Question 4: 11 pts
Elena wants to earn at least $180 a week to help her parents with bills. She determines that
she can charge $15 an hour to babysit and can earn $10 an hour bagging groceries. She can
only work 13 hours per week. Write and graph a system of linear inequalities that shows the
number of hours she can work so she can help her parents. Use x for the number of hours
babysitting and y for the number of hours bagging groceries.
Answers
our system of inequalities is:
x + y ≤ 13.
x*$15 + y*$10 ≥ $180.
The graph can be seen at the end.
How to get the system of inequalities?Here we have the variables:
x = number of hours babysitting.y = number of hours bagging groceries.We know that she can only work 13 hours per week, then we have:
x + y ≤ 13.
And she wants to earn at least $180 per week, then:
x*$15 + y*$10 ≥ $180.
So our system of inequalities is:
x + y ≤ 13.
x*$15 + y*$10 ≥ $180.
The graph of the system can be seen below. The solution set is defined by the zone where the two shaded regions intersect (where we also should add the restrictions x >0, y > 0).
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Related Questions
Migdalia is a consultant. She works 3 days a week in the company's headquarters and 2
week at a production site.When she works at the company headquarters, she takes a bus
from work. When she goes to production sites, she uses her car and travels 52 ms
cast for using the bus is $48.00 for 10 one-way trips. The cost of using her car she
30 per mile Migdalia budgets $50 per week for travel expenses to and from work whether or not she has set aside enough money.
Answers
Since she has set aside only $50 for the trip, she hasn't set aside enough money for the trip
How to find the expenses and know if it's enough?She works 3 days in a week in the headquarter and 2 days a week at the production site.
When she works at the company headquarters, she takes a bus to and from work. The cost for using the bus is $48.00 for 10 one-way trips.
Therefore,
each one way trip = 48 / 10 = $4.8
To and from the headquarters = 4.8 × 2 = $9.6
Hence,
Therefore,
three days cost = 9.6 × 3 = $28.8
The cost of using her car she estimates at 30 cent per mile. When she goes to production sites, she uses her car and travels 52 miles per day. Therefore,
cost of travelling to production site in a week = 2 × (52 × 0.3) = $31.2
Hence,
cost of expenses per week = 31.2 + 28.8 = $60
Since she has set aside only $50 for the trip, she hasn't set aside enough money for the trip
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graph the equation y+3=2(x+3)?
Answers
Answer:
see attached
Step-by-step explanation:
You recognize the equation of the line as being given in point-slope form:
y -k = m(x -h) . . . . . . . line with slope m through point (h, k)
y +3 = 2(x +3) . . . . . . given equation
This tells you the point is (h, k) = (-3, -3), and the slope is m = 2.
__
You can graph the equation by plotting the point (-3, -3) and drawing a line with a slope of 2. It will rise 2 units for each unit to the right.
The diagram shows a line joining O to P.
The gradient of the line is 2
The length of the line is √2645
Work out the coordinates of P.
Answers
Answer: (23, 46)
Step-by-step explanation:
The equation of the line is y = 2x, and we can thus represent point P as (x, 2x)
Substituting into the distance formula,
[tex]\sqrt{2645}=\sqrt{(x)^{2}+(2x)^{2}}\\\\2645=x^2 + (2x)^2\\\\2645=x^2 + 4x^2\\\\2645=5x^2\\\\529=x^2\\\\x=23[/tex]
Thus, the coordinates of P are (23, 46)
Draw a
box-and-whisker plot for the set of data.
27, 35, 44, 51, 52, 54, 56, 69, 69, 79, 80, 100, 100
a.
b.
C.
d.
0510 15 20 25 30 35 40 45 50 55 60 65 70
05 10 15 20 25 30 35 40
45 50-55
HHH
05
#2
0 5 10 15 20 25 30 35 40 45 50 55
60 65 70
60 65 70
10 15 20 25 30 35 40 45 50 55 60 65 70
75 80 85 90
75 80 85 90
75
75
95 100
80 85 90
95 100
80 85 90 95 100
95 100
Answers
Answer: B
Step-by-step explanation:
The maximum is 100 and the minimum is 27.
The only option that shows this is B.4 Pencils and 2 rulers cost $8. 2 pencils and 4 rulers cost $10. Find the cost of 3 rulers and 3 pencils
Answers
Answer:
$9
Step-by-step explanation:
Let, the price of pencils is x, and the price of rulers is y.
