Mathematics College

## Answers

**Answer 1**

**Answer:**

50) Midpoint: (5.5, 0)

51) Midpoint: (6, -8)

**Step-by-step explanation:**

We can find the midpoint between two points using the midpoint formula, which is m = (x1 + x2) / 2, (y1 + y2) / 2, where

m is the midpoint,(x1, y1) are one point,and (x2, y2) are another point

**50) **We can allow (10, 10) to be our (x1, y1) point and (1, -10) to be our (x2, y2) point:

x-coordinate of midpoint of (10, 10) and (1, -10):

(10 + 1) / 2

11 / 2

5.5

y-coordinate of midpoint of (10, 10) and (1, -10):

(10 + (-10)) / 2

(10 - 10) / 2

0 / 2

Thus, the midpoint of the line segment with the endpoints (10, 10) and (-1, 10) is (5.5, 0).

**51) **We can allow (3, -6) to be our (x1, y1) point and (9, -10) to be our (x2, y2) point:

x-coordinate of midpoint of (3, -6) and (9, -10):

(3 + 9) / 2

12 / 2

6

y-coordinate of midpoint of (3, -6) and (9, -10):

(-6 + -10) / 2

(-16) / 2

-8

Thus, the midpoint of the line segment with the endpoints (3, -6) and (9, -10) is (6, -8).

## Related Questions

Question 4Mple Choice Worth 2 points)

Ares of Polygons and Composite Figures MC)

A composte figure is shown

024413

028.445²

1.15 in

Which of the following represents the total area of the figure?

010 663 ²

034.335 ²

4.6 in.

3h 563

P

### Answers

The** total area **of the composite figure which has **triangle** and rectangle is 24.41 square inches

The given composite figure has two triangles and one rectangle

**Area** of rectangle =length × width

=4.6×3.15

=14.49 square inches

Area of left side triangle, it has base of 3.3 in and height 3.15 inches

Area of **triangle** = 1/2×3.3×3.15

=5.1975 square inches

Area of triangle on right side

Base = 3 in

Height = 6.3-3.15=3.15 in

Area of triangle = 1/2×3×3.15

=4.725 square inches

**Total area** = 14.49 + 5.1975 + 4.725

=24.41 square inches

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What is the answer to this question.

Find the indicated values.

Arcs

mab

mabc

mbac

macb

### Answers

The measures of the following **arcs **are :

m∡AB = 49°

m∡ABC = 253°

m∡BAC = 156°

m∡ACB = 311°

What is the explanation for this?

Note that the sum total of the **arcs **in a **circle **is** 360°**

m∡AB = 49° - Given

m∡ABC = 360° 107° = 253°

m∡BAC = 107 + 49 = 156°

m∡ACB = 360 - 49 = 311°

A curve's **arc **length is significant because it represents the distance between two locations on the curve. The **circumference **of a circle is equal to its arc length. The arc length of an **ellipse **equals the ellipse's perimeter.

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Suppose a new postoperative procedure is administered to a number of patients in a large hospital. The researcher can ask the question, Do the doctors feel differently about this procedure from the nurses, or do they feel basically the same way? Note that the question is not whether they prefer the procedure but whether there is a difference of opinion between the two groups.

To answer this question, a researcher selects a sample of nurses and doctors and tabulates

the data in table form, as shown. Use a significance level of 5%.

### Answers

To determine whether there is a difference of opinion between doctors and nurses regarding a new **postoperative **procedure, the researcher conducted a survey and tabulated the data in a table form. The next step is to analyze the data using statistical methods and a significance level of 5%.

To begin the analysis, the researcher can use a statistical test such as the chi-square test for **independence**. This test will examine whether there is a significant association between the opinions of doctors and nurses regarding the procedure.

The chi-square test will compare the observed frequencies in each category (e.g., doctors who feel differently, doctors who feel the same, nurses who feel differently, nurses who feel the same) with the frequencies that would be expected if there was no association between the profession and opinion.

