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3 years ago

The arrow on the spinner is to be spun once.

Mathematics

2 answers:

liubo4ka [24]3 years ago

7 0

I think your anwser is D

Sholpan [36]3 years ago

7 0

The arrow on the spinner is to be spun once. The sample space = D. {1, 2, 3, 4, 5, 6};

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P:-3x + 8x - 5x = x q: (3x)(5y) = 15xy Which of the following statements is false?

Varvara68 [4.7K]

Answer: Statement p is false.

Step-by-step explanation:

In both cases, we need to isolate the variables:

p: -3*x + 8*x - 5*x = x

(-3*x - 5*x) + 8*x = x

-8x + 8*x = x

0 = x

This will be true only for one value of x, so this is not always true, which means that the statement is false.

q: (3*x)*(5*y) = 15*x*y

let's solve the left side:

3*x*5*y = 15*x*y

(3*5)*(x*y) = 15*x*y

15*x*y = 15*x*y

This is true for every value of x and y, then this statement is true.

5 0

2 years ago

Solve equation show work

Naddika [18.5K]

Answer:

h= -8/3

Picture Explanation:

Divide 3 on both sides of the equal sign, as shown above, so (h) can be alone.
Since negative 8, let alone positive 8, can't be divided into 3, you simply leave the fraction as is. So you're left with (h= -8/3)

Hope this makes sense.

7 0

3 years ago

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:

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