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andrezito [222]

3 years ago

8

Every ninth person in line at a movie theater gets free popcorn. Every sixth person gets free apple juice. Shani says that the t

hirty-sixth customer to get both free popcorn and free apple juice. Is she right? If not, describe her mistake

1 answer:

Blababa [14]3 years ago

5 0

It is right, because 36 is dividable by 6 and 9 (haha thats the funny number)

You might be interested in

What is the range of the following function:<br> y = 2(5^x) - 1

Orlov [11]

<h2>Hello!</h2>

The answer is:

The range of the function is:

Range: y>2

or

Range: (2,∞+)

<h2>Why?</h2>

To calculate the range of the following function (exponential function) we need to perform the following steps:

First: Find the value of "x"

So, finding "x" we have:

$y=2(5^{x}-1)\\\frac{y}{2}=5^{x}-1\\\\\frac{y}{2}-1=5^{x}\\\\Log_{5}(\frac{y}{2}-1)=Log_5(5^{x})\\\\x=Log_{5}(\frac{y}{2}-1)$

Second: Interpret the restriction of the function:

Since we are working with logarithms, we know that the only restriction that we found is that the logarithmic functions exist only from 0 to the possitive infinite without considering the number 1.

So, we can see that if the variable "x" is a real number, "y" must be greater than 2 because if it's equal to 2 the expression inside the logarithm will tend to 0, and since the logarithm of 0 does not exist in the real numbers, the variable "x" would not be equal to a real number.

Hence, the range of the function is:

Range: y>2

or

Range: (2,∞+)

Note: I have attached a picture (the graph of the function) for better understanding.

Have a nice day!

5 0

3 years ago

What is the vertex of f(x) = |5x| 2?

Sveta_85 [38]

The Vertex of f(x)=|5x|+2 is (0,2)
and vertex of f(x)=|5x|-2 is (0,-2)

8 0

3 years ago

You want $5000 4 years from nowfor a down payment for a car. How much money must be deposited monetly into an account earning 4.

timama [110]

Answer:

$95.5090 must be deposited monthly

Step-by-step explanation:

From the information given:

The annual interest rate (r) = 4.2% = 0.042

Let assume that an amount Y is deposited, then after one month, it will increase to:

$Y ( 1+ \dfrac{0.042}{12})$

The total amount after 4 years will be:

$= Y ( 1+ \dfrac{0.042}{12})^{48}+Y ( 1+ \dfrac{0.042}{12})^{47} +Y ( 1+ \dfrac{0.042}{12})^{46} +...+ Y ( 1+ \dfrac{0.042}{12})$

$= Y ( 1.0035)^{48}+Y ( 1.0035)^{47} +Y( 1.0035)^{46} +...+ Y( 1.0035)$

Using the sum of a geometric progression:

$= Y (1.0035) \dfrac{ (1.0035^{48}-1)}{(1.0035-1)}$

$= Y (1.0035) \dfrac{ (1.0035^{48}-1)}{0.0035}$

The above amount is then equal to $5000

i.e

$= Y (1.0035) \dfrac{ (1.0035^{48}-1)}{0.0035} = 5000$

$Y = \dfrac{5000\times 0.0035}{(1.0035)(1.0035^{48}-1)} \\ \\ \mathbf{Y = \$95.5090}$

8 0

3 years ago

What does the value of the y-intercept represent?

egoroff_w [7]

On the problem you have given, the y ingercept shows the amount of time in hours it takes for the number of customers, so it would cross at 5 and represent 0 customers

8 0

3 years ago

Read 2 more answers

How to solve this showing all work ! Also explain why they aren’t polynomials if you can :)

Lesechka [4]

Polynomials are linear combinations of positive integer powers. For example,

$x^{100}+30x^2-\sqrt 2\,x+21$

is a polynomial, but

$-x^{-1}-4x^\pi+x^{3/2}$

is not.

(In case you're unfamiliar with the term, a linear combination of two quantities is the sum of scaled versions of those quantities, e.g. a general linear combination of $a$ and $b$ is $k_1a+k_2b$ , where $k_1,k_2$ are any numbers.)

$8x^2-18\sqrt x+5x-3$ is not a polynomial; the offending term is $-18\sqrt x$ , or $-18x^{1/2}$ .

7 0

3 years ago