If the calculated chi-square value exceeds the critical value at a significance level of 5%, it suggests that there is a significant difference in opinion between the two **groups**.

The researcher should calculate the chi-square value, degrees of freedom, and compare it to the critical value from the chi-square distribution table.

If the calculated chi-square value exceeds the critical value, the researcher can conclude that there is a significant difference of opinion between doctors and nurses regarding the postoperative procedure.

It is important to note that statistical significance does not imply practical significance. Even if there is a significant difference, the **magnitude** of the difference should be considered in the context of the study.

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last year a company made a profit of one and a quarter million dollars each year the company reinvests 1/3 of the profit how much of this profit will they reinvest

### Answers

The amount of **profit **that will be reinvested is 5/12 million.

How much profit will be reinvested?

**Profit **is the excess of revenue over cost.

Profit = revenue - total cost

In order to determine the profit that will be **reinvested, **multiply the fraction that is reinvested by the value of the profit.

Amount that will be **reinvested ** = profit x fraction that is reinvested

1 1/4 x 1/3 =

5/4 x 1/3 = 5/12 million

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lan is 1.83m tall

Donna is 6cm shorter

What is Donna's height in metres?

### Answers

**Answer:**

**Step-by-step explanation:**

lan is 1.83m tall. Donna is 6cm shorter. What is Donna's height in metres? 1.77m. Bath. √34°. 20m. 11m. 11x14. Work out the range. 3 8 4 8 3 5 9. 9-3=6.

If the probability that an identified hurricane will make a direct hit on a certain stretch of beach is 1/4, what are the odds against a direct hit?

A)3 to 1

B)1 to 3

C)1 to 4

### Answers

The **odds against** a direct hit is 3 to 1.

Given that the **probability** of a hurricane hitting at a coast is 1/4 = 0.25.

Therefore, the **probability** of not hitting = 1-0.25

= 0.75

we know that,

**Odds** against direct hit = [P(no direct hit)]/P[(direct hit)] = 0.75/0.25 = 3/1

= 3:1

Hence the **odds against** a direct hit is 3 to 1.

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Drag each number to a box to complete the table. Each number may be used once or not at all.

8,000533,00021,000

Kilometers Meters

1

2,000

5,000

8

### Answers

Each **number **should be dragged to a box to complete the **table** as follows;

Kilometers Meters

1 1,000

2 2,000

3 3,000

5 5,000

8 8,000

What is a conversion factor?

In Science and Mathematics, a **conversion factor** is a number that is used to convert a **number** in one set of units to another, either by dividing or multiplying.

Generally speaking, there are one (1) **kilometer** in one thousand (1,000) meters. This ultimately implies that, a proportion or ratio for the conversion of **kilometer** to meters would be written as follows;

Conversion:

1 **kilometer** = 1,000 meters

2 kilometer = 2,000 meters

3 kilometer = 3,000 meters

4 **kilometer** = 4,000 meters

5 kilometer = 5,000 meters

6 kilometer = 6,000 meters

7 kilometer = 7,000 meters

8 **kilometer** = 8,000 meters

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

please help i don’t feel like typing

### Answers

**Answer: q=13**

**Step-by-step explanation:**

add the separate the q, add 4 to the 9= 13

13=q

The parabola y = x^2 is scaled vertically by a factor of 1/10

### Answers

The **parabola** y = x² **scaled vertically **by a factor of 1/10 gives y = x²/10

Calculating the image of the vertical scale

From the question, we have the following parameters that can be used in our computation:

The **parabola** y = x² is scaled vertically by a factor of 1/10

The rule of this **transformation **is

Image = (x, ay)

Where

a = 1/10

So, we have

y = 1/10 * x²

Evaluate

y = x²/10

Hence, the **image **of the **function **is y = x²/10

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Franklin Lyons is married and claims 3 withholding allowances. He gets paid overtime if he works over 40 hours in a week. His gross pay is $958.38. Find the Federal Withholding Tax.

