Mathematics College

## Answers

**Answer 1**

**Answer:**

**The amount in dollars of wheat saved by the first operator is;**

[tex]\text{ \$1,556.10}[/tex]

**Explanation:**

Given that Peter hired two combine operators to harvest his 260 acres of wheat.

And it yeilds 50 bushels per acre.

The total amount of bushels of wheat on the field is;

[tex]\begin{gathered} T=260\times50 \\ T=13,000\text{ bushels} \end{gathered}[/tex]

Since each operator harvest the same amount;

[tex]\text{opertor 1= Operator 2 = }\frac{13000}{2}=6500\text{ bushels each}[/tex]

If operator 1 loss 3%, the remaining amount is;

[tex]\begin{gathered} A_1=6500-3\text{ \% of 6500} \\ A_1=6500-(0.03)6500 \\ A_1=6305\text{ bushels} \end{gathered}[/tex]

Operator 2 loss 5%, the remaining amount is;

[tex]\begin{gathered} A_2=6500-0.05(6500) \\ A_2=6175\text{ bushels} \end{gathered}[/tex]

The amount of bushels save by the first operator compared to the second operator is;

[tex]\Delta A=A_1-A_2=6305-6175=130\text{ bushels}[/tex]

if wheat is sold for $11.97 per bushel, the amount in dollars of wheat saved by the first operator is;

[tex]\begin{gathered} C=130\text{ bushels }\times\text{ \$11.97 per bushel} \\ C=\text{ \$1,556.10} \end{gathered}[/tex]

**The amount in dollars of wheat saved by the first operator is;**

[tex]\text{ \$1,556.10}[/tex]

## Related Questions

Which experession is equivalent to 4(9+7)

### Answers

**Answer:**

64

**Step-by-step explanation:**

9+7=16

16(4)=64

why do trees have wood (fre3 po1nts

### Answers

**Answer: The tree takes the Carbon dioxide from the air and converts it to wood.**

This is my homework by the way.You can represent the measures of an angle and its complement as x° and (90 -x)° Similarly, you can represent the measures of an angle and its supplement as and (180 -- x)°. Use these expressions to find the measures of the angles described.The measure of an angle is three times the measure of it's supplement.The measure of the supplement of an angle is three times the measure of it's complement.The measure of an angle increased by 20° is equal to the measure of it's complement.

### Answers

The sum of complemenatry angles = 90

The sum of supplementary angles = 180

You were using a ladder at your construction job. You started off at ground level and climbed down 10 feet to see the basem*nt. Then you climbed up 20 feet to see the second floor. Finally, you climbed down 9 feet. What is your height relative to ground level?

### Answers

**Answer:**

1 foot above the ground, positive 1

**Step-by-step explanation:**

you start at ground level let's call that 0

you go 10 down 0-10=-10

Now you climb up 20 feet so -10+20=10

Then you finally climb down 9 feet and 10-9=1

So you are one foot above the ground.

determine whether the given numbers are solutions of the inequality 2t +6 <4-t a 0 b 1 c -3 d 5

### Answers

[tex]\begin{gathered} 2t+6<4-t \\ 2t+t<4-6 \\ 3t<-2 \\ t<-\frac{2}{3} \end{gathered}[/tex]

The value of t must be less than -2/3, that is, the correct answer must be a negative number, in this case it would be the letter **C) -3**

What is the value of z for the equation fraction 1 over 4z = −fraction 7 over 8 + fraction 1 over 8z? −3−737

### Answers

**-7**

**Explanation**

**Step 1**

given

[tex]\frac{1}{4}z=-\frac{7}{8}+\frac{1}{8}z[/tex]

subtrac (1/4)z in both sides

[tex]\begin{gathered} \frac{1}{4}z=-\frac{7}{8}+\frac{1}{8}z \\ \frac{1}{4}z-\frac{1}{4}z=-\frac{7}{8}+\frac{1}{8}z-\frac{1}{4}z \\ 0=-\frac{7}{8}-\frac{1}{8}z \end{gathered}[/tex]

**Step 2**

add 7/8 in both sides

[tex]\begin{gathered} 0=-\frac{7}{8}-\frac{1}{8}z \\ 0+\frac{7}{8}=-\frac{7}{8}-\frac{1}{8}z+\frac{7}{8} \\ \frac{7}{8}=-\frac{1}{8}z \\ \end{gathered}[/tex]

finally, multiply both sides by -8 in order to isolate z

[tex]\begin{gathered} \frac{7}{8}=-\frac{1}{8}z \\ \frac{7}{8}*-8=-\frac{1}{8}z*-8 \\ -7=z \end{gathered}[/tex]

therefore, **the answer is**

**-7**

I hope this helps you

adult female Labrador Retrievers weigh an average of 65 lbs with a standard deviation of 4 lb adult female German Shepherds weigh an average of 62 pounds with a standard deviation of 3 lbs one sets teacher owns and underweight lab in an underweight German Shepherd the lab weighs 58 pounds and the German Shepherd weighs 59 pounds what is the Z score for the lab.

