Baseball Players’ Salaries. We have access to data regarding the salaries of all professional baseball players in 2012. That is, if we consider all professional baseball players in 2012 our subjects of interest, then we have information on every individual in the population. In this problem, we are going to examine how varying the sample size impacts the sampling distribution of the sample mean. We will be using an applet called StatKey to complete this problem. Start by opening a web browser on your computer and going to the following website: http://lock5stat.com/statkey/sampling_1_quant/sampling_1_quant.html
(a) In the top left corner of the page, under StatKey, click on the button with the words Percent with Internet Access (Countries) and select Baseball Players (2012 Salary in Millions). The top graph on the right hand side displays the distribution of the population as well as some numerical summaries describing the population. Use this graph and the numerical summaries to answer the following questions.
i. Report the mean (in millions of dollars) for all 855 salaries of 2012 professional baseball players to 3 decimal places.
ii. Report the standard deviation (in millions of dollars) for all 855 salaries of 2012 professional baseball players to 3 decimal places.
iii. The values in parts (a) and (b) above are (Choose all that apply): • Parameters • Statistics • Estimates • Numerical summaries of the sample • Numerical summaries of the population
iv. (Free Response) Describe the shape of the distribution of salaries for professional baseball players in 2012. Be sure to comment on skewness, modality, and outliers.
(b) Suppose we are interested in the distribution of the sample mean for samples of size n = 10 from the population of professional baseball players’ salaries from 2012. Specify the sampling distribution of the sample mean when n = 10.
i. What is the mean of the sampling distribution of the sample mean (in millions of dollars) when n = 10? (Report to the nearest 3 decimal places.)
ii. What is the standard error of the sampling distribution of the sample mean (in millions of dollars) when n = 10? (Report to the nearest 3 decimal places.) iii. What is the shape of the sampling distribution of the sample mean when n = 10? (Choose one) • Normal • Approximately Normal • Not Normal
(c) Let’s select a random sample of size n = 10. Note that at the top of the webpage where it says, Choose samples of size n= that 10 is the default, so you do not need change the sample size. Click on Generate 1 Sample in the top left corner of the webpage. Note that the bottom graph on the right hand side of the page shows a histogram of the 10 observations selected for your sample. In addition, above the bottom graph are the mean and the standard deviation of the observations in your sample. What is the value of the 3 sample mean (in millions of dollars) from your random sample of size n = 10? (Report to the nearest 3 decimal places.)
(d) Click Generate 1 Sample a second time. What is the value of the sample mean (in millions of dollars) from your second random sample of size n = 10? (Report to the nearest 3 decimal places.)
(e) Click Generate 1 Sample a third time. What is the value of the sample mean (in millions of dollars) from your third random sample of size n = 10? (Report to the nearest 3 decimal places.)
(f) In the big graph, you should notice that 3 points have been added. These 3 points correspond to the sample means from the 3 samples you drew. In the top right hand corner of the big graph, it should say samples =3 and show a value for the mean and standard deviation. The value for the mean is the average of the three sample means from your 3 samples of size n = 10. Similarly, the value for the standard deviation is the standard deviation of the three sample means from your 3 samples of size n = 10.
i. What is the mean of your three sample means? (Report to the nearest 3 decimal places.)
ii. What is the standard deviation (i.e. standard error) of your three sample means? (Report to the nearest 3 decimal places.)
(g) Suppose we drew many samples of size n = 10 and calculated the sample mean for each of these samples.
i. What value would you expect to see for the mean of the sample means (in millions of dollars) of size n = 10? (Report to the nearest 3 decimal places.)
ii. What value would you expect to see for the standard error of the sample means (in millions of dollars) of size n = 10? (Report to the nearest 3 decimal places.)

Answer:

Brent paid $306 for the system.

Step-by-step explanation:

To figure out what he paid for his system, you will use multiplication to figure out how much the discount took off.

First, you would multiply the original cost to the discount they gave him, which is 15%.

360 * .15 = 54

The discount would take $54 off his purchase.

Next, you would use subtraction to find out what he paid in total.

