(3x^2-2x+1) + (x^2 + 4x -3)

Answer:

Step-by-step explanation:

I'll try to make this make as much sense as possible. If we have a cone with a liquid in it, this liquid takes up volume. Therefore, our main equation, at least at first, is to find the volume. This is because if we pump the liquid out of the tank, the thing that changes is the amount of liquid in the tank which is the tank's volume. The formula for the volume of a circular cone is

[tex]V=\frac{1}{3}\pi r^2h[/tex]  and here's what we know:

r = 2 and h = 8. The formula for volume has too many unknowns in it, so let's get the radius in terms of the height and sub that in so we only have one variable. The reason I'm getting rid of the radius is because in the problem we are being asked how much work is done by pumping the liquid to the top of the tank, which is a height thing. Solve for r in terms of h using proportions:

[tex]\frac{r}{2}=\frac{h}{8}[/tex] and solve for r:

[tex]r=\frac{2}{8}h =\frac{1}{4}h[/tex] so we will plug that in and rewrite the equation:

[tex]V=\frac{1}{3}\pi(\frac{1}{4}h)^2h[/tex] and simplify it til it's a simple as it can get.

[tex]V=\frac{1}{3}\pi(\frac{1}{16}h^2)h[/tex] and

[tex]V=\frac{\pi}{48}h^3[/tex] and since the volume is what is changing as we pump liquid out, we find the derivative of this equation.

[tex]\frac{dV}{dt}=\frac{\pi}{48}*3h^2\frac{dh}{dt}[/tex] and of course this simplifies as well:

[tex]\frac{dV}{dt}=\frac{\pi}{16}h^2\frac{dh}{dt}[/tex]

Work is equal to the amount of force it takes to move something times the distance it moves. In order to find the force it takes to move this liquid, we need to multiply the amount (volume) of liquid times the weight of it, given as 1000 kg/m³:

F = [tex]1000(\frac{\pi}{16}h^2\frac{dh}{dt})[/tex] and the distance it moves is 8 - h since the liquid has to move the whole height of the tank in order to move to the top of the 8-foot tank. That makes the whole integral become:

[tex]W=\int\limits^8_0 {1000(\frac{\pi}{16}h^2(8-h)) } \, dh[/tex] and we'll just simplify it down all the way:

[tex]W=62.5\pi\int\limits^8_0 {8h^2-h^3} \, dh[/tex] and you're done (except for solving it, which is actually the EASY part!!)

Answer:

a)125/291

b) 48/73

Step-by-step explanation:

a) total of yes/total asked

b) total above average yes/ total above average (yes and no)

Answer:

See explanation. You didn't specify on whether the problem asks for a fraction or decimal, so I put both decimal and fraction.

Step-by-step explanation:

First we answer a:

Total amount of people polled is 291. Number of people who wear glasses is: [tex]48 + 51 + 26 = 125[/tex]

Divide to get the proportion: [tex]\frac{125}{291}[/tex] which is also equal to: 0.4295532646

Then we answer b:

b asks for the proportion of all above average readers who wear glasses, so the total number would be: [tex]48 + 25 = 73[/tex]. The number of above average readers who wear glasses is then 48.

We then get the proportion: [tex]\frac{48}{73}[/tex], which is also equal to 0.6575342466.

Answer:

76 students scored above 80%.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The mean examination mark of a random sample of 1390 students is 67% with a standard deviation of 8.1%.

This means that [tex]\mu = 67, \sigma = 8.1[/tex]

Proportion above 80:

1 subtracted by the p-value of Z when X = 80, so:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{80 - 67}{8.1}[/tex]

[tex]Z = 1.6[/tex]

[tex]Z = 1.6[/tex] has a p-value of 0.9452.

1 - 0.9452 = 0.0548.

Out of 1390 students:

0.0548*1390 =  76

76 students scored above 80%.

Answer:

9

Step-by-step explanation:

8 5/6

5/6 is close to 1 so it will round up

8+1 = 9

8 5/6 rounds to 9

Answer:

[tex]9[/tex]

Step-by-step explanation:

Step 1:  Round [tex]8\frac{5}{6}[/tex] to the nearest whole number

In order to round up, the fraction needs to be either 1/2 or greater than 1/2.  In our case, it is greater than half therefore we will round up to 9.

Answer:  [tex]9[/tex]

Answer:

The answer is 1/9 and 1/2

Answer:

[tex]Area = \infty[/tex]

Points of intersection: (1.225,-1.58) and (1.225,1.58)

Step-by-step explanation:

Given

[tex]x = \sqrt{4 - y^2}[/tex]

[tex]y^2 = 1 + x^2[/tex]

Required

The region area

Plot the graphs of [tex]x = \sqrt{4 - y^2}[/tex] and [tex]y^2 = 1 + x^2[/tex]

Make y the subject in both equations

[tex]x = \sqrt{4 - y^2}[/tex]

Square both sides

[tex]x^2 = 4 - y^2[/tex]

Rewrite

[tex]y^2 = 4 - x^2[/tex]