### Answers

Labrador Retrievers weigh an average of 65 lbs with a standard deviation of 4 lb

German Shepherds weigh an average of 62 pounds with a standard deviation of 3 lbs

Destinee's house is located at (2, 3) on the coordinate grid. El Ticonzito is located at (-4,-2).

If El Ticonzito is the midpoint between Destinee's house and Ana's house, what is the approximate distance between Ana's house and Destinee's house?

A. 6.63 miles

B.

C.

D.

7.50 miles

11.00 miles

10

15.62 miles

### Answers

The** distance** between Destinee's house and Anna's house is 15.62 miles

Midpoint of a Line

To find the **coordinate** of the Anna's house, we can use the formula of **midpoint **on this. This is given as

[tex]midpoint(x,y) = \frac{x_2 + x_1}{2}, \frac{y_2 + y_1}{2}[/tex]

In the question, El Ticonzito's house is at **midpoint** between Destinee's house and Anna's house.

[tex]midpoint(x,y) = \frac{x_2 + x_1}{2}, \frac{y_2 + y_1}{2}\\-4 = \frac{2 + x_1}{2} = -8 = 2 + x_1\\x_1 = -8 - 2 = -10\\\\-2 = \frac{3 + y_1}{2} \\-4 = 3 + y_1\\-4 - 3 = y_1\\y_1 = -7[/tex]

The coordinate's of Anna's point is (-10, -7).

Let's use this to calculate the distance (d) between the two points.

[tex]d = \sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2} \\d = \sqrt{(-10-2)^2 + (-7 - 3)^2} \\d = \sqrt{(-12)^2 + (-10)^2} \\d = \sqrt{244}\\ d = 15.62 miles[/tex]

The **distance** between the two points is 15.62 miles

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HELP ASAP!!

Find the product of (x − 6)^2 and is the product a polynomial.

x^2 − 12x + 36; is a polynomial

x^2 − 12x + 36; may or may not be a polynomial

x^2 − 36; is a polynomial

x^2 − 36; may or may not be a polynomial

### Answers

**Answer: Choice A**

x^2-12x+36; is a polynomial

===================================================

Explanation:

Use the rule that (A-B)^2 = A^2 - 2AB + B^2 to show (x-6)^2 = x^2-12x+36 is an identity. In this case, A = x and B = 6

You could also use the FOIL rule or the distributive property as two alternatives.

The result is a polynomial because it consists of summing or subtracting various monomials. If we had terms that had say exponents of decimal numbers or negative values, then we wouldn't have a polynomial.

Jon just received a job offer that will pay him 12% more than what he makes at his current job. If the salary at the new job is 68,000. What is his current salary? Round to the nearest cent.

### Answers

Let be "x" Jon's current salary.

According to the information given in the exercise, the salary at the new job is 68,000 and this is 12% more than his salary at his current job.

To convert from percent to a Decimal number, you can divide by 100. Then:

[tex]\frac{12}{100}=0.12[/tex]

Therefore, knowing that information, you can set up the following equation:

[tex]x+0.12x=68,000[/tex]

Now you can solve for "x" in order to find its value:

[tex]\begin{gathered} 1.12x=68,000 \\ \\ x=\frac{68,000}{1.12} \\ \\ x\approx60,714.29 \end{gathered}[/tex]

**The answer is:**

[tex]60,714.29[/tex]

f(x)=ln(2x+1) inverse

### Answers

**Answer:**

f−1(x)=ex+11−2ex

**Step-by-step explanation:**

Let y=f(x)=ln(x−1)−ln(2x+1). ⇒y=ln(x−12x+1). ⇒x−12x+1=ey. ⇒2xey+ey=x−1. ⇒x(1−2ey)=ey+1.

If you travel southeast from one city to another city that is 314 km away, and the trip takes you 4.00 hours, what is your average velocity?

### Answers

**Answer:**

78.5

**Step-by-step explanation:**

i just know

6

Mrs. Drake buys 72 peanut butter cups and

64 boxes of Nerds. She wants to make goody

bags for her students for Halloween. Mrs.

