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andrew-mc [135]
3 years ago
9

Complete the following sentences.Mark is rolling a number cube with sides labeled 1 through 6 and is looking for the probability

of it stopping on any number except for a 5. The total number of outcomes is , and the number of ways the event occurs is . The probability of Mark’s event occurring is and listed as a percentage, it is approximately .
Mathematics
1 answer:
max2010maxim [7]3 years ago
6 0
Total number of outcomes = 6
Number of ways the event occurs = 5
Probability = 5/6
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A piece of PVC material weighs 0.063 pounds per cubic inch. What's the weight of a 36-inch piece of PVC pipe with an outside dia
nalin [4]

The weight of a 36-inch piece of PVC pipe is 0.20 pounds

<h3>How to determine the weight of a 36-inch piece of PVC pipe?</h3>

The given parameters about the 36-inch piece of PVC pipe are

Height, h = 36 inches

Outside diameter, D = 0.82 inches

Inside diameter, d= 0.75 inches

The volume of the PVC pipe is then calculated as:

V = πh(D/2)^2 - πh(d/2)^2

Substitute the known parameters in the above equation

V = 3.14 * 36 * (0.82/2)^2 - 3.14 * 36 * (0.75/2)^2

Evaluate the quotients

V = 3.14 * 36 * 0.41^2 - 3.14 * 36 * 0.375^2

Evaluate the exponents

V = 3.14 * 36 * 0.1681 - 3.14 * 36 * 0.140625

Evaluate the products

V = 19.002024 - 15.89625

Evaluate the difference

V = 3.105774 cubic inches

From the question, we have:

Weight =  0.063 pounds per cubic inch

So, the total weight is

Total weight = 3.105774 cubic inches * 0.063 pounds per cubic inch

Evaluate the product

Total weight = 0.195663762 pounds

Approximate

Total weight = 0.20 pounds

Hence, the weight of a 36-inch piece of PVC pipe is 0.20 pounds

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5 0
1 year ago
What is the fully factored form of 32a3 12a2? 4a2(8a 3) 4a(8a2 3a) 12a2(3a 1) 12a(3a2 a)
scZoUnD [109]

we have

32a^{3}+12a^{2}

<u>Find the greatest Common Factor GCF</u>

we know that

32=2^{5} \\ Factors=1,2,4,8,16,32\\ \\ a^{3} \\ Factors=1,a,a^{2} ,a^{3} \\ \\ 12=2^{2} *3\\ Factors=1,2,3,4,6,12\\ \\ a^{2} \\ Factors=1,a,a^{2}

The GCF is equal to 4a^{2}

so

the fully factored form is equal to

32a^{3}+ 12a^{2}=4a^{2}(8a+3)

<u>the answer is</u>

4a^{2}(8a+3)

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The given situation above is an example of a geometric sequence with first term equal to three and the common ratio equal to 3. For the second day, Raul used 9 bags of cement. He used 27 bags on the third and 81 on the fourth. To answer the question, add the number of bags from second to fourth day. The answer is equal to 117 bags of cement. 
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