Mathematics College

## Answers

**Answer 1**

**Answer:**

The sum of 33, 78, 23, 21, 98, and 32 is 325.

## Related Questions

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

### Answers

**Answer:**

**B. 108 ft³**

**Step-by-step explanation:**

solution given:

**We have Volume of solid = Area of base * length**

over here

base : 9ft

height : 6 ft

length : 4ft

Now

Area of base : Area of traingle:½*base*height=½*9*6=27 ft²

Now

Volume : Area of base*length

Volume: 27ft²*4ft

Therefore **Volume of the solid=108 ft³**

Express log 161 in the form of loga + logb.

### Answers

**log 161** can be expressed as **log 7 + log 23** in the form of loga + logb.

To express log 161 in the form of loga + logb, first we need to find suitable values for a and b such that their **logarithmic** **product is equal to log 161.**

Let's find the factors of 161 :

161 = 7 * 23

Now, we can express log 161 as product of two logarithms :

log 161 = log (7 + 23)

Using the logarithmic property **log(a*b) = log a + log b :**

log 161 = log 7 + log 23

Therefore, log 161 can be expressed as log 7 + log 23.

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Find the volume of a cone of radius 3.5cm and vertical height 12 cm.

### Answers

**Answer:**

Volume ≈ 153.93804 cm^3

Rounded to the nearest whole number, the volume of the cone is approximately 154 cm^3.

**Step-by-step explanation:**

1. Simplify: |-11 +3|

Answer

A-8

B -14

C 8

D 14

### Answers

**Answer: C **

**Step-by-step explanation:**

**|-8| = 8**

9. Determine the area of the figure below.

5.5 cm

8 cm

12 cm

6.8 cm

### Answers

Area of the given figure would be :

" Sum of area of Trapezoid and Semicircle "

Lets calculate the area of Trapezoid first ~

its " 1/2 times (sum of parallel sides) times (perpendicular distance between them) "

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{1}{2} \times ( 8+ 12) \times (5.5)[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{1}{2} \times (20) \times (5.5)[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 10 \times 5.5[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 55 \: \: cm {}^{2} [/tex]

Next, area of Semicircle ~

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{ \pi {r}^{2} }{2} [/tex]

[tex] \textsf{[ diameter (d) = 8 cm, radius (r) = d/2 = 8/2 = 4 cm ]} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{3.14 \times ( {4)}^{2} }{2}[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 1.57 \times 16[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 25.12 \: \: cm {}^{2} [/tex]

Now, Area of the composite figure :

- Area of Trapezoid + Area of Semicircle

[tex]\qquad\displaystyle \tt \dashrightarrow \: 55 + 25.12 = 80.12 \: cm²[/tex]

In the figure below, k || 1 and m II n. Find the values of x and y.

xo

(Sy-98)

#

77°

X =

y=

### Answers

x+77=180

x=180-77=103°

x+5y-98=180

=> 103+5y-98=180

=> 5y=180-5

=> y=175/5=35°

variable of 10(n+3)=1,000,00

### Answers

**Answer: Distribute the 10 on the left side of the equation:**

**10n + 30 = 1,000,000**

**Subtract 30 from both sides of the equation to isolate the term with n:**

**10n = 1,000,000 - 30**

**10n = 999,970**

**Divide both sides of the equation by 10 to solve for n:**

**n = 999,970 / 10**

**n = 99,997**

**Therefore, the value of the variable n that satisfies the equation 10(n + 3) = 1,000,000 is n = 99,997.**

**Step-by-step explanation:**

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

### Answers

**To determine the radius of each wheel, we can use the formula for the circumference of a circle:**

**Circumference = 2πr,**

**where "Circumference" represents the circumference of the wheel and "r" represents the radius of the wheel.**

**Given that the circumference of each wheel is 22 inches, we can set up the equation as follows:**

**22 = 2πr.**

**To solve for the radius, we'll isolate "r" by dividing both sides of the equation by 2π:**

**22 / (2π) = r.**

**Using a calculator for the approximation, we get:**

**r ≈ 3.5 inches.**

**Therefore, to the nearest length, the radius of each wheel is approximately 3.5 inches.**

**Answer:**

C) 3.5 inch

**Step-by-step explanation:**

{[(30+40)+(40-30)]x(20+10)}

### Answers

Let's simplify the expression step by step:

First, let's simplify the inner parentheses:

(30 + 40) = 70

(40 - 30) = 10

The expression now becomes:

[(70) + (10)] x (20 + 10)

Next, let's simplify the addition within the parentheses:

(70) + (10) = 80

(20 + 10) = 30

The expression further simplifies to:

80 x 30

Finally, let's multiply:

80 x 30 = 2400

Therefore, the final result of the expression [(30+40)+(40-30)]x(20+10) is 2,400.

