1) Fully factorise each expression 2x +8

Answers

Answer 1

2(x+4)

hope this helps!!!


Related Questions

1.what is the surface area of a cone with a radius of 5m and a slant height of 8m?

2.a box has a side of 9cm what is its surface area?

3.compute for the surface area of a cube with a side of 8cm

4.an aquarium has a length of 6m width of 10m and a height of 7m what is its surface area?

5.find the surface area of a rectangular prism with a length of 5cm width of 8cm and a height of 6cm

6.what is the surface area of a square pyramid with a side of 9cm and a height of 7cm.​

Answers

1. The surface area of a cone can be found using the formula: πr² + πrℓ, where r is the radius of the base of the cone, and ℓ is the slant height. Plugging in the values given, we get:

Surface area = π(5m)² + π(5m)(8m)
Surface area = π(25m²) + π(40m²)
Surface area = 25πm² + 40πm²
Surface area ≈ 188.5m²

Therefore, the surface area of the cone is approximately 188.5 square meters.

2. The surface area of a cube can be found using the formula: 6s², where s is the length of one side of the cube. Plugging in the value given, we get:

Surface area = 6(9cm)²
Surface area = 6(81cm²)
Surface area = 486cm²

Therefore, the surface area of the cube is 486 square centimeters.

3. The surface area of a cube can be found using the formula: 6s², where s is the length of one side of the cube. Plugging in the value given, we get:

Surface area = 6(8cm)²
Surface area = 6(64cm²)
Surface area = 384cm²

Therefore, the surface area of the cube is 384 square centimeters.

4. The surface area of a rectangular prism can be found using the formula: 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height of the prism. Plugging in the values given, we get:

Surface area = 2(6m)(10m) + 2(6m)(7m) + 2(10m)(7m)
Surface area = 120m² + 84m² + 140m²
Surface area = 344m²

Therefore, the surface area of the aquarium is 344 square meters.

What does the correspondence of angles mean

Answers

Answer:

the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line

please help !!!!!!
MULTIPLY (3x + 4)(4x + 5)

Answers

Answer:

B. 12x^2 + 31x + 20

Step-by-step explanation:

Use FOIL (First, Outer, Inner, Last)

(3x + 4)(4x + 5)

12x^2 + 15x +16x + 20

12x^2 + 31x + 20

Answer:

B

Step-by-step explanation:

You are going to want to use the FOIL method. First outer inner last. Multiply 3x*4x to get 12x^2 then multiply 3x*5 to get 15x then multiply 4*4x to get 16x and last multiply 4*5 to get 20. Since 15x and 16x are like terms we add them together to get 31x

Choose the algebraic description that maps abc onto abc in the given figure.

Answers

So the transformation is: (x, y) → (x + -8, y - 4) which is equivalent to option B.

What is transformation?

In mathematics, a transformation is a process that manipulates the position, size, or shape of a geometric object. Transformations can include translations, rotations, reflections, and dilations. They are used to study geometric properties and relationships and are often used in fields such as geometry, algebra, and computer graphics. Transformations are important in understanding symmetry and congruence, as well as in solving problems involving geometric figures.

Here,

We can see that the transformation takes each point of the form (x, y) in ABC to a corresponding point of the form (x', y') in A'B'C'. To find the correct transformation, we need to determine how the coordinates of the points in ABC are related to the coordinates of the corresponding points in A'B'C'. One way to do this is to use the fact that the transformation should preserve the relative distances and angles between the points. Another way is to use the known coordinates of three corresponding points to determine the transformation directly.

In this case, we can see that the transformation maps (-3,-2) to (5,2), (-1,-4) to (7,0), and (-6,-5) to (2,-1). We can use these points to find the transformation:

(x, y) → (x', y')

To map (-3,-2) to (5,2), we need to add 8 to the x-coordinate and add 4 to the y-coordinate:

x' = x + 8

y' = y + 4

To map (-1,-4) to (7,0), we again add 8 to the x-coordinate, but this time we only add 4 to the y-coordinate:

x' = x + 8

y' = y + 4

To map (-6,-5) to (2,-1), we subtract 4 from the x-coordinate and subtract 4 from the y-coordinate:

x' = x - 4

y' = y - 4

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what is the proportional relationship between x 2 6 8 10 and y 6 18 24 30

Answers

The proportional relationship is y = 3x.

