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juin [17]
3 years ago
6

What is the effect on the volume of a sphere if the radius is divided by 3?

Mathematics
1 answer:
Neko [114]3 years ago
6 0

For this case we have by definition, that the volume of a sphere is given by:

V = \frac {4} {3} \pi * r ^ 3

Where:

r: It is the radius of the sphere

If the radius is divided by 3 we have:

\frac {r} {3}:

V = \frac {4} {3} \pi * (\frac {r} {3}) ^ 3\\V = \frac {4} {3} \pi * \frac {r ^ 3} {27}\\V = \frac {4} {81} \pi * r ^ 3

ANswer:

the volume decreases considerably because the denominator increases

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Given a set of data, what steps would you take to identify whether the data showed linear or exponential growth?
emmasim [6.3K]
The very first thing to do to identify whether the data showed linear or exponential growth is to plot the data. By plotting the data, you are able to visualize the form or trend of your data. You can also see if your data trend forms a line. If it forms a line, it is linear. If your data shows somehow a rapid increasing magnitude of slope then, it is exponential.
5 0
2 years ago
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Use this data in the problem below. Follow the steps carefully. Round to the nearest tenth. Lot 1: Week 1: 600 Week 2: 300 Week
Dafna11 [192]

Answer:

Step-by-step explanation:

The given data set is:

Week 1: 600

Week 2: 300

Week 3: 500

Week 4: 900

The following are the steps to find the standard deviation:

Step 1. Jim enters the data and calculates the average or mean.

Mean=\frac{600+300+500+900}{4}=\frac{2300}{4}=575

Step 2. Jim calculates the deviation from the mean by subtracting the mean from each value.

Data value (x)                                                             x-{\overline{x}}

600                                                                           25

300                                                                         -275

500                                                                         -75

900                                                                          325

Step 3. Jim squares each deviation to remove negative signs.

Data value (x)                                                           (x-{\overline{x}})^2

600                                                                       625

300                                                                    75625

500                                                                      5625

900                                                                   105625

Step 4. Jim sums the squares of each deviation and divides by the count for the variance.

Variance=\frac{625+75625+5625+105625}{4}=46875

Step 5.Jim takes the square root of the variance to find the standard deviation.

Standard deviation=\sqrt{46875}=216.50

4 0
3 years ago
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In a certain​ state, 50​% of adults indicated that sausage is their favorite pizza. Suppose a simple random sample of adults in
KatRina [158]

Answer:

n = 23

x = 17

p = 0.50

Step-by-step explanation:

For a binomial experiment we have the following variables:

<u>1) Number of trials or Sample size:</u>

The number of trials is represented by n. In the given scenario 23 adults were asked about their favorite pizza, so the number of trials in this will be 23. Thus

n = 23

<u>2) Number of success</u>

The number of success is denoted by x. Number of success indicates that how many trials resulted in the favorable outcome. In the given case, choosing a sausage pizza is a success. Since 17 adults chose the sausage, so

x = 17

<u>3) Probability of success on single trial</u>

This is represented by p. It is stated that 50% adults say sausage is their favorite pizza. So,

p = 50% = 0.50

4 0
3 years ago
Is -5 2/3 the multiplicative inverse of 3/-17? ​<br><br>PLEASE HELP!!
Ostrovityanka [42]

Answer:

Yes

Step-by-step explanation:

Multiplicative Inverse of rational number:

       When we multiply a rational number and its multiplicative inverse, we get 1

     \sf -5 \dfrac{2}{3}=\dfrac{-17}{3}

  Now,multiply this with (3/-17)

          \sf \dfrac{-17}{3}*\dfrac{3}{-17} = 1

So, -5 2/3  is the multiplicatice inverse of 3/-17

3 0
2 years ago
) If the gradient of ff is ∇f=xi⃗ +yj⃗ +3zyk⃗ ∇f=xi→+yj→+3zyk→ and the point P=(−6,−6,−2)P=(−6,−6,−2) lies on the level surface
Paha777 [63]

Answer:

-3x-3y-z=38

Step-by-step explanation:

To find the equation of the tangent plane you can use

\bigtriangledown f_x(x_0,y_0,z_0)(x-x_0)+\bigtriangledown f_y(x_0,y_0,z_0)(y-y_0)+\bigtriangledown f_z(x_0,y_0,z_0)(z-z_0)=0

the point P is (-6,-6,-2). Hence you have

(-6)(x-(-6))+(-6)(y-(-6))+(-2)(z-(-2))=0\\-6x-36-6y-36-2z-4=0\\-6x-6y-2z=76\\-3x-3y-z=38

hope this helps!!

5 0
3 years ago
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