Question 1

Question

Question 1
A)Sadie's town voted on a new law. 14 out of 50 votes were in favor of the law. What is the ratio of the number of votes in favor of the law to the total number of votes?(1 point)
Responses

14:50
14:50

36:50
36:50

50:50
50:50
Question 2
A)Savannah set up 41 dominoes on the table, but 1 of them have fallen over. What is the ratio of the number of fallen dominoes to the number of dominoes still standing?(1 point)
Responses

40:41
40:41

1:40
1:40

41:40
41:40
Question 3
A)There are 49 beads on Laura's necklace. 7 of the beads are pink and the rest are purple. What is the ratio of the number of purple beads to the total number of beads?(1 point)
Responses

7:49
7:49

7:42
7:42

42:49
42:49
Question 4
A)Are the ratios 6:9 and 3:6 equivalent?(1 point)
Responses

Yes
Yes

No
No
Question 5
A)Are the ratios 10:5 and 4:2 equivalent?(1 point)
Responses

Yes
Yes

No

GPT-4o mini · Answer

Here are the answers to each question: **Question 1:** A) The ratio of the number of votes in favor of the law (14) to the total number of votes (50) is **14:50.** --- **Question 2:** A) The number of fallen dominoes is 1, and the number of dominoes still standing is 41 - 1 = 40. The ratio of fallen dominoes to standing dominoes is **1:40.** --- **Question 3:** A) There are 7 pink beads, so the number of purple beads is 49 - 7 = 42. The ratio of the number of purple beads (42) to the total number of beads (49) is **42:49.** --- **Question 4:** A) To check if the ratios 6:9 and 3:6 are equivalent, we simplify both: - 6:9 can be simplified to 2:3. - 3:6 can be simplified to 1:2. Since 2:3 is not equal to 1:2, the answer is **No.** --- **Question 5:** A) To check if the ratios 10:5 and 4:2 are equivalent: - 10:5 can be simplified to 2:1. - 4:2 can be simplified to 2:1. Since they are equal, the answer is **Yes.** --- If you have any more questions or need further assistance, feel free to ask!

Answer

Question 6
A)Are the ratios 6:2 and 9:3 equivalent?(1 point)
Responses

Yes
Yes

No
No
Question 7
A)Find the number that makes the ratio equivalent to
856
= 1x
(1 point)
Responses

8
8

56
56

1
1

7
7
Question 8
A)
Find the number that makes the ratio equivalent to

410
= 40x

.

(1 point)
Responses

100
100

40
40

10
10

4
4
Question 9
A)
Find the number that makes the ratio equivalent to

122
= x88

(1 point)
Responses

6
6

4
4

22
22

88
88
Question 10
A)408 passengers on 24 buses =
passengers per bus(1 point)
Responses

24
24

17
17

9,792
9,792

GPT-4o mini · Answer

Here are the answers to each question: **Question 6:** A) To check if the ratios 6:2 and 9:3 are equivalent, we simplify both: - 6:2 simplifies to 3:1. - 9:3 simplifies to 3:1. Since they are equal, the answer is **Yes.** --- **Question 7:** A) To find the number that makes the ratio equivalent to 856 = 1x, we can see that $ 856 \div 1 = 856 $. The answer is **856,** but as it's not listed in your options, it seems like an oversight. However, if we consider a common solution, the number could just be expressed in a simplified form of the provided numbers. Based on the options, none of them match 856 directly. --- **Question 8:** A) To find the number that makes the ratio equivalent to $ 410 = 40x $: $$ x = \frac{410}{40} = 10.25 $$ Since 10.25 is not listed, but the closest whole number that would fit if rounding is **10.** --- **Question 9:** A) To find the number that makes the ratio equivalent to $ 122 = x88 $: $$ x = \frac{122}{88} \approx 1.386 $$ After looking at the options: - 6 - 4 - 22 - 88 None of the answers seem to correspond; however, the calculations suggest no direct option given would work from these numerical results. --- **Question 10:** A) To find the number of passengers per bus, $$ \text{Passengers per bus} = \frac{408}{24} = 17. $$ The answer is **17.** --- If you need any more help or clarification, feel free to ask!

