A system of inequalities is graphed below. The variable x represents the number of cans someone is buying, and y represents the number of bottles. Conditions on the maximum amount of total weight and volume lead to two of the inequalities.
Which descriptions correspond to solutions of this system?
7 cans and 140 bottles
12 cans and 40 bottles
8 cans and 120 bottles
9 cans and 70 bottles

Answers

Answer 1

we have that
We will analyze each case to verify the answer
see the attached figure

Point A) 7 cans and 140 bottles------------> (x,y)=(7,140)----> is not solution
Point B) 12 cans and 40 bottles------------> (x,y)=(12,40)----> is not solution
Point C) 8 cans and 120 bottles------------> (x,y)=(8,120)----> is a solution
Point D) 9 cans and 70 bottles------------> (x,y)=(9,70)-------> is a solution

the answer is
the solutions are
8 cans and 120 bottles
9 cans and 70 bottles

Related Questions

A. 11 cm^3
B. 14 cm^3
C. 15 cm^3
D. 25 cm^3

Answers

Lets get started :)

We need to find the radius of the larger cylinder

V = [tex] \pi [/tex]r²h
960 = [tex] \pi [/tex]r²(16)
[tex] \frac{960}{16} = \pi r^2[/tex]
60 = [tex] \pi r^2[/tex]
[tex] \frac{60}{ \pi } = r^2 [/tex]
r = [tex] \sqrt{ \frac{60}{ \pi } } [/tex]
r ≈ 4.27 cm

The ratio of the bigger cylinder to smaller is:
16 : 4

Therefore, the big cylinder is 4 times bigger than the small cylinder

[tex] \frac{4.37}{4} [/tex] = r
r = 1.09 cm (radius of small cyclinder)

V (small cylinder) = [tex] \pi [/tex](1.09)²(4)
= 15 cm³

Your answer will be C. 15 cm³

the volume of a cylinder= height * base area
while the base area = [tex] \pi r^{2}[/tex]
since the two cylinders are similar then the ratio between the two radii= the ratio between the two heights =16/4 =4
then the volume of the large cylinder with respect to the smaller dimensions= [tex] \pi * (4r)^{2} *(4*4)=(\pi r^{2} *4)*4*16[/tex]
but [tex] the volume of the smaller one = \pi r^{2} *4[/tex]
then the volume of the large cylinder = the volume of the smaller cylinder*4*16=960
then the smaller's volume= [tex] \frac{960}{4*16}=15[/tex]

Which value(s) of x would result in Set B being a function of the values in Set A? Select Function or Not a Function for each value of x. Are the following numbers a function or not a function

Answers

To determine if Set B is a function of the values in Set A, we need to ensure that each value of x in Set A has only one corresponding value in Set B:

-2: Function5: Function0: Not a Function1: Function-3: Function

For each value of x, we can determine if Set B is a function or not by checking if there is only one corresponding value in Set B.

For x = -2, there is only one corresponding value in Set B, so it is a function.

For x = 5, there is only one corresponding value in Set B, so it is a function.

For x = 0, there are multiple corresponding values in Set B, so it is not a function.

For x = 1, there is only one corresponding value in Set B, so it is a function.

For x = -3, there is only one corresponding value in Set B, so it is a function.

Therefore, Set B is a function of the values in Set A for all values of x except for x = 0.

The slope of the line whose equation is x+2y=3 is

Answers

See picture for answer.

Let m = slope in the picture.

A key difference between calculating the sample mean and the population mean is that:
a.we use and n instead of µ and n.
b.we divide the sum of the observations by n - 1 instead of n.
c.the sample observations are ranked and the middle value is selected as the population mean.
d.there are no differences.

Answers

Final answer:

The key difference between calculating the sample mean and the population mean is that when calculating the sample mean, we use x and n instead of µ and n. Additionally, we divide the sum of the observations by n - 1 instead of n. Correct Option -B

Explanation:

The reason for dividing by n - 1 in the sample mean calculation is that it provides a better estimate of the population variance. Dividing by n - 1 instead of n accounts for the fact that the sample mean is an estimate of the population mean based on a limited set of data.

