Kyle works at a donut​ factory, where a​ 10-oz cup of coffee costs 95¢​, a​ 14-oz cup costs​ $1.15, and a​ 20-oz cup costs​ $1.50. During one busy​ period, Kyle served 14 cups of​ coffee, using 204 ounces of​ coffee, while collecting a total of ​$16.70. How many cups of each size did Kyle​ fill?
Kyle filled ___ ​10-oz cup(s), ___ 14-oz cup(s), and ___ ​20-oz cup(s).

Answers

Answer 1

Answer:

Kyle filled 4 10-oz cups, 6 14-oz cups, and 4 20-oz cups.

Step-by-step explanation:

Let 10-oz, 14-oz, and 20-oz coffees be represented by the variables a, b, and c, respectively.

Since a total of 14 cups of coffee was served:

[tex]a+b+c=14[/tex]

A total of 204 ounces of coffee was served. Therefore:

[tex]10a+14b+20c=204[/tex]

A total of $16.70 was collected. Hence:

[tex]0.95a+1.15b+1.5c=16.7[/tex]

This yields a triple system of equations. In order to solve a triple system, we should isolate the system to only two variables first.

From the first equation, let's subtract a and b from both sides:

[tex]c=14-a-b[/tex]

Substitute this into both the second and third equations:

[tex]10a+14b+20(14-a-b)=204[/tex]

And:

[tex]0.95a+1.15b+1.5(14-a-b)=16.7[/tex]

In this way, we've successfully created a system of two equations, which can be more easily solved. Distribute:

For the Second Equation:

[tex]\displaystyle \begin{aligned} 10a+14b+280-20a-20b&=204\\ -10a-6b&=-76\\5a+3b&=38\end{aligned}[/tex]

And for the Third:

[tex]\displaystyle \begin{aligned} 0.95a+1.15b+21-1.5a-1.5b&=16.7\\ -0.55a-0.35b&=-4.3\end{aligned}[/tex]

We can solve this using substitution. From the second equation, isolate a:

[tex]\displaystyle a=\frac{1}{5}(38-3b)=7.6-0.6b[/tex]

Substitute into the third:

[tex]-0.55(7.6-0.6b)-0.35b=-4.3[/tex]

Distribute and simplify:

[tex]-4.18+0.33b-0.35b=-4.3[/tex]

Therefore:

[tex]-0.02b=-0.12\Rightarrow b=6[/tex]

Using the equation for a:

[tex]a=7.6-0.6(6)=4[/tex]

And using the equation for c:

[tex]c=14-(4)-(6)=14-10=4[/tex]

Therefore, Kyle filled 4 10-oz cups, 6 14-oz cups, and 4 20-oz cups.


Related Questions

The following data represent the maximum wind speed (in knots) and atmospheric pressure (in millibars) for a random sample of hurricanes that originated in the Atlantic Ocean.

Atmospheric Pressure (mb) Wind Speed (knots) Atmospheric Pressure (mb) Wind Speed (knots)
993 50 1006 40
995 60 942 120
994 60 1002 40

Required:
a. Find the y-intercept of the least-squares regression line, treating atmospheric pressure as the explanatory variable (round to four decimal places.)
b. Find the slope of the least-squares regression line, treating atmospheric pressure as the explanatory variable (round to four decimal places.)
c. Is it reasonable to interpret the y-intercept of the least-squares regression line, treating atmospheric pressure as the explanatory variable? Why or why not?