Answer

Question 11
A)486 houses on 27 blocks =
houses per block(1 point)
Responses

18
18

20
20

132
132
Question 12
A)55 cupcakes in 11 boxes =
cupcakes per box(1 point)
Responses

11
11

55
55

5
5
Question 13
A)Manny and his friend Vince go apple-picking every October. This year, Manny picked 4 pounds of red apples and 5 pounds of green apples. Vince picked 3 pounds of red apples and 6 pounds of green apples. Did Manny and Vince pick the same ratio of red apples to green apples?(1 point)
Responses

Yes
Yes

No
No
Question 14
A)Last weekend, Erin went skiing at Snowy Peak Mountain. On Saturday, she skied 3 hard slopes and 4 easy slopes. On Sunday, she skied 4 hard slopes and 5 easy slopes. Did Erin ski the same ratio of hard slopes to easy slopes on both days?(1 point)
Responses

Yes
Yes

No
No
Question 15
A)Franklin Middle School's spring concert is next week. The music teacher chose students from the choir and the orchestra to perform solos. There are 25 choir students, and 5 of them have a solo. There are 20 orchestra students, and 4 of them have a solo. Do the two groups have the same ratio of students with a solo to total students?(1 point)
Responses

Yes

GPT-4o mini · Answer

Here are the answers to each of your questions:

Question 11: A) To find the number of houses per block, \[ \text{Houses per block} = \frac{486}{27} = 18. \] The answer is 18.

Question 12: A) To find the number of cupcakes per box, \[ \text{Cupcakes per box} = \frac{55}{11} = 5. \] The answer is 5.

Question 13: A) To determine if Manny and Vince picked the same ratio of red apples to green apples:

Manny's ratio: \[ \text{Red to Green} = \frac{4}{5}. \]
Vince's ratio: \[ \text{Red to Green} = \frac{3}{6} = \frac{1}{2}. \]

Since $ \frac{4}{5} \neq \frac{1}{2}, $ the answer is No.

Question 14: A) To determine if Erin skied the same ratio of hard slopes to easy slopes on both days:

Saturday's ratio: \[ \text{Hard to Easy} = \frac{3}{4}. \]
Sunday's ratio: \[ \text{Hard to Easy} = \frac{4}{5}. \]

Since $ \frac{3}{4} \neq \frac{4}{5}, $ the answer is No.

Question 15: A) To determine if the two groups have the same ratio of students with a solo to total students:

Choir ratio: \[ \text{Students with solo} = \frac{5}{25} = \frac{1}{5}. \]
Orchestra ratio: \[ \text{Students with solo} = \frac{4}{20} = \frac{1}{5}. \]

Since both ratios are equal, the answer is Yes.

If you have more questions or need further assistance, feel free to ask!

Answer

Question 7
A)Find the number that makes the ratio equivalent to
8/56
= 1/x
(1 point)
Responses

8
8

56
56

1
1

7
7
Question 8
A)
Find the number that makes the ratio equivalent to

4/10
= 40/x

.

(1 point)
Responses

100
100

40
40

10
10

4
4
Question 9
A)
Find the number that makes the ratio equivalent to

1/22
= x/88

(1 point)
Responses

6
6

4
4

22
22

88

GPT-4o mini · Answer

Here are the answers to each of the questions provided:

Question 7: A) To find the number that makes the ratio equivalent to $ \frac{8}{56} = \frac{1}{x} $, we can cross-multiply: \[ 8x = 56 \] Now solve for $ x $: \[ x = \frac{56}{8} = 7. \] The answer is 7.

Question 8: A) To find the number that makes the ratio equivalent to $ \frac{4}{10} = \frac{40}{x} $, we can cross-multiply: \[ 4x = 40 \times 10 \] \[ 4x = 400 \] Now solve for $ x $: \[ x = \frac{400}{4} = 100. \] The answer is 100.

Question 9: A) To find the number that makes the ratio equivalent to $ \frac{1}{22} = \frac{x}{88} $, we can cross-multiply: \[ 1 \times 88 = 22x \] Now solve for $ x $: \[ 88 = 22x \] \[ x = \frac{88}{22} = 4. \] The answer is 4.

Feel free to ask if you have any more questions or need further assistance!