Evaluate
Find (f + g) (4) given f(x) = x - 1 and g(x) = x + 2.

The amount of money that it will cost to paint the whole shed excluding the roof would be = $122.5

To calculate the cost of the shed, we will first determine the area of the shed that needs to be painted which excludes the roof.

The area of the shed = area of 2 square + area of rectangular floor+ area of 4 trapezium(for the pentagon shaped sides)

Area of 2 square =2( L×w) = 2(12×12) = 2×144 = 288ft²

Area of rectangular floor = l×w = 18×12 = 216ft²

Area of trapezium = 1/2(a+b)h ×4

= 1/2(22+18) × 9×4

= 20×9×4 = 720ft²

The area of the shed = 288+216+720 = 1,224ft²

But 1 gallon = 250ft²

X gallon = 1,224 ft²

X gallons = 1,224×1/250

= 4.9 gallons

But 1 gallon = $25

4.9 gallons = X

make X the subject of formula;

X = 4.9×25 = $122.5

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The slope of one user per second is not correct based on the February and April numbers of users.

The slope refers to the unit rate or the constant of proportionality.

The slope also refers to the gradient.

The slope is determined as the quotient between the Rise and the Run.

The number of days between February 1 and April 30 = 88 days

The number of seconds between February 1 and April 30 (the Run) = 7,603,200 seconds (88 x 24 x 60 x 60)

The difference between 90,000,000 and 80,000,000 users (the Rise) = 10,000,000 users (90,000,000 - 80,000,000)

The slope = 1.315 (10,000,000 ÷ 7,603,200)

Thus, we can conclude that the slope of one user per second is not correct but 1.315 users per second.

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The values of A and B are,

⇒ A = 16

⇒ B = 4

We have to given that;

The expression is,

⇒ x² + 8x

Now, Complete the square of the expression as;

⇒ x² + 8x + 16

⇒ (x + 4)²

Hence, By comparing we get;

The values of A and B are,

⇒ A = 16

⇒ B = 4

Thus, The values of A and B are,

⇒ A = 16

⇒ B = 4

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The expected profit for selling action movies is given as follows:

$15,583.20.

The expected profit for selling action movies is obtained applying the proportions in the context of the problem.

The proportion of action movies on the last month is given as follows:

2150/(2150 + 1721 + 829 + 300) = 0.43.

Hence, out of 8000 movies, the expected number of action movies is given as follows:

0.43 x 8000 = 3440.

The expected profit for each movie is of $4.53, hence the expected profit for action movies is given as follows:

4.53 x 3440 = $15,583.20.

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The solutions for the equation (3x + 12)(x + 4) = (4x² + 8x + 18x²)/2 are given by, x = -3/2, 4.

Given that the equation is,

(3x + 12)(x + 4) = (4x² + 8x + 18x²)/2

we have to find the solution that is the value(s) of the x for which this relation is true.

Solving the the equation we get,

3x*x + 12x + 3x*4 + 12*4 = (22x² + 8x)/2

3x² + 12x + 12x + 48 = 2 (11x² + 4x)/2

3x² + 24x + 48 = 11x² + 4x

11x² - 3x² + 4x - 24x - 48 = 0

8x² - 20x - 48 = 0

4(2x² - 5x - 12) = 0

2x² - 5x - 12 = 0

2x² - 8x + 3x - 12 = 0

2x(x - 4) + 3(x - 4) = 0

(2x + 3)(x - 4) = 0

Either 2x + 3 =0

x = -3/2

Or, x - 4 = 0

x = 4

Hence the solutions are, x = -3/2, 4.

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Answer:

To factor -3x^2 + 17x - 20 completely, we need to find two binomials that when multiplied together give us the original quadratic expression.

First, we can multiply the leading coefficient (-3) by the constant term (-20) to get -60. Then, we need to find two numbers that multiply to -60 and add up to the coefficient of the x-term (17). After some trial and error, we find that the two numbers are 12 and -5.

Now, we can rewrite the quadratic expression as:

-3x^2 + 17x - 20 = -3x^2 + 12x - 5x - 20

Next, we group the first two terms and the last two terms:

(-3x^2 + 12x) + (-5x - 20)

We can factor out 3x from the first group and -5 from the second group:

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

Now we can factor out a negative one from the second grouping:

3x(x - 4) - 5( -1)(x + 4)

And simplify:

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

Therefore, the quadratic expression -3x^2 + 17x - 20 can be factored completely as (3x - 5)(x - 4).

As a result, the proportionality constant in the supplied recipe that connects the number of cups of cereal to the number of cups of pretzel sticks is 2.5.

In a proportional connection, the constant of proportionality is the value by which one variable is multiplied to get the other variable. For example, if we have two proportional variables, x and y, we may write the connection as y=kx, where k is the proportionality constant.

k = y/x

where k is the proportionality constant.

Because the recipe calls for 10 cups of cereal and 4 cups of pretzel sticks in this example, we may enter these numbers into the formula:

k = 10/4

When we simplify, we get:

k = 2.5

As a result, the proportionality constant in the supplied recipe that connects the number of cups of cereal to the number of cups of pretzel sticks is 2.5.

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Hydrofluoric acid used to make anti-depressant medications can be considered as  industrial good

The industrial goods are products that are used in the production process of other goods or services.

