What is the value of x?
40
20
12
At
P60°
8x-4
a
b

Proved that if two parallel lines are cut by a transversal then the alternate exterior angles are congruent.

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

By the property of alternate interior angles;

From the figure attached;

∠XWY ≅ ∠ZYW

The Property of the alternate angles states that if two parallel lines are cut by a transversal, then the alternate angles are congruent.

Here, ∠XWY and ∠ZYW shows the interior angles between the parallel lines and the transversal.

The interior alternate angles ∠XWY and ∠ZYW will be congruent.

Hence, Proved that if two parallel lines are cut by a transversal then the alternate exterior angles are congruent.

Learn more about interior and exterior angles here:

https://brainly.com/question/14173422

#SPJ1

"When creating a graph, it is important to assign the x and y axis."

Assigning the x and y axes is crucial when making a graph because the x-axis is referred to as the line on a Cartesian coordinate system that runs horizontally. A point or line's separation from the y-axis can be determined using the x-axis. The y-axis displays a point's location on a Cartesian plane in the y (vertical) direction. Additionally, it serves as the origin (zero) point for calculating how far a point is from the x-axis.

A graph is a structure that resembles a set of objects in mathematics, more specifically in graph theory, in which some pairs of the objects are conceptually "related." The objects are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

Two parallel lines, known as axes (pronounced AX-eez), that are perpendicular to each other make up a coordinate grid. Typically, the term "x-axis" refers to the horizontal axis. The y-axis is the common name for the vertical axis. The origin is the location where the x- and y-axes intersect.

"When creating a graph, it is important to assign the x and y axis."

Because the x-axis is referred to as the line on a Cartesian coordinate system that runs horizontally, determining the x and y axes is essential when creating a graph. The x-axis can be used to calculate a point or line's distance from the y-axis. A point's position on a Cartesian plane is shown on the y-axis in the y (vertical) direction. It also acts as the origin (zero) point for determining a point's distance from the x-axis.

To know more about graph,

https://brainly.com/question/92258?referrer=searchResults

#SPJ13

The probability of no loads occurring during that period is at most 0.3 exists 3.2 years.

Given: Mean time between occurrence = 0.4 year

A number of loads expected to occur during a 4 year period

Period = 4

Mean time = 0.4

Let the formula = Period/Mean Time

The number of loads expected to occur during a 4-year period

= 4/0.4 = 10 loads

B. Probability that more than 11 loads occur during 4 year period

The expected number of loads during 4-year period = 10 (from A above)

mean = 10

Using Poisson distribution,

P(k events in interval)= (λ^k * e^-k)/k!

where: k = 0, 1, 2,3,4, . . ., 11 and λ = 10.

P(k = 0) = (1[tex]0^0[/tex] × [tex]e^{-10[/tex])/0! = 0.000045

P(k = 1) = (1[tex]0^1[/tex] ×  [tex]e^{-10[/tex])/1! = 0.000454

P(k = 2) = (10² ×  [tex]e^{-10[/tex])/2! = 0.00227

P(k = 3) = (10³ ×  [tex]e^{-10[/tex])/3! = 0.007567

P(k = 4) = (1[tex]0^4[/tex] ×  [tex]e^{-10[/tex])/4! = 0.018917

P(k = 5) = (1[tex]0^5[/tex] ×  [tex]e^{-10[/tex])/5! = 0.037833

P(k = 6) = (1[tex]0^6[/tex] ×  [tex]e^{-10[/tex])/6! = 0.063055

P(k = 7) = (1[tex]0^7[/tex] ×  [tex]e^{-10[/tex])/7! = 0.090079

P(k = 8) = (1[tex]0^8[/tex] ×  [tex]e^{-10[/tex])/8! = 0.112599

P(k = 9) = (1[tex]0^9[/tex] ×  [tex]e^{-10[/tex])/9! = 0.12511

P(k = 10) = (1[tex]0^{10[/tex] ×  [tex]e^{-10[/tex])/10! = 0.12511

P(k = 11) = (1[tex]0^{11[/tex] ×  [tex]e^{-10[/tex])/11! = 0.113736

The probability that more than 11 loads occur during a 4-year period is then given by the following Express