What is the proportional relationship?

If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.

Here, we have

Given:

x:  2, 6, 8, 10

y:  6, 18, 24, 30

We have to find the proportional relationship between x and y.

So, we can see from inspection and visual observation that there is a proportional relationship between x and y.

6 = 3  2,  18 = 3  6, 24 = 3  8, 30 = 3  10.

Hence, The proportional relationship is y = 3x.

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a production process produces 2.5% defective parts. a sample of five parts from the production process is selected. what is the probability that the sample contains exactly two defective parts? group of answer choices 0.2637 0.0058 0.0000 0.0250

Answers

The probability that the sample contains exactly two defective parts is 0.0058.

We may utilize the binomial probability formula to resolve this issue:

P(X = k) is equal to (n pick k) * p * k * (1-p) (n-k)

where n is the sample size, k denotes the number of successes, p denotes the likelihood that a success will occur, and (n pick k) denotes the binomial coefficient, which indicates the number of possible ways to select item k from n.

Here, n = 5, k = 2, and p = 0.025 (due to the fact that 2.5% of the pieces are flawed).

P(X = 2) therefore equals (5 pick 2)*0.025*2*(1 - 0.025)*3

We calculate P(X = 2) = 0.0058 using a calculator.

As a result, there is a 0.0058 percent chance that the sample has exactly two defective components.

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I need some help please

Answers

I think it is 0
I’m sorry if I’m wrong

Chad drinks 64. 88 fluid ounces of water per day. How much water does he drink in 6 days

Answers

Chad drinks  389.28  fluid ounces of water in 6 days.

What is ounces?

A unit of weight equal to ¹/₁₂ troy pound see Weights and Measures Table. : a unit of weight equal to ¹/₁₆ avoirdupois pound. : a small amount. an ounce of sense.

An ounce (oz) is a unit of weight that is equal to one-sixteenth of a pound. Items that weigh approximately one ounce include a slice of bread and a pencil. A fluid ounce is a unit of liquid volume that is equal to one-eighth of a cup. A medicine cup has a volume of approximately one fluid ounce.

given that,

chad drinks 64.88 fluid ounces of water per day,

so in 6 days

he will drink = 6 x water drink per day

= 6 x 64.88

= 389.28

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What is the range of f? A coordinate plane. The x- and y-axes both scale by one. The graph of the function f starts at negative six, negative two, which is plotted. Then is decreases at a non linear rate to negative five, negative five, where it increases at a non linear rate to negative two, one and one-half. At two, one and one-half the function decreases at a non linear rate through the origin and to the point two, negative one and one-half. Then the function increases at a non linear rate until five, five, which is plotted.

A coordinate plane. The x- and y-axes both scale by one. The graph of the function f starts at negative six, negative two, which is plotted. Then is decreases at a non linear rate to negative five, negative five, where it increases at a non linear rate to negative two, one and one-half. At two, one and one-half the function decreases at a non linear rate through the origin and to the point two, negative one and one-half. Then the function increases at a non linear rate until five, five, which is plotted.

Choose 1 answer:

(Choice A) The f(x)-values -6, -3, 0, 2, and 5

(Choice B) The f(x)-values -5, -2, 0, 2, and 5

(Choice C) -6 ≤ f(x) ≤ 5

(Choice D) − 5 ≤ f(x) ≤ 5

Answers

The range of f include the following: D. -5 ≤ f(x) ≤ 5.

What is a domain?

In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {-6, 5} or -6 ≤ x ≤ 5.

Range = {-5, 5} or -5 ≤ f(x) ≤ 5.

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An electronic book device had a value of t dollars before a holiday. The value decreased by 15% after the holiday. Which expressions show the value of the electronic book device after the holiday? Select all the expressions that apply.