Drake wants to make sure that every bag has

the same number of each type of candy.

What is the greatest number of goody bags

she can make?

### Answers

64 because it is the least amount she has because if she made anymore she wouldn’t have enough nerds

Is 21.23 a rational number Show evidence

### Answers

**Answer:**

Yes, 21.23 is a rational number.

[tex]21.23=\dfrac{2123}{100}[/tex]

**Step-by-step explanation:**

**Terminating decimal numbers** are decimals that have a finite number of decimal places.

A **Rational Number **is the division of an integer by another integer.

Therefore, 21.23 is a **terminating decimal** since it has a **finite number** of **decimal places**.

Let x be the **rational number**.

[tex]\implies x=21.23[/tex]

**Multiply **both sides by 100 so that the right side is an **integer**:

[tex]\implies 100x=2123[/tex]

**Divide **both sides by 100:

[tex]\implies x=\dfrac{2123}{100}[/tex]

(This fraction cannot be reduced any further).

Therefore, we have proved that 21.23 is a **rational number**.

**Answer:**

It is a rational number.

**Step-by-step explanation:**

Given value,

→ 21.23

Converting into rational number,

→ (21.23/1) × (100/100)

→ (21.23 × 100)/(1 × 100)

→ 2123/100

Hence, it is a rational number.

Can anyone help me with this true or false question

### Answers

**ANSWER**

**A. True**

**EXPLANATION**

Let the complex number be z = a+ ib, so its complex conjugate is z* = a - ib, where a and b are real numbers. Let's find the product,

The product is,

[tex](a+ib)(a-ib)=a\cdot a-a\operatorname{\cdot}ib+ib\operatorname{\cdot}a-ib\operatorname{\cdot}ib[/tex]

Solve the products,

[tex](a+ib)(a-ib)=a^2-iab+iab-i^2b^2[/tex]

Simplify: note that the second and third terms are opposites, so they cancel out. Remember that i² is equal to -1,

[tex](a+ib)(a-ib)=a^2+0-(-1)b^2=a^2+b^2[/tex]

Since a and b were real numbers, then the sum of their squares is also a real number.

Hence, **this statement is ****true****.**

Write the equation of the line (in standard form) that goes through point (5,-1) and is parallel to the equation 3x + 2y = 19.

### Answers

3x+2y=10 This is the **equation **of the new line in **standard form**

Calculate the equation of the line in standard form?

Two **parallel **lines have the same slope, to compute the slope (m) of the equation 3x+2y=19. This can be obtained by converting the equation into slope-intercept form (i.e., y=mx+b, where m is the slope):

by subtracting 3x from both sides, and then simplifying:

3x+2y-3x=19-3x

2y =-3x+19

Then, let's divide both sides by 2, to obtain slope-intercept form:

y = (-3/2)x+(/2) From this, we know that the slope (m) is -3/2

To determine the **equation **of the line we're being asked to solve for. If we know the slope (in this case m=-3/2) along with any given point on the line ((x0,y0); in this case (4,1)), the equation of the line can be determined as y-y0=m(x-x0)

So substituting, the equation of the line is y-1=(-3/2)(x-5)

We now need to put this into standard form, with both x and y terms on the left side of the equation:

First, distribute the 3/2 on the right side: y-1=(-3/2)x+(3/2)5 or y-1

= (-3/2)x+6

Next,** add (3/2)x to both sides, **add 1 to both sides, and simplify:

(3/2) x + y = 5

multiply both sides by 2, to eliminate the fraction (3/2):** 3x+2y = 10** This is the equation of the new line in standard form

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Which equation represents a line that is perpendicular to the line passing through (-4,7) and (1,3)?A. y =x + 8B.y =-x + 6C.y =x - 3D. y = -x - 2

### Answers

If two lines of slopes m1 and m2 are perpendicular, then:

[tex]m_1\cdot m_2=-1[/tex]

The slope of a line passing through points (x1, y1) and (x2, y2) is:

[tex]\begin{equation*} m=\frac{y_2-y_1}{x_2-x_1} \end{equation*}[/tex]

We are given the points of the first line (-4, 7) and (1, 3). Calculate the slope

[tex]m_1=\frac{3-7}{1+4}=-\frac{4}{5}[/tex]

The slope of the perpendicular line is:

[tex]m_2=-\frac{1}{m_1}=-\frac{1}{-\frac{4}{5}}=\frac{5}{4}[/tex]

The equation of the perpendicular line has the form:

[tex]y=\frac{5}{4}x+b[/tex]

None of the options has the correct answer.