4x+2y=8.....(i)
2x+4y=10......(ii)
From eq(i),
2(2x+y)=8
2x+y=4
y=4-2x eq(iii) .....put in eq(ii)
2x+4(4-2x)=10
2x+16-8x=10
-6x=10-16
x=-6/-6
x=1 put in eq (iii)
y=4-2(1)
y=2
Now, the price of 3 rulers and 3 pencils = 3x+3y=3(1)+3(2)
=9
Please give me brainlist.
Let assume the price of pencil is x and the price of rulers is y. While doing the operations we can remove the units which is $ (for price).
So now we can rewrite the first statement as 4x + 2y = 8.
As everything is dividant of 2, I'm simplifying the eqution by dividing everything by 2.
So, 2x + y = 4 ----(1)
Similarly the second statement is, 2x+4y = 10.
So, 2x + 4y = 10 ----(2).
To solve this we need to make any of the variable (either x or y) zero. We can do that in multiple ways, Here I am trying to make the x =0 by substrating equation 1 from equation 2.
2x + 4y = 10 -
2x + y = 4
___________
-0 + 3y = 6
3y = 6
So y= 6/3=2
Now we have the value of y, to find x apply it in any eqution that has x
I'm applying it in eqution 2
2x + 2 = 4
2x = 2
x=1
Now we want to value the cost of 3 rulers and 3 pencils
3x + 3y = 3(1) + 3(2) = 3 + 6 = 9
So
solve for x for this problem
Answers
Answer:
x = 5 and 6
Step-by-step explanation:
1. Square both sides
x - 5 = (x - 5)(x - 5)
2. Simplify the right side
x - 5 = x^2 - 10x + 25
3. Add 5 to both sides
x = x^2 - 10x + 30
4. Subtract x from both sides
0 = x^2 - 11x + 30
5. Factor
0 = (x-5)(x-6)
x = 5,6
Answer:
x = 5 , x = 6
Step-by-step explanation:
[tex]\sqrt{x-5}[/tex] = x - 5 ( square both sides )
x - 5 = (x - 5)² ← expand using FOIL
x - 5 = x² - 10x + 25 ← subtract x - 5 from both sides
0 = x² - 11x + 30 ← in standard form
0 = (x - 5)(x - 6) ← in factored form
equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x - 6 = 0 ⇒ x = 6
As a check
substitute these values into the equation and if both sides are equal then these values are the solutions.
x = 5
left side = [tex]\sqrt{5-5}[/tex] = [tex]\sqrt{0}[/tex] = 0
right side = 5 - 5 = 0
then x = 5 is a solution
----------------------------------
x = 6
left side = [tex]\sqrt{6-5}[/tex] = [tex]\sqrt{1}[/tex] = 1
right side = 6 - 5 = 1
then x = 6 is a solution
Camp pine cone has 20 campers for every 6 counselors if there are 60 campers how many counselors are needed
Answers
Answer:
18
Step-by-step explanation:
20*3=60 so do 6*3 to get your answer
You observe a plane approaching overhead and assume that its speed is 700 miles per hour. The angle of elevation of the plane is 15° at one time and 59° one minute later. Approximate the altitude of the plane. (Round your answer to two decimal places.)
Answers
Answer:
3 miles
2.73 miles=3 miles
The product of the length of 2 unequal poles before cutting 2 cm from each was 285 cm. Their present sum after cutting 2cm from each is 30cm. What is the length of the shorter pole? The product of the length of 2 unequal poles before cutting 2 cm from each was 285 cm . Their present sum after cutting 2cm from each is 30cm . What is the length of the shorter pole ?
Answers
Answer:
15 cm
Step-by-step explanation:
The length of the shorter pole can be found by forming and subsequently solving 2 equations.
Start by defining the variables that are going to be used in the working.
Let the original length of the shorter pole be a cm and that of the longer pole be b cm.
'Product' refers to the multiplication operation.
ab= 285 -----(1)
On the other hand, 'sum' refers to the addition operation.
