A spherical balloon is inflated with gas at a rate of 500 cubic centimeters per minute. Find the rates of change of the radius when r = 70 centimeters and r = 95 centimeters.

Answer:

53.32114

Step-by-step explanation:

Answer:

the answer is 4800

Answer:

What is mental math?

Mental math is definitely what it sounds like—doing math in your head. But it’s also more nuanced than that. Being good at mental math tricks doesn’t mean that you’re able to solve 8974387 x 396 in your head instantly; while cool, that wouldn’t be very practical for daily life. So what does mental math mean?

It really just means being able to calculate in your head. It doesn’t mean you can solve every type of problem every time, nor is it a skill that you either “have” or “don’t have”; it’s a skill that you can learn, practice, and improve so that you can solve a bigger range of problems. And mental math certainly doesn’t have to be entirely in your head, either. Jotting down the numbers you need to remember to give you a head start (no pun intended), or writing down your solutions at each “step,” does not negate the “mental”-ness of the math.

Is mental math useful?

Ask this question again next time you’re trying to figure out a tip or doing any kind of construction or home improvement project! And, in addition to handy practical uses, knowing how to do mental math can also just keep your brain sharp and curb your reliance on calculators. Because, come on, doesn’t it feel good to reach for a calculator only to realize, “Wait, I don’t need it!” and figure out the answer in your head? (Spoiler: It does!) Not to mention knowing how to mentally solve small, simple math problems can save you some steps and help you out if you do need to solve a more complicated, difficult problem. There are always going to be some math problems that it would be silly to not solve with a calculator, but, yes, mental math is useful. And if you’re wondering if math itself is useful, math lessons you’ll actually use in real life.

Step-by-step explanation:

Answer:

6 hundreds

1 tens

0 ones

4 tenths

7 hundredths

Answer:

A

Step-by-step explanation:

By solving (x+6)(x-9), we get x^2 - 3x - 54. By looking at our y-intercept, we can see that only option A has the correct intercept.

Answer:

A

Step-by-step explanation:

Answer:

the speed value that the radar equipment outputs.

Step-by-step explanation:

A random variable in an experiment is also (and most times the case) called a dependent variable. In this scenario, the random variable would be the speed value that the radar equipment outputs. This is because this value depends on the actual velocity of the cars that pass by the equipment. The faster the car is moving when it passes the radar the higher value will be displayed on the equipment. Therefore, depending completely on the vehicles.

Answer:

3.55 miles

Step-by-step explanation:

You add the mileage of the two trails which is 1.75+1.8=3.55 miles

Answer:

Choice D. [tex]y = 0.75\, x + 5[/tex].

Step-by-step explanation:

The general equation for the slope-intercept form of a line in a cartesian plane is [tex]y = m\, x + b[/tex], where:

Start by finding the value of [tex]m[/tex]. The slope of a line is equal to its rise-over-run. For the two points in this question:

Calculate the slope of this line:

[tex]\displaystyle m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{-12}{-16} = 0.75[/tex].

The equation of the line becomes:

[tex]y = \underbrace{0.75}_{m}\, x + b[/tex].

Substitute the coordinates of either of the two points to find [tex]b[/tex]. For example, for the first point [tex](12, -4)[/tex], substitute in the following:

The equation becomes:

[tex]-4 = 0.75 \times (-12) + b[/tex].

Solve for the value of [tex]b[/tex]:

[tex]b = 5[/tex].

Hence, the slope-intercept form of this line shall be:

[tex]y = 0.75\, x + 5[/tex].

Answer:

The probability that the vaccine is not effective in more than 1 of the 20 individuals is equal to:

P = 1 - P(1) - P(0)

Where:

P(1) = probability that the vaccine is not effective in one individual

P(0) = probability that the vaccine is not effective in 0 individuals.

The probability that the vaccine is effective is 0.95

Then the probability that the vaccine is not effective is 0.05.

Then to calculate P(1), suppose that the vaccine is not effective in the first case and then is effective 19 times, this is:

p(1) = (0.05^1)*(0.95^19)

But this only for one case, we have 20 possible permutations (the vaccine is not effective in the first case, the second case, third case, etc)

Then the actual probability is:

P(1) = 20*((0.05^1)*(0.95^19)) = 0.377

And P(0) is easy to compute:

P(0) = (0.05^0)*(0.95^20) = 0.358

And here we have only one possible permutation, so we do not worry about that.

Then P = 1 - P(1) - P(0) = 1 - 0.377 - 0.358 = 0.265

This means that the probability that the vaccine is not effective in more than one individual is of 0.265 (or 26.5% in percentage form)

Answer:

$1.12

Step-by-step explanation:

When you multiply 8/7 of 56, you get 64.

This shows that you will need 64 paperclips to make 56 inches worth of paper clips. If each paper clip costs two cents, you need to multiply 56 paperclips by 2 cents. 56x0.02=1.12 so it will cost you 1 dollar and twelve cents

Answer:

(-15)

Step-by-step explanation:

10-25 = (-15)

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Answer: Each towel costs $1.90

Step-by-step explanation:

$15.20 divided by 8 = $1.90

Answer: rotation of 180' clockwise about the origin and then dilation with a scale factor of -1, centered at the origin

Step-by-step explanation:

Two triangles are congruent if all the corresponding angles are equal, and if the corresponding side lengths are equal.