A. 1.15
B. 0.85
C. −0.15
D. 1−0.15
E. −0.85
F. (1−0.15)

Answers

The expressions that correctly show the value of the electronic book device after the holiday are B and D, which represent the percentage decrease of 15% as 0.85 (or 1-0.15).

Which expressions show the value of the electronic book device after the holiday?

The value of an electronic book device before a holiday is represented by the variable t. After the holiday, the value of the device decreased by 15%. To find the value of the device after the holiday, we need to multiply the original value by the percentage decrease, which is 0.85 (or 1-0.15). Therefore, the expressions that correctly show the value of the electronic book device after the holiday are B and D.

Option A (1.15) represents the percentage increase and not the decrease, so it is incorrect. Option C (-0.15) represents the percentage decrease, but it cannot be used alone to find the new value. Option E (-0.85) is the negative of the percentage decrease, so it is also incorrect. Finally, option F is equivalent to option D, so it is also correct.

In summary, the expressions that correctly show the value of the electronic book device after the holiday are B and D, which represent the percentage decrease of 15% as 0.85 (or 1-0.15).

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An 18 gram sample of a substance that's used to detect explosives has a k-value of 0.215.

Find the substance's half-life in days. Round your answer to the nearest tenth.

Answers

The substance's half-life in days is 3 days.

What is exponential decay?

If a quantity declines at a pace proportionate to its current value, exponential decay may be present. The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time.

Here, we have

Given: An 18-gram sample of a substance that's a by-product of fireworks has a k-value of 0.215.

We have to find the substance's half-life in days.

Using the formula for the exponential decay that is N = N₀e⁻ⁿˣ,

we have N = 18/2, N₀ = 18, and n = 0.215.

N = N₀e⁻ⁿˣ

9 = 18e⁻⁰°²¹⁵ˣ

9/18 = e⁻⁰°²¹⁵ˣ

1/2 = e⁻⁰°²¹⁵ˣ

Taking logs on both sides, we get

㏑(1/2) = -0.215x

x = ㏑(1/2)/(-0.215)

x = -0.6931/(-0.215)

x = 3.22

Hence, the substance's half-life in days is 3 days.

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There are four times as many cows as horses on a farm. There are twice as many horses as pigs on the farm. Which list shows the number of each type of animal on this farm?

Answers

As per the unitary method, the list shows the number of each type of animal on this farm is

Number of pigs = x

Number of horses = 2x

Number of cows = 8x

Let us start by assigning variables to each type of animal on the farm. Let's say the number of pigs is "x".

From the problem statement, we know that there are twice as many horses as pigs. Therefore, the number of horses would be 2x.

Further, we know that there are four times as many cows as horses. So, the number of cows would be 4 times the number of horses. Mathematically, we can represent it as:

Number of cows = 4 * Number of horses

Or, Number of cows = 4 * (2x) = 8x

Therefore, we have the number of each type of animal on the farm as follows:

Number of pigs = x

Number of horses = 2x

Number of cows = 8x

This is the same ratio as we found using the unitary method.

Therefore, our solution is correct.

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A scale drawing of a famous statue uses a scale factor of 230:1. If the height of the drawing is 1.2 feet, what is the actual height of the statue?

191.7 feet
228.2 feet
231.2 feet
276 feet

Answers

The actual height of the statue is option C 231.2 feet.

What is scale factor?

A scale factor is a number used in mathematics to scale or multiply a quantity or measurement by another factor in order to establish a proportional relationship between two identical figures or objects.

In other terms, the scale factor is the ratio of the corresponding lengths, widths, or heights of the two figures or objects if they are similar, that is, they have the same shape but may range in size. This implies that you may determine the dimension of the second object by multiplying one dimension of one object by the scale factor.

Given that the scale factor is 230:1.

Thus,

actual height of statue / 230 = height of drawing / 1.2 feet

Now,

actual height of statue = (1.2 feet / 1.2 feet) * 230

actual height of statue = 230 feet

Hence, the actual height of the statue is option C 231.2 feet.

