A company produces a product for which the variable cost per unit is $8 and fixed cost is $70,000. Each unit has a selling price of $12. Determine the number of units that must be sold for the company to earn a profit of $50,000.

The statement "It is valid because Victoria added the same amount to each side of the equation" correctly explains whether equation 3 in Victoria's work is valid in solving the equation.

In equation 3, Victoria added 3 to both sides of the equation x-3=4/21. This operation is valid because she added the same amount (3) to both sides, which maintains the equality between the two sides of the equation. The resulting equation is x-3+3=4/21+3, which simplifies to x=4/21+63/21 or x=67/21.

Therefore, equation 3 is a valid step in solving the equation x-3=4/21.

learn more about simplification: https://brainly.com/question/28595186

#SPJ1

The formula for standard error of proportion is √(pq/n) where p is the sample proportion, q = 1-p, and n is the sample size. Here, the sample proportion is 0.75, q is 0.25, and n is 160. Therefore, the standard error of proportion is √(0.75*0.25/160) = 0.035

The probability that between 120 and 128 patents (inclusive) are friends with their children can be calculated using the z-score formula:
z = (x - np)/√(npq)
where x is the number of parents between 120 and 128 who are friends with their children,
np = 160*0.75 = 120, and pq = 160*0.25 = 40.
Therefore,√(npq) = √(120*40) = 24.49
z = (120 - 120)/24.49 = 0
z = (121 - 120)/24.49 = 0.04
z = (122 - 120)/24.49 = 0.08
z = (123 - 120)/24.49 = 0.12
z = (124 - 120)/24.49 = 0.16
z = (125 - 120)/24.49 = 0.2
z = (126 - 120)/24.49 = 0.24
z = (127 - 120)/24.49 = 0.29
z = (128 - 120)/24.49 = 0.33

Using a z-table or a calculator, the probability that z is between 0 and 0.33 is 0.1292. Therefore, the probability that between 120 and 128 parents are friends with their children is 0.1292.

To know more about  probability  refer here:

https://brainly.com/question/11234923

#SPJ11

Answer:

I think its 560

Step-by-step explanation:

Answer:

17,000

Step-by-step explanation:

17000 in words is written as Seventeen-thousand. The number 17000 represents a value equivalent to it.

A middle school basketball player makes a free throw with a probability of 0.6. Assuming each free throw is an independent event,the probability the player makes zero of their next three free throws is  0.064. The correct answer is A.

The probability that a middle school basketball player makes zero of their next three free throws can be calculated using the formula P(A) = P(A')ⁿ, where P(A) is the probability of the event occurring, P(A') is the probability of the event not occurring, and n is the number of trials.

In this case, P(A) is the probability of the player making zero free throws, P(A') is the probability of the player missing a free throw (1 - 0.6 = 0.4), and n is the number of free throws (3).

Using the formula, we can calculate the probability of the player making zero free throws as follows:

P(A) = P(A')ⁿ
P(A) = (0.4)³
P(A) = 0.064

Therefore, the correct answer is (A) 0.064.

Learn more about probability at https://brainly.com/question/20913662

#SPJ11

Answer:

C

Step-by-step explanation:

The equation that shows the whole amount of pizza Miah ate on Saturday is 3/32 of the whole pizza

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.

This word problem are interpreted to mathematical equation

The left over is calculated is 3/8

therefore 5/8 of the pizza is left for Saturday

On Saturday she ate 1/4 of the pizza

= 1/4 × 3/8

= 3/32

therefore Miah ate 3/32 of the whole pizza on Saturday.

learn more about word problem from

https://brainly.com/question/21405634

#SPJ1

Javier has 90 more uncommon cards than rare cards.