360 - 54 = 306

Brent paid $306 in total after the discounts.

Answer:

99992

Step-by-step explanation:

Ming can carry a maximum of 1676 wood boards in the car. Ming rental car for her bike to carry tools and Wood to school for a science project her toolbox weighs 20 pounds in the car can make carry messing with 5050 pounds each wood board weighs 3 pounds.

Ming rents a cart for her bike to carry tools and wood to school for her science project. Her toolbox weighs 20 pounds and the cart can carry a maximum of 50 pounds. Each wood board weighs 3 pounds. Let w represent the number of wood boards she can carry.

Let x be the number of wood boards Ming can carry.

Then, the weight of the wood boards is 3x pounds.

Adding the weight of the toolbox, the total weight is 20 + 3x pounds.

The car can carry a maximum of 5050 pounds, so we can set up an inequality:

20 + 3x ≤ 5050

Subtracting 20 from both sides:

3x ≤ 5030

Dividing both sides by 3:

x ≤ 1676.67

Since x represents the number of wood boards, it must be a whole number. Therefore, Ming can carry a maximum of 1676 wood boards in the car.

Ming rents a cart for her bike to carry tools and wood to school for her science project. Her toolbox weighs 20 pounds and the cart can carry a maximum of 50 pounds. Each wood board weighs 3 pounds. Let w represent the number of wood boards she can carry.

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36-8z = 4(9-2z) this is the factored form of 36-8z.

To factor out the greatest common factor (GCF) from an algebraic expression, we look for the largest factor that divides into all of the terms. In this case, the terms 36 and 8z have a common factor of 4, which is the GCF.

To factor out the GCF, we divide each term by 4, which gives us:

36/4 = 9

8z/4 = 2z

Therefore, we can rewrite 36-8z as:

36-8z = 4(9-2z)

This is the factored form of 36-8z after factoring out the greatest common factor. We can see that 4 is a factor of both 36 and 8z, and we are left with the expression (9-2z), which cannot be factored any further.

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Answer:

x = 1.5

Step-by-step explanation:

using the property of logarithms

• [tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]

then

[tex]log_{2}[/tex] (2x + 5) = 3

2x + 5 = [tex]2^{3}[/tex] = 8 ( subtract 5 from both sides )

2x = 3 ( divide both sides by 2 )

x = 1.5

Answer: 11.24

Step-by-step explanation:

add them all together and then divide by 2

Step-by-step explanation:

Let x be the number of leather jackets and y be the number of nylon jackets.

The total cost of leather jackets is $100x and the total cost of nylon jackets is $88y.

The problem states that the inventory of men's jackets is at least $4400, so we have:

100x + 88y ≥ 4400

This is the system of inequalities:

100x + 88y ≥ 4400

x ≥ 0 (since we cannot have a negative number of jackets)

y ≥ 0 (since we cannot have a negative number of jackets)

Answer:394.5

Step-by-step explanation:

diameter of circle is 26 so,

radius=r=d/2=13

Area of trapezium=(a+b)/2*h=(19+26)/2*5=45*5/2=225/2=112.5

Area of circle=

[tex]\pi R^{2}=169\pi \\if \ we \ assume \ \pi =3,\\169\pi =169*3=507[/tex]

Area of shaded shape=507-112.5=394.5

Answer:140125

Step-by-step explanation:

Answer: 5605 x 25 is 140,125

Step-by-step explanation:

Multiply the ones digit in the bottom number by each digit in the top number

6 × 4 = 24

Put the 4 in Ones place

Carry the 2 to Tens place

6 × 3 = 18

Add the 2 that you carried = 20

Put the 0 in the Tens place

Carry the 2 to the Hundreds place

Add the 2 that you carried = 14

This is the last number to multiply so write the whole number answer. No need to carry the 1.

Move one place to the left. Multiply the tens digit in the bottom number by each digit in the top number.