Answers

Answer:

Step-by-step explanation:

X                  Y                 X²                              Y²                  XY

993              50               986049                 2500              49650

995              60               990025                 3600              59700

994              60               988036                  3600              59640

1006             40               1012036                 1600              40240

942             120               887364                 14400              113040

1002             40               1004004                 1600              40080

[tex]\sum X: 5932[/tex]   [tex]\sum Y : 370[/tex]     [tex]\sum X^2 : 5867514[/tex]    [tex]\sum Y^2 = 27300[/tex]    [tex]\sum XY : 362350[/tex]

To determine the regression:

[tex]Mean \ (X) = \dfrac{\sum X }{n} \\ \\ = \dfrac{5932}{6} \\ \\ = 988.67[/tex]

[tex]Mean \ (Y) = \dfrac{\sum Y}{n} \\ \\ = \dfrac{370}{6} \\ \\ = 61.67[/tex]

Intercept [tex]b_o = \dfrac{\sum YX *\sum X^2 - \sum X \sum Y}{n(\sum X^2) - (\sum X)^2}[/tex]

[tex]=\dfrac{370(5867514) -(5932)(370)}{6(5867514) - (5932)^2}[/tex]

= 131760.9563

Slope [tex]b_1 = \dfrac{n(\sum XY) -(\sum X *\sum Y) }{n(\sum X^2)-(\sum X)^2}[/tex]

[tex]b_1 = \dfrac{6(362350) -(5932*370) }{6(5867514)-(5932)^2}[/tex]

[tex]b_1 = -1.2600[/tex]

The regression line equation [tex]Y = b_o +b_1X[/tex]

[tex]Y = 131760.96 -1.2600 X[/tex]

We then make a comparison of the slope of the equation to y = mx+c

slope of the equation = -1.2600

the y-intercept corresponds to when X = 0, thus:

y-intercept = 131760.9563

Yes, it is reasonable to interpret the y-intercept of the regression line, Using atmospheric pressure as an explanatory variable due to the fact that:

X is the independent variable and Y exists as the dependent variable.

Solve each question (a, b, c) and show your work. Thank you <3

Answers

Answer:

a) 112 ft.

b) 256 ft. and 3 seconds

c) 7 seconds

Step-by-step explanation:

a) The model rocket is lauched from a platform. To find the height of the platform, we need to find h when t = 0, because the rocket starts from the platform when no time has elapsed:

[tex]h=-16t^2+96t+112[/tex]

[tex]h=-16*0+96+0+112\\\\h=112[/tex]

Therefore, the height of the platform is [tex]\fbox{112}[/tex] ft.

b) If you learned calculus before, we can find the maximum height easily. We take the derivative of h and set it equal to 0. Remember, the derivative of a function is simply the slope of it at an instantaneous point. At the maximum point of a function, it's slope equals to 0.

[tex]h=-16t^2+96t+112\\h'=-32t+96+0\\h'=-32t+96[/tex]

Ok! Let's set the derivative of h to 0!

[tex]0=-32t+96\\-96=-32t\\t=3[/tex]

We now know how long it takes for the rocket to reach maximum point (t represents seconds), but we also need to find the maximum height. We can simply plug our t=3 into the function of h, because t=3 is the point where the rocket reaches maximum height:

[tex]h(3)=-16(3)^2+96*3+112\\h(3)=-144+288+112\\h(3)=256[/tex]

The maximum height of the rocket is [tex]\fbox{256}[/tex] ft and the rocket takes [tex]\fbox{3}[/tex] seconds to reach the height.

c) The rocket reaches the ground when h equals 0. We can set up the equation to solve for it:

[tex]h=-16t^2+96t+112\\0=-16t^2+96t+112\\0=-16(t+1)(t-7)\\0=(t+1)(t-7)\\t=-1, t=7[/tex]

However, time can never be negative.

Therefore, it takes the rocket [tex]\fbox{7}[/tex] seconds to reach the ground.

I hope this helps! Let me know if you have any questions :)

find the quotient of 8 divided by one-third, multiply 8 by
A:1/8
B:1/3
C:3
D:8
are the possible answers

Answers

Answer:

find the quotient of 8 divided by one-third, multiply 8 by

A:1/8

B:1/3( true

C:3

D:8

are the possible answers

Sketch the region enclosed by the given curves and calculate its area.
y=4-x^2 ,y=0

The answer is 32/3. But how do I get to that answer?

