

(20 + 2x)(10 + 2x) - 200 = 264

(200 + 40x + 20x + 4x^2) - 200 = 264

4x²+ 60x = 264

4x² + 60x - 264 = 0

Factoring out a common factor of 4:

4(x² + 15x - 66) = 0

Factoring the quadratic equation:

(x + 18)(x - 3) = 0

The width of the deck is x = 3 meters.

The dimensions of the deck can be found by adding twice the width to the length and width of the pool:

Length of the deck = 20 + 2x = 20 + 2(3) = 26 meters

Width of the deck = 10 + 2x = 10 + 2(3) = 16 meters

Therefore, the dimensions of the deck are 26 meters by 16 meters.

To calculate the length of fencing required, we need to consider the perimeter of the deck.

Perimeter of the deck = 2×(Length of the deck + Width of the deck)

Perimeter of the deck = 2 × (26 + 16)

Perimeter of the deck = 2 × 42

Perimeter of the deck = 84 meters

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Approximately 13 percent  of the student body in the 9th grade don't play a sport.

To find the percentage of the student body in the 9th grade who don't play a sport, we need to calculate the number of 9th-grade students who don't play a sport and divide it by the total number of students, then multiply by 100 to get the percentage.

From the table, we can see that the number of 9th-grade students who don't play a sport is 32. The total number of students is 240.

Percentage = (Number of 9th-grade students who don't play a sport / Total number of students) * 100

= (32 / 240) * 100

= 0.133333 * 100

≈ 13.33

Rounded to the nearest whole number, the percentage is 13.

Therefore, approximately 13% of the student body in the 9th grade don't play a sport.

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The coordinates of point P that represents the weighted average of the set of points are (-8/5, y).

Given that point A weighs 3 times as much as point C. This implies that the weight of point C is 1, and the weight of point A is 3.

To find the weighted average of the points, we can use the formula:

[tex]P = \dfrac{(w_1 \times A + w_2 \times B + w_3 \times C)}{(w_1 + w_2 + w_3)}[/tex]

where P is the weighted average point, w₁, w₂, and w₃ are the weights of points A, B, and C, respectively, and A, B, and C are the coordinates of the points.

Substituting the given values, we have:

P = (3 × (-5) + 0 + 1 × 7) / (3 + 1 + 1)

P = (-15 + 7) / 5

P = -8/5

Therefore, the coordinates of point P that represents the weighted average of the set of points are (-8/5, y).

The y-coordinate cannot be determined without additional information.

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Answer:

THE CORRECT ANSWER IS C. "The description does not show a linear relationship or a proportional relationship."

Step-by-step explanation:

Answer:5$

Step-by-step explanation:

Both of Nick's bags weigh 41 kilograms combined.

In mathematical terms, if we let W1 be the weight of the first bag and W2 be the weight of the second bag, then the total weight of both bags can be expressed as W1 + W2.

Substituting the given values, we get:

Total weight of both bags = 24 + 17 = 41 kilograms.

This is a simple addition problem that involves adding the weights of two bags to find the total weight.

The complete question is:

Nick is going on vacation. one of his bags weighs 24 kilograms. the other bag weighs 17 kilograms. how much do both of nick's bags weigh combined?

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The function that represents the situation is,

y = 1049(1.080)ˣ.

To determine the equation which closely models the data, we need to first plot the data points on a graph and analyze the trend.

Year Population

1 1049

2 1137

3 1229

4 1326

5 1434

6 1542

7 1662

We can see that the population is increasing each year, so we can assume that it follows an exponential growth pattern.

To find the equation that models the data, we can use the exponential growth formula:

y = abˣ

where y is the population, x is the year, a is the initial population, and b is the growth factor.

Using the data for year 1 and year 7, we can find the values of a and b:

a = 1049

y = abˣ

1662 = 1049b⁷

b = (1662/1049)¹/⁷ = 1.080

Now we can substitute the values of a and b into the formula:

y = 1049(1.080)ˣ.

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The 90% confidence interval suggests that we are 90% confident the proportion of disapproving small-business owners is between 69.2% and 74.8%.

To compute the 90% confidence interval for the population proportion of small-business owners who do not approve of the changes, we can use the sample proportion and the properties of confidence intervals.

Given that the sample size is 570 and the sample proportion is 72%, we can calculate the standard error using the formula:

Standard Error = [tex]sqrt((p * (1 - p)) / n)[/tex]

where p is the sample proportion and n is the sample size.

Substituting the values, we get:

Standard Error = [tex]sqrt((0.72 * (1 - 0.72)) / 570)[/tex] ≈ 0.017

Next, we can calculate the margin of error by multiplying the standard error by the appropriate z-score for a 90% confidence level. For a 90% confidence level, the z-score is approximately 1.645.

Margin of Error = z * Standard Error = 1.645 * 0.017 ≈ 0.028

Finally, we can construct the confidence interval by subtracting and adding the margin of error from the sample proportion:

Confidence Interval = Sample Proportion ± Margin of Error

Confidence Interval = 0.72 ± 0.028

Therefore, the 90% confidence interval for the population proportion of small-business owners who do not approve of the changes is approximately 0.692 to 0.748 (rounded to 3 decimal places). This means we can be 90% confident that the true proportion of small-business owners who do not approve of the changes lies between 69.2% and 74.8%.

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The pollster should survey approximately 2,401 U.S. voters to estimate the true proportion of voters who oppose capital punishment with 95% confidence and a margin of error of 2%.

