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3 years ago

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Twenty years ago a small town in Texas had a population of 10,000. The population has increased 8% each year since then. What eq

uation would be used to solve this population growth problem? a. P = 20 10,000)^.08 b. P = 10,000(8)^20 c. P = 10,000(20)^1.08 d. P = 10,000(1.08)^20

1 answer:

andrezito [222]3 years ago

4 0

Answer:

yea

Step-by-step explanation:

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If DKL =.PVX, which of the following statements must also be true? Check all that apply.

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An unbalanced die is manufactured so that there is a 20% chance of rolling a “six." The die is rolled 6

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Answer:

Probability of rolling at least 4 sixes is 0.01696.

Step-by-step explanation:

We are given that an unbalanced die is manufactured so that there is a 20% chance of rolling a “six." The die is rolled 6 times.

The above situation can be represented through binomial distribution;

$P(X = r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r};x=0,1,2,3,.......$

where, n = number trials (samples) taken = 6 trials

r = number of success = at least 4

p = probability of success which in our question is probability of

rolling a “six", i.e; p = 0.20

<u><em>Let X = Number of sixes on a die</em></u>

So, X ~ Binom(n = 6, p = 0.20)

Now, Probability of rolling at least 4 sixes is given by = P(X $\geq$ 4)

P(X $\geq$ 4) = P(X = 4) + P(X = 5) + P(X = 6)

= $\binom{6}{4} \times 0.20^{4} \times (1-0.20)^{6-4}+\binom{6}{5} \times 0.20^{5} \times (1-0.20)^{6-5}+\binom{6}{6} \times 0.20^{6} \times (1-0.20)^{6-6}$

= $15 \times 0.20^{4} \times 0.80^{2}+6 \times 0.20^{5} \times 0.80^{1}+1 \times 0.20^{6} \times 0.80^{0}$

= 0.0154 + 0.00154 + 0.000064

= 0.01696

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Therefore, probability of rolling at least 4 sixes is 0.01696.

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Determine algebraically whether the function is even, odd, or neither even nor odd.

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For a function (fn) to be odd:
f(x) = - f(-x)
For a fn to be even:
f(x) = f(-x)
For a fn to be neither even nor odd
f(x) != f(-x) [No Relation]

(-x)^n = x^n for n -> even
(-x)^n = -x^n for n -> odd
In your example:

f(x) = -4x^3 + 4x
f(-x) = -4 (-x)^3 + 4 (-x)^1 ( 3 and 1 are odd powers )
f(-x) = 4x^3 - 4x (take -1 common to do the check)
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f(x) = - f(-x)
so the function is odd also called symmetric about the origin

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3 years ago