By law, an industrial plant can discharge no more than 500 gallons of waste water per hour, on the average, into a neighboring lake. Based on other infractions they have noticed, an environmental action group believes this limit is being exceeded. Monitoring the plant is expensive, and a random sample of four hours is selected over a period of a week. Software reports:
Variable No. Cases Mean SD SE of Mean
WASTE 4 1000.0 400.0 200.0
(a) Test whether the mean discharge equals 500 gallons per hour against the alternative that the limit is being exceeded. Find the P-valuc and interpret.
(b) Explain why the test may be highly approximate or even invalid if the population distribution of discharge is far from normal.
(c) Explain how your one-sided analysisimplicitly tests the broader null hypothesis that µ <>

Answer:

40200

Step-by-step explanation:

(8x7x6x5x4x3x2x1) - (5x4x3x2x1)

Or simply plug 8! - 5! into the calc.

Answer:

Step-by-step explanation:

40200

Sarah's fuel efficiency is approximately 32.91 miles per gallon.

From the question, we are to calculate Sarah's fuel efficiency.

To find Sarah's fuel efficiency in miles per gallon, we need to convert the distance she drove to miles and the amount of gasoline she used to gallons.

From the given information,

1 km = 0.6214 mi

1 gal = 3.8 L

First, let's convert the distance from kilometers to miles:

691.4 km × 0.6214 mi/km = 430.10196 mi

So, Sarah drove a distance of 430.1 miles.

Also,

Convert the amount of gasoline from liters to gallons:

49.7 L ÷ 3.8 L/gal = 13.0789 gal

So, Sarah used 13.0789 gallons of gasoline.

Calculate her fuel efficiency in miles per gallon:

Fuel efficiency = distance ÷ gasoline used

Fuel efficiency = 430.1 mi ÷ 13.0789 gal

Fuel efficiency = 32.9065 mi/gal

Hence, Sarah's fuel efficiency is 32.91 mi/gal

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There is insufficient information so the joint probability mass function of X and Y.

given that

there are three bowls they are a red bowl , a green bowl and a blue bowl  are on the kitchen table

alan places one egg into a randomly selected bowl.

X = # of eggs placed into the red bowl

Y = # of empty bowls at the end of the experiment.

the joint probability mass function of X and Y

1. Not sufficient

R=5

let us consider when G = 2 , B = 1 => P(G) = 2/8

when G=1, B=2 => P(G) = 1/8

2. Not Sufficient

P(B) = 1/3 = x/3x

But this doesn't tell us anything about B or total because P(B) = 1/3 , but it could also be 2/6 or 3/9 so on..

So we can have different B . Thus we can have different G combinations.

Together - Not Sufficient

P(B) = x/(3x) , R = 5

P(G) = 1- P( not G )

= 1- P(R or B)

But we cannot calculate this with out knowing P(R) and P(B).

we cannot solve this problem because there is no proper information is given.

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Answer:

area = 6.5 square units

Step-by-step explanation:

Use the area of a triangle in coordinate geometry formula:

\(\triangle GHI =\frac{1}{2} |x_1(y_2- y_3) + x_2(y_3 -y_1) + x_3(y_1 -y_2)|\)

where \((x_1,y_1)=(-8,-8) \ \ \ \ (x_2,y_2)=(-6,-7) \ \ \ \ (x_3,y_3)=(-9,-2)\)

      \(\triangle GHI =\frac{1}{2} |x_1(y_2- y_3) + x_2(y_3 -y_1) + x_3(y_1 -y_2)|\)

\(\implies \triangle GHI =\frac{1}{2} |-8(-7+2) -6(-2 +8) -9(-8 +7)|\)

\(\implies \triangle GHI =\frac{1}{2} |40 -36 +9|\)

\(\implies \triangle GHI =6.5\)

Answer:

4 5/8

Step-by-step explanation:

Rewriting our equation with parts separated

=4+12+18

Solving the fraction parts

12+18=?

Find the LCD of 1/2 and 1/8 and rewrite to solve with the equivalent fractions.

LCD = 8

48+18=58

Combining the whole and fraction parts

4+58=458

Answer:

The new price is 8.80

Step-by-step explanation:

First find the increase

8 * 10%

8 * .10

.80

Add this to the original price

8 + .80

8.80

The new price is 8.80

Answer:

the answer is $8.80 :))

Answer:

h(x)=6x-26

Step-by-step explanation:

f(x)=5x-10

g(x)=x-16

h(x)=f(x)+g(x)=(5x-10)+(x-16) = 6x-26

Answer:

x = 9/4 y = 15/4

Step-by-step explanation:

Answer:

\(\frac{x^3}{3}+2x^2 + K\\\\\)

Step-by-step explanation:

We can equate the expression x^2+4x to f(x) and specify the variable of integration , the integrand and the symbol simply like this ,

Let,

\(f(x)=x^2+4x\\\\F'(x)=f(x)\\\\\int f(x)\ dx=F(x) + K\)

Where the integrand is f(x) , x is the variable of integration , c is the constant of integration , and ∫ is the symbol of integration.

