The mean speeds of fastball pitches from two different baseball pitchers are to be compared. A sample of 14 fastball pitches is measured from each pitcher. The populations have normal distributions. The table below shows the result. Scouters believe that Rodriguez pitches a speedier fastball.
Pitcher/Sample Mean Speed of Pitches (mph)/Population Standard Deviation
Wesley/86/3
Rodriguez/92/7
A) State the null and alternative hypotheses. (Let W represent Wesley and R represent Rodriguez.) (out of the following)
H0: μW ≥ μR
Ha: μW < μR
H0: μW = μR
Ha: μW ≠ μR
H0: μW ≤ μR
Ha: μW > μR
H0: μW < μR
Ha: μW ≥ μR
H0: μW > μR
Ha: μW ≤ μR
B) What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.)

5 packages of patties = 40

4 packages of buns =40

Answer:

4 packages of buns, and 5 packages of chicken patties.

Step-by-step explanation:

8 = 2 X 2 X 2

10 = 5 X 2

The Least Common Multiple of 8 and 10 = 2 X 2 X 2 X 5 = 40, now divide 40/10 = 4 and 40/8 =5 therfore you need to buy: 4 packages of buns, and 5 packages of chicken patties.

Darwin's geometric ratio of increase pertains specifically to the growth rate of populations in biological organisms. According to Darwin's theory of evolution, populations have the potential to increase exponentially over time if certain conditions are met. The geometric ratio of increase, often denoted as "r" or the intrinsic rate of natural increase, represents the factor by which a population multiplies during each reproductive cycle or generation.

In the context of natural selection, individuals with higher reproductive rates (higher r-values) have a greater chance of passing on their genetic traits to the next generation. Over time, this can lead to significant population growth and evolutionary changes within a species. However, the geometric ratio of increase is limited by various factors, such as availability of resources, competition, predation, and environmental constraints, which can result in a balance between population growth and environmental carrying capacity.

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The weights of the three girls are 55 kg, 60.5 kg, and 66 kg, respectively, and their weight ratio is 1: 1.1: 1.2.

Let the weight of the three girls be x, 1.1x, and 1.2x, respectively. Since the total weight of the three girls is 181.5 kilograms, we can write the equation:

x + 1.1x + 1.2x = 181.5

Simplifying the equation, we get:

3.3x = 181.5

x = 55

Therefore, the weight of the first girl is x = 55 kilograms, the weight of the second girl is 1.1x = 60.5 kilograms, and the weight of the third girl is 1.2x = 66 kilograms.

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The question is -

Three girls have a combined weight of 181.5 kilograms. If the weight of three girls is in the ratio of 1 : 1.1: 1.2, what is the weight of each girl?

The total weight is 18.5 kilograms

Answer:

312.5

Step-by-step explanation: 25 percent of 1250 is 312.5(calculated)

to check your answer we multiply 312.5 by 4 as its (25%=1/4)

Answer:

0.625

Step-by-step explanation:

Just take a calculator and devide it

Answer: What is the rest of the question

Step-by-step explanation:

In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.

The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.

We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.

Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.

Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000

We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)

Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0

Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.

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Answer:

n=4

Step-by-step explanation:

itis it is already multiplying by -5 we have to multiply it by a postive will remain a negative 20

Answer: n = 4

-5n = -20

n = 4

Answer:

y = -9

x = -8

Step-by-step explanation:

x = 28 + 4y

7y - 6(28 + 4y) = -15

7y - 168 - 24y = - 15 ---> *distribute the -6, not positive 6*

-17y = 153

y = -9

x = 28 + 4(-9)

x = -8

In the above condition of positive correlation, the higher a person scores on involvement, the higher they tend to score on life satisfaction. Therefore, the option B holds true.

Positive correlation can be referred to or considered as the correlation, wherein the relationship between two or more elements, that are taken into consideration, is direct. The direct relationship means that the movement of a change in one element leads to an equal movement in the other. Positive correlation also states about the measure of life satisfaction in the above condition.

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Complete question

A researcher finds a positive correlation between a measure of community involvement and a measure of life satisfaction. How should we interpret the relationship between these variables?

A) There is no relationship between involvement and life satisfaction.

B) The higher a person scores on involvement, the higher they tend to score on life satisfaction.

C) The higher a person scores on involvement, the lower they tend to score on life satisfaction.

D) Involvement and life satisfaction are probably the same variable

How do we help????????

The correct answer is D. Wording the question in this manner implies that being female by itself makes you less qualified than a male…it says “if she were qualified in every other way.”

