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2 years ago

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Which statement describes a unit rate? Group of answer choices Sara is reading 97 words in 1 minute. Sara ate 3 crackers and 1 a

pple. Sara ate 1 cookie. Sara is driving 16 miles.

1 answer:

castortr0y [4]2 years ago

6 0

Answer:

97 words in 1 minute

Step-by-step explanation:

A unit measure is so many somethings done usually per unit time. Examples

1 orange in 1 minute.
10 tomatoes per tomato plant
50 miles in one hour
10 cookies per week

3 crackers and 1 apple is not. For ever apple, she ate 3 crackers would be

1 cookie is not. It is not per anything.

Driving 16 miles is not. Again, it is not per anything.

The answer is 97 words in 1 minute.

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Giving 100 points.

Nitella [24]

Answer:

1. <u>Cost per customer</u>: 10 + x

<u>Average number of customers</u>: 16 - 2x

$\textsf{2.} \quad -2x^2-4x+160\geq 130$

3. $10, $11, $12 and $13

Step-by-step explanation:

<u>Given information</u>:

$10 = cost of buffet per customer
16 customers choose the buffet per hour
Every $1 increase in the cost of the buffet = loss of 2 customers per hour
$130 = minimum revenue needed per hour

Let x = the number of $1 increases in the cost of the buffet

<u>Part 1</u>

<u></u>

<u>Cost per customer</u>: 10 + x

<u>Average number of customers</u>: 16 - 2x

<u>Part 2</u>

The cost per customer multiplied by the number of customers needs to be <u>at least</u> $130. Therefore, we can use the expressions found in part 1 to write the <u>inequality</u>:

$(10 + x)(16 - 2x)\geq 130$

$\implies 160-20x+16x-2x^2\geq 130$

$\implies -2x^2-4x+160\geq 130$

<u>Part 3</u>

To determine the possible buffet prices that Noah could charge and still maintain the restaurant owner's revenue requirements, solve the inequality:

$\implies -2x^2-4x+160\geq 130$

$\implies -2x^2-4x+30\geq 0$

$\implies -2(x^2+2x-15)\geq 0$

$\implies x^2+2x-15\leq 0$

$\implies (x-3)(x+5)\leq 0$

Find the roots by equating to zero:

$\implies (x-3)(x+5)=0$

$x-3=0 \implies x=3$

$x+5=0 \implies x=-5$

Therefore, the roots are x = 3 and x = -5.

<u>Test the roots</u> by choosing a value between the roots and substituting it into the original inequality:

$\textsf{At }x=2: \quad -2(2)^2-4(2)+160=144$

As 144 ≥ 130, the <u>solution</u> to the inequality is <u>between the roots</u>:

-5 ≤ x ≤ 3

To find the range of possible buffet prices Noah could charge and still maintain a minimum revenue of $130, substitute x = 0 and x = 3 into the expression for "cost per customer.

[Please note that we cannot use the negative values of the possible values of x since the question only tells us information about the change in average customers per hour considering an <em>increase </em>in cost. It does not confirm that if the cost is reduced (less than $10) the number of customers <em>increases </em>per hour.]

<u>Cost per customer</u>:

$x =0 \implies 10 + 0=\$10$

$x=3 \implies 10+3=\$13$

Therefore, the possible buffet prices Noah could charge are:

$10, $11, $12 and $13.

8 0

1 year ago

The sum of a number p and seven is divided by twelve. the result is three. What is the number

Nitella [24]

P is equal to 29. You take the question backwards: 12*3 then subtract 7

4 0

2 years ago

Read 2 more answers

Solve the quadratic function using square root X+10x+25 =18

lawyer [7]

Answer:

= − 7 /1 1 in fraction form

Step-by-step explanation:

STEP 1: Multiply by 1

1 + 1 0 + 2 5 = 1 8

+ 1 0 + 2 5 = 1 8 STEP 2: Combine like terms

+ 1 0 + 2 5 = 1 8

1 1 + 2 5 = 1 8 STEP 3: Subtract 2 5 from both sides of the equation

11x+25=18

1 1 + 2 5 − 2 5 = 1 8 − 2 5

STEP 4: Simplify by subtracting the numbers

1 1 + 2 5 − 2 5 = 1 8 − 2 5

11x+25−25=18−25 1 1 = 1 8 − 2 5 1 1 = -7

STEP 5: Divide both sides of the equation by the same term 1 1 = − 7 11x/ 11x = −7/ 1 1 (set up as a fraction) STEP 6: Cancel terms that are in both the numerator and denominator

= − 7 /1 1 SOLUTION

= − 7 /1 1

5 0

2 years ago

I WILL GIVE BRAINLIEST!!

Afina-wow [57]

Answer:

$\text{D. The terms may be combined.}$

Step-by-step explanation:

Recall that $\sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}$ . Using this, we can simplify and combine the two terms:

$6\sqrt{32}-12\sqrt{72},\\=6\cdot \sqrt{4}\cdot \sqrt{8}-12\cdot \sqrt{9}\cdot \sqrt{8},\\=6\cdot 2\cdot \sqrt{8}-12\cdot 3\cdot \sqrt{8},\\=12\sqrt{8}-36\sqrt{8},\\=-24\sqrt{8}=-24\cdot\sqrt{4}\cdot\sqrt{2}=\boxed{-48\sqrt{2}}$ . Therefore, the terms may be combined.

8 0

2 years ago

How many "words" can be written using exactly five A's and no more than three B's (and no other letters)?

kakasveta [241]

This is a problem of Permutations. We have 3 cases depending on the number of B's. Since no more than three B's can be used we can use either one, two or three B's at a time.

Case 1: Five A's and One B

Total number of letters = 6

Total number of words possible = $\frac{6!}{5!*1!}=6$

Case 2: Five A's and Two B's

Total number of letters = 7

Total number of words possible = $\frac{7!}{5!*2!}=21$

Case 3: Five A's and Three B's

Total number of letters = 8

Total number of words possible = $\frac{8!}{5!*3!}=56$

Total number of possible words will be the sum of all three cases.

Therefore, the total number of words that can be written using exactly five A's and no more than three B's (and no other letters) are 6 + 21 + 56 = 83

8 0

2 years ago

Read 2 more answers