Clem Colfax had $10 to buy groceries. He needed milk costing 70 cents a carton, bread costing 60 cents a loaf, breakfast cereal costing 50 cents a box, and meat costing $1.50 a pound. He bought twice as many cartons of milk as he did loaves of bread, the number of boxes of cereal was one more than the number of loaves of bread, and the number of pounds of meat was the same as the number of boxes of cereal. How many of each did he buy if the total he spent was exactly $10?

Answers

Answer 1

The first thing we must do for this case is to define variables:
w: pounds of meat
x: carton of milk
y: loaf of bread
z: cereal breakfast box
We write the system of equations:
0.70x + 0.60y + 0.50z + 1.50w = 10
x = 2y
z = y + 1
w = z
Solving the system we have:
w = 3
x = 4
y = 2
z = 3
Answer:
3 pounds of meat
4 cartons of milk
2 loaves of bread
3 boxes of breakfast cereal

Related Questions

What are the next three terms in the sequence? -6,5,16,27, ...

A.38, 49, 60
B.37, 47, 57
C.36, 45, 54
D.36, 46, 56

Answers

The sequence is +11 for every number, so it would be A

The next three terms of the given sequence are 38, 49, and 60. The correct option is A.38, 49, 60

Linear sequence

From the question, we are to determine the next three terms in the given sequence

The given sequence is

-6,5,16,27, ...

From the given sequence, we can observe that the common difference of the sequence is 11

That is,

5 - -6 = 5 + 6 = 11

16 - 5 = 11

27 - 16 = 11

Thus, the next term after 27 will be

27 + 11 = 38

The next one will be

38 + 11 = 49

The next one will be

49 + 11 = 60

Hence, the next three terms of the given sequence are 38, 49, and 60. The correct option is A.38, 49, 60

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find the least common multiple LCM of 10 and 5

Answers

1,2
The least common multiple is 2

Answer: I hope this is helpful

Step-by-step explanation:

10LCM of 5 and 10 is 10. LCM, also known as Least Common multiple or Lowest common multiple, is the smallest or the least positive integer that is divisible by the given set of numbers. In the given set of numbers 5 and 10, 10 is the least number that is divisible by both 5 and 10.

a cone with radius 2 feet and height 8 feet is shown.

Answers

The volume of the cone is approximately 33.51 cubic feet when rounded to the nearest hundredth

Use the formula for the volume of a cone, which is:

[tex]V = \frac{1}{3} \pi r^2 h[/tex]

Where:

[tex]V[/tex] is the volume of the cone,[tex]r[/tex] is the radius of the base of the cone,[tex]h[/tex] is the height of the cone.

Given:

Radius [tex]r = 2\;\text{ft}[/tex]Height [tex]h = 8\;\text{ft}[/tex]

Substitute the given values into the volume formula:

[tex]V = \frac{1}{3} \pi (2)^2 (8)[/tex]

Calculate the radius squared:

[tex]2^2 = 4[/tex]

Multiply the squared radius by the height and [tex]\pi[/tex]:

[tex]4 \times 8 \times \pi = 32\pi[/tex]

Divide by 3 to get the volume:

[tex]V = \frac{32\pi}{3} \approx \frac{32 \times 3.14159}{3} \approx 33.51\;\text{cubic feet}[/tex]

Complete question

A cone with a radius of 2ft and height 8ft is shown. Find the volume of the cone in cubic feet. Round your answer to the nearest hundredth

hey can you please help me posted picture of question

Answers

We can determine the correct graph by finding its roots

x² - 4x - 12 = 0

x² - 6x + 2x - 12 = 0

x(x-6) +2(x-6) = 0

(x+2)(x-6) = 0

This means the roots of the function are x=-2, and x=6 and the graph will cross x axis at these two points. From the given graphs, the graph B seems to cross these points.

So the answer to this question is option B

1.
Find the annual percentage rate, using the annual percentage rate table.
Amount Financed: $2,650

Finance Charge: $484.69

Number of Payments: 36

Answers

Amount Financed: $2,650
Finance Charge: $484.69
Number of Payments: 36

(Finance Charge)/(Amount Financed)*100$=($484.69)/($2,650)*100$
(Finance Charge)/(Amount Financed)*100$=(0.1829)*100$
(Finance Charge)/(Amount Financed)*100$=$18.29

In the row of number of Payments 36, we look for:
(Finance Charge)/(Amount Financed)*100$=$18.29, and we see to which annual porcentage rate it corresponds in the first row

Answer: 11.25%

Suppose you are the treasurer of the drama club.The cost of scripts for the spring musical is $254. The cost of props and costumes is $400. You must also pay $1.20 per ticket to the play's director. You charge $4.00 per ticket and you also expect to make $150 on refreshments. How many tickets will the drama club need to sell to break even?

Answers

Expected net costs are
$254 +400 -150 = $504

Expected income per ticket is
$4.00 -1.20 = $2.80

To break even, the number of tickets that must be sold is
$504/$2.80 = 180

The drama club needs to sell 180 tickets to break even.

