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3 years ago

Suppose that x and y are positive integers such that x^2 * y^3=46656. What is the sum of all possible values of x?

Mathematics

1 answer:

Nostrana [21]3 years ago

3 0

Answer:

252

Step-by-step explanation:

x² * y³=46656

Prime factors of 46656:

46656 = 2⁶3⁶

Possible values of x:

(2*3)³= 216
3³ = 27
2³ = 8
1

Sum of them:

216 + 27 + 8 + 1 = 252

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Help!! I think I got these wrong, so please help!! Thank you!

Andrew [12]

Answer:

(x+3)(x+4)(x-4)

x+2 and x-3 are not factors but x-4 is

Step-by-step explanation:

let's factor it :)

x^3 + 3x^2 - 16x -48

first we will factor this:

x^3 + 3x^2

x^2(x + 3)

then factor the second part :

- 16x - 48

-16(x + 3)

so now,

x^2(x + 3) - 16(x + 3)

factor out x+3

(x+3)(x^2 - 16)

factor x^2 - 16

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8 0

3 years ago

According to a survey, 60 % of the residents of a city oppose a downtown casino. Of these 60 % about 8 out of 10 strongly opp

katrin [286]

Answer:

(a) 0.48

(b) 0.20

(c) it is not unusual for a radomly selected resident to oppose the casino and strongly oppose the casino.

Step-by-step explanation:

(a) Find the probability that a randomly selected resident opposes the casino and strongly opposes the casino.

The probability that a radomly selected resident opposes the casino and strongly opposes the cassino is the product of the two probabilities, that a resident opposes the casino and that it strongly opposes the casino (once it is in the first group) as it is shown below.

Use this notation:

Probability that a radomly selected resident opposes the casino: P(A)

Probability that a resident who opposes the casino strongly opposes it: P(B/A), because it is the probability of event B given the event A

i) Determine the probability that a radomly selected resident opposes the casino, P(A)

Probability = number of favorable outcomes / number of possible outcomes

P(A) is given as 60%, which in decimal form is 0.60

ii) Next, determine,the probability that a resident who opposes the casino strongly opposes it, P(B/A):

It is given as 8 out of 10 ⇒ P(B/A) = 8/10

iii) You want the probability of both events, which is the joint probability or intersection: P(A∩B).

So, you can use the definition of conditional probability:

P(B/A) = P(A∩B) / P(A)

iv) From which you can solve for P(A∩B)

P(A∩B) = P(B/A)×P(A) = (8/10)×(0.60) = 0.48

(b) Find the probability that a randomly selected resident who opposes the casino does not strongly oppose the casino.

In this case, you just want the complement of the probability that a radomly selected resident who opposes the casino does strongly oppose the casino, which is 1 - P(B/A) = 1 - 8/10 = 1 - 0.8 = 0.2.

(c) Would it be unusual for a randomly selected resident to oppose the casino and strongly oppose the casino?

You are being asked about the joint probability (PA∩B), which you found in the part (a) and it is 0.48.

That is almost 0.50 or half of the population, so you conclude it is not unusual for a radomly selected resident to oppose the casino and strongly oppose the casino.

8 0

3 years ago

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Andreas93 [3]

Answer:

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3 years ago

Given the terms a10 = 3 / 512 and a15 = 3 / 16384 of a geometric sequence, find the exact value of the term a30 of the sequence.

GenaCL600 [577]

The answer is $\frac {3}{2^{29}}$