5 × 4 = 20

Add a row to your multiplication answer

When you write your answer, shift one column to the left

Put the 0 in Ones place

Carry the 2 to Tens place

5 × 3 = 15

Add the 2 that you carried = 17

Put the 7 in the Tens place

Carry the 1 to the Hundreds place

5 × 2 = 10

Add the 1 that you carried = 11

This is the last number to multiply so write the whole number answer. No need to carry the 1.

Add the numbers in the columns using long addition

4 + 0 = 4

0 + 0 = 0

4 + 7 = 11

write the 1 and carry 1

1 + 1 + 1 = 3

Once you add the columns you can see the long multiplication result: 234 × 56 = 13104.

Answer: 10 sticks

Step-by-step explanation:

First one is one stick second is 4 sticks and 3rd is 7 sticks

add 3 extra sticks and you get 10

No, the residual plot indicates that the linear model is just not appropriate since it shows a distinct pattern, which is supported by the linear model's inappropriateness.

A line that, using the bivariate data gathered, summarises the linear relationship (as well as linear trend) between it two variables in either a linear regression study.

An assessment of the line that depicts the actual, but unidentified, linear connection that exists between the two variables is called a regression line. When the value of the determinant is known, the regression line's equation can be employed to predict (or forecast) the value of both the response variable.

equation of the least- squares regression line :

ý = 0.0093-0.00121x

In which,

y = concentration

x = number of hours since the pill taken.

From the graph:

There is a clear pattern formed in this residual line.

Thus, No, the residual plot indicates that the linear model is just not appropriate since it shows a distinct pattern, which is supported by the linear model's inappropriateness.

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Answer:

Step-by-step explanation:

[tex]-\frac{4}{5} (30x-40)+(42x+4)=-\frac{4}{5} (10)(3x-4)+2(21x+2)[/tex]

                                         [tex]=-8(3x-4)+2(21x+2)[/tex]

                                         [tex]=-24x+32+42x+4[/tex]

                                         [tex]=-18x+36[/tex]

                                         [tex]=-18(x-2)[/tex]

Using the given data, the equation of the regression line is y=7.033+0.683x.

An equation is a mathematical statement that two expressions are equal. It is composed of two expressions, one on either side of an "equals" sign. Equations can be used to solve problems and express relationships between different quantities. Equations can also provide insights into the behavior of a system. Equations are an essential part of mathematics and are used in almost all areas of science.

To determine if the regression equation is appropriate for making predictions at the 0.05 level of significance, a t-test must be performed. The t-statistic associated with the slope is 3.521 and is significant at the 0.01 level of significance (p-value < 0.01). Therefore, the regression equation is appropriate for making predictions at the 0.05 level of significance.

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The regression line's equation for the provided data is y=7.033+0.683x.

What is equation?

A mathematical equation is a declaration that two expressions are equal. Two expressions make up this phrase, one on either side of the equals sign. Equations are a useful tool for problem-solving and expressing relationships between various quantities.

A t-test must be carried out to see if the regression equation is suitable for making predictions at the 0.05 level of significance. At the 0.01 level of significance, the slope's t-statistic of 3.521 is significant (p-value < 0.01). Hence, at the 0.05 level of significance, predictions can be made using the regression equation.

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Can predict the friction coefficient as a function of temperature with high accuracy.

We can interpret the following from the value of RMSE:The value of RMSE is a metric used to measure the accuracy of the predicted and observed data. A lower value of RMSE indicates that the experimental data is in agreement with the theoretical model used, while a higher value of RMSE indicates that the experimental data does not agree with the theoretical model used.The RMSE value of 0.000711079 in the experiment implies that the experimental results are in good agreement with the model, and the model used can predict the friction coefficient as a function of temperature with high accuracy.

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Yes her plan to construct a square inscribed in a circle is her plan correct.

Let's check if her plan is correct:

In order to construct a square inscribed in a circle,

the following steps should be followed

STEP 1:Draw a circle and its centre, O.

STEP 2:Draw a diameter PQ through the centre of the circle.

STEP 3:Mark the midpoint R of PQ.

STEP 4:Draw a perpendicular bisector of PQ, it should pass through R

STEP 5:It cuts PQ at right angles at R. Label the point where the perpendicular bisector cuts PQ as T.

