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3 years ago

Given the function f(x) = 2^x, find the value of f^−1(32).

Mathematics

1 answer:

klio [65]3 years ago

5 0

$f(x)= 2^{x}$

We are to find the value of $f^{-1}(32)$

First we need to find the inverse of f(x) . The inverse of $2^{x}$ is $\frac{ln(x)}{ln(2)}$ .

Steps to find inverse of f(x) are shown below in the image.

So $f^{-1}(32)$ = $\frac{ln(32)}{ln(2)}=5$

Therefore, the correct answer is option C

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Answer:

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Step-by-step explanation:

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3 years ago

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crimeas [40]

Answer:

r^2=(A/pi)

Step-by-step explanation:

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The amount of time needed for a certain machine to process a job is a random variable with mean EXi = 10 minutes and Var(Xi)=2 m

lana66690 [7]

Answer:

0.98732

Step-by-step explanation:

Given that :

Mean = 10 minutes

Variance = 2 minutes

For less than equal 40 jobs

Mean (m) = 40 * 10 = 400 minutes

Variance = 2 * 40 = 80 minutes

Standard deviation (s) = √variance = √80

Converting hours to minutes

X = 60 * 7 = 420 minutes

P(X≤ 420) :

Z = (x - m) / s

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4 0

3 years ago

Suppose that in a random selection of 100 colored candies, 28% of them are blue. The candy company claims that the percentage

Zigmanuir [339]

Answer:

We conclude that the percentage of blue candies is equal to 29%.

Step-by-step explanation:

We are given that in a random selection of 100 colored candies, 28% of them are blue. The candy company claims that the percentage of blue candies is equal to 29%.

Let p = population percentage of blue candies

So, Null Hypothesis, $H_0$ : p = 29% {means that the percentage of blue candies is equal to 29%}

Alternate Hypothesis, $H_A$ : p $\neq$ 29% {means that the percentage of blue candies is different from 29%}

The test statistics that will be used here is One-sample z-test for proportions;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of blue coloured candies = 28%

n = sample of colored candies = 100

So, the test statistics = $\frac{0.28-0.29}{\sqrt{\frac{0.29(1-0.29)}{100} } }$

= -0.22

The value of the z-test statistics is -0.22.

Also, the P-value of the test statistics is given by;

P-value = P(Z < -0.22) = 1 - P(Z $\leq$ 0.22)

= 1 - 0.5871 = 0.4129

Now, at a 0.10 level of significance, the z table gives a critical value of -1.645 and 1.645 for the two-tailed test.

Since the value of our test statistics lies within the range of critical values of z, so we insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the percentage of blue candies is equal to 29%.

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3 years ago

At the beginning of the month, there were 80 ounces of peanut butter in the pantry. Since then, the family ate 0.3 of the peanut

givi [52]

Answer:

B i think

Step-by-step explanation:

you are supposed to multiply the 80*.3 and that will give you 24 and subtract from 80 but im not sure

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