Megan went to the store and bought 4 notebooks and 9 pencils for a total of $8.25. Joanne went to the same store and bought 7 notebooks and 14 pencils for a total of $14. What was the price per pencil and the price per notebook?

Answers

Answer 1
Let notebooks be x and let pencils be y

4x+9y=8.25 (equation 1)
7x+14y=14.00 (equation 2)

Multiply equation 1 by 7
So that you get 28x+63y=57.75

Multiply equation 2 by 4
So that you get 28x+56y=56.00

28x+63y=57.75 -
28x+56y=56.00
-----------------------
7y=1.75

Divide both sides by 7
1.75/7 is 0.25

So, now we know that one pencil costs 0.25 cents

Sub this y value into equation one

4x+9(0.25)=8.25

4x+2.25=8.25

Move 2.25 to the other side as a negative number

4x= 6

Divide both sides by 4

6/4 is $1.50

So, one pencil is equal to 0.25 cents and one notebook is equal to $1.50

Related Questions

Using the inverse trig functions, find the measure of angle A to the nearest degree.
1. 43 degrees
2. 37 degrees
3. 90 degrees
4. 53 degrees

Answers

1. 37 degree. A triangle has 180 there is a right angle 90 and then c is 53 which leaves 37 for a

geometry help please !

Answers

Answer:

5 is the correct answer.............

Solve for X
5(3X-2)=5

Answers

The correct answer would be that x=1

Which of the following are true statements?
Check all that apply

Answers

Answer:

a and d

Step-by-step explanation:

Four runners are training for long races. Noah ran 5.123 miles, Andre ran 6.34 miles, Jada ran 7.1 miles, and Diego ran 8 miles.

What is the total running distance of the four runners?

Answers

26.563/26.5/27 | those are possible answer choices

Jason buys 8 colored markers at the art store. He handed the cashier $15. The cashier gave him back $1. How much did each marker cost?

Answers

Answer:

2.25

Step-by-step explanation:

i think though

Each colored marker costs $1.75.

What is Unit Rate?

The amount of one quantity in another single quantity is termed as the unit rate of that quantity.

For example, speed is a unit rate in terms of distance and speed.

Number of colored markers Jason bought = 8

Cash that Jason gives the cashier = $15

Cash that cashier gives back = $1

Price of 8 colored markers = 15 - 1

                                             = $14

We have to find the unit rate of the colored marker, that is the price of one colored marker.

Let x be the cost of the one colored marker.

Using proportion,

8 : 14 = 1 : x

8/14 = 1/x

Doing cross multiplication,

8x = 14

x = 14/8

x = 1.75

Hence the unit rate of the colored marker or the cost of one colored marker is $1.75.

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Moving the decimal point to the right 4 places in a number is the same as?

Answers

Answer:

0^4

Step-by-step explanation:

lets say the number is 1.0 if you where to move the decimal to the right 4 place the number would then be 10,000.0. basically if it says 10^4 add 4 0's

Answer:

it is  10^4

Step-by-step explanation:

Miranda cuts grass (g) for $20 and hour and trims hedges (h) for $25 an hour. She is trying to make enough money during the summer to buy a car for $4200.

Which inequality represents the number of hours Miranda needs to cut grass and trim hedges.

Answers

Answer:

20g + 25h ≥ 4200

Step-by-step explanation:

Miranda needs nothing less than $4200 to but a car

If the expected value (the mean) of successes in a binomial experiment of 100 trials is 55. Which of the following are not true?Let x = the no. of successes of the 100 trials. Then P(s) = p = 55/100 = 0.55The standard deviation of the binomial distribution is approximately σ = √(npq) = √(100x0.55x0.45) ≈ 4.97The probability distribution of x = B(100, 0.55) can be approximated by N(55, 4.97)a) I onlyb) II onlyc) I and IId) All of the statements are true

Answers

Answer:

All of the statements are true

Step-by-step explanation:

Given that :

Number of trials (n) = 100

Expected number of successes = 55

The number of successes of the 100 trials :

Number of successes / number of trials = 55 / 100 = expected number of successes / n = 55/ 100 = 0.55

Using Normal approximation :

Standard deviation (σ) = √(npq) ; q = 1 - p = 1 - 0.55 = 0.45

σ = √(100 * 0.55 * 0.45) = √24.75 = 4.975

The probability distribution of x = B(n, p) = x = B(100, 0.55)

Using approximation ; N(p, σ) = N(55, 4.97)

Hence, All of the statements are true


What is an equation of the line that passes through the points (4, -2) and (8, – 7)?