STEP 6:Connect OT and RT to intersect the circle at points S and U respectively.

Now we have a square INSIDE the circle, where O is the center, and the square's diagonal is the circle's diameter, while the square's sides are the circle's radii.

So, Molly's plan is correct.

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the answer depends on how Eva has arranged the leaves on the rulers. If she has not counted any leaves with a length of 2 inches, then the answer is 0. If she has counted some leaves with a length of 2 inches, then the answer is 3 or less, depending on how many she has counted.

by the question.

If we assume that all the leaves are different and none of them are cut or torn, then we can count the number of leaves with a length of 2 inches.

Since the rulers are 6 inches long, we can use them to measure the length of the leaves. If a leaf is 2 inches long, then it is one-third the length of a ruler. Therefore, we can place three 2-inch leaves end-to-end on the ruler.

Since Eva has two rulers, she can measure the length of six leaves in total. If we assume that all the leaves are different, then there are two possibilities:

All six leaves are longer than 2 inches. In this case, we cannot count any leaves with a length of 2 inches.

At least one leaf is 2 inches long. In this case, we can count the number of 2-inch leaves by counting how many times we can place three 2-inch leaves end-to-end on the rulers.

For example, if Eva places three 2-inch leaves on one ruler and none on the other, then she has counted 3 leaves with a length of 2 inches. If she places two 2-inch leaves on one ruler and one on the other, then she has also counted 3 leaves with a length of 2 inches.

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Answer:

The amount of the discount is calculated by multiplying the subtotal by 15%:

discount = 0.15 x 85.28 = 12.79

The new subtotal after the discount is applied is:

new subtotal = 85.28 - 12.79 = 72.49

The tax on the new subtotal is calculated by multiplying the new subtotal by 6.5%:

tax = 0.065 x 72.49 = 4.71

The final bill, including the tax, is the sum of the new subtotal and the tax:

final bill = 72.49 + 4.71 = 77.20

Therefore, the final bill after the coupon is applied and the tax is paid is $77.20.

Dunn's TV is 13 inches lοng and 6 inches wide.

A quadratic equatiοn is a type οf pοlynοmial equatiοn in which the highest degree οf the variable (usually x) is 2. It has the general fοrm:

ax² + bx + c = 0

Let x be the width οf the TV. Since the TV is 7 inches lοnger than it is wide, its length wοuld be x + 7.

The area οf a rectangle is equal tο its length multiplied by its width. Therefοre, we can set up the equatiοn:

area = length x width

Substituting the values we have:

78 = (x + 7) x x

Simplifying:

78 = x² + 7x

Re-arranging and setting the equatiοn tο zerο:

x² + 7x - 78 = 0

This is a quadratic equatiοn that can be sοlved using the quadratic fοrmula:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1, b = 7, and c = -78.

Plugging these values intο the fοrmula, we get:

x = (-7 ± √(7² - 4(1)(-78))) / 2(1)

Simplifying:

x = (-7 ± √(49 + 312)) / 2

x = (-7 ± √(361)) / 2

x = (-7 ± 19) / 2

We take the pοsitive rοοt because x represents a length, which must be a pοsitive value. Therefοre:

x = (12) / 2 = 6

This means that the width οf the TV is 6 inches, and its length is 6 + 7 = 13 inches.

Hence, Dunn's TV is 13 inches lοng and 6 inches wide.

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Area of sector = 56.977 square inches and Arc length = 15.380 inches (rounded to three decimal places).in order to get these answer we need to use simple sector area formula

what is Area of sector ?

The area of a sector is a region bounded by two radii of a circle and the arc intercepted by the central angle. The formula for the area of a sector is:

Area of sector = (angle / 360) x πr²

In the given question,

To find the area of a circle sector, we need to use the formula:

Area of sector = (angle / 360) x πr²

where r is the radius of the circle, and angle is the central angle of the sector in degrees.

