Given f(x)2x and g(x) = x^2+3 , find f(g(x)).

Answer:

\(x=8, y=3\)

Step-by-step explanation:

Recall that if a matrix multiplication of two matrices is defined, then the number of columns of the first matrix is equivalent to the number of rows of the second matrix.

Since matrix M has (11-x) columns and matrix N has y rows, and MN is defined, so it follows:

\(y=11-x----(1)\)

Since matrix N has (y+5) columns and matrix M has x rows, and NM is defined, so it follows:

\(y+5=x----(2)\)

Substitute (1) into (2):

\(11-x+5=x\\2x=16\\\therefore x=8--(3)\)

Substitute (3) into (1):

\(y=11-8=3\)

The Operating income is $172,500.

To calculate the margin of safety, contribution margin ratio, and operating income, we need to use the given information.

a. Margin of Safety:

Margin of Safety = Actual Sales - Break-even Sales

Given that the break-even point is at $750,000 in sales revenue and actual sales are $1,100,000, we can calculate the margin of safety:

Margin of Safety = $1,100,000 - $750,000 = $350,000

Therefore, the margin of safety is $350,000.

b. Margin of Safety as a Percentage of Sales:

Margin of Safety Percentage = (Margin of Safety / Actual Sales) * 100

Using the values from the previous calculations:

Margin of Safety Percentage = ($350,000 / $1,100,000) * 100 = 31.82%

Therefore, the margin of safety expressed as a percentage of sales is approximately 31.82%.

c. Contribution Margin Ratio:

Contribution Margin Ratio = (Contribution Margin / Sales) * 100

To calculate the contribution margin, we need to subtract variable costs from sales:

Contribution Margin = Sales - Variable Costs = $1,100,000 - $645,000 = $455,000

Using the values, we can calculate the contribution margin ratio:

Contribution Margin Ratio = ($455,000 / $1,100,000) * 100 = 41.36%

Therefore, the contribution margin ratio is approximately 41.36%.

d. Operating Income:

Operating Income = Sales - Variable Costs - Fixed Costs

Using the values provided:

Operating Income = $1,100,000 - $645,000 - $282,500 = $172,500

Therefore, the operating income is $172,500.

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Answer:

1 2/3 times 5 = 8 1/3

Step-by-step explanation:

first we make the fraction an improper fraction or 5/3. then we take 5 and turn that into 5/1. then we multiply. 5/3 times 5/1 is equal to 25/8 now we simplify this into 8 1/3 and that is your answer.

hope you found this helpful and good luck on your test

:D

The domain is all real numbers, and the range is (y ≤ -4.855). (option b)

To sketch the graph of a quadratic equation, you can use a graphing calculator, which is a handy tool that can produce a visual representation of the equation. For instance, let's take the quadratic equation y = -0.5x² + 0.7x - 5.1 and sketch its graph using a graphing calculator.

When we enter this equation into the graphing calculator, we can see a U-shaped curve that is symmetric about the vertical line passing through the vertex. The vertex is the point where the parabola changes direction and is given by the formula x = -b/2a, y = f(x), where f(x) is the value of y at the vertex.

Now let's examine the given options and determine their domain and range based on the graph of the quadratic equation.

all real numbers, R: (y ≤ -4.855)

For this option, we can observe that the parabola opens upward, and the vertex is at (0.7, -5.35).

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Answer:

253

Step-by-step explanation:

23 x 11 = 253

As you can see, each number in the pattern is obtained by adding 4 to the previous number.

An equation is a mathematical statement that shows the equality of two expressions, usually with an equal sign "=" in between them. An equation can contain variables, constants, and operators. The variables are represented by letters and can take on different values, while constants are fixed values that do not change. Operators include mathematical symbols like plus, minus, multiplication, and division, as well as exponents and logarithms.

Here,

Sure, here's a pattern for the rule a + 4:

a = 1: 1 + 4 = 5

a = 2: 2 + 4 = 6

a = 3: 3 + 4 = 7

a = 4: 4 + 4 = 8

a = 5: 5 + 4 = 9

a = 6: 6 + 4 = 10

a = 7: 7 + 4 = 11

a = 8: 8 + 4 = 12

a = 9: 9 + 4 = 13

a = 10: 10 + 4 = 14

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Answer: 24

Step-by-step explanation: multiply the amounts given

4x2=8

8x3= 24

Answer:

24

Step-by-step explanation:

Answer:

AB=30

AC=22.5

Step-by-step explanation:

8/15=12/x

x=22.5 (AC)

8/15=16/x

x=30 (AB)

Answer:

1. No, a decade is 10 years

2. No way of telling

3. No way of telling

Step-by-step explanation:

Answer:

x = 20

Step-by-step explanation:

We know that the vertically opposite angles are equal.

