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yawa3891 [41]
3 years ago
13

On Friday, a local restaurant served 150 customers. Of these, 114

Mathematics
1 answer:
ipn [44]3 years ago
5 0
The answer is D, because we will divide 114 by 150 and the total converted to percentage is 76
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Factor 9x^2+66xy+121y^2
Korvikt [17]
Answer: (3x + 11y)^2

Demonstration:

The polynomial is a perfect square trinomial, because:

1) √ [9x^2] = 3x

2) √121y^2] = 11y

3) 66xy = 2 *(3x)(11y)

Then it is factored as a square binomial, being the factored expression:

 [ 3x + 11y]^2

Now you can verify working backwar, i.e expanding the parenthesis.

Remember that the expansion of a square binomial is:

- square of the first term => (3x)^2 = 9x^2
- double product of first term times second term =>2 (3x)(11y) = 66xy
- square of the second term => (11y)^2 = 121y^2

=> [3x + 11y]^2 = 9x^2 + 66xy + 121y^2, which is the original polynomial.

7 0
3 years ago
Since we don’t have math books to review can someone help with this and explain
vivado [14]

Answer:

Celsius is going up by 10's while Fahrenheit is going up by 18

Step-by-step explanation:

by subtracting the first two numbers then the next two you will see the pattern.

6 0
3 years ago
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
2 years ago
Torri had 20$ to buy a birthday presents for her dad. She decided to buy a DVD for 10$. The sales tax is 7%. Does she have enoug
Trava [24]

Answer:

Yes

Step-by-step explanation:

She has enough money because 7% tax on a 10.00$ item would be 7% of 10.00$ which is 70 cents.

6 0
3 years ago
A filling machine puts an average of four ounces of coffee in jars, with a standard deviation of 0.25 ounces. forty jars filled
Lunna [17]
Let's attack this problem using the z-score concept.  The sample std. dev. here is (0.25 oz)/sqrt(40), or 0.040.  Thus, the z score representing 3.9 oz. is
        3.9 - 4.0
z = -------------- = -2.5
          0.040 

In one way or another we must find the area under the std. normal curve that lies to the left of z = -2.5.  Use a table of z-scores or a calculator with built-in statistics functions.  According to my TI-83 Plus calculator, that area is

0.006.  One way of interpreting this that with so small a standard deviation, most volumes of coffee put into the jars are very close to the mean, 4 oz.
4 0
3 years ago
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