Audrina brought $35.25 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1 6 as much as the sketchbook, and the sketchbook cost 3 4 the cost of the paint set. Audrina had $1.50 leftover after buying these items. What was the cost of each item?

Answers

Answer 1

Answer:

The brush cost $5.44, the sketchbook cost 10.88 and the paint set cost 14.50, approximately.

Step-by-step explanation:

Givens

Audrian has $35.25The brush was 1/6 as much as the sketchbook.The sketchbook cost 3/4 the cost of the paint set.Audrina had $1.50 leftover.She bough a brush, a sketchbook and a paint set.

Based on the given information, we can form the following equations.

[tex]b=\frac{1}{2}s[/tex]

Where [tex]b[/tex] is the brush and [tex]s[/tex] is the sketchbook.

[tex]s=\frac{3}{4}p[/tex]

Where [tex]p[/tex] is paint set.

Now, the sum of all three items would give $1.50 of leftover.

[tex]p+b+s=35.25-1.50[/tex]

Replacing expressions, we have

[tex]p+\frac{1}{2}s+\frac{3}{4}p=30.75\\ \frac{7}{4}p +\frac{1}{2}(\frac{3}{4} p)=30.75\\\frac{7}{4}p+\frac{3}{8}p=30.75\\ \frac{56p+12p}{32}=30.75\\ 68p=984\\p=\frac{984}{68}=14.50[/tex]

Then, we use this value to find the other variables

[tex]s=\frac{3}{4}(14.50)=10.88[/tex]

[tex]b=\frac{1}{2}(10.88)=5.44[/tex]

Therefore, the brush cost $5.44, the sketchbook cost 10.88 and the paint set cost 14.50, approximately.

Answer 2

Answer: paint set costs $18

sketchbook costs $13.5

Brush costs $2.25

Step-by-step explanation:

Let x represent the cost of the paint set.

The sketchbook cost 3/4 the cost of the paint set. It means that the cost of the sketchbook is

3/4 × x = 3x/4

The brush was 1/6 as much as the sketchbook. It means that the cost of the brush is

1/6 × 3x/4 = 3x/24 = x/8

Audrina brought $35.25 to the art supply store. If Audrina had $1.50 leftover after buying these items, it means that the amount spent on the items is

35.25 - 1.5 = 33.75

Therefore,

x + 3x/4 + x/8 = 33.75

Multiplying through by 8, it becomes

8x + 6x + x = 270

15x = 270

x = 270/15

x = 18

The cost of the sketchbook is

(3 × 18)/4 = 13.5

The cost of the brush is

1/8 × 18 = 2.25


Related Questions

the radius of a circle is 2 in what is the length of the 45 arc?

Answers

Answer:

1.5707

Step-by-step explanation:

i solved it using the formula :

[tex]2\pi \times r \frac{45}{360} [/tex]

Can somebody solve this...

Answers

Answer:

J-12-16KL(-12, -16)MO

Sorry. I cannot really the points and graphs clearly.

I hope I helped you! If my answer is correct, please mark me brainiest. Thanks!

Which property is illustrated?

15 + (5 + 7) = (15 + 5) + 7

distributive property
identity property of addition
commutative property of addition
associative property of addition

Answers

Answer:

distributive property

Answer:

associative property

Step-by-step explanation:

The associative property states that you can reorder or regroup numbers and still get the same answer.  In this example, we are regrouping the numbers (parenthesis around different numbers)

NEED HELP ASAP ON TIMER 30 MINUTES LEFT
find the least common multiple (lcm) of:

25y^5 and 5xy and 2x^3y

Answers

Answer:

50 x^3 y^2

Step-by-step explanation:

25y^5 = 5*5 * y*y

5xy  = 5*x*y

2x^3y = 2*x*x*x*y

The least common multiply is  found by taking the least number of times each appears

5 appears 2 times

2 appears 1 time  

x appears 3 times

y appears 2 times

5*5*2  * x*x*x * y*y

50 x^3 y^2

Answer:

50 x^3 y^2

Step-by-step explanation:

25y^5 = 5*5 * y*y

5xy  = 5*x*y

2x^3y = 2*x*x*x*y

The least common multiply is  found by taking the least number of times each appears

5 appears 2 times

2 appears 1 time  

x appears 3 times

y appears 2 times

5*5*2  * x*x*x * y*y

50 x^3 y^2

Find the volume of a right circular cone that has a height of 10.5 in and a base with a circumference of 7.1 in. Round your answer to the nearest tenth of a cubic inch.

