Mathematics College

## Answers

**Answer 1**

**Answer:**

Area of shaded part = 113 mm² (Approx.)

**Step-by-step explanation:**

**Given:**

Diameter of Semi-circle = 24 mm

**Find:**

Area of shaded part

**Computation:**

Radius of semi-cicrle = Diameter of Semi-circle / 2

Radius of semi-cicrle = 24 / 2

Radius of semi-cicrle = 12 mm

So,

Radius of small circle = 12 / 2

Radius of small circle = 6 mm

Area of shaded part = Area of semi circle - Area of small circle

Area of shaded part = [πR² / 2] - [πr²]

Area of shaded part = [(3.14)(12)² / 2] - [(3.14)(6)²]

Area of shaded part = [(3.14)(144) / 2] - [(3.14)(36)]

Area of shaded part = 226.08 - 113.04

Area of shaded part = 113.04

**Area of shaded part = 113 mm² (Approx.)**

## Related Questions

PLZ HELP!!!!!!!!!!!!!!!!

### Answers

**Answer:**

B) 119.1

**Step-by-step explanation:**

First, find your circle area

[tex]A=\pi r^{2} \\A=\pi 7^{2} \\A=153.9[/tex]

Then get the area of the square, we will worry about the tringles on each side in the last step.

l=12

w= 14 (Radius of circle times 2)

A=wl

A=14*12

A=168

Now the triangle

h=14 (Radius of circle times 2)

b=(27 - 12) / 2 = 7.5 ( total length 27 minus 12 divided, by 2 since there's 2 triangles on each side.

[tex]A=h\frac{b}{2} \\A=14\frac{7.5}{2} \\A=52.5[/tex]

Now add 2 triangles, the square and substract the circle

52.5+52.5+168 = 273

273 - 153.9 = 119.1 in^2

If 25 counters are a whole set how many are there in four fifths of the set

### Answers

**Answer:**

20

**Step-by-step explanation:**

**25*4/5=5*4=20**

**Answer:**

20

**Step-by-step explanation:**

25 x 4/5=100/5=20

An engine runs for 3.2 hours. How many seconds did it run?

### Answers

**Answer:**

11520 seconds

**Step-by-step explanation:**

3.2 x 60= 192 minutes

192 x 60= 11520 seconds

Solve

3w - 4z = 8

2w + 3z = -6

A) w = -2

z = -2

B) w = -2

z = 0

C) w = 0

z = 2

D) w = 0

z = -2

### Answers

**Answer:**

D

**Step-by-step explanation:**

Multiplying the first equation by 2 yields 6w - 8z = 16.

Multiplying the second equation by 3 yields 6w + 9z = -18.

Subtracting the two equations gives -17z = 34, and thus z = -2.

Substituting this back into the first equation gives that 3w+8=8, and thus w=0.

A rectangle has a perimeter of 14 cm and length x cm. show that the width of the rectangle is (7-x)cm and hence that the area A of the rectangle is given by the formula A= x(7-x). Draw the graph, plotting x on the horizontal axis with a scale of 2cm to 1 unit, and A on the vertical axis with a scale of 1cm to 1 unit

take x from 0 to 7. From the graph find:

a) the area of the rectangle when x = 2.25cm

b) the dimensions of the rectangle when its area is 9cm^2

c) the maximum area of the rectangle

d) the length and width of the rectangle corresponding to the maximum area

e) what shape of the rectangle has the largest area

### Answers

**Answer:**

B

**Step-by-step explanation:**

the dimensions of the rectangle when its area is 9cm^2

A bag contains 5 blue, 4 red, 7 black and 2 white marbles. What is the probability of selecting a marble that is NOT white?

### Answers

5+4+7+2=18

18-2=16

16/18

88% chance of selecting a marble that isnt white

**Answer:**

8/9

**Step-by-step explanation:**

P(white) = (2) ÷ (5+4+7+2) = (2)/(18) = 1/9

P(not white) = 1 - P(white) = 1 - 1/9 = 8/9

A car dealer just took delivery on forty new cars. He plans to put four of these cars on display at the front of the lot. In how many ways can the dealer combine four of the forty cars if order is not important?

A. 1,096,680

B. 91,390

C. 45,695

D. 2,193,360

### Answers

**Answer:**

B. 91,390

**Step-by-step explanation:**

I've had this question before, I don't like'em, but that's the answer.

