Hawk thinks his heartrate will increase as he increases his skateboarding speed. To see if this relationship exists, he records six different speeds and models it with a scatterplot and regression output.

A scatterplot is shown with the x axis labeled Speed, miles per hour, and the y axis labeled Pulse, beats per minute. The points on the graph increase from 9.5 and 68 to 15.8 and 116.


Regression Statistics
Multiple R 97.28153%
R Square 94.63696%
Adjusted R Square 93.29620%
Standard Error 4.806846736
Observations 6


df SS MS F
Regression 1 1,630.910231 1,630.910231 70.58453
Residual 4 92.42310217 23.10577554
Total 5 1,723.333333


Coefficients Standard Error t Stat p-Value
Intercept 1.301246992 10.66036651 0.122064001 0.908735
Speed 7.315685846 0.870763656 8.401459797 0.001098


Part A: Write the equation of the regression line using the regression output. (2 points)

Part B: What do the slope and intercept parameters mean using the context of the problem? (4 points)

Part C: Compute the margin of error that Hawk should use if he wants to provide a 99% confidence interval for the slope. Assume that conditions for inference are satisfied. (4 points)

Answer:

Let's start by using algebra to solve for the original amount that Alex paid for his shares.

Let X be the original amount that Alex paid for his shares.

We know that his shares dropped in value by 35%, so after the drop, he had 65% of his original investment left:

0.65X = $72,800

Solving for X:

X = $72,800 / 0.65

X = $112,000

Therefore, Alex paid $112,000 for his shares to begin with.

The standard deviation for the given distribution is 8.739 using either the direct method or the shortcut method.

Standard deviation is defined as a measure of how spread out numbers are. It is also referred to as the square root of the Variance, and then the Variance is the average of the squared differences from the Mean.

To calculate the standard deviation for the given distribution, we will utilize either the direct method or the shortcut method.

Direct method:

Calculate the mean wage (F) for the distribution:

Mean = (20 + 22 + 27 + 30 + 31 + 32 + 35 + 45 + 40 + 48)/10

Mean = 34

Calculate the differences between each wage and the mean wage:

20 - 34 = -14

22 - 34 = -12

27 - 34 = -7

30 - 34 = -4

31 - 34 = -3

32 - 34 = -2

35 - 34 = 1

45 - 34 = 11

40 - 34 = 6

48 - 34 = 14

Square each of the differences:

(-14)² = 196

(-12)² = 144

(-7)² = 49

(-4)² = 16

(-3)² = 9

(-2)² = 4

1² = 1

11² = 121

6² = 36

14² = 196

Add up the squared differences: 196 + 144 + 49 + 16 + 9 + 4 + 1 + 121 + 36 + 196 = 756

Divide the sum of the squared differences by the number of workers: 756/10 = 75.6

Take the square root of the result to get the standard deviation:

√75.6 = 8.739

Shortcut method:

The mean wage (F) for the distribution:

(20 + 22 + 27 + 30 + 31 + 32 + 35 + 45 + 40 + 48)/10 = 34

The sum of the squares of the differences between each wage and the mean wage:

(20 - 34)² + (22 - 34)² + (27 - 34)² + (30 - 34)² + (31 - 34)² + (32 - 34)² + (35 - 34)² + (45 - 34)² + (40 - 34)² + (48 - 34)² = 756

Divide the sum by the number of workers: 756/10 = 75.6

Take the square root of the result to get the standard deviation:

Standard deviation = √75.6 = 8.739

Therefore,

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Complete question is:

Calculate standard deviation for the following

distribution by direct and shortcut method.

Assume mean as 32.

Serial No. of Workers

1

2

3

4

5

6

7

8

9

10

Wage (F)

20

22

27

30

31

32

35

45

40

48

Carson can line up his textbooks on his bookshelf in 24 different ways

What is Permutation?

Permutations are a way to count the number of ways that a set of objects can be arranged in a particular order. A permutation is an ordered arrangement of objects.

What is Combination?

The combination is a way to count the number of ways that a set of objects can be selected without regard to order. A combination is an unordered selection of objects.

According to the given information:

Carson has four textbooks that he wants to line up on his bookshelf. The number of different ways that he can do this is given by the permutation formula:

n! / (n - r)!

where n is the total number of objects (in this case, 4 textbooks), and r is the number of objects that he wants to arrange in a particular order (in this case, all 4 textbooks).

