A standard United States Flag has the dimensions of 3 feet x 5 feet. Which of the following could be scaled versions of this flag? Select all that apply!
6 feet by 15 feet
2 feet x 4 feet
1 foot x 2 feet
15 feet by 25 feet
30 feet by 50 feet
2 feet x 4 feet
1 foot x 2 feet
Why?
A scaled version of a flag maintains the same proportional dimensions as the original flag. Since the original flag is 3 feet x 5 feet, any scaled version must have the same height-to-width ratio.
2 feet x 4 feet and 1 foot x 2 feet both have a height-to-width ratio of 1:2, which is the same as the original flag. Therefore, they can be scaled versions of the US flag.
However, the other options: 6 feet x 15 feet, 15 feet by 25 feet, and 30 feet by 50 feet do not have the same height-to-width ratio as the original flag, so they cannot be scaled versions.
Azeriah is making punch with orange juice and pomegranate juice. She mixes the two juices according to the amounts indicated in the table below. How many cups of pomegranate juice should she add to 20 cups of orange juice?
Number of cups of orange juice
4
16
Number of cups of pomegranate juice
3
12
___ cups of pomegranate juice?
To find out how many cups of pomegranate juice Azeriah should add to 20 cups of orange juice, we need to determine the ratio of pomegranate juice to orange juice.
The table gives us the following values:
Number of cups of orange juice: 4, 16
Number of cups of pomegranate juice: 3, 12
If we simplify the ratio, we get:
3/4 = 12/x
To solve for x, we can cross-multiply:
3x = 48
Dividing both sides by 3:
x = 16
Therefore, Azeriah should add 16 cups of pomegranate juice to 20 cups of orange juice.
Why 16?
Apologies for the incorrect response. Let's recalculate based on the correct table of values:
Number of cups of orange juice: 4, 16
Number of cups of pomegranate juice: 3, 12
The ratio of pomegranate juice to orange juice is consistent across the table:
3 cups of pomegranate juice corresponds to 4 cups of orange juice.
12 cups of pomegranate juice corresponds to 16 cups of orange juice.
If we divide both sides of the equation by 4, we can find the ratio for 1 cup of orange juice:
3/4 = 12/x
Simplifying, we have:
3x = 48
Dividing both sides by 3:
x = 16
Therefore, Azeriah should add 16 cups of pomegranate juice to 20 cups of orange juice.
Choose the option that has the following numbers in order from LEAST to GREATEST:
-1, 5, -1/2, -4, |-3|
To arrange the numbers in order from least to greatest, we start by comparing their values.
-4 is the smallest number because it has the most negative value.
Next, we have |-3|, which is the absolute value of -3. The absolute value of -3 is 3, so |-3| = 3.
Next, we have -1.
Next, we have -1/2, which is a negative fraction.
Lastly, we have 5, which is the largest number.
Therefore, the numbers in order from least to greatest are:
-4, 3, -1, -1/2, 5