Answers

Answer:

14 cubic inches

Step-by-step explanation:

First, we have to find the radius from the circumference. We know that the circumference can be found using the equation c = 2pi(r). Set c equal to 7.1, and solve for r by dividing by 2pi.

Now, we have a radius of 1.13. Using this, we can plug the radius and the height into the equation used to find the volume of a cone: v = pi(r^2)(h/3)

This leads us to 14.04, or 14, when rounded to the nearest tenth of a cubic inch.

6/7 times 3/4=?????????

Answers

Answer:

[tex] \frac{9}{14} [/tex]

Step-by-step explanation:

times top numbers and bottom numbers

6 × 3 = 18

7 × 4 = 28

18/28

*simplify*

9/14

solve for x 6000=-2x^2+20x-42

Answers

Answer:

3 or 7

Step-by-step explanation:

[tex]-2x^2+20x-42=0\\-2(x^2-10x+21)=0\\-2(x-7)(x-3)=0\\x=7, 3[/tex]

Hope this helps!

What’s the answer to this

Answers

Answer B

Step-by-step explanation:

2x+1+14

Answer:

B.)

Step-by-step explanation:

B)2x+15


Enrollment in a dance studio has grown exponentially since the studio opened. A graph depicting this growth is shown. Determine the percentage rate of growth.


0.25%
1.25%
2.5%
25%

Answers

Answer:

Option (4). 25%

Step-by-step explanation:

The graph attached shows the exponential growth.

Let the graphed function is y = [tex](1+\frac{r}{100})^{t}[/tex]

Here 'r' = Rate of growth

t = Duration of time in years

y = enrollments after time 't' years

Graph shows at time 't' = 0 or initially number of enrollments = 20

After 8 years number of enrollments will be

120 = [tex]20(1+\frac{r}{100})^{8}[/tex]

[tex]\frac{120}{20}=(1+\frac{r}{100})^{8}[/tex]

6 = [tex](1+\frac{r}{100})^{8}[/tex]

log 6 = [tex]8\text{log}(1+\frac{r}{100})[/tex]

0.77815 = [tex]8\text{log}(1+\frac{r}{100})[/tex]

[tex]\text{log}(1+\frac{r}{100})[/tex] = 0.0972689

[tex](1+\frac{r}{100})=1.251[/tex]

[tex]\frac{r}{100}=0.251[/tex]

r = 25.1%

r ≈ 25%

Therefore, Option (4) will be the answer.

Answer:

25%

Step-by-step explanation:

did test and it was right

A bag of sweets contains coca cola bottles , milk bottles and jellybeans at a ratio of 3:7:5 there are 6 coca cola bottles how many milk bottles are there how many jelly beans are there

Answers

Answer:

Coca cola bottles = 6

Milk bottles = 14

Jellybeans = 10

Step-by-step explanation:

We are given that a bag of sweets contains coca cola bottles, milk bottles and jellybeans.

The ratio of these sweet bottles is given as,

3:7:5

It is known that there are 6 coca cola bottles.

We are asked to find the quantity of milk bottles and jellybeans.

Coca cola bottles:

Since the ration is 3:7:5

3 parts of coca cola bottle = 6

1 part of coca cola bottle = 6/3 = 2

Milk bottles:

So 7 parts of milk bottle = 7*2 = 14

Jellybeans:

So 5 parts of milk bottle = 5*2 = 10

Therefore,

Coca cola bottles = 6

Milk bottles = 14

Jellybeans = 10

Verification:

6:14:10

Simply the ratio by dividing it with 2

3:7:5

Which reduces to the given ratio hence results are correct.

What is the mean of the given data set. 39,82,74,96,64,52,74

Answers

Hey there!

Another word for the mean is the average. To find the mean in a set of numbers, you add up the numbers and then divide by the number of numbers!

39+82+74+96+64+52+74=481

Now, we see that we have seven numbers. So, we divide by seven!

481/7≈68.71 (rounded to nearest hundredth)

I hope that this helps!

-3/4j+1/5=3/6
Can someone help me find j

Answers

Answer:

j= -0.4

Step-by-step explanation:

multiply both sides by 60

=45j(+12)=30-12

take the 12 ti the right hand side and the sign changes

= -45j=18 then divide by 45 on both sides

j= -2/5

j= -0.4

f(x) = (x+2)^2+4 . what are the coordinates of the vertex?

Answers

Answer:

[tex](-2,\, 4)[/tex].