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5x(x - 4) = 3x + 4 someone help me pls

Answers

Answer: x=23±√609/10

Step-by-step explanation:

Explain what values must be known to write the explicit formula for both an arithmetic and geometric sequence?
PLEATHE!!

Answers

The explicit formula for an arithmetic sequence is:

an = a1 + (n-1)d

The explicit formula for a geometric sequence is:

an = a1 * [tex]r^{(n-1)}[/tex]

What is arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.

To write the explicit formula for both an arithmetic and geometric sequence, the following values must be known:

For an Arithmetic Sequence:

The first term (a1) of the sequence.

The common difference (d) between consecutive terms in the sequence.

The explicit formula for an arithmetic sequence is:

an = a1 + (n-1)d

Where:

an is the nth term of the sequence.

a1 is the first term of the sequence.

d is the common difference between consecutive terms.

n is the position of the term in the sequence.

For a Geometric Sequence:

The first term (a1) of the sequence.

The common ratio (r) between consecutive terms in the sequence.

The explicit formula for a geometric sequence is:

an = a1 * r^(n-1)

Where:

an is the nth term of the sequence.

a1 is the first term of the sequence.

r is the common ratio between consecutive terms.

n is the position of the term in the sequence.

Therefore, The explicit formula for an arithmetic sequence is:

an = a1 + (n-1)d

The explicit formula for a geometric sequence is:

an = a1 * [tex]r^{(n-1)}[/tex]

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a production process is designed to fill 100 soda cans per minute with with 6.8 ounces of soda, on average. overfilling is costly and under-filling risks a large fine. you are the production chief and instruct your staff to take regular random samples to test the process. what is the correct way to set up the hypotheses test?

Answers

Answer:

6.8 ounces

To set up a hypothesis test for this production process, we need to define the null and alternative hypotheses. The null hypothesis (H0) is that the average amount of soda in each can is equal to 6.8 ounces, while the alternative hypothesis (Ha) is that the average amount of soda in each can is not equal to 6.8 ounces.

We can then collect data by taking regular random samples from the production process and calculate the sample mean and standard deviation. We can then perform a statistical test such as a t-test or z-test to determine whether we can reject or fail to reject the null hypothesis.

If we reject the null hypothesis, we can conclude that there is evidence that the average amount of soda in each can is different from 6.8 ounces. If we fail to reject the null hypothesis, we cannot conclude that there is evidence that the average amount of soda in each can is different from 6.8 ounces.

I hope this helps! Let me know if you have any other questions.

What is the value of x in this triangle?

Answers

x=47°

The degree of a triangle is equal to 180°.

Since a triange=180°, you would subtract 180 by 102+31 because the other two angles are 102° and 31°.

180-102-31=47°

Therefore the answer would be x=47°

a student takes an exam containing 11 true or false questions. if a student randomly guesses on the entire exam, what is the standard deviation of the number of incorrect answers? round your answer to two decimal places.

Answers

The first step is to find the mean number of incorrect answers. Since there are 11 questions, and each question has a 50/50 chance of being answered incorrectly, we can expect the student to get 5.5 questions wrong on average.

Next, we need to calculate the variance. To do this, we can use the formula:

Variance = p(1-p)n

Where p is the probability of getting a question wrong (0.5), and n is the number of questions (11).

Variance = 0.5(1-0.5)11 = 1.375

Finally, we can find the standard deviation by taking the square root of the variance:

Standard deviation = sqrt(1.375) = 1.17 (rounded to two decimal places)

Therefore, the standard deviation of the number of incorrect answers on the exam is 1.17.

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true or false? use cases can help with developing quantitative and measurable usability tests. group of answer choices

Answers

The given statement about developing quantitative and measurable usability tests is true.

Explain about how this given statement is true?

Use cases can help with developing quantitative and measurable usability tests. Use cases are scenarios that describe how a user might interact with a system or product in a specific situation.

By developing use cases, researchers can identify specific tasks that users may need to perform and design usability tests to measure how well users can perform those tasks.

This can help make the usability tests more objective and measurable, as researchers can use metrics such as completion rates, task time, and errors to assess the usability of the system or product.