There are 10 people on a team. 5 are chosen. which expression gives number of ways

Answers

The number of ways in this case will involve computation of number of combinations available. That is,
Number of ways to select 5 = Total number C Number to be chosen. Where "C" stands for combination

Substituting;
Number of ways to select 5 from 10 people = 10C5 = 10!/{5!*(10-5)!} = 10!/(5!*5!) = 252 ways

what is the answer for this math question

Answers

1/10÷2/3=KCF (keep,change,flip)
1/10×3/2=3/20 cups
0.15=15%=3/20 as decimal*percent

Of all rectangles with area 9 which one has the minimum perimeter

Answers

A 3x3 rectangle would be the smallest it could get

A straight line has the equation 2y-8x=5x-12. If point C, (4, n) lies on this straight line, find n.

Answers

we have that
2y-8x=5x-12----> 2y=13x-12

we know that
If point C, (4, n) lies on this straight line
so
in the straight line
for x=4
the value of y must be n
2y=13x-12-----> 2y=13*4-12----> 2y=52-12----> 2y=40----> y=20

the value of n must be 20

the answer is
n is 20

Heather and Joel bought a house for $157,200 and know that the house appreciates every year. They keep track of their house value for 5 years and model their data with the exponential equation

Answers

Given that they want to estimate the cost of the house after 8 years, the best equation will be obtained as follows:
FV=P(1+r)^n
where:
n=time
p=principle
r=rate
First we need to estimate the rate. The value of the house after 5 years is $ 190,000
thus plugging the values in the equation and solving for r we get:
190000=157200(1+r)^5
1.20865=(1+r)^5
getting the fifth root of both sides we obtain:
1.0386=1+r
thus
r=0.0386~3.86%
thus the value of the house after 8 years will be:
FV=157200(1.0386)^8
FV=$212,879.6936

Final answer:

The question relates to house appreciation and quality in mathematics. The house's value appreciates each year, an occurrence that Heather and Joel could monitor. House appreciation allows them to determine the annual interest rate and the value of their house after a particular period, and Ben and Freda's specifics help illustrate this situation.

Explanation:

The question pertains to the concept of housing appreciation and equity in Mathematics. In this situation, Heather and Joel will observe that the value of their home increases annually due to appreciation. The value of their home after a certain period can be modeled using an exponential equation, taking the initial amount as the purchasing price, and the rate as the annual appreciation percentage.

For example, looking at Freda's situation, she bought a house for $150,000. Now, if she were to sell it, she would get $250,000. This increase in price from $150,000 to $250,000 would demonstrate the appreciation of her house over time. Similarly, Ben bought a house for $100,000 and borrowed the rest after a 20% down payment. As he pays the loan, his equity in the house increases and the house's increase in value also appreciates his equity.

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***HELP***
Given that ABC ~ DEC, find the value of x. If necessary, round your answer to two decimal places.

Answers

If these are similar triangles, this means that the ratio of corresponding sides is equivalent. In this case, AB corresponds to DE as CB corresponds to CE. In ratio and proportion form:
AB / CB = DE / CE
x / 5 = (18 - x) / 25
5x = 18 - x
6x = 18
x = 3

Q #7 please solve the equation

Answers

The relation between a and s is given to be:

a = 640s

where,

a = number of acres
s = number of square miles

We are to find the number of acres for 7.5 square miles.

This means, s = 7.5

Using the value in the formula, we get:

a = 640 x 7.5 = 4800 acres

So the answer to this question is option B

The figure is made up of a cylinder and a half sphere. What is the volume of the composite figure? Round to the nearest hundredth.
radius: 4mm
cylinder length: 7mm

Answers

we know that
[volume of the composite figure]=volume of cylinder + volume hemisphere

volume cylinder=pi*r²*h
r=4 mm
h=7 mm
volume cylinder=pi*4²*7----> 351.68 mm³

volume of hemisphere=(4/6)*pi*r³
r=4 mm
volume of hemisphere=(4/6)*pi*4³----> 133.97 mm³

[volume of the composite figure]=351.68+133.97----> 485.65 mm³

5 ln ( x + 8 ) solve the equation for x

Answers

You have not given an equation.

If we make it an equation, then we can solve for x.
a = 5*ln(x +8)
a/5 = ln(x +8) . . . . . . . divide by 5
e^(a/5) = x +8 . . . . . . take the antilog
e^(a/5) -8 = x . . . . . . . subtract 8

If your expression is equal to "a", then x is ...
x = e^(a/5) -8

How do I find the hypotenuse of a triangle when given 90 degrees and one side length?

Answers

You need one more fact either an angle or a side in order to be able to answer. I take it you have neither. But there must be something more you can tell us from the question. List the question exactly as it is asked with a diagram if necessary. I'll follow and use either comments or I'll edit.

The direct answer to your question is that you can't.

Please help me with this.

Answers

[tex] a_{n} = +(n-1)d [/tex]

We are given the first term and the common difference.

So,

[tex]a_{1}=-10 \\ \\ d=5[/tex]

Using these values in the given equation, we get:

[tex] a_{n} =-10+(n-1)*5 \\ \\ a_{n} = -10 + 5n - 5 \\ \\ a_{n} = 5n -15[/tex]

So, option C gives the correct answer.

