2. There are 212 students at a local college taking an Introduction to Statistics course. The
following are the final exam scores of 30 randomly selected students. What would you estimate
to be the mean score for all the students in the course? Round your answer to the nearest whole
number.
Final Exam Scores
97 54 78 75 86
94 96 68 62 76
89 91 73
65
80
72
62 81 57
77 88 82 100 58
63 74 85 95 52 64
A table has 5 rows and 6
columns of integers ranging
from 52 to 100.

Answer:

5.6

Step-by-step explanation:

5x/8=7/2

10x=56

x=5.6

Answer:

366.6 mm²

Step-by-step explanation:

Step 1: find XY using the Law of sines.

Thus,

\( \frac{XY}{sin(W)} = \frac{WY}{sin(X)} \)

m < W = 180 - (70+43) (sum of angles in a triangle)

W = 180 - 113 = 67°

WY = 24 mm

X = 43°

XY = ?

\( \frac{XY}{sin(67)} = \frac{24}{sin(43)} \)

Cross multiply:

\( XY*sin(43) = 24*sin(67) \)

\( XY*0.68 = 24*0.92 \)

Divide both sides by 0.68 to solve for XY

\( \frac{XY*0.68}{0.68} = \frac{24*0.92}{0.68} \)

\( XY = 32.47 \)

XY ≈ 32.5 mm

Step 2: find the area using the formula, ½*XY*WY*sin(Y).

Area = ½*32.5*24*sin(70)

Area = ½*32.5*24*0.94

= 32.5*12*0.94

Area = 366.6 mm² (nearest tenth)

A. The 95% confidence interval for the mean weight of all fridges is (97.01 kg, 102.99 kg).

B. The confidence interval means that we can be 95% confident that the true population mean weight of all fridges falls within this range. This means that if we were to collect multiple samples and calculate their confidence intervals, approximately 95% of those intervals would contain the true population mean. In this case, it means that we are 95% confident that the true average weight of all fridges is between 97.01 kg and 102.99 kg.

C. Without calculating another confidence interval, we can say that a 90% confidence interval would be less precise than the 95% confidence interval created in part a). This is because a higher confidence level requires a wider interval to capture the true population mean with a higher degree of certainty. Since a 90% confidence interval is less confident than a 95% confidence interval, it would need to be narrower. Therefore, a 90% confidence interval would be less precise, as it would provide a smaller range of values for the population mean.

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AIn problems 7 and 8, we need to find the solution of the given initial-value problem where x(0) = 1 and x'(0) = -3x. To solve this differential equation, we can separate the variables and integrate both sides. This gives us x(t) = e^(-3t/2). Thus, the solution of the initial-value problem is x(t) = e^(-3t/2) with x(0) = 1. The behavior of the solution as t approaches infinity is that x(t) approaches zero. This is because the exponential term e^(-3t/2) decays to zero as t becomes large.

To solve the given initial-value problem, we can use separation of variables. We start by separating the variables and get dx/x = -3/2 dt. Integrating both sides, we get ln|x| = -3t/2 + C, where C is a constant of integration. Solving for x, we get x = Ce^(-3t/2). We can then use the initial condition x(0) = 1 to find C. Plugging in x = 1 and t = 0, we get C = 1. Thus, the solution of the initial-value problem is x(t) = e^(-3t/2) with x(0) = 1.

To describe the behavior of the solution as t approaches infinity, we can look at the exponential term e^(-3t/2). As t becomes larger and larger, e^(-3t/2) approaches zero. This means that x(t) approaches zero as t approaches infinity. We can also see this by looking at the graph of the solution, which decays to zero as t becomes larger.

In conclusion, the solution of the initial-value problem x(0) = 1 and x'(0) = -3x is x(t) = e^(-3t/2). The behavior of the solution as t approaches infinity is that x(t) approaches zero. This is because the exponential term e^(-3t/2) decays to zero as t becomes large.

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Answer: 30.26%

Step-by-step explanation:

Answer:

Answer:

its c

Step-by-step explanation:

easy 23 simple mulitply then add

Quantities that are proportional to each other are,

A) radius and diameter of a circle

B) radius and circumference of a circle

C) radius and area of a circle

D) diameter and circumference of a circle

E) diameter and area of a circle​

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

We know the radius of a circle is r and the diameter of a circle is 2r.

We also know that the circumference of a circle is 2πr and the area of a circle is π(r)².

Now the quantities that will be related to each other are the quantities that are together linked in the formula of circumference and area.

∴ Radius and diameter of a circle, Radius, and circumference of a circle, Radius and area of a circle, Diameter and circumference of a circle, and Diameter and area of a circle​ all are related to each other and are directly proportional.

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The calorie intake is y.

The number of pounds of weight lost per day is x.

m = Change of y with respect to x

when no weight is lost per day the amount of calories taken so \(x=0\) and \(y=2200\)

\(y=m\times 0+2200\\\Rightarrow y=2200\)

So, y intercept, \(c=2200\)

When 3900 calories are lost one pound is lost so \(x=1\) and \(y=-3900\)

\(y=m+2200\)

\(\\\Rightarrow -3900=m+2200\\\Rightarrow m=-6100\)

So, the linear equation would be \(y=-6100x+2200\).

