A data set had values ranging from 117 to 139. A new data point of 30 was
added to the data set. Would this point affect the mean or the median more? How
(increase/decrease) and why? (2 points)

Answer:

A. x = -5

2(-5) + 10 = -3(-5) - 15

0 = 0

Answer:

\(\pm24\)

Step-by-step explanation:

To find the geometric mean of two numbers, you find their product and then take the square root of that product:

\(GM=\sqrt{16*36}=\sqrt{576}=\pm24\)

Answer:

Because y is a common variable, we can assume that they are equal to each other.

Solving for the circumference and using the formula for the circumference we got the radius as 74.95 feet

Given Data

1/4 of the circumference = 117.75 feet.

Let the circumference be x feet

1/4*x = 117.75

x/4 = 117.75

cross multiplying

x = 4*117.75

x = 471 feets

The expression for the circumference is given as

C = 2πr

471 = 2πr

Making r subject of formula we have

r =  = 471/2*3.142

r = 471/6.284

r = 74.95 feet

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Answer:

10% probability that the part has at least one flaw

Step-by-step explanation:

We have these following probabilities:

90% probability of the part being flawless.

8% probability of the part having a minor flaw

2% probability of the part having major flaws.

What is the probability that the part has at least one flaw

Minor or major flaws. So 8% + 2% = 10%

10% probability that the part has at least one flaw

Answer:

\(\displaystyle \frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Step-by-step explanation:

This can be solved with either the washer (easier) or the shell method (harder). For the disk/washer method, the slice is perpendicular to the axis of revolution, whereas, for the shell method, the slice is parallel to the axis of revolution.  I'll show how to do it with both:

Shell Method (Horizontal Axis)

\(\displaystyle V=2\pi\int^d_cr(y)h(y)\,dy\)

Radius: \(r(y)=2-y\) (distance from y=2 to x-axis)

Height: \(h(y)=2-(-\ln y)=2+\ln y\) (\(y=e^{-x}\) is the same as \(x=-\ln y\))

Bounds: \([c,d]=[e^{-2},1]\) (plugging x-bounds in gets you this)

Plugging in our integral, we get:

\(\displaystyle V=2\pi\int^1_{e^{-2}}(2-y)(2+\ln y)\,dy=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Washer Method (Parallel to x-axis)

\(\displaystyle V=\pi\int^b_a\biggr(R(x)^2-r(x)^2\biggr)\,dx\)

Outer Radius: \(R(x)=2-e^{-x}\) (distance between \(y=2\) and \(y=e^{-x}\))

Inner Radius: \(r(x)=2-1=1\) (distance between \(y=2\) and \(y=1\))

Bounds: \([a,b]=[0,2]\)

Plugging in our integral, we get:

\(\displaystyle V=\pi\int^2_0\biggr((2-e^{-x})^2-1^2\biggr)\,dx\\\\V=\pi\int^2_0\biggr((4-4e^{-x}+e^{-2x})-1\biggr)\,dx\\\\V=\pi\int^2_0(3-4e^{-x}+e^{-2x})\,dx\\\\V=\pi\biggr(3x+4e^{-x}-\frac{1}{2}e^{-2x}\biggr)\biggr|^2_0\\\\V=\pi\biggr[\biggr(3(2)+4e^{-2}-\frac{1}{2}e^{-2(2)}\biggr)-\biggr(3(0)+4e^{-0}-\frac{1}{2}e^{-2(0)}\biggr)\biggr]\\\\V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\biggr(4-\frac{1}{2}\biggr)\biggr]\)

\(\displaystyle V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\frac{7}{2}\biggr]\\\\V=\pi\biggr(\frac{5}{2}+4e^{-2}-\frac{1}{2}e^{-4}\biggr)\\\\V=\pi\biggr(\frac{5}{2}+\frac{4}{e^2}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4}{2e^4}+\frac{8e^2}{2e^4}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4+8e^2-1}{2e^4}\biggr)\\\\V=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Use your best judgment when deciding on what method you use when visualizing the solid, but I hope this helped!