What property is used to solve 9x + 5 = 21 and 9x + 5 -5 = 21 - 5

### Answers

**Problem**

What property is used to solve 9x + 5 = 21 and 9x + 5 -5 = 21 - 5

**Solution**

9x +5 =21

If we subtract 5 in both sides we got:

**9x +5-5 =21-5**

**Subtraction property of equality**

Given point Q equals negative 6 radical 3 comma negative 6 in rectangular coordinates, what are the corresponding polar coordinates?

### Answers

Given the rectangular coordinates of point Q:

[tex]Q(-6\sqrt{3},-6)[/tex]

You need to remember that the form from rectangular oordinates to polar coordinates is:

[tex](x,y)\rightarrow(r,\theta)[/tex]

By definition:

[tex]\begin{gathered} r=\sqrt{x^2+y^2} \\ \\ \theta=tan^{-1}(\frac{y}{x}) \end{gathered}[/tex]

In this case, you can identify that:

[tex]\begin{gathered} x=-6\sqrt{3} \\ y=-6 \end{gathered}[/tex]

Then, you can determine that:

[tex]\begin{gathered} r=\sqrt{(-6\sqrt{3})^2+(-6)^2}=12 \\ \\ \theta=tan^{-1}(\frac{-6}{-6\sqrt{3}})=\frac{5\pi}{6} \end{gathered}[/tex]

Therefore, the polar coordinates are:

[tex](12,\frac{5\pi}{6})[/tex]

Hence,** the answer is: Second option.**

5x+10+11x+2=58 please help i’m confused

### Answers

Simplifying

5x + 10 + 11x + 2 = 58

Reorder the terms:

10 + 2 + 5x + 11x = 58

Combine like terms: 10 + 2 = 12

12 + 5x + 11x = 58

Combine like terms: 5x + 11x = 16x

12 + 16x = 58

Solving

12 + 16x = 58

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-12' to each side of the equation.

12 + -12 + 16x = 58 + -12

Combine like terms: 12 + -12 = 0

0 + 16x = 58 + -12

16x = 58 + -12

Combine like terms: 58 + -12 = 46

16x = 46

Divide each side by '16'.

x = 2.875

Simplifying

x = 2.875

**Answer:**

x = [tex]\frac{23}{8}[/tex] or 2 [tex]\frac{7}{8}[/tex]

**Step-by-step explanation:**

1. Add the numbers

10 + 2 = 12

5x+12+11x = 58

2. Combine like terms

5x + 11x = 16x

16x+12 = 58

3. Subtract 12 from both sides

16x + 12-12 = 58-12

x = [tex]\frac{23}{8}[/tex]

Kira, Justin, and Reuben have a total of $82 in their wallets. Kira has $10 more than Justin. Reuben has 2 times what Kira has. How much do they have in their wallets?

### Answers

Kira have $23 in his **wallet**.

Justin have $13 in his wallet.

Reuben have $46 in his wallet.

Given,

There are three persons, Kira, Justin, Reuben.

The **total amount **in their wallet = $82

The amount in Justin's wallet = x

The amount in Kira's wallet = x + 10

The amount in Reuben's wallet = 2(x + 10)

We have to find the** amount** in their wallets.

Here,

x + x + 10 + 2(x + 10) = 82

2x + 10 + 2x + 20 = 82

4x + 30 = 82

4x = 82 - 30

x = 52/4 = 13

Now,

The amount in Justin's** wallet** = x = $13

The amount in Kira's wallet = x + 10 = 13 + 10 = $23

The amount in Reuben's wallet = 2(x + 10) = 2(13 + 10) = 2 × 23 = $46

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EFG and GFH are a linear pair, mEFG = 2n +17, and mGFH = 4n +31. What are mEFG and mGFH?

### Answers

mEFG and mGFH is 61 and 119 respectively.

What is **linear pair **of angle**?**

**Linear pair** of angle are formed when two lines intersect each other at a single point and sum of angles of linear pair is always 180.

given, mEFG = 2n+17 and mGFH = 4n+31 and they both are linear.

Hence,

mEFG+mGFH = 180

2n+17+4n+31 = 180

6n+48=180

6n = 132

n = 22

hence, mEFG = 2(22)+17= 61 and mGFH = 4(22)+31 = 119

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If you are selling your house with a local realtor who requires a 5% commission fee, what can you expect to pay the realtor if your house sells for $176,000?

### Answers

given data:

The cost of house is $176000.

The percentage the house realtor requires is 5%.

That is,

[tex]\begin{gathered} \frac{5}{100}\times176000 \\ =8800 \end{gathered}[/tex]

Thus 5% of 176000 is 8800.