### Answers

Based on the assumptions, the estimated **Federal** **Withholding** Tax for Franklin **Lyons** would be approximately $191.68.

Determine Franklin's **taxable** **income**:

To calculate the **taxable** **income**, we need to subtract any deductions or exemptions from his gross pay. We'll consider his gross pay as the taxable **income**.

Taxable Income = Gross Pay = $958.38

Estimate the Federal Withholding **Tax** **rate**:

The Federal Withholding Tax rate depends on the taxable income and the individual's filing status. Let's assume a general **tax** rate** **of 20% for this estimation.

Federal Withholding Tax rate = 20%

Calculate the Federal Withholding Tax:

To find the withholding tax, multiply the **taxable** **income** by the tax rate:

Federal Withholding Tax = Taxable Income * Federal Withholding Tax rate

= $958.38 * 0.20

= $191.68

Thus, the answer is $191.68.

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The radius of a circle is 17 centimeters. What is the circle's circumference?

### Answers

**Answer: **

The circle's circumference is approximately 106.81 centimeters.

**Explanation:**

The formula for the circumference of a circle is C = 2πr, where C is the circumference, π is pi (approximately 3.14), and r is the radius of the circle.

So, for a circle with a radius of 17 centimeters, its circumference can be found by:

C = 2πr

C = 2 x 3.14 x 17

C ≈ 106.81 cm

*Therefore, the circumference of the circle is approximately 106.81 centimeters.*

what’s is the surface area of this rectangular prism?

### Answers

**Answer:**

220 in²

**Step-by-step explanation:**

surface area = [area of the 4 vertical faces] + area of the base + area of top.

surface area = [2(4 X 10) + 2(5 X 10)] + (4 X 5) + (4 X 5)

= (80 + 100) + 20 + 20

= 220 in²

it is due today, please help me. If you just want points get out of my question page...

### Answers

To completely solve the problem, Karim should convert the product back into **standard decimal notation**.

We cannot directly apply the **product **of **powers property **because the **binomial **is not raised to a power itself.

Miscellaneous problem

(1) To convert a number from **scientific notation **to standard decimal notation, we multiply the coefficient (0.0258) by 10 raised to the power of the exponent (-8).

0.0258 × [tex]10^{-8[/tex] = 0.0258 × 0.00000001

= 0.000000000000258

(2) The product of **powers property** states that when you raise a term with an exponent to another exponent, you can simplify it by multiplying the exponents.

In the expression [tex](3z + y)^3[/tex], we have a **binomial term** (3z + y) raised to the power of 3. This is not a situation where we can directly apply the product of powers property because the binomial is not raised to a power itself.

To simplify the expression, we need to expand it using the **binomial theorem **or by applying the concept of binomial expansion.

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Solve each equation by completing the square.

d² - 24d + c

### Answers

**Answer:**

d² - 24d + c = (d - 12)² - 144 + c

The mean of a, 31, 42, 65, and b is 51. The greatest number is 67 more than the least number. What are the missing numbers? Please explain.

### Answers

**Answer:**

a=25

b=92

**Step-by-step explanation:**

Because the average of the five numbers is 51, the sum of the five numbers is 255.

a+b+73+65=255

138+a+b=255

a+b=117

a+67=b

Therefore,

**a=25**

**b=92**

Feel free to tell me if I made a mistake! :)

Find the value of x. Round to the nearest tenth .

### Answers

**Answer:**

23.8

**Step-by-step explanation:**

In a right-angled triangle, x ² + b ² = c ²

30.5 is c, we can choose b to be 19.1.

x ² + b ² = c ²

x ² = c ² - b ²

= 30.5² - 19.1²

= 565.44

x = √565.44

= 23.8 (to 3 significant figures)

Audio Button Question The volume of a cylindrical container is 251 cubic inches. The radius of the container is 4 inches. Find the height of the container. Round your answer to the nearest inch.

### Answers

The **height **of the **cylindrical container **is approximately 5 inches.

What is the height of the cylinder?