To find out how many more uncommon cards Javier has than rare cards, we need to multiply the number of packs he has by the number of each type of card in a pack, and then subtract the number of rare cards from the number of uncommon cards. We can do this with the following equation:

Uncommon cards - Rare cards = Difference

First, we'll multiply the number of packs by the number of each type of card:

45 packs × 3 uncommon cards = 135 uncommon cards
45 packs × 1 rare card = 45 rare cards

Now we'll subtract the number of rare cards from the number of uncommon cards to find the difference:

135 uncommon cards - 45 rare cards = 90

So, the number of uncommon cards is 90 more than the rare cards.

Learn more about Difference here: https://brainly.com/question/17695139.

#SPJ11

To solve the given equations, we need to follow these steps:

1. Isolate the radical on one side of the equation.
2. Square both sides of the equation to eliminate the radical.
3. Solve the resulting equation for the variable.
4. Check for extraneous solutions by plugging the solution back into the original equation.
5. If there are rational exponents, use the same steps but raise both sides of the equation to the reciprocal of the exponent.

Let's apply these steps to the sample problems:
1. V4x + 1 - Vx+ 10 = 2
First, isolate the radical on one side:
V4x + 1 = Vx+ 10 + 2
V4x + 1 = Vx+ 12
Next, square both sides to eliminate the radical:
(4x + 1) = (x+ 12)^2
4x + 1 = x^2 + 24x + 144
Solve for x:
0 = x^2 + 20x + 143
Using the quadratic formula:
x = (-20 ± √(20^2 - 4(1)(143)))/(2(1))
x = (-20 ± √(400 - 572))/2
x = (-20 ± √(-172))/2
x = (-20 ± √172i)/2
There are no real solutions for this equation.

2. V2x+30 = (x+3)
Isolate the radical:
V2x+30 = x+3
Square both sides:
2x + 30 = (x+3)^2
2x + 30 = x^2 + 6x + 9
Solve for x:
0 = x^2 + 4x - 21

Using the quadratic formula:
x = (-4 ± √(4^2 - 4(1)(-21)))/(2(1))
x = (-4 ± √(16 + 84))/2
x = (-4 ± √100)/2
x = (-4 ± 10)/2
x = 3 or x = -7
Check for extraneous solutions by plugging the solutions back into the original equation:
V2(3)+30 = (3+3)
V36 = 6
6 = 6 (True)
V2(-7)+30 = (-7+3)
V16 = -4
4 = -4 (False)

Therefore, the only solution is x = 3.

To know more about rational exponents refer here:

https://brainly.com/question/3009444

#SPJ11

Answer: C, 2 2/8

Step-by-step explanation: To turn a mixed number into an improper fraction, multiply the whole number by the denominator. Then, add the numerator. So in this example it would be:

4 3/8 = 35/8

2 1/8 = 17/8

Now, since the denominators are equivalent, all we need to do is subtract the numerators.

35/8 - 17/8 = 18/8

The answer needs to be changed back to a mixed number. For this problem, there is an easy way to do this.

18/8 = 8/8 + 8/8 +2/8, which as a mixed number would be 2 2/8.

So the correct choice would be (C).

Answer: 5.25

Step-by-step explanation:

In the picture there is a smaller triangle inside a bigger triangle. You have to find the size it grows by dividing a side of the bigger triangle to the same side of the smaller triangle.

16.8/6.4 = 2.625

Then you find x by multiplying the adjacent side by the size it grows.

2*2.626 = x

2*2.626 = 5.25

Answer:

Step-by-step explanation:

For this triangle, we can find the angle adjacent to side length 4 using trig:

tan(theta) = 7/4

theta = tan^-1(7/4)

theta = 60.26

Now we use sine to find x:

sin(60.26) = 7/x

x = 7/sin(60.26)

x = 8.06

I don't know how far you need to round, so it can either be this or 8.1

Hope this helps!

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=4 \end{cases}\implies V=\pi (3)^2(4)\implies \stackrel{ \pi =3.14 }{V=113.04}[/tex]

The required solutions are as follows,
(a) The parabola will open downwards and have a maximum.
(b) The axis of symmetry for this function is t = 15.

