Use the properties of operations to add 9(k + 1/3) + 10(1/2k - 1)
A. 14k + 13
B. 19 1/2 * k - 2/3
C. 14k - 7
D. 14k - 2/3
To add 9(k + 1/3) + 10(1/2k - 1), we can use the distributive property to simplify.
First, we distribute 9 to both terms inside the first parentheses: 9k + 9/3
Next, we distribute 10 to both terms inside the second parentheses: 10/2k - 10
Simplifying the fractions, 9/3 = 3 and 10/2 = 5.
Now we can combine like terms: 9k + 3 + 5k - 10
Combining like terms, we get: 14k - 7
Therefore, the simplified expression is 14k - 7.
The correct answer is C. 14k - 7.
Use the table to answer the question.
8 48
10 60
x 72
y 84Analyze the ratios in the table to find the missing values.(1 point)
Responses
22; 34
22; 34
432; 504
432; 504
12; 14
12; 14
18; 26
To find the missing values, let's analyze the ratios in the table.
The first ratio can be found by dividing each y-value by the corresponding x-value: 48/8 = 6 and 60/10 = 6. So, we can conclude that the ratio is 6.
The second ratio can be found by dividing each y-value by the corresponding x-value: 72/x = 6. To find the value of x, we can divide 72 by 6: x = 72/6 = 12.
The last ratio can be found by dividing each y-value by the corresponding x-value: 84/x = 6. To find the value of x, we can divide 84 by 6: x = 84/6 = 14.
Therefore, the missing values are x = 12 and y = 14.
The correct answer is 12; 14.
Use the given tables to compare the ratios 3:5
and 2:3
.
3 5
6 10
9 15
12 20
15 25
2 3
4 6
6 9
8 12
10 15
(1 point)
Responses
More rows need to be added to the tables to be able to compare the ratios.
More rows need to be added to the tables to be able to compare the ratios.
3:5 > 2:3
3:5 > 2:3
3:5 < 2:3
ratio of 3 to 5 is less than ratio of 2 to 3
3:5 = 2:3
To compare the ratios 3:5 and 2:3, we need to consider equivalent ratios.
By looking at the first table:
For the 3:5 ratio, we can see that every 3 corresponds to 5.
For the 2:3 ratio, we can see that every 2 corresponds to 3.
If we multiply the 2:3 ratio by 2, we get 4:6.
Now we can compare the ratios:
3:5 is not equal to 4:6 because 3 does not equal 4 and 5 does not equal 6.
Since we do not have any other equivalent ratios to compare, we cannot determine which ratio is greater or lesser.
Therefore, the correct response is: More rows need to be added to the tables to be able to compare the ratios.
The following tables show the amount of fat for a given number of crackers for two types of crackers. Which type of cracker has less fat per cracker?
Cracker A
Grams of Fat Number of Crackers
8 10
16 20
24 30
32 40
40 50
48 60
Cracker B
Grams of Fat Number of Crackers
6 12
12 24
18 36
24 48
30 60
36 72
(1 point)
Responses
The two types of crackers have the same amount of fat per cracker.
The two types of crackers have the same amount of fat per cracker.
Cracker A
Cracker A
More rows need to be added to the tables to be able to compare the crackers.
More rows need to be added to the tables to be able to compare the crackers.
Cracker B
Cracker B
To determine which type of cracker has less fat per cracker, we need to compare the ratios of grams of fat to the number of crackers for each type of cracker.
For Cracker A, the ratio of grams of fat to the number of crackers is:
8/10 = 0.8 grams of fat per cracker
16/20 = 0.8 grams of fat per cracker
24/30 = 0.8 grams of fat per cracker
32/40 = 0.8 grams of fat per cracker
40/50 = 0.8 grams of fat per cracker
48/60 = 0.8 grams of fat per cracker
For Cracker B, the ratio of grams of fat to the number of crackers is:
6/12 = 0.5 grams of fat per cracker
12/24 = 0.5 grams of fat per cracker
18/36 = 0.5 grams of fat per cracker
24/48 = 0.5 grams of fat per cracker
30/60 = 0.5 grams of fat per cracker
36/72 = 0.5 grams of fat per cracker
From the ratios, we can see that the amount of fat per cracker is consistently lower for Cracker B. Therefore, Cracker B has less fat per cracker compared to Cracker A.