On substituting the values in the formula,

4! / (4 - 4)! = 4! / 0! = 4 x 3 x 2 x 1 / 1 = 24

Therefore, Carson can line up his textbooks on his bookshelf in 24 different ways.

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The curved surface area of the cone is 148 cm².

Given that we need to find the curved surface area of the cone with height of 8 cm and radius of 5 cm,

The curved surface area gives the area of the face of an object.

The CSA of a cone = π × radius × slant height.

Slant height = √r²+h²

= √64+25

= 9.43 cm.

Now the csa = 3.14 × 5 × 9.43

= 148

Hence the curved surface area of the cone is 148 cm².

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Since the containers were not given in the question, In a case whereby Ruth has a cylindrical cup that is filled with water where the cup has a diameter of 2 inches and a height of 6 inches,  the  volume of cylinder cup is 18.85inch^3.

Note that ; the container were not given in the question, so  we will just need to calculate the volume of the cylindrical cup to know how much water it can hold .

The volume of a cylinder can be caluculated using te exppresion  π r² h

Then from the question the  diameter = 2 inches radius = 2/2 = 1 inches

height =6 inches

π r² h

=π  * 1^2 * 6

=18.85inch^3

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Answer:

Step-by-step explanation:

6x² - 10x + 21x - 35 = 6x² + 11x - 35

6x² - 6x² + 11x - 11x - 35 + 35 = 0

0 = 0

The equation is an identity. Its solution set is {all real numbers}.

The probability that a sample of size n = 158 is randomly selected with a mean greater than 242.4 is 0.751.

z = (x - μ) / (σ/√n)

where x is the sample mean.

Substituting the values, we get:

z = (242.4 - 246) / (89.7/√158) ≈ -0.670

We want to find the probability of obtaining a sample mean greater than 242.4, which is equivalent to finding the probability of obtaining a standardized sample mean greater than z = -0.670. We can use a standard normal distribution table or calculator to find this probability.

P(z > -0.670) ≈ 0.751

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The median weekly earnings of the data set of the workers in the occupations listed for 2010 is calculated as: $971.

To find the median weekly earnings for the occupations listed in 2010, we need to first arrange the earnings in order from least to greatest:

$501, $900, $971, $977, $1071

The median is the middle value in this ordered list. Since there are an odd number of values, the median is simply the middle value.

Therefore, the median weekly earnings of workers in the occupations listed for 2010 is $971.

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The values of missing variables are given by:

x = 51°, y = 105°, z = 90°.

We know that the sum of external and internal angles is 180°.

So from the given figure we can see that y° is the external angle and the corresponding internal angle is 75°.

So, 75° + y° = 180°

y° = 180° - 75° = 105°

And also external angle is right angle that is 90° and the corresponding internal angle is z°.

So, z° + 90° = 180°

z° = 180° - 90° = 90°

This is a pentagon and the sum of all internal angles = (5 - 2)180° = 3*180° = 540°

According to the given figure the sum of all internal angles of the pentagon is = (180° - 36°) + z° + (180° - x°) + (180° - 78°) + 75° = 144° + 90° + 180° - x + 102° + 75° = 591° - x.

So, 591° - x = 540°

x = 591° - 540° = 51°

Hence the value of missing variables are: x = 51°, y = 105°, z = 90°.

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Answer:

52 is the  least common dominator

Answer:

52/65

Step-by-step explanation:

The same fraction we can express in many different forms. If the numerator and denominator ratio is the same, the fractions represent the same rational number.

The least common denominator of a set of fractions is the least number that is a multiple of all the denominators: their least common multiple

The method of calculating the LCD is the same as the calculation least common multiple of fractions denominators.

The simple method for common computing denominators (not least at all) is to multiply all denominators.

Answer:

50° F

Step-by-step explanation:

35 - -15= 50

Check
-15 + 50 = 35

And 35 - 50 = -15

Using the tangent ratio, the value of x in the right triangle shown is calculated to the nearest tenth as: 2.6  units.

The tangent ratio is part of the trigonometry ratios that is applied when solving a right triangle, and it is expressed as:

tan ∅ = length of the opposite side / length of the adjacent side.

We are given the following information from the image above:

Reference angle (∅) = 43 degrees

length of the opposite side = x

length of the adjacent side = 2.8

Plug in the values:

tan 43 = x/2.8

2.8 * tan 43 = x

x = 2.6 [to the nearest tenth]

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Some of the common order of operation mistakes that students make when evaluating expressions are the use of basic mathematical operations.

You should know that an error or fault results from defective judgment, deficient knowledge, or carelessness.

