Write the equation of the line that passes through the points ( – 3, 2) and ( - 1,6).

The list of elements in the sets are as follows:

A.  A ∩ B = {2, 9}

B. B ∩ C = {2, 3}

C. A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D. B ∪ C = {2, 3, 5, 7, 9, 10}

Set are defined as the collection of objects whose elements are fixed and can not be changed.

Therefore,

universal set = U = {1,2,3, 4, 5, 6, 7, 8, 9, 10​}

A = {1, 2, 7, 8, 9}

B = {2, 3, 5, 9}

C = {2, 3, 7, 10}

Therefore,

A.

A ∩ B = {2, 9}

B.

B ∩ C = {2, 3}

C.

A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D.

B ∪ C = {2, 3, 5, 7, 9, 10}

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9514 1404 393

Answer:

  a8 = 4

Step-by-step explanation:

Put 8 where n is and do the arithmetic.

  a8 = (1/2)(8) = 8/2 = 4

The 8th term of this arithmetic sequence is 4.

The radius of the semicircle protractor is approximately 4.693 cm.

Given,Perimeter of a semicircle protractor = 14.8 cm.

To find:The radius of a semicircle protractor.Solution:We know that the perimeter of a semicircle protractor is the sum of the straight edge of a protractor and half of the circumference of the circle whose radius is the radius of the protractor.

Circumference of a circle = 2πrWhere, r is the radius of the circle.If the radius of the semicircle protractor is r, then Perimeter of a semicircle protractor = r + πr [∵ half of the circumference of a circle =\((1/2) × 2πr = πr]14.8 = r + πr14.8 = r(1 + π) r = 14.8 / (1 + π)r ≈ 4.693\) cm.

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Answer:

52.5

Step-by-step explanation:

Answer:

52.5 miles

2/15=7/x

15x7=105

105/2=52.5

Answer: 30/23

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

Step 2: Subtract 4x from both sides.

Step 3: Subtract 5 from both sides.

Step 4: Multiply both sides by 6/(-23).

lolz have a nice day!!!

Answer:

Multiply the whole equation to 6 to make it simple.

So you get:

X + 30 = 24

So: X = 24 - 30 = ( - 6 )

Answer:

9514 1404 393

Answer:

 $67,200

Step-by-step explanation:

The amount if interest is given by the formula ...

I = Prt

where P is the amount invested, r is the annual rate, and t is the number of years. Here, we want to find P when r = 0.05 and t = 1/2 such that I = 1680.

 P = I/(rt) = $1680/(0.05·0.5) = $1680/0.025

 P = $67,200

The amount invested was $67,200.

Step-by-step explanation:

17/90

To find the ratio 34 minutes to 3 hours in lowest terms, both the numerator and the denominator must be in the same unit.

1 hour = 60 minutes

3 hours = 3 x 60 = 180 minutes

34 minutes to 3 hours can therefore be expressed as:

Using a graphing calculator :

The scatter plot will look thus:

Answer:

D

The light reflected during the first quarter and third quarter moon phases appears equal because the sun, moon, and Earth are at right angles.

Answer:

10c-4+11d Welcome :D

Step-by-step explanation:

Answer:

The answer is 50.

Step-by-step explanation:

Use MDAS

Multiplication, Division, Addition and Subtraction

2 + 6 * 8 =

Multiply first then add

2 + 6*8 = ?

= 2 + 48

= 50

We will have that the product of k and eighth decreased by three times k is the following:

Answer:

The inverse is,

\(f^{-1}(x) = \sqrt[5]{x} - 3\)

Step-by-step explanation:

f(x) = (x+3)^5

Finding the inverse,

\(f(x) = (x+3)^5\\or,\\y = (x+3)^5\)

We replace x with y and vice versa

so,

\(x = (y+3)^5\)

Solving for y,

the the 5th root,

\(\sqrt[5]{x} = y + 3\\y = \sqrt[5]{x} - 3\)

hence the inverse function is,

\(f^{-1}(x) = \sqrt[5]{x} - 3\)

Step-by-step explanation:

f(x)=(x+3)×5

Y=5X+15

now

interxchanging x and y we get,

x=5y+15

5y=x-15

y=x-15/5

therefor f~1(x)=x-15/5

The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

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Answer:

(C) 12

Step-by-step explanation:

To solve this problem, we can use the following steps:

Find half of 80: 80/2 = 40

Add 20 to half of 80: 40 + 20 = 60

Find one fifth of the result: 60/5 = 12

Therefore, one fifth of twenty more than half of 80 is equal to 12. The correct answer is (C) 12.

Answer:

(C) 12

Step-by-step explanation:

What is one fifth of twenty more than half of 80

0.5 × 80 = 40

What is one fifth of twenty more than half of 80

40 + 20 = 60

What is one fifth of twenty more than half of 80

1/5 × 60 = 60/5 = 12

Answer:

d is 6

b is 7

c is 4

e is 5

a is 1

Step-by-step explanation:

The probability of getting at least 6 heads is3/256 or 0.0117

Probability shows possibility to happen an event, it defines that an event will occur or not. The probability varies from 0 to 1.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of occurrences that follow a probability distribution.

Probability is a measure of how likely something is to occur. Calculating probability involves dividing the total number of outcomes by the number of possible ways an event may occur.

Given that,

A fair coin is tossed = 8 time.

We have to find the probability of getting at least 6 heads.

Since, the probability of getting head, when one coin is tossed = 1/2

And the probability of getting tale = 1/2  

The probability of getting head at least  6 times when coin is tossed 8 times can be given as,

The head can come 6 times, then probability = \((1/2)\x^{6} (1/2)\x^{2}\) =  (1/2)⁸

The head can come 7 times, then probability = (1/2)⁷(1/2) = (1/2)⁸

The head can come 8 times, then probability = (1/2)⁸

The probability of getting head at least 6 times

= (1/2)⁸ + (1/2)⁸ +  (1/2)⁸ = 3(1/2)⁸ = 3/256 = 0.0117

The probability of getting at least 6 heads is3/256 or 0.0117

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Answer:

60/2.5 = 24 cm

Step-by-step explanation:

if you are satisfied with the results then plz make me genius

Answer:

The answer is 24 inches.

Step-by-step explanation:

Given:

1 inch = 2.5 cm

or, 1 cm = 1/2.5 inch............... eqn (i)

Now,

Wideness of envelope = 60 cm

= 60 (1/2.5) inches [From eqn (i)]

= 60/2.5 inches

= 24 inches Ans

Answer:

by measuring in feet

Step-by-step explanation:

its the easiest way to find what your looking for

Answer:

You can find the length of an unknown leg using the Pythagorean theorem

Step-by-step explanation:

\(a^2+b^2=c^2\)

or

\(c^2-a^2=b^2\)

or

\(c^2-b^2=a^2\)

note c = hypotenuse and b and a = legs

Answer:

2/3

Step-by-step explanation:

Gradient of line

= (y1-y2) /(x1-x2)

= (3-(-1))/(4-(-2))

= (3+1)/(4+2)

= 4/6

= 2/3

The order of the matrices of each product is given as follows:

AB is nonexistent, BA is nonexistent.

Multiplication of matrices is applied multiplying the rows of the first matrix by the columns of the second matrix, and hence the number of columns of the first matrix must be equal to the number of rows of the second matrix.

For the product AB, we have that:

Hence the product is nonexistent.

For the product BA, we have that:

Hence the product is nonexistent.

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The airplane's groundspeed is approximately 242.25 km/h, and the resultant bearing is approximately 55.04° (relative to true north, measured clockwise).

How to solve for the airplane's groundspeed

To determine the resultant velocity of the airplane, we need to break down the airplane's velocity and the wind's velocity into their respective components and add them. Let's assume that the angles are measured clockwise from true north.