I hope this helps! :)

{[(30+40)+(40-30)]x(20+10)}

{[70 + 10]x 30}

{80 x 30}

2400

2.

5 m

50 m

18 m

25 m

### Answers

As per the given data, the **area** of the rectangular **field** is approximately 204 square meters.

To find the area of the **rectangular** **field**, we need to multiply its length by its width.

Given that the **length** is 18 2/5 m and the **width** is 11 2/23 m, we need to convert these mixed fractions into improper fractions for easier calculation.

Length: 18 2/5 m = (5 * 18 + 2)/5 = 92/5 m

Width: 11 2/23 m = (23 * 11 + 2)/23 = 255/23 m

Now, we can calculate the **area** of the rectangular field:

Area = Length * Width

= (92/5) m * (255/23) m

= (92 * 255)/(5 * 23) m^2

= 23460/115 m^2

= 204 m^2 (rounded to the nearest whole number)

Therefore, the **area** of the rectangular field is approximately 204 square meters.

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Your question seems incomplete, the probable complete question is:

A rectangular field is 18 2/5 m long and 11 2/23 m wide. Find its area.

Solve (D ^ 2 - 6D + 9) * y = 0

### Answers

The solution to the given **differential equation** is y(x) = (C1 + C2x) * e^(3x), where C1 and C2 are arbitrary constants.

To solve the given differential equation, we need to find the function y(x) that **satisfies **the equation:

(D^2 - 6D + 9)y(x) = 0,

where D represents the differentiation operator.

Let's break down the solution process step by step:

Characteristic Equation

First, we'll find the **characteristic **equation associated with the given differential equation. For a second-order linear homogeneous differential equation of the form aD^2y + bDy + cy = 0, the characteristic equation is obtained by replacing D with λ:

λ^2 - 6λ + 9 = 0.

Solving the Characteristic Equation

Now, we solve the characteristic equation to find the **values **of λ. Factoring the equation, we get:

(λ - 3)^2 = 0.

From this, we see that λ = 3 (with a multiplicity of 2).

General Solution

The general **solution **of the differential equation is given by:

y(x) = C1e^(λ1x) + C2xe^(λ2*x),

where C1 and C2 are **arbitrary **constants, and λ1, λ2 are the distinct roots of the characteristic equation.

In our case, since we have repeated roots, the general solution simplifies to:

y(x) = C1e^(3x) + C2xe^(3*x).

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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

### Answers

The** length **of the **arc** LM is 8.72 cm.

We have,

The** length** of an **arc** is the distance that runs through the curved line of the circle making up the arc.

The** length **of an arc is expressed as;

l = tetha/360 × 2πr

tetha = R

R = 100°

and, radius = 5 units

so, we get,

l = 100/360 × 2 × 3.14 × 5

l = 8.72 cm (1.dp)

therefore the **length **of th**e arc** LM is 8.72 cm

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Please answer these questions by today

### Answers

41.

Out of the 18 **parts**, we **shade** 5 parts

Out of the 27 **parts**, we **shade** 4 parts

42.

There are 60 **pieces**.

43.

The **fractional** **part** for each person.

44.

10(1/2), 1/21, 2(14/15), and 18.

We have,

41.

a.

1/3 x 5/6

= 5/18

This means,

Out of the 18 parts, we **shade** 5 parts

b.

2/9 x 2/3

= 4/27

This means,

Out of the 27 parts, we **shade** 4 parts

42.

String = 15 feet

Length of each piece = 1/4 feet

Now,

The number of 1/4 feet pieces.

= 15/(1/4)

= 15 x 4

= 60 **pieces**

43.

Original pizza = 1

Half pizza = 1/2

Number of people = 3

Now,

The **fractional** **part** for each person.

= 1/2 ÷ 3

= 1/6

44.

a.

7/6 x 9

= 7/2 x 3

= 21/2

= 10(1/2)

b.

1/7 ÷ 3

= 1/(7 x 3)

= 1/21

c.

4/5 x 3(2/3)

= 4/5 x 11/3

= 44/15

= 2(14/15)

d.

