Find the arc length of the circle with a central angle of 30 degrees and a radius 12. Leave the answer in terms of π.

Answer:

p(a tail on the second toss) = 4/8

p(exactly one head) = 3/8

p(a head on each of the last two tosses) = 2/8

Step-by-step explanation:

At first we should calculate Monthly income by multiplying 2 then After multiplying by 12 to calculate Annual income

Answer:

Anything more than $13

Step-by-step explanation:

Considering the definition of combination, she could choose 190 different pairs of team.

Combinations of m elements taken from n to n (m≥n) are called all the possible groupings that can be made with the m elements in such a way that not all the elements enter; the order does not matter and the elements are not repeated.

To calculate the number of combinations, the following formula is applied:

[tex]C=\frac{m!}{n!(m-n)!}[/tex]

The term "n!" is called the "factorial of n" and is the multiplication of all numbers from "n" to 1.

Ms. lewis has 20 students in her p.e. class. She puts each student's name in a hat and will select the names of 2 students at random as team leaders for a volleyball game.

So, you know that:

Replacing in the definition of combination:

[tex]C=\frac{20!}{2!(20-2)!}[/tex]

Solving:

[tex]C=\frac{20!}{2!18!}[/tex]

C= 190

Finally, she could choose 190 different pairs of team.

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Answer:

Step-by-step explanation:

The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.

  M = (A +B)/2

__

  M = (3 +5, -6 +8)/2 = (8, 2)/2 = (4, 1)

The midpoint coordinates are (4, 1).

__

  M = (-4 +1, -2 -3)/2 = (-3, -5)/2 = (-3/2, -5/2)

The midpoint coordinates are (-3/2, -5/2).

Answer:

x=14

Step-by-step explanation:

collect like terms, like so

Answer:4(x−2)−8=4+2x

Use the distributive property to multiply 4 by x−2.

4x−8−8=4+2x

Subtract 8 from −8 to get −16.

4x−16=4+2x

Subtract 2x from both sides.

4x−16−2x=4

Combine 4x and −2x to get 2x.

2x−16=4

Add 16 to both sides.

2x=4+16

Add 4 and 16 to get 20.

2x=20

Divide both sides by 2.

x=

2

20

​

Divide 20 by 2 to get 10.

x=10

Step-by-step explanation:

The area of the pentagon, rounded to the nearest tenth will be 32.7 square cm. Then the correct option is C.

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

A regular pentagon has an apothem measuring 3 cm and a perimeter of 21.8 cm.

Then the side length of the pentagon will be

5 x Side length = 21.8 cm

     Side length = 4.36 cm

Then the area of the pentagon, rounded to the nearest tenth will be

Area of pentagon = 5 x area of triangle

Area of pentagon = 5 x 1/2 x 4.36 x 3

Area of pentagon = 32.7 square cm

Thus, the correct option is C.

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Answer:

the correct answer is d

Step-by-step explanation:

w(s)=weeks saved and 20s is the gain of 20 dollars every week. and the 95 is the starting amount that sam had

Answer:

The number is 740

Step-by-step explanation:

Hello!

Let the number that we want to solve for be x.

100% of x is x, but a decrease of 5% if 95% of x.

The number is 740.

The solution is correct.

Answer:

57/100

Step-by-step explanation: 0.57 can also be written as 57/100 which is equal to 0.57

The composition of the function and its inverse function is always one. Then the correct option is C.

Suppose that the given function will be

f: X → Y

Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is

 f⁻¹: Y → X

such that:

[tex]\forall \: x \in X : f(x) \in Y, \exists \: y \in Y : f^{-1}(y) \in X[/tex]

(and vice versa).

It simply means that the inverse of 'f' is a reverse operator, that takes back the effect of 'f'

Suppose that f and g are functions that are inverse of each other.

When f is composed of g or vice versa. Then the composition will be

We know that the composition of the function and its inverse function is always one. Then we get

When f is composed of g or vice versa. Then the composition will be 1.

Thus, the correct option is C.

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Answer: 4) 24

Step-by-step explanation:

Answer:

949$

Step-by-step explanation:

You get 460$ the first year, then 488 in the second.

[tex]\\ \rm\Rrightarrow \dfrac{7513/100\times 5x^3}{3x^2}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{75.13(5)x^3}{3x^2}[/tex]

[tex]\\ \rm\Rrightarrow {125.22x}[/tex]

Natalia Net worth will be 550 having Assets= 7285 and liabilities= 6735

Net worth= 550

Assets are the items your company owns that can provide future economic benefit. Liabilities are what you owe other parties.

Given that: Assets= 7285, liabilities= 6735

As we know,

Total Net worth=  Total Assets - Total Liabilities

                          =  7285- 6735

                          = 550

The Net worth= 550

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Step-by-step explanation:

x, x+1, x+2 are the 3 consecutive positive integers.