1 - [P(k = 0) + P(k = 1) + P(k = 2) + . . . + P(k = 11)]

substitute the values in the above equation, we get

= 1 - [0.000045 + 0.000454 + 0.00227 + 0.007567 + 0.018917 + 0.037833 + 0.063055 + 0.090079 + 0.112599 + 0.12511+ 0.12511 + 0.113736]

simplifying the equation, we get

= 1 - 0.571665 = 0.428335

C. How long must a time period be so that the probability of no loads occurring during that period is at most 0.3

(λ^0 * e^-λ)/0! = 0.3

⇒ e^-λ/1 = 0.3

simplifying the above equation, we get

⇒ e^-λ = 0.3

⇒ -λ = ln 0.3

⇒ -λ = -1.204

⇒ λ = 1.204

The time period = 4 years / 1.204

Time period = 3.2 years

To learn more about Poisson distribution refer to:

https://brainly.com/question/24098004

#SPJ4

The value of f(x) - g(x) = 2x³ - 4x² + 6x + 4

What is Function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Given,

f(x) = 7x³ - 3x² + 5x+1

g(x) = 5x³+x²-x-3

We have to find the value of:

f(x) - g(x)

Substituting the value of f(x) and g(x)

f(x) - g(x) = (7x³ - 3x² + 5x+1 ) - (5x³+x²-x-3)

Now, open the brackets

f(x) - g(x) = 7x³ - 3x² + 5x+1 - 5x³ - x²+ x + 3

Now, arranging them by like terms

f(x) - g(x) = 7x³ - 5x³ - 3x² - x² + 5x + x +1 + 3

               = 2x³ - 4x² + 6x + 4

Hence, f(x) - g(x) = 2x³ - 4x² + 6x + 4

To learn more about Function click on the link

https://brainly.com/question/10439235

#SPJ9

Answer:

(x² -5x +13) + (x² +3x -6)

Step-by-step explanation:

(x² -5x +13) + (x² +3x -6)

x² -5x +13 + x² +3x -6

|x² + x²| |-5x + 3x| |+13 -6|

2x² -2x +7

Answer: He is incorrect

Step-by-step explanation:

3/21 = 0.142857142857143

21/3 = 7

They are two different equations with different answers.

Answer:

He is not correct

Step-by-step explanation:

Luke is not correct because 3/21 is 0.142 while 21/3 is 7.

Answer:

Step-by-step explanation:

round up

√3 = √4

70-√4= 70-2

=68

Answer: 31

Step-by-step explanation:

The numbers are increasing by 1, then 2, then 3, ...

In other words, the second difference is 1.

So, the next number is likely [tex]24+7=31[/tex].

Answer:

y=8X

Explanation:

The ratio 13 to X = 13:X

The ratio 104 to y = 104:y

If they are equivalent, we have that:

We write the ratios in fraction form.

We then make y the subject of the equation.

We can simplify further to get:

This is the equation that represents y in terms of X.

Answer:

Step-by-step explanation:

erm

A triangle is 180 degrees

Add both angles then subtract by 180

Given the triangle KLM, you can find the measure of angle L by using the Law of Sines. This states that:

Where "a", "b" and "c" are sides of the triangle, and "A", "B", and "C" are the angles.

In this case, you can set up this equation:

Knowing that:

You can substitute values into the equation and solve for "L". Remember the use the Inverse Trigonometric Function Arcsine, in order to solve for the angle:

Hence, the answer is:

It will be similar to the original triangle.

The shape of the density curve for a dataset is like a triangle, that is, as we move to the left of the horizontal axis, it starts from zero height, then rises linearly until some peak, then declines linearly until reaches zero, then stays zero from there onward. If we standardize the dataset by calculating the standard scores, the geometrical shape of the density curve will more or less be the same. i.e., similar to the original triangle. Scale of it will be just changed.

You can learn more about triangle from:

https://brainly.com/question/2773823

#SPJ4

The unit rate of Printer B = 25 pages per minute, which is greater than the unit rate of Printer A that is 15 pages per minute.

The unit rate of a graph can b determined by using any point, (x, y), on the graph and solve by finding, m, which is the ratio of y to x, if x and y represents the variables of the relationship that is graphed.