Answers

Answer:

y = -1.25x + 3

Step-by-step explanation:

To see if the coordinate pairs are on this line, plug x into the equation above.

y = -5 + 3

y = -2, so (4, -2) is on that line.

y = -1.25(8) + 3

y = -10 + 3

y = -7, so (8, -7) is also on that line.

Answer:

y = -1.25x + 3

Step-by-step explanation:

i got it right

A survey of 280 homeless persons showed that 63 were veterans. Construct a 90% confidence interval for the proportion of homeless persons who are veterans.

Answers

Answer:

[0.184, 0.266]

Step-by-step explanation:

Given:

Number of survey n =280

Number of veterans = 63

Confidence interval = 90%

Computation:

Probability of veterans = 63/280

Probability of veterans =0.225

a=0.1

Z(0.05) = 1.645 (from distribution table)

Confidence interval = 90%

So,

p ± Z*√[p(1-p)/n]

0.225 ± 1.645√(0.225(1-0.225)/280)

[0.184, 0.266]

You draw a 52-card deck. Then the card is replaced in the deck, the deck ls shuffled and you draw again. Find the probability of drawing a red card each time

Answers

Answer:

we know that the probability of drawing black card is 26/52. Probability of drawing a king is 4/52

Step-by-step explanation:

700 in standard form

Answers

Answer:

7 × 10²

Step-by-step explanation:

→ The first digit has to be above 1 and below 10

In 2017, the population of a city is 11500, and is increasing exponentially at a rate of 3.1% per year (a) What will the population be in the year 2033? Population size = (b) In what year will the population have tripled? Year = Note You can earn partial credit on this problem

Answers

Answer:

(a) The population in the year 2033 is 18630.

(b) After nearly 36years from the starting population of 11500 we will get our population tripled.

Step-by-step explanation:

In 2017, the population of a city is 11500, and is increasing exponentially at a rate of 3.1% per year

This can be formulated with the compound interest formula, also we can think the given situation as we have 11500 rupees which increases at the rate of 3.1% per year.

we can formulate the given situation using the compound interest formula.

A = P(1 + [tex]\frac{r}{n}[/tex])^n*t

A is the final population

P is the initial population = 11500

r is the rate at which the population increases = 3.1A =% = 0.031

n denotes the number of times the population increases per year = 1

t is the time or year = 1

A = [tex]11500( 1 + 0.031)[/tex]^1*t

(a) The number of years to reach the year 2033 from 2017 is 16years.

so we have the value of t = 16

 so the final population in the year 2033 will be

A = 11500(1+0.031)^1*16

   = 11500(1.031)^16

   = 11500*1.63

A = 18630

Therefore the population size in the year 2033 will be 18630.

(b) We need to find the year in which the population gets tripled. we will triple our population from the population which was in 2017

 so the our equation will be

 11500*3 = 11500(1+0.031)^1*t

  3 = (1.031)^t

upon taking logarithm both sides we get

log(3) = t*log(1.031)    ( using the property log(a^b) = blog(a)

0.477 = t*0.133

t = 0.477/0.0133

t = 35.86years

upon taking approximation we will get 36 years.

Therefore after nearly 36years from the starting population of 11500 we will get our population tripled.


Which value, when placed in the box, would result ina system of equations with infinitely many solutions?
y=-2x + 4
6x + 3y = O
-12
-4
4
12

Answers

Answer:

-4

Step-by-step explanation:

How do I Solve 2-V=17

Answers

Answer:

solution

-V=17-2

-V=15

Move (2) to the right of the equal sign and since it is crossing the equal sign it changes into a negative. Then subtract 17-2. And the answer would be -v=15. So the answer is v=-15

Answer correct plz if u steal points ill report

Answers

Answer:

I think it might be y= x+2

Step-by-step explanation: because it is going up times 2 every time

OWO

Find the slope of the line.

a. Undefined
b. 0
c. 3/2
d. -1​

Answers

Im pretty sure the answer is. a) Undefined

Answer:

Haven't found the answer but in the comments above me someone said it was D and it was def not D so try anything other than that, I just took the test on Edg2020

Step-by-step explanation:

These points are linear. Find the slope.

