A cardboard box in the shape of a rectangular prism has the
dimensions shown.
a. Write a polynomial that represents the volume of the box.
b. The volume of the box is 60 cubic inches. What are the
length, width, and height of the box?

The two plans cost the same for 60 minutes of calls. And  the two plans cost the same for 60 minutes of calls.

We can set the cost of the two plans equal to each other and solve for the number of minutes:

Plan A: $15 + $0.12x (where x is the number of minutes)

Plan B: $8 + $0.17x

$15 + $0.12x = $8 + $0.17x

Subtracting $8 from both sides:

$7 + $0.12x = $0.17x

Subtracting $0.12x from both sides:

$7 = -0.05x + $0.17x

Adding 0.05x to both sides:

$7 + 0.05x = $0.17x

Dividing both sides by 0.12:

x = (7 / 0.12) / (1 - 0.17/0.12) = 60 minutes

So the two plans cost the same for 60 minutes of calls. To find the cost, we can plug x = 60 into either equation:

Plan A: $15 + $0.12 x 60 = $15 + $7.20 = $22.20

Plan B: $8 + $0.17 x 60 = $8 + $10.20 = $18.20

So the two plans cost the same when there are 60 minutes of calls, and they both cost $18.20

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Complete Question

A telephone company offers two monthly plans. The a plan costs $15 plus $0. 12 additional for each minute of calls. Plan b costs $8 plus an additional 0.17 for each minute of calls For how many minutes of calls do the two plans cost the same? What is the cost at which two plans cost the same?

Answer:

Step-by-step explanation:

o solve the compound inequality, we'll start by solving each inequality separately, and then find the intersection of their solutions.

For the first inequality: 8r - 3 ≥ 7r - 7

Adding 7r to both sides: 8r - 3 + 7r ≥ 7r - 7 + 7r

Combining like terms: 15r - 3 ≥ 14r

Subtracting 14r from both sides: 15r - 14r - 3 ≥ 0

Combining like terms: r - 3 ≥ 0

Adding 3 to both sides: r ≥ 3

For the second inequality: 2r + 4 ≤ r - 3

Subtracting 2r from both sides: 2r + 4 - 2r ≤ r - 3 - 2r

Combining like terms: 4 ≤ -r - 3

Adding r and 3 to both sides: 4 + r + 3 ≤ -r

Combining like terms: 7 ≤ -r

Multiplying both sides by -1: r ≤ -7

The solution to the compound inequality is the intersection of the solutions to each inequality, which is the range of r that satisfies both conditions. So, the solution is 3 ≤ r ≤ -7.

To graph the solution, we can plot the two inequalities on the number line, and shade the region between 3 and -7:

Due to the fact that secured loans often have lower interest rates than unsecured loans, they are less expensive. They require collateral. They are less risky for the financial institution. The correct option is D.

A secured loan is one in which the borrower pledges an asset as security for the loan, turning the pledged asset into a secured debt owing to the lender (the creditor).

Some loans may be backed by assets other than your house; for instance, they may be backed by your automobile, jewelry, or other possessions. Because lenders can collect the asset in the event of a default on a secured loan, secured loans often have lower interest rates than unsecured loans.

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Answer:

Step-by-step explanation:d = 14t + 21t = 35t

So, after 3 hours, the distance between the boats will be:

d = 35 * 3 = 105 miles

Therefore, the Serenity and the Mystic will be 105 miles apart after traveling for 3 hours.

Answer:

Step-by-step explanation:

no idea sorry :/

The length of the altitude CH is 17.234.

Altitude of a triangle is defined as the perpendicular line segment joining the vertex to the opposite side.

The figure for the triangle is given below.

Here the area of a triangle can be found in two ways.

Area of a triangle = [tex]\frac{1}{2}[/tex] × base × height

Consider the triangle ABC given below.

Area of the triangle when considered base as BC and altitude as AC is,

Area, A = [tex]\frac{1}{2}[/tex] × BC × AC

BC = AB Sin (50) = 35 sin(50)

AC = AB Sin (40) = 35 sin(40)

A = [tex]\frac{1}{2}[/tex] × (35 sin(50)) × (35 sin(40))

Area of the triangle when considered base as AB and altitude as CH is,

Area, A = [tex]\frac{1}{2}[/tex] × AB × CH

A = [tex]\frac{1}{2}[/tex] × 35 × CH  

Area of the same triangle will be equal when find in different ways.