PLEASE HELP ASAP! BRAINLIEST TO BEST/RIGHT ANSWER

Answers

the CORRECT answer is B because the person got it wrong saying A

Please HELP.. MEDAL/ FAN
The ages of students in a school are normally distributed with a mean of 15 years and a standard deviation of 2 years. Approximately what percent of the students are between 14 and 18 years old?
24.17%
62.47%
30.85%
93.32%,

Answers

The percentage of the students are between 14 and 18 years old is 62.47% .
So the solution for this is that P(students between 14 and 18 years) = 0.9332 - 0.3085 = 0.6247.
To get the percentage, just multiply it by 100 and you will get the answer.

To solve a problem, we often _________ the given information into algebraic expressions and equations.

Example: The phrase "4 more than twice a number" becomes '2n + 4'.,

Answers

To solve a problem, we often transform the given information into algebraic expressions and equations. Example: The phrase "4 more than twice a number" become "2n + 4". Another example can be : " 6 more than a quarter of a number" become " 6 + 1/4n". The number is usually expressed by letter "x".

Answer:

Translate or transform

Step-by-step explanation:

Took the test (USA test prep)

A circular pool is surrounded by a circular walkway. The radius of the pool is y − 4 and the radius of the full circle formed by the walkway is y + 4. Write a polynomial that represents the area of just the walkway itself, not including the space covered by the pool. (The area of a circle is given by A = πr ^2, where r represents the radius of the circle.)

Answers

Final answer:

The polynomial representing the area of the walkway is the difference between the area of the large circle (π(y + 4)²) and the small circle (π(y − 4)²).

Explanation:

To find the polynomial that represents the area of the walkway surrounding a circular pool, we need to calculate the difference between the area of the larger circle (walkway plus pool) and the area of the smaller circle (just the pool).

The radius of the pool is y − 4, and the radius of the walkway plus the pool is y + 4. The area of a circle is given by A = πr².

First, calculate the area of the large circle:

Area of the large circle = π(y + 4)²

Then, calculate the area of the small circle:

Area of the small circle = π(y − 4)²

Finally, the polynomial for the area of the walkway is found by subtracting the area of the small circle from the area of the large circle:

Area of the walkway = π(y + 4)² − π(y − 4)²

Final answer:

The polynomial that represents the area of just the walkway (not including the pool) is π(8y + 32).

Explanation:

To find the area of just the walkway, we need to subtract the area of the pool from the area of the full circle formed by the walkway. The area of the pool is given by A = πr ^2, where r is the radius of the pool (y - 4). The area of the full circle is given by A = πr ^2, where r is the radius of the walkway (y + 4). Therefore, the area of the walkway is (π(y + 4) ^2) - (π(y - 4) ^2). Simplifying this expression, we get the polynomial: π(8y + 32).

a building in san francisco is shaped like a square pyramid it has a slant height og 856.1 feet and each side of its base is 145 feel long find the lateral area of the building

Answers

we know that

for a Square Pyramid
[lateral area]=4*[a*s/2]--------> 2aS
where
a is the length side of the square base
S is the slant height
a=145 ft
S=856.1 ft
[lateral area]=2*145*856.1---------> 248269 ft²

the answer is 248269 ft²

What is 8.3x10^-9 in standard form?

Answers

.0000000083

( eight zeros.)

What is the value of x in the figure below? In this diagram, ΔABD ~ ΔCAD

Answers

x/10 = 10 / 16
16x = 100
x = 100/16
x = 25/4

answer is F. 25/4

Value of x for the similar triangles ΔABD ~ ΔCAD is equals to [tex]\frac{25}{4}[/tex].

What are similar triangles?

" Similar triangles are defined as the triangles with same shape but different in their size, corresponding sides of similar triangles are always in proportion."

According to the question,

As per the diagram,

ΔABD and ΔCAD are similar triangles.

AB = 10 units

BD = x units

BC = 16 units

CD = BC - BD

= 16 - x

ΔABD is a right angle triangle.

Therefore,

Using Pythagoras theorem,

[tex]AD ^{2} = 10^{2} -x^{2}[/tex]

ΔABD corresponding ΔCAD as per the given diagram.

From the definition of similar triangles corresponding sides are in proportion.