Answer:

p value is 0.1343

Step-by-step explanation:

Null: u>= 442

Alternative: u < 442

Using the formula for z score:

(x - u)/sd/√n

Where x is 438, u = 442 sd can be determined from the variance = √variance =√576 = 24 and n = 44

z score = 438-442 / (24/√44)

z score = -4/(24/6.6332)

z = -4/3.6182

z =-1.1055

Now let's find the p value at 0.1 significance level using a z score of -1.1055, using a p value calculator, p value is 0.1343 which greatest than 0.1 meaning the day is not sufficient enough to conclude that the machine is underfilling the bags.

In 2014, the predicted population of Boca Raton will be 100000.

Given that the population function of Boca Raton is,

p(n) = 74760+1940n

So when the population of Boca Raton is 100000, then

p(n) = 100000

So,

100000 = 74760+1940n

1940n = 100000-74760

1940n = 25240

n = 25240/1940 = 14 (approximately)

So, the year in which the predicted population of Boca Raton reach 100000 is = 2000+14 = 2014

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According to the given data the equation of the new function is (D) f(x) = 2x - 4.

An equation is a mathematical statement that indicates that two expressions are equal. It contains an equals sign "=" and may involve variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, etc.

If we translate the function h(x) = 2x - 9 up by 5 units, the new function f(x) will have the form:

f(x) = h(x) + 5

Substituting the definition of h(x) into this equation, we get:

f(x) = 2x - 9 + 5

Simplifying, we have:

f(x) = 2x - 4

Therefore, the equation of the new function is (D) f(x) = 2x - 4.

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Siama and Wills used different methods to find the differences between (5x + 6x) and (2x - 1) but they both arrived at the same answer.

I prefer Wills method because it is easier and less complicated.

Wills method:

(5x + 6x) - (2x - 1)

Subtract both 2x and -1

5x + 6x - 2x - - 1

5x + 4x + 1

In conclusion, Wills method is preferred when both methods are compared.

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The simplified form of -20/2(7 2/3) is -230/3.

To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

First, let's convert the mixed number 7 2/3 to an improper fraction.

7 2/3 = (7 * 3 + 2) / 3 = 23/3

Now, let's substitute the value back into the expression:

-20/2 * (23/3)

Next, we simplify the multiplication:

-10 * (23/3)

To multiply a fraction by a whole number, we multiply the numerator by the whole number:

-10 * 23 / 3

Now, we perform the multiplication:

-230 / 3

Therefore, the simplified form of -20/2(7 2/3) is -230/3.

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Answer:

3/5=360 mph 11/12=550 4/15=160

Step-by-step explanation:

Answer: To find the monthly payment R necessary to pay off a loan, we can use the following formula:

R = P * (r/12) / (1 - (1 + r/12)^(-12n))

where P is the loan amount, r is the annual interest rate (as a decimal), and n is the number of years of the loan.

To complete parts a through c, we'll need to make some assumptions about the loan. Let's assume:

P = $10,000

r = 5% (0.05 as a decimal)

n = 3 years

a) Calculate the number of monthly payments.

Since the loan is for 3 years, the number of monthly payments will be:

n = 3 * 12 = 36

So there will be 36 monthly payments.

b) Calculate the monthly payment.

Substituting the given values into the formula, we get:

R = 10000 * (0.05/12) / (1 - (1 + 0.05/12)^(-12*3))

R = $299.71 (rounded to the nearest cent)

So the monthly payment necessary to pay off the loan is $299.71.

c) Verify that the loan is paid off in 3 years.

To verify that the loan is paid off in 3 years, we can multiply the number of monthly payments by the monthly payment amount:

36 * $299.71 = $10,789.56

Since the original loan amount was $10,000, and the total paid over 36 months is $10,789.56, the loan is paid off in 3 years (with a bit extra paid due to the interest).

Step-by-step explanation:

The standard form of the equation of the line passing through (8,-3) that is parallel to the line 3y=4x+8 is 4x - 3y = 41

The equation of the line in standard form can be represented as follows:

Ax + By = C

where

Therefore, the standard form of the equation of the line through (8,-3) that is parallel to the line 3y = 4x + 8 is a s follows;

Parallel lines have the same slope.

