A school counselor heard that teenagers sleep an average of 9 hours per night on the weekend. The counselor
wants to test if this figure holds true for students at their school, so they take a random sample of students and
ask them about their weekend sleep habits.
Let u represent the average amount of sleep that students at this school get per night on the weekend.
Which of the following is an appropriate set of hypotheses for their significance test?

Answer:

b

Step-by-step explanation:

Answer:

a. F = 26214.4π lb/ft-s²∫₋₁₀⁰(y + 10)dy

b. W = 104857.6π lb-ft/s²∫₋₁₀⁰(y + 10).dy

Step-by-step explanation:

(a) Write down an integral for the total fluid force on the side of the tank.

We know force, F = ∫PdA where P = pressure and dA = differential area element in tank surface.

Let the position of the bottom of the tank be y = -h where h = height of tank and y = 0 be the top of the tank. So, the height of any point y of the tank H is y - (-h) = y + h = y + 10

The pressure P = ρgH where ρ = density of oil in tank = 51.2 lb/ft³ and g = acceleration due to gravity = 32 ft/s²

P = ρgH

P = ρg(y + 10)

The differential area element of a point on the side of the tank is dA = 2πrdy

So, F = ∫PdA

F = ∫ρg(y + 10)2πrdy

we integrate y from y = -h = -10 to y = 0

So, F = ∫₋₁₀⁰ρg(y + 10)2πrdy

F = ∫₋₁₀⁰2πrρg(y + 10)dy

F = ∫₋₁₀⁰2π(8 ft)(51.2 lb/ft³)(32 ft/s²)(y + 10)dy

F = ∫₋₁₀⁰26214.4π lb/ft-s²(y + 10)dy

F = 26214.4π lb/ft-s²∫₋₁₀⁰(y + 10)dy

(b) Suppose all the kerosene is pumped to ground level. Write down an integral for the work required to pump the oil.

The work done W = ∫F.dy

W = ∫F.dy

F = ρgV where V = volume of tank = πr²H = πr²(y + 10)

F = ρgπr²(y + 10)

So, W = ∫F.dy

W = ∫ρgπr²(y + 10).dy

Since the water is pumped to ground level, we integrate y from y = -h = -10 to y = 0

W = ∫₋₁₀⁰ρgπr²(y + 10).dy

W = ∫₋₁₀⁰π(51.2 lb/ft³)(32 ft/s²)(8 ft)²(y + 10).dy

W = ∫₋₁₀⁰104857.6π lb-ft/s²(y + 10).dy

W = 104857.6π lb-ft/s²∫₋₁₀⁰(y + 10).dy

Answer:

how much people are there

... . . ..........

Answer:

2/3

(-4, 2) and (-16, -6)

slope = m = (y2 - y1) / (x2 - x1) = (-6 - 2) / (-16 - -4) = -8 / -12 = 2 / 3 = 0.667

I hope you got it right :)

Answer:

Full question?

Step-by-step explanation:

Answer:

9(3q^2−1)

Step-by-step explanation:

Answer:

(0,9),(9,2)

Step-by-step explanation:

Answer:

10 students

Step-by-step explanation:

Hope this helps!

Answer:

10%×200=20

Step-by-step explanation:

25%×200=50

35%×200=70

Answer:

Your total is now $36

Step-by-step explanation:

Multiply 60 times 40%

and it will show that you saved $24

subtract $60 - $24

there's your answer.

Answer:

The numerator factors to

[tex](x + 2)(x - 1)[/tex]

The denomenator factors to

[tex](x + 4)(x - 1)[/tex]

9514 1404 393

Answer:

  x = (A -40)/7

Step-by-step explanation:

Maybe you want to solve for x.

  A = 7x +40 . . . . . given

  A -40 = 7x . . . . . subtract 40

  (A -40)/7 = x . . . divide by 7

The value of x will be ...

  x = (A -40)/7

Answer:

π

Step-by-step explanation:

s = (∅/360) * (2πr)

s = (60/360) * (2π*3)

s = (1/6) * (6π)

s = π

Answer:

59,280

Step-by-step explanation:

the answer is base in my previous learning.. hope it helps..

Answer:

Option C

Step-by-step explanation:

System of equations have been given as,

y - 4x = 16

y = 4x + 16 ------(1)

By comparing with slope-intercept form of the linear equation,

y = mx + b

Here, m = slope of the line

b = y-intercept

Therefore, m₁ = 4

2y = 8x + 16

y = 4x + 8 -------(2)

Slope of the line m₂ = 4

m₁ = m₂

Therefore, both the lines are parallel and both will not intersect each other.

Hence, there will be no solution of the system of equations.

Option C will be the correct option.

