Data was collected from 32 random students on the number of hours spent studying for the final and their corresponding exam score in a statistics class. If a 99% confidence interval for resulted in (3.59, 6.96), what is the most you would expect the exam score to increase by if the student studied an extra 3 hours

Answer:

9

Step-by-step explanation:

31-4= 27

27/3 = 9

3(9)+4=31

Answer:

The magnitude is sqrt((-4)^2 + (-9)^2) = 9.85. The angle is atan(-9/-4) = 180 deg + 66 deg = 246 deg = -114 deg.

Step-by-step explanation:

hope it help

Answer:

9.85

Step-by-step explanation:

|v|= √9²+(-4)²

=√81+16

=√97

|v|= 9.85

Answer:

Step-by-step explanation:

Comment

The surface area for a sphere is 4 pi * r^2

Givens

Surface Area X = 1808.64

Surface Area T = 452.16

Solution

Sphere X

Surface Area = 4 pi r^2

Surface Area X = 4 * 3.14

1808.64 = 12.56 * r^2                          Divide both sides by 12.56

1808.64/12.56 = 12.56 r^2/12.56

r^2 = 144                                              Take the square root of both sides

√^2  = √144

r = 12

Sphere T

Surface Area = 4 pi r^2

452.16  = 12.56 r^2                              Divide by 12.56

452.16 / 12.56 = 12.56 r^2/12.56

r^2 = 36                                                Take √ of both sides

√r^2 = √36

r = 6

Conclusion

radius x: radius T :: 12/6

radius x: radius T :: 2/1    

Answer:

Option (4)

Step-by-step explanation:

Transformations like translation, rotation, dilation and reflection are the examples of rigid transformations.

Since, size and shape remains unchanged in the rigid transformation,

Image of a parallelogram will remain the same (congruent) after the given transformations.

Therefore, Option (4) will be the answer.

Answer:

1, .8, .5

Step-by-step explanation:

Anything larger than 0 is positive

True. If p(x) is the Taylor series for f centered at 0, then p(x-1) is not the Taylor series for f centered at 1. Instead, to obtain the Taylor series for f centered at 1, you would need to compute a new series with the center shifted to 1.

True. Shifting the center of a Taylor series by adding or subtracting a constant simply results in a new Taylor series centered at the shifted point. In this case, we are shifting the center from 0 to 1 by replacing x with (x-1) in the Taylor series for f, resulting in p(x-1).
In mathematics, the Taylor series or Taylor expansion of a function is an infinite number of points defined by the function at one point. For most ordinary functions, the partial function and its Taylor series are equal at point. The first n + 1 terms of the Taylor series form an n-order polynomial called the nth-order Taylor polynomial function. Taylor polynomials are generally approximate for functions that get better as n increases. Taylor's theorem provides a quantitative estimate of the resulting error using this approach. If the series of Taylor functions converge, the sum is the limit of an infinite number of Taylor polynomials.

A function can diverge from the equation of the Taylor series even if the Taylor series converges. A function is the definition of a point x if it is equal to the sum of the Taylor series over an open interval (or opening in the complex plane) containing x. This means that transactions are resolved anywhere on the clock (or disk).

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Answer:

B

Step-by-step explanation:

g(x)=(4-4)²

g(x) =0

and f(x)=x²

f(x)=0²

Answer:

B 2

Step-by-step explanation:

Because the leading term makes the difference on whether a parabola opens upward or downward.

If the leading coefficient of the leading term (which is 2) is negative it opens downward. If it is positive like it is in the equation then it opens upward.

Hope that helps :)

For the normal approximation to be valid, the sample size should be at least 30, which means that n should be greater than or equal to 30.

Assuming that the probability that each spin points up or down is 0.5, and we have n spins, then the probability of exactly n of them pointing up is given by

P(n) = (n C n) * (0.5)^n = (0.5)^n, where (n C n) is the number of ways to choose n items out of n, which is simply 1.