Length of shorter pole after cutting= a -2
Length of longer pole after cutting= b -2
(a -2) +(b-2)= 30
a +b -4= 30
Adding 4 to both sides:
a +b= 30 +4
a +b= 34 -----(2)
From (2):
a= 34 -b -----(3)
Let's solve by substitution:
Substitute (3) into (1):
b(34 -b)= 285
Expand:
34b -b²= 285
b² -34b +285= 0
Factorise:
(b -15)(b -19)= 0
b -15= 0 or b -19= 0
b= 15 or b= 19
Substitute into (1):
a(15)= 285 or a(19)= 285
a= 285 ÷15 or a= 285 ÷19
a= 19 or a= 15
Since a <b, a= 15 and b= 19.
Thus, the length of the shorter pole is 15 cm.
The surface area of a cone is 250 square centimeters. The height of the cone is double the length of its radius.
What is the height of the cone to the nearest centimeter?
A.
10 centimeters
B.
20 centimeters
C.
15 centimeters
D.
5 centimeters
Answers
Answer: C
Step-by-step explanation:
just took it
The height of the cone to the nearest centimetre is 10 centimetres. Therefore, option A is the correct answer.
Given that, the surface area of a cone is 250 square centimetres. The height of the cone is double the length of its radius.
We need to find what is the height of the cone to the nearest centimetre.
What is the surface area of a cone?The area occupied by the surface/boundary of a cone is known as the surface area of a cone. It is always measured in square units. Stacking many triangles and rotating them around an axis gives the shape of a cone. As it has a flat base, thus it has a total surface area as well as a curved surface area.
If the radius of the base of the cone is "r" and the slant height of the cone is "l", the surface area of a cone is given as total surface area, T = πr(r + l) square units
Now, let the radius of a cone be x.
Then the height of the cone is 2x.
Slant height=√x²+4x²
=√5x
So, the surface area of cone=πx(x+2.24x)
⇒250=3.14 × 3.24x²
⇒x²=24.57
⇒x=4.95≈5 centimetre
So, height=2x=10 centimetre
The height of the cone to the nearest centimetre is 10 centimetres. Therefore, option A is the correct answer.
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Find the average of the numbers 6 4/7, 1 5/56, 9 1/7, 3 5/8. Write the solution as a mixed number or a fraction in lowest terms.
Answers
Answer:
[tex]\frac{187}{112}[/tex]
Step-by-step explanation:
Just add them all up in the calculator and divide by the number of numbers, which in this case is 4
Step-by-step explanation:
follow the steps in the attached
Determine which of the following statements about the given triangles is true.
Answers
Answer:
The answer be the 2 one
Step-by-step explanation:
I do it and it come right
An object’s position in meters and motion in meters per second can be described by x = −12 − 5t + 3t^2 during the time interval 0[tex]\leq[/tex]t[tex]\leq[/tex]1.
Which of the following statements is the best description of the object’s motion?
A
The acceleration of the object is zero.
B
The initial position of the object is −12 meters.
C
The object’s speed is increasing.
D
The average velocity of the object is −5 m/s.
Answers
Answer:
B
Step-by-step explanation:
Comment
Thank you for editing the choices.
The reason the answer is B is because the object begins to move when t = 0. Only - 12 will be left after that.
The acceleration is 3. I don't know how to explain that because I'm using calculus and I don't know if you have taken that or not. I assume not by the right answer you are not in a calculus class. You'll have to ask your instructor about the actual answer. Not A
The same is true of D. The answer is - 5 m/s. It is - 4 Not D
All the minus signs indicate a decrease during that interval. Not C
has a slope of 2 and contains what point? y-3=2(x+4)
Answers
We know immediately that the line must pass through (-4, 3).
Find the solution to the system
of equations.
432G
K
3
-4-3-2-1 1 2 3 4
-1
==x+2
21
4234
([?], [ ])
Enter
Answers
Answer:
(-2, 0)
Step-by-step explanation:
The solution to the system is the point where the graphs intersect.
Which of the following is equivalent to the radical expression below when
x>=2?
(√x-2)(√x+9)
Answers
The equivalent expression of [tex](\sqrt x - 2)(\sqrt x + 9)[/tex] is [tex]x + 7\sqrt x - 18[/tex]
How to determine the equivalent equation?The expression is given as:
[tex](\sqrt x - 2)(\sqrt x + 9)[/tex]
Expand the expression
[tex]x - 2\sqrt x + 9\sqrt x - 18[/tex]
Evaluate the like terms
[tex]x + 7\sqrt x - 18[/tex]
Hence, the equivalent expression of [tex](\sqrt x - 2)(\sqrt x + 9)[/tex] is [tex]x + 7\sqrt x - 18[/tex]
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Jack and Susan bought together 28 books. Susan bought 11 books. Which one of the
following equations represents the number of books bought by Jack? Let x be the
number of books bought by Jack.
