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3 years ago

Write log1/4(1/64)=3 in exponential form

1 answer:

6 0

For logarithmic equations,
log
b
(
x
)
=
y
log
b
(
x
)
=
y
is equivalent to
b
y
=
x
b
y
=
x
such that
x
>
0
x
>
0
,
b
>
0
b
>
0
, and
b
≠
1
b
≠
1
. In this case,
b
=
1
4
b
=
1
4
,
x
=
1
64
x
=
1
64
, and
y
=
3
y
=
3
.
b
=
1
4
b
=
1
4
x
=
1
64
x
=
1
64
y
=
3
y
=
3
Substitute the values of
b
b
,
x
x
, and
y
y
into the equation
b
y
=
x
b
y
=
x
.
(
1
4
)
3
=
1
64

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Answer:

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Rihanna says she can draw different functions that have the same x-intercepts and the same domain and range. Her teammates say,

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1) Yes, there are many functions that have those x-intercepts with the same domain.

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Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 104 eligible vot

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Answer:

The probability that exactly 27 of 104 eligible voters voted is 0.057 = 5.7%.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this case, assume that 104 eligible voters aged 18-24 are randomly selected.

This means that $n = 104$ .

Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted.

This means that $p = 0.22$

Mean and standard deviation:

$\mu = 104*0.22 = 22.88$

$\sigma = \sqrt{104*0.22*0.78} = 4.2245$

Probability that exactly 27 voted

By continuity continuity, 27 consists of values between 26.5 and 27.5, which means that this probability is the p-value of Z when X = 27.5 subtracted by the p-value of Z when X = 26.5.

X = 27.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{27.5 - 22.88}{4.2245}$

$Z = 1.09$

$Z = 1.09$ has a p-value of 0.8621

X = 26.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{26.5 - 22.88}{4.2245}$

$Z = 0.86$

$Z = 0.86$ has a p-value of 0.8051

0.8621 - 0.8051 = 0.057

The probability that exactly 27 of 104 eligible voters voted is 0.057 = 5.7%.

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3 years ago

A card is selected at random from a deck of 52 playing cards, the probability that a card 2 is selected will be ______________.

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Answer:

b) 4/52

Step-by-step explanation:

Since there are only 4 playing cards in a full deck that are labeled '2', and there are 52 cards in total - then there is a 4 out of 52 chance that a '2' card will be selected!

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