Explanation:

One of the factors that can make a study flaw is bias, this means the study includes questions or content influenced by personal judgements or that tries to influence the answers of the respondents. This occurs in the question "‘Would you vote for a female candidate for President if she were qualified in every other way?” because the phrase "if she were qualified in every other way" indirectly tells respondents women are less qualify or might not be qualified to be in the role of a president, which shows a personal judgment. Also, this wording might influence respondents to answer they would not vote for a woman.

Answer:

acute angle measure less than 90 degrees, right angle measure 90 degrees, Obtuse angle measure more than 90 degrees, straight angle equal to 180 degrees, reflex angle is an angle greater than 180° and less than 360°, complementary angle either of two angles whose sum is 90°, supplementary angle either of two angles whose sum is 180°

There are a total of 2598960 ways to make a five-card hand with two pairings.

There are 52 cards in a typical card deck. There are 13 cards in each of the four suits (spades, clubs, hearts, and diamonds) (1 through 10; Jack, Queen, and King; let's call them Ordinals).

4 * 13 = 52

Let's now work through the number of 5 card hands that are 2 pairs.

We use combinations to solve the cases.

Each of the first two cards in the two pairs will be dealt. We require one of the 13 ordinals available, therefore we can say that as follows;

¹³C₂ = \(\frac{13!}{2!*(13-2)!}\)

       = 78

The following step is to choose two cards for each ordinal from each suit. One time only can be expressed as;

⁴C₂ = \(\frac{4!}{2!*(4-2)!}\)

      = 6

We need to do it twice for the other suit.

⁴C₂ = \(\frac{4!}{2!*(4-2)!}\)

      = 6

The fifth card in a five-card hand must also be taken into consideration. There are 11 ordinals available, but we only need 1;

¹¹C₁ = 11

and from that one ordinal, we need 1 suit,

⁴C₁ = 4

We multiply them all together to obtain the quantity of 2-pair hands:

⇒ 78 * 6 * 6 * 11 * 4 = 2598960

Hence, a total of 2598960 ways is to form a 5 - card hand with two pairs.

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Answer:

7.2 × 10^-6

Step-by-step explanation:

7.2 are the two last digits of the notation

and the reason its to the power of -6 is because there are 6 digits until you reach 7

The value is 24 square units is parallel to the face of the right rectangular prism.

We can see that the face of the given rectangular prism shows a width 4 and a height of 6. If we cut the figure at any point along the length 20, such that the cross-section is parallel to the face, the cross-section, which occurs at x length, will always have the same dimensions, which are 4 and 6.

So the area of the cross-section which is parallel to the face of the given rectangular prism is given by:

A = 6 × 4

A = 24

Thus, the value is 24 square units is parallel to the face of the right rectangular prism.

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A = 6 × 4

A = 24

Thus, the value is 24 square units is parallel to the face of the right rectangular prism.

Answer:

725

Step-by-step explanation:

Answer:

5x - 8y =17

y+5 =3x

Answer | (3,4)

Step-by-step explanation:

I used a calculator

To find det(A-¹ + 4 adj A), where A is a 3x3 matrix and det A = 2, we need to compute the determinant of the given expression. The answer can be found by substituting the values of A and evaluating the determinant.

Given that A is a 3x3 matrix and det A = 2, we can use the properties of determinants to find det(A-¹ + 4 adj A).

First, let's find the inverse of matrix A, denoted as A-¹. Since A is a 3x3 matrix, A-¹ exists if and only if det A ≠ 0. In this case, det A = 2, so A-¹ exists.

Next, let's find the adjugate of matrix A, denoted as adj A. The adjugate of A is obtained by taking the transpose of the cofactor matrix of A.

Now, we can substitute the values of A-¹ and adj A into the expression A-¹ + 4 adj A and calculate the determinant of the resulting matrix.

The determinant of the given expression det(A-¹ + 4 adj A) evaluates to 364.

Therefore, the correct answer is (a) 364.

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If working adults aged 22-25 spend an average of $14.27 a day on food with a standard deviation of $2.25, then Jeremy would spend approximately $23.27 per day if his expenditure is 4 standard deviations above the average.

To calculate how much Jeremy spends per day, we need to find a value that is 4 standard deviations above the average.

Mean (average) = $14.27

Standard deviation = $2.25

To find the amount Jeremy spends per day, we multiply the standard deviation by 4 and add it to the mean:

Jeremy's daily spending = Mean + (4 * Standard deviation)

Jeremy's daily spending = $14.27 + (4 * $2.25)

Jeremy's daily spending = $14.27 + $9.00

Jeremy's daily spending = $23.27

Therefore, Jeremy spends approximately $23.27 per day, rounded to 2 decimal places.

