A utility company wants to compare the variability of the wind speeds at two proposed sites for their new wind based power plant. Past studies show that the wind speed at each site has a normal distribution. a random sample of n1=13 wind speed recordings taken at random intervals from site one has a mean speed of xbar1=14.2 mph and a standard deviation of s1=2.5 mph, and a random sample of n2=7 wind speed recordings taken at random intervals from site two has a mean speed of xbar2=15.8 mph and a standard deviation of s2=5.2 mph. If the company wants to test for the equality of the two population variances at 10% significance level, what will be the rejection region(s) at 10% significance level? (Note: TS=Test Statistic)

Answer:

brittany is 42

Step-by-step explanation:

if he is 40 years older than her and the sum of there ages is 82

82-40 = 42

Considering the sequences given, the first number that appears in both sequences is given by: 45.

The rule is multiply by 3 starting from 5, hence the numbers are:

(5, 15, 45, 135, ...).

The rule is add 9 starting from 18, hence the numbers are:

(18, 27, 36, 45, ...).

45 is the first number that appeared in both sequences.

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Algebra transformation

for  Graph1 f(x)=f(x)+4

for  Graph2 f(x)=-f(x-4)

for  Graph3 f(x)=f(x-7)

for  Graph4 f(x)=f(x-2)-5

In mathematics, the reflection of a graph is a transformation that produces a mirror image of the original graph across a specific line or point. The line or point across which the reflection occurs is called the axis of reflection.

Graph1

Transform the graph by +4 units in y direction.

f(x)=f(x)+4

Graph2

Transform the graph by +4 units in x direction.

f(x)=f(x-4)

Now take the reflection of graph about x axis

f(x)=-f(x-4)

Graph3

Transform the graph by +7 units in x direction.

f(x)=f(x-7)

Graph5

Transform the graph by -5 units in y direction.

f(x)=f(x)-5

Now Transform the graph by -2 units in x direction.

f(x)=f(x-2)-5

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According to the given information, the letter that comes next in the given alphanumeric series is "N".

What is alphanumeric series?

An alphanumeric series is a sequence of letters and/or numbers that follows a certain pattern or rule. For example, "A, B, C, D, E..." is an example of an alphabetical series, and "1, 3, 5, 7, 9..." is an example of a numerical series. An alphanumeric series may combine both letters and numbers, such as "A1, B2, C3, D4, E5...". The pattern or rule followed by an alphanumeric series may be based on numerical or alphabetical order.

The given series V, Q, M, J, H, ... follows a pattern where each letter is the 6th letter from the previous letter. So, the next letter in the series would be 6 letters after H, which is N.

Therefore, the letter that comes next in the given alphanumeric series is "N".

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Answer:

Step-by-step explanation:

Let

T = number of trees

A = number of acorns

Given:

A =  18T + 4 ...........................(1)

A = 20T -4 .........................(2)

Equate A from (1) and (2)

20T-4 = 18T+4

simplify and solve for T

20T - 18T = 4+4

2T = 8

T = 4 trees

A = 18T + 4 = 72+4 = 76 acorns, or

A = 20T - 4 = 80 - 4 = 76 acorns.

If an object is dropped from a height of 40.6 meters, then 28.21m/s is the velocity does it hit the ground

Velocity defines the direction of the movement of the body or the object. Speed is primarily a scalar quantity.

Velocity is essentially a vector quantity. It is the rate of change of distance.

Given,

An object is dropped from a height of h meters and hits the ground with a velocity of v meters per second. Then v =⎷19.6h

an object is dropped from a height of 40.6 meters

h=40.6

Now substitute h value in V

v =⎷19.6×40.6=√795.76

v=28.21

Hence, 28.21m/s is the velocity does it hit the ground

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Answer:

should be - 8

Step-by-step explanation:

-2*-2=4 4*-2=-8

Answer:

Sandy should have evaluated (negative 2) cubed as –8.

Step-by-step explanation:

Got it right on the test

Answer: 2.25

Step-by-step explanation: divide 13.50 by 6 and then you get 2.25 to check you can do 2.25 times 6 and get 13.50

Answer:

478

Step-by-step explanation:

559.45-457.41=102.04

102.04/559.45*100

approximately 478

The sum of the measures of the interior angles of a nonagon is 1260 degrees

The measure of each interior angle of a regular octagon is 135 degrees

A nonagon is a polygon with nine sides, and the formula to calculate the sum of the measures of the interior angles of a polygon with n sides is:

Sum of interior angles = (n-2) x 180 degrees

Therefore, the sum of the measures of the interior angles of a nonagon is:

Sum of interior angles = (9-2) x 180 degrees = 1260 degrees

An octagon is a polygon with eight sides, and the formula to calculate the measure of each interior angle of a regular polygon with n sides is:

Measure of each interior angle = (n-2) x 180 degrees / n

Therefore, the measure of each interior angle of a regular octagon is:

Measure of each interior angle = (8-2) x 180 degrees / 8 = 135 degrees

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Answer:. 151/99

Step-by-step explanation:

Take the repeating digits from the decimal equivalent, 52 and place them as the numerator of a fraction with 99 as the denominator. That is 52/99

We can verify this value by doing the long division, or enter the values as 52÷99 on a calculator.

For the improper fraction:

Convert the whole number, 1, to its equivalent, 99/99. ( If the whole number is other than 1, multiply it by the denominator and use the product as the numerator. )

Add the numerators: 52 + 99 = 151

Our improper fraction equivalent of 1.525252 is 151/99

Answer:

d,c,a

Step-by-step explanation:

guess it helps

The total distance of the obstacle course can be calculated by finding the distance between each pair of consecutive points and adding them up. The distance between two points (x1, y1) and (x2, y2) can be calculated using the formula: distance = sqrt((x2 - x1)^2 + (y2 - y1)^2).

Using this formula, we can calculate the distances between each pair of consecutive points as follows:

Start to Tire Race: distance = sqrt((-40 - (-40))^2 + (-30 - (-10))^2) = 20 yards

Tire Race to Rope Climb: distance = sqrt((40 - (-40))^2 + (-30 - (-30))^2) = 80 yards

Rope Climb to Monkey Bars: distance = sqrt((40 - 40)^2 + (20 - (-30))^2) = 50 yards

Monkey Bars to Finish: distance = sqrt((10 - 40)^2 + (20 - 20)^2) = 30 yards

Adding up all these distances, we get a total distance of 20 + 80 + 50 + 30 = 180 yards for the obstacle course.

The set of points related to an exponential function and matched with set of translated points are, respectively:

(x, y) = (- 1, 0.5) → (x', y') = (2, - 1.5)

(x, y) = (0, 1) → (x', y') = (3, - 1)

(x, y) = (2, 4) → (x', y') = (5, 2)

(x, y) = (3, 8) → (x', y') = (6, 6)

(x, y) = (1, 2) → (x', y') = (4, 0)

(x, y) = (- 2, 0.25) → (x', y') = (1, - 1.75)

According to statemente, we find the case of set of points related to an exponential function and a set of translated points, after a quick inspection we derive the transformation rule:

Horizontal translation: 3 units right, vertical translation: 2 units down.

Now we check the statement on each ordered pair:

(x, y) = (- 1, 0.5):

(x', y') = (- 1, 0.5) + (3, - 2) = (2, - 1.5)

(x, y) = (0, 1):

(x', y') = (0, 1) + (3, - 2) = (3, - 1)

(x, y) = (2, 4):

(x', y') = (2, 4) + (3, - 2) = (5, 2)

(x, y) = (3, 8):

(x', y') = (3, 8) + (3, - 2) = (6, 6)

(x, y) = (1, 2):

(x', y') = (1, 2) + (3, - 2) = (4, 0)

(x, y) = (- 2, 0.25):

(x', y') = (- 2, 0.25) + (3, - 2) = (1, - 1.75)

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If you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.

To calculate the Social Security tax, we need to know the tax rate for Social Security and the taxable wages. Let's assume the Social Security tax rate is 6.2% for both the employee and the employer.

Given that your taxable wages for Social Security purposes are $1,100, and your previous taxable wages are $102,000, we can determine the Social Security tax amount.

First, we need to calculate the Social Security tax on the previous taxable wages of $102,000. Multiply $102,000 by 6.2% (0.062) to find the Social Security tax for that amount:

Social Security tax = $102,000 x 0.062 = $6,324

Next, we calculate the Social Security tax on the current taxable wages of $1,100. Multiply $1,100 by 6.2% to find the tax amount:

Social Security tax = $1,100 x 0.062 = $68.20

Therefore, if you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.

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The minor arcs of the circle C are given as follows:

The arcs of a circle can be classified as minor arcs or major arcs, depending on their angle measures, as follows:

The entire circumference of the circle is of 360º, hence we have that segment LN, connecting two points on the circumference of the circle through the center, represents the diameter of the circle, with an arc length of 180º.

Hence the minor arcs are all the arcs that are smaller than LN, given as follows:

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Answer:

The probability that a call lasts less than 4 minutes  

 P(X<4) = P(Z<-1.25) = 0.1056

Step-by-step explanation:

Step(i):-

Given mean of the population = 6.5 minutes

Given standard deviation of the Population = 2 minutes

Let 'X' be the random variable in normal distribution

Given X = 4

\(Z= \frac{x-mean}{S.D} = \frac{4-6.5}{2} = -1.25\)

Step(ii):-

The probability that a call lasts less than 4 minutes

P(X<4) = P(Z<-1.25)

           = 1-P(z>1.25)

          = 1 - ( 0.5 +A(1.25)

         = 1-0.5 - A(1.25)

       = 0.5 - 0.3944    ( from normal table)

       = 0.1056

Final answer:-

The probability that a call lasts less than 4 minutes  

 P(X<4) = P(Z<-1.25) = 0.1056

Answer: Hope this helps, these are some tips for investing and the different types of them definitions.

Step-by-step explanation:

Take Some Notes

Strategy 1: Value Investing

Strategy 2: Growth Investing

Strategy 3: Momentum Investing

Strategy 4: Dollar-Cost Averaging

Answer:

The probability that, in successive drawing of chips, the colors of the first four chips alternate = 0.0751

Step-by-step explanation:

Step 1:

The probability that, in successive drawing of chips, the colors of the first four chips alternate, can occur in two ways: RED-WHITE-RED-WHITE (RWRW) or WHITE-RED-WHITE-RED (WRWR).

Step 2:

Given that an urn contains three white and four red chips and that each time we draw a chip, we look at its color. If it is red, we replace it along with two new red chips, and if it is white, we replace it along with three new white chips.

Probability of RWRW is given as follows:

Probabilty of the first being a red = 4/7

Probability of the next being a white = 3/9 = 1/3

Probability of the next being a red = 6/12 = 1/2

Probability of the next being a white = 6/14 = 3/7

Thus, probability of RWRW = 4/7 × 1/3 × 1/2 × 3/7 = 0.0408

Probability of WRWR is given as follows:

Probabilty of the first being a white = 3/7

Probability of the next being a white = 4/10 =2/5

Probability of the next being a red = 6/12 = 1/2

Probability of the next being a white = 6/15 = 2/5

Thus, probability of WRWR = 3/7 × 2/5 × 1/2 × 2/5 = 0.0343

Step 3:

Probability of RWRW or WRWR = 0.0408 + 0.0343 = 0.0751

Therefore, the probability that, in successive drawing of chips, the colors of the first four chips alternate = 0.0751

Answer: z=1−x+w/r

Step-by-step explanation:

Subtract x from both sides.

z-w/r=1-x

Add w/r to both sides.

z=1−x+w/r

hope i helped

-lvr

Answer: Graph A

Step-by-step explanation:

Graph A. If you find the y-intercept by plugging in 0 for x, you get 2.5 = y, so therefore graph A is correct.

The solution for A(3) in the function when the function A(x) = 4 − (x + 3)⁵ is -772

From the question, we have the following equation that can be used in our computation:

A ( x ) = 4 − ( x + 3 )^5

To make the equation legible, we need to rewrite it

So, we have the following representation

A(x) = 4 − (x + 3)⁵

Also from the question, we have

A(3)

This means that the value of x is 3, and we calculate A(x) when x = 3

Substitute the known values in the above equation, so, we have the following representation

A(3) = 4 − (x + 3)⁵

So, we have the following equation

A(3) = 4 − (3 + 3)⁵

There are constants to add or subtract to both sides of the equation

However, there is no factor to multiply or divide from both sides of the equation

So, we have the following representation

A(3) = 4 − (6)⁵

Solving further, we have

A(3) = 4 − 7776

Evaluate the difference

A(3) = −7772

Hence, the solution is −7772

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Possible question

Given A ( x ) = 4 − ( x + 3 )^5, find A(3).

The total surface area of solid is,

S = 220 m²

And,  The volume of the prism is, 200 m³

We have to given that;

A solid prism is shown in figure.

Since, The surface area of a prism is,

S = (2 × Base Area) + (Base perimeter × height)

Where, "S" is the surface area of the prism.

Hence, We get;

base area = 5 x 10 = 50 m²

height = 4 m

Base Perimeter = 2 (5 + 10) = 30

Hence, We get;

S = (2 x 50) + (30 x 4)

S = 100 + 120

S = 220 m²

Since, A prism is a solid shape that is bound on all its sides by plane faces. The volume of a prism is expressed as;

V = base area × height.

Now, For given figure,

Volume of the prism = base area × height

base area = 5 x 10 = 50 m²

height = 4 m

Hence, Volume = 50 × 4 m³

= 200 m³

Thus, The volume of the prism is, 200 m³

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Answer:

k = 1/2

Step-by-step explanation:

2y = x + 8

y = (1/2)x + 4

slope = 1/2

y-intercept = 4

y - (1/2)x = 2

y =  (1/2)x + 2

slope = 1/2

y-intercept = 2

2k = 4

k = 1/2

The Expression x^2 - 6x + 9 when x = 2 + i   is -2i

To evaluate the expression x^2 - 6x + 9 when x = 2 + i, we substitute the value of x into the expression:

(2 + i)^2 - 6(2 + i) + 9

Simplifying the first term, we get:

(2 + i)^2 = 2^2 + 2(2)(i) + i^2 = 4 + 4i + i^2

Since i^2 = -1, we can substitute that in and simplify further:

(2 + i)^2 = 4 + 4i - 1 = 3 + 4i

Now we substitute this into the original expression:

(2 + i)^2 - 6(2 + i) + 9 = (3 + 4i) - 6(2 + i) + 9

Simplifying further, we get:

= 3 + 4i - 12 - 6i + 9

= 0 - 2i

= -2i

Therefore, the value of x^2 - 6x + 9 when x = 2 + i is -2i.

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Answer:

\(\begin{aligned}x &= 16\sqrt3 \\ &\approx 27.7\end{aligned}\)

Step-by-step explanation:

We can see that the longer leg (a) of a right triangle is half of the circle's radius. Since we are given the other two sides of the triangle (shorter leg and hypotenuse), we can solve for the length of the longer leg using the Pythagorean Theorem:

\(a^2 + b^2 = c^2\)

↓ plugging in the given values

\(a^2 + 2^2 = 14^2\)

↓ subtracting 2² from both sides

\(a^2 = 14^2 - 2^2\)

\(a^2 = 196 - 4\)

\(a^2 = 192\)

↓ taking the square root of both sides

\(a = \sqrt{192\)

↓ simplifying the square root

\(a = \sqrt{2^6 \cdot 3\)

\(a = 2^{\, 6 / 2} \cdot \sqrt3\)

\(a = 2^3\sqrt3\)

\(a = 8\sqrt3\)

Now, we can solve for the radius (x) using the fact that the longer leg of the triangle is half of it.

\(a = \dfrac{1}{2}x\)

↓ plugging in the a-value we solved for

\(8\sqrt3 = \dfrac{1}2x\)

↓ multiplying both sides by 2

\(\boxed{x = 16\sqrt3}\)