(x+1)(x+2) = 2(x+1) + 2×(x+x+1+x+2)

x² + 3x + 2 = 2x + 2 + 2×(3x + 3)

x² + 3x + 2 = 2x + 2 + 6x + 6 = 8x + 8

x² - 5x - 6 = 0

we can solve this by finding the factoring.

that means we find a, b so that

(x - a)(x - b) = x² - 5x - 6 = 0

because then x = a and x = b are the 2 solutions of the quadratic equation.

we have

x² - ax - bx + ab = x² - (a+b)x + ab = x² - 5x - 6

a+b = 5

ab = -6

that means, either a or b must be 6 and the other -1.

so we get

(x - 6)(x + 1) = 0

x = 6

or

x = -1

since we are only looking for positive integers, the x = -1 solution is invalid, and we get only x = 6 as solution.

therefore the 3 consecutive positive integers are

6, 7, 8

Answer:

  17.3 cm³

Step-by-step explanation:

The volume of a pyramid is given by the formula ...

  V = 1/3Bh

where B is the area of the base, and h is the height.

__

The volume of a square pyramid with base area 5.5 cm² and height 6.4 cm is ...

  V = 1/3(5.5 cm²)(6.4 cm) ≈ 17.333... cm³

The volume of the pyramid is about 17.3 cm³.

Using the assumed coordinates of point F, the coordinates of point D are (3,3)

The given parameters are:

Ratio, m : n = 2 : 5

E = (3.8, -3)

The coordinates of point D is calculated using:

[tex]D = \frac{1}{m + n} * (mx_2 +nx_1,my_2 +ny_1)[/tex]

So, we have:

[tex]D = \frac{1}{2 + 5} * (2x_2 +5*3.8,2y_2 +5*-3)[/tex]

Evaluate the sum and the products

[tex]D = \frac{1}{7} * (2x_2 +18,2y_2 -15)[/tex]

Assume the coordinates of point F are:

F = (1.5,18);

The equation becomes

[tex]D = \frac{1}{7} * (2*1.5 +18,2*18 -15)[/tex]

Evaluate

[tex]D = \frac{1}{7} * (21,21)[/tex]

This gives

D = (3,3)

Hence, the coordinates of point D are (3,3)

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Answer:

8

Step-by-step explanation:

To get a fraction of a number, we will simply multiply this fraction by the number.

Based on the number of unit cubes that are fastened together, the number of cubes which will have at least one face painted on is 488 cubes.

The cubes formed one large cube which means that each surface is one cube deep. So two cubes will be painted.

The number of unpainted cubes per surface is therefore:

= 10 - 2

= 8 cubes

Number of unpainted cubes is:

= 8 x 8 x 8

= 512 cubes

Number of cubes with one face painted:

= Total cubes - Number of unpainted cubes

= 1,000 - 512

= 488 cubes.

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Step-by-step explanation:

this simply means that the coordinates are multiplied by the scale factor.

(a, b) -> (a×k, b×k)

that's it.

so, the first answer is correct.

Answer:

Graph B

Step-by-step explanation:

Point-line graphs are usually used to compare data over a course of time, and bar graphs are more commonly used to compare statistics between different data sets (in this case it is between different countries)

Answer:

slope m = - [tex]\frac{7}{3}[/tex]

Step-by-step explanation:

The probability of not picking a red marble is 0.2.

The probability of picking a yellow or green marble is 0.5

The probability of drawing an even number of a number greater than 4 is  1.

The probability of getting heads and an even number is 1.

The probability of drawing a 2 or a 4 is 0.25.

Probability determines how likely it is for an event to happen. The chances of the event occurring lies between 1 and 0.

The probability of not picking a red marble = (number of all the marbles - red marbles) / total marbles

4/20 = 0.2

The probability of picking a yellow or green marble = (number of yellow marbles / total number of marbles) + (number of green marbles / total number of marbles)

2/20 + 8/20 = 10/20 = 0.5

The probability of drawing an even number of a number greater than 4 = (number of even numbers / total numbers) + (numbers greater than 4 / total numbers)

5/10 + 5/10 = 1

The probability of getting heads and an even number is = (side that is head / total sides) x (even numbers on a die / total numbers on a die)

1/2 x 3/6 = 1

The probability of drawing a 2 or a 4 = 1/8 + 1/8 = 2/8 = 0.25

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The team-lead gets $2000 if the team of 3 QA testers and l QA team lead is working on a project. The team finishes the job and is paid.

It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.

Let's suppose the team lead salary is x and the team-lead receives, $600 more than the average salary of the entire team then,

The team lead salary:

[tex]\rm x = \dfrac{1200+1200+1200+x}{4} + 600[/tex]

4x = 3600+ x+ 2400

3x = 6000

x = $2000

Thus, the team lead gets $2000 if the team of 3 QA testers and l QA team lead is working on a project. The team finishes the job and is paid.

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Answer:

[tex]\sf \bf {remainder}: -\dfrac{3}{8}[/tex]

In order to find remainder:

Follow this short technique:

Set the divisor which is x-½  to zero.

x - 1/2 = 0

x = 1/2

Then insert this following into dividend.

insert x = ½

simplify

Answer:

-3/8

Step-by-step explanation:

Let's assume x - 1/2 is a zero of the polynomial :

-3/8 is the remainder.

Answer- 200m

: Right now Sam is 200m far from her starting point

Answer:

Coordinates of the midpoint are ( 9/2 , -6 )