Need help with the introduction to probability lesson, photo is attached below.

The numbers in Set A = {5, 9, 12, 14, 18} that are elements of both Set B and Set C, shown below Set B = {even numbers} Set C = {multiples of 3} will be 12 and 18.

It should be noted that even numbers can be divided by 2.

The multiple of 3 in the numbers are 12 and 18 that can be divided by 2 as well.

Therefore, the numbers in Set A = {5, 9, 12, 14, 18} that are elements of both Set B and Set C, shown below Set B = {even numbers} Set C = {multiples of 3} will be 12 and 18.

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Answer:

54 as a percentage of 216% is 116.64.

Step-by-step explanation:

100% of 54 is 54 so 54 x 2 would be 108. We have solved 200% of it now for the 16%. The percentage of 54 of 16% would be 8.64. Now add up all we have learned.

108 + 8.64 = 116.64

Answer: c=6, d=-6

Step-by-step explanation:

c+12d=-66

-4c+3d=-42

(-4c+3d=-42)*4

-16c+12d=-168      ==> subtract this

c+12d=-66           ==> by this

-17c=-168-(-66)       ==> subtract the top two equations

-17c=-168+66

-17c=-102

c=6

c+12d=-66

6+12d=-66

12d=-72

d=-6

Answer:

8^3

Step-by-step explanation:

there are three 8s soo all u do is count the number and then how many of that same number you can put into an exponent

Answer: kinda

Step-by-step explanation:

as long as you have a passing grade you will be fine, just work on the "F" :)

Answer:

  The given point satisfies both equations of a line, hence is common to the two lines.

Step-by-step explanation:

Given two lines, one joining the points (6,-7,0) to (16,-19,-4), and the other joining the points (0,3,-6) to (2,-5,10), you want to show that the point (1, -1, 2) is common to those lines.

The equation of a line through points (x1, y1, z1) and (x2, y2, z2) can be written:

  (x -x1)/(x2 -x1) = (y -y1)/(y2 -y1) = (z -z1)/(z2 -z1)

For the first pair of points, the equation of the line is ...

  (x -6)/(16 -6) = (y +7)/(-19 +7) = (z -0)/(-4 -0)

  (x -6)/10 = -(y +7)/12 = -z/4 . . . . . line 1

For the second pair of points, the equation of the line is ...

  (x -0)/(2 -0) = (y -3)/(-5 -3) = (z +6)/(10 +6)

  x/2 = -(y -3)/8 = (z +6)/16 . . . . . line 2

If the given point is on each of these lines, then it will satisfy each of the equations.

Line 1: (1 -6)/10 = -(-1 +7)/12 = -2/4   ⇒   -5/10 = -6/12 = -2/4 . . . true

The given point is on Line 1.

Line 2: (1)/2 = -(-1-3)/8 = (2+6)/16   ⇒   1/2 = 4/8 = 8/16 . . . true

The given point is on Line 2.

The given point is common to both lines.

__

Alternate solution

For points A and B and parameter p, we can write the parameterized equation of each line as ...

  (x, y, z) = A +p(B -A)

Using parameters t and s for the two lines, we get ...

  Line 1: (x, y, z) = (6, -7, 0) +t(16 -6, -19 +7, -4 -0) = (6 +10t, -7 -12t, 0 -4t)

  Line 2: (x, y, z) = (0, 3, -6) +s(2 -0, -5 -3, 10 +6) = (0 +2s, 3 -8s, -6 +16s)

A common point will be found where (x, y, z) for some value of t matches (x, y, z) for some value of s. We can find those values of s and t by solving simultaneous equations for any pair of the variables (x, y, z). The equations are ...

By any of your favorite methods, these equations have the solution (t, s) = (-0.5, 0.5). The point the lines have in common is ...

  (6 +10(-0.5), -7 -12(-0.5), 0 -4(-0.5)) = (6 -5, -7 +6, 2) = (1, -1, 2)

The common point to the two lines is (1, -1, 2).

If you had to drive for more than 300 miles for the first day you need to stop for gas fill up.

