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3 years ago

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The diameter d of a sphere is twice the radius r. The volume of the sphere as a function of its radius is given by v(r)= 4/3(3.4

)(r)^3 A) write the diameter d of the sphere as a function of the radius r

1 answer:

Goryan [66]3 years ago

5 0

Answer:

A) d = 2r

Step-by-step explanation:

A) The first sentence in the problem statement tells you the diameter is twice the radius:

d = 2r

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Calculate the sample standard deviation and sample variance for the following frequency distribution of hourly wages for a sampl

lidiya [134]

Answer:

(a) The sample variance is 16.51

(a) The sample standard deviation is 4.06

Step-by-step explanation:

Given

$\begin{array}{cc}{Class} & {Frequency} & 8.26 - 10.00 & 20 &10.01-11.75 & 38 &11.76 - 13.50& 36 & 13.51-15.25 &25&15.26-17.00 &27 &\ \end{array}$

Solving (a); The sample variance.

First, calculate the class midpoints.

This is the mean of the intervals.

i.e.

$x_1 = \frac{8.26+10.00}{2} = \frac{18.26}{2} = 9.13$

$x_2 = \frac{10.01+11.75}{2} = \frac{21.76}{2} = 10.88$

$x_3 = \frac{11.76+13.50}{2} = \frac{25.26}{2} = 12.63$

$x_4 = \frac{13.51+15.25}{2} = \frac{28.76}{2} = 14.38$

$x_5 = \frac{15.26+17.00}{2} = \frac{32.26}{2} = 16.13$

So, the table becomes:

$\begin{array}{ccc}{Class} & {Frequency} & {x} & 8.26 - 10.00 & 20&9.13 &10.01-11.75 & 38 &10.88&11.76 - 13.50& 36 &12.63& 13.51-15.25 &25&14.38&15.26-17.00 &27 &16.13\ \end{array}$

Next, calculate the mean

$\bar x = \frac{\sum fx}{\sum f}$

$\bar x = \frac{20*9.13 + 38 * 10.88+36*12.63+25*14.38+27*16.13}{20+38+36+25+27}$

$\bar x = \frac{1845.73}{146}$

$\bar x = 12.64$

Next, the sample variance is:

$\sigma^2 = \frac{\sum f(x - \bar x)^2}{\sum f - 1}$

So, we have:

$\sigma^2 = \frac{20*(9.13-12.63)^2 + 38 * (10.88-12.63)^2 +...........+27 * (16.13 -12.63)^2}{20+38+36+25+27-1}$

$\sigma^2 = \frac{2393.6875}{145}$

$\sigma^2 = 16.51$

The sample standard deviation is:

$\sigma = \sqrt{\sigma^2}$

$\sigma = \sqrt{16.51}$

$\sigma = 4.06$

6 0

2 years ago

The are of the shape is __ square centimeter

tensa zangetsu [6.8K]

Answer:

35 cm

Step-by-step explanation:

To find the area of the bottom portion, you would use the formula for finding out a triangle (B*H*1/2) which is:

(4+4)*5.75*1/2=<u>23</u>

Then, for the top portion, one would find the area of the triangles on the sides (with two marks going through). Since along the middle is 8cm, and along the top is 4, we can see that there is 2cm on either side, so that is the length of the base of the triangle. To solve for the top triangles, you would do almost the same thing as the last one:

2*2*1/2=2

But since there's two identical triangles on either side, we can multiply that by two, which would bring it to <u>4.</u>

That just leaves the rectangle that is left between the two triangles. To solve this, it's just B*H and luckily both of those are labeled for you already:

4*2=<u>8</u>

Now, to find the total area, all you have to do is add up the areas of the different sections:

23+4+8=35 cm

Hope this helps!

4 0

3 years ago

(40 points + Brainliest)

statuscvo [17]

Answer is A.

rate = 10/1 = 10ft and passing origin (0,0)

7 0

3 years ago

Read 2 more answers

The inside of tank is in the shape of a right rectangular prism. The base of the prism is 85 cm by 64 cm. What is the minimum he

Allisa [31]

Answer:

16.9 cm

Step-by-step explanation:

The volume of a prism = Area of base × height

For a rectangular prism, the base of the area = length × breadth

The volume of the liquid = 92 L

Since 1 L = 1000 cm³, 92 L = 92000 cm³

92000 = 85 × 64 × h

5440 h = 92000

h = 92000 ÷ 5440 = 16.9 cm

8 0

2 years ago

Suppose a van gets 22 mi/gal. The distance traveled D(g) is a function of the gallons of gas used

babymother [125]

Answer:

a) Table and graph showed

b) The distance will be 231 miles

c) Yes

Step-by-step explanation:

We know the van gets 22 mi/gal, so the distance D in miles traveled by the van can be expressed as

D(g)=22g, being g the number of gallons of gas used

a) The graph of the function D and its corresponding table of values is shown below.

b) If the van used g=10.5 gallons of gas, the distance would be:

D(10.5)=22 x 10.5 = 231 miles

c) The values of g are real in nature because they represent the amount of gas consumed by the van and it can be any real positive number. Being D a linear function of g, it also happens to take positive real values. Then it makes sense to connect the points with lines.

5 0

3 years ago