In order to estimate the true proportion of U.S. voters who oppose capital punishment with a 95% confidence level and a margin of error of 2%, the pollster should survey approximately 2,401 voters.



To calculate the sample size needed for this estimation, we can use the formula:

n = (Z² * p * q) / E²

where n is the sample size, Z is the z-score corresponding to the confidence level (in this case, 1.96 for 95% confidence), p is the estimated proportion of voters who oppose capital punishment, q is the estimated proportion of voters who support capital punishment (which is 1-p), and E is the desired margin of error (in this case, 0.02).

Assuming a conservative estimate of p = q = 0.5, we can plug in the values and solve for n:

n = (1.96² * 0.5 * 0.5) / 0.02² ≈ 2,401

Therefore, the pollster should survey approximately 2,401 U.S. voters to estimate the true proportion of voters who oppose capital punishment with 95% confidence and a margin of error of 2%.



In conclusion, to estimate the true proportion of U.S. voters who oppose capital punishment with a 95% confidence level and a margin of error of 2%, the pollster should survey approximately 2,401 voters. This sample size calculation is based on the formula for calculating sample size using the z-score, estimated proportions, and desired margin of error

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[tex](\stackrel{\stackrel{ adjacent }{x}}{-3}~~,~~\stackrel{\stackrel{ opposite }{y}}{-\sqrt{7}})\hspace{5em}\textit{let's find the \underline{hypotenuse}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{-3}\\ o=\stackrel{opposite}{-\sqrt{7}} \end{cases}[/tex]

[tex]c=\sqrt{ (-3)^2 + (-\sqrt{7})^2}\implies c=\sqrt{ 9 + 7 } \implies c=\sqrt{ 16 }\implies c=4 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cos(\theta )=\cfrac{\stackrel{adjacent}{-3}}{\underset{hypotenuse}{4}}~\hfill[/tex]

No, the variances are not similar enough to use the pooled t test. The ratio of the two variances (25/8) is greater than 3, which is the typical cutoff for determining similarity of variances. Therefore, an alternative method such as the Welch's t-test or a non-parametric test should be used to compare the means.

To determine if the variances are similar enough to use a pooled t-test, you can perform an F-test for equality of variances. Follow these steps:

1. Calculate the F statistic by dividing the larger variance by the smaller variance: F = var2 / var1 = 25 / 8 = 3.125.

2. Determine the degrees of freedom for each group: df1 = 10 - 1 = 9 and df2 = 10 - 1 = 9.

3. Check the F critical value for the given degrees of freedom and chosen significance level (e.g., 0.05) using an F-distribution table or a calculator. For df1 = 9 and df2 = 9 at a 0.05 significance level, the F critical value is approximately 3.18.

4. Compare the calculated F statistic to the F critical value: 3.125 < 3.18.

Since the F statistic is less than the F critical value, we fail to reject the null hypothesis that the variances are equal. Therefore, the variances are similar enough to use the pooled t-test to evaluate differences in the means. The answer is yes.

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Answer:

1a. Let’s assume that the length of the north side of the house is represented by ‘x’. Then the polynomial that represents the length of the north side of the house is x.

1b. There is no expression to simplify.

2a. Your cousin is not correct.

2b. The length of the north side of the house is represented by ‘x’ and not by ‘9y+2y’. Therefore, your cousin is not correct.

The polynomial stated by the cousin as the length of the north side of the house, 9y + 2y, simplifies to 11y. Thus, the cousin is not correct. Polynomials and simplifying expressions are part of basic algebra skills.

Based on your cousin's statement, the polynomial representing the length of the north side of the house is 9y + 2y. To determine the correctness of this polynomial, we must first simplify the expression. By combining like terms (terms with the same variable and exponent), the expression simplifies to 11y. So, the length of the north side is represented by 11y, not 9y + 2y. Hence, your cousin's statement is not correct.

Understanding how to combine like terms, simplify expressions, and handle polynomials is an important part of basic algebra skills. Polynomials can be used to represent many real world quantities such as the length of a side of a house as in this problem. Remember that it is crucial to perform all calculations accurately to avoid errors.

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Answer:

x = 5  or x = -3

Step-by-step explanation:

2(x-1)^2 +7= 39

Subtract 7 from each side.

2(x-1)^2 +7-7= 39 -7

2(x-1)^2 = 32

Divide each side by 2.

2/2(x-1)^2 = 32/2

(x-1)^2 = 16

Take the square root of each side.

sqrt((x-1)^2)= sqrt(16)

x-1 = ±4

Add 1 to each side.

x =   ±4 +1

x = 5  or x = -3

Answer:

x = 5 or x = -3

Step-by-step explanation:

We know that,

( a + b )² = a² + 2ab + b²

( a - b )² = a² - 2ab + b²

Accordingly, let us solve this.

2 ( x - 1 )² + 7 = 39

First, solve the brackets.

2 ( x² - 2x + 1 ) + 7 = 39

2x² - 4x + 2 + 7 = 39

Subtract 39 from both sides.

2x² - 4x - 30 = 0

Divide the whole equation by 2.

x² - 2x - 15 = 0

Solve the quadratic equation.

x² + 3x - 5x - 15 = 0

x ( x + 3 ) - 5 ( x + 3 ) = 0

( x - 5 ) ( x + 3 ) = 0

∴ x - 5 = 0                      x + 3 = 0

   x = 5          or              x = -3