**Answer:**

option B

**Step-by-step explanation:**

[tex]40C_4 = \frac{40\times 39 \times 38 \times 37}{1 \times 2 \times 3 \times 4} = 91,390[/tex]

Which function represents the area of the rectangle? 6x2 – 8x + 36 6x2 – 27x + 36 6x2 – 35x + 36 6x2 + 35x + 36

### Answers

**Answer:**

[tex]Area = 6x^2 - 35x + 36[/tex]

**Step-by-step explanation:**

**Given**

[tex]g(x)=3x-4[/tex]

[tex]f(x)=2x-9[/tex]

**Required**

The area

**This is calculated as:**

[tex]Area = f(x) * g(x)[/tex]

[tex]Area = (3x -4) * (2x - 9)[/tex]

**Open bracket**

[tex]Area = 6x^2 - 27x - 8x + 36[/tex]

[tex]Area = 6x^2 - 35x + 36[/tex]

**Answer:**

6x2 – 35x + 36

**Step-by-step explanation:**

Calculate the average rate of change in the amount of the surcharge for non-account holders between 2004 and 2008. Write the result in a sentence of interpretation. (Round your answer to two decimal places.)

### Answers

**Answer:**

The average rate of change in the amount of the surcharge for non-account holders between 2004 and 2008 is $0.08

**Step-by-step explanation:**

**Given**

[tex]s(t) = 0.72 * 1.081^t[/tex]

[tex]3 \le t \le 13[/tex]

[tex]t \to[/tex] years since 2001

**Required**

Average rate of change between 2004 and 2008

In 2004,

[tex]t = 2004 - 2001[/tex]

[tex]t =3[/tex]

So:

[tex]s(t) = 0.72 * 1.081^t[/tex]

[tex]s(3) = 0.72 * 1.081^3[/tex]

[tex]s(3) = 0.9095[/tex]

In 2008,

[tex]t = 2008 - 2001[/tex]

[tex]t = 7[/tex]

So:

[tex]s(t) = 0.72 * 1.081^t[/tex]

[tex]s(7) = 0.72 * 1.081^7[/tex]

[tex]s(7) = 1.2420[/tex]

**The average rate of change (m) is calculated as:**

[tex]m = \frac{s(a) - s(b)}{a - b}[/tex]

**In this case:**

[tex](a,b) = (3,7)[/tex]

**So, we have:**

[tex]m = \frac{s(3) - s(7)}{3 - 7}[/tex]

[tex]m = \frac{s(3) - s(7)}{-4}[/tex]

**Substitute values for s(3) and s(7)**

[tex]m = \frac{0.9095 - 1.2420}{-4}[/tex]

[tex]m = \frac{-0.3325}{-4}[/tex]

[tex]m = 0.083125[/tex]

[tex]m = 0.08[/tex]** --- approximated**

What is the value of N in this proportion 16/40= 8/n

### Answers

**Answer:**

n = 20

**Step-by-step explanation:**

[tex]\frac{16}{40} = \frac{8}{n}[/tex]

Cross multiplication would result in:

16 * n = 8 * 40

16n = 320

n = 320 / 16

n = 20

Therefore the value of "n" in this proportion is 20.

**Hope this helps!**

Use angle addition formula to find the expression for cos(a+b). Use the same formula to

find cos(a+a).

### Answers

**Answer:**

we have

Cos (a+b)=Cos aCosb-SinaSinb

for

Cos (a+a)=Cos aCosa-SinaSina=**Cos²a-Sin²a**

is a required answer.

What they said!!!!!!!!!!!!

A triangle on the coordinate plane has vertices (-8,3), (3,9), and (9,3). What is the area, in square units, of the

triangle?

Please help

### Answers

**Answer:**

51 sq units

**Step-by-step explanation:**

after plotting the vertices, the height of the triangle is 6 and the base is 17

A = 1/2(6)(17)

A = 51 sq units

D

Find mZW.

X

WK (11x - 29)

Z

(6x + 5)

mZW

### Answers

Answer:

m<W = 103°

Step-by-step explanation:

First, find the value of x

m<W + m<Y = 180° (opposite angles in a cyclic quadrilateral are supplementary)

11x - 29 + 6x + 5 = 180 (substitution)

Add like terms

17x - 24 = 180

Add 24 to both sides

17x = 180 + 24

17x = 204

Divide both sides by 17

17x/17 = 204/17

x = 12

Find m<W:

m<W = 11x - 29

Plug in the value of x

m<W = 11(12) - 29 = 132 - 29

m<W = 103°

Help plz:)))I’ll mark u Brainliest

### Answers

**Answer:**

[tex]sin^{-1}(\frac{51}{53})\\=74.21[/tex]

≈74

Question 9

Two sides of a triangle have lengths 10 and 15.

What must be true about the length of the third side?

Greater than 5 but less than 25

Less than 15

Less than 25

### Answers

**Answer:**

Two sides of a triangle have lengths 10 and 15.

What must be true about the length of the third side?