Answers

Answer:

Step-by-step explanation:

1.) we need to find the bounds of integration which is just the points of intersection

here is it (-2,0) and (2,0)

which means we will integrate from -2 to 2

next, we take the upper equation and subtract that from the lower one

kind of confusing but it would look like (sketch it out if you're not sure)

(4-x²)-0= 4-x²

then we can integrate

[tex]\int\limits^2_{-2} {4-x^2} \, dx =4x-\frac{x^3}{3}|_{-2}^{2}=(4*(2)-\frac{2^3}{3})-(4(-2)-\frac{-2^3}{3})=5.333333-(-5.3333333)= 10.666666667=\frac{32}{3}[/tex]

What number is 18% more than 1257 Round your answer to two decimal places needed,

Answers

1,483.26, multiply 1257 by 1.18 to get to your answer

Answer fast please and thanks!

Answers

Answer:

tan 30 = x / 15

General Formulas and Concepts:

Trigonometry

[Right Triangles Only] SOHCAHTOA[Right Triangles Only] tanθ = opposite over adjacent

Step-by-step explanation:

Step 1: Define

Identify variables

Angle θ = 30°

Opposite Leg = x

Adjacent Leg = 15

Step 2: Solve for x

Substitute in variables [tangent]:                                                                     tan 30 = x / 15

Answer:

3rd one

Step-by-step explanation:

Recall that

Sin = opposite over hypotenuse

Cos = adjacent over hypotenuse

Tan = opposite over adjacent

For the angle with a measure of 30 degrees we are given it's adjacent side length and need to find it's opposite side length

When dealing with opposite and adjacent we use tangent

If tan = opposite over adjacent

Then tan30 = x / 15 and the correct answer choice is the third one

what is 72 Times 27 equal

Answers

Answer:

1,944

Step-by-step explanation:

72x27=1,944

Have a wonderful day or night

Answer

1944

Step-by-step explanation:

72*27 = 1944

the image above should clarify how you're actually supposed to do it! couldn't submit this without 20 characters :,)

mong moi nguoi giup do

Answers

mong moi do giup mguoi

What is a demand schedule?
А.
a chart that shows the demand for a type of product at various prices
B.
a graph that shows the demand for a product at a single price point
C.
a chart that shows the demand for a product at various prices

Answers

Answer:

Answer is C

Step-by-step explanation:

In demand when the price goes up the quantity goes up and when the price goes down the quantity also goes down

In Supply when the price goes up the quantity goes down and when the price goes down the quantity goes up

Demand Schedule is a Chart

Demand Curve is a graph

Supply Schedule is a Chart

Supply Curve is a graph

Hope this helps

Answer: C

WHAT IS A DEMAND SCHEDULE?

Demand schedule is a plotting of demand for goods and services as part of economic analysis. The demand schedule refers to a table depicting the demand in quantity terms for goods or services at varying price levels.=========================================

A CHART THAT SHOWS THE DEMAND FOR A PRODUCT AT A SINGLE PRICE POINT?

Demand Curve

A CHART THAT SHOWS THE DEMAND FOR A PRODUCT AT VARIOUS PRICES?

Demand schedule

Step-by-step explanation:

[tex]hope \: it \: helps[/tex]

Simplify the expression

Answers

Answer:

6

Step-by-step explanation:

3 sqrt(20) / sqrt(5)

We know that sqrt(a) /sqrt(b) = sqrt(a/b)

3 sqrt(20/5)

3 sqrt(4)

3 *2

6

what the person above me said

Write the word sentence as an equation.

The quotient of a number n and 5 is 18.

Answers

Answer:

n/5 = 18

Step-by-step explanation:

Quotient means division.

n/5 = 18

I got 7 to go :( help plz

Answers

Answer:

I think the second one is the answer ; 2√b

The 2nd one is the answer i’m pretty sure.

Do you guys know this

Answers

Answer:

Kindly check attached picture

Step-by-step explanation:

The expected graph is attached in the picture below :

Since additional fee is charged on only luggage exceeding 50 pound weight :

The inequality is :

Additional fee applied to :

Weight > 50

Hence x our arrows starts from 50 to the right of the number line

A trinomial is a perfect square when two terms are
a. Positive
b.negative
c. Neither positve
d. Either negative

Answers

Answer:

a trinomial is a perfect square trinomial if it can be factorized into a binomial multiplies to itself. In a perfect square trinomial, two of your terms will be perfect squares.