Step-by-step explanation:

To find the vertex of this parabola, start by rewriting it in the vertex form [tex]f(x) = a\, (x - h)^2 + k[/tex].

Start with the original expression:

[tex]f(x) = (x + 2)^2 + 4[/tex].

Note that in the vertex form, the sign in front of [tex]h[/tex] should be a minus. However, in [tex]f(x) = (x + 2)^2 + 4[/tex], the sign in front of [tex]2[/tex] is a plus. Since adding

[tex]f(x) = (x - (-2))^2 + 4[/tex].

Therefore:

[tex]h = -2[/tex],[tex]k = 4[/tex].

Hence, [tex](-2,\, 4)[/tex] is the vertex of this parabola.

Select the correct answer.
If a six-sided die is rolled 30 times, how many times can you expect to get a 6?

Answers

Answer:

5

Step-by-step explanation:

the probability of getting a 6 every time you roll the die once is just 1/6. multiply that by 30 and we get our answer, which is 5 times.

f(x) = 3^x; find f(0)​

Answers

Answer:

f(0)=1

Step-by-step explanation:

The question asks us to find f(0). We want to find what f(x), or y is, when x is equal to 0.

f(x)=3^x

Therefore, we can substitute 0 in for x.

f(0)=3^0

Evaluate the exponent, 3^0.

Any number raised to the power of zero is equal to 1.

f(0)=1

Answer:

1

Step-by-step explanation:

f(0) = 3^0

f(0) = 1

anything to the 0th power = 1

How is the surface area of any prism determined?

Answers

Answer:

In order to find the surface area, you will need to add up the areas of each face of the prism. ... In this prism, the length is also the side of the hexagon, and the width of the rectangle is the height of the prism. Now, multiply the area of the rectangle by to find the total area of all of the sides of the prism.

Step-by-step explanation:

A furnace operates at 2,300°F. Before it can be used to extract metal from an ore, the temperature must be raised to 3,600°F. This takes place at a rate of 250°F per quarter-hour. Identify the slope and y-intercept in an equation for the temperature in terms of x quarter hours.

Enter your answer using the equation y=mx+b

Answers

Answer: google will help

Step-by-step explanation:

What is the result of adding these two equations?

-2x + 7y = -5
-2.0 - 4y = 6​

Answers

Answer:

[tex]y=-\frac{6x}{5}[/tex]

Step-by-step explanation:

[tex]-2x + 7y = -5\\-2.0 - 4y = 6[/tex]

[tex]y=-\frac{6x}{5}[/tex]

If you roll two fair six-sided dice, what is the probability that the dice show the same number

Answers

Answer:

6/36  

Step-by-step explanation:

Trust me I got it right on Khan academy :)

Answer:

6/36

Step-by-step explanation:

I got it right too on khan academy

which expression is equivalent to 100n2-1

Answers

Answer:

10 x 10n^2 -1

Step-by-step explanation:

any expression as long as they equal the same as your equation (100n^2-1)

Answer:

(10n + 1)(10n - 1)

Step-by-step explanation:

f (x) = 3x^2 - 7x - 32
What is the value of f(-4)?

Answers

Answer:

f (-4) = 3x(-4)^2 - 7x(-4) - 32 =  44

Step-by-step explanation:

you should replace every x with the number given which is here equals -4

A bag of marbles contains 8 yellow marbles, 6 blue marbles, 4 red marbles, and 2 green marbles. Two marbles are chosen at random, WITHOUT replacement. What is the probability a red marble is chosen and then a blue marble?

Answers

Answer:

6/95

Step-by-step explanation:

First, let's find the total # of outcomes. There are 8+6+4+2 = 20 marbles in the bag. We have 20 options for the first draw, and 19 for the second. 20*19 = 380 total possible outcomes.

Now, let's fin the successful outcomes. There are 4 red and 6 blue marbles, so 4 for the firs tpick and 6 for the second pick. 4*6 = 24 successful outcomes. To find probability, we do successful outcomes/total outcomes, and in this case, that is 24/380, or 6/95. Hope that helps!

Answer:

Step-by-step explanation:I don't say you have to mark my ans as brainliest but my friend if it has really helped you plz don't forget to thank me...