A combination of numbers, letters, and relational operators containing at least one operation is deemed a mathematical expression. Additionally, it must also include variables and/or numbers, excluding an equal sign.

Some prevalent errors include using both a positive and a negative sign, using two negative signs, and misusing brackets.

By being unable to comprehend the problems accurately, learners often commit significant errors while assessing formulations, which underscores the importance of employing fundamental mathematical operations.

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Answer:

301.4 in^3

Step-by-step explanation:

Divide 12 by 2 to get the radius

12/2=6

Square 6 and multiply by 3.14 according to the area of a circle formula πr^2.

6^2=36 36*3.14=113.04

We now have the area of the base.

Multiply it by the height and divide by three to follow the formula for the volume of a cone, 1/3bh.

113.04*8=904.32. 904.32/3= 301.44, or 301.4 after rounding.

Answer:

x^2(x+5)-6(x+5)!!!!!!!!

The discussion for both cases is shown below.

Part a:

H0: there is no association between climate change and certainty.

H1: there is no association between climate change and certainty.

It seems that the null hypothesis (H0) and the alternative hypothesis (H1) are identical, which doesn't make sense. Typically, the null hypothesis states that there is no association or effect, while the alternative hypothesis states that there is an association or effect.

The statement also mentions that the p-value is a non-zero number, but it doesn't provide the actual value. The p-value is used to determine the statistical significance of the association and should be compared to a predetermined significance level (e.g., 0.05) to make a decision.

Part 2:

H0: there is no association between sleeping and the income class.

H1: there is a association between the income class and sleeping.

Similarly, the null hypothesis (H0) and the alternative hypothesis (H1) are stated incorrectly. The null hypothesis should state no association or effect, while the alternative hypothesis should state that there is an association or effect.

Again, the statement mentions a non-zero p-value but doesn't provide the actual value. The p-value needs to be compared to a significance level to determine the statistical significance of the association.

In both cases, it is important to provide the actual p-value and compare it to the significance level to make a proper conclusion about the association between the variables.

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The total amount that the Bells will pay for their house would be $313, 680.

The cost that would be interest is $193, 680

The amount of the first payment going to mortgages is $165. 24

Find the down payment :

Down payment = House price - Mortgage amount = $120,000 - $90,000 = $30,000

Then the points paid at closing :

= $ 90,000 x 0. 02 = $1,800

Total amount paid = Total mortgage payments + Down payment + Points cost

= 281, 880 + 30, 000 + 1, 800

= $ 313, 680

The total that is interest is:

Total interest paid = Total interest paid through monthly payments + Points cost

Total interest paid = $ 191, 880 + $ 1, 800 = $193, 680

The amount of the first payment going to principal is:

Principal portion of first payment = 90, 000 - 89, 834.76 = $165. 24

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Answer:

100

Step-by-step explanation:

The number has the same digit in its hundreds place and its hundredths place. The digit in the hundreds place is 100 times greater than the digit in the hundredths place (https://ccssmathanswers.com/hundredth-place-in-decimals). Therefore, the value of the digit in the hundreds place is 100 times greater than the value of the digit in the hundredths place.

Therefore, the answer is 100.

The measure of ∠ADC is equal to 180 degrees.

The measure of ∠ABC is equal to 90 degrees.

In Mathematics and Geometry, a circle simply refers to a closed, two-dimensional (2D) curved geometric shape with no edges or corners. Additionally, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).

Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can reasonably infer and logically deduce that the measure of angle ADC (∠ADC) is equal to 180 degrees.

In conclusion, the angle subtended by chord AB at point B has a measure of 90 degrees.

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Answer:

the variance of X is 0.126.

Step-by-step explanation:

The number of white balls drawn X follows a hypergeometric distribution with N = 20 (total number of balls), K = 4 (number of balls drawn), and n = 4 (number of white balls). The probability mass function (pmf) of X is given by:

P(X = k) = (nCk)(N-nCk) / (NCk)

where C denotes the combination function.

(a) Expectation of X:

E(X) = np = nK/N = (4/20) * 4 = 0.8

Therefore, the expected number of white balls drawn is 0.8.

(b) Variance of X:

Var(X) = np(1-p)[(N-K)/(N-1)] = nK(N-K)(N-n)/(N^2(N-1)) = (4/20) * 4 * (20-4) * 16 / (20^2 * 19) = 0.126

Therefore, the variance of X is 0.126.

Answer:

The expected number of white balls drawn is 0.4 and the variance of X is 0.24.