2 ÷ 1/9

= 2 x 9/1

= 18

Thus,

41.

Out of the 18 **parts**, we **shade** 5 parts

Out of the 27 **parts**, we **shade** 4 parts

42.

There are 60 **pieces**.

43.

The **fractional** **part** for each person.

44.

10(1/2), 1/21, 2(14/15), and 18.

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HELP PLEASEE PLEASE I NEED TO PASS THIS LESSON

### Answers

The **function **[tex]G(t)= 1024(0.5)^{t-1[/tex] models the number of computer games sold where t is the number of days since the release date and G(t) is the number of computer games sold.

The given table is

Days After Number of

Release Date Games sold

0 1024

1 512

2 256

3 128

Here, the common ratio = 512/1024

= 1/2

The formula to find nth term of the** geometric sequence** is aₙ=arⁿ⁻¹. Where, a = first term of the sequence, r= common ratio and n = number of terms.

Here, [tex]G(t)= 1024(0.5)^{t-1[/tex]

Therefore, the **function **[tex]G(t)= 1024(0.5)^{t-1[/tex] models the number of computer games sold where t is the number of days since the release date and G(t) is the number of computer games sold.

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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

### Answers

Angle C of the triangle **measures **68°.

**Side** AC = 22.90

**Side** BC = 14.26

**Given** triangle,

∠A = 37°

∠B = 75°

AB = 22

**Now**,

Sum of all the** interior **angles of triangle is 180.

**So**,

∠A + ∠B +∠C = 180°

37° + 75° + ∠C = 180°

∠C = 68°

Now,

**According** to sine rule,

**Ratio** of side length to the sine of the opposite angle is equal.

Thus,

a/SinA = b/SinB = c/SinC

**Let**,

BC = a

AC = b

AB = c

So,

a/Sin37 = b/Sin75 = c/Sin68

a/0.601 = b/0.965 = 22/0.927

**Solving**,

BC = a = 14.26

AC = b = 22.90

Thus with the properties of** triangle** side length and angles can be calculated.

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4

(1 pa

10. The table shows the results from home games for a specific team during the season leading up

to the World Series. The team's home field has a roof that can be closed for weather. If it is

closed, the fans could make more noise for the home team and possibly give them an

advantage. Find the test statistic needed to test independence for the contingency table.

Closed roof

Open roof

034.215

00.093

00.798

03.841

Win

36

15

Loss

17

11

### Answers

The **test** **statistic** χ² is approximately 1.47.

We have,

To **test** **independence** for the contingency table, we need to calculate the **test** **statistic**.

The most commonly used test statistic for testing independence in a 2x2 contingency table is the chi-square test statistic.

The **chi**-**square** test statistic (χ²) is calculated using the formula:

χ² = Σ [(Observed - Expected)² / Expected]

Where:

Σ represents the sum over all cells of the contingency table.

Observed is the observed frequency in each cell.

Expected is the expected frequency in each cell if the variables were independent.

First, we calculate the expected frequencies for each cell. To do this, we use the formula:

**Expected** **frequency** = (row total x column total) / grand total

Grand total = sum of all frequencies = 36 + 17 + 15 + 11 = 79

Expected frequency for the cell "Closed roof - Win" = (53 * 51) / 79 = 34.49

Expected frequency for the cell "Closed roof - Loss" = (53 * 28) / 79 = 18.51

Expected frequency for the cell "Open roof - Win" = (26 * 51) / 79 = 16.51

Expected frequency for the cell "Open roof - Loss" = (26 * 28) / 79 = 9.49

Now, we can calculate the test statistic using the formula:

χ² = [(36 - 34.49)² / 34.49] + [(17 - 18.51)² / 18.51] + [(15 - 16.51)² / 16.51] + [(11 - 9.49)² / 9.49]

Calculating each term and summing them up:

χ² ≈ 0.058 + 0.482 + 0.58 + 0.35 ≈ 1.47

Therefore,

The **test** **statistic** χ² is approximately 1.47.

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If you reflect AFGH across the y-axis, What will be the coordinates of the vertices of the image AFGH?

### Answers

The **coordinates** of the vertices of the **image** F'G'H' after **reflecting** FGH across the y-axis are:

F' = (2, -1)

G' = (-2, 2)

H' = (-4, -3)

We have,

When **reflecting** a point across the y-axis, the x-coordinate of the point is negated while the y-coordinate remains the same.