Answers

The answer is 3. You do y2-y1 over x2-x1

Of the 200 students in school 90 volunteered to work the book sale. what percent of students volunteered?

Answers

Answer:

45%

Step-by-step explanation:

90/200 = 0.45

0.45 = 45%

noob

45% of students volunteered in the book sale

When P(x) is divided by x-2 the quotient is Q(x) and the remainder is 5.When Q(x) is divided by x^2+2x+4 the remainder is 2x-3.What is remainder when P(x) is divided by x^3-8

Answers

Step-by-step explanation:

P(x)

= (x - 2)Q¹(x) + 5

= (x - 2)[(x² + 2x + 4)Q²(x) + 2x - 3] + 5.

Since x³ - 8 = (x - 2)(x² + 2x + 4),

(x - 2)[(x² + 2x + 4)Q²(x) + 2x - 3] + 5

= (x - 2)(x² + 2x + 4)Q²(x) + (x - 2)(2x - 3) + 5

= (x³ - 8)Q²(x) + (2x² - 7x + 11).

Hence when P(x) is divided by (x³ - 8),

the remainder is 2x² - 7x + 11.

Select Is a Function or Is not a Function to correctly classify each relation.
{(3, 2),(6, 4),(9, 6),(12, 8)}

{(2, 3),(2, 5),(3, 6),(9, 4)}

{(2, 4),(6, 3),(4, 8),(6, 6)}

{(3, 4),(5, 2),(6, 8),(6, 4)}

Which ones are functions and which ones aren't?

Answers

Answer:

first is a function second third ad fourth arent function

Step-by-step explanation:

{(3, 2),(6, 4),(9, 6),(12, 8)} is a function.{(2, 3),(2, 5),(3, 6),(9, 4)} is not a function.{(2, 4),(6, 3),(4, 8),(6, 6)} is not a function.{(3, 4),(5, 2),(6, 8),(6, 4)} is not a function.

What is Function?

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The collection of values that could result in a function's outputs is known as the co-domain.

Given:

As, we know the relation is said to be a function if we have distinct inputs.

If the inputs are repeated then it is not a function.

So, {(3, 2),(6, 4),(9, 6),(12, 8)} is a function.

Also, {(2, 3),(2, 5),(3, 6),(9, 4)} is not a function.

{(2, 4),(6, 3),(4, 8),(6, 6)} is not a function.

{(3, 4),(5, 2),(6, 8),(6, 4)} is not a function.

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Use the graph to find the solution y=x+4 y=-2x-2

Answers

Answer:

(-2 , 2)

Step-by-step explanation:

y=x+4

y=-2x-2

x+4=-2x-2

3x=-6

x=-2

y=2

graph attached

Answer:

[tex]\large\boxed{\boxed{\pink{\bf \leadsto (-2,2) \ is \ the \ solution \ of \ the \ given \ linear \ equations .}}}[/tex]

Step-by-step explanation:

Given to equations to us are ,

[tex]\qquad \red{\bullet} \: y = x + 4 \\\\\qquad \red{\bullet} \: y = -2x - 2 [/tex]

And we need to find the solution using graphical method.

So , after plotting the graph of both equations the point where both lines intersect will be the solution of the graph.

And , for plotting we need at least two points .

For equation (1) :-

[tex]\implies y = x + 4 [/tex]

When x = (-4) .

[tex]\implies y = -4+4\\\\\bf\implies y = 0 [/tex]

When x = (-3)

[tex]\implies y = -3+4\\\\\bf\implies y = -1 [/tex]

[tex]\large\boxed{\begin{tabular}{|c|c|c|} \cline{1-3} \bf x & (-4) & (-3) \\\cline{1-3} \bf y & 0 & 1 \\\cline{1-3}\end{tabular}}[/tex]

For equation 2 :-

[tex]\implies y = -2x - 2 [/tex]

When x = (-1) .

