Eric can spend a maximum if $270 on office supplies. each team of paper costs $6. each link cartridge costs $18. which of the following graphs represents the possible combinations of paper and ink cartridges can he buy,
Answers
Data:
Team of paper: x
Link cartridge: y
Cost:
Team of paper: 6x
Link cartridge: 18y
As the maximum Eric can spend is $270:
\(6x+18y\leq270\)You use this inequation to find the graph:
1. Find two points by using the equation:
If x=0 y=?
Substitute the x in the equation by 0:
\(\begin{gathered} 6(0)+18y=270 \\ 18y=270 \\ y=\frac{270}{18} \\ \\ y=15 \end{gathered}\)If y=0 x=?
Substitute the y in the equation by 0:
\(\begin{gathered} 6x+18(0)=270 \\ 6x=270 \\ x=\frac{270}{6} \\ \\ x=45 \end{gathered}\)Then, you have the next coordinates (x,y) for the graph:
(0 , 15) and ( 45, 0)
2. Put the points in the x-y plane and draw a line:
As the inequality is less than or equal to 270 you shade the area under the line.
Then, you get the next graph:
Related Questions
11 over 7=6 over v what is v
Answers
Answer:
42/11
Step-by-step explanation:
11/7 = 6/v
cross multiply:
11v = 6x7 = 42.
v = 42/11 ≈ 3.81
Simplify using the distributive property
Which number can be distributed across two terms inside parentheses
Answers
Answer:
3/5 is the number that can be distributed across two terms inside parentheses.
you might not need it but:
x = 5
Step-by-step explanation:
3/5(x - 10) = 18 - 4x - 1
using distributive property, open the parentheses:
3/5x - 6 = 18 - 4x - 1
Simplify:
3/5x + 4x = 17 + 6
4⅗x = 23
x = 5
Answer:
It's 3/5
Step-by-step explanation:
It's 3/5
sound travels 1129 feet per second air. how far can sound travel in 2 seconds when traveling through hair
Answers
Answer:
Sound travels 2258 feet in 2 seconds while travelling through air.
Step-by-step explanation:
or 27.097 inches
or 752.6667 yards
14. Solve y2 + 4y - 32 = 0 using the zero product property.
O A. y = 8,4
O B. y = -8,4
O c. y = -8,6
O D. y = 3
Answers
Answer: B. y = -8, 4
Step-by-step explanation:
Given expression
y² + 4y - 32 = 0
Cross factorize the expression
y 8
y -4
Factorize the expression
(y + 8) (y - 4) = 0
Finalize the factor of the expression by the zero product property
\(\boxed{y=-8,4}\)
Hope this helps!! :)
Please let me know if you have any questions
Steve drew line segments CDEF, GHI, ADH, and BEH as shown in the
diagram below. Scalene ADEH is formed.
If segment CDEF is parallel to segment GHI, which statement is true? *
Answers
Answer:
BEF=IHEStep-by-step explanation:
ADE=DHG
FEH=IHE
ADE=DHE
ADC=EHI
BEF=IHE <This would be the correct answer if segment CDEF is parallel to segment GHI.
In a poll of 510 human resource professionals, %45.9% said that body piercings and tattoos were big personal grooming red flags. Complete parts (a) through (d) below.
Answers
By sample distribution, (0.431,0.487) is Complete parts (a) through (d) below.
What does a statistical sample distribution mean?
An accurate probability distribution of a statistic is known as a sampling distribution, and it is created by repeatedly sampling a certain population. It depicts a spectrum of potential results for a statistic, such as the mean or mode of a variable, for a population.
Given
Favourable cases (X)=?
Sample size(n)=510
Sample proportion (p_hat)=X/n=0.459
X=np_hat=510*0.459=234.09=234
Confidence level(1-α)=99%=0.99
α=0.0
The critical value for α=0.01 is Zc=2.576
The margin of error is E=Zc* √((p_hat(1-p_hat)/n))
E=2.576* √((0.459(1-0.459)/510))=0.0568
The 99% confidence interval for p
CI=(p_hat-E,p_hat+E)
CI=(0.459-0.0568,0.458+0.0568)
CI=(0.402,0.516)
Confidence level(1-α)=80%=0.80
α=0.20
The critical value for α=0.2 is Zc=1.282
The margin of error is E=Zc* √((p_hat(1-p_hat)/n))
E=1.282* √((0.459(1-0.459)/510))=0.0283
The 80 % confidence interval for p
CI=(p_hat-E,p_hat+E)
CI=(0.459-0.0283,0.458+0.0283)
CI=(0.431,0.487)
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Sue has 18 sweets.