16. Using divisibility tests, check whether the number 240720 is divisible by
2, 3, 4, 5, 6, 8, 9, 10 and 11. (Give reason)

Answers

2: it is, because last digit is even
3: it is, because the sum of the digit, 2+4+7+2=15, is divisible by 3
4. it is, because the last 2 digits, 20, is divisible by 4
5. it is, because last digit is 0
6. it is, because it is divisible by 2 and 3
8. it is, because the last 3 digits, 720, is divisible by 8
9. It is not, because the sum of the digits, which is 15, is not divisible by 9
10. It is, because the last digit is 0
11. It is not, because the difference of alternating digits, which is 2+0+2-4-7-0, is not divisible by 11

If f(x)=2x²-x find f(-3)

Answers

Answer:

21

Step-by-step explanation:

f(x) = 2x^2 - x

f(-3) = 2*(-3)^2 - (-3)

=2*9 +3

=18 +3

=21

Answer: 21

Step-by-step explanation: To find f(-3) or the value of the function when x = -3, we plug in a -3 for the x in our function and we have 2(-3)² - (-3).

Start by simplifying the exponent to get 9.

So we have 2(9) - (-3) or 18 + 3 which is 21.

The sum of three numbers is fourteen. The first number minus three times the third number is the second number. The second number is six more than the first number. Find the three numbers.

Answers

Answer:

1st number (x) = 5

2nd number (y) = 11

3rd number (z) = -2

Step-by-step explanation:

Let the generic solution for this problem be x + y + z = 14.  

The first number minus three times the third number equals the second number, so x - 3z = y.  The second number is 6 more than the first number, so y = 6 + x.  

x - 3z = y, we know that y = 6 + x, so the equation becomes x - 3z = 6 + x.

After some arithmetic, we find that z = -2.  

Plugging our knowns back into the generic solution becomes:

x + x - 3z + z = 14

2x - 3(-2) - 2 = 14

2x + 6 - 2 = 14

2x + 4 = 14

2x = 10

x = 5

So we know that z = -2, and x = 5, it's just simple substitution from there.  

5 + y + (-2) = 14

5 + y = 16

y = 11

PLEASE HELP ME WILL MARK YOU JF YOU HELP ME PLEASE!!!

Answers

Answer:

2, 3, 4, 7, 8, 10 I hope

Answers

Congruent by AAS (shown in the example)Congruent by SASCongruent by SSSCongruent by ASANot enough info  (shown in the second example)Congruent by AASCongruent by SASCongruent by SSSCongruent by AASNot congruent

=================================================

Explanations:

As the example shows, we have two pairs of congruent angles and a pair of congruent sides. The side are not between the angles in question. So AAS is slightly different from ASA.We have two pairs of congruent sides, and a pair of congruent angles. The angles are between the sides. So we use SAS which is a valid congruence theorem. Recall that SSA is not a valid theorem, so the order matters.We have three pairs of congruent sides, so we go with SSS. The order doesn't matter here.Similar to problem 1, but now the sides are between the angles. So we go with ASA this time instead of AAS.We unfortunately don't have enough info to determine if the triangles are congruent or not. We need to know something about the side lengths to determine congruency.As the hint suggests, marking the vertical angles will produce the other pair of congruent angles. So that's why we go for AAS (the side is not between the angles).This is similar to problem 2, as both use SAS. Note the unmarked vertical angles which are congruent.This is similar to problem 3. We use SSS here because we have 3 pairs of congruent sides as indicated by the tickmarks.The unmarked vertical angles can get double arcs to show they are congruent. We have a pair of congruent sides that are not between the two pairs of congruent angles, so we go for AAS (problems 1 and 6 also use AAS).For the triangle on the left, the arc is between the tickmarked sides. The triangle on the right has the arc not between the tickmarked sides. So there's no way the triangles are the same. The arc needs to be between the marked sides for each triangle, if we wanted them to be congruent (using SAS).