Greater than 5 but less than 25

Less than 15

Less than 25

**Step-by-step explanation:**

Eugene and Jenny are selling cookie dough for a school fundraiser. Customers can buy packages

of chocolate chip cookie dough and packages of gingerbread cookie dough. Eugene sold i

package of chocolate chip cookie dough and 10 packages of gingerbread cookie dough for a total

of $174. Jenny sold 4 packages of chocolate chip cookie dough and 2 packages of gingerbread

cookie dough for a total of $50. Find the cost each of one package of chocolate chip cookie

dough and one package of gingerbread cookie dough.

.

.

Two sides of a triangle have lengths 10 and 15.

What must be true about the length of the third side?

Greater than 5 but less than 25

Less than 15

Less than 25

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The time spent waiting in the line is approximately normally distributed. The mean waiting time is 55 minutes and the variance of the waiting time is 11. Find the probability that a person will wait for more than 33 minutes. Round your answer to four decimal places.

### Answers

**Answer:**

1 = 100% probability that a person will wait for more than 33 minutes.

**Step-by-step explanation:**

**Normal Probability Distribution:**

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

**The mean waiting time is 55 minutes and the variance of the waiting time is 11.**

This means that [tex]\mu = 55, \sigma = \sqrt{11}[/tex]

**Find the probability that a person will wait for more than 33 minutes.**

This is 1 subtracted by the p-value of Z when X = 33. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{33 - 55}{\sqrt{11}}[/tex]

[tex]Z = -6.63[/tex]

[tex]Z = -6.63[/tex] has a p-value of 0.

1 - 0 = 1

1 = 100% probability that a person will wait for more than 33 minutes.

SOMEBODY PLEASE HELP I NEED THIS ASAP

### Answers

**Answer:**

**a = 1000 cm²**

**Step-by-step explanation:**

Center square

20 * 20 = 400cm²

------------------------

Triangle side

a = (1/2)(20)(15)

a = 150

There are 4 sides

a = 4 * 150

a = 600 cm²

-----------------------

Total area

a = 400 - 600

**a = 1000 cm²**

convert 495.05 to fraction

### Answers

**Answer:**

9901 / 2000

**Step-by-step explanation:**

might be wrong

find a value of (2power-1*4power-1)

### Answers

2^( - 1 ) × 4^( -1 ) =

2^( -1 ) × 2^( 2 × ( - 1) ) =

2^( - 1 ) × 2^( - 2 ) =

2^( - 1 - 2 ) =

2^( - 3 ) =

1/ 2^( 3 ) =

1/8

which expression is equivalent to (5^-2) ^5 x 5^4

### Answers

**Answer:**

6.4 × 10 ^-5

**Step-by-step explanation:**

(0.04)^5 × 625 = 6.4 × 10^-5 (6.4e-5)

Please help me I need these ASAP. I'll mark as brilliant!

make c the subject: (a+c)^2=t

make x the subject: p=3(y+2x)^2

### Answers

[tex](a + c) ^{2} = t \\ c = \sqrt{t } - a \\ c = - \sqrt{t} - a[/tex]

[tex]p = 3(y + 2x) ^{2} \\ x = \frac{ \sqrt{3p} }{6} - \frac{y}{2} \\ x = - \frac{ \sqrt{3p} }{6} - \frac{y}{2} [/tex]

Which pair of functions are inverses of each other?

Wanting to make sure of answers in this pretest

### Answers

**Answer:**

The only pair of functions that are inverses of each other are the ones for option D.

**Step-by-step explanation:**

Two functions, f(x) and g(x), are inverses if and only if:

f( g(x) ) = x

g( f(x) ) = x

So we need to check that with all the given options.

A)

[tex]f(x) = \frac{x}{7} + 10 \\g(x) = 7*x - 10\\[/tex]

then:

[tex]f(g(x)) = \frac{7*x + 10}{7} -10 = x + \frac{10}{7} - 10[/tex]

This is clearly different than x, so f(x) and g(x) are not inverses.

B)

[tex]f(x) = \sqrt[3]{11*x} \\g(x) = (\frac{x}{11} )^3[/tex]

Then:

[tex]f(g(x)) = \sqrt[3]{11*(\frac{x}{11})^3 } = \sqrt[3]{\frac{x^3}{11^2} } = \frac{x}{11^{2/3}}[/tex]

This is different than x, so f(x) and g(x) are not inverses.

C)

[tex]f(x) = \frac{7}{x} -2 \\g(x) = \frac{x + 2}{7}[/tex]

Then:

[tex]f(g(x)) = \frac{7}{\frac{x + 2}{7} } - 2 = \frac{7*7}{x + 2} - 2[/tex]

Obviously, this is different than x, so f(x) and g(x) are not inverses.

