Complete the table, and graph the pairs of values.

Given f(x)=3^(x-2) and g(x)=f(3x)+4, write the function rule for function g and describe the types of transformations that occur

klio [65]

Answer with Step-by-step explanation:

We are given that

$f(x)=3^{x-2}$

$g(x)=f(3x)+4$

We have to write the rule for function g and describe the transformation between f and g.

Compress the function by scale factor 3 and the translation rule is given by

$(x,y)\rightarrow (3x,y)$

Then, we get $h(x)=f(3x)=3^{3x-2}$

Now, shift the y coordinate 4 units above the origin.

Then, the translation rule is given by

$(x,y)\rightarrow (x,y+4)$

Then , we get

$g(x)=3^{3x-2}+4$

3 0

3 years ago

Some people use a rule to see how many hours a child

Viktor [21]

12 hrs. 30-6 is 24/2 gives you 12

3 0

3 years ago

Write the following decimals as fractions in simplest form

rewona [7]

-19/25 if you simply it by 4

7 0

3 years ago

Suppose that you take a sample of 250 adults. If the population proportion of adults who watch news videos is 0.58, what is the

aliina [53]

Answer:

0.36% probability that fewer than half in your sample will watch news videos

Step-by-step explanation:

To solve this question, i am going to use the binomial approximation to the normal.

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 samples 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 problem, we have that:

$n = 250, p = 0.58$

So

$\mu = E(X) = 250*0.58 = 145$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{250*0.58*0.42} = 7.80$

If the population proportion of adults who watch news videos is 0.58, what is the probability that fewer than half in your sample will watch news videos

Half: 0.5*250 = 125

Less than half is 124 or less

So this is the pvalue of Z when X = 124

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

$Z = \frac{124 - 145}{7.8}$

$Z = -2.69$

$Z = -2.69$ has a pvalue of 0.0036

0.36% probability that fewer than half in your sample will watch news videos

8 0

3 years ago

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Can someone help me and explain it to me

Alex_Xolod [135]

Answer:

1) 6

2)4

3)27

4)126

5)15

Step-by-step explanation:

1. We need to see how many 8-miles are in 24 miles, than multiple it with 2in.

(24/8)*2=3*2=6in

2. Fist we calcue how many 17-feets are in 68feets, and multiple that with 1in.

(68/17)*1=4

3. We first see how many 3ins are in 9ins, and than multiple that with 9feet

(9/3)*9=3*9=27

4. First see how many 2ins are in 36ins, and then multiple it with 7.

(36/2)*7=18*7=126feet

5. See how many 15fts are in 75ft And than multiple it with 3.

(75/15)*3=5*3=15

4 0

4 years ago

Read 2 more answers