The expression 0.90(d - 5) refers to a product of 0.90 and the difference between d and 5. This can be determined from the structure of the expression, where 0.90 is multiplied by (d - 5).
This expression could also be written as 0.90d - 4.5, by applying the distributive property.
What does the expression 0.90(d – 5) refer to? How do you know? How else
could this expression be written?
11 answers
c. Choose a value for d that is greater than $25 and less than $100. Calculate the
total cost of each of the possible presents for the value you chose. Then write a
short paragraph telling Winona and Takoda which present they should buy and
explaining why.
total cost of each of the possible presents for the value you chose. Then write a
short paragraph telling Winona and Takoda which present they should buy and
explaining why.
Let's choose a value for d as $50.
To calculate the total cost of each possible present, we can substitute this value into the expression 0.90(d - 5).
For Present A:
0.90(50 - 5) = 0.90(45) = $40.50
For Present B:
0.90(50 - 5) = 0.90(45) = $40.50
For Present C:
0.90(50 - 5) = 0.90(45) = $40.50
For Present D:
0.90(50 - 5) = 0.90(45) = $40.50
Based on the calculations, Present A, B, C, and D all have the same total cost of $40.50.
Therefore, Winona and Takoda could choose any of the presents A, B, C, or D, as they all cost the same amount. It may be beneficial for them to consider other factors such as the recipient's personal preferences or the uniqueness of each present to make their decision.
To calculate the total cost of each possible present, we can substitute this value into the expression 0.90(d - 5).
For Present A:
0.90(50 - 5) = 0.90(45) = $40.50
For Present B:
0.90(50 - 5) = 0.90(45) = $40.50
For Present C:
0.90(50 - 5) = 0.90(45) = $40.50
For Present D:
0.90(50 - 5) = 0.90(45) = $40.50
Based on the calculations, Present A, B, C, and D all have the same total cost of $40.50.
Therefore, Winona and Takoda could choose any of the presents A, B, C, or D, as they all cost the same amount. It may be beneficial for them to consider other factors such as the recipient's personal preferences or the uniqueness of each present to make their decision.
A county planner prepares the following table showing population trends in three local
towns. The first column gives the name of the town. The second column gives the
population as of the last census. The third column gives the estimated increase or
decrease in population since that census, expressed as a percentage of the previous
population.
Town Census Population Percentage Change
Pleasantville x –2%
Amity Center y +5%
Harmony Corners z +7%
a. Choose one of these towns. Use the second and third columns to write two
expressions showing the current estimated population of the town in terms of
x, y, or z.
towns. The first column gives the name of the town. The second column gives the
population as of the last census. The third column gives the estimated increase or
decrease in population since that census, expressed as a percentage of the previous
population.
Town Census Population Percentage Change
Pleasantville x –2%
Amity Center y +5%
Harmony Corners z +7%
a. Choose one of these towns. Use the second and third columns to write two
expressions showing the current estimated population of the town in terms of
x, y, or z.
Let's choose the town Pleasantville, represented by the variable x.
To calculate the current estimated population of Pleasantville using the second and third columns, we can write two expressions:
1. Expression 1: The population after the change
The population after the change is given by the formula:
(x) + (-2/100)(x) = x - 0.02x = (1 - 0.02)x = 0.98x
2. Expression 2: The current estimated population
Since the table does not provide the current estimated population directly, we can calculate it by adding the estimated increase or decrease to the population as of the last census. Therefore:
Current estimated population = Census population + (Percentage change / 100) * Census population
Current estimated population = x + (-2/100)(x) = x - 0.02x = (1 - 0.02)x = 0.98x
Both expressions, 0.98x and x - 0.02x, represent the current estimated population of Pleasantville in terms of x.
To calculate the current estimated population of Pleasantville using the second and third columns, we can write two expressions:
1. Expression 1: The population after the change
The population after the change is given by the formula:
(x) + (-2/100)(x) = x - 0.02x = (1 - 0.02)x = 0.98x
2. Expression 2: The current estimated population
Since the table does not provide the current estimated population directly, we can calculate it by adding the estimated increase or decrease to the population as of the last census. Therefore:
Current estimated population = Census population + (Percentage change / 100) * Census population
Current estimated population = x + (-2/100)(x) = x - 0.02x = (1 - 0.02)x = 0.98x
Both expressions, 0.98x and x - 0.02x, represent the current estimated population of Pleasantville in terms of x.
Add a fourth row to the table showing the population information for the town
of Concord. Concord’s population as of the last census was p people; for its
percentage change, choose a negative integer not divisible by two. Write two
expressions showing the current estimated population of Concord in terms of p.
of Concord. Concord’s population as of the last census was p people; for its
percentage change, choose a negative integer not divisible by two. Write two
expressions showing the current estimated population of Concord in terms of p.
