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zhenek [66]
1 year ago
14

5. If 1/4 inch represents 5 yards, the number of inches needed to show a football field 100yards long is:​

Mathematics
1 answer:
alexdok [17]1 year ago
4 0

Answer:

The answer is 20/80.

Step-by-step explanation:

1/4=5 yards

? =100 yards

100÷5=20

1/4×20

=20/80.

PLEASE MARK ME AS THE BRAINIEST.

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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
If an employer reduces the working week from 40 hours to 35 hours, with no
tangare [24]

Answer:

14.285714285714 %

Step-by-step explanation:

suppose the weekly payment is of x dollars

Then

Previous payment : $(x/40) per hour

New payment : $(x/35) per hour

Then

The percentage increase in the hourly rate of pay is :

=\frac{\frac{x}{35} -\frac{x}{40} }{\frac{x}{40} } \times100

=\frac{\frac{5x}{1400} }{\frac{x}{40} }  \times100

=\frac{5x}{1400} \times \frac{40}{x} \times100

=\frac{200}{1400} \times100

=\frac{1}{7} \times100

=14.285714285714

6 0
2 years ago
If a rectangular prism with a length of 12 feet and width of 9 feet has a surface area of 930 square feet, find its height.
MaRussiya [10]

Answer:

17 feet

Step-by-step explanation:

A=2(wl+hl+hw)

5 0
3 years ago
Read 2 more answers
The owner of a luxury motor yacht that sails among the 4000 Greek islands charges $540 per person per day if exactly 20 people s
lora16 [44]

Answer:

Step-by-step explanation:

Charges up to 20 passengers = $540 per person per day

Total charges = 540 × 20 = $10800

If x passengers above 20 sign up for the cruise then total number of passengers = (20 + x)

Total revenue = $(20+x)

But each fare is reduced by $7 for additional passenger above 20 then revenue generated R(x) = 540(20+x) - 7x

R(x) = 10800 + 540x - 7x

R(x) = 10800 + 533x

a). Revenue per day realized R = 10800 + 533x

b). R(48) = 10800 + 48×533

              = $36,384

C). R(78) = 10800 + 78×543

              = $53,154

5 0
3 years ago
Please Help will give points PLEASE!!!!
Paul [167]

Answer:

I to 16

Step-by-step explanation:

The first point was put on one and the last was on 16

8 0
3 years ago
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