[tex]\frac{1}{2}[/tex] × (35 sin(50)) × (35 sin(40)) = [tex]\frac{1}{2}[/tex] × 35 × CH  

Cancelling the terms which are on both sides,

CH = 35 sin(50) sin(40)

CH = 35 × 0.766 × 0.643

CH = 17.234

Hence the length of the altitude is 17.234.

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The value of the function expression evaluation; f (x) + g (x) - h (x) as required is; 3x² + 6x + 2.

It follows from the task content that the expression which represents f (x) + g (x) - h (x) be determined.

Since;

F(x) = 3x + 5

G(x) = 4x² - 2

H(x) = x² - 3x + 1

Therefore,

f (x) + g (x) - h (x) = 3x + 5 + 4x² - 2 - (x² -3x + 1)

= 3x² + 6x + 2

Ultimately, the value of f (x) + g (x) - h (x) is; 3x² + 6x + 2.

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The value of the given function f(4 + h) - f(4) is 5h(x)² + 40h(x)

A function is a mathematical concept that maps a set of inputs to a set of outputs with a definite rule. In mathematics, a function is a set of ordered pairs (input, output) where each input is associated with exactly one output. The input is usually referred to as the argument of the function and the output is the value of the function at that argument.

f(x) = 5x²

f(4 + h) - f(4)

f(4 + h(x)) = 5(4 + h(x))²

f(4) = 80

Substituting the values into each other;

5(4+h(x))² - 80

f(4 + h) - f(4) = 5h(x)² + 40h(x)

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a. The amount of copper in a bronze brooch weighing 360g is 216g.

b. The total weight of the bronze brooch is 745g.

If an item is made of two different items, the ratio of the quantities of those two items contributes to the amount of the compound item. With the help of that ratio, the unknown quantity can be determined.

a.

The ratio of copper to tin in bronze is 9:1.

So, the portion of copper in the bronze is 9 out of 10, that is, 0.9.

The total weight of the bronze brooch is 360g.

Find the amount of copper in that brooch.

360×0.9=324

Therefore, the copper in a 360g bronze brooch is 324g.

b.

The amount of copper in the bronze brooch is 670.5g.

Also, the portion of copper in the bronze is 0.9.

Let, the total weight of the bronze brooch is Xg.

So, the equation becomes 0.9X=670.5.

Find the value of X.

0.9X=670.5

X=745

Therefore, the total weight of the bronze brooch is 745g.

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Answer:

y = 3x + 10

Step-by-step explanation:

slope intercept form​ is y = mx + b

y - 4 = 3(x+2)

y - 4 = 3x + 6

y = 3x + 10

So, the answer is y = 3x + 10

The coordinates of vertex D of the parallelogram is; (0, 1)

We are given the coordinates of the parallelogram as;

A(2,4), B(5,2) and C(3,-1)

Now, we know that the diagonals of a parallelogram bisect each other. So, the midpoint of AC is same as the mid point of BD.

The formula for the midpoint between two coordinates is;

(x1 + x2)/2, (y1 + y2)/2

Thus;

Midpoint of AC = (2 + 3)/2, (4 - 1)/2 = 5/2, 3/2

Midpoint of BD = (5 + x)/2, (2 + y)/2

Thus;

(5 + x)/2 = 5/2

x = 0

(2 + y)/2 = 3/2

2 + y = 3

y = 1

Coordinate of D = (0, 1)

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The angle that VSR would correspond to, given that polygon ABCDE is congruent to polygon TVSRK, is 2. Angle C.

When polygons are said to be congruent, then it means that their sides are the same lengths, and they have the same angles which means that they are corresponding.

This therefore means that the angle at A in polygon ABCDE would be congruent to the angle at T in TVSRK.

This therefore means that the angle VSR would correspond to the angle C in ABCDE because S is the third letter in TVSRK and C is the third letter in ABCDE.

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The full question is:

Polygon ABCDE is congruent to polygon TVSRK. what do angle VSR correspond to _____?

1. Angle B

2. Angle C

3. Angle D

4. Angle A

The experimental probability that the number rolled was odd is

23 over 60.

What is experimental probability?

Actual experiments and sufficient documentation of the occurrence of occurrences serve as the foundation for experimental probability, sometimes referred to as empirical probability. A trial is a repeating of an experiment that is performed a certain number of times.

We are given a table showing he frequency of each number rolled.

We know that the odd number outcomes are 1, 3 and 5.