The concept used to solve the problem is based on the standard deviation and the number of standard deviations above the mean.

In statistics, the standard deviation measures the amount of variation or dispersion in a dataset. It tells us how spread out the data points are from the mean.

To find Jeremy's daily spending, we are given the average daily spending ($14.27) and the standard deviation ($2.25). Since Jeremy's spending is described as 4 standard deviations above the average, we need to multiply the standard deviation by 4 to get the amount.

By multiplying the standard deviation ($2.25) by 4, we obtain the additional amount Jeremy spends above the average. Adding this to the mean ($14.27) gives us Jeremy's daily spending of $23.27.

This approach allows us to calculate the value of Jeremy's spending based on the average, standard deviation, and the given number of standard deviations above the mean.

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Answer:

(0,-2.5)

Step-by-step explanation:

oof

So the maximum number of edges in an undirected graph with 100 vertices is 4950.

In an undirected graph, each edge connects two vertices, and as such, it is counted twice, once for each vertex it connects. Therefore, the total number of edges in the graph is the sum of the degrees of all vertices, divided by 2.

In a complete graph with n vertices, every vertex is connected to every other vertex, except itself, and so the degree of each vertex is n-1 (it is connected to n-1 other vertices). Therefore, the total number of edges in the graph is:

n * (n-1) / 2

Substituting n = 100, we get:

100 * 99 / 2 = 4950

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It is already in the simplest form.

Amount of money in the account after 19 years when no deposits or withdrawals are done for the invested amount $3,500 with 3.5% interest rate compounded quarterly is equal to $6,800(nearest hundred dollars).

As given in the question,

Amount  invested by Nathan is principal 'P' = $3,500

Interest rate 'r' = 3.5% compounded quarterly

Number of compounding periods per year for given quarterly 'n'  = 4

Time period 't'= 19 years

Amount of money in the account after 19 years when no deposits or withdrawals are done.

Let 'A' be the amount.

Formula used:

 \(A = P \times ( 1+ \frac{r}{n} )^{nt}\)

Substitute the value in the formula we get,

A = 3500 × [ 1 + (0.035/4) ]⁽⁴⁾⁽¹⁹⁾

   =  3500 × [ 1 + 0.00875]⁽⁴⁾⁽¹⁹⁾

   =  3500 × [ 1.00875]⁷⁶

   = 6,786.06 (approximately)

   = $6800 (nearest hundred dollars)

Therefore, amount of money in the account after 19 years when no deposits or withdrawals are done for the invested amount $3,500 with 3.5% interest rate compounded quarterly is equal to $6,800(nearest hundred dollars).

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- The volume of each box increases as the size of the base edges increases.

a. The scale factor between the pyramids is 3/2.

b. The ratio of their surface areas is 3/2.

c. The ratio of their volumes is 27/8.

- The estimated volume of the larger hamster ball is approximately 905 in³.

- The classmate's error is assuming similarity based solely on the ratio of side lengths without considering the proportionality of all corresponding dimensions.

- The volume of the smaller cylinder is 486 m².

a. The ratio of their heights is approximately 3.17.

b. The ratio of the area of their bases is approximately 7.07.

We have,

Nesting Gift Boxes:

The volume of each box can be determined by multiplying the area of the hexagonal base by the height of the box.

Since the height is not specified, we can assume that all three boxes have the same height.

Comparing the volume of each box:

The volume of the large box is larger than the medium box, and the volume of the medium box is larger than the small box.

The ratio of the volumes will be proportional to the cube of the ratio of the corresponding side lengths.

Similar Pyramids:

a. The scale factor between two similar pyramids can be found by comparing their corresponding heights.

In this case, the scale factor is 9/6 = 3/2.

b. The ratio of their surface areas can be found by comparing the square of their corresponding side lengths.

Since the surface area is proportional to the square of the side length, the ratio will be (9/6)^2 = 3/2.

c. The ratio of their volumes can be found by comparing the cube of their corresponding side lengths.

Since the volume is proportional to the cube of the side length, the ratio will be (9/6)³ = 27/8.

Larger Hamster Ball:

The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius.

To estimate the volume of the larger hamster ball, we can use the ratio of the cube of their diameters since the volume is proportional to the cube of the diameter.

The ratio of their volumes will be (14/8)³ = 3.375.

Multiplying this ratio by the volume of the smaller ball (268 in³), we estimate that the volume of the larger hamster ball is approximately 268 in³ x 3.375 ≈ 905 in³.

Error Analysis:

The classmate's error is assuming a similarity between the two rectangular prisms based solely on the ratio of their side lengths. Similarity requires that all corresponding angles are equal, not just the side lengths.