The correct answer is: Cracker B.
3 of 53 of 5 Items
Which of the following tables could you use to compare the ratios 2:5 and 3:4?(1 point)
Responses
2 5
4 10
3 4
6 82 5 4 10 3 4 6 8
2 5
4 10
6 15
8 20
10 25
3 4
6 8
9 12
12 16
15 202 5 4 10 6 15 8 20 10 25 3 4 6 8 9 12 12 16 15 20
2 5
6 15
10 25
3 4
9 12
16 202 5 6 15 10 25 3 4 9 12 16 20
2 5
3 10
4 15
5 20
6 25
3 4
4 8
5 12
6 16
7 20
To compare the ratios 2:5 and 3:4, we need to find a table that contains equivalent ratios for both ratios.
Let's analyze the options:
Option 1:
2:5 is present, but 3:4 is not.
Option 2:
2:5 and 3:4 are both present.
Option 3:
3:4 is present, but 2:5 is not.
Option 4:
2:5 is present, but 3:4 is not.
Therefore, the correct option is option 2:
2 5
4 10
6 15
8 20
10 25
3 4
6 8
9 12
12 16
15 20
Option 2 provides an equivalent ratio for 2:5 (4:10), as well as an equivalent ratio for 3:4 (6:8). Therefore, this table can be used to compare the ratios 2:5 and 3:4.
The correct answer is option 2.
Compare the ratios 7:4 and 12:5 using the following tables. Finish the tables by filling in the missing values A and B.
7 4
14 8
21 12
28 16
A B
12 5
24 10
36 15
48 20
60 25
(1 point)
Responses
A = 35 and B = 18.
upper A equals 35 and upper B equals 18 .
A = 35 and B = 20.
upper A equals 35 and upper B equals 20 .
A = 32 and B = 20.
upper A equals 32 and upper B equals 20 .
A = 32 and B = 18.
upper A equals 32 and upper B equals 18 .
To compare the ratios 7:4 and 12:5, we need to find equivalent ratios in the tables provided.
From the given table, we see that the first ratio, 7:4, is already provided.
To find the equivalent ratio for 12:5, we can divide 12 by 6 to get 2, and then multiply 2 by 5 to get 10. So, the equivalent ratio is 12:5 = 24:10.
Now, to fill in the missing values A and B:
Looking at the second column, we see that 24 corresponds to 10. Since 12 corresponds to A, we can set up a proportion:
12/24 = A/10
Multiplying both sides by 24, we get:
A = 12 * 10/24 = 120/24 = 5
Hence, A = 5.
Now, looking at the first column, we see that 7 corresponds to 4. So, since 5 corresponds to A, we can set up another proportion:
5/7 = B/4
Multiplying both sides by 7, we get:
B = 5 * 4/7 = 20/7
Thus, B = 20/7.
Therefore, the missing values are A = 5 and B = 20/7.
The correct answer is: A = 5 and B = 20/7.
pick one of the listed answers and pick the correct one
Apologies for the confusion. Based on the given response options, the correct answer is:
A = 35 and B = 18.
Let me know if you have any further questions.
Use the given tables to compare the ratios 16:18 and 5:6 . Which ratio is greater?
8 9
16 18
24 27
32 36
5 6
10 12
15 18
20 24(1 point)
Responses
The two ratios are equal.
The two ratios are equal.
More rows need to be added to the tables to be able to compare the ratios.
More rows need to be added to the tables to be able to compare the ratios.
5:6 is greater.
ratio of 5 to 6 is greater.
