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Mr. Imani wants to purchase paper and notebooks for his classroom. At Dollar Discount he can buy packs of paper, p, for $1.25 each and notebooks, n, for $2.50 each. This is modeled by 1.25p + 2.50n. Evaluate for p = 10 and n=30 to find how much it will cost Mr. Imani to purchase 10 packs of paper and 30 notebooks. (1 point)

Responses

$87.50
$87.50

$450.00
$450.00

$62.50
$62.50

$43.75

11 answers

To find the total cost for Mr. Imani to purchase 10 packs of paper and 30 notebooks, we can use the equation:

\[ \text{Total Cost} = 1.25p + 2.50n \]

Substituting \( p = 10 \) and \( n = 30 \):

\[ \text{Total Cost} = 1.25(10) + 2.50(30) \]

Calculating each term:

\[ 1.25(10) = 12.50 \] \[ 2.50(30) = 75.00 \]

Now, we add these two results together:

\[ \text{Total Cost} = 12.50 + 75.00 = 87.50 \]

Thus, the total cost for Mr. Imani to purchase 10 packs of paper and 30 notebooks is $87.50.

Answer: $87.50

The formula for finding the volume of a square prism is s2h, where s is the length of each side of the square base and h is the height of the prism. Evaluate to find the volume given values of s = 4 and h = 6.(1 point)
Responses

576 cubic centimeters
576 cubic centimeters

144 cubic centimeters
144 cubic centimeters

48 cubic centimeters
48 cubic centimeters

96 cubic centimeters

To find the volume of a square prism using the formula \( V = s^2 h \), where \( s \) is the length of each side of the square base and \( h \) is the height of the prism, you can substitute the given values \( s = 4 \) and \( h = 6 \):

  1. Calculate \( s^2 \): \[ s^2 = 4^2 = 16 \]

  2. Now, use the formula to find the volume: \[ V = s^2 \cdot h = 16 \cdot 6 \]

  3. Calculate the volume: \[ V = 96 \text{ cubic centimeters} \]

Therefore, the volume of the square prism is 96 cubic centimeters.

Answer: 96 cubic centimeters

Each month Ms. Tanaka is paid a base salary of $2,500 in addition to $100 for each television that she sells. This is modeled by 2,500 + 100t , where t represents the number of televisions. Evaluate for t = 12 to find how much Ms. Tanaka will earn for selling 12 televisions this month.(1 point)
Responses

$3,700
$3,700

$2,612
$2,612

$31,200
$31,200

$2,600

To find out how much Ms. Tanaka will earn for selling 12 televisions, we can use the formula:

\[ \text{Total Earnings} = 2,500 + 100t \]

where \( t \) represents the number of televisions sold. Given \( t = 12 \), we can substitute this value into the formula:

\[ \text{Total Earnings} = 2,500 + 100(12) \]

Now, calculate \( 100(12) \):

\[ 100(12) = 1,200 \]

Now, add this to the base salary:

\[ \text{Total Earnings} = 2,500 + 1,200 = 3,700 \]

Therefore, Ms. Tanaka will earn $3,700 for selling 12 televisions this month.

Answer: $3,700

Robert is preparing a poster-board presentation. He wants to make a decorative pattern with 10 squares to fill part of the poster. The area of the poster board is 720 square inches. To find how much space Robert will have left for his presentation if he uses squares with 7-inch sides, evaluate 720 − 10s2 when s = 7.(1 point)
Responses

580 square inches
580 square inches

230 square inches
230 square inches

34,790 square inches
34,790 square inches

9,940 square inches

To find out how much space Robert will have left for his presentation after using squares with 7-inch sides, we need to evaluate the expression \( 720 - 10s^2 \) with \( s = 7 \).

First, we calculate \( s^2 \):

\[ s^2 = 7^2 = 49 \]

Next, we multiply that by 10:

\[ 10s^2 = 10 \times 49 = 490 \]

Now, we can find the remaining space by substituting into the expression:

\[ 720 - 10s^2 = 720 - 490 \]

Now, perform the subtraction:

\[ 720 - 490 = 230 \]

Thus, the amount of space Robert will have left for his presentation is 230 square inches.

Answer: 230 square inches

Mr. Rodriguez has a vegetable garden that borders his house. He wants to put a fence around it. It costs $7 per yard for the materials. Evaluate 7(l + 2w), where l is the length and w is the width of his garden, to find the cost for a garden that has a length of 5 yards and a width of 2 yards.(1 point)
Responses

$98
$98

$39
$39

$16
$16

$63

To find the cost of fencing around Mr. Rodriguez's vegetable garden, we can use the formula \( 7(l + 2w) \), where \( l \) is the length and \( w \) is the width of the garden.

Given:

  • Length \( l = 5 \) yards
  • Width \( w = 2 \) yards

Now, substitute the values into the formula:

  1. First, calculate \( l + 2w \): \[ l + 2w = 5 + 2(2) = 5 + 4 = 9 \]

  2. Now, calculate the cost by substituting this result into the formula: \[ \text{Cost} = 7(l + 2w) = 7(9) = 63 \]

Therefore, the cost for the garden fencing will be $63.

Answer: $63

before i submit are you sure all of these answers are correct?

Yes, let's quickly review each problem and their respective solutions to ensure accuracy:

  1. Total Cost for Mr. Imani (packs of paper and notebooks):

    • Formula: \(1.25p + 2.50n\)
    • Values: \(p = 10\), \(n = 30\)
    • Calculation: \(1.25(10) + 2.50(30) = 12.50 + 75.00 = 87.50\)
    • Answer: $87.50 (correct).

  2. Volume of a Square Prism:

    • Formula: \(V = s^2 h\)
    • Values: \(s = 4\), \(h = 6\)
    • Calculation: \(4^2 \cdot 6 = 16 \cdot 6 = 96\)
    • Answer: 96 cubic centimeters (correct).

  3. Earnings for Ms. Tanaka (televisions sold):

    • Formula: \(2,500 + 100t\)
    • Value: \(t = 12\)
    • Calculation: \(2,500 + 100(12) = 2,500 + 1,200 = 3,700\)
    • Answer: $3,700 (correct).

  4. Remaining Area for Robert's Poster:

    • Formula: \(720 - 10s^2\)
    • Value: \(s = 7\)
    • Calculation: \(10(7^2) = 10(49) = 490\); \(720 - 490 = 230\)
    • Answer: 230 square inches (correct).

  5. Cost of Fencing for Mr. Rodriguez's Garden:

    • Formula: \(7(l + 2w)\)
    • Values: \(l = 5\), \(w = 2\)
    • Calculation: \(l + 2w = 5 + 2(2) = 9\); \(7(9) = 63\)
    • Answer: $63 (correct).

All calculations and answers provided are accurate based on the problems as presented. You can submit with confidence! If you have any additional concerns or questions, feel free to ask.