The derivate of what function is x^2 + 4x?

To find that out we integrate the function because Integrating a differentiate is the process of obtaining the original process because Integrals are also called as Anti-derivatives.

So,

\(\int\ x^2+4x \ dx\)

This is an indefinite integral which would result in an addition of a constant later on because it does not have limits. The variable of integration is x because there is only one variable present in this expression so naturally the variable of concern is x

so now we solve,

\(\int\ x^2+4x \ dx\\\\\frac{x^3}{3}+4(\frac{x^2}{2}) + K\\\\\frac{x^3}{3}+2x^2 + K\\\)

Where K is the constant of the indefinite integral.

Answer:

assuming that you start at the origin (0,0)

(-4,-1) would be the poiny

x coord = -4

y coord = -1

the point is in the 3 quadrant

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

i did 300 divided by 60%

Step-by-step explanation:

300 Divide By 60 percent

Answer:

The domain of the function should be:

'x greater than or equal to negative -5'.

Hence, option A is true.

Step-by-step explanation:

Given the expression

\(2\sqrt{x-5}\)

The domain of a function is the set of input or arguments for which the function is real and defined

We know that the value, inside the radicand, is the number found inside a radical symbol which must be greater than 0, otherwise, it would make the function undefined,

i.e.

x-5 ≥ 0

x ≥ 5

In other words, the domain of the function should be:

'x greater than or equal to negative -5'.

Therefore, the domain of the function:

x ≥ 5

\(\mathrm{Domain\:of\:}\:2\sqrt{x-5}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\ge \:5\:\\ \:\mathrm{Interval\:Notation:}&\:[5,\:\infty \:)\end{bmatrix}\)

Hence, option A is true.

The domain of the function y = 2√(x - 5) will be x greater-than-or-equal-to 5. Then the correct option is C.

The domain means all the possible values of x and the range means all the possible values of y.

The function is given below.

y = 2√(x - 5)

Then the domain of the function will be

We know that the value inside the square root should be greater than or equal to zero. Then the domain will be

x - 5 ≥ 0

Simplify the inequality, then the domain of the function will be

x - 5 ≥ 0

x ≥ 5

The domain of the function y = 2√(x - 5) will be x greater-than-or-equal-to 5.

Then the correct option is C.

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Expanding the desired form, we have

\(A \sin(\omega t + \phi) = A \bigg(\sin(\omega t) \cos(\phi) + \cos(\omega t) \sin(\phi)\bigg)\)

and matching it up with the given expression, we see that

\(\begin{cases} A \sin(\omega t) \cos(\phi) = 2 \sin(4\pi t) \\ A \cos(\omega t) \sin(\phi) = 5 \cos(4\pi t) \end{cases}\)

A natural choice for one of the symbols is \(\omega = 4\pi\). Then

\(\begin{cases} A \cos(\phi) = 2 \\ A \sin(\phi) = 5 \end{cases}\)

Use the Pythagorean identity to eliminate \(\phi\).

\((A\cos(\phi))^2 + (A\sin(\phi))^2 = A^2 \cos^2(\phi) + A^2 \sin^2(\phi) = A^2 (\cos^2(\phi) + \sin^2(\phi)) = A^2\)

so that

\(A^2 = 2^2 + 5^2 = 29 \implies A = \pm\sqrt{29}\)

Use the definition of tangent to eliminate \(A\).

\(\tan(\phi) = \dfrac{\sin(\phi)}{\cos(\phi)} = \dfrac{A\sin(\phi)}{\cos(\phi)}\)

so that

\(\tan(\phi) = \dfrac52 \implies \phi = \tan^{-1}\left(\dfrac52\right)\)

We end up with

\(y(t) = 2 \sin(4\pi t) + 5 \cos(4\pi t) = \boxed{\pm\sqrt{29} \sin\left(4\pi t + \tan^{-1}\left(\dfrac52\right)\right)}\)

where

• amplitude:

\(|A| = \boxed{\sqrt{29}}\)

• angular frequency:

\(\boxed{4\pi}\)

• phase shift:

\(4\pi t + \tan^{-1}\left(\dfrac 52\right) = 4\pi \left(t + \boxed{\frac1{4\pi} \tan^{-1}\left(\frac52\right)}\,\right)\)

Answer:

4.6

Step-by-step explanation:

the first equation will be y=1.2x+4.6

the second will be y=0.8x+54.6

then i plugged the system of equations and that was where they met at :)

Answer:

for sure B

Step-by-step explanation:

The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

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Answer:

\(y-4=2\,(x+1)\)

which agrees with answer C in your list of possible answers.