If n is large, the probability can be approximated using the normal distribution with mean and variance given by

μ = np = n * 0.5σ² = np(1 - p) = n * 0.25T he probability can be approximated as:

P(n) ≈ N(μ, σ) = N(np, sqrt(np(1 - p))), where N is the normal distribution with mean np and variance np(1 - p). Additional conditions for the approximation to be valid:

Therefore, for the normal approximation to be valid, the sample size should be at least 30, which means that n should be greater than or equal to 30.

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The ways in which companies can attract and retain employees are given below.

The term human resources (HR) refers to the department responsible for managing employee-related resources.

It's an essential partner in an organization's success.

Given is that to answer some ways in which companies can attract and retain employees.

The ways in which companies can attract and retain employees are -

Therefore, the ways in which companies can attract and retain employees are given above.

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The sample variance for the given data is 4.4 minutes. This corresponds to option e. in the list of choices provided.

The sample variance is a measure of how much the individual data points in a sample vary from the mean.

It is calculated by finding the average of the squared differences between each data point and the mean.

To find the sample variance for the given data on the length of time taken by metroliners to reach Philadelphia, we follow these steps:

Calculate the mean (average) of the data set:

Mean = (93 + 89 + 91 + 87 + 91 + 89) / 6 = 540 / 6 = 90

Subtract the mean from each data point and square the result:

(93 - 90)^2 = 9

(89 - 90)^2 = 1

(91 - 90)^2 = 1

(87 - 90)^2 = 9

(91 - 90)^2 = 1

(89 - 90)^2 = 1

Calculate the sum of the squared differences:

9 + 1 + 1 + 9 + 1 + 1 = 22

Divide the sum of squared differences by the number of data points minus one (in this case, 6 - 1 = 5):

Variance = 22 / 5 = 4.4

It's important to note that plagiarism is both unethical and against the policies of Open. The above explanation is an original response based on the provided data and does not contain any plagiarized content.

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The rational function represented in the given graph is; f(x) = 1/(x - 4)

From the given graph , the vertical asymptote is at x = 4

Let's find out the vertical asymptote of each function

To find out vertical asymptote we set the denominator = 0

A) x + 4 = 0

x = -4

This is not correct

B) 4x = 0

x = 0

Not correct

C) Denominator does not have a variable and so is also incorrect

D) x - 4 = 0

x = 4

Thus, this is correct

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The probability that a randomly chosen family with two or more children has children of the same gender is 1/2

To find the probability that a randomly chosen family with two or more children has children of the same gender, we can use the following information:

The probability of having a boy is 1/2 and the probability of having a girl is 1/2

The number of children is 2 or more

The sample space is all possible families with two or more children.

We can use the formula of conditional probability:

P(A|B) = P(A and B) / P(B)

Where A is the event of having children of the same gender, and B is the event of having two or more children.

We can use the formula of conditional probability to find the probability of having children of the same gender given that they have two or more children.

P(A and B) = P(A) * P(B|A)

Where P(A) is the probability of having children of the same gender, which is 1/2.

P(B|A) is the probability of having two or more children given that they have children of the same gender, which can be found using the formula of conditional probability as well.

P(B|A) = 1 - P(not B|A)

Where P(not B|A) is the probability of having less than two children given that they have children of the same gender.

Given that the family has children of the same gender, the probability of having less than two children is 0, because if the family has children of the same gender, it implies that the family has at least two children.

So, P(B|A) = 1- 0 = 1

Now we can substitute these values to the first equation:

P(A|B) = P(A) * P(B|A) / P(B) = (1/2) * 1 / P(B)

The only thing left to find is P(B) which is the probability of having two or more children. We don't have the exact number, but we know that the number of children is 2 or more, so P(B) is greater than 0.

We can say that P(A and B) = P(A) * P(B|A) = (1/2) * 1 = 1/2

Thus, the probability that a randomly chosen family with two or more children has children of the same gender is 1/2.

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The average temperature in December is 0 degrees Celsius.

We have in July, the average temperature in one US city equals to 29 degrees Celsius and by December ,the average temperature had fallen by 29 degrees Celsius.