A **cylinder **is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.

The **volume **of a **cylinder **is expressed as;

V = π × r² × h

Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 )

Given that:

Volume V = 251 cubic inches

Radius r = 4 inches

Height h = ?

Plug the given values into the above formula and solve for **height**.

V = π × r² × h

251 = 3.14 × 4² × h

251 = 3.14 × 16 × h

251 = 50.24 × h

h = 251/50.24

h = 5 inches.

Therefore, the **measure **of the **height **is 5 inches.

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Find the surface area of the composite solid to the nearest hundredth.

A composite solid of a square prism with a square pyramid extending from the top and bottom face of the prism. The width, length, and height of the prism are all 5 inches. The slant height of the pyramid on the bottom of the prism is 7.5 inches. The height of the pyramid on top of the prisim is 3 inches.

### Answers

The **surface area** of **the composite solid** is 255 square inches.

How to find the **surface area** of **the composite solid?**

We will compute the **surface area** of each component and then add them together to find the surface area of the **composite solid**.

First, the surface area of the square **prism**:

Given: The square prism has a width, length, and height of 5 inches each.

Formula for the surface area of a rectangular prism: 2lw + 2lh + 2wh

Surface area of the prism = 2(5 * 5) + 2(5 * 5) + 2(5 * 5)

= 2(25) + 2(25) + 2(25)

= 50 + 50 + 50

= 150 square inches

Next, the surface area of the square **pyramid** at the bottom:

Given: The slant height of the pyramid on the bottom of the prism = 7.5 inches.

The base of the pyramid is a square with a side length of 5 inches.

Formula to find the lateral surface area of a square pyramid: (perimeter of base) * slant height / 2.

The base is a square, the perimeter is 4 times the side length.

Lateral surface area of the bottom pyramid = (4 * 5) * 7.5 / 2

= 20 * 7.5 / 2

= 150 / 2

= 75 square inches

Then, the Surface area of the square pyramid at the top:

Given: The height of the pyramid on top of the prism = 3 inches.

The base of the pyramid is a square with a side length of 5 inches.

Lateral surface area of the top pyramid = (4 * 5) * 3 / 2

= 20 * 3 / 2

= 60 / 2

= 30 square inches

Finally, we shall find the total surface area by **summing up** the surface areas of each component in this way:

Total surface area = Surface area of the prism + Surface area of the bottom pyramid + Surface area of the top pyramid

= 150 + 75 + 30

= 255 square inches

Therefore, the **surface area** of the composite solid = 255 square inches.

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A survey of 800 nurses yielded the following information. 555 were health club members, 430 were smokers, and 320 of the health club members were smokers. How many of the 800 surveyed nurses were health club members or were smokers

### Answers

**Step-by-step explanation:**

800 in total.

555 health club members.

430 smokers.

320 health club members (that means out of the total of 555) were smokers.

that means that

555 - 320 = 235 health club members were not smokers.

and out of the 430 smokers 320 were also health club members.

that means that

430 - 320 = 110 smokers were not health club members.

the question how many were health club members or smokers means how many people were either health club members or smokers.

so, we need to combine the sets of health club members and smokers.

the number of elements in the resulting set is not just the sum of elements of both sets, because some elements are in both sets and would be counted twice.

therefore, we have a few alternatives :

1. add both sets and then subtract the common part (people being in both sets), as this removes the double counting :

555 + 430 - 320 = 665

2. start with the common part (people that are in both sets) and add the extra people in both sets (health club members that do not smoke, and smokers that are not health club members) :

320 + 235 + 110 = 665

3. start with one of the full sets (e.g. all health club members) and add the extra people of the other set (all smokers that are not also health club members) :

555 + 110 = 665

or all smokers plus all health club members that were not smokers :

430 + 235 = 665

as you can see, as expected, the answer is always the same :

out of the 800 nurses 665 were health club members or smokers.

A manager drew this box-and-whisker plot to represent the number of minutes each of his 27 employees took on their break. Each employee took a different amount of time.