Answers
Answer:
11 + x = 28
Step-by-step explanation:
The number of books they bought must add to 28.
A snack bar offers chili and/or cheese on its hot dogs for an additional fee.
The owner kept track of the hot dog orders over the course of a week. His
data are shown in a relative frequency table.
Answers
A relative frequency table is a chart that depicts the popularity or pattern of a specific piece of data based on the population sampled. The correct option is D.
What is a relative frequency table?A relative frequency table is a chart that depicts the popularity or pattern of a specific piece of data based on the population sampled. When we look at relative frequency, we are comparing the number of times a given event occurs to the overall number of events.
The complete question is mentioned in the below image with the relative frequency table.
As per the relative frequency table, the value 0.2 highlighted in the table represents that 20% of his customers ordered cheese but no chili on their hot dogs.
Hence, the correct option is D.
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simplify (8x^2y^3)/(2x^4y)
Answers
Answer:
[tex]=\frac{4y^2}{x^2}[/tex]
Step-by-step explanation:
[tex]\frac{(8x^2y^3)}{(2x^4y)}[/tex]
[tex]=\frac{(8x^2y^3)}{(2x^4y)}\\[/tex]
[tex]=\frac{8y^2}{2x^2}[/tex]
[tex]=\frac{4y^2}{x^2}[/tex]
I Hope This helps :)
Pls help! Answer the question in the pic. I will give five stars, thanks, and brainliest!
*20 POINTS*
Answers
71°
Step-by-step explanation: Let's have look on triangle BDH
Angle B + Angle D + Ange H = 180
Angle DHB = 180 - 71
Angle DHB = 109
Angle X = 180 - 109
Angle X = 71 ° Ans .
What is the circumference of a circle with a diameter of 5 feet? Use 3.14 for
TT.
Answers
Answer: 15.7
Step-by-step explanation:
[tex]C=\pi d\\\\C=5\pi[/tex]
Using [tex]\pi=3.14[/tex], we get [tex]C \approx 5(3.14)=\boxed{15.7 \text{ ft}}[/tex]
[tex]\triangleright[/tex]Hii! [tex]\triangleleft[/tex]
___________________________________________________________
Answer: Circumference = 15.7 ft ✅
Step-by-step explanation:
Do you need to know the circumference of a circle with a diameter of 5 ft? No problem! Luckily, there's a formula to find it! (:
CircumferenceLet's work out the circumference. This is the formula that is going to help us. [tex]\rightsquigarrow\boldsymbol{C=\pi d}[/tex] C=circumference π=pi d=diameter
Now, stick in the values (note that we can use 3.14 for pi; pi is irrational, so we use 3.14 instead of pi to avoid irrational numbers)
[tex]\boldsymbol{C=3.14\cdot5}[/tex]. Upon simplifying we obtain
[tex]\boldsymbol{C=15.7\;ft}[/tex]. Which is our final answer.
------
Hope that this helped! Best wishes.
[tex]\boldsymbol{Reach \quad far. \quad Aim \quad high. \quad Dream \quad big.}[/tex]
#StudyWithBrainly (:
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---------
A line passes through the point (5,-11) and has slope of -2.
Find an equation of this line.
y = -2x – 1
y = 5x – 11
y = 5x – 2
y = -2x – 11
Answers
Answer:
y=-2x -1
Step-by-step explanation:
(y-y1) = m(x-x1)
y-(-11) = -2(x-5)
y+11 = -2x + 10
subtract 11 on both sides thus
y = -2x -1
Find the slope of the line
Answers
Answer:
3/2
Step-by-step explanation:
comparing the straight line with ax + bx + c = 0,
we get a = 3 and b = -2
we know,
slope of line = -a/b
= -3/-2
= 3/2
Hope it helped
evaluate 2b^3 where b = 3
Answers
Answer:
Answer=54
Step-by-step explanation:
Given:- b=3
2b³
Solution:-
2 x b³
2 x 3 x 3 x 3
6 x 9
54 (answer)
Hope this helps you
Have a good day.