Applying this **transformation** to each vertex, we get:

F' = (-(-2), -1) = (2, -1)

G' = (-(2), 2) = (-2, 2)

H' = (-(4), -3) = (-4, -3)

Therefore,

The **coordinates** of the vertices of the **image** F'G'H' after **reflecting** FGH across the y-axis are:

F' = (2, -1)

G' = (-2, 2)

H' = (-4, -3)

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A truck travels from warehouse A at (–4,8) to warehouse B at (–4,–1). If each unit represents 20 miles per hour, how long will it take the truck to travel this distance?

### Answers

It will take the truck 9 **hours **to travel from warehouse A to warehouse B.

To determine the time it takes for the truck to **travel **from warehouse A at (-4, 8) to warehouse B at (-4, -1), we need to calculate the distance between these two points and then convert it to time using the given unit of 20 miles per hour.

First, let's find the vertical **distance **between the two points. The y-coordinate of warehouse A is 8, and the y-coordinate of warehouse B is -1. So the vertical distance is 8 - (-1) = 9 units.

Next, we **convert** the vertical distance to miles. Since each unit represents 20 miles per hour, we multiply the vertical distance by 20: 9 units × 20 miles/unit = 180 miles.

Now, we can calculate the time it takes to travel this distance. We divide the distance by the **speed **of the truck, which is 20 miles per hour: 180 miles / 20 miles per hour = 9 hours.

Therefore, it will take the truck 9 hours to travel from **warehouse **A to warehouse B.

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There are books on a shelf. of these books are new. The rest of them are used. what is the ratio of used books to all books on the shelf?

### Answers

Let's denote the total number of books on the shelf as 'total_books', and the number of new books as 'new_books'.

The number of used books can be calculated as the difference between the total number of books and the number of new books:

used_books = total_books - new_books

To find the ratio of used books to all books on the shelf, we divide the number of used books by the total number of books:

Ratio of used books to all books = used_books / total_books

Substituting the expression for used_books, we have:

Ratio of used books to all books = (total_books - new_books) / total_books

Simplifying further:

Ratio of used books to all books = 1 - (new_books / total_books)

Therefore, the ratio of used books to all books on the shelf is equal to 1 minus the ratio of new books to total books.

The volume of a cone with height h and radius r can be found using the formula V= 1/3 π r^2h

Find the volume of a cone with radius 9 feet and height 4 feet. Round your answer to two decimal places.

### Answers

**Answer: **To find the volume of a cone with radius 9 feet and height 4 feet, we can use the formula:

V = (1/3) * π * r^2 * h

Plugging in the values:

V = (1/3) * π * (9^2) * 4

Calculating:

V = (1/3) * π * 81 * 4

V ≈ 108.19 cubic feet

Therefore, the volume of the cone is approximately 108.19 cubic feet (rounded to two decimal places)

edmentum question:

-post test: similarity and proof

in the diagram, the ratios __ and ___ are equal

### Answers

We can deduce here that in the **diagram **the **ratios **AD : DB and AE : EC are equal.

What are similar triangles?

**Triangles **that resemble one another but may differ in size are said to be similar triangles. They have equal corresponding angles and proportional **corresponding **sides, in other words.

Two triangles are **similar **if and only if the following conditions are met:

Angle-Angle (AA) SimilaritySide-Angle-Side (SAS) SimilaritySide-Side-Side (SSS) Similarity

The corresponding sides of two **triangles **that are comparable are proportionate. The length of the comparable side in the other triangle can be obtained by multiplying the length of a side in one triangle by the same factor.

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Solve following modular equation, using reverse Euclidean algorithm:

[tex](5 * x) mod 91 = 32[/tex]

### Answers

The **required **reverse Euclidean algorithm is the solution to the **modular equation **(5x) mod 91 is

x = 6(mod 91).

**Given **that (5*x) mod 91 =32.

To solve the **modular **equation (5*x) mod 91 =32 using reverse Euclidean algorithm is to find the modular **inverse **of 5 modulo 91.

**Consider **(5*x) mod 91 =32.

5x = 32(mod 91)

Apply the **Euclidean **algorithm to find GCD of 5 and 91 is

91 = 18 * 5 + 1.

Rewrite it in **congruence **form,

1 = 91 - 18 *5

On **simplifying **the equation,

1 = 91 (mod 5)

The **modular **inverse of 5 modulo 91 is 18.

**Multiply **equation by 18 on both sides,

90x = 576 (mod91)

To obtain the **smallest **positive solution,

91:576 = 6 (mod 91)

**Divide **both sides by the coefficient of x:

x = 6 * 90^(-1).

