8 times 10^5 + 5 times 10^4 = ? In scientific notation

Giving 100 points.

Nitella [24]

Answer:

1. Cost per customer: 10 + x

Average number of customers: 16 - 2x

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

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

Step-by-step explanation:

Given information:

$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

Part 1

Cost per customer: 10 + x

Average number of customers: 16 - 2x

Part 2

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

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

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

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

Part 3

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.

Test the roots 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 solution to the inequality is between the roots:

-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 increase in cost. It does not confirm that if the cost is reduced (less than $10) the number of customers increases per hour.]

Cost per customer:

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

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

Therefore, the possible buffet prices Noah could charge are:

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

8 0

1 year ago

What is the explicit rule for this sequence? -5, 15, – 45, 135, ...

hoa [83]

Answer:

Step-by-step explanation:

In a geometric sequence, consecutive terms differ by a common ratio. The formula for determining the nth term of a geometric progression is expressed as

an = a1r^(n - 1)

Where

a represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms.

From the given sequence,

a1 = - 5

r = 15/- 5 = - 3

Therefore, the explicit rule for this sequence is

an = - 5(- 3)^n - 1

4 0

3 years ago

a hiking trail has a slope of 7/32. what is the measure of the angle it makes with the horizontal line

Ahat [919]

10 degree slope angle

5 0

3 years ago

Find the solution of the quadratic equation x^2+4x-12=0 MUST SHOW WORK!!!

bezimeni [28]

Answer:

x = 2,−6

Step-by-step explanation:

Move all terms to the left side and set equal to zero. Then set each factor equal to zero

3 0

3 years ago

10=7-m two step equations

poizon [28]

Step-by-step explanation:

10=7-m

10-7=-m

3=-m

m=-3

4 0

2 years ago

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