4 + d = -12
I need work and answer
WILL GIVE BRAINLIEST

Answers

Answer:

d= -16

Step-by-step explanation:

-16 +4=-12

Answer:

d=−16  

Step-by-step explanation:

d+4−4=−12−4

d=−16

Which are the solutions of x2 = –13x – 4?
dont gime bs just answer it
85 points btw

Answers

Step-by-step explanation:

Step 1:  Add 13x to both sides

[tex]x^2 + 13x = -13x + 13x - 4[/tex]

[tex]x^2 + 13x = -4[/tex]

Step 2:  Add 4 to both sides

[tex]x^2 + 13x + 4 = -4 + 4[/tex]

[tex]x^2 + 13x + 4[/tex]

Step 3:  Use Quadratic Formula

[tex]x = \frac{ -b \pm \sqrt{ b^2 - 4ac } }{2a}[/tex]

[tex]x = \frac{ -(13) \pm \sqrt{ 13^2 - 4(1)(4)} } { 2(1)}[/tex]

[tex]x = \frac{-13 \pm \sqrt{153}}{2}[/tex]

[tex]x = \frac{-13\pm3\sqrt{17} }{2}[/tex]

Answer:  [tex]x = \frac{-13\pm3\sqrt{17} }{2}[/tex]

Answer:

-0.3 and - 12.7

Step-by-step explanation:

Rewrite in quadratic form:

x2 + 13x + 4 = 0

The best approximations, given the options, are 0 and - 13

The actual solution is -

What is the volume of the cube shown? 2 1/4

Answers

Volume of a cube is Volume = S^3, where S is the length of one side.

Volume = 2 1/4^3 = 2 1/4 x 2 1/4 x 2 1/4 = 11 25/64 in^3

The answer is D.

Answer: 30 3/8

Step-by-step explanation:

h(x)=x-4 Determine whether it is in the domain of h or not.

Answers

Answer:

-4

Step-by-step explanation:

Answer: im pretty sure it is a domain

Step-by-step explanation:

Plot - 7 in the complex plane.

Answers

Answer:

see below

Step-by-step explanation:

-7 = -7 + 0i

On a plane mark -7 on real axis and go 0 units on imaginary axis

2 triangular prisms and a cube. The cube is 2 by 2. The triangular prisms have rectangular sides of 3 by 5, 3 by 3, and 3 by 4. The triangular sides have a base of 3 and height of 4.
To find the surface area of the figure shown, Mia found the surface area of the two triangular prisms and the rectangular prism. From this, Mia subtracted 6 ft2. Did Mia make an error?
Mia should have subtracted 16 square feet.
Mia needs to subtract another 6 square feet.
Mia must calculate each triangle separately.
There is no error—Mia is correct.

Answers

Answer:B. Mia needs to subtract another 6 square feet.

Step-by-step explanation:

Answer:

yeah the dude above me is right

Step-by-step explanation:

b r u h moment compilation #27

what is the series written in sigma notation?

Answers

Answer:

Correct option: D

Step-by-step explanation:

First we need to find the rate of the series, and we can do that subtracting one term by the term before:

Second term minus first: 13/10 - 1/2 = 13/10 - 5/10 = 8/10 = 4/5

Third term minus second: 21/10 - 13/10 = 8/10 = 4/5

So the series increases by 4/5 for every term, and the first term is 1/2

We also need to find the number of terms of this series.

The last term is 93/10, so we have that:

1/2 + (4/5)*k = 93/10

(4/5)k = 88/10

k = 11

The index of the summatory should go from 0 to 11.

So the correct option is D

The base of a right triangle is 13 less than 2 times the height. The area of the triangle is 12 square cm. What is the height of the triangle in cm? *

Answers

Answer:

The height of the triangle is 8 cm

Step-by-step explanation:

First we need to write down the question in a mathematical format and then solve.

let b be the base of the triangle and h be the height of the triangle

"The base of a right triangle is 13 less than 2 times the height" can be written as

b = 2h - 13 -----------------------------------------------------(1)

"The area of the triangle is 12 square cm" can be written as;

area of the triangle = 12 cm²

but area of a triangle = [tex]\frac{1}{2}[/tex] ×b × h

This implies that

[tex]\frac{1}{2}[/tex] ×b × h = 12 cm²

bh = 24 cm² --------------------------------------------------(2)

substitute equation (1) in equation (2)

(2h - 13)h = 24

2h² - 13h = 24

2h² - 13h - 24 = 0 ----------------------------------------------(3)

The above is now a quadratic equation, so we will solve by completing the square method.