D)

[tex]f(x) = 9*x - 6\\g(x) = \frac{x + 6}{9}[/tex]

Then:

[tex]f(g(x)) = 9*\frac{x + 6}{9} - 6 = x + 6 - 6 = x\\g(f(x)) = \frac{(9*x - 6) + 6}{9} = x[/tex]

In this case we can conclude that f(x) and g(x) are inverses of each other.

Find QR.

Write your answer as an integer or as a decimal rounded to the nearest tenth.

QR = ___

### Answers

**Answer:**

**Step-by-step explanation:**

take 64 degree as reference angle

using cos rule

cos 64=adjacent/hypotemuse

0.43=QR/10

10*0.43=QR

4.3=QR

I need help asap. Math Writing Expressions.

### Answers

**Answer:**

1:

6y-3+y

**D =7y-3**

2.

**50C**

3.

**6÷K**

4.

**7-x**

5.

**8p-4p**

6.

**2g-3**

7.

1-7/p

**D.(p-7)/p**

Find all solutions

for cotx=-1

### Answers

**Answer:**

[tex]\cot(x) = -1[/tex] whenever [tex]\displaystyle x = k\, \pi-\frac{\pi}{4}[/tex] radians, where [tex]k[/tex] could be any integer ([tex]k \in \mathbb{Z}[/tex], which includes positive whole numbers, negative whole numbers, and zero.)

**Step-by-step explanation:**

[tex]x = 45^\circ[/tex] (as in isoscele right triangles) would ensure that [tex]\displaystyle \cot(x) = 1[/tex]. Since cotangent is an odd function, [tex]\cot(-45^\circ) = -1[/tex].

Equivalently, when the angles are expressed in radians, [tex]\cot(-\pi / 4) = -1[/tex].

The cycle of cotangent is [tex]\pi[/tex] (or equivalently, [tex]180^\circ[/tex].) Therefore, if [tex]k[/tex] represents an integer, adding [tex]k\, \pi[/tex] to the input to cotangent would not change the output. In other words:

[tex]\displaystyle \cot\left(k\, \pi - \frac{\pi}{4}\right) = \cot(-\pi / 4) = -1[/tex].

Hence, [tex]\displaystyle x = k\, \pi-\frac{\pi}{4}[/tex] would be a solution to [tex]\cot(x) = -1[/tex] whenever [tex]k[/tex] is an integer.

Since [tex](-\pi / 4)[/tex] is the only solution to this equation in the period [tex](0,\, \pi)[/tex], all real solutions to this equation would be in the form [tex]\displaystyle x = k\, \pi-\frac{\pi}{4}[/tex] (where [tex]k[/tex] is an integer.)

There are 6 red marbles, 4 blue marbles, and 15 green marbles in a jar. If you reach in and randomly draw one, what is the probability that you will choose a red marble?

### Answers

**Answer:**

6+4+15 = 25 and since there are 6 red marbles the answer is 6/25

**Answer:**

6 out of 25 chance/ 24%

**Step-by-step explanation:**

15 + 4 = 19 + 6 = 25

6/25 = 0.24 = 24%

Can somebody please help me. I am really stuck and the tutor option really isn’t working!!!!

### Answers

**Answer:**

its fourth one in my opinoin

If you know how to solve this, Please answer it. Thank You

The first one to answer the question right, will get Brainlist!

I PROMISE!!!!!

### Answers

20 / 12 = 5 / y

y = 5 × 12 / 20

y = 60 / 20

y = 3

If mCD = 60 and m

find mAB!

### Answers

**Answer:**

246= AB

**Step-by-step explanation:**

Angle Formed by Two Secants= 1/2(difference of Intercepted Arcs)

<P = 1/2 ( AB - CD)

93 = 1/2 ( AB - 60)

Multiply by 2

186 = ( AB-60)

Add 60 to each side

186+80 = AB

246= AB

a street light is mounted at the top of a 15-foot pole. A 6-foot tall man walks away from the pole along a straight path. How long is his shadow when he is 40 feet from the pole

### Answers

Answer:

[tex]x=26.67[/tex]

Step-by-step explanation:

From the question we are told that:

Height of Pole [tex]h_p=15 foot[/tex]

Height of Man [tex]h_m =6ft[/tex]

Distance from Pole [tex]d_p=40ft[/tex]

Generally the equation for similar Property is mathematically given by

[tex]\frac{h_p}{h_m}=\frac{d_p+x}{x}[/tex]

[tex]x=\frac{h_m*(d_p+x)}{h_p}[/tex]

[tex]x=\frac{6*(40+x)}{15}[/tex]

[tex]x=\frac{240+6x}{15}[/tex]

[tex]x=16+0.4x\\x-0.4x=16[/tex]

[tex]x=16\0.6[/tex]

[tex]x=26.67[/tex]