What is the greatest common factor of 12, 2, and 84?

Using the hypergeometric distribution, it is found that there is a 0.1363 = 13.63% theoretical probability of 5 students from your school being selected as contestants out of 10 possible contestant​ spots.

The formula is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The values of the parameters are given as follows:

N = 130, k = 40, n = 10.

The theoretical probability of 5 students from your school being selected is P(X = 5), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 5) = h(5,120,10,40) = \frac{C_{40,5}C_{80,5}}{C_{120,10}} = 0.1363[/tex]

0.1363 = 13.63% theoretical probability of 5 students from your school being selected as contestants out of 10 possible contestant​ spots.

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Answer:

2.5

Step-by-step explanation:

The amplitude of a function is the amount by which the graph of the function travels above and below its midline.

The distance from the highest most point to the lowest point vertically is 5, meaning that the midpoint is 2.5 units from either end.

Answer:

Coordinates (0, -8/3)

The point-slope form of the equation for the line is y - 3 =1/2(x - 2)

From the question, we are to determine the point-slope form of the equation for the line

The point-slope form of the equation of a line is given by

y - y₁ = m(x - x₁)

Where (x₁, y₁) is a point on the line

and m is the slope of the line

From the given information,

Slope, m = 1/2

and we have the point (2,3)

∴ The point-slope form of the equation for the line is

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

Hence, the point-slope form of the equation for the line is y - 3 =1/2(x - 2)

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The area of a regular hexagon with an apothem 18.5 inches long and a side 21 inches is 1, 165. 5 In²

The formula is given thus;

Area of hexagon = (1/2) × a × P

where a = the length of the apothem

P = perimeter of the hexagon

Given a = 18. 5 inches

Note that Perimeter, p = 6a with 'a' as side

p = 6 × 21 = 126 inches

Substitute values into the formula

Area, A = 1 ÷2 × 18. 5 × 126 = 1 ÷2 × 2331 = 1, 165. 5 In²

Thus, the area of the regular hexagon is 1, 165. 5 In²

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Answer:

3

Step-by-step explanation:

Volume of prism = 0.5 times height times length times width

60 = (0.5)(8)(5)(x)

120 = 8(5)(x)

120 = 40x

x =  3

Let me know if its right

Length of another side of base x = 3 unit

A prism has a solid shape consisting of two identical ends (such as triangle, square, rectangle, etc.), flat faces or surfaces and uniform cross-section across its length. The cross-section looks like a triangle hence called triangular prism. The shape of the prism does not have any curve. Therefore, a prism can have square, rectangular, pentagonal and other polygon shapes but not the circular shape.

Height of the prism = 8units

Length of one side of base = 5 units

Length of another side of Base = x

Base is a right angle

Base Area = 5x/2

Volume of prism = 60 unit³

Volume of Prism = Base Area × Height

60 = (5x/2) × 8

60/8 = 5x/2

x = 120/40

x = 3 unit.

Hence,  x = 3 unit which is length of another side of base.

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The area of the target which earns 30 points on a throw.

[tex]\huge\boxed{Formula: a= \pi{r}^{2}}[/tex]

[tex]4+3[/tex]

[tex]=7[/tex]

Let's solve

We have to find the answer in terms of π so, we'll just have to multiply the radius by itself.

[tex]a={7}^{2}[/tex]

[tex]\large\boxed{a= 49 \pi\: {in}^{2}}[/tex]

Hence, the area of the target which earns 30 points on a throw is 49π square inches.