Thus, unit rate (m) = y/x.

The printing rate for Printer A is represented by the graph. To find the unit rate for Printer A, use a point on the graph, (2, 30) to find the unit rate, m.

Printer A's Unit rate (m) = y/x = 30/2

Printer A's unit rate (m) = 15 pages per minute.

The printing rate for Printer B is given as 25 pages per minute. 25 pages per minute is a greater unit rate compared to 15 pages per minute.

Therefore, we can conclude that Printer B has a greater printing rate than Printer A, because the unit rate of 25 pages per minute is greater than 15 pages per minute.

Learn more about the unit rate on:

https://brainly.com/question/19493296

#SPJ1

Using the normal approximation to the binomial, it is found that there is a 35.57% probability that the number of individuals in Lance's sample is.

In a normal distribution with mean and standard deviation, the z-score of a measure X is given by:

z = x - [tex]\mu[/tex]/ [tex]\sigma[/tex]

Normal Probability Distribution measures how many standard deviations the measure is from the mean.  

In this problem:

The proportion of young adults ages 20–39 who regularly skip eating breakfast is given as 0.238, hence p = 0.238

A sample of 500 hence n = 500

The mean and the standard deviation are given by:

[tex]\mu[/tex] = 500 ( 0.238) = 119

[tex]\sigma[/tex] = 9.5225

The probability that the number of individuals in Lance's sample who regularly skip breakfast will be greater than 122, using continuity correction, then the p-value of Z when X = 122.5.

z = x - [tex]\mu[/tex]/ [tex]\sigma[/tex]

z = 122.5 - 119/ 9.5225

z = 0.37

Then p-value of 0.6443.

1 - 0.6443 = 0.3557.

0.3557 = 35.57%is the probability that the number of individuals in Lance's sample who regularly skip breakfast is greater than 122.

Learn more about probability here:

brainly.com/question/1210781

#SPJ1

After performing some mathematical operations, we know that the total cost of 8 popcorn bags and 5 drinks is $53.

So, the total cost:

Cost of a total of 8 bags of popcorn and 5 drinks:

Therefore, after performing some mathematical operations, we know that the total cost of 8 popcorn bags and 5 drinks is $53.

Know more about mathematical operations here:

https://brainly.com/question/28937023

#SPJ13

The correct question is given below:

Zahra and some friends are going to the movies. At the theater, they sell a bag of popcorn for $3.50 and a drink for $5. How much would it cost if they bought 8 bags of popcorn and 5 drinks?

To solve the system of equation using substitution method only, here are the steps.

1. Since the 2nd equation has been equated already into x = or y = , we can use this value to substitute the "x" value in the first equation.

2. Then, solve for y.

a. Eliminate first the parenthesis by multiplying the number outside it to the number inside it. (3 x 2/3y = 2y)

Therefore, the value of y is 3.

3. Plug in the value of "y" to either of the equation to solve for x. For this solution, we will plug it in to the second equation.

The value of x = 2.

To check whether these values are true for both equations, we can plug them in.

Indeed, the values of x and y are true to both equations. The solution x = 2, y = 3 correct.

Answer:

1) multiply and divide by 2 on right hand side

2) multiply by 24 on both sides ( LHS and RHS)

3) divide by -1 on both sides so that negative sign on RHS will be cancelled

The inequality of the function is 36 + 4x < 95 and Rahul can use 14 gigabyte while staying within his budget

The given parameters are:

The above means that;

The total charges per month is

C(x) = Flat cost + Rate per gigabyte x Number of gigabyte

So, we have

C(x) = 36 + 4x

For the bill to be under $95, we have

36 + 4x < 95

Solving further, we have

4x > 59

Divide by 4

x < 14.75

Hence, the inequality is 36 + 4x < 95

Read more about inequality at:

https://brainly.com/question/25275758

#SPJ1

The value of interior angle is 60.

What is triangle?

A triangle is a simple polygon with 3 sides and 3 interior angles. It is one of the basic shapes in geometry in which the 3 vertices are joined with each other and it is denoted by the symbol.

What is interior angle?