So,

P (x = 1) = 8/60

P (x = 3) = 6/60

P (x = 5) = 9/60

So, the experimental probability that the number rolled was odd is

⇒P ( x is odd) = P (x = 1) + P (x = 3) + P (x = 5)

⇒P ( x is odd) = 8/60 + 6/60 + 9/60

⇒P ( x is odd) = 23/60

Hence, the experimental probability that the number rolled was odd is 23 over 60.

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The equation 5x + 6y = 4, 10x + 12y = 8 has infinitely many solution.

System of equation can be solved using elimination method, substitution method and graphical method.

Therefore, let's solve the system of equation using elimination method.

5x + 6y = 4

10x + 12y = 8

multiply equation(i) by 2

Hence,

10x + 12y = 8

10x + 12y = 8

subtract the equations

0 = 0

Therefore, the equation has infinitely many solution.

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a) The percentage of flashlights that have a life of 55 to 65 is about 36%

b) The percentage of the batteries that have a life of 52 to 68 hours is about 75%.

Standard normal distribution is a type of continuous distribution with a mean of zero and standard deviation of one. The random variables are standardized into z scores using z score formula.

a) The Chebyshev's theorem states that; for sample or population, percentage (p) of values are contained within two, three or more standard deviations within the mean, provided that the values of k is greater than 1:

P(%) = [tex]1-\frac{1}{k^2}[/tex]

Calculate the value of k:

[tex]k =\frac{65-60}{4}=1.25[/tex]

The percentage is calculated as;

p(%) = [tex]1-\frac{1}{1.25^2}[/tex] = 36%

The percentage of flashlights that have a life of 55 to 65 is about 36%

b) k = [tex]\frac{68-60}{4}=2[/tex]

p(%) = [tex]1-\frac{1}{2^2}[/tex] = 75%

The percentage of the batteries that have a life of 52 to 68 hours is about 75%.

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0.21, 0.21, 0.22, 0.22 is the sequence from least to greatest.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

0.22, 21%, 0.21, 0.22

Now,

21% = 21/100 = 0.21

So,

0.22, 0.21, 0.21, 0.22

Arranging from least to greatest.

0.21, 0.21, 0.22, 0.22

Thus,

0.21, 0.21, 0.22, 0.22 is the sequence from least to greatest.

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Side a is 2.5 inches long, side b is 5 inches long and side c is 6.5 inches long. Therefore, option C is the correct answer.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

Given that, scale factor =2:1

Scale drawing to object the scale factor is 2:1.

Now,

a=1/2 *5 =2.5 inches

b= 1/2 *10 = 5 inches

c= 1/2 * 13 = 6.5 inches

Therefore, option C is the correct answer.

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In a case whereby three numbers are in the ratio 2:3:5 and the sum of their cube is 34560 then the numbers are  12, 18, and 30.

The given Ratio of three numbers can be expressed as 2:3:5

Then we can represent the three numbers  as: 2x, 3x, and 5x.

We were given the Sum of their cubes as  34560

Thern we can cube them as 2x^3 + 3x^3 + 5x^3 =34560

The we will have 8x^3 + 27x^3 + 125x^3 =34560

Then we have 160x^3 = 34560

x^3 =34560/160

x= 6.

then we can find the values of the ratio as :

2x =( 2×6)

= 12

3x = (3×6 )

= 18

5x = (5×6 )

= 30

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The solution is Option E.

The solution to the system of equations is the point of intersection of line and the lines intersect at the point A ( 3 , 2 )

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( -3 , -4 )

Let the second point be Q ( 7 , 6 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope m = 10 / 10 = 1

Now , the equation of line is y - y₁ = m ( x - x₁ )

y - 6 = 1 ( x - 7 )

y - 6 = x - 7

y = x - 1   be equation (1)

Now , the point of intersection of lines is at ( 3 , 2 )

Substitute the value of x and y in the equation , we get

when x = 3 , y = 2

2 = 3 - 1

2 = 2

Hence , the solution to the equation is ( 3 , 2 )

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The answer in fractions is 59/100

When a statistic is given as a percentage, we assume that the sample size of the survey is

100

persons.

So, in the aforementioned question, we simply need to express the percentage as a fraction where the

numerator

represents the number of people who are in favor of the argument that their teens are addicted to cell phones which is

59

the denominator of the fraction represents the total number of people in the sample survey size which is

100.

simply using the above logic we can deduce the percentage into a fraction which is

59/100

.

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Answer:

2/3 cups

Step-by-step explanation:

The recipe calls for 2/4 cup of onion and 1/6 cup of celery. To find the total, we need to add the two fractions together; the amount of onions(2/4 cup or 1/2 a cup if simplified), and the amount of celery(1/6). To do this, we need to find a common denominator. We can do this buy finding a common multiple between 2 and 6.