Answer= Option B

Step-by-step explanation:

length = 2×width + 6

84 = 2×length + 2×width

now using the first in the second equation :

84 = 2×(2×width + 6) + 2×width = 4×width + 12 + 2×width

84 = 6×width + 12

72 = 6×width

width = 12 cm

length = 2×width + 6 = 2×12 + 6 = 24 + 6 = 30 cm

Answer: 33

Step-by-step explanation:

Because corresponding sides of similar triangles are in proportion, [tex]\frac{x}{22}=\frac{39}{26} \longrightarrow x=\boxed{33}[/tex]

Answer:

Step-by-step explanation:

The profit = 150 000 - 120 000 = 30 000

………………………………………………………

The profit percentage is :

[tex]=\frac{30000}{120000} \times 100=0.25 \times 100 = 25 \%[/tex]

Answer:

it makes 15 gadgets in 5 minutes

Step-by-step explanation:

you take thw 1 gadget every 20 seconds there are 60 seconds in 1 minutes so 60 ÷ 20 is 3 so it makes 3 gadgets every minute so 3 x 5 is 15 so it makes 15 gadgets every 5 mins

Answer:

15 gadgets

Step-by-step explanation:

look above

hope ot helps

Answer:

Part A:

In order to find a coterminal angle, or angles of the given angle, simply add or subtract 360 degrees of the terminal angle as many times as possible.

Part B:Simply put, coterminal angles start at 0° and end at the same place, though in different directions and multiple times around (you're probably going to want to make that sound a little more formal). Since each time around is 360°, boom

Part C: 75° is in Quadrant II, right? If I go one more time around, 75 + 360 = 435°. I can also go "backward. Starting at 0 and going clockwise, I'm going 75 fewer degrees than all the way around, so 360-75 = 285° but since I'm going "backward" 75 - 360 = -285°. One more is on you.    

Step-by-step explanation:

The difference of the two numbers in scientific form is:

[tex]493*10^{-9} = 0.00000493[/tex]

Here we want to solve:

[tex](5*10^{-7}}) - (7*10^{-9})[/tex]

To solve this, we should have the same exponent in both sides, to get that, we can rewrite the first number as:

[tex]5*10^{-7} = 500*10^{-9}[/tex]

Replacing that, we will get:

[tex](500*10^{-9}) - (7*10^{-9}}) = 493*10^{-9}[/tex]

To write it in standard form, we need to move the decimal point 9 times to the left, so we get:

[tex]493*10^{-9} = 0.00000493[/tex]

The difference is equal to 0.00000493.

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Answer:

(1.333, 0) and (3, 0)

Step-by-step explanation:

Use desmos to input your equations then click on the solutions (zeroes)

Implementing the LSA from your other question

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One can can paint 400ft²

Total cans

9cans you need

Answer:

-2, 1 or 3 only

Step-by-step explanation:

just did it

Answer:

Line s

Step-by-step explanation:

They are the same distance apart, so this makes them parallel.

By the definition of parallel lines, the line r is parallel to line s.

Arrangement of reference lines or curves used to identify the location of points in space is called as Coordinate System.

We have to find the line which is parallel to line r.

Parallel lines are the lines that do not intersect or meet each other at any point in a plane.

They are always parallel and are at equidistant from each other.

Parallel lines are non-intersecting lines.

We can also say Parallel lines meet at infinity.

As we observe the figure line s is parallel to line r and it is equidistant from r.

Hence, line s is parallel to line r.

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Step-by-step explanation:

the area of a rectangular is

length × width

we know the area and one side, let's say it's the width (it does not matter, as multiplication are commutative, and a×b = b×a).

so,

7.5 = length × 0.3

length = 7.5 / 0.3 = 25 m

the perimeter of a rectangle is

2×length + 2×width = 2×25 + 2×0.3 = 50 + 0.6 = 50.6 m

Answer:

(-4,-3)

Step-by-step explanation:

Answer:

(-4, -3)

Step-by-step explanation:

well, the only points possible are 3 points, a first, 2nd, and 3rd point. And the 2nd point is the mid-point.

Answer:

[tex]\displaystyle ME=\frac{z\cdot s}{\sqrt{n}}[/tex]

Step-by-step explanation:

[tex]z[/tex] represents the critical value, [tex]s[/tex] represents the sample standard deviation, and [tex]n[/tex] represents the sample size.

