Respuesta :
Answer:
1. [tex]Expression: 3(5a + 2)[/tex]
2. [tex]Total\ charges = 6.25(s+g)[/tex]
3. [tex]Total = 65x + 18 + 65y[/tex]
4. Michelle
5. 20 friends
6. Thor
8. [tex]x\leq 5[/tex]
9. [tex]x + x + 5 = 32[/tex]
10. [tex]7n + 9 \leq 44[/tex] so: [tex]n \leq 5[/tex]
11. [tex]40 + 5n \leq 70[/tex] So: [tex]n \leq 6[/tex]
12. [tex]10.01 p + 9.96 \leq 50[/tex] so [tex]p \leq 4[/tex]
Step-by-step explanation:
1. Given
[tex]Expression: 15a + 6[/tex]
Required
Determine the equivalent expression
[tex]Expression: 15a + 6[/tex]
Expand:
[tex]Expression: 3 * 5a + 3 * 2[/tex]
Factorize:
[tex]Expression: 3(5a + 2)[/tex]
Hence, the equivalent expression of the given expression is [tex]3(5a + 2)[/tex]
2.
Given
[tex]Charges = \$6.25[/tex]
s = seventh grade students
g = eight grade students
Required
Determine the total charges
First, we need to calculate the total number of charges:
[tex]Total=s+g[/tex]
[tex]Total\ charges = Charges * Total[/tex]
[tex]Total\ charges = 6.25(s+g)[/tex]
3. Given
Ken
[tex]Duration = x\ weeks[/tex]
[tex]Extra\ Earnings = \$18[/tex]
[tex]Weekly\ Earnings = \$65[/tex]
Paul
[tex]Weekly\ Earnings = \$65[/tex]
[tex]Duration = y\ weeks[/tex]
Ken's total charges is:
[tex]Weekly\ Earnings * Duration + Extra\ Earnings[/tex]
[tex]65 * x + 18[/tex]
[tex]65x + 18[/tex]
Paul's total charges is:
[tex]Weekly\ Earnings * Duration[/tex]
[tex]65 * y[/tex]
[tex]65 y[/tex]
[tex]Total = Ken + Paul[/tex]
[tex]Total = 65x + 18 + 65y[/tex]
4.
To calculate the percentage, we simply divided the number of pop albums by the total number of albums.
For Michelle.
[tex]\%Pop = \frac{33}{60} * 100\%[/tex]
[tex]\%Pop = \frac{3300\%}{60}[/tex]
[tex]\%Pop = 55\%[/tex]
For Sasha
[tex]\%Pop = \frac{36}{78} * 100\%[/tex]
[tex]\%Pop = \frac{3600\%}{78}[/tex]
[tex]\%Pop = 46.2\%[/tex]
For Kat:
[tex]\%Pop = \frac{40}{89} * 100\%[/tex]
[tex]\%Pop = \frac{4000\%}{89}[/tex]
[tex]\%Pop = 44.9\%[/tex]
For Monica:
[tex]\%Pop = \frac{24}{59} * 100\%[/tex]
[tex]\%Pop = \frac{2400\%}{59}[/tex]
[tex]\%Pop = 40.7\%[/tex]
From the calculation above, Michelle has the highest percentage of Pop music
5.
[tex]People = 80[/tex]
[tex]Fortnite = 0.55[/tex]
[tex]Among\ Us = 30\%[/tex]
Required
Determine number of friends that prefer fortnite more than among us
First, we need to calculate the number of people that prefer Fortnite.
[tex]Fortnite = 0.55 * 80[/tex]
[tex]Fortnite = 44[/tex]
Next, we need to calculate the number of people that prefer Among Us.
[tex]Among\ Us = 30\% * 80[/tex]
[tex]Among\ Us = 24[/tex]
The difference is:
[tex]Difference = 44 - 24[/tex]
[tex]Difference = 20[/tex]
Hence, 20 more people preferred Fortnite to Among Us
6.
[tex]Hulk = 0.25[/tex]
[tex]Iron\ Man = 12[/tex]
[tex]Thor = 35\%[/tex]
Captain America cleaned the rest
[tex]Total = 60[/tex]
Number of cities by each is:
[tex]Hulk = 0.25 * 60[/tex]
[tex]Hulk = 15[/tex]
[tex]Iron\ Man = 12[/tex]
[tex]Thor = 35\%[/tex]
[tex]Thor = 35\% * 60[/tex]
[tex]Thor = 21[/tex]
[tex]Captain\ America = 60 - 15 -12 - 21[/tex]
[tex]Captain\ America = 12[/tex]
By comparison, Thor cleaned the highest number of cities
7. This question is not clear
[tex]Total = \$70[/tex]
[tex]Glass = \$30[/tex]
[tex]Each\ Cape = \$8[/tex]
Let the number of cape be x.
We have that:
[tex]8 * x + 30 \leq 70[/tex]
[tex]8 x +\leq 70 - 30[/tex]
[tex]8 x +\leq 40[/tex]
[tex]x\leq 5[/tex]
9.
Let the first number be x and the second be y
[tex]x + y = 32[/tex]
[tex]y = x + 5[/tex]
Substitute x + 5 for y in the first equation
[tex]x + x + 5 = 32[/tex]
10.
[tex]Savings = \$9[/tex]
Earnings = $7 per hous
Total = $44
The inequality is:
[tex]7 * n + 9 \leq 44[/tex]
[tex]7n + 9 \leq 44[/tex]
[tex]7n \leq 44 - 9[/tex]
[tex]7n \leq 35[/tex]
[tex]n \leq 5[/tex]
11.
Earnings = $40
Extra = $5 per lasso
Total Earnings = At least $70 daily
The inequality is:
[tex]40 + 5n \leq 70[/tex]
[tex]5n \leq 70 - 40[/tex]
[tex]5n \leq 30[/tex]
[tex]n \leq 6[/tex]
12.
[tex]Each\ Cake = \$0.01[/tex]
[tex]Shipping = \$9.96[/tex] per order
[tex]Available = \$50[/tex] --- maximum
The inequality is:
[tex]10.01 * p + 9.96 \leq 50[/tex]
[tex]10.01 p + 9.96 \leq 50[/tex]
[tex]10.01 p \leq 50 - 9.96[/tex]
[tex]10.01 p \leq 40.04[/tex]
[tex]p \leq 4[/tex]