Hence,

3y = 4x + 8

y = 4  / 3 x + 8 / 3

The slope of the line is 4 / 3. Hence, the line passes through (8, -3). let's find the y-intercept.

y = 4 / 3 x + b

-3 = 4 / 3 (8) + b

b = -3 - 32 / 3

b =  -9 - 32/ 3

b = -41 / 3

Hence,

y = 4 / 3 x - 41 / 3

multiply through by 3

3y = 4x - 41

Therefore, the standard form is 4x - 3y = 41

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The solution to the system of equations is (x, y) = (-261/47, 44/47) as an ordered pair.

To solve the given system of equations:

Equation 1: 8x + 9y = -36

Equation 2: x + 7y = 1

We can use the method of substitution or elimination to find the values of x and y. Let's use the method of substitution:

From Equation 2, we can solve for x:

x = 1 - 7y

Substituting this value of x into Equation 1:

8(1 - 7y) + 9y = -36

8 - 56y + 9y = -36

-47y = -44

y = 44/47

Substituting the value of y back into Equation 2 to find x:

x + 7(44/47) = 1

x + 308/47 = 1

x = 1 - 308/47

x = (47 - 308)/47

x = -261/47

Therefore, as an ordered pair, the solution to the system of equations is (x, y) = (-261/47, 44/47).

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Answer:

797.42

Step-by-step explanation:

Given the Output of a linear regression data using R;

From the result table;

Intercept = 72.807562

Gradient or slope = 0.009792

General form of a linear equation:

y = mx + c

Where y = response variable ; x = explanatory variable ; c = intercept and m = gradient / slope

Hence, the regression equation becomes :

y = 0.009792x + 72.807562

Using these regression results, what is the estimated repair cost on a car that has 74,000 miles on it?

x = 74,000

y = 0.009792(74000) + 72.807562

y = 724.608 + 72.807562

y = 797.42

Answer:

The estimated repair cost on a car that has 74,000 miles on it is $797.42.

Step-by-step explanation:

The statement: Im(formula = Repair.Costs ~ Miles.Driven, data = Dataset) implies that the variable "Repair.Costs" is the dependent variable and the variable "Miles.Driven" is the independent variable.

From the provided data the regression equation formed is:

\(\text{Repair.Costs}=72.807562+0.009792\cdot \text{Miles.Driven}\)

Compute the estimated repair cost on a car that has 74,000 miles on it as follows:

\(\text{Repair.Costs}=72.807562+0.009792\cdot \text{Miles.Driven}\)

                     \(=72.807562+0.009792\cdot 74000\\\\=72.807562+724.608\\\\=797.415562\\\\\approx 797.42\)

Thus, the estimated repair cost on a car that has 74,000 miles on it is $797.42.

The result suggests that the mean wake time might have really reduced since the values barely fall above 100 min as in before treatment with a high degree of confidence. thus , the drug is effective.

Confidence interval is written in the form as;

(Sample mean - margin of error, sample mean + margin of error)

The sample mean represent x , it is the point estimate for the population mean.

Margin of error = z × s/√n

Where s = sample standard deviation = 21.8

n = number of samples = 17

Now the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score

then the degree of freedom, df for the sample.

df = n - 1 = 17 - 1 = 16

Since confidence level = 99% = 0.99, α = 1 - CL = 1 – 0.99 = 0.01

α/2 = 0.01/2 = 0.005

Therefore the area to the right of z0.005 is 0.005 and the area to the left of z0.005 is 1 - 0.005 = 0.995

the t distribution table, z = 2.921

Margin of error = 2.921 × 21.8/√17

= 15.44

The confidence interval for the mean wake time for a population with drug treatments will be; 90.3 ± 15.44

The upper limit is 90.3 + 15.44 = 105.74 mins

The lower limit is 90.3 - 15.44 = 74.86 mins

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The quadratic form ax² + bx + c for the given set of factors is 5x² - 2x - 4.