In this case, the radius is 22 inches, and the central angle is 44 degrees. So, we can plug these values into the formula:

Area of sector = (44/360) x π(22)²

Area of sector = (11/90) x π(484)

Area of sector = 56.977 square inches (rounded to three decimal places)

To find the arc length of the sector, we need to use the formula:

Arc length = (angle / 360) x 2πr

where r is the radius of the circle, and angle is the central angle of the sector in degrees.

In this case, the radius is 22 inches, and the central angle is 44 degrees. So, we can plug these values into the formula:

Arc length = (44/360) x 2π(22)

Arc length = (11/90) x 44π

Arc length = 15.380 inches (rounded to three decimal places).

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Answer:

2/3^-3 = 27/8 = 3 3/8 = 3.375

Step-by-step explanation:

A is the correct answer

a. The radius of the jump ball circle is 6 feet. b. The area of the rectangle (lane) is 228 square feet.

Area is a measure of the size of a two-dimensional shape or surface, typically expressed in square units, such as square meters (m²), square feet (ft²), or square centimeters (cm²). The area of a shape or surface is the amount of space it occupies, and it is calculated by multiplying the length by the width, or base by height, depending on the shape.

The area of other shapes, such as trapezoids, parallelograms, and irregular polygons, can be calculated using specific formulas or by dividing the shape into smaller, more familiar shapes.

Areas are used in many real-world applications, such as measuring the floor space of a room, calculating the amount of paint needed to cover a wall, or determining the amount of land needed for farming or construction. Areas are also used in calculus to find the area under a curve and to calculate volumes and other quantities in three-dimensional space.

a. The area of the circle is given as 113.04 square feet. Using the formula for the area of a circle, A=πr², we can solve for the radius, r:

113.04 = 3.14r²

r² = 113.04/3.14

r² = 36

r = √36

r = 6 feet

Therefore, the radius of the jump ball circle is 6 feet.

b. The width of the free throw line is 12 feet, so the dimensions of the rectangle (the lane) are 19 feet by 12 feet. The area of a rectangle is given by the formula A = lw, where l is the length and w is the width. Thus, the area of the lane is

A = 19 x 12

A = 228 square feet

Therefore, the area of the rectangle (lane) is 228 square feet.

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Answer: 43.5 inches

Step-by-step explanation:

Divide the 87 by the 2 to get the number of half inches it equates to

(a) The value of angle VUW is 31⁰.

(b) The value of angle WUX is 59⁰.

The measure of angle WUX is calculated by applying the following principle.

So angle ∠VUW is calculated as follows;

m ∠VUW = ¹/₂ arc UVW (angle formed by chords at circumference is twice the angle of opposite tangent)

m ∠VUW = ¹/₂ x ( 242 - 180)

m ∠VUW = 31⁰

The value of angle WUX is calculated as follows;

m ∠WUX = 90 - 31⁰ ( sum of angles subtended by the diameter of a circle)

m ∠WUX = 59⁰

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Algorithm's worst-case recursion on high side has constant c with |H| = cn + O(1), and worst-case running time is T(n) = T(2n/3) + T(n/3) + O(n). Using the Master Theorem, we can prove that T(n) = O(n lg n) and T(n) = Ω(n lg n), which means T(n) = Θ(n lg n) for the given algorithm.

Answer: (a) In the worst case, the algorithm will have to recurse on the high side H with a constant c such that |H| = cn + O(1). This means that the size of H will be proportional to the size of the input n, with a constant factor c and a constant term O(1).

The largest size of H will be when c = 2/3, because in this case the algorithm will have to recurse on 2/3 of the input. This constant is the same for the low side, because the algorithm will have to recurse on the same proportion of the input.

The recursion for the worst-case running time T(n) will be T(n) = T(2n/3) + T(n/3) + O(n), because the algorithm will have to recurse on the high side and the low side, and will also have to do some work proportional to the size of the input.

(b) To prove that T(n) = O(n lg n), we can use the Master Theorem.