---------------

Acronyms

SSS = side side side

SAS = side angle side

ASA = angle side angle

AAS = angle angle side

emma can read 4 pages of a book in 8 minutes how many pages can she read per minute if she still had it 24 pages how many pages are there in the book

Answers

Answer:

Emma can read 30 pages per minute

Number of book pages 28

Step-by-step explanation:

There are twelve empty rooms in the office of Acme Softwares, inc. Alif and Laila joins the company. How many ways can they be assigned a room each from these twelve

Answers

Answer:

132.

Step-by-step explanation:

That would be the number of permutations of 2 from 12.

12P2 = 12! / (12-2)!

= 132.

Write the equation of the line that passes through the points (8,-1) and (2,-5) in standard from, given that the point-slope form is y+1=2/3(x-8)

____x+____y=____

Answers

Answer: 2/3x-y=19/3

Step-by-step explanation:

Points are useless since we already know the point slope form and we can just simply that

y+1=2/3(x-8)

y+1=2/3x-16/3

y=2/3x-19/3

2/3x-y=19/3

1/6 of ______ equals 9

What is the blank?

Answers

Answer:

54

Step-by-step explanation:

1/6 × y = 9

y ÷ 6 = 9

y ÷ 6 × 6 = 9 × 6

y = 54

pls help asap!!

For the following geometric sequence, find the recursive formula.

(-80,20,-5...)

Answers

Answer:

For the geometric sequence, it has two forms of formula

We are interested in the recursive formula now

{-80, 20, -5, ...}

The common ratio is (20/-80)=(-5/20)=-1/4=-0.25

So our recursive formula would bea_n=a_{n-1}*(-0.25)=a_{n-1}*(- \frac{1}{4} )an=an−1∗(−0.25)=an−1∗(−41)

Step-by-step explanation:

For the geometric sequence, it has two forms of formula

{-80, 20, -5, ...}

The common ratio is (20/-80)=(-5/20)=-1/4=-0.25

So our recursive formula would be a n=a {n-1}*(-0.25)=a_{n-1}*(- \frac{1}{4} )an=an−1∗(−0.25)=an−1∗(−41)

A stamp collection is purchased for $1,000. Twenty years later, the owner is told that the collection is worth quite a bit of money! If the rate of return on the stamp collection is 4% per year, what is the current value of the stamp collection? In your final answer, include all of your calculations.

Answers

Answer:

The current value of the stamp collection is of $2,191.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

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

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

A stamp collection is purchased for $1,000.

This means that [tex]P = 1000[/tex]

The rate of return on the stamp collection is 4% per year

This means that [tex]n = 1, r = 0.04[/tex]

So

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

[tex]A(t) = 1000(1 + 0.04)^{t}[/tex]

[tex]A(t) = 1000(1.04)^{t}[/tex]

What is the current value of the stamp collection?

This is A(20). So

[tex]A(20) = 1000(1.04)^{20} = 2191[/tex]

The current value of the stamp collection is of $2,191.

Answer:

Step-by-step explanation:

y = 1000(1+0.04)^20

y = 1000(1.04)^20

Rounded to the nearest hundredth

y = 1000(2.19)

y = $2190

Factor completely, then place the factors in the proper location on the grid. 25a2 +9b2 + 30ab

Answers

Answer:

(5a+3b)(5a+3b) or SQ(5a+3b)

Step-by-step explanation:

Now you can plot by referring to the above factors

The diagram below is divided into equal parts. Which shows the ratio of unshaded section to shaded sections

Answers

Answer:

its D

Step-by-step explanation:

Answer:

its D

Step-by-step explanation:

there is 5 unshaded and one shaded

Evan wants to make an array of 32 miniature cars What are all the different ways Evan can place the cars? ​

Answers

Answer:

1 × 32,  2 × 16,  4 × 8,  8 × 4,  16 × 2,  32 × 1

Step-by-step explanation:

There are 6 different ways for Evan to create a array of 32 miniature cars.