A parabola is a cross-section cut out of the cone and represented by an equation shown in the question.

Here,
(a) The function C(t) is a quadratic function with a coefficient of -0.2 in front of the t² term. Since this coefficient is negative, the parabola will open downwards and have a maximum.

(b) The axis of symmetry of a quadratic function in the form of f(x) = ax² + bx + c is given by the formula x = -b/2a.

In this case, the function is C(t) = -0.2t² + 6t + 28.5, so a = -0.2 and b = 6. Thus, the axis of symmetry is:

t = -b/2a = -6/(2*(-0.2)) = 15

Therefore, the axis of symmetry for this function is t = 15.

Learn more about parabola here:

brainly.com/question/4074088

#SPJ1

Check the picture below.

The solution to the inequality 2r - 5 ≤ 9 in interval notation is (-∞, 7].

To solve the inequality 2r - 5 ≤ 9, we need to isolate the variable r on one side of the inequality. Here are the steps to do so:

Now, we can present our answer in interval notation. Interval notation is a way to represent an interval on the number line. It is written in the form of [a, b], where a and b are the endpoints of the interval. The square brackets mean that the endpoints are included in the interval.

Since our inequality is r ≤ 7, our interval notation would be (-∞, 7], where -∞ represents negative infinity and 7 is the endpoint. The square bracket on the 7 means that 7 is included in the interval.

Therefore, the solution to the inequality 2r - 5 ≤ 9 in interval notation is (-∞, 7].

For more information about inequality, visit:

https://brainly.com/question/30238989

#SPJ11

Answer: Using the given functions, we can model the distance, d(t), that the car is from the city as:

d(t) = f(t) + g(t) = 10 + 65t

So, after 2 hours of driving, the distance that the car has traveled from the city is:

d(2) = 10 + 65(2) = 10 + 130 = 140 miles

Therefore, Riordan is incorrect, and the correct distance the car is from the city after 2 hours of driving is 140 miles.

Step-by-step explanation:

The Zeros of the equation would be x = -5/2.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given the equation as;

[tex]f(x)=-8x^3-20x^2[/tex]

We can factor;

4x^2 ( 2x+5)  

Using the zero product property

2x = 0

2x + 5 = 0

x = -5/2

Learn more about equations here;

https://brainly.com/question/25180086

#SPJ1

The properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms ln(√z) = (1/2)ln(z)

What is the logarithms?

Logarithms are mathematical functions that help to solve exponential equations. They are used to express very large or very small numbers in a more convenient and manageable way.

We can use the property of logarithms that states:

logb (a∙c) = logb a + logb c

to expand the expression as a sum of logarithms:

ln(√z) = ln(z^(1/2))

Using the power rule of logarithms, we can simplify this as:

ln(z^(1/2)) = (1/2)ln(z)

Hence, we can write:

ln(√z) = (1/2)ln(z)

To learn more about logarithms, Visit

https://brainly.com/question/25710806

#SPJ1

Answer:

see below

Step-by-step explanation:

put paragraph of words into summarised information 1st.

ie

black : red : total

7 : 2 : 7+2 = 9 is total units

total units = 9 (which is 144 markers)

so 1 unit is .....

144 ÷ 9 = 16 markers

black = 7units

7 x 16 markers = ans

red = 2 units

2 x 16 = ans

The given histogram is right skewed type.

A histogram is a graphic representation of data in a grouped frequency distribution with continuous classes.

They are similar to a bar graphs, but there are no gaps between the consecutive rectangles.

Histograms are widely used for ranging data into groups. It is a highly practical graph due to its clarity and simplicity.

Histogram :-

It is a collection of rectangles next to one another, where each bar represents a different type of data.

In this context, frequency refers to the number of times a number appears in statistical data.

It is known as a frequency distribution when shown in a table.

Here, the distribution here is skewed to the left. Therefore, it is also referred to as a negatively skewed histogram graph.

