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2 years ago

11

Gabriel bought a purse that was on sale at 10% off. If she paid $59.95, including tax, and the sales tax rate was 6%, how much d

id she pay for tax?
$2.02

$2.25

$3.05

$3.39

1 answer:

pochemuha2 years ago

8 0

Answer:

final price:56.56

tax amount: 3.39

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Mrs. Lang is 4 times as old as her daughter Jill. The sum of their ages is 60 years. Set up the two equations that can be used t

KatRina [158]

Answer:

The two equations that can be used to find each of their ages are $x=4 \times y$ and $x+y=60$ .

Step-by-step explanation:

We are given that Mrs. Lang is 4 times as old as her daughter Jill. The sum of their ages is 60 years.

Let the age of Mrs. Lang be 'x years' and the age of her daughter Jill be 'y years'.

Now, according to the question;

The <u>first condition</u> states that Mrs. Lang is 4 times as old as her daughter Jill, that means;

$x=4 \times y$ ----------------- [equation 1]

The <u>second condition</u> states that the sum of their ages is 60 years, that means;

$x+y=60$

$4y + y = 60$ {using equation 1}

$5y=60$

$y=\frac{60}{5}$

y = 12 years

Now, putting the value of y in equation 1 we get;

$x=4 \times y$

$x= 4 \times 12$ = 48 years

Hence, the age of Mrs. Lang is 48 years and her daughter Jill is 12 years old.

8 0

2 years ago

Topic: Recognizing Linear and Exponential and Quadratic Functions.

BigorU [14]

Answer:

Recursive: f(1) = 1; f(n) = f(n-1)/3

Equation: f(x) = 5/3·(1/3)^(x-1)

Step-by-step explanation:

You know this is an exponential function because sequential lines in the table have a common ratio of f(x) values:

f(2)/f(1) = (5/9)/(5/3) = 3/9 = 1/3

f(3)/f(2) = (5/27)/(5/9) = 9/27 = 1/3

and it continues like that.

Besides telling you the function is exponential, it also tells you that each term is 1/3 of the previous term.

<h3>Recursive formula</h3>

The value of f(1) is read from the table. For x = 1, that value is ...

f(1) = 5/3

As we noticed above, each term is 1/3 the previous term, so the recursive relation is ...

f(n) = (1/3)·f(n-1)

<h3>Equation</h3>

The general form of the equation for a geometric (exponential) relation is ...

f(x) = f(1)·r^(x-1) . . . . . . where f(1) is the first term, and r is the common ratio

For this function, we have f(1) = 5/3 and r = 1/3, so the equation is ...

f(x) = 5/3·(1/3)^(x-1)

__

<em>Additional comment</em>

When given values of x that count from 1, we often express the equation in terms of (x-1). That equation can be simplified so the exponent is x.

f(x) = 5·(1/3)^x

5 0

1 year ago

Find the number of ways you can arrange (a) all of the letters and (b) two is the letters in the word ROCK. a. The number of way

QveST [7]

Answer:

a) 24

b) 12

Step-by-step explanation:

a) For the 4 letters of the word ROCK

Selecting any first letter, we have 4 options

for the second, we have 3 options

for the third we have 2 options

for the fourth, we have only one option

So the number of ways will be ;

4 * 3 * 2 * 1 = 24 ways

b) 2 out of 4

For the first letter, we have 4 options, for the second, we have 3 options

so the number of options is 4 * 3 = 12 options

3 0

2 years ago

Two thirds times x plus 13 equals twenty two

Nataly [62]

2/3 * x +13 = 22
2/3x + 13 = 22

if u need to solve it then ....
=> 2/3x = 22 - 13
=> 2/3x = 9
=> 2x = 9*3 = 27
=> x = 27/2

Hope it helps !!!

6 0

3 years ago

According to the table, what was the hiker’s total displacement?

shtirl [24]

Answer:

A: 0

Step-by-step explanation:

Important to remember - total displacement is the direct distance between the start and finish points, and isn't always equal to the total distance travelled.

In the case of the table above, the hiker travels the same distance in opposite directions, which actually means they cancel each other out! Traveling 4 km to the west, then 4 km to east means you end up in the same spot, right? So your total displacement is 0! (or 4 - 4, which equals 0). Same happens with the north-south hikes - the hiker ends up in the same spot, as the displacement is equal to 6 - 6 = 0.

So, the total displacement of the hiker is 0. (Even though the hiker travelled 20 km!)

7 0

2 years ago