A tank initially contains 130 gallons of water. It is then filled with more water, at a constant rate of 8 gallons per minutes. Write an equation that represents how much water is in the tank after m minutes.

Answer:

[tex]1.91\ \text{in}[/tex]

[tex]3.84\ \text{in}[/tex]

Step-by-step explanation:

V = Volume of cylinder = [tex]44\ \text{in}^3[/tex]

h = Height of cylinder

r = Radius of cylinder

Volume of cylinder is given by

[tex]V=\pi r^2h\\\Rightarrow h=\dfrac{V}{\pi r^2}\\\Rightarrow h=\dfrac{44}{\pi r^2}[/tex]

Total surface area of a cylinder is given by

[tex]S=2\pi r^2+2\pi rh\\\Rightarrow S=2\pi r^2+2\pi r\times\dfrac{44}{\pi r^2}\\\Rightarrow S=2\pi r^2+\dfrac{88}{r}[/tex]

Differentiating with respect to radius

[tex]\dfrac{dS}{dr}=4\pi r-\dfrac{88}{r^2}[/tex]

Equating with zero

[tex]4\pi r-\dfrac{88}{r^2}=0\\\Rightarrow 4\pi r=\dfrac{88}{r^2}\\\Rightarrow r^3=\dfrac{88}{4\pi}\\\Rightarrow r=(\dfrac{22}{\pi})^{\dfrac{1}{3}}\\\Rightarrow r=1.91\ \text{in}[/tex]

Double derivative of S

[tex]\dfrac{d^2S}{dr^2}=4\pi+176>0[/tex]

So [tex]r[/tex] is minimum at [tex]\dfrac{dS}{dr}=0[/tex]

[tex]h=\dfrac{44}{\pi r^2}=\dfrac{44}{\pi 1.91^2}\\\Rightarrow h=3.84\ \text{in}[/tex]

So the radius and height of the cylinder is [tex]1.91\ \text{in}[/tex] and [tex]3.84\ \text{in}[/tex] respectively such that the least amount of metal is used.

We have a jumper that jumps from 1500ft above the ground, such that its height as a function of time is given by:

h(t) = -16*t^2 + 1500

The solutions are:

A) 5.59 seconds

B) 5.91 seconds

C) D = (0s, 9.68s)

    R = [0ft, 1500ft]

Notice that when t = 0, h = 1500, then at the initial time (t = 0) the height is 1500 (in ft), which means that the zero of the height is the ground.

a) How long is the jumper free fall if the parachute opens at 1000 ft?

Here we need to solve:

h = 1000 = -16*t^2 + 1500

Now we just need to solve this for t:

16*t^2 = 1500 - 1000 = 500

t^2 = 500/16 = 31.25

t = √31.25 = 5.59

So it takes 5.59 seconds to open the parachute.

B) similar to before, this time we need to solve:

h = 940 = -16*t^2 + 1500

16*t^2  =1500 - 940 = 560

t^2 = 560/16 = 35

t = √35 = 5.91

So it takes 5.91 seconds to open the parachute.

C) The domain is the set of inputs that we can use in the function.

The minimum of the domain is t = 0, when the jumper jumps.

To find the maximum of the domain we need to find the maximum time at which he could open the parachute, that is when h = 0ft, just in the ground.

Then we solve:

h = 0 = -16*t^2 + 1500

16*t^2 = 1500

t = √(1500/16) = 9.68

Then a reasonable domain is (0s, 9.68s)

And the range is the set of possible outputs, which will be all the possible heights of the jumper. We know that all of these are between 0ft and 1500ft, thus the range is [0ft, 1500ft]

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Answer:

.

Step-by-step explanation:

We want to find the expected value for Jessie on the come out roll.

The expected value is EV = $0.50

We know that for an event with outcomes {x₁, x₂, ..., xₙ}, each with probability {p₁, p₂, ..., pₙ}, the expected value is given by:

EV = x₁*p₁ + x₂*p₂ + ... + xₙ*pₙ

Where the probabilities are written in decimal form.

We have the outcomes:

x₁ = winning $5.

p₁ = 0.29

x₂ = losing $5

p₂ = 0.19

x₃ = not win nor lose

p₃ = 1 - 0.19 - 0.29 = 0.52

Then the expected value is:

EV = $5*0.29 - $5*0.19 + $0*0.52 = $0.50

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Answer: x = 10

see in the picture, ΔACE has:

+) BF//AE

+) B and F are  midpoints.

=> BF is the median line of the triangle ACE

=> BF = 1/2. AE

=> AE = 2BF

⇔ 5x - 4 = 2.23 = 46

⇔ 5x = 46 + 4 = 50

⇔ x = 50/5 = 10

Step-by-step explanation:

Answer:

10 minutes

Step-by-step explanation:

Speed = distance ÷ time, so 40 ÷ 4 = 10

hope this helps :)

Answer:

12/4

Step-by-step explanation:

y varies directly with x basically means y÷x so you will have to divide the variables together. In other words, it basically means y varies proportionally as x

so in this case, it would be 12 divided by 4 resembling that y varies directly as x

Answer:

Solving for y gives:

[tex]y = \frac{pq}{3}[/tex]

Step-by-step explanation:

Linear equations are the equations that are degree one equations. When it is asked to solve an equation for a specific variable that means that the specified variable has to be isolated on one side of the equation i.e. in the given question solving for y means isolating y on one side of the equation.