How many employees took a break longer than 49 minutes?

Help please!

Note: Put the correct answer! I don't want to get this wrong!

Thank you <3

### Answers

Approximately 7 **employees** took a break **longer** than 49 **minutes**.

We have,

In a box-and-whisker plot, the box represents the **interquartile** **range** (IQR), which includes the middle 50% of the data.

The line within the box represents the median.

The "whiskers" extend to the minimum and maximum values, excluding any outliers.

Given the information provided:

Median = 41

Q1 = 37

Q3 = 49

Largest = 55

Smallest = 35

Since Q3 represents the upper quartile and corresponds to the boundary for the upper 25% of the data, we can conclude that 25% of the employees took a break longer than 49 minutes.

Now,

The number of **employees** who took a break longer than 49 minutes can be estimated by calculating 25% of the total number of employees:

25% of 27 employees

= (25/100) x 27

= 6.75

Since we cannot have a fractional number of employees, we round up to the nearest whole number.

Therefore,

Approximately 7 **employees** took a break **longer** than 49 **minutes**.

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Need the answer for first picture!

### Answers

The **measure **of <MNL is (71 - 3x²)/2.

We have,

**Far **Arc = 59 - 2x²

**Near **Arc = 12 - x²

Angle = 180- 2x²

Using the **Formula**

Angle= **Average **of vertical **chords**

180 - 2x² = (59 - 2x² + 12 - x²)/2

360 - 4x² = 71 - 3x²

289 = x²

x= 17

So, the **measure **of <MNL

= (71 - 3x²)/2

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please please please please answer

### Answers

The value of the **variable** t of the **exponential equation** [tex]-5\cdot e^{10\cdot t} = - 30[/tex], t = (1 / 10) · ㏑ 6 (EXACT), t = 0.179 (APPROXIMATE).

How to solve an exponential equation

In this problem we need to clear the **variable** t of an **exponential equation** with one variable, this can done by means of relationship of exponential and logarithmic functions, logarithm properties and algebra properties.

Now we proceed to present the complete procedure for the solution to the exponential equation:

[tex]-5\cdot e^{10\cdot t} = - 30[/tex]

[tex]e^{10\cdot t} = 6[/tex]

10 · t = ㏑ 6

t = (1 / 10) · ㏑ 6

t = 0.179

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50 Points! Multiple choice geometry question. Photo attached. Thank you!

### Answers

The **value** of x is 9.

**Given**,

Trapezoid with two bases and **median**.

base 1 = 44

**base 2** = 2x + 10

median = 36

**Now**,

In trapezoid two bases will be parallel to each other.

**Median** = 1/2(sum of two bases)

**From** the formula of median the value of x will be,

Median = 1/2( base 1 + base 2 )

**Substitute** the values,

36 = 1/2( 44 + 2x + 10 )

72 = 54 + 2x

x = 9

**Hence** both the bases of trapezoid are obtained.

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A certain loan program offers an interest rate of 4.5%, compounded continuously. Assuming no payments are made, how

much would be owed after six years on a loan of $1300?

Do not round any intermediate computations, and round your answer to the nearest cent.

$

X 5

?

0

00

B

### Answers

The principal amount of $2,287.26 from **compound interest **at a rate of 4.5% per year owed after six years on a loan of $1300

Since n is the number of times the interest is compounded each year, and 'r' is the rate of **compound interest **annually, sothe final amount after 't' years would be:

[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]

Given that certain loan program offers an interest rate of 4.5%, compounded continuously.

Assuming no payments are made so;

First, convert R as a **percent **to R as a decimal

r = R/100

r = 4.5/100

r = 0.045 per year,

Then, solve the **equation **for P

P = A / (1 + r/n)^nt

P = 1300/ (1 + 0.045 /365)(365)^(15)

P = 1300/ (1 + 0.00010137)^(4745)

P = $2,287.26

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Evaluate a - 13 when a = 33.