[tex]\frac{AD}{CD} =\frac{BD}{AD}[/tex]

⇒[tex]AD^{2} =(BD )(CD)[/tex]

Substitute the value of AD, BD and CD we get,

[tex]10^{2} -x^{2} = (x) (16-x)[/tex]

⇒[tex]100 -x^{2} =16x-x^{2}[/tex]

⇒[tex]100 = 16x[/tex]

⇒[tex]x= \frac{100}{16}[/tex]

⇒[tex]x=\frac{25}{4}[/tex]

Hence, Option(F) is the correct answer.

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Jamie has 4 apples and 6 bananas. Each apple cost 0.75 and each banana cost 0.6” write an expression representing the total cost

Answers

(0.75*4) + (0.6*6) = 6.6

answer: 6.6

Hello!

4 x 0.75 + 6 x 0.6 = 6.6

Enjoy.
~Isabella

How to solve
187=1/2*17(6+X)

Answers

The answer to 187=1/2*17(6+X) is X=16

Two numbers are in the ratio of 2 to 3. If the smaller number is 18, the larger number is _____. 21 27 36 54

Answers

x*3/2 - it's the larger one. The smaller number is 18. => the larger number is 18*3/2=27

the answer is 27

Answer: If two numbers are in a ratio of 2 to 3, this means that two times one number is equal to 3 times the other, or:

2*X = 3*Y, where X and Y are any numbers, and X is the bigger one and Y is the smaller one.

If Y=18, then:

2*X = 3*18 = 54

X=54/2 = 27

So the answer is 27.

find the second, fourth, and eleventh terms of the sequence described by each explicit formula A(n)=2+(n-1)(-2.5)

Answers

Given that the explicit formula is given by:
A(n)=2+(n-1)(-2.5)
where n is the number of terms
To get the terms required we simply substitute our values on the expression
the 2nd term will be:
A(2)=2+(2-1)(-2.5)
A(2)=2+1(-2.5)
A(2)=-0.5

the fourth term will be:
A(4)=2+(4-1)(-2.5)
A(4)=2+3(-2.5)
A(4)=2-7.5
A(4)=-5.5

the eleventh term will be:
A(11)=2+(11-1)(-2.5)
A(11)=2+10(-2.5)
A(11)=2-25
A(11)=-23

Time 6 years Interest rate 1.9% Principal- $850 What amount of simple interest will be earned? $16.15 O $96.90 $946.90 $9,690.00

Answers

Amount of simple interest will be earned is $96.90

Choose the correct discount or markup. If an item has a retail price retail price = $995 and a discount of 15%, how much is the discount? It is $ options a. 149.25 b. 139.25 c. 144.50

Answers

To find the discount, simply multiply $995 times .15 (which is the decimal equivalent of 15%). 995 x .15 = 149.25
So the correct answer is (a). 149.25

Final answer:

The discount amount on an item with a retail price of $995 and a 15% discount is $149.25 that is option a is correct answer.

Explanation:

Discount Amount Calculation:

Calculate the discount amount by multiplying the retail price by the discount percentage.

Discount = $995 x 0.15 = $149.25.

The correct answer is $149.25 (option a).

Find the derivative of f(x) = |x2 – 1| at the point (1, 0).

Answers

[tex]\bf \stackrel{f(x)}{y}=|x^2-1|\implies y=\sqrt{(x^2-1)^2}\implies y=[(x^2-1)^2]^{\frac{1}{2}} \\\\\\ \cfrac{dy}{dx}=\stackrel{chain~rule}{\cfrac{1}{2}[(x^2-1)^2]^{-\frac{1}{2}}\cdot 2x}\implies \cfrac{dy}{dx}=x[(x^2-1)^2]^{-\frac{1}{2}} \\\\\\ \cfrac{dy}{dx}=\cfrac{x}{[(x^2-1)^2]^{\frac{1}{2}}}\implies \cfrac{dy}{dx}=\cfrac{x}{\sqrt{(x^2-1)^2}} \\\\\\ \left. \cfrac{dy}{dx}=\cfrac{x}{|x^2-1|} \right|_{x=1}\implies \cfrac{1}{|1-1|}\implies \cfrac{1}{0}\implies und efined[/tex]

meaning, the function is not differentiable at x = 1, graph wise, it simply means is not a "smooth curve", instead is an abrupt edge, or a "cusp" or a "spike", so the graph may be continuous at x = 1, however, is the extremum is not a smooth curve, notice the picture below.