Tony also has 18 sweets.
Sue gives Tony x sweets.
Sue then eats 5 of her sweets.
Tony then eats half of his sweets.
Write the expression for the number of sweets Sue and Tony now have
Answers
Answer:
Sue : 13 - x Tony : x/2 + 9Step-by-step explanation:
Sue Tony_________________________________________________
initial number of sweets | 18 | 18
| |
Sue gives Tony x sweets | 18 - x | 18 + x
| |
Sue ,eats 5 of her sweets. and | 18 - x - 5 = | (18 + x)/2 =
Tony ,eats half of his sweets | 13 - x | 9 + x/2
2/10 x 1/9 = 2/90 = 1/?
Answers
Answer: 2/90 = 1/45
Step-by-step explanation:
Janet needs to paint the walls of a room shaped like a
rectangular prism. The room
has a length of 10 ft., a width of 15 ft, and a height of 8 ft. How much paint does she need to cover the
Answers
To solve this problem, we will use the formula of rectangular prism surface area.
The formula is:
A=2(wl+hl+hw)
A is the area, w is the width, l is the length, and h is the height.
So we will put in all the numbers.
A=2((15)(10)+(8)(10)+(8)(15))
Multiple all the numbers inside:
A=2(150+80+120)
Add all the numbers inside:
A=2(350)
Multiply:
A=700ft^2
Hope this helped!
The length of a rectangle is twice its width. Find its lenght and width, if its perimeter is 7 1/3 cm.
Answers
The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.
Let's assume the width of the rectangle is "b" cm.
According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.
The formula for the perimeter of a rectangle is given by:
Perimeter = 2 * (length + width)
Substituting the given perimeter value, we have:
7 1/3 cm = 2 * (2b + b)
To simplify the calculation, let's convert 7 1/3 to an improper fraction:
7 1/3 = (3*7 + 1)/3 = 22/3
Rewriting the equation:
22/3 = 2 * (3b)
Simplifying further:
22/3 = 6b
To solve for "b," we can divide both sides by 6:
b = (22/3) / 6 = 22/18 = 11/9 cm
Therefore, the width of the rectangle is 11/9 cm.
To find the length, we can substitute the width back into the equation:
Length = 2b = 2 * (11/9) = 22/9 cm
So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.
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factorize6 + 13mn + 7mn?
Answers
☽------------❀-------------☾
Hi there!
~
Let's simplify step-by-step.
\(6 + 13mn + 7mn\)
Combine Like Terms:
\(= 6 + 13mn + 7mn\\= (13mn+ 7mn) + (6)\\= 20mn + 6\)
❀Hope this helped you!❀
☽------------❀-------------☾
Repost of the last question.. Sorry it wasn't full.
someobe please help me here
Answers
Answer:
\(y < -\frac{4}{5} x+4\)
Step-by-step explanation:
To graph the equation, draw the line \(y = -\frac{4}{5} x+4\) and shade in the lower left part of the graph under the line to illustrate the inequality
Then pick two points to test
Graham wrote the system of equations.
6x−8y=−16y=34x+8
What is true about the system of equations that Graham wrote?
A
It has no solution.
B
It has 1 solution.
C
It has 2 solutions.
D
It has infinitely many solutions.
Answers
Answer:
B
Step-by-step explanation:
6x -8y = - 16y
6x = -8y
8y = 17x + 4
-8y = -17x - 4
6x = -17x - 4
23x = -4
x = -4/23
The parking meter charges $2 for the first hour, then $0.75 for each hour thereafter. Nate only has $5. How many hours can he park?
