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3 years ago

If f^-1(x) is the inverse of f(x), which statement must be true?

2 answers:

8 0

The range of f⁻¹(x) is the domain of f(x) and vice versa
The domain of f⁻¹(x) is the range of f(x) and vice versa
and for every x of te domain: f(f⁻¹(x)) = x and f⁻¹(f(x)) = x

k0ka [10]3 years ago

5 0

F(f-1x) will be equal to x

take a simple example

f(x) = 2x

so x = f(x) / 2

f-1(x) = x/2

f(f-1x) = 2 ( x/2) = 2 * x/2 = x

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The bailey family started a trip with a tank of 7/8 full of gas.The family finished the trip with a tank 1/4 full of gas.If no g

aleksklad [387]

The answer is A.5/8.

Why?

Multiply 1/4 with 2/2 to get the same denominator as 7/8, 8. That will yield 2/8.Then, simply subtract 2/8 from 7/8 (7/8 - 2/8), and that equals 5/8.

Hope this helps!

5 0

3 years ago

Read 2 more answers

A manufacturer of nails claims that only 4% of its nails are defective. A random sample of 20 nails is selected, and it is found

irakobra [83]

Answer:

The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer's claim based on this observation.

Step-by-step explanation:

A manufacturer of nails claims that only 4% of its nails are defective.

At the null hypothesis, we test if the proportion is of 4%, that is:

$H_0: p = 0.04$

At the alternative hypothesis, we test if the proportion is more than 4%, that is:

$H_a: p > 0.04$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

4% is tested at the null hypothesis

This means that $\mu = 0.04, \sigma = \sqrt{0.04*0.96}$

A random sample of 20 nails is selected, and it is found that two of them, 10%, are defective.

This means that $n = 20, X = 0.1$

Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.1 - 0.04}{\frac{\sqrt{0.04*0.96}}{\sqrt{20}}}$

$z = 1.37$

P-value of the test and decision:

Considering an standard significance level of 0.05.

The p-value of the test is the probability of finding a sample proportion above 0.1, which is 1 subtracted by the p-value of z = 1.37.

Looking at the z-table, z = 1.37 has a p-value of 0.9147

1 - 0.9147 = 0.0853

The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer's claim based on this observation.

7 0

3 years ago

Read 2 more answers

Plz help! Ive been stuck on this for hours!!!!

Marysya12 [62]

Answer:

h $\geq$ 8

Step-by-step explanation:

h-(-2) $\geq$ 10=h+2 $\geq$ 10

subtract 2 on both sides to get h $\geq$ 8

3 0

3 years ago

Read 2 more answers

Suppose that prices of recently sold homes in one neighborhood have a mean of $215,000 with a standard deviation of $8900. Using

bonufazy [111]

Answer:

The minimum percentage of recently sold homes with prices between $197,200 and $232,800 is 75%.

Step-by-step explanation:

Chebyshev Theorem

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by $100(1 - \frac{1}{k^{2}})$ .

In this question:

Mean of $215,000, standard deviation of $8900.

What is the minimum percentage of recently sold homes with prices between $197,200 and $232,800?

215000 - 2*8900 = 197200

215000 + 2*8900 = 232800

Within 2 standard deviations of the mean, so:

The minimum percentage of recently sold homes with prices between $197,200 and $232,800 is 75%.

4 0

3 years ago

Trevon bought one package of blueberries for $3. How many packages can Elisa buy if she has $63

kakasveta [241]

Since trevon bought one package for 3 dollars than 3 x 21 equals 63
Answer = 21

8 0

2 years ago