Mathematics College

## Answers

**Answer 1**

we need to make revenue-cost and then maximize

[tex]\begin{gathered} R(x)-C(x) \\ (97x-2x^2)-(2x^2+49x+6) \end{gathered}[/tex]

simplify

[tex]\begin{gathered} =97x-2x^2-\mleft(2x^2+49x+6\mright) \\ =97x-2x^2-2x^2-49x-6 \\ =-2x^2-2x^2+97x-49x-6 \\ =-4x^2+97x-49x-6 \\ =-4x^2+48x-6 \end{gathered}[/tex]

now, to maximize, we need to find the derivate and make it equal to 0

[tex]\begin{gathered} \frac{d}{dx}(-4x^2+48x-6)=0 \\ -8x+48=0 \\ -8x=-48 \\ \frac{-8x}{-8}=\frac{-48}{-8} \\ x=6 \end{gathered}[/tex]

so, the maximum profit is at x = 6

## Related Questions

| В Find the measure of ZA in AABC. Since we are given information here, we can use the following equation to solve for MZA. 55 DONE 35 А C 50

### Answers

[tex]\begin{gathered} \text{Law of Cosine} \\ BC^2=AB^2+AC^2-2\times AB\times AC\times\cos A \\ 55^2=35^2+50^2-2\times35\times50\times\cos A \\ 3025=1225+2500-3500\times\text{cosA} \\ -3500\times\cos A=3025-1225-2500 \\ -3500\times\cos A=-700 \\ \cos A=\frac{700}{3500} \\ A=\cos ^{-1}(0.2) \\ A=78.46^{\circ} \end{gathered}[/tex]

Select all of the expressions equivalent to (m + m)(-4.2m).

Answer choices

2m(-4.2m)

-4.2m³

-2.2m²

4.2m²+4.2m²

-4.2m²+(-4.2m²)

-8.4m²

### Answers

**Answer:**

2m(-4.2m)

-4.2[tex]m^{2}[/tex] + - (4.2[tex]m^{2}[/tex])

-8.4[tex]m^{2}[/tex]

**Step-by-step explanation:**

2m(-4.2m) = -8.4 [tex]m^{2}[/tex]

-4.2 [tex]m^{2}[/tex] + (-4.2 [tex]m^{2}[/tex]) = 8.4[tex]m^{2}[/tex]

1-9.b.C.GROWING, GROWING, GROWING, PART ONECopy the tile pattern shown below onto graph paper.Figure 2Figure 3Figure 4Draw the 1st, 5th, and 6th figures on your paper.How is the pattern changing?What would the 100th figure look like? How many tiles would it have?How can you justify your prediction?

### Answers

**Answer:**

**Explanation:**

a) To draw the 1st , 5th and 6th figures, we need to know the count of squares

For the first figure, we would have 3 squares

The fifth figure would have 35 squares

The sixth figure will have 48 squares

The way to get this is to add 2 to the odd number difference between the last two terms

b) Here, we want to know how the pattern is changing

From the information provided, the first pattern has 8 squares, the second has

15 squares while the last has 24 squares

We can have a formula as follows:

[tex][/tex]

There are 9 athletes at a track meet. How many different ways can they finish first'orsecond?

### Answers

For the first place, we have 9 different options from the athletes, then for the second place, we would only have 8 different options, therefore, there are 9x8=**72 ways they can finish first or second**

Find the range and standard deviation of the set of numbers.38, 47, 43, 44, 44, 41, 44The range is 9.The standard deviation is__(Round to the nearest tenth as needed.)

### Answers

To find the standard deviation of this set of numbers, we will use the formula

[tex]s=\sqrt{\frac{\sum_^(x-\text{ }x_{mean})^2\text{ }}{n-1}}[/tex]

let us explain the parts of this formula, as follows:

[tex]x_{mean}\text{ is the mean of the data \lparen we have to calculate\rparen}[/tex][tex]n\text{ is the total quantity of numbers \lparen in this example 7\rparen}[/tex]

We will proceed by parts, the first thing to do is find the mean of the data

**Calculating the mean**

To find the mean, we will sum all the numbers and divide by the total quantity of numbers, as follows:

[tex]x_{mean}=\frac{\Sigma x}{n}=\frac{38+47+43+44+44+41+44}{7}=\frac{301}{7}=43[/tex]

**That is, the mean of the set is 43. **Now we proceed to find the difference between the data and the mean, and the add them to the power of two, in symbols we have:

[tex]\begin{gathered} \Sigma(x-x_{mean})^2=(38-43)^2+(47-43)^2+(43-43)^2+3\times\text{ }(44-43)^2+(41-43)^2 \\ \text{ =\lparen-5\rparen}^2+4^2+0^2+3\times\text{ }1^2+(-2)^2 \\ =25+16+3+4 \\ =48 \end{gathered}[/tex]

Now we introduce this result into the formula for the standard deviation, we find:

[tex]s=\sqrt{\frac{\Sigma(x-x_{mean})^2}{n-1}}=\sqrt{\frac{48}{7-1}}=\sqrt{\frac{48}{6}}=\sqrt{8}\approx\text{ 2.8}[/tex]

That is, after approximate to the nearest tenth, **we found that the standard deviation of the set of numbers is 2.8**

Which of the following ordered pairs represent a direct variation. Find the missing value. 1. (32, 80) and (x, 100) x = _____ 2. (-28,-7) and (20, y) y = _____

### Answers

When having an ordered pair, we say they are in direct variation if the quotient:

[tex]\frac{y}{x}[/tex]

is constant. For case 1 we have:

[tex]\frac{80}{32}=\frac{100}{x}[/tex]

we can solve for "x" by multiplying by "x" on both sides:

[tex]\frac{x80}{32}=100[/tex]

Now we multiply by 32/80 on both sides:

[tex]x=\frac{100\times32}{80}[/tex]

Solving the operations we get:

[tex]x=40[/tex]

For case 2 we have:

[tex]-\frac{7}{-28}=\frac{y}{20}[/tex]

Now we solve for "y" by multiplying by 20 on both sides:

[tex]\frac{-7\times20}{-28}=y[/tex]

Solving the operations:

[tex]y=5[/tex]

f(t)= 2t/3 For what value of t is f(x)=64?

### Answers

We are given the following function

[tex]f(t)=\frac{2t}{3}[/tex]

We are asked to find out the value of t which results in **f(t) = 64**

Let us substitute **f(t) = 64 **into the above function and solve for **t**

[tex]\begin{gathered} f(t)=\frac{2t}{3} \\ 64=\frac{2t}{3} \\ 3\cdot64=2t \\ 192=2t \\ \frac{192}{2}=t \\ 96=t \\ t=96 \end{gathered}[/tex]

Therefore, the value of **t** is **96**

Evaluate the expression 14-16+8+12\3

### Answers

Let's evaluate the given expression:

[tex]\text{ 14 - 16 + 8 + }\frac{\text{ 12}}{\text{ 3}}[/tex][tex]=\text{ 14 - 16 + 8 + 4}[/tex][tex]\text{ = -2 + 8 + 4}[/tex][tex]\text{ = -2 + 12}[/tex][tex]\text{ = 1}0[/tex]

Therefore, the answer is **10**.

A mother need 6 pieces of ribbon, with lengths of 25 cm each, for her daughter's hair. If the ribbon is only sold per full meter, how many meters does she need to buy?

### Answers

**Given:**

The length of each ribbon is 25 cm.

The number of ribbon need by mother is 6.

**Explanation:**

Determine the length of ribbon for daughter's hair.

[tex]\begin{gathered} 25\cdot6=150\text{ cm} \\ =1.5\text{ m} \end{gathered}[/tex]

Since length is in decimal so we need to find multiple of 25 such that it is more than 150 and multiple of 100.

The multiples of 25 are 25,50, 75, 100, 125, 150, 175, 200, ...

Since 200 is more than 150 and multiple of 100 also.

Determine the length of 200 cm in terms of meters.

[tex]200\text{ cm}\cdot\frac{1\text{ m}}{100\text{ cm}}=2\text{ m}[/tex]

**So mother needs to buy 2 meters of ribbon.**

**Answer: 2 meters**

math worksheet , sets

### Answers

The elements of the **set **given by A∩B is {12,18} .

Set theory, a branch of mathematical logic, studies sets, which are essentially collections of **objects**.

Despite the fact that every form of **object **may be turned into a set, set theory is a branch of mathematics that primarily deals with issues that are relevant to **mathematics **as a whole.

The foundation of **set **theory is a straightforward **binary **link between an object o and a set A.

If o is a **component **(or **member**) of A, it is expressed as o A. When listing members of a **set**, commas are used to indicate their separation, or brackets are used to surround a property of those parts.

Since** **sets** **are objects, they can be connected by the membership **relation**.

Given** set **U = {11,12,13,14,15,16,17,18,19,20}

A = {12,14,16,18,20}

B = {12,15,18}

A∩B = {12,18}

A∪B = {12,14,15,16,18,20}

A' = {11,13,15,17,19}

Therefore the **elements** of the set given by A∩B is {12,18} .

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A fluorescent lighting panel is 12 5/8 inches wide. If three of

the panels are installed next to each other, what will be the

width in inches of the combined panels?

### Answers

The **width **of the combined three **panels** when installed next to each other is [tex]37\frac{7}{8}[/tex] inches.

What is the width of the combined panels?

In order to determine the **width **of the three **combined panels,** multiply** **the width of one **fluorescent lighting panel **by the total number of **panels. **

Multiplication is the mathematical operation that is used to calculate the product of two or more numbers. The sign that represents multiplication panel is ×.

**Width **of the combined **panels **= width of one panel x number of panels

[tex]12\frac{5}{8}[/tex] × 3

[tex]\frac{101}{8}[/tex] x 3 = [tex]\frac{303}{8}[/tex] = [tex]37\frac{7}{8}[/tex] inches

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help meeeeeee pleaseee !!!!

### Answers

So, we are writing a function. c(x) is the manufacturing costs, and x is the amount of bikes manufactured. The y-intercept is 1908 because when no bikes are manufactured it still costs 1908 to run the factory. The slope is 75 because it costs $75 to create a bike. So, y = mx + b, where m is the slope and b is the y-intercept is:

c(x) = 75x + 1908

how to solve for x and round it up to tenth

### Answers

Answer:

4.6

Explanation:

The diagram shown is a right triangle having the following sides;

Opposite = 17

Adjacent = x

Angle of elevation = 75 degrees

Using SOH CAH TOA identity

Tan theta = opposite/adjacent

Tan 75 = 17/x

x = 17/tan 75

x = 17/3.73205

x = 4.6

**Hence the value of x to the nearest tenth is 4.6**

solve for g: g - 0.6 < 3.172. ,part c: in one paragraph explain ur work in parts a and b

### Answers

**Explanation**

[tex]g-0.6\leq3.172[/tex]

**Step 1**

To solve the inequality means to find a range, or ranges, of values that an unknown g can take and still satisfy the inequality.

so

[tex]\begin{gathered} g-0.6\leq3.172 \\ \text{add 0.6 in both sides} \\ g-0.6+0.6\leq3.172+0.6 \\ g\leq3.772 \end{gathered}[/tex]

it means the solution is the set of values equal or smaller than 3.772,so

**Part A: **

[tex]g\leq3.772[/tex]

**Step 2**

**Part B**:the graph of the inequality looks like a marked line in the number line, from3.772 to negative infinite, as the symbol is smaller or equal, the number3.772 is part of the set , so we use a filled circle

**Step 3**

in step 1 we used the addition property of inequality to isolate x, then in step 2 we draw the set solution .

I hope this helps you

What is the decay percentage rate of t h(x) = 20(175)” ?A75%oB.75%Oс25%0D.25%

### Answers

Given the function :

[tex]h(x)=20(0.75)^x[/tex]

So, the decay percentage rate :

[tex]\frac{\triangle h}{\triangle x}=0.75[/tex]

convert the decimal to percentage: 0.75 = 75%

So, the answer is option A) 75%

Help me! i need this answer now i am so dead. if i get it worng please help help please

### Answers

**Answer:**

70.4

**Step-by-step explanation:**

c = 2[tex]\pi[/tex]r

c = 2(3.142)(11.2)

c = 70.3808 Rounded to 1 decimal place

c = 70.4

Answer:

70.4

Explanation:

Circumference = 2 (3.142) radius

Circumference = 2 x 3.142 x 11.2

Circumference = 70.3808

Round ur answer to 1 d.p:

=70.4

The ratio of boys to girls in Janice's classroom is 3:5, and there are a total of 32 students in the class. Using completesentences, explain how you could draw a tape diagram to represent this situation. In your answer, draw a diagramand make sure to include what quantity each bar represents.

### Answers

Teh ratio of boys to girls in JAnice's classroom is 3:5

Total number of students 32

Let the ratio constant is **K**

So,

The equation will be

3K + 5K=32

8K=32

K=32/8

K=4

So,

the boys will be

**4 + 4 + 4 =3K =12**

The number of girls will be :

**4 + 4 + 4 + 4 + 4 = 5K =20**

The Wilsons want to tile their kitchen floor. The floor is 12 feet by 15 feet. The tiles are nine-inch squares.