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To plot the resulting image, you will need to take the original figure and multiply each coordinate by the factor of 3/2. For example, if the original figure had a point at (3,4), the new image will have the point at (4.5,6). This will be true for all points in the original figure.

Coordinate is a point or set of values that is used to determine the position of a point, object, or shape in a two-dimensional or three-dimensional space. Coordinate values usually consist of two or three numbers that represent the distance of the point from the origin (x, y, and/or z).

The answer to this question is to plot the resulting image of a figure that has been dilated by a factor of 2/3. A dilation is a transformation that changes the size of a figure. It can either make the figure larger, or smaller. In this case, the dilation is making the figure smaller by a factor of 2/3.

When a figure is dilated, the origin (the point (0,0)) is the center of the transformation. This means that the figure is scaled down from the center point. In general, a dilation by a factor of k will scale down the figure by a factor of 1/k. In this case, the dilation is by a factor of 2/3 so the figure will be scaled down by a factor of 3/2.

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Answer:

Step-by-step explanation:

\(-3x + 15 > 102\\\\\mathrm{Subtract\:}15\mathrm{\:from\:both\:sides}\\\\-3x+15-15>102-15\\\\Simplify\\\\-3x>87\\\\\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}\\\\\left(-3x\right)\left(-1\right)<87\left(-1\right)\\\\Simplify\\\\3x<-87\\\\\mathrm{Divide\:both\:sides\:by\:}3\\\\\frac{3x}{3}<\frac{-87}{3}\\\\Simplify\\\\x<-29\)

Answer:

x = 3\(\sqrt{3}\)

Step-by-step explanation:

Given y varies directly as x², then the equation relating them is

y = kx² ← k is the constant of variation

To find k use the condition y = 27 when x = 3 , then

27 = k × 3² = 9k ( divide both sides by 9 )

3 = k

y = 3x² ← equation of variation

When y = 81, then

81 = 3x² ( divide both sides by 3 )

27 = x² ( take the square root of both sides )

x = \(\sqrt{27}\) = \(\sqrt{9(3)}\) = 3\(\sqrt{3}\)

Answer:

The correct answer is 75%.

Step-by-step explanation:

If you count all the misses in each trial as one whole miss, then you will have 15 total misses which would then leave to 5 makes. Then you divided 15 by 20 which would give you a perfect 75% of him missing the field goal. So basically, your answer is 75%.

Answer:-63

Step-by-step explanation:

well first you would do 4-11 which is -7 and then -7x9=-63

Answer:

-63

Step-by-step explanation:

1. Subtract 11 from both sides:

\(\frac{x}{9} =-7\)

2. Multiply both sides by 9 to isolate x:

\((9)\frac{x}{9} =-7(9)\)

x = -63

hope this helps!

The diameter of the circle with the circle equation (x+8)² + (y+4)² = 256 is 32 units

The equation of the circle is given as:

(x+8)² + (y+4)² = 256

As a general rule, a circle equation is represented as:

(x - a)² + (y - b)² = r²

Where r is the radius.

By comparing both equations, we have:

r² = 256

Take the square roots of both sides

r = 16

Multiply by 2 to get the diameter

d = 32

Hence, the diameter of the circle is 32 units

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Answer:

15.5 m/s

Step-by-step explanation:

Using the equation, d = ut+1/2gt² where all the variables have meaning as given above, making u subject of the formula, we have

d = ut+1/2gt²

d - 1/2gt² = ut

d/t - 1/2gt²/t = u

u = d/t - 1/2gt

Since d = 200 m, t = 5 s and g = 9.8m/s², substituting the values of the variables into the equation, we have

u = d/t - 1/2gt

u = 200 m/5 s - 1/2 ×  9.8m/s² × 5 s

u = 40 m/s - 49 m/s ÷ 2

u = 40 m/s - 24.5 m/s

u = 15.5 m/s

So, the initial speed of the snowball is 15.5 m/s

Calculating a relationship between college admission scores and freshman gpa requires the  Correlational statistics type of statistics. Correlational statistics are used to measure the strength of the relationship between two variables.

This type of statistic is used when attempting to determine the relationship between college admission scores and freshman GPA. By measuring the correlation between the two variables, it can be determined if there is a correlation between college admission scores and freshman GPA. Correlational statistics can measure the direction, strength, and significance of the relationship between two variables.

This type of statistics can provide information such as the degree to which two variables move together and the extent to which one variable changes as the other variable changes. Correlational statistics can also provide information on how much of the variability in one variable is explained by the other variable. Correlational statistics can be used to determine if there is a correlation between the two variables and, if so, the strength of that correlation.

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Answer:

Step-by-step explanation:

Correct choice is D

\(\frac{\sqrt[4]{3x^2}}{2y}\)  is the simplification of the given expression.

Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are called PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.

It is given an expression \(\sqrt[4]{\frac{24x^6y}{128x^4y^5} }\)

Simplifying the given expression using the PEMDAS technique,

\(\sqrt[4]{\frac{24x^6y}{128x^4y^5} }\\\\\sqrt[4]{\frac{3x^2}{16y^4} }\\\\\frac{\sqrt[4]{3x^2}}{2y}\)

Therefore, the simplified value of the given expression is \(\frac{\sqrt[4]{3x^2}}{2y}\). Thus, the option D is correct.

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Answer:

7

Step-by-step explanation:

I just guessed 7 and believe me its right

Answer:

3

Step-by-step explanation:

The solutions to the system of equations in this problem is given as follows:

(0,1) and (0.25, 0).

The graph is given by the image presented at the end of the answer.

The equations that compose the system in this problem are given as follows:

We solve the system graphically, hence the solution is given by the point of intersection of the graphs of the two functions.

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Answer:

768 dollars

Step-by-step explanation:

Answer:

slope is m = 2

Answer:

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

\(m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\ \)

From the question we have

\(m = \frac{ - 5 - 5}{ - 3 - 2} = \frac{ - 10}{ -5 } = \frac{10}{5} = 2\\ \)

We have the final answer as

Hope this helps you

The derivative of the given function represents the slope of the tangent line. The function is y = x^2 + x + 9.
2x + 1 = 5
2x = 4
x = 2
Putting x = 2
y = (2)^2 + 2 + 9
y = 4 + 2 + 9
y = 15
So, when the slope of the tangent line is equal to 5, the value of y is 15.

To find the value of y where the slope of the tangent line is equal to 5, we need to use calculus. First, we find the derivative of the function y = x^2 + x + 9:
y' = 2x + 1

Then, we set this equal to 5 and solve for x:
2x + 1 = 5
2x = 4
x = 2

Now that we have the x-coordinate of the point where the slope of the tangent line is 5, we can find the corresponding y-value by plugging x = 2 into the original function:
y = 2^2 + 2 + 9
y = 13

Therefore, the value of y where the slope of the tangent line is equal to 5 is 13.

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Answer:

The triangle, square, and trapezoid are the following:

Answer:

Press down the brake firmly and smoothly. ...

Don't brake and swerve the car at the same time. ...

Avoid using your transmission for quick stops. ...

Focus on where you want to go, not what you want to avoid.

We want to determine how many possible outcomes there are when rolling two distinguishable dice that add up to 6. To do this, we can first list all the possible pairs of numbers we can roll on the dice that add up to 6:

- 1 and 5
- 2 and 4
- 3 and 3
- 4 and 2
- 5 and 1

So there are five possible outcomes that satisfy the condition of adding up to 6. Therefore, the cardinality of the set E, which contains all these outcomes, is n(E) = 5.

For the second question, we want to list all the possible outcomes of rolling two distinguishable dice that add up to 9. We can approach this in a similar way to the previous question, by listing all the possible pairs of numbers we can roll that add up to 9:

- 1 and 8
- 2 and 7
- 3 and 6
- 4 and 5
- 5 and 4
- 6 and 3
- 7 and 2
- 8 and 1

So the elements of the set containing all these outcomes would be:

{ (1, 8), (2, 7), (3, 6), (4, 5), (5, 4), (6, 3), (7, 2), (8, 1) }

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Answer: To find the percentage of customers who chose the same meal, we need to divide the number of people who chose the same meal by the total number of customers, and then multiply by 100 to convert to a percentage:

percentage = (34 / 85) x 100

percentage = 40

Therefore, 40% of the customers chose the same meal.

Step-by-step explanation:

Answer:

Its 40%

Step-by-step explanation: you divide 85 by 34 to get your answer

The compound inequality for the given situation is $2.75x + $4.25y ≥ $65 and $2.75x + $4.25y ≤ $75, where x represents the number of daylight cameras and y represents the number of flash cameras.

To solve this compound inequality, we need to find the values of x and y that satisfy both conditions. The inequality $2.75x + $4.25y ≥ $65 represents the lower bound, ensuring that the total cost of the cameras is at least $65. The inequality $2.75x + $4.25y ≤ $75 represents the upper bound, making sure that the total cost does not exceed $75.

To list the solutions involving whole numbers of cameras, we need to consider integer values for x and y. We can start by finding the values of x and y that satisfy the lower bound inequality and then check if they also satisfy the upper bound inequality. By trying different combinations, we can determine the possible solutions that meet these criteria.

After solving the compound inequality, we find that the solutions involving whole numbers of cameras are as follows:

(x, y) = (10, 10), (11, 8), (12, 6), (13, 4), (14, 2), (15, 0), (16, 0), (17, 0), (18, 0), (19, 0), (20, 0).

These solutions represent the combinations of daylight and flash cameras that fulfill the requirements of buying exactly 20 cameras and spending between $65 and $75.

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Answer:The answer is C.

Step-by-step explanation: