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
Related Questions
(2) A store is having a 20%-off sale on all merchandise. If Mai buys one item and saves $13, what was the original price of her purchase? Explain your reasoning. *
Answers
Answer:
$65
Step-by-step explanation:
Let
x = original price of the item
Mai buys one item and saves $13,
This means 20% of the original price of the item = $13
20% of x = 13
20/100 * x = 13
0.2 * x = 13
0.2x = 13
Divide both sides by 0.2
x = 13 / 0.2
= 65
x = $65
Therefore, the original price of the item is $65
The proper way to write a large number in a sentence is:
a.) ten billion
b.) 10 billion
c.) 10,000,000,000
d.) tens of billions
Answers
The probability of a basketball player making a free throw is 76%. In practice she shoots 10 free throws. What is the probability that he makes 7 free throws?
Answers
Answer:
0.243
Step-by-step explanation:
Given that :
Probability of success (p) = 76% = 0.76
Number of free throws (n) = 10
Probability of making 7 free throws = r
Using binomial distribution :
nCr * p^r * (1 - p)^(n-r)
10C7 * 0.76^7 * (1 - 0.76)^(10 - 7)
10C7 * 0.76^7 * 0.24^3
120 * 0.14645 * 0.013824
= 0.24294
Hence probability of making 7 free throws from 10 is 0.243
Answer:
MK
Step-by-step explanation:
15pts and brainliest to whoever can answer
(Also EXPLAIN the reasoning you used to find the value of P
Answers
9514 1404 393
Answer:
p = 3x+10
Step-by-step explanation:
The attached diagram pretty much explains it.
The unknown dimension at the top was the subject of a previous problem. It is the difference in length between the two marked horizontal segments:
(2x +15) -(x) = x +15 . . . . . length of unmarked solid horizontal line
Similarly, the length of the unmarked vertical line on the right is the difference between the marked vertical lines:
(2x -5) -(x -5) = x . . . . . length of unmarked solid vertical line
__
The formula for the area of a rectangle is used to find the areas of the left-side and right-side rectangles. Respectively, those areas are ...
left-side area = x(2x -5)
right-side area = x(x +15)
Then the total area enclosed by the solid line is ...
x(2x -5) +x(x +15) = x(2x -5 +x +15) = x(3x +10)
__
The area of the lot extension is the product of its dimensions:
extension area = x·p
We want this to be the same as the area in the solid line, so ...
x·p = x·(3x +10)
Dividing by the coefficient of p (which is x), we have ...
p = 3x +10
What is the measure of a vertex angle of a triangle if the base angle measures 38° and two congruent sides each measure 42 units?
Answers
Answer:
Bearing in the mind that an ossicle triangle has twin sides and coming out of the vertex they make twin angles at the base check the picture out
Step-by-step explanation:
Same way with 42
Keith has $500 in a savings account at the beginning of the summer. He withdraws $25 each week for food, clothes, and movie tickets. He wants to have an account balance of at least $200 in the account at the end of the summer.
Answers
Answer:
You can put this solution on YOUR website!
the inequality is 500 - 25x >= 200
this insures that he will have at least 200 at the end of the summer.
subtract 200 from both sides of that inequality and add 25x to both sides of that inequality to get 500 - 200 >= 25x
simplify to get 300 >= 25x
divide both sides of that equation by 25 to get 300 / 25 >= x
simplify to get 12 >= x
12 >= x means x <= 12.
when x is smaller than or equal to 12, he will be guaranteed to have at least 200 in the account at the end of the summer.
when x = 12, what is left in the account is 500 - 25 * 12 = 200.
when x = 11, what is left in the account is 500 - 25 * 11 = 225.
when x = 13, what is left in the account is 500 - 25 * 13 = 175.
the maximum number of weeks he can withdraw money from his account is 12.
Step-by-step explanation:
Prove Theorem 6-6. Given:m AB =m CD. Prove: m AB = mCD
Answers
Answer:
Step-by-step explanation:
The measure of angle 1 is equal to the measure of angle 2, its proved by using the theorem angle of tangency using arc measure.
What is the Measure of an Angle of Tangency Using Arc Measure?Let A be a point on a circle and B be the point where a tangent (passing through B and C) intersects the circle. Then, the angle of tangency ∠ABC is half of the measure of the arc AB formed on the same side.
Given that, Arc AB= Arc CD in circle P.
Here, Arc AB= 1/2 ×m∠1 ------(i)
Arc CD= 1/2 ×m∠2 ------(ii)
Equation (i) and (ii) are equal, we get
1/2 ×m∠1=1/2 ×m∠2
m∠1=m∠2
Hence, proved.
To learn more about the circle theorems visit:
https://brainly.com/question/19906313.
#SPJ5
"Your question is incomplete, probably the complete question/missing part is:"
Arc AB= Arc CD in circle P.
Prove that, m∠1=m∠2
12(x - 6) = 2(x - 9)
Answers
Answer:
Exact form: x = 27/5
Decimal form: x = 5.4
Mixed-number form: x = 5 2/5
Step-by-step explanation:
hope this helps :)
helpp simplify thissss
Answers
Answer:
2c^2
Step-by-step explanation:
8c^3d^2/4cd^2
divide the 8 by 4 to get 2
You subtract the powers so c^3-c=c^2 the d^2 cancel each other out
that leaves 2c^2
Explain how to use the regression calculator to make a reasonable prediction given a data table.
Answers
Answer:
Given bivariate data, first determine which is the independent variable, x, and which is the dependent variable, y. Enter the data pairs into the regression calculator. Substitute the value for one variable into the equation for the regression line produced by the calculator, and then predict the value of the other variable.
Step-by-step explanation:
Answer:
Sample Answer: Given bivariate data, first determine which is the independent variable, x, and which is the dependent variable, y. Enter the data pairs into the regression calculator. Substitute the value for one variable into the equation for the regression line produced by the calculator, and then predict the value of the other variable.
Step-by-step explanation:
its from edge
using ratio plz help im stuck i need #5 for one side 1-5 for the other
Answers
Science= 3 * 21 = 63
Math= 5 * 21 = 105
English= 7 * 21 = 147
147- 63 = 84
Answer: 84
—
2) A rope is cut in two in the ratio 3.5:1.75. The difference between the length is 94.5 inches. What was the original length of the rope?
3.5+1.75= 5.25
94.5 + 5.25 = 99.75
Answer: 99.75
—
3) A room is 14 feet long. Find the width of the room, if the ratio of the length to the width of the room is 7:5.
Length= 14
7 • 2 = 14
5 • 2 = 10
Answer: 10 feet
—
4) Steve covers a distance of 0.7 miles in 2 minutes. How much time will it take to travel 14 miles?
0.7 miles in 2 minutes
2 • 7 = 14
0.7 • 7 = 4.9
Answer: 4.9 miles
—
5) Lara and Mae are collecting seashells. For every 9 seashells that Lara picked, Mar gathered 7 seashells. If Lara collected 63 seashells, how many fewer seashells did Mae gather?
Let’s get out the key words here.
Lara gathers 9
Mae gathers 7
Lara collects 63
Mae collects ?
**Fewer seashells**
9 • ? = 63
9 • 7 = 63
This means she would need to gather 9 seashells 7 times to get 63 seashells.
This means Mae would need to get 7 shells 7 times to get her fewer amount.
7 • 7 = 49
Mae would gather 49 seashells. But it says fewer seashells.
63- 49 = 14
Final Answer: Mae would gather 14 less seashells then Lara.
—
5) A sum of 2,700 is shared among Eric, Jo, and Richard. Jo’s share is two times that of Richard’s share. Eric’s share is three times that of Jo’s share. Find Eric’s share.
2700/3= 900
900*2= $1,800
Answer: $1,800
—
I’m not sure if all of the answers are right but I hope this still helps you :)
WILL MARK BRAINLIEST! What is the formula to calculate the slope? Is it y^2-y^1/x^2-x^1? Please type it in for me.
Answers
Answer:
You are correct. Remember: rise over run.
m = [tex]\frac{y2-y1}{x2-x1}[/tex]
Answer:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Step-by-step explanation:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
the 2 and 1 represent which number they are in a series of points. For example, if I were to have points (1,2) and (3,4)
4 would be [tex]y_2[/tex] meaning it is the second y value
2 would be [tex]y_1[/tex] meaning it's the first y value
Same goes for x
3 is [tex]x_2[/tex]
1 is [tex]x_1[/tex]
so the equation for slope is [tex]\frac{4-2}{3-1}[/tex], or 1
Write the quadratic equation whose roots are 1 and -6, and whose leading coefficient is 5.