12 feet = _____ inches

15 feet = _____ inches

Total square inches of the floor = ______ square inches

One tile = _____ square inches

Total number of tiles needed =______ tiles

### Answers

The **number** of tiles required to cover the floor is 2880 **tiles.**

What is the number of Tiles Needed?

To solve this **problem**, we can find the number of tiles by calculating the area of a rectangle:

We have to convert the **dimensions** from feet to inches will be

1 feet = 12 inches

12 feet = 12 * 12 = 144in

15 feet = 12 * 15 = 180in

The area of the **rectangle** can be calculated as:

A = l * w

A = 180 * 144

A = 25920in²

The tiles are 9 squared inches, we can divide the area by 9 to find the number of tiles needed:

25920/9= 2880

Hence, The number of tiles needed will be 2880 **tiles**

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If a one-person household spends an average of $52 per week on groceries, find the maximum and minimum amounts spent per week for the middle 50% of one-person households. Assume the standard deviation is $14 and the variable is normally distributed. Round your answers to the nearest hundredth.Minimum: $Maximum: $

### Answers

**Solution**

For this case we have the following random variable:

X= amount spend on average for groceries by one person

And we have the following properties:

mean= 52

sd= 14

The distribution of the variable is normal

We can find the middle 50% using a graph like this one:

We can find two quantiles from the normal distribution that accumulates 25% of the area on each tail of the distribution and we have:

Z= -0.674 and 0.674

Now we can use the z score formula given by:

[tex]z=\frac{x-\mu}{\sigma},x=\mu\pm z\cdot\sigma[/tex]

So then we have:

**Minimum= 52 - 0.674*14 = 42.56**

**Minimum= 52 + 0.674*14 = 61.44**

Prove that 3x + y = 7 + y and 3(x + y) = 2 + 3x are perpendicular

### Answers

**Answer:**

Since one line is vertical, and one line is horizontal, the lines are perpendicular.

**Step-by-step explanation:**

The product of the slopes of perpendicular lines is -1.

We find the slopes of the 2 lines and multiply them together.

If the product equals -1, then the lines are perpendicular.

To find the slopes of the lines, we write each equation in the y = mx + b form, where m is the slope. In other words, we solve each equation for y.

3x + y = 7 + y

Subtract y from both sides.

3x = 7

x = 7/3

This is not the y = mx + b form since there is no y in the equation. A line with equation x = k, where k is a number, is a vertical line that passes through the point (k, 0), and the x-coordinate of all points on the line is k.

3(x + y) = 2 + 3x

3x + 3y = 2 + 3x

Subtract 3x from both sides.

3y = 2

y = 2/3

y = 0x + 2/3

Slope = m = 0

A line with 0 slope is a horizontal line.

Since one line is vertical, and one line is horizontal, the lines are perpendicular.

Latoya opened a savings account and made an intial deposit. After the intial deposit, she added money into the account each week she added the same amount each week with out any withdrawals after the forth week she had $450 by the ninth week she had $825 what was latoya's intial deposit?

### Answers

She made an initial deposit that we will call "D", as it is one of the unknowns.

We know that she made a weekly deposit (lets call this amount "w").

After 4 weeks she had $450 in the account balance and this is the sum of the initial deposit and 4 weekly deposits, so we can write:

[tex]D+4w=450[/tex]

At the ninth week she had $825, that correspond to the initial deposit and 9 weekly deposits. This can be written as:

[tex]D+9w=825[/tex]

We have a system of linear equations that we will solve by elimination: we will substract the first equation from the second and then find w.

[tex]\begin{gathered} (D+9w)-(D+4w)=825-450 \\ 5w=375 \\ w=\frac{375}{5} \\ w=75 \end{gathered}[/tex]

Now that we know "w", we can calculate D with any of the two equations:

[tex]\begin{gathered} D+4w=450 \\ D+4\cdot75=450 \\ D+300=450 \\ D=450-300 \\ D=150 \end{gathered}[/tex]

**Answer: the initial deposit was $150.**

Find the GCF if the following terms . (30x^5 ,60x^3)

### Answers

The coefficient of the GCF of a set of algebraic terms, wil be the GCF of the coefficients of the terms.

Notice that the coefficients in this case, are 30 and 60.