Find two numbers such that its product will give -48 and its sum will give -13

The two numbers are -16 and 3

Replace -13h by  (-16h +  3h) in equation (3)

2h² - 13h - 24 = 0

2h² - 16h + 3h - 24 = 0

2h(h - 8) + 3(h-8) = 0

(h-8)(2h+3) = 0

either h-8 = 0

           h = 8

OR

2h + 3 = 0

2h = -3

h =-3/8

There is no such thing as negative length, therefore h= 8 is the answer

The height of the triangle is 8 cm

Other Questions
A pathogen enters an organism and infects it. Which statement best describes the general effect of the infection on the organism? *A. The organism experiences a disruption in homeostasis.B. The organism cannot obtain energy.C. The organism cannot reproduce.D. The organism experiences uncontrolled cell growth. who is the first person created light bulb The series 14 + 6 + (2) + (10) + . . . + (154) is arithmetic. How many terms are in the series? To be honest, I really dont understand this and need someone to help me out. Does Pennsylvania state have some kind of ban on texting while driving? Which sentence from a smart cookie provides evidence the supports the conclusion that esperanza thinks highly of her mother Ethan drew a scale drawing of a house. He used the scale 1 millimeter : 5 meters. The actuallength of the garage is 10 meters. How long is the garage in the drawing?millimeters Type the integer that makes the following subtraction sentence true:8 ?= 1 In the talent show, 6 students plan to sing, 7 students plan to dance, and 2 students plan totell jokes. Rick said that the ratio of singers to joke-tellers is 6 to 2. Leah said that the ratio ofjoke-tellers to singers is 1 to 3. Who is correct? Explain why. Help ASAPWhat is the smallest part of the brain? Which season has the least amount of rain in the northern latitudes? winter summer spring fall PLEASE HELP correct answer= 5stars,thank you,10pts and BRAINLIEST!Choose the word or phrase that best completes each sentence.Roman art and architecture can be found *blank*The author organized Paradise Lost to mirror Virgils Aeneid. *Blank*The author liked Virgil so much that he made him his guide in The Inferno. *Blank*The author wrote six different plays about ancient Rome and Greece. *Blank* name three ways drug abuse affects mental/emotional health Where does your organism live? Describe its habitat. Innova uses 1,000 units of the component IMC2 every month to manufacture one of its products. The unit costs incurred to manufacture the component are as follows. Direct materials $61.48 Direct labor 37.19 Overhead 126.50 Total $225.17 Overhead costs include variable material handling costs of $7.16, which are applied to products on the basis of direct material costs. The remainder of the overhead costs are applied on the basis of direct labor dollars and consist of 60% variable costs and 40% fixed costs. A vendor has offered to supply the IMC2 component at a price of $230 per unit. (a) Prepare the incremental analysis for the decision to make or buy IMC2. Make IMC2 (per unit) Buy IMC2 (per unit) Net Income Increase (Decrease) Direct material $ $ $ Direct labor Material handling Variable overhead Purchase price Total unit cost $ $ $ Should Innova purchase the component from the outside vendor if Innovas capacity remains idle? A bowl contains a total of 26 blue and red marbles. There are two more red marbles thanblue marbles. How many blue marbles are in the bowl?Which of the following let statements should you use?Let x = the number of red marbles. Let x + 2 = the numberof blue marbles.Let x = the number of blue marbles. Let 2x = the number ofred marbles.Let x = the number of blue marbles. Let x + 2 = the numberof red marbles. The city of Omaha decided to build a new parking garage in hopes of luring more people to the Old Market district.The city will pay for the parking garage through parking fees. For a random sample of 42 weekdays, daily fees collected averaged $126 with a standard deviation of $16. The consultant who advised the city on the project estimated the potential parking revenues to be $135 per day, though the city believes that estimate is too high. Perform a hypothesis test (by hand) using =0.05 to check the advisor's claim that the revenue would be $135 per day. Include the following:1. Write your hypotheses in both symbols and words. 2. Test an appropriate hypothesis "by hand" using an alpha level of 0.05. Assume conditions are met (so don't check them). Be sure to include the correct probability notation and use the editor for all work. 3. Support your test with the corresponding confidence interval, again "by hand". Use the editor to show all steps. 4. Write your 3-part final conclusion using the test results and interval results. Include a sentence that states whether the test and interval results agree. What are the split complimentary of blue? aRed-Orange and Yellow-Orange bYellow-Green and Blue-Green cBlue-Violet and Red-Violet dGreen and Violet PLEASE ANSWER THIS QUESTION ILL MARK YOU AS THE BRAINLIEST if A= and B=, find BA.