Let's denote:

Vp = airplane's speed = 250 km/h

θp = airplane's heading = 075 degrees

Vw = wind's speed = 85 km/h

θw = wind's heading = 300 degrees

We can then find the eastward (x) and northward (y) components of the velocities:

For the airplane:

Vpx = Vp * cos(θp) = 250 * cos(75 degrees) = 64.95 km/h

Vpy = Vp * sin(θp) = 250 * sin(75 degrees) = 241.92 km/h

For the wind:

Vwx = Vw * cos(θw) = 85 * cos(300 degrees) = 73.60 km/h

Vwy = Vw * sin(θw) = 85 * sin(300 degrees) = -42.50 km/h

We then sum the x and y components of the two velocities to find the resultant velocity components:

Vrx = Vpx + Vwx = 64.95 km/h + 73.60 km/h = 138.55 km/h

Vry = Vpy + Vwy = 241.92 km/h - 42.50 km/h = 199.42 km/h

The magnitude of the resultant velocity, which represents the groundspeed (Vr), is found using the Pythagorean theorem:

Vr = sqrt((Vrx)^2 + (Vry)^2) = sqrt((138.55)^2 + (199.42)^2) = 242.25 km/h

The bearing (θr) of the resultant velocity (relative to north) can be found using inverse tangent:

θr = atan2(Vry, Vrx) = atan2(199.42, 138.55) = 55.04 degrees

Therefore, the airplane's groundspeed is approximately 242.25 km/h, and the resultant bearing is approximately 55.04° (relative to true north, measured clockwise).

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Therefore, the number of students who study only one subject is n(H-only) + n(G-only) = 14 + 28 = 42.

In mathematics, a set is a collection of distinct objects, which are called its elements. These objects can be anything, such as numbers, letters, or even other sets. Sets are usually denoted by capital letters and the elements of a set are listed within braces, separated by.

Given by the question.

i. n (H ∩ G) can be found using the formula:

n(H ∩ G) = n(H) + n(G) - n(H U G)

where n (H U G) represents the number of students who study either History or Government or both.

We know that n(H) = 2x and n(G) = 3x. Also, n(U) = 54, which means the total number of students is 54. Therefore, we can write:

n (H U G) = n(H) + n(G) - n (H ∩ G)

54 = 2x + 3x - x

54 = 4x

x = 13.5

Since x must be a whole number, we can round it up to 14. Therefore, n (H ∩ G) = x = 14.

ii. The number of students who study only one subject can be found by subtracting n (H ∩ G) from n(H) and n(G) respectively, and then adding the number of students who study neither History nor Government.

n(H-only) = n(H) - n (H ∩ G) = 2x - x = x = 14

n(G-only) = n(G) - n (H ∩ G) = 3x - x = 2x = 28

n(Neither) = n(U) - n (H U G) = 54 - 14 = 40

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Equation \(x^{2}-6x=-5\)

Solving:

\(x^2 - 6x+5=0\\\\(x-5)(x-1)=0\\\\x=1, 5\)

Answer: the sun is 389.015069067 times further away from earth to the moon

Step-by-step explanation: 92935700/238990=389.015069067

The required correct answer is (a) x-intercept is (-8,0) and the y-intercept is (0,8).

In the context of a linear equation, an intercept is a point where the graph of the equation crosses or intersects with one of the axes in a coordinate system. There are two types of intercepts:

Here,
To find the x-intercept, we set y = 0 in the equation y = x + 8 and solve for x:

0 = x + 8

x = -8

Therefore, the x-intercept is (-8, 0).

To find the y-intercept, we set x = 0 in the equation y = x + 8 and solve for y:

y = 0 + 8

y = 8

Therefore, the y-intercept is (0, 8).

So the correct answer is (a) the x-intercept is (-8,0) and the y-intercept is (0,8).

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Answer:

What are you supposed to do?

Step-by-step explanation:

The probability that a Statistics student is also in African-American Literature is 18%.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.

Let, The total number of students is 100.

Given, 30% of the seniors are in statistics.

Therefore, The probability of choosing a student in statistics is,

= 30/100.

= 3/10.

Similarly, The probability of choosing a student in African-American Literature is,

= 18/100.

= 9/50.

We know the probability of A given B is P(A∩B)/P(B).

Therefore, The likelihood that a student majoring in statistics will also study African-American literature is,

= [(3/10)×(9/50)]/(3/10).

= 0.054/0.3.

= 0.18 Or 18%.

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