Apply the **Euclidean **algorithm,

91 = 1*90 + 1.

**Simplify **the equation,

1 + 1 mod (90)

The modular **inverse **of 90 modulo 91 is 1.

Substitute the **modular **inverse in the given question gives,

x = 6*1(mod 91)

x= 6 (mod91)

Therefore, the solution to the **modular **equation (5x) mod 91 is

x = 6(mod 91).

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Ochenta y nueve en número romano ??

### Answers

**Answer:**

LXXXIX

**Step-by-step explanation:**

ochenta y nueve es 89.

89 en numero romano es LXXXIX.

The slop of the graphed line is 2/3

### Answers

The formulas that represent the** linear function **in this problem are given as follows:

y - 2 = 2/3(x - 1).y - 4 = 2/3(x - 4).f(x) = 2x/3 + 4/3.

How to define a linear function?

The **slope-intercept **equation for a linear function is presented as follows:

y = mx + b

The line has a **slope of 2/3, **hence:

y = 2x/3 + b.

When x = 1, y = 2, hence the** intercept b **is obtained as follows:

2/3 + b = 2

b = 6/3 - 2/3

b = 4/3.

Hence the **slope-intercept** equation of the line is given as follows:

f(x) = 2x/3 + 4/3.

The line goes through points (1,2) and (4,4), hence the **point-slope equations** to the line are given as follows:

y - 2 = 2/3(x - 1).y - 4 = 2/3(x - 4).

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Janice is painting a portion of a gymnasium court. If Janice paints the shaded area, then how many square feet will she paint?

16ft and 40ft

a.378.6ft

b.861.7ft

c.439.04ft

d.527.58ft

### Answers

the answer is letter d

asdaadadadasdadasdasdadsadasdasdasdasda

### Answers

**This is not a question. Next time, please add a question so that others might be able to help you with it**

in the histogram above I'm which interval does most of the data lie

### Answers

Answer: The Mode

Step-by-step explanation:

The mode is the data value that occurs the most often in a data set

Phil spends no more than 12 hours per week knitting. It takes him 2 hours to knit a hat and

3 hours to knit a scarf. He uses 150 yards of yarn for each hat and 400 yards of yarn for each

scarf. Which combinations of complete hats and scarves can Phil knit if he has 900 yards of yarn?

Select all of the correct answers.

A. 1 hat, 1 scarf

B. 3 hats, 2 scarves

C. 6 hats, 0 scarves

D. 4 hats, 1 scarf

E. 0 hats, 4 scarves

F. 2 hats, 1 scarf

### Answers

The correct options regarding the **inequality** are:

A. 1 hat, 1 scarf

D. 4 hats, 1 scarf

F. 2 hats, 1 scarf

How to explain the inequality

Based on the time **constraint**, Phil can spend a maximum of 12 hours knitting, so we can set up the following inequality:

2h + 3s ≤ 12,

Phil can knit at most 6 hats per week, because 6 hats * 2 hours/hat = 12 hours.

Phil can knit at most 4 scarves per week, because 4 **scarves** * 3 hours/scarf = 12 hours.

Phil can use at most 900 **yards** of yarn, because he has 900 yards of yarn.

Phil can knit 1 hat and 1 scarf, because 1 hat * 150 yards/hat + 1 scarf * 400 yards/scarf = 550 yards < 900 yards.

Phil can **knit** 4 hats and 1 scarf, because 4 hats * 150 yards/hat + 1 scarf * 400 yards/scarf = 900 yards.

Phil can knit 2 hats and 1 scarf, because 2 hats * 150 yards/hat + 1 scarf * 400 yards/scarf = 700 yards < 900 yards.

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find the quotient of 5/31 divided by 15/23 . reduce your answer to the lowest fraction

### Answers

To find the quotient of 5/31 divided by 15/23, first invert the divisor and multiply. This gives us (5/31) x (23/15). We can simplify this expression by canceling out the common factors of 5 and 15, which gives us (1/31) x (23/1) = 23/31. Therefore, the quotient of 5/31 divided by 15/23, reduced to the lowest fraction, is 23/31.

FIND THE VALUE OF X IN THE DIAGRAM BELOW

Please help me ASAP I will give 20 points

### Answers

a = 30°

b = 180-135 = 45°

total angle inside triangle = 180°

x = 180-(30+45) = 105°