Accordingly,

41 = 2x + 1

Subtract 1 from both sides.

41 - 1 = 2x

40 = 2x

Divide both sides by 2.

x = 20

Answer:

jjejejkwkwkqkkqkqkqkkqkqkq

Answer:(x 3−2x2−2x−4)⋅(x−1)

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Step-by-step explanation:

                    (x3 - 2x2 - 2x - 4) • (x - 1) —————————————————————————————

                                       x - 2    

A linear programming problem consists of a linear function to be to be maximized or minimized. It is subject to a set of constraints given in the form of linear equations or inequalities.

Linear programming is the programming in which selecting the best possible choice from those available alternatives whose constraint function and the objective function can be referred to as the linear mathematical function.

Linear programming is used for the optimization of linear objective.

It is used as constrained optimization, from where the objective functions and constraints all are linear.

If a maximization linear programming problem consists of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, then rounding down the linear programming optimal solution values of the decision variables

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Answer:

6

Step-by-step explanation:

I think the answer is 5 is the answer

Answer:

She should add 6 cups.

Answer 6

Step-by-step explanation: 4 divided by 2/3

The first question:

"A spinner has an equal chance of landing on each of its eight numbered regions. After spinning, what is the probability you land on region three and region six?"

Since the spinner has an equal chance of landing on each of its eight regions, the probability of landing on region three is 1/8, and the probability of landing on region six is also 1/8.

To find the probability of both events occurring (landing on region three and region six), you multiply the probabilities together:

P(landing on region three and region six) = P(landing on region three) * P(landing on region six) = (1/8) * (1/8) = 1/64.

Therefore, the probability of landing on both region three and region six is 1/64.

The events are mutually exclusive because it is not possible for the spinner to land on both region three and region six simultaneously.

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The second question:

"A bag contains six yellow jerseys numbered 1-6. The bag also contains four purple jerseys numbered 1-4. You randomly pick a jersey. What is the probability it is purple or has a number greater than 5?"

To find the probability of either event occurring (purple or number greater than 5), we need to calculate the probabilities separately and then add them.

The probability of picking a purple jersey is 4/10 since there are four purple jerseys out of a total of ten jerseys.

The probability of picking a jersey with a number greater than 5 is 2/10 since there are two jerseys numbered 6 and above out of a total of ten jerseys.

To find the probability of either event occurring, we add the probabilities together:

P(purple or number greater than 5) = P(purple) + P(number greater than 5) = (4/10) + (2/10) = 6/10 = 3/5.

Therefore, the probability of picking a purple jersey or a jersey with a number greater than 5 is 3/5.

The events are overlapping since it is possible for the jersey to be both purple and have a number greater than 5.

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The third question:

"A box of chocolates contains six milk chocolates and four dark chocolates. Two of the milk chocolates and three of the dark chocolates have peanuts inside. You randomly select and eat a chocolate. What is the probability that it is a milk chocolate or has no peanuts inside?"

To find the probability of either event occurring (milk chocolate or no peanuts inside), we need to calculate the probabilities separately and then add them.

The probability of selecting a milk chocolate is 6/10 since there are six milk chocolates out of a total of ten chocolates.

The probability of selecting a chocolate with no peanuts inside is 7/10 since there are seven chocolates without peanuts out of a total of ten chocolates.

To find the probability of either event occurring, we add the probabilities together:

P(milk chocolate or no peanuts inside) = P(milk chocolate) + P(no peanuts inside) = (6/10) + (7/10) = 13/10.

Therefore, the probability of selecting a milk chocolate or a chocolate with no peanuts inside is 13/10.

The events are mutually exclusive since a chocolate cannot be both a milk chocolate and have no peanuts inside simultaneously.

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The fourth question:

"You flip a coin and then roll a fair six-sided die. What is the probability the coin lands heads up and the die shows an even number?"

The probability of the coin landing heads up is 1/2 since there are two possible outcomes (heads or tails) and they are equally likely.

The probability of rolling an even number on the die is 3

/6 or 1/2 since there are three even numbers (2, 4, and 6) out of a total of six possible outcomes.