Thus, **you need to give $8800 to the local realtor.**

I have a few different questions :) first off I need this domain and range found

### Answers

**ANSWER**

[tex]\begin{gathered} \text{Domain: -7 }\leq x\leq3 \\ \text{Range: }-1\text{ }\leq y\leq9 \end{gathered}[/tex]

**EXPLANATION**

We want to find the domain and range of the function.

The domain of a function is the set of all input values of the function. Basically, **the set of all x values of a function**.

The range of a function is the set of all output values of the function. Basicallly, **the set of all y values of a function.**

To find the domain of the function, we have to **look at the smallest and largest values of x.**

The smallest value of x is -7.

The largest value of x is 3.

So, the domain is:

[tex]-7\text{ }\leq x\text{ }\leq3[/tex]

To find the range of the function, we have to** look at the smallest and largest values of y.**

The smallest value of y is -1.

The largest value of y is 9.

So, the range is:

[tex]-1\text{ }\leq y\leq9[/tex]

18 of the animals in the shelter arecats. If there are 40 animals in theshelter, what percent of the animalsare cats?

### Answers

There are 40 animals in the shelter, 18 of that animals are cats.

We need to find the percent of the animals that are cats.

Then, 40 animals represent 100% in the shelter.

We can use the rule of three to find the cat's percent:

Therefore:

40 animals -------------- 100%

18 cats ------------------------ x

x = (18*100)/40

x =45

So, 45 % of the animals are cats.

Question 15Please answer quickly, i don’t need much explanation and just want this to be done so I can use it as an example

### Answers

SOLUTION:

Step 1:

In this question Number 15, we are given the following:

During a sale, a store offered a 15% discount on a stereo system that originally sold for $400. After the sale the discount price of the stereo system was marked up by 15%. To the nearest whole number, what percent of the original price was the price after mark up

### Answers

**Problem Statement**

We are told a store offers 15% discount on the sale of a stereo originally costing $400. After the sale, the new price is marked up by 15%.

We are asked to find what percentage of the original price is the new marked up price.

** Method**

T

(1 point) Use the figure below to estimate the indicated derivatives. If a derivative does not exist, enter dne in the answer blank. The graph of f(x) is black and has a sharp corner at x=2. The graph of g(x) is blue.

Let j(x)=g(x)f(x). Find

j'(3)

### Answers

Applying the **quotient **rule, the **derivative **of the given function at x = 3 is of -2/3.

What is the quotient derivative rule?

A quotient function is defined as follows:

i(x) = g(x)/f(x)

Applying the quotient rule, the **derivative **of the function defined above is of:

i'(x) = [g'(x)f(x) - f'(x)g(x)]/f(x)².

Hence, at x = 3, the **numeric value** of the derivative is given as follows:

i'(3) = [g'(3)f(3) - f'(3)g(3)]/f(3)².

Function **f(x)** is a linear function with slope of -3/2, hence:

f'(3) = -3/2 (for a linear function, the derivative is constant).f(3) = 3/2 (from the graph).

Function **g(x)** is a linear function with slope of -1/2, hence:

g'(3) = -1/2.g(3) = 1/2.

Then the **derivative **is given as follows:

[tex]g^{\prime}(3) = \frac{-\frac{1}{2} \times \frac{3}{2} - \frac{3}{2} \times \frac{1}{2}}{\left(\frac{3}{2}\right)^2} = -\frac{\frac{6}{4}}{\frac{9}{4}} = -\frac{6}{9} = -\frac{2}{3}[/tex]

Hence the numeric value of the derivative at x = 3 is of -2/3.

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A rectangle is 7 times as long as it is wide. The perimeter is 32 feet. Find the dimensions.The length isfeet where the width isfeet.

### Answers

Let l and w be the length and width of the rectangle, respectively.

Therefore, according to the question,

[tex]\begin{gathered} l=7w \\ and \\ P=32 \\ P=2l+2w \end{gathered}[/tex]

Therefore, solving for l and w,

[tex]\begin{gathered} l=7w \\ 2(l+w)=32 \\ \Rightarrow l=7w,l+w=16 \\ \Rightarrow7w+w=16 \\ \Rightarrow w=2 \\ and \\ \Rightarrow l=7*2=14 \end{gathered}[/tex]The answer is length=14ft, width=2ft

Given that P(B AND A)=0.07 and P(B|A)=0.20, what is P(A)?

### Answers

**Answer: P A is paranthathesis add**

**Step-by-step explanation: so frist u do ( + ( = ((**

**then ((-)))=-)**