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I NEED HELP ON THIS ASAP!

Answers

The exponential function for the new participants is f(x) = 3 * 4^x

Writing the exponential function for the new participants

Let's start with the initial number of participants who sent selfies on Day 0.

We know that Aliyah, Kim, and Reese each sent selfies to 4 friends, so there are 3 x 4 = 12 participants on Day 1.

On Day 2, each of these 12 participants will send selfies to 4 friends, so we will have 12 x 4 = 48 new participants.

We can see that the number of new participants each day is increasing exponentially. In fact, the number of new participants each day is multiplied by 4, since each participant sends selfies to 4 friends.

Therefore, we can write an exponential function of the form:

f(x)=a * 4^x

Where x is the number of days since the challenge started, and $a$ is the initial number of participants who sent selfies on Day 0.

We know that a = 12 from our earlier calculations.

So, we have

f(x) = 3 * 4^x

Hence, the function is f(x) = 3 * 4^x

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Joel wants to fence off a triangle portion of his yard for his chickens. The three pieces of fencing he has measured 8 ft, 15 ft, and 20 ft. will Joel be able to make a right triangle with the current lengths of fencing? why or why not?

Answers

Joel cannot make a right triangle with the current lengths of fencing.

What is right triangle?

A right triangle is a triangle that has one angle that measures exactly 90 degrees (a right angle). This means that the other two angles of the triangle are acute (measuring less than 90 degrees). The side opposite the right angle is called the hypotenuse, and it is always the longest side of the triangle. The other two sides are called the legs of the triangle.

To check if Joel can make a right triangle with the current lengths of fencing, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (legs) is equal to the square of the length of the longest side (hypotenuse).

So, let's check if the measurements satisfy the Pythagorean theorem:

8²  + 15² = 64 + 225 = 289

20²  = 400

According to the Pythagorean theorem, a triangle with sides of length 8 ft, 15 ft, and 20 ft would be a right triangle if it satisfies the equation a²  + b²  = c² , where a and b are the shorter sides (legs) and c is the longest side (hypotenuse). However, in this case, we can see that the sum of the squares of the shorter sides (8²  + 15² ) is not equal to the square of the longest side (20² ), so the measurements cannot form a right triangle.

Therefore, Joel cannot make a right triangle with the current lengths of fencing.

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I need help ASAP mean absolute deviation (mad)

Answers

The absolute deviation for the observation of 16 in the data-set is given as follows:

5.

How to calculate the mean of a data-set?

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

Hence the mean of the data-set in this problem is given as follows:

(19 + 16 + 4 + 9 + 7)/5 = 11.

The absolute deviation of 16 is given by the difference between 16 and the mean of 11, hence:

16 - 11 = 5.

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Madison is reading a book that is 860 pages long. She reads 25 pages in 0.5 hours. At that rate, how long will it take for her to read the entire book

Answers

Answer:

17.2 hours, or 17 hours and 12 minutes

Step-by-step explanation:

If she reads 50 pages per hour, then 860/50 = 17.2

In an all boys school, the heights of the student body are normally distributed with a mean of 69 inches and a standard deviation of 3.5 inches. What is the probability that a randomly selected student will be taller than 63 inches tall, to the nearest thousandth?​

Answers

The probability that a randomly selected student will be taller than 63 inches tall is 0.9332, to the nearest thousandth.

Questions seven and eight please

Answers

The results are:

7a) Explicit = h(n) = [tex]0.87^{n-1}[/tex] * 200.

Recursive = h(0) = 200 and h(n) = 0.87 * h(n-1)

7b) Rebound height = 99.76 cm (rounded to the nearest hundredth).

8a) Explicit formula: A(n) = 575 + 47.50n

Recursive formula: A(0) = 575, A(n) = A(n-1) + 47.50

8b) 30 weeks to save $2000'

Step by step explanation:

7a) Explicit: h(n) = [tex]0.87^{n-1}[/tex] * 200 (

where h(n) = height of the golf ball after n bounces,

0.87 is the rebound factor,

200 is the initial height)

h(n) = [tex]0.87^{n-1}[/tex] * 200

Recursive:  h(0) = 200

h(n) = 0.87 * h(n-1)

where h(n) = the height after n bounces,

h(n-1) = height after (n-1) bounces,

0.87 = rebound factor.