In a triangle, there are three interior angles at each vertex. The sum of those interior angles is always 180°. The bisectors of these angles meet at an point known as incenter. As the sum of interior angles of a triangle is 180°, there is only one possible right angle or obtuse angle possible in each triangle.

The sum of interior angle is 180

Given angles is 30, 90, x.

Therefore, sum is given by

90 + 30 + x = 180

120 + x = 180

x = 180-120

x = 60

To know more about triangles and interior angle, visit:

https://brainly.com/question/26113765

#SPJ9

Answer:

No questions are shown.  See attached graph for more details.

Step-by-step explanation:

See attachment

Answer:

I don't know the value of X. The question says it's in question 2.

Step-by-step explanation:

Explanation on picture

we have the function

Part A

For t=0

substitute

Part B

For t=5 years -------> Convert to months

t=60 months

substitute

Part C

Determine horizontal asymptote

The horizontal asymptote is given by the ratio of

P(t)=2,400 ---------> horizontal asymptote

that means

as the value of time t increases ------> the value of the population tends to 2,400 insects

the population cannot be greater than 2400 insects

The range for the function P(t) is the interval [20, 2400)

All real numbers greater than or equal to 20 insects and less than 2400 insects

Part D

Using a graphing tool

The amount of charge on the capacitor after 0.06 seconds = 0.042 millicoulombs

An electric circuit is defined as the device that aids in transmission of electricity generated by a battery or a generator.

A capacitor is defined as the device that has the ability to store energy in an electric circuit.

The amount of charge in a capacitor decreases in one second by = 30%

The original charge on the capacitor = 1 millicoulombs

30 % of 1millicoulombs = 30/100 * 1 = 0.3

1millicoulombs - 0.3 millicoulombs = 0.7 millicoulombs .

If 0.7 millicoulombs = 1 second

X millicoulombs = 0.06 second

Make X millicoulombs the subject of formula;

X millicoulombs = 0.06 × 0.7 = 0.042 millicoulombs.

Learn more about capacitor here:

https://brainly.com/question/27393410

#SPJ1

Answer:

1655.64 miles

Step-by-step explanation:

because 108 people times 15.33 miles for all the total people would be 1655.64 miles

Given data:

The given expression is -4/9 x=3/8

The given expression can be written as,

The product is less than both the factors.

Thus, option C) is correct.

Answer:

1/5

Step-by-step explanation:

"percent" means "per hundred"

(because cent means hundred like years in a century or cents in a dollar)

anyway

20% means

20 per 100

write it as 20/100



Now simplify it.

20/100

= 2/10

= 1/5

The equation of the line is 4y = x + 32 which passes through the point (-8,6) and has a slope of 1/4.

We have been given the required line that passes through the point (-8,6) and has a slope of 1/4.

The slope of a line is defined as the angle of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

Let the required line would be as

⇒ y - y₁ = m (x - x₁ )

The required line passes through the point (-8,6)

Here x₁ = -8 and y₁ = 6 and m = 1/4

Substituting these inputs into the above equation obtains the line equation.

⇒ y - 6 = 1/4 (x - (-8))

⇒ y - 6 = 1/4 (x + 8)

⇒ 4y - 24 = x + 8

⇒ 4y = x + 8 + 24

⇒ 4y = x + 32

Thus, the equation of the line is 4y = x + 32 which passes through the point (-8,6) and has a slope of 1/4.

Learn more about the Lines here:

brainly.com/question/14511992

#SPJ1

The correct option is option D) it has range of 22

What is the range of a dataset?

It the difference between the minimum and maximum value of the dataset.

We are given a dataset with a histogram and we are asked to find out which of the given options does not describe the data

We find the answer by eliminating the correct option

Our given dataset contains 10 points

Hence the median will be the average of 5th and 6th element

Here the 5th and 6th elements are 17

Hence the median of the dataset is 17

Similarly 17 is repeated 4 times in the dataset. i.e highest number of times

Hence 17 is the mode of the dataset

If you look clearly at the histogram from median it is symmetrical that is left side equal to the right side

But if you look at the range the minimum value is 13 and maximum value is 21

Hence the range of the function is 21-13=8

And not 22

Hence the correct option is option D)

To learn more about median please refer

https://brainly.com/question/26151333

#SPJ13