What is the fundamental principle of multiplication?

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

An array would constitute the shape of a parallelogram, in which you are essentially solving for s₁ and s₂.

Since there are 32 miniature cars in all, in which both sides, when multiplied, must result in said number:

32 x 1 = 32

2 x 16 = 32

4 x 8 = 32

8 x 4 = 32

16 x 2 = 32

1 x 32 = 32

Hence, There are 6 different ways for Evan to create a array of 32 miniature cars.

Learn more about multiplications;

https://brainly.com/question/14059007

#SPJ2

Differentiate the function. y = (2x - 5)^2 (5 - x)?​

Answers

Answer:

[tex]\displaystyle y' = -(2x - 5)(6x - 25)[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Distributive Property

Algebra I

Terms/CoefficientsFactoring

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹

Derivative Rule [Product Rule]:                                                                                    [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]

Derivative Rule [Chain Rule]:                                                                                       [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

y = (2x - 5)²(5 - x)

Step 2: Differentiate

Derivative Rule [Product Rule]:                                                                        [tex]\displaystyle y' = \frac{d}{dx}[(2x - 5)^2](5 - x) + (2x - 5)^2\frac{d}{dx}[(5 - x)][/tex]Chain Rule [Basic Power Rule]:                                                                        [tex]\displaystyle y' = [2(2x - 5)^{2 - 1} \cdot \frac{d}{dx}[2x]](5 - x) + (2x - 5)^2\frac{d}{dx}[(5 - x)][/tex]Simplify:                                                                                                             [tex]\displaystyle y' = [2(2x - 5) \cdot \frac{d}{dx}[2x]](5 - x) + (2x - 5)^2\frac{d}{dx}[(5 - x)][/tex]Basic Power Rule:                                                                                             [tex]\displaystyle y' = [2(2x - 5) \cdot 1 \cdot 2x^{1 - 1}](5 - x) + (2x - 5)^2(1 \cdot -x^{1 - 1})][/tex]Simplify:                                                                                                             [tex]\displaystyle y' = [2(2x - 5) \cdot 2](5 - x) + (2x - 5)^2(-1)[/tex]Multiply:                                                                                                             [tex]\displaystyle y' = 4(2x - 5)(5 - x) - (2x - 5)^2[/tex]Factor:                                                                                                               [tex]\displaystyle y' = (2x - 5)[4(5 - x) - (2x - 5)][/tex][Distributive Property] Distribute 4:                                                                 [tex]\displaystyle y' = (2x - 5)[20 - 4x - (2x - 5)][/tex][Distributive Property] Distribute negative:                                                    [tex]\displaystyle y' = (2x - 5)[20 - 4x - 2x + 5][/tex][Subtraction] Combine like terms (x):                                                              [tex]\displaystyle y' = (2x - 5)[20 - 6x + 5][/tex][Addition] Combine like terms:                                                                        [tex]\displaystyle y' = (2x - 5)(25 - 6x)[/tex]Factor:                                                                                                               [tex]\displaystyle y' = -(2x - 5)(6x - 25)[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e

using the digits 0-9 at most one time each fill in the boxes so that the fraction equals the decimal

Answers

Step-by-step explanation:

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336"083"2553

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Rewrite the equation by completing the square.
x^2 + 7x + 12 = 0

Answers

Answer:

x^2 + 7x + 12 = 0

x^2 + 7x  = -12

(+3)(+4)=0

=−3

=−4

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Hope This Helps!!!

Answer:

(x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{1}{4}[/tex] = 0

Step-by-step explanation:

Given

x² + 7x + 12 = 0

To complete the square

add/subtract ( half the coefficient of the x- term)² to x² + 7x

x² + 2([tex]\frac{7}{2}[/tex] )x + [tex]\frac{49}{4}[/tex] - [tex]\frac{49}{4}[/tex] + 12 = 0

(x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{49}{4}[/tex] + [tex]\frac{48}{4}[/tex] = 0 , that is

(x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{1}{4}[/tex] = 0

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