Unitary method is a mathematical tool for finding the value of single unit then deriving the given units according to the question.

According to the given question your car's gas tank holds 13 gallons, and you expect to get about 25 miles per gallon.

Given that you never want to run out of gas to not face this issue you always keep 1 gallon of gas in the tank.

So when you fill your tank completely you fill for 12 gallons of gas because 1 gallon is already there.

Also given that the car can go 25 miles per gallon.

So, for 12 gallons of gas you can go (25 × 12 ) miles which is

= 300 miles.

If you had to drive for more than 300 miles then you need to stop for gas in first day's drive.

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The total square footage (area) of the apartment is 337 square feet.

It is given in the question that, In a small apartment:-

Dimensions of the bedroom = 10 ft by 10ft

Dimensions of the bathroom = 5 ft by 5 ft

Dimensions of the living room/kitchen = 14 ft by 18 ft

We have to find the total square footage (area) of the apartment.

We know that,

Area of square = [tex]side^2[/tex]

Hence,

Area of the bedroom = 100 square feet

Area of the bathroom = 25 square feet

Area of the living room/ kitchen = 212 square feet

Hence,

Total square footage of the apartment = 100 + 25 + 212 = 337 square feet.

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The expected value for your profit is 2.53.

The probability is the number that indicates the likelihood that an event will occur and is defined as the ratio of favorable outcomes to all outcomes.

Given,

You can solve for the necessary anticipated value below.

There will be 600 tickets available for purchase overall.

So,

$ 5 each and sell go tickets

one $3,000 grand prize = ( 1/600) × 3000

two $500 second prizes = (2/600) × 500

thirteen $40 third prizes = (13/600) × 40

Any discrete variable X's anticipated value is calculated as:

E(x) = ( 1/600) × 3000 + (2/600) × 500 + (13/600) × 40 + (600-1-2-13/600).0-5

E(x) = 2.53

The expected value for your profit is  2.53.

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The cost of the carpet will be $983.33

From the question, we are to calculate how much the carpet will cost

From the given information,

The carpet has a length of 20 feet

and a width of 15 feet

First, we will covert the dimension to yard

NOTE: 1 foot = 1/3 yards

Thus,

20 feet = 20/3 yards

and

15 feet = 15/5 yards = 5 yards

Now, we will calculate the area of the carpet

Using the formula,

Area = Length × Width

Area of the carpet = 20/3 × 5 square yard

Area of the carpet = 33.33 square yard

Now, we have that

The carpet costs $29.50 per square yard

∴ The cost of the carpet = 20/3 × 5 × $29.50

The cost of the carpet = $ 983.33

Hence, the cost of the carpet will be $983.33

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Answer: g(4)=-17

Step-by-step explanation:

You just plug in 4 into x.

-3(4)-5
-12-5
=17

Answer:

g(4) = -17

Step-by-step explanation:

Hello!

Substitute 4 for x in the equation.

g(4) is -17.

I believe the answer is 200.

Answer:

h = 10m

Step-by-step explanation:

[tex]A=\frac{bh}{2}[/tex]
[tex]90=\frac{18h}{2}[/tex]

[tex]18h=(90)(2)[/tex]

[tex]h=\frac{180}{18} =10[/tex]

Hope this helps

Answer:

15

Step-by-step explanation:

105/7

15

Hope It Helps

Linear equation: a, b, c, and r are real numbers (and if a, b, and c are not all equal to 0)

then ax + by + cz = r is called a linear equation in three variables. (The

“three variables” are the x, the y, and the z.)

The numbers a, b, and c are called the coefficient of the equation. The

number r is called the constant of the equation

y(a-b)=c(y+a)

ya-yb=cy+ca

ya-yb-cy=ca

y(a-b-c)=ca

[tex]y=\frac{ca}{a-b-c}[/tex]

case 1:

if either C and a are zero the y is zero,

case 2:

if

[tex]c\neq 0 \\a\neq 0\\y\neq 0[/tex]

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Answer: D (the bottom right)

Step-by-step explanation: The first problem stated is that Niki scored 20 points (positive) so you would point the arrow directed positively. Then she lost 10 points, which would be negative so the direction of the arrow would point back to a positive 10. Then lost another 25 points, leading to -15 (10+(-25)= -15

At 6 am temperature was 71 degrees and rises 4 degrees per hour then at 9 am temperature reach 83 degrees.

