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BlackZzzverrR [31]
3 years ago
7

The height of the pyramid in the diagram is three times the radius of the cone. The base area of the pyramid is the same as the

base area of the cone. What is the expression for the volume of the pyramid in terms of the radius r of the cone?
Mathematics
2 answers:
drek231 [11]3 years ago
4 0
B(cone)=B(pyramid)=r²π
V(pyramid)=1/3 * B * H = 1/3 * r² π * 3 r ( 3 will cancel out )= r³ π
Answer: r³ π
Inessa [10]3 years ago
4 0
Hello,

base of the pyramid :πr²
height=r

Volume=b*h/3=1/3* π*r^3


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there are 20 guests at a party the host has 8 gallons of punch he estimates that each guess within 2 cups of punch if his estima
AlekseyPX
STEP 1:
convert gallons to cups & calculate total number of cups

1 gallon= 16 cups

= 8 gallons * 16 cups/gallon
= 128 cups total


STEP 2:
calculate total cups estimated for 20 guests

= 20 guests * 2 cups/guest
= 40 cups needed for guests


STEP 3:
subtract the difference between step 1 and step 2 to find leftover punch

= 128 cups - 40 cups
= 88 cups leftover

OR

GALLONS LEFTOVER
= 88 ÷ 16 cups/gallon= 5 1/2 gallons


ANSWER: There will be 88 cups or 5 1/2 gallons of punch leftover.

Hope this helps! :)
4 0
4 years ago
Mid-West Publishing Company publishes college textbooks. The company operates an 800 telephone number whereby potential adopters
Mumz [18]

The various answers to the question are:

  • To answer 90% of calls instantly, the organization needs four extension lines.
  • The average number of extension lines that will be busy is Four
  • For the existing phone system with two extension lines, 34.25 % of calls get a busy signal.

<h3>How many extension lines should be used if the company wants to handle 90% of the calls immediately?</h3>

a)

A number of extension lines needed to accommodate $90 in calls immediately:

Use the calculation for busy k servers.

$$P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{k} \frac{\left(\frac{\lambda}{\mu}\right)^{t}}{i !}}$$

The probability that 2 servers are busy:

The likelihood that 2 servers will be busy may be calculated using the formula below.

P_{2}=\frac{\frac{\left(\frac{20}{12}\right)^{2}}{2 !}}{\sum_{i=0}^{2} \frac{\left(\frac{20}{12}\right)^{t}}{i !}}$$\approx 0.3425$

Hence, two lines are insufficient.

The probability that 3 servers are busy:

Assuming 3 lines, the likelihood that 3 servers are busy may be calculated using the formula below.

P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{2} \frac{\left(\frac{\lambda}{\mu}\right)^{i}}{i !}}$ \\\\$P_{3}=\frac{\frac{\left(\frac{20}{12}\right)^{3}}{3 !}}{\sum_{i=0}^{3} \frac{\left(\frac{20}{12}\right)^{1}}{i !}}$$\approx 0.1598$

Thus, three lines are insufficient.

The probability that 4 servers are busy:

Assuming 4 lines, the likelihood that 4 of 4 servers are busy may be calculated using the formula below.

P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{k} \frac{\left(\frac{\lambda}{\mu}\right)^{t}}{i !}}$ \\\\$P_{4}=\frac{\frac{\left(\frac{20}{12}\right)^{4}}{4 !}}{\sum_{i=0}^{4} \frac{\left(\frac{20}{12}\right)^{7}}{i !}}$

Generally, the equation for is  mathematically given as

To answer 90% of calls instantly, the organization needs four extension lines.

b)

The probability that a call will receive a busy signal if four extensions lines are used is,

P_{4}=\frac{\left(\frac{20}{12}\right)^{4}}{\sum_{i=0}^{4} \frac{\left(\frac{20}{12}\right)^{1}}{i !}} $\approx 0.0624$

Therefore, the average number of extension lines that will be busy is Four

c)

In conclusion, the Percentage of busy calls for a phone system with two extensions:

The likelihood that 2 servers will be busy may be calculated using the formula below.

P_{j}=\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}$$\\\\$P_{2}=\frac{\left(\frac{20}{12}\right)^{2}}{\sum_{i=0}^{2 !} \frac{\left(\frac{20}{12}\right)^{t}}{i !}}$$\approx 0.3425$

For the existing phone system with two extension lines, 34.25 % of calls get a busy signal.

Read more about extension lines

brainly.com/question/13362603

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8 0
2 years ago
Mags is 2 years older than Vector. Which equation will
Salsk061 [2.6K]

Answer:

m = v + 2

Step-by-step explanation:

Since Mags (m) is 2 years older than Vector (v)

You can use the equation V + 2 which is Vector's age + 2 years. Which would be equal to Mags' age.

6 0
3 years ago
Gail purchase 5 raffle tickets. The grand prize is a vacation to Aruba. A total of 1,500 raffle tickets were sold. There is only
Aleks04 [339]
If it is in fraction you could do 5/1500 and reduce it to 1/300 , to change 1/300 to whole number it would be 3 , to change 1/300 to decimal it would be .03
8 0
3 years ago
Which statements about the graph of the function f(x) = –x2 – 4x + 2 are true? Check all that apply.
Ipatiy [6.2K]
Statements 2, 3, and 5 are true based on the graph of this function.

4 0
4 years ago
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