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2 years ago

If you vertically stretch the exponential function, f(x) = 2x, by a factor of 4, what is the equation of the new function?

Mathematics

2 answers:

Blababa [14]2 years ago

7 0

Answer: Equation of new function will be $f(x)=4(2^x)$

Step-by-step explanation:

Since we have given that

The exponential function f(x) is denoted by

$f(x)=2^x$

We need to stretch the exponential function vertically by a factor of 4.

So, let say c = 4.

So, our new equation becomes,

$f(x)=2^x\times c\\\\f(x)=4(2^x)$

Hence, equation of new function will be $f(x)=4(2^x)$

Tema [17]2 years ago

3 0

To vertically strech a function by a factor of c, multiply the whole function by c

so

f(x) vertically streched by a factor of 4 is 4f(x)
so we get
the new function is f(x)=4(2)ˣ

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A rectangular room has a width of 5 yards and length of 6 yards. How many square-feet carpet will be required for carpeting the

Sindrei [870]

Answer:

Option B $270\ ft^{2}$

Step-by-step explanation:

we know that

The area of the rectangle room, is equal to

$A=LW$

where

L is the length

W is the width

we have

$L=6\ yd$

$W=5\ yd$

Remember that

1 yard= 3 feet

Convert yards to feet

$L=6*3=18\ ft$

$W=5*3=15\ ft$

The area is equal to

$A=(18)(15)=270\ ft^{2}$

4 0

2 years ago

3.30 Survey response rate. Pew Research reported in 2012 that the typical response rate to their surveys is only 9%. If for a pa

Artist 52 [7]

Answer:

0% probability that at least 1,500 will agree to respond

Step-by-step explanation:

I am going to use the binomial approximation to the normal to solve this question.

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:

$n = 15000, p = 0.09$

$\mu = E(X) = np = 15000*0.09 = 1350$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{15000*0.09*0.91} = 35.05$

What is the probability that at least 1,500 will agree to respond

This is 1 subtracted by the pvalue of Z when X = 1500-1 = 1499. So

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

$Z = \frac{1499 - 1350}{35.05}$

$Z = 4.25$

$Z = 4.25$ has a pvalue of 1.

1 - 1 = 0

0% probability that at least 1,500 will agree to respond

6 0

2 years ago

The table below shows the amount of lemon juice and sugar needed to make three different-sized batches of lemonade using the sam

mash [69]

Answer:

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Lemon juice (mL) Sugar (gr)

Batch A 500 200

Batch B 750 300

Batch C 1,500 600

2. Write an equation to describe the relationship between j, the amount of lemon juice in mL, and s, the amount of sugar in g.

Ratio = Amount of lemon juice/Amount of sugar

Ratio = 500/200 = 750/300 = 1,500/600

Ratio = 2.5

Now, we can write the equation, this way:

8 0

2 years ago

Read 2 more answers

Which graph represents the piecewise-defined function?

chubhunter [2.5K]

Answer: The correct option is 1.

Explanation:

The given piecewise function is,

$y=\begin{cases}-\frac{4}{5}x-3 & \text{ if } x$

It means if x<0, then

$f(x)=-\frac{4}{5}x-3$

If $x\geq2$ , then

$f(x)=3x-10$

Since the f(x) is defined for x<0 and $x\geq2$ , therefore the function f(x) is not defined for $0\leq x$ .

From the graph 2, 3 and 4 we can easily noticed that for each value of x there exist a unique value of y, therefore the function is defined for all values of x, which is not true according to the given piecewise function.

Only in figure the value of y not exist when x lies between 0 to 2, including 0. It means the function is not defined for $0\leq x$ , hence the first option is correct.

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2 years ago

Vector bought 15.6 pounds of paintballs. all together, the balls cost 35.99. About how much dis the psinballs cost per pond?

nevsk [136]

Paintballs are $2.30 per pound.

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2 years ago

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