Step-by-step explanation:

Answer:

Step-by-step explanation:

An inequality can be represented graphically as a region on one side of a line. Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.

Answer:

3

Step-by-step explanation:

3 * 3 = 6

1/2 * 6 = 3 not 4.5

Because, when we multiply with 1/2, we are actually dividing the number by 2, and 6/2 = 3.

The 3 x 3 part turns into 9

So we have 1/2 x 9 or 9/2

Use long division to find that 9/2 gives a quotient of 4 and remainder 1

Imagine you had 9 cookies and 2 friends. Each friend would get 4 cookies each, eating 4*2 = 8 cookies overall. Then there's 9-8 = 1 cookie as the remainder.

The "remainder 1" then leads to 1/2 = 0.5

quotient = 4

remainder = 1 ---> decimal portion = 1/2 = 0.5

So that's how we get to 4+0.5 = 4.5

You can use a calculator to see that 9/2 = 4.5

The unknown angles in the circle are as follows:

a. m∠AEB = 73°

b. arc angle VW = 155°

a.

If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

Therefore,

m∠AEB = 1 / 2 (99 + 47)

m∠AEB = 146 / 2

m∠AEB = 73 degrees

b.

If two secants intersect outside a circle , then the measure of an angle formed by the two lines is one half the positive difference of the measures of the intercepted arcs .

Therefore,'

arc angle VW = x

55 = 1 / 2 (x - 45)

55 = 0.5x  - 22.5

0.5x = 55 + 22.5

0.5x = 77.5

divide both sides by 0.5

x = 77.5 / 0.5

x = 155 degrees

Therefore,

arc angle VW = 155 degrees

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If the total distance available is 92.75 yards, and there is a sign 5 yards before the starting line, the actual distance available for the race is:

92.75 - 5 = 87.75 yards

Since there are 5 sections of the race, each section covers:

87.75 / 5 = 17.55 yards

Therefore, each section of the race is 17.55 yards long.

The matrix after the row operation is given as follows:

[tex]\left[\begin{array}{ccc}1&-\frac{4}{7}&\frac{8}{7}\\-12&7&-13\end{array}\right][/tex]

The matrix in the context of this problem is defined as follows:

[tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex]

We want to have element 1 into row 1 and column 1, that is, the element of 7 must assume a value of -1.

A valid row operation is the multiplication of the row by a constant, and as the element has a value of 7, the constant to obtain a value of 1 is:

7/k = 1

k = 7.

Dividing every element of the first row by 7, the matrix is given as follows:

[tex]\left[\begin{array}{ccc}1&-\frac{4}{7}&\frac{8}{7}\\-12&7&-13\end{array}\right][/tex]

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a) The measure of 9π/5 radians in degrees is approximately 324 degrees.

b) The measure of -π/3 radians in degrees is approximately -60 degrees.

To convert the given angle measures from radians to degrees, we can use the formula:

angle in degrees = (angle in radians) × (180/π)

a) To convert 9π/5 radians to degrees, we can substitute the given value in the above formula as:

angle in degrees = (9π/5) × (180/π) ≈ 324 degrees (rounded to two decimal places)

b) To convert -π/3 radians to degrees, we can substitute the given value in the above formula as:

angle in degrees = (-π/3) × (180/π) ≈ -60 degrees (rounded to two decimal places)

In general, we can convert an angle measure from radians to degrees by multiplying it by 180/π. Since π is an irrational number, the conversion factor 180/π is an irrational number as well. Therefore, when we round the result to two decimal places, we are actually approximating the true value of the angle measure.

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Note that the limit of the expression as x approaches infinity is 1/2.

start by multiplying both the numerator and denominator by the conjugate  expression

√ (x ² - 9x + 1) + x,

this will eliminates the root in the numerator

lim x->∞ [(√(x ² - 9x + 1) - x)  * (√(x² - 9x + 1) + x)] / (√(x² - 9x + 1) + x)

Expanding the numerator

lim x- >∞ [(x² - 9x + 1) - x^2] / (√(x² - 9x + 1) + x)

Simplifying further:

lim x->∞ [(1 - 9/x + 1/ x²)] / (√(1 - 9/x + 1 /x²) + 1)

we can see that the 1/x ² term approaches zero, and the expression simplifies to

lim x->∞ [(1 - 0)]  / (√(1 - 0) + 1)

= 1/2

So it is correct to state that the limit of the expression as x approaches infinity is 1/2.

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