The greatest comon factor of this set, is 30, since:

[tex]\begin{gathered} 30=30\cdot1 \\ 60=30\cdot2 \end{gathered}[/tex]

On the other hand, the variable *x* appears with an exponent of 5 in one case and an exponent of 3 in the other case. The greatest common factor for the variable *x* will be the lowest power, in this case, 3. Notice that:

[tex]\begin{gathered} x^3=x^3\cdot1 \\ x^5=x^3\cdot x^2 \end{gathered}[/tex]

Then, we can factor out the following:

[tex]30x^3[/tex]

Notice that each term can be written as a product of this factor:

[tex]\begin{gathered} 30x^5=30x^3(x^2)^{}^{}^{}_{} \\ 60x^3=30x^3(2)^{}_{} \end{gathered}[/tex]

**Therefore, the greatest common factor (GCF) is:**

[tex]30x^3[/tex]

A storage tank has a height of 10 feet and a diameter of 6 feet. The tank is half filled with oil. 6 ft Approximately how much oil, in cubic feet, is currently in the cylindrical tank? A 90 ft B 360r ft3 C 455 Ft D 180rt ft3

### Answers

ok

Volume of a cilinder = pi*r^2*h

Substitution

Volume of a cilinder = 3.14*3^2* 6

Simplification

Volume of a cylinder = 170 ft^3

**Approximately, there are 180 ft^3 of oil**

if you have 1/4 cup how many eighths do you have

### Answers

U have 2/8 cup……………….

MATHEMATICALLY WE SAY

BE AWARE THAT EIGHTHS IS

[tex] \frac{1}{8} [/tex]

THEY ARE ASKING HOW MANY

[tex] \frac{1}{8} [/tex]

ARE THERE IN

[tex] \frac{1}{4} [/tex]

[tex] = \frac{1}{4} \div \frac{1}{8} \\ = \frac{1}{4} \times \frac{8}{1} \\ = \frac{8}{4} \\ = 2[/tex]

YOU HAVE 2 .

hwlp

The length of a rectangle is 6 feet more than twice the width. If the perimeter is 132 feet, find the dimensions.

### Answers

P = 2L + 2w

Length=

L = 2w + 6

New equation =

P = 2(2w + 6) + 2w

P = 4w + 12 + 2w

P = 12 + 6w

As stated in the question, the perimeter is 132 feet:

So,

132 = 12 + 6w

120 = 6w

W = 20

Now let’s find length using width:

L = 2w + 6

L = 2(20)+ 6

L = 40 + 6

Now we know that

W = 20

L = 46

Y varies inversely with the square of x. When x=4, then y=3. Find y when x=2

### Answers

**Answer:**

y = 6

**Step-by-step explanation:**

y= [tex]\frac{1}{x}[/tex]

3 = [tex]\frac{1}{4}[/tex]k Solve for k by multiplying both sides by 4

12 = k

y = [tex]\frac{1}{2}[/tex](12)

y = [tex]\frac{12}{2}[/tex]

y= 6

what is the answer for this equation 20x2-45=0

### Answers

**Answer:**

-5

**Step-by-step explanation:**

A number when rounded to 3 decimal places, is equal to

0.029

Find the upper and lower bound of

The number

### Answers

3-0.029=2.971 this only how I can answer this question

The circumference of a circle is 67 inches. What is the area in

terms of π ?

### Answers

A = 4489/(4π)

If we look at the equations for circumference and area (of a circle), we see that they both share the variable “r”. Therefore, we can solve for r in the circumference equation and insert it into area equation. Evaluate to find the answer.

See details:

A rectangle has a length that is 3 more than twice the width. Its perimeter is 96 inches. Which equation models this? A. 2w + 3 = 96 B. w + 2m + 3 = 96 C. 2(w) + 2(w + 3) = 96 D. 2(w) + 2(2w + 3) = 96

### Answers

**ANSWER**

**EXPLANATION**

Let the length of the rectangle be L.

Let the width of the rectangle be w.

The length of the rectangle is 3 more than twice the width.

This means that:

L = 3 + (2 * w)

**L = 2w + 3**

The perimeter of a rectangle is given as:

**P = 2w + 2L**

The perimeter of the rectangle is 96 inches. This means that:

96 = 2L + 2w

**Recall that**: L = 2w + 3

=> 96 = 2(w) + 2(2w + 3)

=> 2(w) + 2(2w + 3) = 96