(a) 46

(b) 20

(c) -46

(d) -20

### Answers

**Answer:**

(b) 20

**Step-by-step explanation:**

We are trying to solve a-13 = ____ for when a=33.

Substitute 33 for a.

33-13 = 20

the answer is b) 20

The sales tax rate for the state of Washington was 9.2%.

a) What is the state sales tax on a $2,800 used car in Washington?

b) What is the final cost of the car, including tax?

### Answers

**a) **The** state sales tax** on a $2,800 used car in Washington is given as follows: $257.6.

**b) **The** total cost** of the car, including tax, is given as follows: $3,057.6.

How to obtain the sales tax and the total cost of the car?

The sales tax and the total cost of the car are obtained applying the **proportions **in the context of the problem.

The sales tax **rate **is given as follows:

9.2%.

Hence, for a car of $2,800, the** sales tax **is given as follows:

0.092 x 2800 = $257.6.

The **total cost** is then obtained adding the base cost to the sales tax, as follows:

2800 + 257.6 = $3,057.6.

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A cube has a depth of 9 dm. What is the volume of the cube?

### Answers

The **volume **of the cube is 729 dm³

How to find the volume of the cube?

Remember that all the **dimensions **on a cube are the same ones, then we have:

Length = Width = Depth.

And for any prism, the **volume **is the product between the 3 dimensions, then for any cube the volume is:

V = Length*Width*Depth.

In this case we know that the depth is 9dm, then also is the length and the width, and thus, the volume of this cube is:

V = 9dm*9dm*9dm = 729 dm³

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mara works for an electronics store and receives a 6.5% commission on her sales. She also recevies a weekly salary 460. mara's boss asks her to specialize in the sale of flat screen televisions that cost $414 each, which means those are the only items she will sell. write and sole an equation to find the number of televisions, t, she sells in one week if she earns 890.56 for the week

### Answers

**Answer:**

16 tvs

**Step-by-step explanation:**

Maura's earnings for the week equal her weekly salary (460) plus she earns 6.5% commission x number of flat screens sold x $414.

So: Total Earnings = 460+ 0.065*414*t where t is the number of tvs she has sold.

If total earnings = 890.56, just substitute that above and solve for t.

890.56= 460+ 0.065*414*t

430.56=0.065*414*t

430.56=26.91*t

430.56/26.91 = t

16 = t

She sold 16 tvs to earn 890.56.

Can someone answer this question?

### Answers

The **graph** represents

[tex]{y \to -\infty}[/tex] as [tex]{x \to \infty}[/tex]

[tex]{y \to \infty}[/tex] as [tex]{x \to -\infty}[/tex]

From the given graph we can see that,

The curve represent** cubic** function

And we know that such cubic** function **is of the form

f(x) = y = -(ax³ + bx² + cx + d)

Since,

A function can approach two separate **limits**: one in which the **variable **approaches its limit by using values more than the limit, and one in which the variable approaches its limit by using values less than the limit.

Case 1:

Take limit of x approaching to** infinity**,

[tex]\lim_{n \to \infty} f(x) = y = -\infty[/tex]

Hence,

As x approaches to infinity the

y approaches to negative infinity.

Case 2:

Take limit of x approaching to negative of infinity,

Now since **degree** of function is 3 which is odd

Therefore,

[tex]\lim_{n \to -\infty} f(x) = y = \infty[/tex]

Hence,

As x approaches to negative infinity then

y **approaches** to infinity.

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Can you solve the hcf of 20and 10

### Answers

The **HCF** **(highest common factor) ** of 20 and 10 is 10.

To **determine** the 20 and 10's highest common factor (HCF).

We must identify the highest number that can divide both 20 and 10 without producing a remainder in order to determine the HCF.

1, 2, 4, 5, 10, and 20 are the **variables** that make up 20.

1, 2, 5, and 10 make up the number 10.

The biggest element that both 20 and 10 have as a shared **component** is 10.

The HCF of 20 and 10 is hence 10.

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