Step-by-step explanation:

We can use the general point-slope form of a line of slope m and going through the point \((x_0, y_0)\):

\(y-y_0=m(x-x_0)\)

which in our case, given the info on the slope (2) and the point (-1, 4) becomes:

\(y-y_0=m\,(x-x_0)\\y-4=2\,(x-(-1))\\y-4=2\,(x+1)\)

The range of the function on the graph is y > -6

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

The graph

The graph is an exponential function

The rule of an exponential function is that

The domain is the set of all real numbers

This means that the input value can take all real values

However, the range is always greater than the constant term

In this case, it is -6 i.e. the point where it intersects with the y-axis

So, the range is y > -6

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Answer:

No it cannot be

Step-by-step explanation:

Since an obtuse angle is more than 90 degrees, it can't have a complement

Hope this helps!

ok

P1 = (0, 3)

P2 = (1,6)

1.- Find the slope

m = (y2 - y1) / (x2 - x1)

m = (6 - 3) / (1 - 0)

m = 3/1

m = 3

2.- Find the equation of the function

y - y1 = m(x - x1)

y - 3 = 3(x - 0)

y - 3 = 3x

y = 3x + 3 This is the equation of the function

3.- This is a linear function. The domain of a linear function is all real numbers and the range of a linear function are also all real numbers.

Answer:

(40, 100) (x,y) Also, In the image below

Step-by-step explanation:

I used this website to do this. It is a very accurate website I used it all the time in algebra. So it should be right

I hope this helps!!!

Please mark Brainliest :)

Answer:

wouldn't it be 1/25 black??

Answer:

qwertyuiopplkhgf12345678rrd6

Step-by-step explanation:

Preciate ittttttttttt

Answer:

85.2

Step-by-step explanation:

17,892 ÷ 210

85.2

Best of Luck!

The Expected Value for the player is -$2.40, which is negative. This means that on average, the player can expect to lose $\(2.40\) for each game played.

To calculate the Expected Value for the player, we can multiply the probability of winning by the amount won, and subtract the probability of losing by the amount paid.

Expected Value = (Probability of Winning * Amount Won) - (Probability of Losing * Amount Paid)

Given the following information:

Probability of winning \(= 0.13\)

Amount won = $15

Probability of losing \(= 0.87\)

Amount paid = $5

Plugging these values into the formula:

Expected Value \(= (0.13 \times $15) - (0.87 times $5)\)

Expected Value \(= $1.95 - $4.35\)

Expected Value = \(-$2.40\)

If a person plays this game a very large number of times over the years, we expect them to come out financially behind, as the Expected Value is negative. This indicates that, on average, the player will lose money over time by playing this game repeatedly.

Therefore, The Expected Value for the player is -$2.40, which is negative. This means that on average, the player can expect to lose $2.40 for each game played.

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Answer:

w≈8.33

Step-by-step explanation:

Greetings !

Firstly recall rectangle area formula

Thus,

\(area \: of \: rectangle \: = length \: \times \: width\)

Given values:-

require value:-

solution/ work-out:-

\(width = \: \frac{area \: of \: rectangle}{length} \)

\(w = \frac{125}{15} \)

\(w = 8.333...\)

Hope it helps !!!

1. The distance all the way across the cooker. In this case, 136 cm.

1. The coordinates of the edges of the cooker can be determined by considering the distance from the vertex to the edge of the cooker. Given that the distance from the vertex to the edge is 68 cm, and the vertex is at (-32, 0), we can find the coordinates of the edges as follows:

One edge of the cooker: (-32 + 68, 0) = (36, 0)

The other edge of the cooker: (-32 - 68, 0) = (-100, 0)

The distance all the way across the cooker. In this case, it is 36 - (-100) = 136 cm.

2. To write an equation for the parabolic mirror, we can use the standard form of a parabolic equation, which is y = a(x - h)² + k, where (h, k) represents the vertex of the parabola.

In this case, the vertex is at (-32, 0).

The equation becomes y = a(x + 32)² + 0.

Substituting these coordinates into the equation, we get:

0 = a(36 + 32)² + 0

0 = a(68)²

0 = 4624a

From this, we can see that a = 0, which means the equation simplifies to y = 0, indicating that the parabolic mirror is a straight line along the x-axis.

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Answer:

62

Step-by-step explanation:

t=digit in the tens place

u=digit in the units place

t=3*u

original number=t*10+u

number with reversed digits=u*10+t

u*10+t=t*10+u-36

u*10+(3*u)=(3*u)*10+u-36

10u+3u-30u-u=-36

-18u=-36

u=2

t=3*u=6

Original number = 62

Check the solution:

6=3*2 ok

26=62-36 ok

Answer:

Step-by-step explanation:

total interest paid is given as $4,643.46.

total payments = $429.95 x 36 months = $15,478.20

total lease payments = total payments - total interest

total lease payments = $15,478.20 - $4,643.46 = $10,834.74

Remaining balance = Total cost of the lease - Total lease payments

$23,495 - $10,834.74 = $12,660.26

Answer:

The change is 245 members

Step-by-step explanation:

7x35=245