Take square roots

[tex]y = \sqrt{4 - x^2[/tex]

So, we have:

[tex]f(x) = \sqrt{4 - x^2}[/tex]

[tex]y^2 = 1 + x^2[/tex]

Take square roots

[tex]y = \sqrt{1 + x^2}[/tex]

So, we have:

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

The point of intersection is:

[tex]f(x) = g(x)[/tex]

[tex]\sqrt{4 - x^2} = \sqrt{1 + x^2}[/tex]

Square both sides

[tex]4 - x^2 = 1 + x^2[/tex]

Collect like terms

[tex]x^2 + x^2 = 4 - 1[/tex]

[tex]2x^2 = 3[/tex]

Divide by 2

[tex]x^2 = 1.5[/tex]

Take square roots

[tex]x = 1.225[/tex]

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

[tex]g(x) = \sqrt{1 + 1.5}[/tex]

[tex]g(x) = \sqrt{2.5}[/tex]

[tex]g(x) = \±1.581[/tex]

So, the point of intersection is at: (1.225,-1.58) and (1.225,1.58)

See attachment

From the attached image, we can see that the curves do not enclose

Hence:

[tex]Area = \infty[/tex]

Answer:

Step-by-step explanation:

The formula to find arc length is

[tex]AL=\frac{\theta}{360}*\pi d[/tex] where theta is the measure of the central angle and d is the diameter. If we are dealing with a semicircle, the measure of the central angle is 180 degrees. Filling in:

[tex]AL=\frac{180}{360}*\pi (18)[/tex] which simplifies a bit to

[tex]AL=\frac{1}{2}*\pi (18)[/tex] and a bit more to

AL = 9π. That answer is obviously in terms of π; if you need it in terms of whatever your measurement is (feet, inches, cm, etc.) the answer would be, rounded to the nearest tenth, 28.3 units

Answer:

A). 2x^2(2x^2 + 5x + 1)

B). (x + 6)(x + 7)

Step-by-step explanation:

A). 4x^4+10x^3+2^2

I assume the problem is

4x^4 + 10x^3 + 2x^2

Look at he number parts, 4, 10, 2. They have a common factor of 2.

Now look at the variable parts, x^4, x^3, x^2. They have a common factor of x^2.

We factor out 2x^2 from every term.

4x^4 + 10x^3 + 2x^2 =

= 2x^2(2x^2 + 5x + 1)

B). x^2 + 13x + 42

We need to find two numbers whos product is 42 and whose sum is 13. The numbers are 6 and 7.

x^2 + 13x + 42 =

= (x + 6)(x + 7)

Answer:

B.

Step-by-step explanation:

every x, for which |x| > 3.

that is every x < -3 and every x > 3

Answer:

it's true

Step-by-step explanation:

To factorise you need to work out a number that add up to the number with a letter and multiply to the last number

Answer:  

<  

<  

>

<  

>

Step-by-step explanation:

-12<-4

-15<-2

-7>-29

0<20

-101>-159

Answer:

(a) (-8)+(-4) < (-8)-(-4)

(b) (-3)+7-(19) < 15-8+(-9)

(c) 23-41+Il > 23-41-11

(d) 39+(-24)-(15) < 36+(-52)-(-36)

(e)-231+79+51 >-399+159+81

note:

-1 is greater than-20

Answer:

200 (12+3)

Step-by-step explanation:

They sold 200 tickets at a price of (12+3)

200 (12+3)

qualitative

Step-by-step explanation:

b cos the question is in quality format

Answer:

cutee!

SUP???

Hiii friend :]

cuteee~!

prettyyy

Answer b

Step-by-step explanation:

800 divided by 4 is 200, and 1/200 is 0.5 and that as a percent is 0.005

Answer:

(r/s)(6) = r(6)/s(6) = 3(6)-1 / 2(6)+1 = 18-1 / 12+1 = 17/3

So basically the first one is the correct answer.

Step-by-step explanation:

I hope this helped and please kindly mark Brainliest. Thank You <3

Answer:

2.7°C.

Step-by-step explanation:

If it was -7.4°C. at 5 am, then -4.7°C. at 9am, then the temperature rose by 2.7°C.

Proof:

-7.4

-4.7

--------

2.7

Answer:

D

Step-by-step explanation:

3k +4k+2k+10+6

Collect like terms

9k +16

Answred Gauthmath

Answer:

D 3k + 4k + 2k + 10 +6

Step-by-step explanation:

A 4 + 5k + 10 +6 Combine like terms

5k+ 20  not equal

B 4 + 3k + 2k + 10 +6 Combine like terms

5k +20

C 2k +7 + 10 + 6  Combine like terms

2k + 23

D 3k + 4k + 2k + 10 +6  Combine like terms

9k+ 16

Step-by-step explanation:

Actually, it tells you exactly what to do.