Given equation is:

[tex]p = \frac{3y}{q}[/tex]

Multiplication property of equality(Multiplying both sides by q)

[tex]p*q = \frac{3y}{q} * q\\pq = 3y[/tex]

Division property of equality(Dividing both sides by 3)

[tex]\frac{pq}{3} = \frac{3y}{3}\\\frac{pq}{3} = y[/tex]

Hence,

Solving for y gives:

[tex]y = \frac{pq}{3}[/tex]

Answer:

The correct answer is D.

Step-by-step explanation:

Answer:

The equation for the profit made on the car wash is y = 5x – 75. Here, y is the profit made and x is the number of cars washed. So if the team washes 0 cars, x will be 0.

y = 5(0) – 75

y = -75

The point that represents this is (0, -75). Here, the value of the y-coordinate of the point is -75. Since it has a negative sign, it means that instead of making a profit, the team suffers a loss. So, if the baseball team washed no cars, it would lose $75.

Step-by-step explanation:

Answer:

y-9=34

y=34+9

y= 43

Step-by-step explanation:

please Mark as brainliest

Answer:

y= -25 because if you add -25 to 9 it gives you -34

Answer:

#6 slope is -1/2 and y intercept is 4

#8 slope is 1/3 and y intercept is -2

Step-by-step explanation:

Answer:

I believe it is D. not sure tho

Answer:

The answer must be either C or D but I think it is D

Step-by-step explanation:

sorry if I am wrong

Answer:

13

Step-by-step explanation:

20÷1.5 since there is not X

Answer:

area is equal to 198 cm^2

Step-by-step explanation:

the height h of the left triangle can be obtained by

Pytagoras theorem:

[tex]5^2+h^2=13^2\\25+h^2=169\\h^2=169-25\\h^2=144\\h=\sqrt{144} \\h=12[/tex]

the, the area of the left triangle is

[tex]A_1=\frac{5*12}{2} \\A_1=5*6\\A_1=30[/tex]

the area of the right triangle is

[tex]A_2=\frac{2*12}{2} \\A_2=12[/tex]

and the area of the rectangle in the middle is

[tex]A_3=(13)(12)\\A_3=156[/tex]

Por tanto, el area total sera

[tex]A=A_1+A_2+A_3\\A=30+12+156\\A=198[/tex]

Step-by-step explanation:

Let X be a random variable with PDF given by

fX(x)={ cx2 |x|≤1 0 otherwise

Find the constant c.

Find EX and Var(X).

Find P(X≥

1

2

).

Answer:

three out of the eight homes have red doors. so 3 homes have red doors

Step-by-step explanation:

Answer:

20% discount

Step-by-step explanation:

275 - 220 = 55

55/275 = 0.2

The discount is 20%

Answer:

20% discount

Step-by-step explanation:

275 - 220 = 55

55/275 = 0.2

0.2(100)=20

There is a 20% discount.

Answer:

Sven would type 2280 words every 40 minutes.

Step-by-step explanation:

Multiply 57 by 40 and that should get you 2280.

Now, if it was truly an hour, you would multiply 57 by 60. The answer should be 3420.

We want to compare two prefixes, kilo and tera, and see why one seems to be more important than the other.

The prefix "kilo" is used for thousands, while the prefix "tera" is used for trillions.

Now if you go to your day-to-day life, you will see that the thousands appear a lot more than the trillions.

For example, is more common to walk one or two kilometers than one terameter.

Or also is more common to buy a kilogram of potatoes than one teragram of potatoes.

This is mainly why kilo is more important (actually is more used, I wouldn't say that is more important) than tera.

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Answer:

Step-by-step explanation:

Jmeu eimejrimr

The number between -8.423 and -8.395 will be - 8 2/5.

What is Fraction?

A fraction is a part of whole number, and a way to split up a number into equal parts.

Given that;

Two numbers are,

⇒ - 8.423 and - 8.395

Now,

Since, Two numbers are,

⇒ - 8.423 and - 8.395

Clearly, - 8.1 is greater than - 8.423 and - 8.395.

Hence, It is not between the numbers - 8.423 and - 8.395.

Clearly, - 8.75 is less than - 8.423 and - 8.395.

Hence, It is not between the numbers - 8.423 and - 8.395.

Clearly, - 8 1/2 is less than - 8.423 and - 8.395.

Hence, It is not between the numbers  - 8.423 and - 8.395.

Clearly, - 8 2/5 = - 8.4 is in between - 8.423 and - 8.395.

Hence, It is between the numbers  - 8.423 and - 8.395.

Thus, The number between -8.423 and -8.395 will be - 8 2/5.

Learn more about the fraction visit:

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#SPJ6

Answer: 8

please see below for work!

Answer: C

Step-by-step explanation:

step 1: I

step 2: just

step 3: took

step 4: it

final answer: i took the test and got a 100 so its definitely C.

<3

Answer:

24%

i think

Step-by-step explanation:

Answer:

The correct answer is $1,500

Step-by-step explanation:

hope this helps

Answer:

(f - g)(x) = -x² + 4x + 4

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

f(x) = 4x - 1

g(x) = x² - 5

(f - g)(x) = f(x) - g(x)

Step 2: Find