Bella bought b boxes of cookies to bring to a party. She decides to keep two boxes. Each box contains 18 cookies. She brings 90 cookies to the party. Which equation can be used to find the number of boxes, b, Bella bought? How many boxes did she buy?(1 point)
Responses
18b−2=90; b=5
18b−2=90; b=5
2b−18=90; b=54
2b−18=90; b=54
18b−36=90; b=7
18b−36=90; b=7
18b−36=90; b=6
The correct equation is 18b-2=90. To solve for b, we add 2 to both sides of the equation, giving us 18b = 92. Then, we divide both sides by 18 to solve for b, giving us b = 5. Therefore, Bella bought 5 boxes of cookies.
Delia spent $250 to rent a boat for 6 hours. The rental company charges a base rate of $150 for the first two 2 hours, and then an hourly rate for each additional hour. How much does each additional hour of boat rental cost?(1 point)
Responses
$20
$20
$17
$17
$67
$67
$25
To find out how much each additional hour of boat rental costs, we need to subtract the base rate from the total cost of renting the boat.
The base rate is $150 for the first 2 hours.
So, the cost of renting the boat for the remaining 4 hours would be $250 - $150 = $100.
To find the cost per additional hour, we divide the remaining cost ($100) by the number of additional hours (4):
$100 / 4 = $25.
Therefore, each additional hour of boat rental costs $25.
The equation that can be used to find the number of boxes, b, Bella bought is 18b - 2 = 90. By solving the equation, we find that the value of b is 5. Therefore, she bought 5 boxes.
To solve this problem, we need to establish an equation that represents the given information.
Let's break down the information we have:
1. Bella bought b boxes of cookies.
2. She decides to keep two boxes, meaning she brings b - 2 boxes to the party.
3. Each box contains 18 cookies.
4. She brings a total of 90 cookies to the party.
Based on these details, we can create the equation:
(total number of cookies in the boxes Bella brings) = (total number of boxes Bella brings) * (number of cookies in each box)
Since the total number of cookies in the boxes Bella brings is 90 and the number of cookies in each box is 18, the equation becomes:
90 = (b - 2) * 18
To find the number of boxes, b, Bella bought, we can solve for b by rearranging the equation:
Divide both sides by 18:
90/18 = (b - 2)
Simplify:
5 = b - 2
Add 2 to both sides:
5 + 2 = b
So, the equation to find the number of boxes, b, Bella bought is:
18b - 2 = 90
And the number of boxes she bought is:
b = 7
Therefore, the correct equation and the number of boxes she bought is:
18b - 2 = 90; b = 7
Solve the equation for y.
−1/5y+3=−7
(1 point)
Responses
50
50
-35
-35
15
15
55
To solve the equation -1/5y + 3 = -7 for y, we need to isolate y on one side of the equation.
First, let's subtract 3 from both sides of the equation:
-1/5y + 3 - 3 = -7 - 3
Simplifying, we have:
-1/5y = -10
To eliminate the coefficient of -1/5 in front of y, we can multiply both sides of the equation by -5:
-5 * -1/5y = -5 * -10
Simplifying, we get:
y = 50
Therefore, the value of y is 50.
Darcy and JoJo are decorating cupcakes for a party. Darcy decorates 8 cupcakes which is 2 more than 13
the number of cupcakes that JoJo decorates. How many cupcakes does JoJo decorate?(1 point)
Responses
18
18
2
2
30
30
3
Let's use algebra to solve this problem.
Let's assume that the number of cupcakes JoJo decorates is x.
According to the given information, Darcy decorates 8 cupcakes, which is 2 more than 13 cupcakes that JoJo decorates.
This can be represented as the equation:
8 = 13 + 2x
We need to solve for x, so let's isolate x.
Subtract 13 from both sides of the equation:
8 - 13 = 13 + 2x - 13
-5 = 2x
Next, divide both sides of the equation by 2:
-5/2 = 2x/2
-5/2 = x
Therefore, JoJo decorates -5/2 cupcakes, which doesn't make sense in this context.
There seems to be an error in the problem statement or the given options, as the solution doesn't result in a valid number of cupcakes for JoJo.