Jill had an AGI of $25,000. She had $2800 in medical expenses, paid $6000 in rent, and had to buy a new uniform for work, which was not reimbursed by her employer. Which expense(s) can she itemize on her tax return?

A.Nonreimbursed work expenses, mortgage interest, and medical expenses
B.Mortgage interest and medical expenses
C.Medical expenses and nonreimbursed work expenses.
D.Mortgage interest only

Answers

Answer:

C.Medical expenses and nonreimbursed work expenses.

Step-by-step explanation:

just did it on apex

Answer:

Step-by-step explanation:

Medical expenses and nonreimbursed work expenses.

evaluate the principal square root of 36 .
answer ??? help plz thank u :)),

Answers

The principal square root of a number is the positive square root of that number √36 can be +6 or -6 But the positive square root is +6 and that is the principal square root.

Which high school math course, algebra or geometry, is more closely related to engineering? justify your answer?

Answers

First we will define both courses:
Algebra: is the name that identifies a branch of Mathematics that uses numbers, letters and signs to be able to refer to multiple arithmetic operations.
Geometry: Part of the mathematics that studies the extension, the way of measuring it, the relationships between points, lines, angles, planes and figures, and the way they are measured.

For the study of engineering requires extensive knowledge in different fields of mathematics. However, as the engineer must handle an endless number of equations, more knowledge in algebra is more important.
Answer:Algebra.

Final answer:

Both algebra and geometry are integral to engineering, with algebra being more directly related to the numerical problem-solving aspects, and geometry being crucial for spatial understanding and design. A well-rounded engineering education incorporates both, to prepare students for advanced mathematical concepts and engineering science courses.

Explanation:

Both algebra and geometry are closely related to engineering, but they serve different purposes within the field. Algebra is fundamental for problem-solving and numerical analysis in engineering. It allows for the creation of mathematical models that can describe physical processes, and is often used alongside computer programs to solve complex real-life problems. Geometry, on the other hand, is essential for a thorough understanding of spatial relationships and structures, which are critical in fields such as mechanical, civil, and architectural engineering.

A prism with a volume of 3125 ft³ is scaled down to a volume of 200 ft³.

What is the scale factor?
Enter your answer, as a decimal or a fraction in simplest form, in the box.

I think it's 2/5 or 0.4

Answers

the right answer is 2/5

Answer:

The scale factor is equal to [tex]0.4[/tex] or [tex]\frac{2}{5}[/tex]

Step-by-step explanation:

we know that

If two figures are similar. then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z------> the scale factor

x------> the volume of the dilated prism

y------> the volume of the original prism

[tex]z^{3}=\frac{x}{y}[/tex]

we have

[tex]x=200\ ft^{3}[/tex]

[tex]y=3,125\ ft^{3}[/tex]

substitute

[tex]z^{3}=\frac{200}{3,125}[/tex]

[tex]z=\sqrt[3]{\frac{200}{3,125}}[/tex]

[tex]z=0.4[/tex] or [tex]z=\frac{2}{5}[/tex]

I need both answers now!

Answers

Part A:
Answer Is (B)

Part B:
Answers are: (C and E)

Hope this helps.

Find the length of a line segment with endpoints of -9 and 7.
I don't understand how to do this.

A.-16
B.-2
C.16
D.26,

Answers

If you imagine a straight line, with -9 all the way on the left, then mark along the line in one number increments until you get up to 7, you will find that in total the line is 16 segments in total. Mathematically, this is a question of absolute value, ie absolute value of -9 = +9, and therefore 9 + 7=16.

PLEASE HELP ASAP!! WILL GIVE BRAINLIEST

Answers

I believe that it is D, so sorry if it's wrong, I haven't done this in a while.

i think you should have studied because it's real easy

And it's obvious that it's d

Which of the following is equal to (2x/3 - 7) + 7

A. (2x - 7) + 21

B. 2x - 21/3

C. 3x/2

D. 2x/3

@texaschic101

Answers

Which of the following is equal to: (2x/3 - 7) + 7
The order of the mathematical operations is PEMDAS.
Therefor the first step you will take is to solve the operation inside the parenthesis.
(2x/3 - 7) =(2x/3 - 7)* 3/3 = 2x/3 - 21/3 = (2x - 21)/3
While adding or subtracting fractions, dont forget to check that each term have the same denominator.

