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Question 1

A)An internet service provider had a total of 17,156 customers last year. They gained a net of 1,802 customers this year. They hope to reach at least 35,000 customers in ten years. Estimate the number of customers they need to reach their goal.(1 point)
They need approximately $$ more customers to reach their goal.
Question 2
A)Estimate the value of x given this equation: 4x−189=578.(1 point)
Responses

100
100

160
160

150
150

200
200
Question 3
A)A carnival wants to estimate its total potential revenue on popcorn sales. They have 19,717 grams of popcorn kernels, and each serving uses 196 grams. Each serving sells for $5. If they sell all the popcorn, approximately how much potential revenue will the carnival make?(1 point)
Responses

$500
$500

$100
$100

$475
$475

$950
$950
Question 4
A)Estimate the value of x given this equation: 11x+29=82.(1 point)
Responses

6
6

10
10

11
11

5
5

1 answer

Let's go through each question step-by-step.

Question 1:

The internet service provider currently has:

  • Last year's customers: 17,156
  • Net gain this year: 1,802

So, this year's total customers: \[ 17,156 + 1,802 = 18,958 \]

They want to reach:

  • Goal: 35,000 customers

To find out how many more customers they need: \[ 35,000 - 18,958 = 16,042 \] Thus, they need approximately 16,042 more customers to reach their goal.

Question 2:

The equation provided is: \[ 4x - 189 = 578 \] First, add 189 to both sides: \[ 4x = 578 + 189 \] \[ 4x = 767 \] Now, divide by 4: \[ x = 767 / 4 = 191.75 \] The closest whole number is 200 since it rounds up when estimating.

Question 3:

The carnival has:

  • Total grams of popcorn: 19,717
  • Grams per serving: 196
  • Revenue per serving: $5

First, calculate the number of servings: \[ \text{Number of servings} = \frac{19,717}{196} \approx 100.1 \] Approximately 100 servings.

Now calculate potential revenue: \[ \text{Revenue} = 100 \text{ servings} \times $5 = $500 \]

Question 4:

The equation provided is: \[ 11x + 29 = 82 \] First, subtract 29 from both sides: \[ 11x = 82 - 29 \] \[ 11x = 53 \] Now, divide by 11: \[ x = \frac{53}{11} \approx 4.818 \] The closest whole number here is 5.

Summary of Answers:

  1. Approximately 16,042 more customers to reach their goal.
  2. The estimated value of x is 200.
  3. Potential revenue is approximately $500.
  4. The estimated value of x is 5.