Goods costing $2,300 are purchased on account on July 15 with credit terms of 2/10, n/30. On July 18, a $100 credit memo is received from the supplier for damaged goods. Give the journal entry on July 24 to record payment of the balance due within the discount period using a perpetual inventory system
Answers
The journal entry on July 24 to record payment of the balance due is $2156
What is Discount Period ?Discount period is the time period given by the supplier to the consumer for getting discount if the payment is made by the due date.
Debit Credit
Accounts payable (2300-100 ) 2200
Cash (2200 - (2200* 2%)) 2156
Purchase Discount / Merchandise Inventory 44
To record the payment of accounts within discount period
Amount Paid = 2300 - 200 -44 = 2156
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Suppose two sets of scores have the same mean, but different
standard deviations, o, and o₂, with 0₂ > 0₁ Which statement
1
2
best describes the variability of these data sets?
02
(1) Data set one has the greater variability.
(2) Data set two has the greater variability.
(3) The variability will be the same for each data set.
(4) No conclusion can be made regarding the variability of
either set.
Answers
Data set two has the greater variability option (2) Data set two has the greater variability is correct.
What is the standard deviation?It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
[tex]\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}[/tex]
σ is the standard deviation
xi is each value from the data set
X is the mean of the data set
n is the number of observations in the data set.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have:
Two sets of scores have the same mean, but different standard deviations.
σ₁ and σ₂ (σ₂ > σ₁)
Coefficient of variation = [SD/(mean)]×100
[tex]\rm CV = \dfrac{\sigma }{|x|}\times100[/tex]
σ₂ > σ₁
Divide by |x| on both sides
σ₂/|x| > σ₁/|x|
[tex]\rm \dfrac{\sigma }{|x_1|}\times100 > \dfrac{\sigma }{|x_2|}\times100[/tex]
(CV)₂ > (CV)₁
Thus, data set two has the greater variability option (2) Data set two has the greater variability is correct.
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Alex Meir recently won a lottery and has the option of receiving one of the following three prizes: (1) $90,000 cash immediately, (2) $35,000 cash immediately and a six-period annuity of $9,400 beginning one year from today, or (3) a six-period annuity of $17,700 beginning one year from today. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.)
1. Assuming an interest rate of 5%, determine the present value for the above options. Which option should Alex choose?
2. The Weimer Corporation wants to accumulate a sum of money to repay certain debts due on December 31, 2030. Weimer will make annual deposits of $180,000 into a special bank account at the end of each of 10 years beginning December 31, 2021. Assuming that the bank account pays 6% interest compounded annually, what will be the fund balance after the last payment is made on December 31, 2030?
Answers
Based on the annuities calculated, he should choose option 1.
How to calculate the annuities?Present value = $35,000 + (Annuity amount * Present value of an ordinary annuity of $1)
= $35,000 + ($9,400 * (5%,6))
= $35,000 + ($9,400 * 5.07569)
= $35,000 + 47,711
= $82,711
Present value = (Annuity amount * Present value of an ordinary annuity of $1)
= $17,700 * (5%,6)
= $17,700 * 5.07569
= $89,840
Alex should choose Option 1
Future value annuity = Annuity amount * Future value of an ordinary annuity of $1
= $180,000 * (6%,10)
= $180,000 * 13.1808
= $2,372,544
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Find the critical point for f(x)=x^2-2x+4 and determine their nature.
Select one:
O a. (3, 1) minimum point
O b. (1, 3) minimum point
O c. (1, 3) maximum point
O d. (3, 1) maximum point
Answers
The school is planning a field trip to the science center. Tickets are originally $28, but school
groups receive an $8 discount on each ticket that is purchased. The expression t(28 - 8)
represents the total cost for t tickets.
What does the quantity 28 - 8 represent?
the number of tickets
the original price of a ticket
4) the amount of the discount
the total cost
the number of students
the discounted price of each ticket
Answers
28-8 is the discount price of each ticket, and the (28-8) is equal to (=) -----> 24(28-8
Step-by-step explanation:
that is the answer
Write 1 3/4 as a decimal and as a percent
Answers
Answer:
Decimal: 1.75
Percentage: 175%
Hey there!
1 3/4
= 1 * 4 + 3 / 4
= 4 + 3 / 4
= 7 / 4
= 7 ÷ 4
= 1.75
= 1.75 * 100
= 175%
Therefore, your answer should be:
• 1.75 (as your decimal form)
• 175% (as your percentage form)
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
