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Related Questions
Janine babysits for $14.50 per hour. She also works as a dishwasher at her family's restaurant for $9.50 per hour. Her family needs her to be at the restaurant at least 7 hours per week, but she can't work there more than 10 hours per week. She also does not want to work more than a total of 15 hours each week. She wants to make at least $140 per week.
Write a system of inequalities that represents the constraints on Janine's part-time jobs. Explain what your inequalities represent in the context of the problem.
Janine wants to earn as much money as possible next week. What combination of hours should she spend at each job to do this? Justify your reasoning.
Answers
Answer:
1) 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
Janine should work as a dishwasher for 7 hours, and as a babysitter for 8 hours, to earn as much money
Represent the hours babysitting with b, and the hour dishwashing with d.
So, we have the following systems of inequalities
[tex]14.5b + 9.5d \ge 140[/tex] ---her earnings[tex]7\le d \le 10[/tex] -- the time she can spend at the restaurant[tex]b + d \le 15[/tex] --- her weekly work hoursNext, we plot the graphs of the inequalities that represent the hours she can work.
i.e. the graphs of [tex]7\le d \le 10[/tex] and [tex]b + d \le 15[/tex]
From the attached graph, we have the following possible values
[tex](b,d) =(5,10) (8,7)[/tex]
Substitute these values in [tex]14.5b + 9.5d \ge 140[/tex]
So, we have:
At (5,10):
[tex]Earnings = 14.5 \times 5 + 9.5 \times 10[/tex]
[tex]Earnings = 167.5[/tex]
At (8,7):
[tex]Earnings = 14.5 \times 8 + 9.5 \times 7[/tex]
[tex]Earnings = 182.5[/tex]
The earnings at point (8,7) is greater than (5,10).
Hence, she should work as a dishwasher for 7 hours, and as a babysitter for 8 hours, to earn as much money
Read more about inequalities at:
https://brainly.com/question/18881247
what situations can be modeled with fraction multiplication and division
Answers
Linda needs 2200 calories per day to maintain her present weight and daily activities. She wants to lose x pounds per day. Each pound of body weight lost is equivalent to 3400 calories. Write her daily calorie intake as a linear function of the number of pounds of weight lost per day. (Let y represent the calorie intake and x represent the number of pounds of weight lost per day.)
Answers
Answer:
y = - 5600x + 2200
Step-by-step explanation:
Given that:
x = number of pounds lost per day
y = calorie intake
Using the linear relation :
y = mx + c
When calorie intake = 2200, no loss or gain in weight ; x = 0 ; hence intercept c = 2200
y = 0 + 2200
Each pound of body weight lost = - 3400 calories
Hence, equation when x = 1
-3400 = m(1) + 2200
-3400 = m + 2200
-3400 - 2200 = m
-5600 = m
Hence,
y = mx + c
y = - 5600x + 2200
there were 40 questions on Roberts test. How many problems did Robert get right if he received an 87.5% oh his test?
Answers
Answer:
Robert got 35 problems right if he received an 87.5% oh his test.
Step-by-step explanation:
Total questions = 40As Robert got right 87.5% on his test.
so the expression becomes
87.5% × 40
= 87.5/100 × 40
= 0.875 × 40
= 35
Therefore, Robert got 35 problems right if he received an 87.5% oh his test.
A rectangular prism is shown below.
What is the volume of the rectangular prism?
A. 260 cm
B. 240 cm
C. 220 cm
D. 200 cm
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200 sq. cm. or 200^3
10x5=50
50x4=200
What is the less of side a? Round to the nearest tenth of an inch.
Answers
Answer:
About 14 in the exact value is 14.38 smthn
Elena and her best friend found some money in an envelope. They split the money evenly, each getting $25. How much money did they find? Write and solve the equation for this probl
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2(25)=50
wait do you need to use x?
what is the sum of the 2nd square number and the 5th cube number
Answers
Answer:
129
Step-by-step explanation:
4+125=129
The sum of the 2nd square number and the 5th cube number is 129.
What is the number system?A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.
As per the given question, the required solution would be as:
1, 2, 3, 4, 5....
1, 4, 9, 16, 25 ...
So, the second square number will be 4.
1, 8, 27, 64, 125, ...
So, the fifth cube number will be 125.
The sum of the second square number and the fifth cube number is :
4 + 125 = 129.
Learn more about the number system here:
brainly.com/question/21751836
#SPJ2
What is the value of n in the equation 1/2(n-4)-3=3-(2n+3)
Answers
Answer:
2
We first use the distributive property on both sides:
1/2(n)-1/2(4)-3 = 3-(2n)-(3)
1/2n - 2 - 3 = 3 - 2n - 3
Combining like terms on both sides,
1/2n - 5 = -2n
Subtracting 1/2n from both sides:
1/2n - 5 - 1/2n = -2n - 1/2n
-5 = (-2 1/2)n
Divide both sides by -2 1/2:
-5/(-2 1/2) = (-2 1/2)n/(-2 1/2)
2 = n
It is 85 miles from Central city to Smithville and 125 miles from Smithville to Jonesburg . How many gallons of gas will it take to drive from Central City to Smithville to jonesburg in a car which gets 30 miles per gallon .