16:18 is greater.
To compare the ratios 16:18 and 5:6, we can analyze the given tables.
For the first ratio, 16:18, we can see that the second number is 2 greater than the first number.
For the second ratio, 5:6, we can see that the second number is 1 greater than the first number.
Since the second number in the first ratio (18) is greater than the second number in the second ratio (6), we can conclude that the ratio 16:18 is greater than the ratio 5:6.
Therefore, the correct answer is: 16:18 is greater.
Declan is making a batch of cookies that contains eight cups of ingredients. Two cups of ingredients are sugar. What percent of the cookie ingredients are sugar?(1 point)
To find the percentage of sugar in the batch of cookies, we need to divide the number of cups of sugar by the total number of cups of ingredients, and then multiply by 100.
In this case, there are 2 cups of sugar out of 8 cups of ingredients.
Calculating the percentage:
(2/8) * 100 = 0.25 * 100 = 25
Therefore, 25% of the cookie ingredients are sugar.
The correct answer is 25%.
Write 12/30 as a percent.(1 point)
12/30 =
%
To write 12/30 as a percent, we need to divide 12 by 30 and then multiply by 100.
Calculating the percentage:
(12/30) * 100 = 0.4 * 100 = 40
Therefore, 12/30 is equal to 40%.
The correct answer is 40%.
Find a percent that is equivalent to 15300 .(1 point)
Responses
5%
5 percent
45%
45 percent
20%
20 percent
15%
To find a percent that is equivalent to 15300, we need to divide 15300 by 100.
Calculating the percentage:
15300 / 100 = 153
Therefore, 15300 is equivalent to 153%.
The correct answer is 153 percent.
Find a percent that is equivalent to 15/300 .(1 point)
Responses
5%
5 percent
45%
45 percent
20%
20 percent
15%
To find the percent that is equivalent to 15/300, we can divide 15 by 300 and then multiply by 100.
Calculating the percentage:
(15/300) * 100 = 0.05 * 100 = 5
Therefore, 15/300 is equivalent to 5%.
The correct answer is 5%.
Eli is making soup for his family. He adds 3 cups of vegetables, 4 cups of broth, 1 cup of chicken, and 2 cups of noodles to the soup. What percent of the soup is vegetables?(1 point)
Responses
300%
300 percent
30%
30 percent
3%
3 percent
33%
To find the percent of the soup that is vegetables, we need to divide the number of cups of vegetables by the total number of cups of soup ingredients and then multiply by 100.
In this case, there are 3 cups of vegetables out of a total of 3 + 4 + 1 + 2 = 10 cups of soup ingredients.
Calculating the percentage:
(3/10) * 100 = 0.3 * 100 = 30
Therefore, 30% of the soup is vegetables.
The correct answer is 30 percent.
Write 260400 as a percent.(1 point)
Responses
26%
26 percent
15.3%
15.3 percent
65%
65 percent
60%
To write 260400 as a percent, we divide 260400 by 100 and express it as a percentage.
Calculating the percentage:
260400/100 = 2604
Therefore, 260400 is equivalent to 2604%.
The correct answer is 2604 percent.
What is 90% of 200?(1 point)
Responses
90
90
18
18
180
180
160
To find 90% of 200, we need to multiply 200 by 90% (or 0.9):
200 * 0.9 = 180
Therefore, 90% of 200 is 180.
The correct answer is 180.
Abdel just got a job babysitting his neighbors 3 afternoons a week. He wants to save 60%
of his earnings each week. If he will make $80
a week, how much will he be saving each week?(1 point)
Responses
$48
48 dollars
$13.33
13.33 dollars
$60
60 dollars
$36
To calculate how much Abdel will be saving each week, we need to find 60% of his earnings of $80.
Calculating the savings:
60% of $80 = (60/100) * $80 = 0.6 * $80 = $48
Therefore, Abdel will be saving $48 each week.
The correct answer is $48.