(Use the letter x to represent the variable.)
Answers
Answer:
[tex]f(x)=5x^2+25x-30[/tex]
Step-by-step explanation:
Quadratic Equation
If the roots of a quadratic equation are known, we can form the equation as follows:
[tex]f(x)=a(x-x_1)(x-x_2)[/tex]
where x1 and x2 are the known roots, and a is the leading coefficient.
We are given the roots as x1=1 and x2=-6, and the leading coefficient as a=5, thus:
[tex]f(x)=5(x-1)(x+6)[/tex]
Operating:
[tex]f(x)=5(x^2-x+6x-6)[/tex]
Simplifying:
[tex]f(x)=5(x^2+5x-6)[/tex]
Multiplying:
[tex]\mathbf{f(x)=5x^2+25x-30}[/tex]
Events which do not influence each other are called
Answers
Answer:
Independent Events
Step-by-step explanation:
Independent Events are events which do not affect each other.
HTH :)
What is the length of segment AB?
10
12
13
15
Answers
Answer:
Side AB is 13 plots long.
Step-by-step explanation:
Square sides A and side B
12 x 12 = 144
5 x 5 = 25
Now add the sides together. Then, find the square root of the sum.
144 + 25 = 169
[tex]\sqrt{169}[/tex] = 13
Check your work:
13 x 13 = 169
please help :,) identify an equation in slope-intercept form for the line parallel to y=3x+5 that passes through (4,-1)
Answers
Answer:
A. y + 1 = -3(x - 4)
Step-by-step explanation:
If the equations are perpendicular, then that means they have the same slope, just with the opposite sign. In this case, the given equation's slope is 3, which means that the other equation's slope is -3. Now that we know the slope and one point, we can write the equation in point-slope form:
y - y1 = m(x - x1)
y - (-1) = -3(x - 4)
y + 1 = -3(x - 4)
The equation in point-slope form is answer choice A. y + 1 = -3(x - 4).
Hope this helps :)
Use inductive reasoning to describe the pattern of the sequence. Then find the next two terms. 6, 24, 96, 384, ...
A. Multiply by 3; 672, 960.
B. Multiply by 4.5; 402, 420.
C. Multiply by 4; 1536, 6144.
D. Multiply by 3.5, 576, 764.
Answers
Answer:
1536 and 6144
Step-by-step explanation:
you are multiplying by 4
I hope this helps you to understands better
The next two-term of the sequence is 1536 and 6144 and the multiplicity is 4
Given the sequence of numbers expressed as 6, 24, 96, 384, ...
The given sequence is a geometric sequence. The nth term of the sequence is expressed as;
[tex]T_n = ar^{n-1}[/tex]
a is the first term
r is the common ratio or multiplicity
n is the number of terms
Given the following parameters
a = 6
r = 24/6 = 96/24 = 4
n = 5 and 6 (5th and 6th term)
For the fifth term;
[tex]T_{5} = 6(4)^{5-1}\\T_5=6(4)^4\\T_5 = 1536[/tex]
For the sixth term;
[tex]T_{6} = 6(4)^{6-1}\\T_6=6(4)^5\\T_6 = 6144[/tex]
Hence the next two-term of the sequence is 1536 and 6144 and the multiplicity is 4
Learn more here: https://brainly.com/question/9300199
Simplify the expression.
3x3 - 2x2
Answers
Answer:
3x^3 - 2x^2
Step-by-step explanation:
This is the answer because for the equation 3x^3 - 2x^2, nothing further can be done to this equation since there are no like terms.
CAN SOME ALGEBRA 2 PERSON PLEASE HELP ITS DUE IN A FEW HOURS!!!!!
PLEASE SHOW UR WORK, IT IS QUESTIONS 12-29! ;w;
Answers
12. 5x² - 180 = 0
5x² = 0 + 180
5x² = 180
x² = 180/5
x² = 36
x = √36
x = 6
13. 3x² - 100 = 332
3x² = 332 + 100
3x² = 432
x² = 432/3
x² = 144
x = √144
x = 12
14. ⅔x² - 8 = 16
⅔x² = 16 + 8
⅔x² = 24
2x² = 24 × 3
2x² = 72
x² = 72/2
x² = 36
x = √36
x = 6
15. ½x² - 5 = 5
½x² = 5 + 5
½x² = 10
x² = 10 × 2
x² = 20
x = √20
16. x² + 1 = 3x² - 13
1 + 13 = 3x² - x²
14 = 2x²
14/2 = x²
7 = x²
√7 = x
17. 2(x² + 4) = 10
2x² + 8 = 10
2x² = 10 - 8
2x² = 2
x² = 2/2
x² = 1
x = √1
x = 1
18. 3(x² - 1) = 9
3x² - 3 = 9
3x² = 9 + 3
3x² = 12
x² = 12/3
x² = 4
x = √4
x = 2
19. 2(x + 3)² = 8
2(x² + 3² + 2×x×3) = 8
2(x² + 9 + 6x) = 8
2x² + 18 + 12x = 8
2x² + 12x = 8 - 18
2x² + 12x = -10
2(x² + 6x) = -10
x² + 6x = -10/2
x(x + 6) = -5
x + 6 = -5/x
6 = -5/x - x
6 = -5/x - x²/x
6 = (-5 -x²)/x
6x = -5 - x²
What is the square root of 450 divided by 5?
Answers
Answer:
The square root of 450 is irrational, meaning it never ends. As an estemate though the answer is 4.24
Step-by-step explanation:
Simplify: -(-9) - 8(6 - 2)
Answers
-39+16=
-23
Hope this helps!
Answer:
28
Step-by-step explanation:
-(-9) -8(6-2)
-(-9)-8(4)
-(-9)-32
9 - 32
28
I need help ASAP will reward a lot of points and mark BRAINLIEST
Answers
11 is b because the bottom needs to be 5 to dived the amount by 5 minutes and the top is the amount of words she types in 5 minutes
What is the solution to the equation?
5 = 2/5 a O 2 O4 3/5 O 12 1/2. O 25
Person who answers first gets brainliest
Answers
Julio predicted that the average high temperature for January would be Negative 7 degrees Celsius. The actual average high temperature was 4 degrees higher than Julio’s prediction. Which describes the actual average high temperature for January?
–11°C
–3°C
3°C
11°C
Answers
Answer:
B (-3)
Step-by-step explanation:
Good Luck!
Write a unit rate for the situation.
270 miles in 6 hours
___miles per hour
Answers
Answer:
I believe it it 13 miles per hour.
Step-by-step explanation:
We know that an object travels 270 miles, so the rate is 270 miles.
---------------------------------
6 hours
1 mile = 5,280 feet 1 day = 24 hours
5,280 x 270 = 425,600 1 hour = 3600 seconds
270 miles = 425,600 feet 3600 x 6 = 21,600
3600 x 24 = 86,400
Fraction: Fraction:
425,600 feet 4,256 ft 21,600 sec 1
------- = ----- ------------ = -------- hour
5,280 feet 528 ft 86,400 sec 4
4,256/528 ÷ 1/4 = 4,256/528 x 4/1 (reciprocal) = 17,024/528 = 439/33 = 13
Hope this helps! :)
It takes Mark 45 minutes to ride his bike 5 miles. At this rate, how long will it take him to ride 8 miles?
Answers
Answer:
1 hour and 12 mins
Step-by-step explanation:
Simplify the expression.
pls i need help
Answers
Answer:
7x+1
Step-by-step explanation:
Ms. Costo is shopping for a new car. The salesman tells her the price will be $18,795 before a 10% discount. Ms. Costo isn’t sure she is getting the best price, so she sends Ms. Deele to ask the price of the same car. This time the salesman tells her the price is $17,050. Who is offered the better price? What is the price of the better deal after paying the 6% sales tax?
Answers
Answer:
The first deal is the best deal. After the sales tax, the second deal is the better deal. I hope this helps!!
Answer:
978678
Step-by-step explanation:
kjgh
Mike has a recipe that feeds one person that calls for 3/8 teaspoon
of salt. How much salt is needed to make the recipe if he needs to cook
the recipe for 3 people? thank u if u help and need this ASAP
Answers
Answer: 1 1/8 teaspoons
Step-by-step explanation:
1 person = 3/8 teaspoons
3/8 x 3 = 1 1/8 teaspoons
Find the value of f(-2) for the function f(x) = 4x + 10.
Answers
Answer:
f(-2)=2
Step-by-step explanation:
Replace all x’s with -2’s.
f(-2)=4(-2)+10
f(-2)=-8+10
f(-2)=2
The answer is 2