Solve please. Correctly -9

The system of inequalities are
14.5·x + 9.5·y ≥ 140
7 ≤ y ≤ 10
x + y ≤ 15
2) 14.5·x + 9.5·y ≥ 140 represents the total amount of money Janine can earn
7 ≤ y ≤ 10 represents the range of values, Janine can spend dishwashing
x + y ≤ 15 represents the total number of hours Janine will like to work each week
3) 8 hours babysitting, 7 hours dishwashing
Step-by-step explanation:
The given parameters are;
The amount per hour Janine makes from babysits = $14.50
The amount per hour Janine makes from dishwashing = $9.50
The minimum number of hours Janine can spend dishwashing = 7 hours
The maximum number of hours Janine can spend dishwashing = 10 hours
The maximum number of hours Janine can work each week = 7 hours
The minimum amount she wants to make each week = $140
Let x represent the number of hours Janine spends babysitting and let y represent the number of hours Janine spends dishwashing
1) From the question, we have;
14.5·x + 9.5·y ≥ 140
7 ≤ y ≤ 10
x + y ≤ 15
2) Where
14.5·x + 9.5·y ≥ 140 represents the total amount of money Janine can earn
7 ≤ y ≤ 10 represents the range of values, Janine can spend dishwashing
x + y ≤ 15 represents the total number of hours Janine will like to work each week
Making, y, the subject of the formula of the above inequalities and plotting as functions is given as follows;
y ≥ 140/9.5 - (14.5/9.5)·x
y ≤ 15 - x
3) In order to earn as much money as possible given that the amount Janine earns from babysitting is more than the amount she earns from dishwashing, Janine should spend the least amount of time dishwashing, which is 7 hours, as given, and then spend the remaining 8 hours babysitting to receive $14.5 × 8 + $9.5×7 = $182.5

3 0

3 years ago

How long will it take to have R30 000 for a trip to Europe if I invest R20 000 now at 15% per year, compounded quarterly?

maw [93]

Compound interest formula

$A=P(1+ \frac{r}{n} )^{nt}$

Where

A= Future value
P = the Principal (the initial amount of money)
r = annual interest rate

t = time

n= number of times compounded in one t

Remark
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r is generally a percentage like 3%, 7% etc and are applied in the formula as 0.03, 0.07...,

the interest is compounded generally annually (n=1), quarterly (n=4), monthly (n=12), etc...

t is in years,

In our problem:

A= 30 000

P =20 000

r = 15%=0.15

time = t = ?

n= 4

applying the formula:

$A=P(1+ \frac{r}{n} )^{nt}\\\\30,000=20,000(1+ \frac{0.15}{4} )^{4t}\\\\ \displaystyle{\frac{30,000}{20,000} =(1.0375)^{4t}$

$\displaystyle{ 1.5={(1.0375^4)}^t\\\\$

$1.5=1.159^t\\\\ \displaystyle { t=log_{1.159}1.5=2.75$

75% of 12 months is 3/4 of 12 months, which is 9 months

Answer: 2 years, 9 months

3 0

3 years ago

Angles 1 and 2 are complementary and congruent. what is the measure of angle 1? 30° 45° 50° 75°

lesantik [10]

see the attached figure to better understand the problem

we know that

1) If angle 1 and angle 2 are complementary angles

then

m∠1+m∠2= $90\°$ ------> equation A