Answers
Answer:
It will take 7 gallons of gas
Step-by-step explanation:
85 miles + 125 miles = 210 miles to drive
30 miles a gallon
210 ÷ 30 = 7
7 gallons needed
Hi. Please I need help with these questions.
It's urgent .
No jokes. This time
Answer No 14
Answers
9514 1404 393
Answer:
21x² +20x +100 = 0
Step-by-step explanation:
We know the sum of the roots of x² +bx +c = 0 is -b, and their product is c. If the roots are α and β, then ...
α+β = -bαβ = cThe sum of the roots of the new equation will be ...
-b' = (α+1/β)+(β+1/α) = (α+β) +(1/α +1/β) = (α+β)(1 +1/(αβ))
The product of the roots of the new equation will be ...
c' = (α+1/β)(β+1/α) = αβ +2 +1/(αβ)
Using the above relations for (α+β) and αβ, we find that ...
-b' = (-b)(1 +1/c)
c' = c + 2 + 1/c
For the given equation, our definition of b and c is ...
b = 2/3
c = 7/3
so the new equation has values ...
b' = (2/3)(1 + 1/(7/3) = (2/3)(10/7) = 20/21
c' = 7/3 + 2 + 1/(7/3) = 13/3 + 3/7 = 100/21
So, the equation with the roots of interest is ...
x² +20/21x +100/21 = 0
Multiplying by 21 gives ...
21x² +20x +100 = 0
B. What fraction of the letters of the English language are vowels? (points)
Answers
Answer:
5/26.
If you count y as a vowel it is 3/13
Step-by-step explanation:
Teresa wants to buy 2 new tires for her mountain bike. She has budgeted $120 for the tires, but after researching costs, knows she may end up
spending within $25 of that amount.
Write an inequality that Teresa could use to find the cost of each tire. Use the inequality to complete this statement.
Teresa may spend at least $
and at most $
for each new tire.
Answers
Answer:
Inequality: 95 ≤ x ≤ 145
Minimum = 95
Maximum = 145
Step-by-step explanation:
Given
Budget = $120
Range = $25
Solving (a) Write an inequality to determine how much she could spend.
The range implies that she can spend less or more of the budgeted amount.
Let the amount to spend be represented by x.
If she spends more, the maximum would be
Max = Budget + Range
Max = 120 + 25
Max = 145
If she spends less, the minimum would be
Min = Budget - Range
Min = 120 - 25
Min = 95
So, this means that x could fall within the range of the minimum and the maximum.
Mathematically, this is:
Min ≤ x ≤ Max
So, the inequality would be:
95 ≤ x ≤ 145
Solving (b): The minimum and maximum.
The minimum and the maximum amount have been solved in (a) above.
Minimum = 95
Maximum = 145
Answer:
Step-by-step explanation:
Which number is not a whole number ? A. 8. B. -10. C. 0. D.18/3
Answers
Answer:
B. -10 its a negative number
A recipe calls for 6 cups of milk. If you have 4
pints of milk, how many cups will you have left
over?
Answers
system equations -2x-6y=-16
Answers
........................
Answer:
x=−3y+8
Step-by-step explanation:
Step 1: Add 6y to both sides
−2x=6y−16
Step 2: Divide both sides by -2
−2x/−2 = 6y−16/−2
x=−3y+8
Im hoping this was very helpful : )
1. 0.071 64 correct to 2 significant figures is
Answers
Answer:
0.07
Step-by-step explanation:
show proof for all of these (for points, brainlist.) 880 x 12 = 10560 (proof)
-
197 divided 7 = 28
1 Remainder (proof)
-
$98 x $687= 67 326 U.S (proof)
-
936 x 39 =36504 (proof)
-
39 x 936 = 36504 (proof)
-
804 x 93 = 74772
(PROOF)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
SHOW PROOF FOR ALL OF THEM! TY (ASAP)
Answers
Answer: Multiply 93 by 804 and that will give you
74772x
Multiply 12 by 880 and that will give you
10560x
Exact Form:
1977
Decimal Form:
28.14285714…
Mixed Number Form:
2817
Multiply 687 by 98 that will give you
67326
Multiply 936 by 39 and that will give yoou
36504x
Step-by-step explanation:
Find the missing terms in each geometric sequence.
1. 3, 12, 48 __, __
2. __, __, 32, 64, 128, ...
3. 120, 60, 30, __, __
4. 5, __, 20, 40, __, __
5. __, 4, 12, 36, __, __
Answers
2. 8, 16 (it was adding the number together 8+8)
3. 15, 7.5 ( it was half of the number)
4. 10, 80, 160 ( times 2 )
5. .75, 108, 324 ( times 4 )
Hope this helped! Lmk if you need more help!
dont put anything random plsi ned
Answers
Answer:
I'll go from the top row and then do the bottom row from left to right. I put the letters next to them too if that makes it any easier.
Step-by-step explanation:
First one is already done
Second one:
Slope: -3 ( letter O)
Y-intercept: (0,4) (letter N)
Third One:
Slope: 2/3 ( letter P)
Y- intercept: (0,-3) (letter J)
Fourth One:
Slope:-1/2 (letter M)
Y-intercept: (0,3) (letter F)
Fifth one: ( first one on second row)
Slope: 1 ( letter i)
Y-intercept: (0,2) (letter S)
Sixth one:
Slope: -1/3 ( letter D)
Y-intercept: (0,-2) (letter B)
seventh one:
slope: 1/4 (letter E)
y-intercept: (0,-4) (letter H)
eighth one:
Slope:2 ( letter G)
Y-intercept: (0,0) ( letter A)
Hopefully these are all correct and it's not too confusing :)
the price of an item has risen to 300$ today. yesterday it was 125$. Find the percentage increse.
Answers
Answer:
140
Step-by-step explanation:
Trust Me
you jog 3.6 miles in 30 minutes. at the rate how long will it take you to jog 4.8 miles?
Answers
hope this helps
have a good day
The library had 301 shelves of books. Each shelf had 13 books. Librarians checked out 807 books to students. How many books does the library have remaining
Answers
Answer:
3106 books
Step-by-step explanation:
From the question:
The library had 301 shelves of books. Each shelf had 13 books.
Hence, the total number of books in the library =
Number of shelves × Number rod books in a shelf
= 301 × 13 books
= 3913 books
The total number of books in the library is 3913 books
Librarians checked out 807 books to students.
How many books does the library have remaining?
This is calculated as:
Total number of books - Number of books checked out
= 3913 books - 807 books
= 3106 books
The library has 3106 books remaining.
Do u like my drawing? I was supposed to become an artist for a day and I messed up soooo i went with it lol
Answers
Answer:
The drawing looks goood.
Answer:
good
Step-by-step explanation:
it looks good better than mine
f(4) if f(x)=-3+15 ?
Answers
Answer:
12
Step-by-step explanation:
f(4) means that we need to substitute 4 into x to get
f(4) = -3 + 15
and -3 + 15 = 12
5. AAA Dance Shoes makes dancing shoes with leather soles. The shoes cost $29 each to
manufacture. The fixed cost for the product line is $45,000. The company has
determined their demand function to be q=-200p+30,000, where p is the price for each
pair of shoes. What is the revenue function in terms of price? S
(10 Points)
R
200p + 915,000
O R = -200p + 30,000
O R = -200p2 + 30,000
O R = 200p2 + 870,000
Answers
Answer: 200p² + 870,000
Step-by-step explanation:
Revenue is calculated as price multiplied by quantity. In this case,
Price = P
Quantity (Q) = q=-200p+30,000
Revenue = p × q
Revenue = (200p + 30,000) × p
= 200p² + 30000p
= 200p² + 30000(29)
= 200p² + 870,000
The revenue function is 200p² + 870,000
Complete the statement. Round to the nearest hundredth if necessary
14 m to ft
The answer is not 45.93 or 46.
Answers
Answer:
[tex]45.9[/tex]
Step-by-step explanation:
Remember that the hundredths place value is the second number after the decimal point and to round that number has to be greater than five in order to round up.
[tex]1m=3.28084[/tex]
[tex]3.28084\times14=45.93176[/tex]
Hundredths place value = 3
Round:
[tex]3<5[/tex]
[tex]=45.9[/tex]
Hope this helps.
What are some random fun facts about you?
LOL I want to work at Starbucks but idek how to make my own coffee.
Answers
i work at my uncle’s restaurant but idr work
Answer:
lmbo
Step-by-step explanation:
Select the correct answer. Which number best represents the slope of the graphed line?
A.-5
B.-1/5
C.1/5
D.5
Answers
Answer:
1/5
Step-by-step explanation:
Answer:
(1/5)
Step-by-step explanation: I did it, got it right.
I don’t understand slopes at all! Can someone please help?Write an equation in slope-intercept form for a line that goes through the points (-3, 5) and (2, 8).
Answers
Answer:
Step-by-step explanation:
y2-y1
x2-x1=
y=mx+b
8-5
2+3=
3/5 = slope
b=0
y=3/5x