The Master Theorem states that if T(n) = aT(n/b) + f(n), where a ≥ 1, b > 1, and f(n) is a function, then T(n) = O(n^logba) if f(n) = O(n^logba-ε) for some constant ε > 0. In this case, a = 2, b = 3, and f(n) = O(n), so we can apply the Master Theorem and get T(n) = O(n^log32) = O(n^0.63) = O(n lg n).

Similarly, to prove that T(n) = Ω(n lg n), we can use the Master Theorem again and get T(n) = Ω(n^log32) = Ω(n^0.63) = Ω(n lg n). Therefore, T(n) = O(n lg n) and T(n) = Ω(n lg n), which means that T(n) = Θ(n lg n).

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Answer:

Step-by-step explanation:

divide 150 by sides of rectangle = 4 .
= 37.5 then multiply x3 = 112.5

y = 2x + 4 is the equation of the line that connects the coordinates (0, 4) and (1, 6).

The points that the line passes through are (0, 4) and (1, 6). The equation of a line can be found by using the point-slope form:

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is one of the line's points.

Then, we may determine the line's slope:

[tex]m = \frac{(y2 - y1)}{(x2 - x1)}[/tex]

where (x1, y1) = (0, 4) and (x2, y2) = (1, 6)

[tex]m = (6 - 4) / (1 - 0) = 2[/tex]

Now we can use the point-slope form with one of the points, say (0, 4):

y - 4 = 2(x - 0)

Simplifying, we get:

y - 4 = 2x

Adding x to both sides, we get:

y = 2x + 4

So the equation of the line that passes through the points (0, 4) and (1, 6) is y = 2x + 4.

The complete question is"=

Find the equation of the line. Use exact numbers. y=y=y, equals x+x+x, plus

A coordinate plane. The x- and y-axes each scale by one. A graph of a line goes through the points zero, four and one, six.

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The probability that the two marbles are the same colour is 3/7. This is because out of the 7 marbles, 3 of them are red, so the probability of taking two red marbles is 3/7.

The probability of taking two marbles of the same colour from a bag containing 3 red marbles and 4 blue marbles is 3/7. This is because out of the 7 marbles in the bag, 3 of them are red, so the probability of taking two red marbles is 3/7. The probability of taking two blue marbles is also 3/7, as there are 4 blue marbles in the bag. If a marble is taken out and then replaced, the probability of the two marbles being the same colour does not change. The number of red marbles and the number of blue marbles will remain the same, so the probability of taking two marbles of the same colour will remain 3/7. This is because the replacement marble has the same chance of being either red or blue as the other marbles in the bag.

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The salesman earned a total sum of $2,165.

Given that, a shoe salesman sold $4,125 in shoes and earns a 4% commission, his base salary is $2000.

The amount of commission earned by the shoe salesman is equal to the product of the total sales and the commission rate, which is 4% or 0.04 as a decimal:

Commission = Total sales x Commission rate

Commission = $4,125 × 0.04

Commission = $165

To find the total earnings of the salesman, we add his commission to his base salary:

Total earnings = Base salary + Commission

Total earnings = $2,000 + $165

Total earnings = $2,165

Therefore, the salesman earned $2,165.

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The only difference between the JK-FF (and JK-latch) and the SR-FF (and SR-latch) is that the JK-FF (and JK-latch) has an additional JK control line. This additional control line allows the device to toggle its state when the control line is pulsed.

The JK-FF and JK-latch function similarly to the SR-FF and SR-latch. The J acts like the S and the K acts like the R.

When the J and K lines are both low, the device acts like the S and R lines are both low for the SR-FF.

However, when the J and K lines are both high, the device will toggle its state, which does not happen with the SR-FF.

The additional JK control line can be used to create different circuits, like a toggle circuit or a pulsed output circuit.

The toggle circuit will change the output from one state to another each time the control line is pulsed, while the pulsed output circuit will produce an output pulse of fixed length.

The JK-FF and JK-latch can also be used to create a counter circuit which counts up or down depending on the J and K lines.

The only difference between the JK-FF (and JK-latch) and the SR-FF (and SR-latch) of the following is that the JK-FF (and JK-latch) has an additional JK control line.

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