As given in the question,

On Thursday at 6 am temperature = 71 degrees

Rise in temperature = 4 degrees per hour

Temperature at

7 am = 71+ 4

         = 75 degrees

8am = 75 + 4

       = 79 degrees

9am = 79 +4

        = 83 degrees

Therefore, at 6 am temperature was 71 degrees and rises 4 degrees per hour then at 9 am temperature reach 83 degrees.

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Using Chebyshev's Theorem, the minimum proportion of scores that fall within 1.8 standard deviations on both sides of the mean is 69.14%.

When the distribution is unknown, Chebyshev's Theorem is used. It states that:

For this problem, we have that k = 1.8, hence the percentage is:

[tex]P = 100\left(1 - \frac{1}{1.8^{2}}\right) = 69.14[/tex]

The minimum proportion of scores that fall within 1.8 standard deviations on both sides of the mean is 69.14%.

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The device numbers should be less than 18.

Given, internet service provider is charging a rate of $175 per month.

The new plan would charge $94 plus an additional $4.50 per device connected to the network.

we need to find the number of devices for which the cost of the new plan is less than the cost of the current plan.

old plan = $175

New plan = $94 plus $4.50 per device

let us suppose 'x' devices can be connected.

so, 94 ₊ 4.5x < 175

4.5x < 175 ₋ 94

4.5x < 81

x < 81/4.5

x < 18

less than 18.

Hence there should be less than 18 devices connected for the new plan.

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The circumference of a circle with radius, r = 9.5m is 19π

What is circumference of circle?

The perimeter of a circle or ellipse is its circumference. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter.

What does a circle's circumference mean?

The complete length of a circle's arc is known as its circumference. The circumference of the circle is another name for it. The radius of the circle is the distance measured from any point on the circle to its center.

Given,

radius of the circle = 9.5m

The formula to calculate the circumference is -

C = 2πr

where r = radius of the circle

⇒ 2 × π × 9.5

⇒ 19π

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The area enclosed by the ellipse [tex]\frac{x^2}{4}+\frac{y^2}{81}=1[/tex] is 60 square units.

The general form of the equation of ellipse is  [tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]

Given the equation of ellipse is,  [tex]\frac{x^2}{4}+\frac{y^2}{81}=1[/tex]

⇒ [tex]\frac{x^2}{2^2}+\frac{y^2}{9^2}=1[/tex]

That is, a = 2 and b = 9

Now,  [tex]\frac{y^2}{9^2} = 1 -\frac{x^2}{2^2}[/tex]

⇒ [tex]y=\frac{9}{2} \sqrt{4-x^2}[/tex]

Area enclosed by the ellipse = 4 x Area of ellipse in the first quadrant

Therefore, Area of ellipse in the first quadrant, A = [tex]\int\limits^a_0{\frac{9}{2} \sqrt{4-x^2}} \, dx[/tex]

Using Substitution ,x = 2cosθ, then dx = -2sinθdθ and x = 0⇒ θ = π/2 and x = 2⇒ θ = 0

A = [tex]\int\limits^a_0{\frac{9}{2} \sqrt{4-4cos^2\theta}} \, dx[/tex]

  = [tex]\int\limits^2_0{\frac{9}{2}\times2 \sqrt{1-cos^2\theta}} \, dx[/tex]

  = [tex]\int\limits^2_0{9 sin^2\theta} \, dx[/tex]

 = [tex]\int\limits^0_\frac{\pi}{2} {9 sin^2\theta} (-2sinx)\, d\theta[/tex]

  = [tex]\int\limits^\frac{\pi}{2} _0{18 sin^3\theta} \, d\theta[/tex]

  = [tex]\int\limits^\frac{\pi}{2} _0{18 (\frac{3sin\theta-sin3\theta}{4} )} \, d\theta[/tex]

  = [tex]\frac{9}{2} \int\limits^\frac{\pi}{2} _b {3sin\theta} \, d\theta -\frac{9}{2} \int\limits^\frac{\pi}{2} _0 {sin3\theta} \, d\theta[/tex]

  = 27/2 x (-cosθ) - 9/6 x (-cos3θ) |  θ = 0 to  θ =  π/2

  = 15 square units.