Multiples of 2: 2, 4, 6, 8, 10, 12...

Multiples of 6: 6, 12, 18, 24, 30...

A common multiple is 6. 1/2x3/3=3/6 <--- an equivalent fraction of 1/2

Now both fractions have the same denominator:

Onions: 3/6

Celery: 1/6

3/6+1/6 = 4/6

4/6 simplifies to 2/3.

The total amount of celery and onion need for the soup is 2/3 cup

Answer:

2/3 cups

Step-by-step explanation:

The two values of y such that the barn is 50 yards from the well are given as follows:

y = -47 and y = 53.

Suppose that we have two points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The shortest distance between them is given by the following equation:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

For this problem, we have that D = 50, hence the equation is given as follows:

sqrt[(-2 - (-2))² + (y - 3)²] = 50

y - 3 = ±50.

Hence the values of y are given as follows:

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If Mark and jada share 5 yards of ribbon equally, then each one will get 2.5 yards of ribbon using division method.

When Mark and Jada share 5 yards of ribbon equally, it means that they will divide the total amount of ribbon equally between the two of them. This is a common type of problem in mathematics that involves dividing a given quantity equally among a certain number of people or objects.

To solve this problem, we used the division operation to divide the total amount of ribbon (5 yards) by the number of people who are sharing it (2). The resulting quotient (2.5 yards) represents the amount of ribbon that each person will receive.

Using the division operation, we can write,

5 yards ÷ 2 = 2.5 yards

This problem illustrates an important concept in mathematics: the division of quantities into equal parts. This concept is used in many real-world applications, such as dividing up a pizza among a group of people or allocating resources in a company among different departments or teams.

Understanding how to divide quantities into equal parts is an important skill that can be applied in many different contexts, making it a valuable mathematical concept to learn and understand.

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Lines a, b, c, and d are all straight lines in a two-dimensional coordinate system.

Line a has an equation of y=-x-2, which is the slope-intercept form of the equation of a line. This line has a slope of -1 and a y-intercept of -2. Line b is defined by two points (-6,1) and (3,-14), which can be used to find the equation of the line using the point-slope form of a line.

This line has a negative slope and passes through the points (-6,1) and (3,-14). Line c has two points (-1,8) and (4,11), which can also be used to find its equation using the point-slope form. This line has a positive slope and passes through the points (-1,8) and (4,11). Finally, line d has the equation -5x+3y=6, which is the standard form of the equation of a line. This line has a slope of -5/3 and a y-intercept of 2. These four lines are all different but all exist in the same two-dimensional coordinate system.

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Answer:

120 general admission

280 with student with a student ID

Step-by-step explanation:

x is tickets for general admission

y is tickets with a student ID

5x+3.5y=1580

x+y=400

y=400-x

5x+3.5(400-x)=1580

5x+1400-3.5x=1580

1.5x=180

x=120

120+y=400

y=280

The equation of the quadratic curve are:

Quadratic equation when the directrix is at y direction is of the form:

(x - h)² =  4P (y - k)

OR

standard vertex form, y = a(x - h)² + k     where a = 1/4p

The vertex for curve 1

v (h, k) = (-5, 4)

h = -5

k = 4

substitution of the values into the equation gives

y = a(x - h)² + k

y = a(x + 5)² + 4

Using (-3, 0) to solve for a

y = a(x + 5)² + 4

0 = a(-3 + 5)² + 4

-4 = a (2)²

a = -1

The equation is y = -(x + 5)² + 4

The vertex for curve 2

v (h, k) = (5, -4)

h = 5

k = -4

substitution of the values into the equation gives

y = a(x - h)² + k

y = a(x - 5)² - 4

Using (3, 0) to solve for a

y = a(x - 5)² - 4

0 = a(3 - 5)² - 4

4 = a (-2)²

a = 1

The equation is y = (x + 5)² + 4

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Answer:

Step-by-step explanation:

is this a bot or girl

Answer:

Step-by-step explanation:

Use PEMDAS to determine order of operations.

P = Parentheses

E = Exponents

M/D = Multiplication/Division

A/S = Addition/Subtraction

The operation in the parentheses must be performed first, which is the addition of 6.1 + 12.

The next operation to perform is multiplication, which is 415 times (6.1 + 12).

The last operation to perform is the subtraction of 415 times (6.1 + 12) from 8.3.

6.1 + 12 = 18.1

8.3 - 415(18.1)

8.3 - 7511.5 = -7503.2