To find the probability of both events occurring (coin lands heads up and die shows an even number), we multiply the probabilities together:

P(coin lands heads up and die shows an even number) = P(coin lands heads up) * P(die shows an even number) = (1/2) * (1/2) = 1/4.

Therefore, the probability of the coin landing heads up and the die showing an even number is 1/4.

The events are independent since the outcome of flipping the coin does not affect the outcome of rolling the die.

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Answer:

  48 inches

Step-by-step explanation:

The greatest common factor of 144 and 240 is 48. If Hector orders 48" square tiles, he can use 3 of them in the direction of the short dimension, and 5 of them in the direction of the long dimension.

The tiles can be 48 inches square.

__

Using Euclid's algorithm to find the GCF, we have ...

  240/144 = 1 r 96

  144/96 = 1 r 48

  96/48 = 2 r 0 . . . . . 48 is the GCF

At each step, if the remainder from the division is not zero, we replace the larger number with the remainder and do the division again. The divisor that gives a zero remainder is the GCF.

Answer:

Step-by-step explanation:

\(y=(\frac{1}{g} )x\)

Constant up a proportionally is  \(\frac{1}{g}\).

Answer:

0.16%

Step-by-step explanation:

From the statement of the question;

Number of Laryngeal cancer due to smoking = 160

Population of smokers = 100,000

Hence the percentage of smokers liable to have Laryngeal cancer = 160/100000 ×100/1

=0.16%

Hence 0.16% of smokers are liable to Laryngeal cancer

The surface area of the triangular prism is 313.47 cm².

Given is a triangular prism, we need to find the surface area,

A triangular prism is a 3D shape with two identical faces in the shape of a triangle connected by three rectangular faces. The rectangular faces are referred to as the lateral faces, while the triangular faces are called bases. The bases are also called the top and the bottom (faces) of the prism.

Triangular Prism Meaning: A triangular prism is a 3D polyhedron with three rectangular faces and two triangular faces. The 2 triangular faces are congruent to each other, and the 3 lateral faces which are in the shape of rectangles are also congruent to each other. Thus, a triangular prism has 5 faces, 9 edges, and 6 vertices. Observe the following image of a triangular prism in which l represents the length of the prism, h represents the height of the base triangle, and b represents the bottom edge of the base triangle.

so, the surface area of a triangular prism =

perimeter × length + 2 × base area

So,

SA = (4.5+7.2+9) × 8.1 + 2 × 8.1 × 9

= 167.67 + 145.8

= 313.47

Hence the surface area of the triangular prism is 313.47 cm².

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Answer:

Option B

83°

Step-by-step explanation:

Since,

To prove it as a kite then according it,

Ac should be a perpendicular bisector of BD

Hence,

<APB = 90°

Also given,

<APB = (x + 7)°

Therefore, by the problem,

=> x + 7 = 90

=> x = 90 - 7

=> x = 83°(Ans)

Least time required to reach the point Q as per the distance and the speed rate is equal to 2 hours.

As given in the question,

Nearest point on the coast is 2 miles far away

rate of the row = 1mile per hour

Walk at the rate of 3 miles per hour

Let 'x' hours be the least time to reach point Q.

Time = distance / speed

Time taken to reach the point Q = [√ 1 + ( 3 - x)² ]/ 3

Time taken to reach the coast = (√ 4 + x² ) / 1

Total  time taken 't' = (√ 4 + x² ) / 1 + [√ 1 + ( 3 - x)² ]/ 3

To find least time dt/dx = 0

t  = (√ 4 + x² ) / 1 + [√ 1 + ( 3 - x)² ]/ 3

⇒dt/dx = [ x / √ 4 + x² ] + ( 3 - x) / √( 10 -6x + x² )

⇒x / √ 4 + x² = ( x - 3) / √( 10 -6x + x² )

Squaring both the side we get,

x² / (4 + x²) = ( x - 3)² / ( 10 -6x + x² )

⇒3x² -24x +36 =0

⇒ x² -8x + 12 = 0

⇒ x = 2 or 6 hours

Therefore , the least time taken to reach the point Q is equal to 2 hours.

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Answer:

$192.00

Step-by-step explanation:

Hope this helps!!

Love: Deku~ <3

PS. Draco Malfoy ;w;

heres your proof Malfoy-

Answer:

Step-by-step explanation:

We know that:

To find the other diagonal, we must compare the two formulas of a rhombus.

Hence, the length of the other diagonal is 20 cm.

Answer:

The Answer is B

Step-by-step explanation:

Answer:

32

Step-by-step explanation: