In tests of a computer component, it is found that the mean time between failures is 520 hours. A modification is made which is supposed to increase the time between failures. Tests on a random sample of 10 modified components resulted in the following times (in hours) between failures. 518 548 561 523 536 499 538 557 528 563 At the 0.05 significance level, test the claim that for the modified components, the mean time between failures is greater than 520 hours. Use the P-value method of testing hypotheses.
H0:
H1:
Test Statistic:
Critical Value:
Do you reject H0?
Conclusion:
If you were told that the p-value for the test statistic for this hypothesis test is 0.014, would you reach the same decision that you made for the Rejection of H0 and the conclusion as above?

Answer:

y = [tex]\sqrt[3]{x-5}[/tex]

Step-by-step explanation:

To find the inverse of any function you basically switch x and y.

function = y = x^3 + 5

Now we switch x and y

x = y^3 +5

Solve for y,

x - 5 = y^3

switch sides,

y^3 = x-5

y = [tex]\sqrt[3]{x-5}[/tex]

Answer:

[tex]\Large \boxed{{f^{-1}(x)=\sqrt[3]{x-5}}}[/tex]

Step-by-step explanation:

The function is given,

[tex]f(x)=x^3 +5[/tex]

The inverse of a function reverses the original function.

Replace f(x) with y.

[tex]y=x^3 +5[/tex]

Switch variables.

[tex]x=y^3 +5[/tex]

Solve for y to find the inverse.

Subtract 5 from both sides.

[tex]x-5=y^3[/tex]

Take the cube root of both sides.

[tex]\sqrt[3]{x-5} =y[/tex]

Answer:

3/11

Step-by-step explanation:

In the above question, we have the following information

Total number of balls = 12

White balls = 4

Blue balls = 3

Red balls = 5

We are to find the chance of probability that if we select 3 balls, all the three are selected.

Hence,

Probability ( all the three balls are selected) = P(White ball) × P(Blue ball) × P( Red ball)

Probability ( all the three balls are selected) = 4/12 × 3/11 × 5/10

= 60/1320

= 1/22

The number of ways by which we can selected all the three balls is a total of 6 ways:

WBR = White, Blue, Red

WRB = White, Red, Blue

RBW = Red, Blue, White

RWB = Red, White, Blue

BRW = Blue, Red, White

BWR = Blue, White, Red

Therefore, the chance that all three are selected :

1/22 × 6 ways = 6/22 = 3/11

=======================================================

Explanation:

Check out the diagram below.

Draw a vertical number line with 0 at the center. The positive values are above it, while the negative values are below it.

Between -15 and -16, closer to -16, plot the value -15.8 to indicate Ben's position. I have done so as the point B.

We move 4.2 units up to arrive at Cam's position

-15.8 + 4.2 = -11.6

So Cam is 11.6 meters below the surface of the water.

Answer:

[tex]X=\begin{bmatrix}5&3\\ -3&2\end{bmatrix}[/tex]

Step-by-step explanation:

We are given the following matrix equation, from which we have to isolate X and simplify this value.

[tex]\begin{bmatrix}2&4\\ \:\:\:5&4\end{bmatrix}X\:+\:\begin{bmatrix}-8&-8\\ \:\:\:12&1\end{bmatrix}=\:\begin{bmatrix}-10&6\\ \:\:\:25&24\end{bmatrix}[/tex]

To isolate X, let us first subtract the second matrix, as demonstrated below, from either side. Further simplifying this equation we can multiply either side by the inverse of the matrix being the co - efficient of X, isolating it in the doing.

[tex]\begin{bmatrix}2&4\\ 5&4\end{bmatrix}X=\begin{bmatrix}-10&6\\ 25&24\end{bmatrix}-\begin{bmatrix}-8&-8\\ 12&1\end{bmatrix}[/tex] (Simplify second side of equation)

[tex]\begin{bmatrix}-10&6\\ 25&24\end{bmatrix}-\begin{bmatrix}-8&-8\\ 12&1\end{bmatrix}=\begin{bmatrix}\left(-10\right)-\left(-8\right)&6-\left(-8\right)\\ 25-12&24-1\end{bmatrix}=\begin{bmatrix}-2&14\\ 13&23\end{bmatrix}[/tex] ,

[tex]\begin{bmatrix}2&4\\ 5&4\end{bmatrix}X=\begin{bmatrix}-2&14\\ 13&23\end{bmatrix}[/tex] (Multiply either side by inverse of matrix 1)

[tex]X=\begin{bmatrix}2&4\\ 5&4\end{bmatrix}^{-1}\begin{bmatrix}-2&14\\ 13&23\end{bmatrix}=\begin{bmatrix}5&3\\ -3&2\end{bmatrix}[/tex]

Our solution is hence option c

Answer:

a. 4

Step-by-step explanation:

-1(-4) = 4

Answer:

A 4

Step-by-step explanation:

opposite of –4 = 4

Answer:

There are 6566 ways to choose 22 croissants with at least one plain croissant, at least two cherry croissants, at least three chocolate croissants, at least one almond croissant, at least two apple croissants, and no more than three broccoli croissants.

Step-by-step explanation:

Given:

There are 5 types of croissants:

plain croissants

cherry croissants

chocolate croissants

almond croissant

apple croissants

broccoli croissants

To find:

to choose 22 croissants with:

at least one plain croissant

at least two cherry croissants

at least three chocolate croissants

at least one almond croissant

at least two apple croissants

no more than three broccoli croissants

Solution:

First we select

At least one plain croissant to lets say we first select 1 plain croissant, 2 cherry croissants, 3 chocolate croissants, 1 almond croissant, 2 apple croissants

So

1 + 2 + 3 + 1 + 2  = 9

Total croissants = 22  

So 9 croissants are already selected and 13 remaining croissants are still needed to be selected as 22-9 = 13, without selecting more than three broccoli croissants.

n = 5

r = 13

C(n + r - 1, r)

= C(5 + 13 - 1, 13)

= C(17,13)

[tex]=\frac{17! }{13!(17-13)!}[/tex]

= 355687428096000 / 6227020800 ( 24 )

= 355687428096000 / 149448499200

= 2380

C(17,13) = 2380

C(n + r - 1, r)

= C(5 + 12 - 1, 12)

= C(16,12)

[tex]=\frac{16! }{12!(16-12)!}[/tex]

= 20922789888000 / 479001600 ( 24 )

= 20922789888000  / 11496038400

= 1820

C(16,12) = 1820

C(n + r - 1, r)

= C(5 + 11 - 1, 11)

= C(15,11)

[tex]=\frac{15! }{11!(15-11)!}[/tex]

= 1307674368000 / 39916800 (24)

= 1307674368000 / 958003200

= 1307674368000 / 958003200

= 1365

C(15,11) = 1365

C(n + r - 1, r)

= C(5 + 10 - 1, 10)

= C(14,10)

[tex]=\frac{14! }{10!(14-10)!}[/tex]

= 87178291200 / 3628800 ( 24 )

= 87178291200 / 87091200

= 1001

C(14,10) = 1001

Adding them:

2380 + 1820 + 1365 + 1001 = 6566 ways

Answer:

x = 2

Step-by-step explanation:

This blue line seems to be horizontal, and so a line perpendicular would have to be vertical. The only vertical line that passes through (2, 6) would be x = 2.

The equation of the line perpendicular to the given line and passes through the point (2, 6) is x = 2.

Equation of a line in slope intercept form is y = mx + b, where m is the slope of the line and b is the y intercept, which is the y coordinate of the point where it touches the Y axis.

Given is a line that passes through the points (-8, -4) and (8, -4).

This line is parallel to the X axis.

A line parallel to X axis has the equation y = b.

The y coordinate is -4 throughout the line.

So equation of the line is y = -4.

A line perpendicular to the given line will be parallel to Y axis.

Parallel lines to Y axis has the equation of the form x = a.

Line passes through the point (2, 6).

x coordinate will be 2 throughout.

So the equation of the perpendicular line is x = 2.

Hence the required equation is x = 2.

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Answer:

5/17

Step-by-step explanation:

This is a question to calculate probability from odds. The formula is given as:

A formula for calculating probability from odds is P = Odds / (Odds + 1)

From the question , we are told that the odds of receiving a gift is

= 5:12

The probability of Jessica receiving a gift =

Probability = Odds / (Odds + 1)

P = 5/12 / ( 5/12 + 1)

P = (5/12)/ (17/12)

P = 5/12 × 12/17

= 5/17

Therefore, the probability of Jessica. receiving a gift is 5/17.

Answer:

There is enough evidence to reject the highway department executive's claim about the distribution of fatal accidents between each month, as the Variance is 14 and the Standard Deviation = 4 approximately.

There is a high degree of variability in the mean of the population as explained by the Variance and the Standard Deviation.

Step-by-step explanation:

Month       No. of              Mean       Squared

           Fatal Accidents  Deviation   Difference

Jan          8                       -4                  16

Feb        15                        3                   9

Mar         9                       -3                   9

Apr         8                       -4                  16

May       13                        1                    1

Jun         6                      -6                 36

Jul         17                       5                 25

Aug       15                       3                   9

Sep       10                      -2                   4

Oct        9                       -3                   9

Nov    18                          6                 36

Dec    12                          0                   0

Total 140                                         170

Mean = 140/12 = 12    Mean of squared deviation (Variance) = 170/12 = 14.16667

Standard deviation = square root of variance = 3.76386 = 4

The fatal accidents' Variance is a measure of how spread out the fatal accident data set is. It is calculated as the average squared deviation of the number of each month's accident from the mean of the fatal accident data set.  It also shows how variable the data varies from the mean of approximately 12.

The fatal accidents' Standard Deviation is the square root of the variance, and a useful measure of variability when the distribution is normal or approximately normal.

Step-by-step explanation:

Putting values

A = - 7(15 + 9)

A = - 7(24)

A = - 168

Answer:

Step-by-step explanation:

[tex]3h\left(2\right)+2k\left(3\right)\\\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\\\=3h\times \:2+2k\times \:3\\\\\mathrm{Multiply\:the\:numbers:}\:3\times \:2=6\\\\=6h+2\times \:3k\\\\\mathrm{Multiply\:the\:numbers:}\:2\times \:3=6\\\\=6h+6k[/tex]

Answer:

Answers for E-dge-nuityyy

Step-by-step explanation:

(h + k)(2) = 5

(h – k)(3) = 9

Evaluate 3h(2) + 2k(3) = 17

The probability that the 4 oldest people in the group were selected is based on combinatorics is 0.00303 or 0.303%.

Given that:

Find how many ways the 4 oldest people can be selected from the group.

Since the 4 oldest people are already determined, there is only 1 way to select them.

To calculate the probability, to determine the total number of ways to select 4 people from the group of 11. This can be found using the combination formula:

Number of ways to choose k items from n items :

C(n,k) = n! / (k!(n-k)!)

Calculate the total number of ways to select 4 people from the group:

Plugging n and k value from given data:

C(11,4 )= 11! / (4!(11-4)!)

On simplifications gives:

C(11, 4) = 330.

Calculate the probability:

Probability = Number of ways 4 oldest people selected / Total number of ways to select 4 people

Plugging the given data:

Probability = 1 / 330

Probability ≈ 0.00303 or 0.303%.

Therefore, the  probability that the 4 oldest people in the group were selected is based on combinatorics is 0.00303 or 0.303%.

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Answer: Given a sample of 200, we are 90% confident that the true proportion of people who watched educational TV is between 72.1% and 81.9%.

Step-by-step explanation:

[tex]\frac{154}{200} =0.77[/tex]

[tex]1-0.77=0.23[/tex]

[tex]\sqrt{\frac{(0.77)(0.23)}{200} }[/tex]=0.049

0.77±0.049< 0.819, 0.721

Answer and Step-by-step explanation: Spherical coordinate describes a location of a point in space: one distance (ρ) and two angles (Ф,θ).To transform cartesian coordinates into spherical coordinates:

[tex]\rho = \sqrt{x^{2}+y^{2}+z^{2}}[/tex]

[tex]\phi = cos^{-1}\frac{z}{\rho}[/tex]

For angle θ:

Calculating:

a) (4,2,-4)

[tex]\rho = \sqrt{4^{2}+2^{2}+(-4)^{2}}[/tex] = 6

[tex]\phi = cos^{-1}(\frac{-4}{6})[/tex]

[tex]\phi = cos^{-1}(\frac{-2}{3})[/tex]

For θ, choose 1st option:

[tex]\theta = tan^{-1}(\frac{2}{4})[/tex]

[tex]\theta = tan^{-1}(\frac{1}{2})[/tex]

b) (0,8,15)

[tex]\rho = \sqrt{0^{2}+8^{2}+(15)^{2}}[/tex] = 17

[tex]\phi = cos^{-1}(\frac{15}{17})[/tex]

[tex]\theta = tan^{-1}\frac{y}{x}[/tex]

The angle θ gives a tangent that doesn't exist. Analysing table of sine, cosine and tangent: θ = [tex]\frac{\pi}{2}[/tex]

c) (√2,1,1)

[tex]\rho = \sqrt{(\sqrt{2} )^{2}+1^{2}+1^{2}}[/tex] = 2

[tex]\phi = cos^{-1}(\frac{1}{2})[/tex]

[tex]\phi[/tex] = [tex]\frac{\pi}{3}[/tex]

[tex]\theta = tan^{-1}\frac{1}{\sqrt{2} }[/tex]

d) (−2√3,−2,3)

[tex]\rho = \sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}+3^{2}}[/tex] = 5

[tex]\phi = cos^{-1}(\frac{3}{5})[/tex]

Since x < 0, use 2nd option:

[tex]\theta = \pi + tan^{-1}\frac{1}{\sqrt{3} }[/tex]

[tex]\theta = \pi + \frac{\pi}{6}[/tex]

[tex]\theta = \frac{7\pi}{6}[/tex]

Cilindrical coordinate describes a 3 dimension space: 2 distances (r and z) and 1 angle (θ). To express cartesian coordinates into cilindrical:

[tex]r=\sqrt{x^{2}+y^{2}}[/tex]

Angle θ is the same as spherical coordinate;

z = z

Calculating:

a) (4,2,-4)

[tex]r=\sqrt{4^{2}+2^{2}}[/tex] = [tex]\sqrt{20}[/tex]

[tex]\theta = tan^{-1}\frac{1}{2}[/tex]

z = -4

b) (0, 8, 15)

[tex]r=\sqrt{0^{2}+8^{2}}[/tex] = 8

[tex]\theta = \frac{\pi}{2}[/tex]

z = 15

c) (√2,1,1)

[tex]r=\sqrt{(\sqrt{2} )^{2}+1^{2}}[/tex] = [tex]\sqrt{3}[/tex]

[tex]\theta = \frac{\pi}{3}[/tex]

z = 1

d) (−2√3,−2,3)

[tex]r=\sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}}[/tex] = 4

[tex]\theta = \frac{7\pi}{6}[/tex]

z = 3

Answer: E) C(10, 2)C(8, 1)C(7, 1)C(6, 1)C(5, 1)C(4, 2)C(2, 2)

Step-by-step explanation:

According to the combinations: Number of ways to choose r things out of n things = C(n,r)

Given word: "georgianna"

It is a sequence of 10 letters with 2 a's , 2 g's , 2 n's , and one of each e, o,r, i.

If we think 10 blank spaces, then in a sequence we need 2 spaces for each of g.

Number of ways = C(10,2)

Similarly,

1 space for 'e' → C(8,1)

1 space for 'o' → C(7,1)

1 space for 'r' → C(6,1)

1 space for 'i' → C(5,1)

1 space for 'a' → C(4,2)

1 space for 'n' → C(2,2)

Required number of different sequences  = C(10,2) ×C(8,1)× C(7,1)× C(6,1)×C(5,1)×C(2,2).

Hence, the correct option is E) C(10, 2)C(8, 1)C(7, 1)C(6, 1)C(5, 1)C(4, 2)C(2, 2)

Answer:

20 %

Step-by-step explanation:

The experimental probability is 4/20 = 1/5 = .2 = 20 %

Answer:

32. A

33. B

Step-by-step explanation:

32. Mean: In order to find the mean, add all of the #up which is 194 then divide by how many # there is

33. Start by crossing out the beginning # and the end # all the way till you get the # without another pair in the end

Answer:

c. both A and B

Step-by-step explanation:

Given that there are two events A and B.

To find:

Intersection of the two sets represents which of the following events:

a. either A or B occurs but not both

b. neither A nor B occur

c. both A and B occur

d. All of these choices are true. a. b. c. d

Solution:

First of all, let us learn about the concept of intersection.

Intersection of two events means the common part in the two events.

Explanation using set theory:

Let set P contains the outcomes of roll of a dice.

P = {1, 2, 3, 4, 5, 6}

And set Q contains the set of even numbers less than 10.

Q = {2, 4, 6, 8}

Common elements are {2, 4, 6}

So, intersection of P and Q:

[tex]P \cap Q[/tex] = {2, 4, 6}

Explanation using Venn diagram:

Please refer to the image attached in the answer area.

The shaded region is the intersection of the two sets P and Q.

When we apply the above concept in events, we can clearly say from the above explanation that the intersection of two events A and B is the event that occurs when both A and B occur.

So, correct answer is:

c. both A and B

Answer:

C.

Step-by-step explanation:

Answer:

Divide by 30.48: It would be 0.0656168 feet.

Step-by-step explanation:

Answer:

0.0656

Step-by-step explanation:

2.54 cm = 1 in

12 in = 1 ft

2.54 * 12 = 30.48

2/30.48 = 0.0656167979

Answer:

0

Step-by-step explanation:

0 because there is a $100 duty free exemption.

answer:

For this problem, use the tables and charts shown in this section.  

A United States Citizen returning to the States declares the following items at the customs office:

3 shirts at $8.50 each

2 dresses at $27.50 each

1 pair of gold cuff links at $17.50 per pair

If he has not used his duty free exemption yet, how much duty should he pay?

$0.00 !

$5.00

$10.00

$300

Answer:

x = 7

Step-by-step explanation:

The angles are alternate interior angles, so for the lines to be parallel, the angle measures must be equal.

7x - 7 = 4x + 14

3x = 21

x = 7

Answer:

Solution : Option D

Step-by-step explanation:

The first thing we want to do here is isolate the cos(t) and sin(t) for both the equations --- ( 1 )

x = - 3cos(t) ⇒ x / - 3 = cos(t)

y = 4sin(t) ⇒ y / 4 = sin(t)

Let's square both equations now. Remember that cos²t + sin²t = 1. Therefore, we can now add both equations after squaring them --- ( 2 )

( x / - 3 )² = cos²(t)

+ ( y / 4 )² = sin²(t)

_____________

x² / 9 + y² / 16 = 1

Remember that addition indicates that the conic will be an ellipse. Therefore your solution is option d.

Answer:

1078

Step-by-step explanation:

The product of 22 and 49 is 1078.

Answer:

1078 is the product

Step-by-step explanation:

Answer:

Step-by-step explanation:

x^2+20=4 first isolate the variable by subtracting 20 on both sides.

x^2=-16 again isolate the variable but this time you square root both sides.

[tex]\sqrt{x}^2[/tex]=[tex]\sqrt{-16[/tex] then simplify

x= ±4

Answer:

d

Step-by-step explanation:

(-7 + 3i) + (2-6i)

=-7 + 3i + 2 -6i

=(-7+2) + (3i -6i)

=-5 -3i

Answer:

(-7+3I)+(2-6I)

= -7+3i+2-6i

= -5-3I

so answer is d ie -5-3i

Answer:

a

  [tex]P( 0.172 < X < 0.178 ) = 0.00354[/tex]  

b

  [tex]P( X >0.025 ) = 0.99379[/tex]

Step-by-step explanation:

From the question we are told that

   The  population proportion is  [tex]p = 0.10[/tex]

