An expression is shown that represents the change in Jake's cafeteria account balance after he bought some giant cookies that cost
each and he was given a credit.
-2/3 (12x - 6) = Response area + Response area
Move a term into each blank to create an equivalent expression.
responses
2
-8
-8x
8x
6x
4
-4
-4x
7 answers
-2/3 (12x - 6) = -8x + 4
Jatzel is practicing his free throws for basketball, so he shoots 100 free throws. Jatzel hits the rim and misses with 3/5 of his shots, hits the backboard and misses with 17% of his shots, and makes the remaining shots. How many free throws did Jatzel make?
Responses
A 17
B 23
C 60
D 77
Responses
A 17
B 23
C 60
D 77
Let's calculate the number of free throws Jatzel made:
He misses 3/5 of his shots, which means he makes 2/5 of his shots.
He hits the backboard and misses with 17% of his shots, which means he makes 83% of his shots.
Let's calculate the combined percentage of shots he makes:
2/5 + 83% = 2/5 + 83/100 = (40 + 83)/100 = 123/100 = 1.23
So, he makes 1.23 out of every 5 shots.
Number of free throws made = 100 x 1.23 = 123
Therefore, Jatzel made 123 free throws.
The closest response is:
D 77
He misses 3/5 of his shots, which means he makes 2/5 of his shots.
He hits the backboard and misses with 17% of his shots, which means he makes 83% of his shots.
Let's calculate the combined percentage of shots he makes:
2/5 + 83% = 2/5 + 83/100 = (40 + 83)/100 = 123/100 = 1.23
So, he makes 1.23 out of every 5 shots.
Number of free throws made = 100 x 1.23 = 123
Therefore, Jatzel made 123 free throws.
The closest response is:
D 77
Mia put two gifts in a shipping box, then filled the box with styrofoam "peanuts".
The dimensions of the shipping box were 12 inches by 5 inches by 5 inches.
One gift was a puzzle cube with a side length of 4 inches.
One gift was a card game that was in a box with dimensions 6 inches by 4 inches by 4 1/2 inches.
What was the volume of the styrofoam "peanuts" in the shipping box?
Responses
A 172 in.3
B 139.5 in.3
C 128 in.3
D 228 in.3
The dimensions of the shipping box were 12 inches by 5 inches by 5 inches.
One gift was a puzzle cube with a side length of 4 inches.
One gift was a card game that was in a box with dimensions 6 inches by 4 inches by 4 1/2 inches.
What was the volume of the styrofoam "peanuts" in the shipping box?
Responses
A 172 in.3
B 139.5 in.3
C 128 in.3
D 228 in.3
First, let's calculate the total volume of the gifts:
Volume of the puzzle cube = side length^3 = 4^3 = 64 cubic inches.
Volume of the card game box = length x width x height = 6 x 4 x 4.5 = 108 cubic inches.
Total volume of the gifts = 64 + 108 = 172 cubic inches.
Now, let's calculate the volume of the shipping box:
Volume of the shipping box = length x width x height = 12 x 5 x 5 = 300 cubic inches.
Subtracting the volume of the gifts from the volume of the box gives the volume of the styrofoam "peanuts":
Volume of the styrofoam "peanuts" = 300 - 172 = 128 cubic inches.
Therefore, the volume of the styrofoam "peanuts" in the shipping box is 128 in.3.
The correct response is:
C 128 in.3
Volume of the puzzle cube = side length^3 = 4^3 = 64 cubic inches.
Volume of the card game box = length x width x height = 6 x 4 x 4.5 = 108 cubic inches.
Total volume of the gifts = 64 + 108 = 172 cubic inches.
Now, let's calculate the volume of the shipping box:
Volume of the shipping box = length x width x height = 12 x 5 x 5 = 300 cubic inches.
Subtracting the volume of the gifts from the volume of the box gives the volume of the styrofoam "peanuts":
Volume of the styrofoam "peanuts" = 300 - 172 = 128 cubic inches.
Therefore, the volume of the styrofoam "peanuts" in the shipping box is 128 in.3.
The correct response is:
C 128 in.3
Part A
The local food pantry is asking for "Gobble Kit" donations - an itemized list of non-perishable food items and a $20 donation for a turkey. The food pantry will purchase the turkeys for the "Gobble Kits". Each "Gobble Kit" will include everything needed for a Thanksgiving meal and will be given to a family in need.
Stacy donated three "Gobble Kits" and spent a total of $114. The equation shown represents the situation.
3 (x + 20) = 114
What does the variable x represent in Stacy's equation?
Responses
A the cost of the non-perishable food items and turkey for 1 "Gobble Kit"the cost of the non-perishable food items and turkey for 1 "Gobble Kit"
C the cost of the turkey for 1 "Gobble Kit"the cost of the turkey for 1 "Gobble Kit"
B the cost of the non-perishable food items for 1 "Gobble Kit"the cost of the non-perishable food items for 1 "Gobble Kit"
D the cost of the non-perishable food items for all 3 "Gobble Kits"the cost of the non-perishable food items for all 3 "Gobble Kits"
Question 2
Part B
Solve Stacy's equation in Part A for x.
x = $ (response area)
The local food pantry is asking for "Gobble Kit" donations - an itemized list of non-perishable food items and a $20 donation for a turkey. The food pantry will purchase the turkeys for the "Gobble Kits". Each "Gobble Kit" will include everything needed for a Thanksgiving meal and will be given to a family in need.
Stacy donated three "Gobble Kits" and spent a total of $114. The equation shown represents the situation.
3 (x + 20) = 114
What does the variable x represent in Stacy's equation?
Responses
A the cost of the non-perishable food items and turkey for 1 "Gobble Kit"the cost of the non-perishable food items and turkey for 1 "Gobble Kit"
C the cost of the turkey for 1 "Gobble Kit"the cost of the turkey for 1 "Gobble Kit"
B the cost of the non-perishable food items for 1 "Gobble Kit"the cost of the non-perishable food items for 1 "Gobble Kit"
D the cost of the non-perishable food items for all 3 "Gobble Kits"the cost of the non-perishable food items for all 3 "Gobble Kits"
Question 2
Part B
Solve Stacy's equation in Part A for x.
x = $ (response area)
For Part A:
From the equation: 3(x + 20) = 114
x represents the cost of the non-perishable food items and turkey for 1 "Gobble Kit". Therefore, the correct response is:
A the cost of the non-perishable food items and turkey for 1 "Gobble Kit"
For Part B:
Solve the equation:
3(x + 20) = 114
3x + 60 = 114
3x = 114 - 60
3x = 54
x = 54 / 3
x = 18
So, x = $18
Therefore, the response area should be "18".
From the equation: 3(x + 20) = 114
x represents the cost of the non-perishable food items and turkey for 1 "Gobble Kit". Therefore, the correct response is:
A the cost of the non-perishable food items and turkey for 1 "Gobble Kit"
For Part B:
Solve the equation:
3(x + 20) = 114
3x + 60 = 114
3x = 114 - 60
3x = 54
x = 54 / 3
x = 18
So, x = $18
Therefore, the response area should be "18".