I dont understand the question

Option C, [tex]\left(\dfrac{\pi}{4},\dfrac{5\pi}{4}\right)[/tex]  is the correct answer such that the function, [tex]f(x)=12sin(x-4\pi)[/tex] where, [tex]x[/tex] is the time in [tex]seconds[/tex] and [tex]f(x)[/tex] is the position of the water wave in [tex]ft[/tex] above and below the normal water level.

The inverse of the function is the mirror image of the function with respect to the dependent variable.

From the figure, the interval of water wave above the normal water level is [tex]\left(\dfrac{\pi}{4},\dfrac{5\pi}{4}\right)[/tex].

So, the interval of the mirror image of the function with respect to the dependent variable [tex]x[/tex] is [tex]\left(\dfrac{\pi}{4},\dfrac{5\pi}{4}\right)[/tex].

As a result, Option C is the correct answer.

Learn more about the inverse of the function here- https://brainly.com/question/2541698

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Answer:

0.9945 = 99.45% probability that the student answers at most four questions correctly

Step-by-step explanation:

For each question, there are only two possible outcomes. Either the student answers correctly, or he/she does not. The probability of the student answering a question correctly is independent of any other question. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

A quiz consists of six multiple choice questions.

This means that [tex]n = 6[/tex]

Each question has four choices. Student guesses randomly.

This means that [tex]p = \frac{1}{4}[/tex]

What is the probability that the student answers at most four questions correctly?

This is:

[tex]P(X \leq 4) = 1 - P(X > 4)[/tex]

In which

[tex]P(X > 4) = P(X = 5) + P(X = 6)[/tex]. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 5) = C_{6,5}.(0.25)^{5}.(0.75)^{1} = 0.0053[/tex]

[tex]P(X = 6) = C_{6,6}.(0.25)^{6}.(0.75)^{0} = 0.0002[/tex]

[tex]P(X > 4) = P(X = 5) + P(X = 6) = 0.0053 + 0.0002 = 0.0055[/tex]

[tex]P(X \leq 4) = 1 - P(X > 4) = 1 - 0.0055 = 0.9945[/tex]

0.9945 = 99.45% probability that the student answers at most four questions correctly

Answer:

Answer: The answer is 15

HOPE THIS HELPS AND HAVE A VERY GOOD DAY

Answer:

we have

b=3mm

c=5mm

a=?

angle =62°

By using cosine rule.

a²=b²+c²-2bc cos angle

a²=3²+5²-2×3×5 cos 62°

a²=19.92

a=√19.92

a=4.5

I had choose cosine rule.

Answer:

1. semicircle=14.1372mm

parallelogram=40 mm

54.1372 mm^2

2. 180 ft

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

D. direct variation

Step-by-step explanation:

Answer:

yes it is direct variation

Step-by-step explanation:

well I'm sorry I Don't know if it's going to be step by step but my own understanding is that what ever happens on one side will affect the other side so if there is an increase in A there will be an increase in B so there's a form of equilibrium. so let's say we throw two stones A and B into a fast flowing river we expect that the water will flow so the more the velocity of the river the faster the stone will flow so as the river is flowing the stone is floating as well but an indirect variation as the river increases it's velocity the stone decreases it's movement so in direct variation as the river increases it's velocity the stone does as well. I hope this is well detailed and I answered your question , thank you

BC = 8i + 6

This is the answer for the first question, i'm so so sorry but i'm not sure what the answer is to the second one.

Answer:

Step-by-step explanation:

(14×2)+(14×4)

7×(3+5)

c, e and g

Answer:

x = 5.2

Step-by-step explanation:

Its because 8 / 2 = 4 so that means 5.2 / 2 = 2.6 :)

(You might wanna check because im not sure)

Answer:

x² - 2x - 180 = 0

Step-by-step explanation:

A square piece of paper has an area of x² square units

w = x

l = x

A rectangular strip with a width of 2 units and a length of x units is cut off of the square piece of paper.

this leaves

l = x

w = x - 2

x(x - 2) = 180

x² - 2x = 180

x² - 2x - 180 = 0

Answer:

x2 − 2x − 120 = 0

Step-by-step explanation:

A square's area is calculated by multiplying each side's length by itself. That is, Area A = s x s, with s denoting the length of each square side. A square with each side measuring 8 feet in length has an area of 8 times 8, or 64 square feet.

Let x  the length side of the original square paper

we know that the area of the original square paper is equal to

[tex]A1=x*x=x^{2} units{2}[/tex]

the area of the remaining piece of paper is equal to

[tex]$A 2=x^{2}-2 x$\\$A 2=120$ units $^{2}$[/tex]

so

[tex]$x^{2}-2 x=120$$x^{2}-2 x-120=0$[/tex]

therefore, the side length of the original square is x2 − 2x − 120 = 0

To know more about area of square click here-

https://brainly.com/question/1968457

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