The quadratic equation that takes the form ax^2+bx+c can be determined from a given set of factors by applying the rule:

Let us expand the eqaution: 2(x-1) (2x+3)

So, we have:

2(x - 1)(2x + 3) ⇒ 4x² + 2x - 6.

= 4x² + 2x - 6 + x² - 4x + 2

Now, let us group like terms, we have:

= 4x² + x² + 2x - 4x - 6 + 2

= 5x² - 2x - 4

Therefore, we can conclude that the quadratic form ax² + bx + c for the given set of factors is 5x² - 2x - 4.

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Answer:

Step-by-step explanation:

R= 2,1 Q= 3,3 P= 1,4

Answer:

C. f(4)=5

Step-by-step explanation:

I got it right on EDG.

Answer:

QT = 13

Step-by-step explanation:

since R is the midpoint of QS, QR = RS = 4

QT = RT + QR = 9 + 4 = 13

Answer:

8

Step-by-step explanation:

2(20-8x)=5x-2

40-16x=5x-2

42=21x

x=2

HK=5x-2 = 5(2)-2 = 10-2 = 8

The correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

To prove that \(BC^2 = AB^2 + AC^2\), we can use the triangle similarity and the Pythagorean theorem. Here's a step-by-step explanation:

Given triangle ABC with right angle at A and segment AD perpendicular to segment BC.

By triangle similarity, triangle ABD is similar to triangle ABC. This is because angle A is common, and angle BDA is a right angle (as AD is perpendicular to BC).

Using the proportionality of similar triangles, we can write the following ratio:

\($\frac{AB}{BC} = \frac{AD}{AB}$\)

Cross-multiplying, we get:

\($AB^2 = BC \cdot AD$\)

Similarly, using triangle similarity, triangle ACD is also similar to triangle ABC. This gives us:

\($\frac{AC}{BC} = \frac{AD}{AC}$\)

Cross-multiplying, we have:

\($AC^2 = BC \cdot AD$\)

Now, we can substitute the derived expressions into the original equation:

\($BC^2 = AB^2 + AC^2$\\$BC^2 = (BC \cdot AD) + (BC \cdot AD)$\\$BC^2 = 2 \cdot BC \cdot AD$\)

It was made possible by cross-product property.

Therefore, the correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

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let number of green balls= x

let number of orange balls=x+4

x+x+4=38

2x=38-4

2x=34

x=17

number of green balls=17

number of orange balls=21

Answer:

Area = 7822.61542 km²

Step-by-step explanation:

Área of a circle is:

area = π (d/2)²

π = 3.1416

d = diameter

In this case:

area = 3.1416 * (99.8/2)²

area = 3.1416 * 49.9²

area = 3.1416 * 2490.01

area = 7822.61542km²

Answer:

The answer is D.............

Answer:

Identity Property of Zero

The identity property of 0 states that if you add or subtract 0 from any number, the number will always stay the same. Here are some examples involving whole numbers: 3+0=3 7−0=7 Therefore, x+0=0+x=x. This is also known as the additive identity property of 0.

Step-by-step explanation:

Hope it helps :)

The group of measures which would lead to the provided conclusion is the range is 7, the mean of the data is 12, the median is 12 and the mode is 11.

Given that, the data is around 12. If another measurement were taken, it would probably be around 12.

We need to find which group of measures would lead to this conclusion.

The mean of the data is the average value of the given data. The mean of the data is the ratio of the sum of all the values of data to the total number of values of data.

The median of the data is the middle value of the data set when it arrange in ascending or descending order. The data is around 12 which suggests that the median is 12.

Median=12

The mode of a data set is the value, which occurs most times for that data set. The value which has the highest frequency in the given set of data is known as the mode of that data set.

Mean and mode is around the median. For this case, the mean of the data is 12 and the mode is 11.

Mode=11

Mean=12

Thus, the group of measures which would lead to the provided conclusion is the range is 7, the mean of the data is 12, the median is 12 and the mode is 11.

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