Answers
First, we will subtract the first hour which is $2 from $5
$5 - $2 = $3
$3 / 0.75 = 4
Hours he can park = 4 + 1 = 5 hours
Match each part of this algebraic expression with this appropriate description
Answers
Answer:
1) x and y --> Variable(s)
2) 1/6 --> Constant(s)
3) 12.1, 4.7, and 6 --> Coefficient(s)
4) 12.1x and 6x --> Like Terms
5) 12.1x, 4.7y, and 1/6 --> Terms
u^3-512=()(u^2+8u+64)
Answers
Answer:
u=8
Step-by-step explanation:
Hi can someone please help me solve the following system of inequalities and state the coordinates in the solution setz
Answers
The graph of the system of the inequalities is attached.
To graph the inequalities y < -x - 4 and y ≥ (3/5)x + 4, we can start by graphing the corresponding equations and then shade the appropriate regions based on the inequality signs.
Let's begin with the equation y = -x - 4:
Choose a range of x-values to plot.
For simplicity, let's use x-values from -10 to 10.
Substitute different x-values into the equation to find corresponding y-values.
For example:
When x = -10, y = -(-10) - 4 = 10 - 4 = 6.
When x = 0, y = -(0) - 4 = -4.
When x = 10, y = -(10) - 4 = -10 - 4 = -14.
Plot these points on the coordinate plane and draw a straight line passing through them.
This line represents the equation y = -x - 4.
Next, let's graph the equation y = (3/5)x + 4:
Again, choose a range of x-values to plot. Let's use the same range of -10 to 10.
Substitute different x-values into the equation to find corresponding y-values. For example:
When x = -10, y = (3/5)(-10) + 4 = -6 + 4 = -2.
When x = 0, y = (3/5)(0) + 4 = 0 + 4 = 4.
When x = 10, y = (3/5)(10) + 4 = 6 + 4 = 10.
Plot these points on the coordinate plane and draw a straight line passing through them.
This line represents the equation y = (3/5)x + 4.
Now, let's shade the regions based on the inequalities:
For y < -x - 4, we need to shade the region below the line y = -x - 4.
For y ≥ (3/5)x + 4, we need to shade the region above or on the line y = (3/5)x + 4.
Hence, the region where the shaded regions overlap represents the solution to both inequalities.
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Your parents have a credit card with a balance of $3,287.90 at an interest rate of 14.5% APR. They pay $1,200.00 each month on the due date until the card is paid off. How many months does it take to pay off the card, and what is the total amount paid including interest?
Be sure to include in your response:
• the answer to the original question
• the mathematical steps for solving the problem demonstrating mathematical reasoning
Answers
Given statement solution is :- It takes 4 months to pay off the card, and the total amount paid, including interest, is $4,871.78.
To find out how many months it takes to pay off the credit card and the total amount paid including interest, we can use the following steps:
Step 1: Calculate the monthly interest rate
Divide the annual percentage rate (APR) by 12 to get the monthly interest rate.
Monthly interest rate = 14.5% / 12 = 0.145 / 12 = 0.01208 (rounded to 5 decimal places)
Step 2: Set up the equation for the number of months
Let's denote the number of months it takes to pay off the card as 'n'. The monthly payment is $1,200.00, and the initial balance is $3,287.90. The monthly interest rate is 0.01208. The equation for the number of months can be written as:
(1) $3,287.90 ×\((1 + 0.01208)^n\) - $1,200.00 ×\([(1 + 0.01208)^n\) - 1] = 0
Step 3: Solve the equation
To find the value of 'n', we need to solve equation (1). However, solving it algebraically can be complex. Instead, we can use numerical methods like trial and error, or we can use a spreadsheet or a calculator to find the solution.
Using a spreadsheet or a calculator, we can input the values and increment 'n' until we find the point where the equation equals zero.
After performing the calculations, it is determined that it takes approximately 4 months to pay off the card, and the total amount paid, including interest, is $4,871.78.
Therefore, the answer to the original question is that it takes 4 months to pay off the card, and the total amount paid, including interest, is $4,871.78.
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35%of students wear glasses.There are 14 students who wear glasses.How many pupils are there in the class?
