What is the equation of the graph shown?

romanna [79]

$y=f(x) =12\sqrt x\\\\\text{Replace x with y and then solve for y:}\\ \\~~~~~~~x = 12\sqrt y\\\\\implies \sqrt y = \dfrac{x}{12}\\ \\\implies y = \dfrac{x^2}{144}\\\\\implies f^{-1} (x) = \dfrac{x^2}{144} \\\\\text{Hence the inverse of the function is}~ \dfrac{x^2}{144}$

5 0

3 years ago

How many terms are in the simplified expression 2x^2-y^2+5xy-2y

madam [21]

6x * 3y * 9x^2y^4 Simplifying 6x * 3y * 9x2y4 Reorder the terms for easier multiplication: 6 * 3 * 9x * y * x2y4 Multiply 6 * 3 18 * 9x * y * x2y4 Multiply 18 * 9 162x * y * x2y4 Multiply x * y 162xy * x2y4 Multiply xy * x2y4 162x3y5

7 0

4 years ago

In a recent Dunkin Donuts (DD) commercial, it states that 58% of Americans prefer to drink their coffee. Of the five hundred ran

Sergio [31]

Answer:

We conclude that the proportion of Americans who prefer to drink DD coffee is actually more than what was advertised.

Step-by-step explanation:

We are given that in a recent Dunkin Donuts (DD) commercial, it states that 58% of Americans prefer to drink their coffee.

Of the five hundred randomly selected people who were asked if they preferred DD coffees, 325 said they did.

Let p = proportion of Americans who prefer to drink DD coffee

SO, Null Hypothesis, $H_0$ : p $\leq$ 58% {means that the proportion of Americans who prefer to drink DD coffee is actually less than or equal to what was advertised}

Alternate Hypothesis, $H_A$ : p > 58% {means that the proportion of Americans who prefer to drink DD coffee is actually more than what was advertised}

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

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

where, $\hat p$ = sample proportion of people who prefer to drink DD coffee in a sample of 500 people = $\frac{325}{500}$ = 65% or 0.65

n = sample of people = 500

So, test statistics = $\frac{0.65-0.58}{{\sqrt{\frac{0.65(1-0.65)}{500} } } } }$

= 3.282

Now at 0.05 significance level, the z table gives critical value of 1.6449 for right-tailed test. Since our test statistics is more than the critical value of z so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the proportion of Americans who prefer to drink DD coffee is actually more than what was advertised.

6 0

3 years ago

On Saturday, Nikki and Tyler walked to the local farmer's market. Nikki bought 8 apples for $6. Tyler bought 3 fewer apples than

andriy [413]

$3.75 because each apple costs 75 cents and if you multiply it by 5 you get 3.75

7 0

3 years ago

Read 2 more answers

What is 3/4 multiplied by 16/9

zloy xaker [14]

Since its multiplication you don't have to have a common denominator so you multiply straight across. The answer is 48/36.

8 0

3 years ago