Air is being pumped into a spherical balloon at a rate of 5 cm^3/min. Determine the rate at which the radius of the balloon is increasing when the diameter of the balloon is 20 cm

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:

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:

I think that d is the answer

Answer:

Step-by-step explanation:

r is the common ratio.

Third term minus first term is 48.

a₃ - a₁ = 48

a₃ = a₁r²

a₁r² - a₁ = 48

a₁(r²-1) = 48

r²-1 = 48/a₁

Fourth term minus second term is 144.

a₄ - a₂ = 144

a₂ = a₁r

a₄ = a₁r³

a₁r³ - a₁r = 144

a₁r(r²-1) = 144

r²-1 = 144/(a₁r)

48/a₁ = 144/(a₁r)

r = 3

:::::

r²-1 = 48/a₁

a₁ = 6

:::::

a₆ = a₁r⁵ = 1458

(i) The common ratio for the given condition is 3.

ii) The first term of the sequence is 6.

iii) The 6th term of the sequence​ is 1458.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity,

It is given that a  is a geometric progression such that the 3rd term minus a first term is 48. The 4th term minus the 2nd term 144.

Each number following the first in a geometric sequence is multiplied by a particular number, known as the common ratio.

As the third term minus the first term is 48.

a₃ - a₁ = 48

a₃ = a₁r²

a₁r² - a₁ = 48

a₁(r²-1) = 48

r²-1 = 48/a₁

The fourth term minus the second term is 144.

a₄ - a₂ = 144

a₂ = a₁r

a₄ = a₁r³

a₁r³ - a₁r = 144

a₁r(r²-1) = 144

r²-1 = 144/(a₁r)

48/a₁ = 144/(a₁r)

r = 3

r²-1 = 48/a₁

a₁ = 6

a₆ = a₁r⁵ = 1458

Thus the common ratio for the given condition is 3, the first term of the sequence is 6 and the 6th term of the sequence​ is 1458.

Learn more about the sequence here:

brainly.com/question/21961097

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The graph of the linear function y = -2x + 5 is attached below.

A linear function is a type of function that describes a relationship between two variables in which the output of the function is directly proportional to the input. It is a type of function that follows a straight-line pattern when graphed. Linear functions can be expressed in the form of an equation, such as y = mx + b, where m is the slope of the line, and b is the y-intercept.

The linear function given is y = -2x + 5

In this function, the slope of the line is -2 and the y-intercept is 5

This shows that the graph will pass through the y-axis at 5 which is a straight line.

Kindly find attached graph below.

Learn more on graph of linear function here;

https://brainly.com/question/7807573

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Answer:a.3/6

Step-by-step explanation:

Because there’s a total of 12 files in each bag which is 6 in each

Answer:

Step-by-step explanation:

Use the change-of-base rule.

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:

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:

[tex]y=\frac{\displaystyle 1}{\displaystyle 7}x+\frac{\displaystyle15}{\displaystyle 7}[/tex]

Step-by-step explanation:

Hi there!

Slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)

1) Determine the slope (m)

[tex]m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_1}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the given points (-1, 2) and (6, 3):

[tex]m=\frac{\displaystyle 3-2}{\displaystyle 6-(-1)}\\\\m=\frac{\displaystyle 3-2}{\displaystyle 6+1}\\\\\m=\frac{\displaystyle 1}{\displaystyle 7}[/tex]

Therefore, the slope of the line is [tex]\frac{\displaystyle 1}{\displaystyle 7}[/tex]. Plug this into [tex]y=mx+b[/tex]:

[tex]y=\frac{\displaystyle 1}{\displaystyle 7}x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=\frac{\displaystyle 1}{\displaystyle 7}x+b[/tex]

Plug in one of the given points and solve for b:

[tex]2=\frac{\displaystyle 1}{\displaystyle 7}(-1)+b\\2=-\frac{\displaystyle 1}{\displaystyle 7}+b[/tex]

Add [tex]\frac{\displaystyle 1}{\displaystyle 7}[/tex] to both sides to isolate b:

[tex]2+\frac{\displaystyle 1}{\displaystyle 7}=-\frac{\displaystyle 1}{\displaystyle 7}+b+\frac{\displaystyle 1}{\displaystyle 7}\\\\\frac{\displaystyle15}{\displaystyle 7} =b[/tex]

Therefore, the y-intercept of the line is [tex]\frac{\displaystyle15}{\displaystyle 7}[/tex]. Plug this back into [tex]y=\frac{\displaystyle 1}{\displaystyle 7}x+b[/tex]:

[tex]y=\frac{\displaystyle 1}{\displaystyle 7}x+\frac{\displaystyle15}{\displaystyle 7}[/tex]

I hope this helps!

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

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:

f(0) = 6

Step-by-step explanation:

Complete question:

The function f (x) is given by the set of ordered pairs 1,0 (-10,2), (0,6) (3,17) (-2,-1) which equation is true

f(-10)=1

f(2)=-10

f(0)=6

f(1)=-10

Given the coordinate (x, y). This shows that the input function is x and the output function is y, i.e. f(x) = y

From the pair of coordinates given, hence;

f(1) = 0

f(-10) = 2

f(0) = 6

f(3) = 17

f(-2) = -1

From the following options, this shows that f(0) = 6 is correct

Answer:

f(0) = 6

Step-by-step explanation:

EDGE

Answer:

a) The 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week is (0.2982, 0.481).

b) 30% = 0.3 is part of the confidence interval, which means that there is no evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population.

Step-by-step explanation:

Question a:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

A survey of 77 teenagers finds that 30 have 5 or more servings of soft drinks a week.

This means that [tex]n = 77, \pi = \frac{30}{77} = 0.3896[/tex]

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3896 - 1.645\sqrt{\frac{0.3896*0.6104}{77}} = 0.2982[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3896 + 1.645\sqrt{\frac{0.3896*0.6104}{77}} = 0.481[/tex]

The 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week is (0.2982, 0.481).

Question b:

30% = 0.3 is part of the confidence interval, which means that there is no evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population.

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

qualitative

Step-by-step explanation:

b cos the question is in quality format

Answer:

cutee!

SUP???

Hiii friend :]

cuteee~!

prettyyy

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:

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:

200 (12+3)

Step-by-step explanation:

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

200 (12+3)

Answer:

36 people

Step-by-step explanation:

The expected value E(X) = mean of sample = np

Where, p = population proportion, p = 9% = 0.09

n = sample size, = 400

The mean of the number of people with genetic mutation, E(X) = np = (400 * 0.09) = 36

36 people

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:

The total sum of angles in a triangle is 180, thus the value of ∠ACB will be obtained as follows:

Given that the triangle is a right triangle, the sum of angles will be:

(4x)°+(7x-20)°+90=180

simplifying and solving for x we get:

4x+7x-20+90=180

11x=180+20-90

11x=110

dividing both sides by 11 we get:

(11x)/11=110/11

this gives us

x=10°

Thus substituting the value of x in:

∠ACB=(7x-20)°  

=(7*10-20)

=70-20

=50°

Answer: 50°

Answer:

50

Step-by-step explanation:

Answer:

351

Step-by-step explanation:

27C2 = 27! / 2! × (27-2)!

= 27×26×25! / 2×1 × 25!

= 27×26 /2

= 27×13

= 351

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: 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

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%.