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KonstantinChe [14]

2 years ago

12

Whitney and Destiny hung out at the mall on Saturday. They spent 45 minutes shopping for clothes and 1 hour at the food court. T

hen they spent 30 minutes at the video arcade before heading home. It was 12:45 P.M. when Whitney and Destiny left the mall. What time did they start shopping for clothes?

1 answer:

mojhsa [17]2 years ago

4 0

Answer:

11.15 i think

Step-by-step explanation:

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2 years ago

Read 2 more answers

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

Natalie and John are both saving coins in jars for a rainy day. Natalie currently has 1 1/8 jars of coins, and John has 9/14 of

aivan3 [116]

Answer:

Natalie will have $1\frac{43}{56}$ jars of coins all together after receiving John's coins.

Step-by-step explanation:

Given that:

Coins Natalie have = $1\frac{1}{8}$ jars of coins

Coins John have = $\frac{9}{14}$ jars of coins

When John will give all his coins to Natalie.

Total coins Natalie have = Her coins + John's coins

Total coins Natalie have = $1\frac{1}{8}+\frac{9}{14}$

Total coins = $\frac{9}{8}+\frac{9}{14}$

Total coins = $\frac{63+36}{56}=\frac{99}{56}$

Total coins = $1\frac{43}{56}$

Hence,

Natalie will have $1\frac{43}{56}$ jars of coins all together after receiving John's coins.

5 0

2 years ago