Then the operation outside the parenthesis,

(2x - 21)/3 + 7 = (2x-21)/3 + 7 * 3/3 = (2x - 21)/3 + 21/3 =

(2x - 21 + 21) / 3 = 2x/3

The final answer is D. 2x/3

The correct answer is D. The number 7 is subtracted from the first term, 2x/3, but then an equal sum is added, and the two effectively cancel each other out. This means that the value of the first expression is essentially 2x/3, which is option D.

6.
Evaluate cot 290º. Round your answer to the nearest hundredth.

–1.06
–0.36
2.92
–2.75,

Answers

The answer to your question is -0.36

The solution this is the following:
cot(110°) = -cot(70°)
cot(70°) = -1/tan(70°)
tan(70°) ≈ 2.75
-1/tan(70°) ≈ -0.36

You are standing 40 feet away from a building that is 115 feet tall. What is the angle from the ground to the top of the building to the nearest degree?

Answers

whats the answer? i got 0.348??

The number of members f(x) in a local swimming club increased by 30% every year over a period of x years. The function below shows the relationship between f(x) and x:

f(x) = 10(1.3)x

Which of the following graphs best represents the function?

Graph of f of x equals 1.3 multiplied by 10 to the power of x
Graph of exponential function going up from left to right in quadrant 1 through the point 0, 0 and continuing towards infinity
Graph of f of x equals 10 multiplied by 1.3 to the power of x
Graph of f of x equals 1.3 to the power of x

Answers

3rd one.

f(x) = 10(1.3)^x

Answer:

The graphs that best represents the function is:

Graph of f(x) equals 10 multiplied by 1.3 to the power of x.

Step-by-step explanation:

The function that shows the relationship between f(x) and x: is:

[tex]f(x)=10\times (1.3)^x[/tex]

Graph of f(x) equals 1.3 multiplied by 10 to the power of x.

This means that the expression is given by:

[tex]f(x)=1.3\times (10)^x[/tex]

Hence, option: a is incorrect since it is not equal to the given function f(x).

Graph of exponential function going up from left to right in quadrant 1 through the point (0, 0) and continuing towards infinity.

In the given function f(x) when x=0 we have:

[tex]f(x)=10\times (1.3)^0\\\\\\f(x)=10\neq 0[/tex]

Hence, option: b is incorrect.

Graph of f(x) equals 10 multiplied by 1.3 to the power of x.

This means that the function f(x) is given by:

[tex]f(x)=10\times (1.3)^x[/tex]

which is obviously true.

Hence, option: c is correct.

Graph of (x) equals 1.3 to the power of x.

This means that the function f(x) is given by:

[tex]f(x)=(1.3)^x[/tex]

which does not m,atches the actual expression.

Hence, option: d is incorrect.

A trinket factory can produce 3,000 trinkets per day. The warehouse has a capacity of 50,000 trinkets. Currently, there are 8,000 trinkets in the warehouse. Assume that no trinkets are going to be shipped out of the warehouse for a while. 1) Write an equation for the number of trinkets in the warehouse after days. 2) How many days will it take to fill the warehouse?

Answers

An equation for the number of trinkets in the warehouse after x days:
8,000 + 3,000x = 50,000

How many days will it take to fill the warehouse?

8,000 + 3,000x = 50,000
3,000x = 42,000
x = 14

The equation for number of trinkets after x days is 8,000 + 3000 * x = y and the number of days required to fill the warehouse is 14.

What is an Equation?

An equation is a mathematical statement that is formed when two algebraic expressions are equated using an equal sign.

The trinket factory can produce 3,000 trinkets per day

Total Capacity of warehouse is 50,000 trinkets

The trinkets in the warehouse is 8,000

The equation for the number of trinkets in the warehouse after x days is

Let y represents the total number of trinkets after x days

8,000 + 3000 * x = y

The days required to completely fill the warehouse is

8,000 + 3,000 * x = 50,000

3,000* x = 42,000

x = 14

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