Answer:

[tex]5^{10} \cdot 5^{-7} = 5^3[/tex]

[tex]\frac{5^{10}}{5^{-7}} = 5^{17}[/tex]

Step-by-step explanation:

You have two equations:

[tex]5^a \cdot 5^b = 5^3[/tex]

[tex]\frac{5^a}{5^b} = 5^{17}[/tex]

But since

[tex]x^a \cdot x^b = x^{a+b}[/tex]

you only need to solve a+b = 3 and a-b=17

Rewrite the second as a = 17+b and plug it into the first:

17+b + b = 3, then you find, 2b = -14, so b = -7.

Then a=3-b, so a = 10.

An equation is formed of two equal expressions. The number of rows in the original pattern will be 4.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the number of rows be represented by x. Now, the pattern has rows that are 5 tiles wide and an unknown number of rows. if you take these tiles and add one additional tile, you can create a pattern that has rows that are 3 tiles wide, with 3 more total rows than the original pattern. Therefore, we can write,

(Number of Tiles before) + 1 tile = (Number of Tiles afterward)

5x + 1 = 3(x+3)

5x + 1 = 3x + 9

5x - 3x = 9 - 1

2x = 8

x = 4

Hence, the number of rows in the original pattern will be 4.

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Answer:

-3

Step-by-step explanation:

Given equation:

[tex]\implies (x^4y^{-3})^n=\dfrac{y^9}{x^{12}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{1}{a^n}=a^{-n}:[/tex]

[tex]\implies (x^4y^{-3})^n=x^{-12}y^9[/tex]

Rewrite -12 as (4 × -3) and 9 as (-3 × -3):

[tex]\implies (x^4y^{-3})^n=x^{(4 \times -3)}y^{(-3 \times -3)}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c[/tex]:

[tex]\implies (x^4y^{-3})^n=(x^4)^{-3}(y^{-3})^{-3}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^c b^c=(ab)^c[/tex]

[tex]\implies (x^4y^{-3})^n=(x^4y^{-3})^{-3}[/tex]

Therefore, the missing value is -3

Answer:

Not enough information to determine the area.

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

There are

16 cups = 1 gallon

3 gallons = 48 cups

48 divided by 4 = 12 batches of rice pudding

Answer

12

Step-by-step explanation:

4 cup of milk = 1 batch of rice pudding

1 gallon of milk= 16 cups of milk

3 gallon of milk = 3x 16

=48 answer

then, 48 cup of milk = 48 ÷ 4

= 12 answer

Hence, stacy can make 12 batch of pudding with 3 gallon of milk.

Answer:

8

Step-by-step explanation:

The median is the number right in the middle. Eight is in the middle of the number line making it the median.

The car will be worth after one year is £ 5753.6.

An exponential function is defined by the formula f(x) = [tex]a^{x}[/tex], where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.

The exponential function is an important mathematical function which is of the form

f(x) =  [tex]a^{x}[/tex]

Where a > 0 and a is not equal to 1.

x is any real number.

Given

Car cost when bought A =  £ 6200

Value of a car decreases by 7.2% each year.

n = 1

r = 7.2% or 0.072

The car will be worth after one year

[tex]y= A (1-r)^{n}[/tex]

⇒ [tex]y =6200(1-0.072)^{1}[/tex]

⇒ [tex]y = 6200(0.928)[/tex]

⇒ y = £ 5753.6

Hence, the car will be worth after one year is £ 5753.6.

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Answer:

x = - 1

Step-by-step explanation:

3(x + 1) = - 2(x - 1) - 4 ←  distribute parenthesis on both sides

3x + 3 = - 2x + 2 - 4

3x + 3 = - 2x - 2 ( add 2x to both sides )

5x + 3 = - 2 ( subtract 3 from both sides )

5x = - 5 ( divide both sides by 5 )

x = - 1

Answer:

Angle 3 = 70

Step-by-step explanation:

This is a geometry property

"opposite angle theorem"

It's pretty easy to prove it as well
180-70 = 110
180-110 = 70