Apply given values:

h(0) = 200

h(n) = 0.87 * h(n-1)

7b) Rebound height, using recursive formula:

h(0) = 200

h(1) = 0.87 * 200 = 174

h(2) = 0.87 * 174 = 151.38

h(3) = 0.87 * 151.38 = 131.70

h(4) = 0.87 * 131.70 = 114.71

h(5) = 0.87 * 114.71 = 99.76 (rounded to the nearest hundredth)

8a)Explicit: A(n) = 575 + 47.50n,

where A(n) = amount of money Jessica has after n weeks,

575 = initial amount given by grandfather,

47.50 = amount Jessica adds each week.

Recursive: A(0) = 575, A(n) = A(n-1) + 47.50,

where A(n) = the amount of money Jessica has after n weeks,

A(n-1) = amount Jessica has after (n-1) weeks

47.50 = amount Jessica adds each week.

8b) Weeks to save $2000:

A(n) = 575 + 47.50n = 2000

Solving for n:

575 + 47.50n = 2000

47.50n = 2000 - 575

47.50n = 1425

n = 1425 / 47.50

= 30 weeks.

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how can the power series method be used to solve the nonhomogeneous equation, about the ordinary point ? carry out your idea by solving the equation. you can either attach your work or type in your work.

Answers

The power series method can be used to solve a nonhomogeneous differential equation about an ordinary point by finding both a homogeneous and particular solution using a series expansion and the method of undetermined coefficients.

The power series method is a technique used to find a series solution of a differential equation. When applied to a nonhomogeneous differential equation, the method involves finding both a homogeneous solution and a particular solution.

Assuming that the nonhomogeneous differential equation has the form

y''(x) + p(x)y'(x) + q(x)y(x) = f(x)

where p(x), q(x), and f(x) are functions of x, we can begin by finding the solution to the associated homogeneous equation

y''(x) + p(x)y'(x) + q(x)y(x) = 0

Using the power series method, we can assume a solution of the form:

y(x) = a0 + a1(x - x0) + a2(x - x0)^2 + ...

where a0, a1, a2, ... are constants to be determined, and x0 is the ordinary point of the differential equation.

Next, we can find the coefficients of the power series by substituting the series solution into the differential equation and equating coefficients of like powers of (x-x0). This leads to a system of equations for the coefficients, which can be solved iteratively.

After finding the homogeneous solution, we can find a particular solution using a similar method. Assuming a particular solution of the form:

y(x) = u(x) + v(x)

where u(x) is a solution to the associated homogeneous equation, and v(x) is a particular solution to the nonhomogeneous equation, we can use the method of undetermined coefficients to find v(x). This involves assuming a form for v(x) based on the form of f(x), and then solving for its coefficients using the same technique as before.

Once we have found both the homogeneous and particular solutions, we can combine them to obtain the general solution to the nonhomogeneous differential equation.

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math please. its for a quiz

Answers

The quotient function of f(x) and g(x) is given as follows:

(f/g)(x) = 3x^(3/4).

How to obtain the quotient function?

The functions in the context of this problem are defined as follows:

f(x) = 3x.g(x) = x^(1/4).

When we want to divide two functions, we just divide each other, hence:

(f/g)(x) = f(x)/g(x) = 3x/x^(1/4).

When we divide two terms with the same base and different exponents, we keep the base and subtract the exponents, hence:

x/x^(1/4) = x^(1 - 1/4) = x^(3/4).

Hence the function is:

(f/g)(x) = 3x^(3/4).