First, translate, i.e., move over, the coordinates up by 3:

[tex](1, 4)\rightarrow (1+3, 4+3) = (4, 7)[/tex]

Then reflect this point about the x-axis and to do this,

[tex](x, y) \rightarrow (x, -y)[/tex]

[tex](4, 7) \rightarrow (4, -7)[/tex]

Answer:

15.072

Step-by-step explanation:

Pls Mark Brainiest okay

Answer:

2.88 pi or approximately 9.0432 cm^2

Step-by-step explanation:

The area of a semicircle is 1/2 the area of a circle

A = 1/2 pi r^2

A = 1/2 pi ( 2.4)^2

A = 2.88 pi cm^2

If we use 3.14 as an approximation for pi

A = 2.88 * 3.14

A =9.0432 cm^2

Answer:

D. Rotation reflection is the right answer

Answer:

Rotation, reflection

Step-by-step explanation:

R and I are equal so if you rotate clockwise you'll see I is in the top left and R would be in the bottom left. By reflecting, it's like flipping a pancake. R will now be in the in the top left on top of I.

(It's kind of weird to explain) Sorry if that was confusing.

Answer:

80

Step-by-step explanation:

Objective: Supplementary Angles.

Supplementary Angles are Angles that add up to 180.

In the problem, Two angles add up to 180. We don't know Angle A and we know Angle B.

Let set up the equation

Let x represent the measure of Angle A and x+20 represent the measure of Angle B

[tex]x + x + 20 = 180[/tex]

Combine Like Terms

[tex]2x + 20 = 180[/tex]

Apply Basics Rules of Algebra

[tex]2x = 160[/tex]

[tex]x = 80[/tex]

This means angle A measure 80 degrees

Answer:

See explanation

Step-by-step explanation:

The question is incomplete, as the function is not given.

However, I will give a general rule.

From the question, we understand that the question requires the value of h(3)

Assume:

[tex]h(t) = 20 - 4t[/tex]

Then:

[tex]h(3) = 20 - 4*3[/tex]

[tex]h(3) = 20 - 12[/tex]

[tex]h(3) = 8[/tex]

Answer: attached below is the missing p chart

a)  0.07133

b)  2

c)  0.098

d) 0.045

Step-by-step explanation:

sample size = 150 castings

number of periods = 10

a) Determine the center Line of the control chart

( 0.06 + 0.0933 + 0.06 + 0.06 + 0.0867 + 0.0533 + 0.08 + 0.067 + 0.08 + 0.073) / 10

mean = 0.07133

standard deviation = 0.01335

b) Determine the value of Z to be used

Given that we are using 2sigma limits .

the value of Z to be used = 2

c) Upper limit control

= mean value +  z-value * std

= 0.0713 + 2*0.01335 =  0.098

d) Lower Control Limit

= mean value - z-value * std

= 0.0713 - 2*0.01335 = 0.045

Consecutive terms in this sequence differ by p.

First term: p

Second term: p + p = 2p

Third term: 2p + p = 3p

and so on. It follows that the n-th term satisfies

np = 336

Presumably you meant to say the "sum of the first n terms" is 7224, which is to say

p + 2p + 3p + … + np = 7224

which can be rewritten as

p (1 + 2 + 3 + … + n) = 7224

p (n (n + 1)/2) = 7224

n (n + 1) p = 14,448

Substitute the first equation in the second one and solve for n :

336 (n + 1) = 14,448

n + 1 = 43

n = 42

Now solve for p :

42p = 336

p = 8

Answer:

Step-by-step explanation:

Formula: Simple interest = PRT

P= 5000

R= 9%

T= 17

So, 5000 x 9/100 x 17 = 7650

(A)

Step-by-step explanation:

This system of equations will no solution if they have the same slope and only differ in the y-intercept values. So let's rewrite the two equations into their slope-intercept forms:

[tex]y = \frac{3}{h-2}x + 5[/tex]

[tex]y = \frac{8}{h}x + \frac{5}{h}[/tex]

For them to have no solution, their slopes must equal each other:

[tex]\dfrac{3}{h-2} = \dfrac{8}{h} \Rightarrow 3h=8h-16[/tex]

or

[tex]h = \dfrac{16}{5}[/tex]

Putting this value into our system of equations, we get

[tex]y = \frac{5}{2}x + 5[/tex]

[tex]y = \frac{5}{2}x + \frac{25}{16}[/tex]

This is a system of equations consisting of two parallel lines and as such, do not intersect and so, no solution.

Answer:

13.9 (if x is the Hypotenuse)

Step-by-step explanation:

which one is the Hypotenuse (the side opposite of the 90 degree angle) ?

because that determines the calculation.

if x is the Hypotenuse then Pythagoras looks like this

x² = 7² + 12² = 49 + 144 = 193

x = sqrt(193) = 13.9

if 12 is the Hypotenuse, then it looks like this

12² = 7² + x²

144 = 49 + x²

95 = x²

x = sqrt(95) = 9.75

Answer:

The cost is $322.88.

Step-by-step explanation:

18% off the list price of $375

Before the sales tax, you pay 100% - 18% = 82% = 0.82 of 375, so:

0.82*375 = 307.5

5% sales tax:

100% + 5% = 105% = 1.05 of 307.5. So

307.5*1.05 = 322.88

The cost is $322.88.