Certainly! Here's the modified table with the population information for the town of Concord:
Town Census Population Percentage Change
Pleasantville x -2%
Amity Center y +5%
Harmony Corners z +7%
Concord p -9%
To express the current estimated population of Concord in terms of p, we can write the following two expressions:
1. Expression 1: The population after the change
The population after the change is given by:
(p) + (-9/100)(p) = p - 0.09p = (1 - 0.09)p = 0.91p
2. Expression 2: The current estimated population
Similar to the previous question, we can calculate the current estimated population by adding the estimated increase or decrease to the population as of the last census. Therefore:
Current estimated population = Census population + (Percentage change / 100) * Census population
Current estimated population = p + (-9/100)(p) = p - 0.09p = (1 - 0.09)p = 0.91p
Both expressions, 0.91p and p - 0.09p, represent the current estimated population of Concord in terms of p.
Town Census Population Percentage Change
Pleasantville x -2%
Amity Center y +5%
Harmony Corners z +7%
Concord p -9%
To express the current estimated population of Concord in terms of p, we can write the following two expressions:
1. Expression 1: The population after the change
The population after the change is given by:
(p) + (-9/100)(p) = p - 0.09p = (1 - 0.09)p = 0.91p
2. Expression 2: The current estimated population
Similar to the previous question, we can calculate the current estimated population by adding the estimated increase or decrease to the population as of the last census. Therefore:
Current estimated population = Census population + (Percentage change / 100) * Census population
Current estimated population = p + (-9/100)(p) = p - 0.09p = (1 - 0.09)p = 0.91p
Both expressions, 0.91p and p - 0.09p, represent the current estimated population of Concord in terms of p.
Choose a number greater than 5,000 and less than 10,000 for the value of p.
Based on the percentage change you chose in part b, calculate the estimated
current population of Concord, rounding to the nearest whole number if
needed. Explain why you used the expression you did to make your calculation.
Based on the percentage change you chose in part b, calculate the estimated
current population of Concord, rounding to the nearest whole number if
needed. Explain why you used the expression you did to make your calculation.
Let's choose p to be 7,500 as a value greater than 5,000 and less than 10,000.
Using the percentage change of -9% for Concord, we can calculate the estimated current population by applying Expression 1: the population after the change.
Expression 1: The population after the change
0.91p = 0.91 * 7,500 = 6,825
By using this expression, we calculated the estimated current population of Concord to be 6,825.
We used Expression 1 because it accounts for the negative percentage change, representing the estimated decrease in population. The expression multiplies the census population (p) by 0.91, the factor obtained from subtracting 9% (0.09) from 1. This calculation adjusts the population downward by 9% to reflect the estimated decrease. Rounding to the nearest whole number wasn't necessary as the result is already a whole number.
Using the percentage change of -9% for Concord, we can calculate the estimated current population by applying Expression 1: the population after the change.
Expression 1: The population after the change
0.91p = 0.91 * 7,500 = 6,825
By using this expression, we calculated the estimated current population of Concord to be 6,825.
We used Expression 1 because it accounts for the negative percentage change, representing the estimated decrease in population. The expression multiplies the census population (p) by 0.91, the factor obtained from subtracting 9% (0.09) from 1. This calculation adjusts the population downward by 9% to reflect the estimated decrease. Rounding to the nearest whole number wasn't necessary as the result is already a whole number.
A’Leila is building a pen for her pet donkey. The pen is a rectangle with one side
measuring b yards and the adjacent side measuring a yards. A’Leila knows that
.
a. Write two different expressions giving the perimeter of the donkey’s pen.
measuring b yards and the adjacent side measuring a yards. A’Leila knows that
.
a. Write two different expressions giving the perimeter of the donkey’s pen.
To find the perimeter of the donkey's pen, we need to sum the lengths of all four sides. Since the given information states that one side measures b yards and the adjacent side measures a yards, we can write two different expressions for the perimeter:
1. Expression 1: Sum of all four sides
Perimeter = a + b + a + b = 2a + 2b
2. Expression 2: Twice the sum of the lengths of the adjacent sides
Perimeter = 2(a + b)
Both expressions represent the perimeter of the donkey's pen, with Expression 1 explicitly adding each side's length and Expression 2 utilizing the property that the sum of the lengths of the adjacent sides is equal to the sum of the lengths of the opposite sides.
1. Expression 1: Sum of all four sides
Perimeter = a + b + a + b = 2a + 2b
2. Expression 2: Twice the sum of the lengths of the adjacent sides
Perimeter = 2(a + b)
Both expressions represent the perimeter of the donkey's pen, with Expression 1 explicitly adding each side's length and Expression 2 utilizing the property that the sum of the lengths of the adjacent sides is equal to the sum of the lengths of the opposite sides.
1 answer