Therefore, the area enclosed by ellipse  [tex]\frac{x^2}{4}+\frac{y^2}{81}=1[/tex] = 4 x A = 4 x 15 = 60 square units.

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The letter A is not drawn to scale in the sketch below. construct ABC next to its below-listed sketch The amount of force applied over a specific distance is referred to as work. Since the problem already specifies the force's value and the length of the distance it is exerted across, the quantity of labor completed requires multiplying these two numbers. As demonstrated below:

work, in physics, measure of energy transfer that occurs when an object is moved over a distance by an external force at least part of which is applied in the direction of the displacement.

Work: Force times Distance

Work = 250 J x 50 N * 5 m

Work = 250 J

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In linear equations x = 3,664 books are the production costs will equal the money from sales .

What is a formula for linear equations?

fixed cost = $32,060

variable cost = $12.75

here cost function

c(x) = fixed cost  +  x( variable cost )

c(x) =  $32,060  +   x($12.75)   ................. 1

now revenue function

R(X) = (Selling price ).x

r(x) =   ( 21.50)x   .............2

where production cost is wqual to selling

              c (X)      = r (x)

   32,0 60  +   x($12.75)  =  ( 21.50)x

        32,060 =  ( 21.50)x  - (12.75)x

         32,060 =  8.75 x

             x = 3,664 books

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Heidi has to walk her bike for (1/8) mile to complete the loop.

Given that:-

Total distance of the loop = 7/8 mile

Distance Heidi rode on her bike before she stopped for rest = 1/2 mile

Distance Heidi rode on her bike after taking the rest = 1/4 mile.

We have to find the distance Heidi has to to walk to complete the loop because she had a flat tire.

Let the distance Heidi has to to walk to complete the loop because she had a flat tire is x miles.

We know that,

Total distance of the loop = Distance Heidi rode on her bike before she stopped for rest + Distance Heidi rode on her bike after taking the rest + distance Heidi has to to walk to complete the loop because she had a flat tire.

Hence, by adding the fractions, we get

7/8 = 1/2 + 1/4 + x

7/8 = (2+1)/4 + x

7/8 = 3/4 + x

7/8 - 3/4 = x

7/8 - 6/8 = x

1/8 mile = x

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The inequality for Leila claim is (0.75 × x) > (0.50 × y) and the support claim is x = 100 and y = 10 and that refutes the claim is x = 1 and y = 200

Inequality:

Inequality are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Given,

Leila says that 75% of a number will always be greater than 50% of any other number.

Here we need to find the inequality and we also need to find one that supports Leila's claim and one to show that she is incorrect.

Let x and y be two numbers.

Leila says that 75% of a number will always be greater than 50% of any other number.

This means that the inequality is,

=> (0.75 × x) > (0.50 × y)

We know that,

75% of x = 0.75 × x

and

50% of y = 0.50 × y

So,

Numbers that support Leila's claim.

Let x = 100 and b = 10

=> 0.75 × x

=> 0.75 × 100 = 75

and

=> 0.50 × 10 = 5

As we know that, based in on the inequality,

=> 75 > 5

Hence, x = 100 and y = 10 support Leila's claim.

Similarly,

Numbers that refutes her claim.

Let x = 1 and y = 200

=> 0.75 × x

=> 0.75 × 1 = 0.75

and

=> 0.50 × 200 = 100

As we know that,

=> 0.75 < 100

Hence, x = 1 and y = 200 refutes Leila's claim.

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