Hence, the given histogram is right skewed type.

Learn more about histograms, click;

https://brainly.com/question/30354484

#SPJ1

A group of 10 people would raise a total value of  $160 if they worked 16 hours.

According to the given information, the amount of money raised, R, varies jointly as the square root of hours worked, h, and the number of people working, p. This means that R = k√h * p, where k is the constant of proportionality.

We are given that six people raise $72 when working 9 hours, so we can use this information to find the value of k:
72 = k√9 * 6
72 = k * 3 * 6
72 = 18k
k = 4

Now that we know the value of k, we can use it to find the amount of money that 10 people would raise if they worked 16 hours:
R = k√h * p
R = 4√16 * 10
R = 4 * 4 * 10
R = 160

Therefore, 10 people would raise $160 if they worked 16 hours.

To know more about square root click on below link:

https://brainly.com/question/29286039#

#SPJ11

Answer:

Step-by-step explanation:

The least common denominator for 1/6 + 3/8 is 24

first find the multiples of 6 and 8

6= 6, 12, 18, 24, 30

8 = 8, 16, 24, 32

Next circle the number that appear in both

That number will be 24 which is the least common denominator.

An expression that shows the total area of five rooms is (3 × 13²) + (2 × 15²)

The correct answer is an option (A)

Let 'a' represents the side length of the square rooms measuring 13 ft each and 'b' represents the side length of the square rooms measuring 15 ft each.

We know that the formula for the area of a square  is A = s²

where 's' is the side of a square.

Sides of three square rooms measure 13 feet each.

So, the area of the three rooms would be:

A₁ = 3 × a²

A₁ = 3 × 13²

And sides of two square rooms measure 15 feet each.,

So, the area of the two rooms would be:

A₂ = 2 × b²

A₂ = 2 × 15²

Total area of the five rooms A =  A₁ + A₂  

So, we get an expression:

A = 3 × 13²  + 2 × 15²

A = 3 × 169 + 2 × 225

A = 957 ft²

Therefore the total area of the five rooms be 957 ft².

Learn more about an expression here:

brainly.com/question/30091997

#SPJ4

The complete question is:

Sides of three square rooms measure 13 feet each, and sides of two square rooms measure 15 feet each. Which expression shows the total area of these five rooms?

a.(3 × 13^2) + (2 × 15^2)

b.(2 × 13^3) + (2 × 15^2)

c.(3 × 15^2) + (2 × 13^2)

d.(3 × 13^2) × (2 × 15^2)

It seems like the question is asking about a system of equations with no restrictions on the variables b1, b2, and b3. However, the question is filled with typos and formatting errors that make it difficult to understand the exact problem and provide an accurate answer. It would be best to ask the student to clarify the question and provide a properly formatted version of the problem before attempting to answer.

Learn more about system of equations

brainly.com/question/12895249

#SPJ11

The measure of the central angle indicated is 60°.

The central angle of a circle is the angle that an arc takes up in the centre. The radius vectors are what make up the angle's arms.

The formula for calculating a central angle is: Central Angle = Arc length (AB) / Radius (OA) = (s 360°) / 2r, where "s" stands for arc length and "r" for circle radius.

Now here in the given diagram,

Let x equal the desired angle.

The central angle that we need to find is:

Now x = 360-120-(90+90)

⇒ x = 360-300

⇒ x = 60°

To know more about central angle, visit:

https://brainly.com/question/15698342

#SPJ1

Answer:

180 p

Step-by-step explanation:your welcome

In the quadrilateral ABCD if AB ||CD and  AB=9 as well as are CD=9. Then, quadrilateral ABCD is both parallelogram and trapezium.

Parallelogram's characteristics

In the quadrilateral ABCD:

Thus, the quadrilateral ABCD is both parallelogram and trapezium.

Know more about trapezium

https://brainly.com/question/27929782

#SPJ1