[tex]\implies y = -2(-1)-2\\\\\bf\implies y = 0 [/tex]

When x = (0)

[tex]\implies y = 0-2\\\\\bf\implies y = -2 [/tex]

[tex]\large\boxed{\begin{tabular}{|c|c|c|} \cline{1-3} \bf x & (-1) & 0 \\\cline{1-3} \bf y & 0 & -2 \\\cline{1-3}\end{tabular}}[/tex]

Now , let's plot their graphs. Graph is in attachment. Hence on plotting the graph we see that both the lines Intersect on (-2,2) . Hence x = -2 and y = 2 is the solution of the given linear equation.

Hence (-2,2) is the solution of the given pair of linear equations in two variables.

Last year Hank cashed out his investment account that earned 4.5% simple interest after 10 years
of investing. He ended up with $350 in interest on the account. How much was his initial investment?
Show your work
I=
P=
R=
T=

Answers

Answer:

Initial investment= $777.78

Step-by-step explanation:

Giving the following information:

Last year Hank cashed out his investment account that earned 4.5% simple interest after 10 years of investing. He ended up with $350 in interest on the account.

To calculate the principal (initial investment), we need to use the following formula:

I= P*r*t

I= $350

r= 0.045

t= 10

P= ?

350= P*0.045*10

350/0.45 = P

$777.78= P

Two families buy large sandwiches of the same size. Family A shares one sandwich equally among 4 people. family B shares one sandwich equally among 2 people. Will a person from Family A get the same amount or a different amount of a sandwich as a person from family B?
there's a drawing of 4 squares to represent the 4 ppl​

Answers

Answer:

Different Amount

Step-by-step explanation:

4 is more than 2 and there would need to be 2 sandwiches in family a in order for them to be equal

Please help!!!!!!!!!!! ​

Answers

Answer:

Step-by-step explanation:

pounds / dollars =

You have to answer 2 questions.

1. Which axis are you reading first. Hint the question says pounds to dollars.

So you must be reading the x axis first. because it is pounds.

2. Where would the next point on the graph go.

You read along the x axis first. 25

then you read along the y axis. 20

The answer is 25,20 and that's where the next point goes.

A rectangle piece of land is 400m*150m.Find the cost of the piece of land if one square meter of land costs ₹15,000.​

Answers

Answer:

900000000

Step-by-step explanation:

Area=400×500

=60000m²

Since

1m² = 15000

60000m² = x

x = 60000×15000

x = 900000000

HELP Find the value of x

Answers

Answer:

90

Step-by-step explanation:

Any two lines coming from the two edges of a diameter when they meet it gives 90

2/3 (a-18)=-6
What is a?

Answers

Answer:

a=9

Step-by-step explanation:

2/3 (a-18)=-6

a−18=−6×( 3/2)

a−18=−6×3/2

a−18= −18/2

a−18=−9

a=−9+18  

a=9

Answer:

A=9

Step-by-step explanation:

Simplify both sides of the equation.

2/3(a−18)=−6

(2/3)(a)+(2/3)(−18)=−6(Distribute)

2/3a+-12=-6

2/3a-12=-6

Add 12 to both sides.

2/3a−12+12=−6+12

2/3a=6

Multiply both sides by 3/2

(3/2)* (2/3a)= (3/2)* (6)

A=9

find the missing value of the direct variation (2,5) (5,y)

Answers

Answer:

The missing value y=12.5 and we have (5,12.5)

Step-by-step explanation:

The formula used for direct variation is:

[tex]y\: \alpha \:x\\y=kx[/tex]

We need to find missing value (2,5)(5,y)

First we will find k, and then y

We have x=2, y=5

Find k:

[tex]y=kx\\5=k(2)\\k=\frac{5}{2}\\k=2.5[/tex]

Now, we cam find missing value in (5,y)

We have x=5, k=2.5 and y=?

[tex]y=kx\\y=2.5(5)\\y=12.5[/tex]

So, the missing value y=12.5 and we have (5,12.5)

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