Darcy and JoJo are decorating cupcakes for a party. Darcy decorates 8 cupcakes which is 2 more than 1/3
the number of cupcakes that JoJo decorates. How many cupcakes does JoJo decorate?(1 point)
Responses
18
18
2
2
30
30
3
Let's use algebra to solve this problem.
Let's assume that the number of cupcakes JoJo decorates is x.
According to the given information, Darcy decorates 8 cupcakes, which is 2 more than 1/3 of the number of cupcakes JoJo decorates.
This can be represented as the equation:
8 = (1/3)x + 2
To solve for x, let's isolate it.
Subtract 2 from both sides of the equation:
8 - 2 = (1/3)x + 2 - 2
6 = (1/3)x
Next, multiply both sides of the equation by 3 to eliminate the fraction:
6 * 3 = (1/3)x * 3
18 = x
Therefore, JoJo decorates 18 cupcakes.
The correct answer is 18.
When multiplying two rational numbers, how is the sign of the product determined?(1 point)
Responses
The product is positive if the signs of the factors are the same.
The product is positive if the signs of the factors are the same.
The product is negative if the signs of the factors are the same.
The product is negative if the signs of the factors are the same.
The sign of the product is always the same as the larger factor.
The product is positive if the signs of the factors are the same.
When multiplying two rational numbers, how is the sign of the product determined?(1 point)
Responses
The product is positive if the signs of the factors are the same.
The product is positive if the signs of the factors are the same.
The product is negative if the signs of the factors are the same.
The product is negative if the signs of the factors are the same.
The sign of the product is always the same as the larger factor.
The sign of the product is always the same as the larger factor.
The sign of the product is always the same as the smaller factor.
The sign of the product is always the same as the smaller factor.
The sign of the product is always the same as the smaller factor.
On a given morning the temperature was 81°F. The temperature dropped 9°F and then rose 5°F. How much does the temperature need to rise or fall to return to the initial temperature of 81°F?(1 point)
Responses
Rise 4°
Rise 4 degrees
Rise 9°
Rise 9 degrees
Fall 4°
Fall 4degree
Fall 5°
To find out how much the temperature needs to rise or fall to return to the initial temperature of 81°F, we need to add the temperature changes together and determine the net change.
The initial temperature was 81°F. The temperature then dropped 9°F, so the temperature was at 81°F - 9°F = 72°F. The temperature then rose 5°F, so the temperature was at 72°F + 5°F = 77°F.
To return to the initial temperature of 81°F, the temperature needs to rise by 81°F - 77°F = 4°F.
Therefore, the temperature needs to rise by 4°F to return to the initial temperature of 81°F.
Divide −3/17
by −2/3
(1 point)
Responses
9/34
9 over 34
2/17
2 over 17
−2/17
negative 2 over 17
−9/34
To divide -3/17 by -2/3, we can use the rule of dividing fractions by multiplying the first fraction by the reciprocal of the second fraction.
Reciprocal of -2/3 is -3/2.
So, the division can be rewritten as: -3/17 * -3/2.
Multiplying the numerators gives: -3 * -3 = 9.
Multiplying the denominators gives: 17 * 2 = 34.
So, -3/17 divided by -2/3 is equal to 9/34.
Therefore, the correct answer is 9/34.
Find the product.
4/7(−20/2)
(1 point)
Responses
−2/35
negative 2 over 35
5 5/7
5 and 5 sevenths
−5 5/7
negative 5 and 5 sevenths
−9 3/7
negative 9 and 3 sevenths
To find the product of 4/7 times (-20/2), we multiply the numerators and denominators separately.
Multiplying the numerators gives: 4 * (-20) = -80.
Multiplying the denominators gives: 7 * 2 = 14.
So, the product is -80/14.
To simplify this result, we can divide both the numerator and denominator by their greatest common divisor, which is 2.
Dividing -80 by 2 gives: -40.
Dividing 14 by 2 gives: 7.
Therefore, the simplified product of 4/7 times (-20/2) is -40/7, which can also be written as -5 5/7.
Therefore, the correct answer is -5 5/7.