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Akimi4 [234]
3 years ago
14

Which of the following functions gives the radius, r(v), of a conical artifact that is 20 inches tall as a function of its volum

e, v, in cubic inches?
Mathematics
1 answer:
nalin [4]3 years ago
5 0
By calculus or elementary geometry, we know that the formula for the volume of a cone, given pi (the constant), its height h and its radius r is:
V=pi*h*r^2/3
Lets solve this relation for the radius:
3V=pi*h*r^2

\frac{3V}{pi*h} =r^2
\sqrt{\frac{3V}{pi*h}} = r
Now we have found a general formula that gives us the radius of a cone, given its volume and height. We need only substitute height (20in) and pi=3.14 to get the numerical equation: r=0.2185*\sqrt{V}
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There are 10 employees in a particular division of a company. Their salaries have a mean of 570,000, a median of $55,000,and a s
harkovskaia [24]

Answer:

a) $160,000

b) $55,000

c) $332264.804

Step-by-step explanation:

We are given that there are 10 employees in a particular division of a company and their salaries have a mean of $70,000, a median of $55,000, and a standard deviation of $20,000.

And also the largest number on the list is $100,000 but By accident, this number is changed to $1,000,000.

a) Value of mean after the change in value is given by;

     Original Mean = $70,000

       \frac{\sum X}{n} = $70,000  ⇒ \sum X = 70,000 * 10 = $700,000

   New \sum X after change = $700,000 - $100,000 + $1,000,000 = $1600000

  Therefore, New mean = \frac{1600000}{10} = $160,000 .

b) Median will not get affected as median is the middle most value in the data set and since $1,000,000 is considered to be an outlier so median remain unchanged at $55,000 .

c) Original Variance = 20000^{2} i.e.  20000^{2} = \frac{\sum x^{2} - n*xbar }{n -1}

    Original \sum x^{2} = (20000^{2} * (10-1)) + (10 * 70,000) = $3,600,700,000

    New \sum x^{2} = $3,600,700,000 - 100,000^{2} + 1,000,000^{2} = 9.936007 * 10^{11}  

    New Variance = \frac{new\sum x^{2} - n*new xbar }{n -1} = \frac{9.936007 *10^{11}  - 10*160000 }{10 -1} = 1.103999 * 10^{11}    Therefore, standard deviation after change = \sqrt{1.103999 * 10^{11} } = $332264.804 .

7 0
3 years ago
Which statements can be concluded from the diagram and used to prove that the triangles are similar by the SAS similarity theore
velikii [3]

Answer:

RS/VU=ST/UT and ∠S≅∠U

Step-by-step explanation:

we know that

The <u>Side-Angle-Side Similarity Theorem </u>states that: If two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar

In this problem the included angle is

∠S≅∠U

therefore

side RS must be proportional to side VU  and side ST must be proportional to side UT

so

RS/VU=ST/UT

<em>Verify</em>

substitute the given values

12/6=16/8

2=2 -----> is true

therefore

The two sides are proportional

6 0
2 years ago
Read 2 more answers
An arts academy requires there to be 4 teachers for every 84 students and 3 tutors for every 30 students. How many students does
Sonja [21]

Answer:

21 students per teacher

10 students per tutor

10 tutors needed for 110 students

Step-by-step explanation:

84 ÷4=21

30÷3=10

110÷10=10

6 0
3 years ago
This is with radicals
Lynna [10]

Answer: -16

Step-by-step explanation:

2(x+4)

———— = 8

- 5

2x+8

——— = 8

-5

2x+8

-5 • ——— = 8(-5)

-5

2x+8 = -40

2x = -32

x = -16

8 0
3 years ago
A study is done on the population of a certain fish species in a lake. Suppose that the population size P(1) after years is give
Andre45 [30]

Answer:

  • Growth
  • 22%

Step-by-step explanation:

<u>Given function:</u>

  • P(t) = 400(1.22)^{t}

<u>Initial population size is when t = 0</u>

  • P(0) = 400(1.22)⁰ = 400(1) = 400

<u>The multiple of 1.22 is applied every year, so the ratio of change is:</u>

  • 1.22 = 122% = 100% + 22%

This is an exponential growth which represents 22% annual growth.

5 0
3 years ago
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