Damian has two summer jobs. He works as a tutor, which pays $12 per hours, and he works as a lifeguard, which pays $9.50 per hour. He can work no more than 20 hours a week, but he wants to earn at least $220 per week. Which of the following systems of inequalities represents this situation, where x is the number of hours worked as a tutor, and y is the number of hours worked as a lifeguard?

A.12x + 9.5y ≤ 220 AND x + y ≥ 20
B.12x + 9.5y ≤ 220 AND x + y ≤ 20
C.12x + 9.5y ≥ 220 AND x + y ≤ 20
D.12x + 9.5y ≥ 220 AND x + y ≥ 20

Answer:

a) True

b) True

C) false

Step-by-step explanation:

just a guess..... Merry Christmas

Answer:

using divisional law of indices logab-logan=log(b/n)therefore logbM-logbN=logb(M/N)

Answer:

1. no solution

2. one solution

3. infinitely many solutions

Step-by-step explanation:

1. 4= -3

false

2. -5=6c+7

2=6c

c=3

3. 5a+7=5a+7

true

Answer:

No solution

One solution

Infinite number of solutions

Step-by-step explanation:

Answer:

P [ X > 23,22 ]  = 0,8798      or  P [ X > 23,22 ]  =  87,98 %

Step-by-step explanation:

P [ X > 23,22 ]  =  1  -  P [X ≤ 23,22 ]

P [X ≤ 23,22 ] =  ( X - μ₀ ) / σ /√n

P [X ≤ 23,22 ] = ( 23,22 - 36,25 )/ 6,50/√36

P [X ≤ 23,22 ] =  - 13,03 *6 / 6,50

P [X ≤ 23,22 ] = - 12,02        or       P [X ≤ 23,22 ] = 12,02 %

(note the - sign only mean that values on the left tail of the bell shape curve)

Then

P [ X > 23,22 ]  =  1  -  0,1202

P [ X > 23,22 ]  = 0,8798      or  P [ X > 23,22 ]  =  87,98 %

Answer:

$6414

Step-by-step explanation:

Step one

given

Principal=$2,000

rate= 6%= 0.06

Time= 20 years

Required

The final amount

Step two:

The compound interest formula is

A= P(1+r)^t

substituting we have

[tex]A=2000(1+0.06)^2^0\\\\ A= 2000(1.06)^2^0\\\\ A=2000*3.207\\\\A=6414[/tex]

The amount given to the college is $6414

Answer:

B

Step-by-step explanation:

Answer:

$586.04 is your answer

Answer:

3.0

Step-by-step explanation:

5.8-2.6=3.2 simplified 3.0

Answer:

1 hour and 15 minuets

Step-by-step explanation:

5 hours and he was hedging for 25% of that time.

25%=.25

5(0.25)

1.25

A quarter of an hour is 15 minutes.

So the final answer would be 1 hour and 15 minuets.

Answer:

[tex]\frac{35}{3}[/tex] or [tex]11 \frac{2}{3}[/tex]

Step-by-step explanation:

Just add them

Answer:

176.

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

Answer:

We should attempt synthetic division to find when

x

3

−

k

x

2

+

2

k

x

−

15

x

−

3

has a remainder of

0

, which would signify that it is a factor of the polynomial.

The synthetic substitution would be set up as:

3

−

∣

∣

∣

1

−

k

2

k

−

15

−−−

−−−

−−−

−−−

−−−

|

0

Treating the synthetic division like any other synthetic division problem, we see that

3

−

∣

∣

∣

1

−

k

2

k

−

15

−−−

−−−

3

−−−−−−−−

−

3

k

+

9

−−−−−−−−

−

3

k

+

27

−−−−−−−−−

1

−

k

+

3

−

k

+

9

|

0

If the remainder equals

0

, then we know that

−

3

k

+

27

+

(

−

15

)

=

0

Solve this to see that

k

=

4

.

Thus,

(

x

−

3

)

is a factor of

x

3

−

4

x

2

+

8

x

−

15

.

Answer:

Part B:

5) She will have $4445.244256 in 3 years

Part C:

1) She will have $8081.130039 in 10 years

2) He will have $13360.55059 in 8 years

Step-by-step explanation:

The formula of the compound interest is A = P [tex](1+\frac{r}{n})^{nt}[/tex], where

Part B:

5)

∵ P = $4250

∵ r = 1.5% = 1.5 ÷ 100 = 0.015

∵ n = 4 ⇒ Compounded quartly

∵ t = 3 years

→ Substitute them in the formula above

∴ A = 4250 [tex](1+\frac{0.015}{4})^{4(3)}[/tex]

∴ A = 4250 [tex](1.00375)^{12}[/tex]

∴ A = 4445.244256

∴ She will have $4445.244256 in 3 years

Part C:

1)

∵ Grace deposits $6000

∴ P = 6000

∵ The account is compounded semi-annually at 3%

∴ r = 3% = 3 ÷ 100 = 0.03

∴ n = 2 ⇒ compounded semi-annually

∵ The time is 10 years

∴ t = 10

→ Substitute them in the formula above

∴ A = 6000 [tex](1+\frac{0.03}{2})^{2(10)}[/tex]

∴ A = 6000 [tex](1.015)^{20}[/tex]

∴ A = 8081.130039

∴ She will have $8081.130039 in 10 years

2)

∵ Danial opens an account that is compounded semi-annually at 5%

∴ r = 5% = 5 ÷ 100 = 0.05

∴ n = 2 ⇒ compounded semi-annually

∵ He deposits $9000

∴ P = 9000

∵ The time is 8 years

∴ t = 8

→ Substitute them in the formula above

∴ A = 9000 [tex](1+\frac{0.05}{2})^{2(8)}[/tex]

∴ A = 9000 [tex](1.025)^{16}[/tex]

∴ A = 13360.55059

∴ He will have $13360.55059 in 8 years

Answer:

It's 3 square units.

Count the "squares" and you get 3 and it's not real units so It's called "Square units".

:)

Answer:

no figures

Step-by-step explanation:

to work with and the answer is can't be determined

Answer: y=-32

Step-by-step explanation:

1. Simplify:

-6y-90=-3y+6

2. Add like terms:

-96=3y

=> y=-32

Have a nice day! :)

Answer:

79 feet

Step-by-step explanation:

The perimeter is all the sides added together.

15+22+10+18+14 =

79 feet

please give thanks :)

if answer is incorrect, your question is not clear enough. this is the best answer I can provide.

Step-by-step explanation:

check the answer it is as same

Answer:

30= 20 so, that’s 10 dollars of

                                            1o+ 7. 5=17. 5+10=27 .50

Step-by-step explanation:

I took the test hope this helps

Answer:

-1

Step-by-step explanation:

slope is always the coeffcient* the number beside the variable

Answer:

3

Step-by-step explanation:

Answer:

1. 8 x 8 ÷ 2

2. 64 ÷ 2 = 32

Step-by-step explanation:

(7+1) becomes 8 and 8 x 8 becomes 64

64 ÷ 2 = 32

Step-by-step explanation:

Step 3 is incorrect, it should be x - 4 + x = x(x - 3).

x - 4 + x = x(x - 3)

2x - 4 = x² - 3x

x² - 5x + 4 = 0

(x - 4)(x - 1) = 0

x = 4 or x = 1.

x = 4 is rejected as 1 / (x - 4) will become 1 / 0 which is undefined.

=> x = 1.

Answer: 0.16666666666

Answer:

Both take time together = 36 / 5 hours = 7.2 hours

Step-by-step explanation:

Given:

Briana take time = 12 hour

Henry take time = 18 hour

Find:

Both take time together

Computation:

Briana 1 hour work = 1/12

Henry 1 hour work = 1/18

Both take time together = 1/[1/12+1/18]

Both take time together = 1/[5/36]

Both take time together = 36 / 5 hours = 7.2 hours

Answer:

8+4t

Step-by-step explanation:

combine 3t and t then do 6t - 4t getting 8+4t

Answer: [tex]=(29.1596\text{ degrees},\ 30.2404\text{ degrees})[/tex]

Step-by-step explanation:

Given: Sample size: n = 41

Sample mean [tex]\overline{x}= 29.7[/tex] degrees

Population standard deviation [tex]\sigma=2.7[/tex] degrees

Confidence level (c) =  80% =0.80

Significance level (a) = 1- c = 1-0.80 = 0.20

z-score for 80% confidence level : z = 1.2816   [from z-table]

Confidence level for population mean :-

[tex]\overline{x}\pm z\dfrac{\sigma}{\sqrt{n}}[/tex]

[tex]=29.7\pm ( 1.2816)\dfrac{2.7}{\sqrt{41}}[/tex]

[tex]=29.7\pm ( 1.2816)\dfrac{2.7}{6.403124}[/tex]

[tex]=29.7\pm ( 1.2816)(0.42167)[/tex]

[tex]=29.7\pm 0.5404[/tex]

[tex]=(29.7-0.5404,\ 29.7+0.5404)[/tex]

[tex]=(29.1596,\ 30.2404)[/tex]

Hence, 80% confidence interval for the temperatures in the freezer [tex]=(29.1596\text{ degrees},\ 30.2404\text{ degrees})[/tex]

Answer:

30°  is one of the degree measures of the angles.

Hence, option (A) is true.

Step-by-step explanation:

Given that the degree measure of one of two complementary angles is twice that of the other.

Complementary angles

Thus the equation becomes

x + 2x = 90°

3x =  90°

Divide both equations by 3

3x/3 = 90°/3

x = 30°

Therefore, 30°  is one of the degree measures of the angles.

Hence, option (A) is true.

The degree measure of one of two complementary angles is twice that of the other. What is one of the degree measures of the angles?

A.) 30 degrees

Let one angle = x

According to statement,

Another angle = 2 × first angle

[tex] \sf : \implies Another \: angle = 2x[/tex]

Now, we know that sum of complementary angles is 90°

Hence,

[tex] \sf : \implies x + 2x = 90^{\circ}[/tex]

[tex] \sf : \implies 3x = 90^{\circ}[/tex]

[tex] \sf : \implies x = \dfrac{\cancel{90}^{\circ}}{\cancel{3}}[/tex]

[tex] \sf : \implies x = 30^{\circ}[/tex]

[tex] \Large \underline{\boxed{\sf{ x = 30^{\circ} }}}[/tex]

Therefore, one of the angle is 30°.

Another angle = 2 × 30° = 60°

Answer:

I also think b one is correct