Answers
Answer: 40 pupils
Step-by-step explanation:
35 14
------- = --------
100 ?
find the denominator.
multiply 14 and 100:
14 x 100 = 1400
divide 1400 by 35
1400/35 = 40
Therefore there are 40 students
If three dice are tossed, their sum could be 7. What is the probability of this?
Answers
brainliest answer please
answer:
The probability of rolling a sum of 7 with three dice is 15/216, which simplifies to 5/72, or approximately 0.0694 (rounded to four decimal places).
So the probability of rolling a sum of 7 with three dice is approximately 0.0694 or 6.94%.
Are lines JN and KM parallel?
Answers
Answer:yes
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
if you remove the triangle, they will continuously go on both sides with one on the other.
One meter of electrical cord costs 3 dollars. How much should one pay for...
2/3 meters?
Answers
ntial)
Given: 21 22
Prove: a b
What is the missing statement in the proof?
1
a
4
ar
b
2
Answers
what is completely factored form or this expression?
y^2-12y+32
a.(y+4)(y+8)
b.(y-4)(y-8)
c.(y+18)(y+2)
d.(y-18)(y-2)
Answers
\(\\\\\\\)
Therefore \(\sf{option~ B~ is ~correct }\)\(\sf{ }\) \(\sf{ }\) \(\sf{ }\)
Answer:
(y-4) (y-8)
Step-by-step explanation:
y^2-12y+32
What two numbers multiply to 32 and add to -12
-8*-4 = 32
-8+-4 = -12
(y-4) (y-8)
Complete the table:
6,000
meters
kilometers
8,000
9,000
5
7
Answers
Answer:
Remember while answering, 1 kilometer = 1,000 meters
5,000 ⇒ 5
6,000 ⇒ 6
7,000 ⇒ 7
8,000 ⇒ 8
9,000 ⇒ 9
Step-by-step explanation:
1 kilometer is 1,000 meters because "kilo" means 1,000
Knowing this we can make an equation to figure this out
When we know x, or meters, we can do y = x/1,000
When we know y, or kilometers, we can do x = 1,000y
What is the most inexpensive way to measure heart rate during exercise?
A. Doing a rate of perceived exertion
B. Taking your pulse
C. Wearing a heart rate monitor
D. None apply
Answers
Answer:
C
Step-by-step explanation:
Taking your own heart rate is the most inexpensive, but it is also accurate if you can measure it correctly.
A coordinator will select 5 songs from a list of 8 songs to compose an event's musical entertainment lineup. How many different lineups are possible?
Answers
The number of lineups possible is the combination of selecting 5 songs from 8 songs.
8C5 = 56.
What is combination?A combination is a mathematical way that evaluates the number of possible arrangements within a collection of items, leaving behind of the order of selection. A combination can select items in any order. Combinations can be confused with permutations Water is a combination of hydrogen and oxygen. The car interior is available in various color combinations. The formula for combinations is nC_r = n/(r!*(n - r)!), where n is the number of items and r is the number of items selected at once. Let's look at an example of how combinations are calculated. There are 10,000 possible combinations of the numbers 0-9 in a 4-digit codeTo learn more about combination from the given link:
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What is the factored form of a quadratic with roots x = 5 and x = -11
Answers
Answer:
x=5×-11
this is the answer
Answer:
Step-by-step explanation:
X=11
X=-5
A circle has a fiat of 14 cm. What is the circumference? Use 3.13 for n,and do not round your answer. Be sure to include the correct unit in your answer.
Answers
Answer:
87.64cm
Explanation:
Circumference of a circle = 2 \pi r
r is the radius of the circle
Given
radius = 14cm
pi = 3.13
Substitute the given values into the formula;
Circumference of the circle = 2 * 3.13 * 14
Circumference of the circle = 6.26 * 14
Circumference of the circle = 87.64cm
Hence the Circumference of the circle is 87.64cm
Help. I’m confused on this question and would like an answer. Thanks.
Answers
Answer:
Angle
Step-by-step explanation:
Since, the figure is in the final step of construction. So, it will have only two rays which as we can see are emerging from a common point.
So, it represents an angle.
An angle has two rays arising out of a common vertex point.