A 4-foot tall person standing with her back to the sun casts an 6-foot long shadow.

To the nearest degree, what angle does the sun make with the ground?

Answers

For this case we have the following trigonometric relationship:
Tan (x) = (4/6)
Clearing the angle we have:
x = Atan (4/6)
x = 33.69006753
Rounding off we have:
x = 34 degrees
Answer:
The angle that sun makes with the ground is:
x = 34 degrees

Determine whether the series is convergent or divergent by expressing sn as a telescoping sum. ∞ 4 n(n + 2) n = 1

Answers

Nothing more can be done to this equation as far as I know

∞ 4n(n +2)n = 1

write 3.6 as a mixed number in the simplest form

Answers

3.6 = 3 3/5

(sorry if it's wrong)

3 60/100 is 3.6 as a mixed number.

What is the factorization of the polynomial below x^2-3x-40

Answers

(x - 8)(x + 5)
________

solve the system using the substituion method
-4x+y=8
x-3y=9

Answers

Hi there!

x - 3y = 9
x = 9 + 3y

-4x + y = 8
-4(9+3y) + y = 8
-36 - 12y + y = 8
-36 - 11y = 8
-11y = 44
-y = 4
y = -4

x - 3y = 9
x - 3(-4) = 9
x + 12 = 9
x = 21

So, your answers are y = -4 and x = 21.

Hope this helps!

enter the ordered pair that is the solution to the system of equations graphed below please :]

Answers

Hello!

Since (1, -2) is the point of intersection, then it is the solution to the system of equations. Let's test our answer to see if it's correct:

[tex]-2 = -4(1) + 2 -2 = -4 + 2 -2 = -2[/tex]

But that's only for the first one, let's test for the second one:

[tex]-2 = 1 - 3 -2 = -2[/tex]

This is how we know that (1, -2) is the solution to the system of equations. Hope I helped! :3

Alice makes 8 bracelets. there are 4 red beads on each bracelets. witch number sentence shows the total number of beads used?

Answers

not sure what you mean by # sentence
But 8 bracelets times 4 red beads equals 32 beads in total
8 * 4 = 32

the correct answer is 32

what is the value of the expression 8.5 - 10.2 + -7.4

Answers

First, subtract 10.2 from 8.5
8.5 - 10.2 = -1.7
Next, add -7.4 to -1.7
-7.4 (+) - 1.7 = -9.1
Your final answer is -9.1

Answer: −9.1

Step-by-step explanation:

8.5−10.2−7.4

=−1.7−7.4

=−9.1

PLEASE MARK BRAINLIEST

Simplify 1 · 0 - 0/y

Answers

The product of any number and 0 is zero. The expression is 1*0-0/y. 1*0 is obviously 0. 0/y is the same thing as 0 * 1/y, which is also zero. 0-0 is 0, so the answer is 0.

hello can you please help me posted picture of question

Answers

The answer is Letter C - 1/2,775

The probability of choosing one of them is 2 out of 75 while the probability of choosing the other one is 1 out of 74. 74 band members, not counting the other person (you or your bother).

Computation:
P = 2 / 75 * 1 / 74
= 0.0266... * 0.01351...
= 1 / 2,775
You can also multiply 75 with 74 to get a total of 5,550 then divide it by 2 students to be selected to get 2,775. Meaning one out of 2,775 possibilities.

The half-life of cobalt-60 is 5.20 yr. how many milligrams of a 2.000-mg sample remains after 6.55 years?

Answers

Answer:

0.835 mg of a 2.000-mg sample remains after 6.55 years.

Step-by-step explanation:

We are given that The half-life of cobalt-60 is 5.20 yr.

Formula of half life : [tex]N(t) = N(0)e^{\frac{-0.693t}{t\frac{1}{2}}}[/tex]

Where N(0) = Initial amount

N(t) = Quantity remaining after time

t = time

[tex]\frac{t}{2} =\text{half life}[/tex]

So, N(0) = Initial amount = 2 mg

t = time = 6.55 years

[tex]\frac{t}{2} =\text{half life} = 5.20 yr [/tex]

Substitute the values in the formula

Therefore,

[tex]N(t) = 2 e^{\frac{-0.693 \times 6.55}{5.20}}[/tex]

[tex]N(t) =0.835[/tex]

Hence 0.835 mg of a 2.000-mg sample remains after 6.55 years.

please show all possible solution by graphing a linear inequality

Answers

We have the following variables:
x = the number of adult tickets
y = the number of children's tickets
We write the inequality:
8x + 6y <= 172
The solution is the set of points that belong to the region shaded in the graph.
Answer:
8x + 6y <= 172
see attached image.

In order to answer your question, first we need to discover the following variables:
x = the number of adult tickets
y = the number of children's tickets

Then write the inequality:
8x + 6y <= 172
Answer:
8x + 6y <= 172 so the solutions of this equation are those who are in the shaded part of the graph.

The ratio of a model car to the size of an actual car is 1:40. If the model is 4.5 inches long, what is the length of the full size car in inches and in feet?

Answers

4.5x40=
4x40=180
.5x40=20
180+20=200

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