In this case, the two prisms have different proportions in terms of their width and height, and therefore they are not similar.

Similar Cylinders:

The lateral area of a cylinder is proportional to its height.

Comparing the lateral areas of the two similar cylinders (64 m² and 144 m²), the ratio of their heights will be √(144/64) = 3/2.

Since the ratio of the heights is 3/2, the ratio of their volumes will also be (3/2)^2 = 9/4.

Given that the volume of the larger cylinder is 216 m², the volume of the smaller cylinder will be (9/4) x 216 m² = 486 m².

Similar Prisms:

a. The ratio of the heights of two similar prisms can be found by taking the cube root of the ratio of their volumes.

In this case, the ratio of their volumes is 5000 ft³ / 135 ft³ = 37.04.

Taking the cube root of 37.04, we find that the ratio of their heights is approximately 3.17.

b. The ratio of the area of their bases will be the square of the ratio of their side lengths.

Since the area of the base is proportional to the square of the side length, the ratio will be \((5000 ft^3 / 135 ft^3)^{2/3}\)= 7.07.

Thus,

- The volume of each box increases as the size of the base edges increases.

a. The scale factor between the pyramids is 3/2.

b. The ratio of their surface areas is 3/2.

c. The ratio of their volumes is 27/8.

- The estimated volume of the larger hamster ball is approximately 905 in³.

- The classmate's error is assuming similarity based solely on the ratio of side lengths without considering the proportionality of all corresponding dimensions.

- The volume of the smaller cylinder is 486 m².

a. The ratio of their heights is approximately 3.17.

b. The ratio of the area of their bases is approximately 7.07.

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The correct option regarding who should the restaurant give samples to generate a representative sample is given as follows:

All diners diners who are willing to pay for the samples.

Sampling is a technique for when a group of elements from a population is taken to represent the entire population.

This group of elements has to be representative of the entire population, as to lead to correct conclusions.

In this problem, all the dinners who are willing to pay for the samples should be sampled, as if they are willing to pay, it means that they are interested in the new dish, hence their opinions should be considered as it would improve the restaurant's revenue with the new dish.

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The correct factor is (2x - 3) and (2x + 3).

It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.

Given

4x² -9 = 0 is a quadratic equation.

The factor of the given equation.

4x² -9 = 0 is a quadratic equation.

According to factorization,

                 4x² - 9 = 0

             (2x)² - 3² = 0

( 2x - 3 ) ( 2x + 3 ) = 0

Thus the correct factor is (2x - 3) and (2x + 3).

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Answer:

The answer is C or the third option.

Step-by-step explanation:

Looking at the tiles for the third option, there are the same amount of negative and positive x-tiles. This means that they cancel each other out. What's left are the 4 x^2 tiles and 9 negative tiles. When put together the equation is 4x^2 - 9. This option represents the factors of 4x^2 - 9 accurately.

∫∫∫e f(x, y, z) dV can be expressed as ∫∫∫e f(x, y, z) dz dy dx for the given solid e bounded by y = 4 - \(x^{2}\) \(z^{2}\) and y = 0.

To express the integral as an iterated integral, we consider the order of integration. In this case, we start with the innermost integral, which integrates with respect to z. The limits of integration for z are determined by the bounds of the solid e, which are given by the surfaces y = 0 and y = 4 - \(x^{2}\) \(z^{2}\)

Next, we move to the middle integral, integrating with respect to y. The limits of integration for y are determined by the intersection points of the surfaces y = 0 and y = 4 - \(x^{2}\) \(z^{2}\). In this case, y ranges from 0 to the value of y determined by the equation 4 - \(x^{2}\) \(z^{2}\) = 0.

Finally, we integrate with respect to x, where the limits of integration for x are determined by the bounds of the solid e. These bounds can be determined by finding the values of x that satisfy the equation 4 - \(x^{2}\) \(z^{2}\) = 0.

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The mean absolute percent error (MAPE) is 25%.

The mean absolute percent error (MAPE) is a measure of forecasting accuracy that quantifies the average deviation between predicted and actual values as a percentage of the actual values. In this case, the mean absolute deviation (MAD) is given as 25 units for the past 10 periods, and the total demand is 1,000 units.

To calculate the MAPE, we need to divide the MAD by the total demand and multiply by 100 to express it as a percentage. In this scenario, the MAPE is calculated as follows:

MAPE = (MAD / Total Demand) * 100

     = (25 / 1,000) * 100

     = 2.5%

Therefore, the MAPE is 2.5%, which means that, on average, the forecasts have a 2.5% deviation from the actual demand.

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