We have investigate why the average temperature in dec was 0 degrees Celsius.

Degree of hotness or coldness measured on a definite scale is called Temperature. When the temperature of the body is high it is called hot body and when it is low it is called cold body.

According to question, we have -

Average temperature in July = 29 degrees Celsius.

The fallen average temperature =  29 degrees Celsius.

Let the average temperature of December be x. Then -

x = Average temperature in July - fallen average temperature

x = 29 - 29 = 0

Hence, the average temperature in December is 0 degrees Celsius.

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Answer:

The value of x so f (x) = 7 is 5.

Step-by-step explanation:

Statement is true because the corresponding sides are congruent. The answer is: BA = LN.

What is Triangle?

A triangle is a closed, two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and is used in many areas of mathematics, science, and engineering.

Since triangle ABC and triangle LMN have congruent corresponding sides, we know that they are similar triangles. This means that their corresponding angles are also congruent.

We are given that angle BAC is 58 degrees and angle MLN is 78 degrees. Since corresponding angles are congruent, this means that angle BAC is congruent to angle MLN.

Therefore, triangle ABC and triangle LMN are similar triangles with two pairs of corresponding congruent angles. This means that all corresponding sides are proportional.

Since AC = LN and BA = ML, we know that the ratio of the lengths of corresponding sides is:

AC / LN = BA / ML

Substituting the given values, we get:

1 = 1

This statement is true because the corresponding sides are congruent.

Therefore, the answer is: BA = LN.

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The area of the rectangular parking lot is 929.03 square meters.

Use the formula for the area of a rectangle to calculate the area of the rectangular parking lot, which is given as:

Area = length × width

We know that the parking lot is 67.5 ft wide and 148 ft long, the area can be calculated as follows:

Area = 67.5 ft × 148 f

t= 9990 sq. ft

However, the question asks for the area in square meters, so we need to convert square feet to square meters. 1 square foot is equal to 0.092903 square meters, so we can use this conversion factor to convert square feet to square meters.

Area in square meters = Area in square feet × 0.092903

= 9990 sq. ft × 0.092903

= 929.03 sq meters

Therefore, the area is 929.03 square meters.

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Answer:

26.5

Step-by-step explanation:

if you see the picture, just by counting we know that:

triangle 1

\(b=3\\\\h=3\\\\A_1=\frac{3*3}{2}=4.5\)

triangle 2

\(b=2\\\\h=2\\\\A_2=\frac{2*2}{2}=2\)

rectangle 3

\(b=5\\\\h=4\\\\A_3=5*4=20\)

the total area is

\(A_T=A_1+A_2+A_3\\\\=4.5+2+20=26.5\)

Answer:

26.5

Step-by-step explanation:

Make the shape into 2 triangles and 1 rectangle

Triangle 1

b = 3

h = 3

3 x 3 /2 = 4.5 ( divide 3x3 which is 9 by 2)

Triangle 2

b = 2

h = 2

2 x 2 /2 = 2 ( divide 2x2 which is 4 by 2)

Rectangle

b = 5

h =4

5 x 4 = 20

( the rectangle isn't divided by 2)

4.5 + 2 = 20 = 26.5 (Add all the areas)

Hope this helpsss

The foci of the ellipse given by the equation 225x^2 + 144y^2 = 32400 can be found by identifying the major and minor axes of the ellipse and using the formula for the foci coordinates. The foci of the ellipse are located at (±c, 0). Therefore, the foci are approximately (±15.87, 0).

The equation of the ellipse can be rewritten in standard form:

(225x^2)/32400 + (144y^2)/32400 = 1

We can identify the major and minor axes of the ellipse by comparing the coefficients of x^2 and y^2. The square root of the denominator gives the lengths of the semi-major axis (a) and semi-minor axis (b) of the ellipse.

a = sqrt(32400/225) = 24

b = sqrt(32400/144) = 18

The foci of the ellipse can be calculated using the formula:

c = sqrt(a^2 - b^2)

c = sqrt(24^2 - 18^2)

c = sqrt(576 - 324)

c = sqrt(252)

c ≈ 15.87

The foci of the ellipse are located at (±c, 0). Therefore, the foci are approximately (±15.87, 0).

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Answer:

C

Step-by-step explanation:

0.060819 inches per second is the radius of the balloon increasing at the instant that the balloon has a radius of 12 inches

Given that

A large helium balloon is being inflated at the rate of 110 cubic inches per second

radius = 12

volume = \(\frac{4}{3}\) \(\pi\)\(r^{3}\)

            = 4/3 \(\pi\) \((12)^{3}\)

            =7234.55

V = 4/3 πr³

dV/dt = 4/3 (3πr² dr/dt) = 4πr² dr/dt

dr/dt = dV/dt / (4πr²)

dr/dt = dV/dt / (4πr²)

= 110/(4\(\pi\)×(\(12^{2}\)))

= 0.060819 inches per second

0.060819 inches per second is the radius of the balloon increasing at the instant that the balloon has a radius of 12 inches

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30% of the eligible students voted.

It is given to us that 650 students at the high school are eligible to vote and 195 of them voted in the last election.

Now let us take the percent of students to be 'x'

x% of 650 students voted whose value is given to be 195.

So the equation can be written as

( x / 100 ) * 650 = 195

x = ( 195 * 100 ) / 650

x = 30

Therefore 30% of  the eligible students voted in the last election.

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The array depicted displays the division represented by the equation

20 ÷ 5 = 4

Division is one of the four basic mathematical operators other include

addition

subtraction and

multiplication

Multiplication is the inverse or opposite of division, this means that when reverting the process of division we et to multiplication

In the array the number to be divided is the counting the whole small boxes which is 20.

Division is used to group the numbers in groups of 4 showing 5 divisions in group of four

This may also be 4 divisions in group of 5

Mathematically this written as

20 / 5 = 4

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The experimental probability of drawing a spade is 0.2

When we perform an experiment N times, and we got a given outcome K times, the experimental probability of said outcome is given by the quotient:

P = K/N

Here the experiment is performed:

N = 6 + 4 + 7 + 3 = 20 times

And a spade is drawn 4 times, then the experimental probability is:

P = 4/20 = 1/5 = 0.20

The correct option is the second one.

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Applying the tangent theorem and the Pythagorean theorem, the length of AB is 45 units.

According to the tangent theorem, a tangent will form a right angle with the radius of a circle at the point of tangency.

Tangents are perpendicular to the radius at the tangent point

Triangle ABO is therefore a right triangle.

AO = CO = 24 units

OC is also radius of circle O,

Therefore OC = 24

OB = OC + CB = 24 + 27 = 51

OB = √( OA² + AB²)      

AB = √( OB²  - OA²)  

= √( 2601 - 576 )

= √2025   = 45

Therefore, the value of AB is 45.

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Answer:

200

Step-by-step explanation:

Mr. Jacob's class reads every day for 20 minutes, which ends up being 20 * 28 because there are 28 days in four weeks. That equals 560

Mrs. Clark's class reads 3 days a week for 4 weeks, so 3*4 = 12. The number of minutes her class reads is 30 minutes so 30*12 = 360.

560-360=200

Answer:

2.2%

Step-by-step explanation:

Use the percent error formula:

% error = | (approx - exact) ÷ approx | x 100

Plug in the approx. and exact values:

| (8.9 - 8.7) ÷ 8.9 | x 100

| (0.2) ÷ 8.9 | x 100

= 2.2

So, the percent error is 2.2%

Answer:1.2%

Step-by-step explanation:

∣experimental−actual∣

​

×100

The formula

∣

8.7

−

8.6

∣

8.6

×

100

8.6

∣8.7−8.6∣

​

×100

Plug in values

∣

0.1

∣

8.6

×

100

8.6

∣0.1∣

​

×100

Subtract

0.1

8.6

×

100

8.6

0.1

​

×100

Take the absolute value

0.0116279

×

100

0.0116279×100

Divide

1.16279

1.16279

Multiply by 100

1.2

%

1.2%