Now, this means that if we have a given triangle, and we apply a dilation/contraction, then the resultant triangle will have different side lengths than the initial triangle, then those two triangles can not be congruent.

So we can already discard all the options with dilations.

Now, remember how the dilation works.

If we have a point that is at a distance L of the origin, and we do a dilation of scale factor K centered at the origin, then the new distance of the point and the origin will be K*L.

Notice that if the scale factor is equal to 1, then there is no change.

In the options, we have one where the scale factor is -1.

The minus sign means that will cause the enlargement to appear on the other side of the center of enlargement. But the scale factor still is of absolute value 1, so it will not change anything.

Then the only option that not dilates the triangle is:

Rotation of 180' clockwise about the origin and then dilation with a scale factor of -1, centered at the origin

So this is the only transformation that results in a figure congruent to the triangle ABC

Answer:

c

Step-by-step explanation:

Step-by-step explanation:

znznzmzspmzlsldfpcf

Answer:

21

Step-by-step explanation:

Answer:

-7 (Not here)

Step-by-step explanation:

1. A negative plus a negative equals a negative/ a negative minus a positive equals a negative so: -10 -4 = -14

2. -14 + 7 = -7 so your answer is -7 and it's not an answer choice so you would select "Not here"

Answer:

c

Step-by-step explanation:

y = mx + b

”m” is the slope, so the slope is -2

”b” is the y - intercept, so the y - intercept is (0 , 1)

Answer:

If 10 men dig a ditch in 12 days .

Total man-days required to dig the ditch

= 10 men × 12 days

= 120 man-days

how long would 15 men take to dig it?

No of days required to finish the job by 15 men

= 120 men-days / 15 men

= 8 days

Answer: 8 days will be required to finish the job by 15 men

Step-by-step explanation:

Hope this helps u

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Answer:

probably 5.00

Step-by-step explanation:

Answer: 15 dollars

Step-by-step explanation:

0.3 * 50

Answer: If we multiply then I guess it’s 26*3=78 and 78*20=1,560

Step-by-step explanation:

Answer:

There are 7 ten-dollar bills and 16 five-dollar bills.

Step-by-step explanation:

Let's call:

T: Number of ten-dollar bills

F: Number of five-dollar bills

The amount of money withdrawn from the ATM is $150:

10T+5F=150

Dividing by 5:

[tex]2T+F=30\qquad\qquad [1][/tex]

We also know there are two more than twice as many five-dollar bills as there are ten-dollar bills:

[tex]F=2+2T\qquad\qquad [2][/tex]

Substituting [2] into [1]:

2T+2T+2=30

Rearranging:

2T+2T=30-2

Simplifying:

4T=28

Solving:

T=28/4=7

From [2]:

F=2+2*7=2+14=16

There are 7 ten-dollar bills and 16 five-dollar bills.

Answer:

11/200

Step-by-step explanation:

This is the correct answer boo

9514 1404 393

Answer:

  170 mph

Step-by-step explanation:

The speed of the airplane can be represented by s. The travel time will be ...

  time = distance/speed

  925/(s +15) = 775/(s -15)

  925(s -15) = 775(s +15)

  150s = 25500 . . . . . . . . . add 13875-775s

  s = 170

The rate of the plane in still air is 170 mph.

Answer:

1.41

Step-by-step explanation:

Answer:

I believe that your answer is C and Moon.

Answer:

124.35 X 6.75

Step-by-step explanation:

The total cost of Anya's purchase of home improvement hardware is 132.74  dollars.

What is percentage?

The percentage is the value per hundredth.

It is given that, the sales tax is 6.75% which is not there in the home improvement hardware which cost 124.35 dollars to Anya.

The total cost of purchase including the sales tax is ( 100 + 6.75)% = 106.75% of 124.35 dollars which is,

= (106.75/100)×124.35 dollars.

= 1.0675×124.35 dollars.

= 132.74 dollars.

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Answer:

Step-by-step explanation:

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Answer:

415 ft/s

Step-by-step explanation:

I've attached a diagram showing the triangle formed between the plane, the person and the radio tower.

From the attached diagram, x represents the position between the person and the position on the ground directly below the airplane while s represents the distance between the person and the plane.

The constant elevation remains 4090 ft while the value of x and s varies with time.

Thus, x varies with respect to time as dx/dt while s varies with respect to time as ds/dt.

Now, we are told that the plane is flying at the rate of 700 ft/s. This means that; dx/dt = 700 ft/s

Now we want to find the rate at which the distance between the person and the plane is increasing when the plane passes over the radio tower.

This means that we want to find ds/dt when x = 3010 ft

From pythagoras theorem if x = 3010 ft and the Elevation remains 4090 ft, we can find s as;

s = √(4090² + 3010²)

s = √25788200

s ≈ 5078.21 ft

Since we want to find ds/dt at x = 3010 ft, from the diagram, we can say from pythagoras theorem that;

x² + 4090² = s²

Differentiating x and s with respect to t, we have;

2x(dx/dt) = 2s(ds/dt)

2 will cancel out to give;

x(dx/dt) = s(ds/dt)

ds/dt = (x/s)(dx/dt)

Plugging in 700 for dx/dt, 3010 for x and 5078.21 for s, we have;

ds/dt = (3010/5078.21) × 700

ds/dt ≈ 415 ft/s