How do I do a question containing powers that are improper fractions?say for example 81 to the power of 3/2. thx

Answers

Answer 1

Answer: ( 81 )^ ( 3 / 2 ) = ( 3 ^ 4 )^ ( 3 / 2 ) = 3 ^( 4 * 3 / 2 ) = 3 ^ 6 = 729.

Answer 2

Answer: $81^{\tfrac{3}{2}}=\n(3^4)^{\tfrac{3}{2}}=\n3^{4\cdot\tfrac{3}{2}}=\n3^(2\cdot3)=\n3^6=\n729$

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What is the sum of (x^2+6x-5) + (2x^2+15)

Answers

Answer:

3x^2 + 6x + 10

Step-by-step explanation:

Because we're adding it, it doesn't matter if we just take out the parenthesis.

X^2 + 2x^2 gives us 3x^2.

6x stays the same.

-5 + 15 gives us 10.

3x^2 + 6x + 10

Dustin says that FGH is an equilateral triangle because the sides appear to be the same length.Is his reasoning valid?Explain

Answers

His reasoning is not valid because they might actually appear to be equal to his sight, but should he measure them they might not exactly be.

So he just can't look at it and conclude. He can say it is equilateral if each angles measures 60 degrees.

If n denotes a number to the left of 0 on the number line such that the square of n is less than 1/100, then the reciprocal of n must be _______.A. less than -10B. between -1 and -1/10C. between -1/10 and 0D. between 0 and -1/10E. greater than 10

Answers

Answer: E. Greater than 10

Step-by-step explanation:

First, know that number to the left of a number line are negative and the square of any negative number will be positive and a perfect square.

Since the square of the unknown number is less than 1/100 i.e 0.01 then the possible unknown number 'n' can be -0.01 itself, of which the square of -0.01 will give us 0.0001 (1/10,000) i.e a value less than 0.01.

The reciprocal of 1/10000 is 10,000 which is a value greater than 10.

A battery manufacturer makes batteries that have a failure rate of .015. That is, 15 out of each 1,000 batteries are defective. What is the probabilitythat a batch of 10,000 batteries will contain at least 175 defective batteries?

Answers

p(success) = 0.015
p(failure) = 1 - 0.015 = 0.985
let x be the random variable that a battery is defective, then
p(x >= 175) = 1 - P(x <= 175)
= 1 - P[z <= (175 - np)/(sqrt(npq))]
= 1 - P[z <= (175 - 10000 * 0.015)/(sqrt(10000 * 0.015 * 0.985))]
= 1 - P[z <= (175 - 150)/(sqrt(147.75))]
= 1 - P[z <= (25/12.16)]
= 1 - P(z <= 2.057)
= 1 - 0.9801
= 0.0199

Caroline delivers flowers and earns $1.25 for each rose and $0.75 for each daisy. What is her total pay for a week in which she sold 288 roses and 432 daisies?