Question

Determine which expression is equivalent to 15a + 6. (5 points)

Answer 1

Answer:

1. $Expression: 3(5a + 2)$

2. $Total\ charges = 6.25(s+g)$

3. $Total = 65x + 18 + 65y$

4. Michelle

5. 20 friends

6. Thor

8. $x\leq 5$

9. $x + x + 5 = 32$

10. $7n + 9 \leq 44$ so: $n \leq 5$

11. $40 + 5n \leq 70$ So: $n \leq 6$

12. $10.01 p + 9.96 \leq 50$ so $p \leq 4$

Step-by-step explanation:

1. Given

$Expression: 15a + 6$

Required

Determine the equivalent expression

$Expression: 15a + 6$

Expand:

$Expression: 3 * 5a + 3 * 2$

Factorize:

$Expression: 3(5a + 2)$

Hence, the equivalent expression of the given expression is $3(5a + 2)$

2.

Given

$Charges = \ 6.25$

s = seventh grade students

g = eight grade students

Required

Determine the total charges

First, we need to calculate the total number of charges:

$Total=s+g$

$Total\ charges = Charges * Total$

$Total\ charges = 6.25(s+g)$

3. Given

Ken

$Duration = x\ weeks$

$Extra\ Earnings = \ 18$

$Weekly\ Earnings = \ 65$

Paul

$Weekly\ Earnings = \ 65$

$Duration = y\ weeks$

Ken's total charges is:

$Weekly\ Earnings * Duration + Extra\ Earnings$

$65 * x + 18$

$65x + 18$

Paul's total charges is:

$Weekly\ Earnings * Duration$

$65 * y$

$65 y$

$Total = Ken + Paul$

$Total = 65x + 18 + 65y$

4.

To calculate the percentage, we simply divided the number of pop albums by the total number of albums.

For Michelle.

$\%Pop = \frac{33}{60} * 100\%$

$\%Pop = \frac{3300\%}{60}$

$\%Pop = 55\%$

For Sasha

$\%Pop = \frac{36}{78} * 100\%$

$\%Pop = \frac{3600\%}{78}$

$\%Pop = 46.2\%$

For Kat:

$\%Pop = \frac{40}{89} * 100\%$

$\%Pop = \frac{4000\%}{89}$

$\%Pop = 44.9\%$

For Monica:

$\%Pop = \frac{24}{59} * 100\%$

$\%Pop = \frac{2400\%}{59}$

$\%Pop = 40.7\%$

From the calculation above, Michelle has the highest percentage of Pop music

5.

$People = 80$

$Fortnite = 0.55$

$Among\ Us = 30\%$

Required

Determine number of friends that prefer fortnite more than among us

First, we need to calculate the number of people that prefer Fortnite.

$Fortnite = 0.55 * 80$

$Fortnite = 44$

Next, we need to calculate the number of people that prefer Among Us.

$Among\ Us = 30\% * 80$

$Among\ Us = 24$

The difference is:

$Difference = 44 - 24$

$Difference = 20$

Hence, 20 more people preferred Fortnite to Among Us

6.

$Hulk = 0.25$

$Iron\ Man = 12$

$Thor = 35\%$

Captain America cleaned the rest

$Total = 60$

Number of cities by each is:

$Hulk = 0.25 * 60$

$Hulk = 15$

$Iron\ Man = 12$

$Thor = 35\%$

$Thor = 35\% * 60$

$Thor = 21$

$Captain\ America = 60 - 15 -12 - 21$

$Captain\ America = 12$

By comparison, Thor cleaned the highest number of cities

7. This question is not clear

$Total = \ 70$

$Glass = \ 30$

$Each\ Cape = \ 8$

Let the number of cape be x.

We have that:

$8 * x + 30 \leq 70$

$8 x +\leq 70 - 30$

$8 x +\leq 40$

$x\leq 5$

9.

Let the first number be x and the second be y

$x + y = 32$

$y = x + 5$

Substitute x + 5 for y in the first equation

$x + x + 5 = 32$

10.

$Savings = \ 9$

Earnings = $7 per hous

Total = $44

The inequality is:

$7 * n + 9 \leq 44$

$7n + 9 \leq 44$

$7n \leq 44 - 9$

$7n \leq 35$

$n \leq 5$

11.

Earnings = $40

Extra = $5 per lasso

Total Earnings = At least $70 daily

The inequality is:

$40 + 5n \leq 70$

$5n \leq 70 - 40$

$5n \leq 30$

$n \leq 6$

12.

$Each\ Cake = \ 0.01$

$Shipping = \ 9.96$ per order

$Available = \ 50$ --- maximum

The inequality is:

$10.01 * p + 9.96 \leq 50$

$10.01 p + 9.96 \leq 50$

$10.01 p \leq 50 - 9.96$

$10.01 p \leq 40.04$

$p \leq 4$