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Construct a two-way frequency table for the data. Include row and column totals. Hint: Let column categories be labeled by after school activity.
Every student at Georgia Southern Middle School participates in exactly one after school activity. The school activities coordinator recorded data on after extracurricular activity
and grade for all 254 students in 7th grade and 8th grade.
The counselor's findings for the 254 students are the following:
• Of the 80 students enrolled in music, 42 are in 7th grade.
.
. Of the 21 students enrolled in student government, 9 are in 8th grade.
.
Of the 65 students enrolled in theatre, 20 are in 7th grade.
. Of the 88 students enrolled in sports, 30 are in 8th grade.

Answers

Answer:

[tex]\begin{array}{|c|c|c|c|c|c|} \cline{1-6} & \text{Music} & \text{Gov} & \text{Theater} & \text{Sports} & \text{Total}\\\cline{1-6}\text{7th grade} & 42 & 12 & 20 & 58 & 132\\\cline{1-6}\text{8th grade} & 38 & 9 & 45 & 30 & 122\\\cline{1-6}\text{Total} & 80 & 21 & 65 & 88 & 254\\\cline{1-6}\end{array}[/tex]

"Gov" refers to "Student  Government".

==================================================

Explanation:

The rows are labeled "7th grade", "8th grade" and "Total".

The columns are labeled "Music", "Student  Government", "Theater", "Sports", and "Total".

I'll abbreviate "Student  Government" to "Gov" so that the table doesn't get too wide.

There are 254 students total. This value goes in the bottom right corner of the table. This is the grand total.

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We have 80 students in music. This value goes at the bottom of the "music" column since we're in a "total" row. Basically it's the total of all the music students regardless of grade.

Of those 80 students in music, 42 are in seventh grade. Write 42 in the first row of this column and 38 just underneath it (because 80-42 = 38). The two values 42 and 38 should add to the 80 mentioned.

----------

There are 21 students in student government. This value goes at the bottom of the "student government" column.

9 of these students are in eighth grade, so the remaining 21-9 = 12 must be in seventh grade.

----------

There are 65 students in theater. This value goes at the bottom of the "theater" column.

There are 20 such students in 7th grade and 45 in 8th grade (because 65-20 = 45).

----------

There are 88 students in sports.

30 are in 8th grade, so 88-30 = 58 must be in 7th.

----------

At this point, you should have these values along the bottom row:

80, 21, 65, 88, 254

The first four values (80, 21, 65, 88) should add to the grand total 254.

Along each row, add up the values to get the row total.

7th grade: 42 + 12 + 20 + 58 = 132

8th grade:  38 + 9 + 45 + 30 = 122

There are 132 seventh graders and 122 eighth graders.

Those subtotals add to 132+122 = 254 total students, which helps confirm we did things correctly.

If a monopolistic firm takes over a perfectly competitive market, we would expect to see market price of the good to rise and the quantity sold to increase. Fall as the monopolist tries to increase sales. Fall because demand is perfectly elastic. Rise and quantity sold to fall

Answers

In the event that a monopolistic firm takes over superbly competitive advertising, we would anticipate seeing the advertising cost of the great rise and the amount sold drop.

Be that as it may, when a monopolistic firm takes over the showcase, it picks up showcase control and the capacity to impact the cost. The monopolist can charge a better cost than the competitive advertising cost since there are no near substitutes for its item. As the monopolist raises the cost, the amount requested will drop, as customers switch to substitutes or decrease their utilization of the item.

we would anticipate seeing the advertising cost of the great rise and the amount sold fall as the monopolist tries to extend benefits by raising costs. This is often in differentiating from impeccably competitive advertising.

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Find a degrees. a 12 13 5

Answers

In the given triangle, α is equal to 67.36°.

What is a triangle's definition?

A triangle is a two-dimensional closed geometric form that has three sides, three angles, and three vertices (corners). It is the most basic polygon, produced by joining any three non-collinear points in a plane. The sum all angles of a triangle is always 180°. Triangles are classed according to their side length (equilateral, isosceles, or scalene) and angle measurement (acute, right, or obtuse).

Now,

Using Trigonometric functions

We can use the sine function

So,

Sin α=Perpendicular/Hypotenuse

Sin α = 12/13

α=67.36°

Hence,

           The value of α will be 67.36°.

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