    The sample size is  [tex]n = 100[/tex]

Generally the standard error is mathematically represented as

       [tex]SE = \sqrt{\frac{ p (1 - p )}{n} }[/tex]

=>   [tex]SE = \sqrt{\frac{ 0.10 (1 - 0.10 )}{100} }[/tex]

=>   [tex]SE =0.03[/tex]

The sample proportion (the proportion living in the dormitories) is between 0.172 and 0.178

   [tex]P( 0.172 < X < 0.178 ) = P (\frac{ 0.172 - 0.10}{0.03} < \frac{ X - 0.10}{SE} < \frac{ 0.178 - 0.10}{0.03} )[/tex]

  Generally  [tex]\frac{ X - 0.10}{SE} = Z (The \ standardized \ value \ of X )[/tex]

    [tex]P( 0.172 < X < 0.178 ) = P (\frac{ 0.172 - 0.10}{0.03} <Z < \frac{ 0.178 - 0.10}{0.03} )[/tex]

    [tex]P( 0.172 < X < 0.178 ) = P (2.4 <Z < 2.6 )[/tex]

   [tex]P( 0.172 < X < 0.178 ) = P(Z < 2.6 ) - P (Z < 2.4 )[/tex]

From the z-table  

      [tex]P(Z < 2.6 ) = 0.99534[/tex]

     [tex]P(Z < 2.4 ) = 0.9918[/tex]

[tex]P( 0.172 < X < 0.178 ) =0.99534 - 0.9918[/tex]  

 [tex]P( 0.172 < X < 0.178 ) = 0.00354[/tex]  

the probability that the sample proportion (the proportion living in the dormitories) is greater than 0.025 is mathematically evaluated as

        [tex]P( X >0.025 ) = P (\frac{ X - 0.10}{SE} > \frac{ 0.0025- 0.10}{0.03} )[/tex]

        [tex]P( X >0.025 ) = P (Z > -2.5 )[/tex]

From the z-table  

        [tex]P (Z > -2.5 ) = 0.99379[/tex]

Thus

      [tex]P( X >0.025 ) = P (Z > -2.5 ) = 0.99379[/tex]

Answer:

Step-by-step explanation:

The slope of a line is found by using the formula

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

where

m is the slope and

(x1 , y1) and ( x2 , y2) are the points

Substituting the above values into the above formula we have

Slope of the line that passes through

(0,1) and (-8, -7) is

[tex]m = \frac{ - 7 - 1}{ - 8 - 0} = \frac{ - 8}{ - 8} = 1[/tex]

Hope this helps you

Answer:

65 ft

Step-by-step explanation:

The area of a rectangle is

A = lw

6045 = 93*w

Divide each side by 93

6045/93 = 93w/93

65 =w

Answer:

[tex]\huge \boxed{\mathrm{65 \ feet}}[/tex]

Step-by-step explanation:

The area of a rectangle formula is given as,

[tex]\mathrm{area = length \times width}[/tex]

The area and length are given.

[tex]6045=93 \times w[/tex]

Solve for w.

Divide both sides by 93.

[tex]65=w[/tex]

The width of the rectangular garden is 65 feet.

Answer:

The expression = [tex] \frac{40}{y - 16} [/tex]

Value of the expression = 4 (when y is 20)

Step-by-step explanation:

Quotient simply means the result you get when you divide two numbers. Thus, dividend (the numerator) ÷ divisor (the denominator) = quotient.

From the information given to us here,

the dividend = 40

the divisor = y - 16

The quotient = [tex] \frac{40}{y - 16} [/tex]

There, the expression would be [tex] \frac{40}{y - 16} [/tex]

Find the value of the expression when y = 20.

Plug in 20 for y in the expression and evaluate.

[tex] \frac{40}{y - 16} [/tex]

[tex] = \frac{40}{20 - 16} [/tex]

[tex] = \frac{40}{4} = 10 [/tex]

The value of the expression, when y is 20, is 4.

Answer:

3x+2+x-3+2x+1+2(2x+5)=360

10x+10=360

x=35