From the given options, only "hydrofluoric acid used to make anti-depressant medications" can be considered an industrial good because it is used as a raw material in the production of anti-depressant medications.

The other options, such as Windex window cleaner, recreational vehicles, and gummy bear candy, are not considered industrial goods as they are not used in the production process of other goods or services, but rather for household cleaning, personal use or enjoyment.

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The avg response time to customer service calls was between 2.50 and 4.50

The captured percentage of the total sales or revenue within any specific market that a corporation or brand earns is called market share.

This measure showcases a company's competitive position in the marketplace and portrays its performance relative to its business rivals. Market share can be determined in multiple ways, namely by volume or value, and can range from being worldwide, nationwide or regional.

Given that it imparts insights into current market trends, tracking this statistic becomes particularly imperative for businesses looking to fashion sound marketing strategies. Without a doubt, market share acts as an indispensable metric for companies seeking to secure a spot in today's world of interminable industrial competition.

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Step-by-step explanation:

Goal: 300

They still need 246 bottles.

There are 67,600,000 possible standard license plates in this system.

The concept used to solve this problem is the multiplication principle of counting, which states that the total number of outcomes for a sequence of independent events is equal to the product of the number of outcomes for each individual event.

Here we have

Standard automobile license plates in a country display 2 digits, followed by 2 letters, followed by 3 digits.

For the first two digits,

As we know the number of digits = 10  [ from 0 to 9 ]

Hence, there are 10 possibilities for each digit (0-9),

The number of possibilities for 2 digits = 10×10 = 100 possibilities.

For the next two letters,

There are 26 possibilities for each letter (A-Z) as there are 26 letters

The number of possibilities for 2 letters = 26×26 = 676 possibilities.

For the last three digits,

There are 10 possibilities for each digit (0-9),

The number of possibilities for 3 letters = 10×10×10 = 1000 possibilities.

To get the total number of possible license plates,

Multiply the number of possibilities

= 100 × 676 × 1000 = 67,600,000

Therefore,

There are 67,600,000 possible standard license plates in this system.

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The new equation after moving 3 units to the right and 3 units up is

[tex]f(x) = (x - 4)^{2} 2 + 1.[/tex]

We need to change the equation to move the function [tex]f(x) = (x - 1)^{2} 2 - 2[/tex] three units to the right and three units up:

To shift the function three units to the right, replace x with (x - 3), which adjusts the graph three units to the right. [tex]f(x) = ((x - 3) - 1)^{2} 2 - 2[/tex], which simplifies to [tex]f(x) = (x - 4)^{2} 2- 2.[/tex]

To move the function three units up, multiply the equation by three.[tex]f(x) = (x - 4)^{2} 2 + 1[/tex] is the final equation.

The new equation is now [tex]f(x) = (x - 4)^{2} 2 + 1.[/tex]

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The coordinates of the point halfway between the origin and point B is [0, 5].

The coordinates of the midpoint of point A and point B is [5, 4].

The coordinates of the midpoint of point P and point Q is [7, 8].

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and then divide by two (2):

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

For line segment BO, we have:

Midpoint of BO = [(0 + 0)/2, (10 + 0)/2]

Midpoint of BO = [0, 10/2]

Midpoint of BO = [0, 5].

For line segment AB, we have:

Midpoint of AB = [(2 + 8)/2, (4 + 4)/2]

Midpoint of AB = [10/2, 8/2]

Midpoint of AB = [5, 4].

For line segment QP, we have:

Midpoint of QP = [(7 + 7)/2, (10 + 6)/2]

Midpoint of QP = [14/2, 16/2]

Midpoint of QP = [7, 8].

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Answer:

Step-by-step explanation:

Using algebra to solve this problem

Let x be the number of adult tickets sold and y be the number of student tickets sold. We can set up a system of two equations to represent the information given in the problem:

x + y = 1098 (equation 1) (the total number of tickets sold is 1,098)
5x + 1y = 2366 (equation 2) (the total amount collected is $2,366)

To solve for x and y, we can use substitution or elimination method. Let's use the substitution method.

From equation 1, we can solve for y as follows:

y = 1098 - x

Substituting this expression for y into equation 2, we get:

5x + 1(1098 - x) = 2366

Simplifying and solving for x, we get:

5x + 1098 - x = 2366
4x = 1268
x = 317

So, 317 adult tickets were sold. To find the number of student tickets sold, we can substitute this value for x into equation 1 and solve for y:

317 + y = 1098
y = 1098 - 317
y = 781

Therefore, 781 student tickets were sold.

Answer:

x+y= 1098

5x+1y= 2366

y= 1098 - x

5x+ 1(1098-x) = 2366

5x + 1098 - x = 2366

4x= 1268

x= 317

x+y= 1098

317 + y= 1098

y= 781

So the answer is: 317 adult tickets and 781 student tickets were sold.

Answer:

A) 208 = (10 + x)( 13 + x)

Step-by-step explanation:

The probability of selecting 2 red balls, 3 blue balls, and 1 yellow ball in that order without replacement is 0.000303.

The probability of selecting 2 red balls, 3 blue balls, and 1 yellow ball in that order is determined as follows:

Probability of selecting the first red ball = 10/24

Probability of selecting the second red ball = 9/23.

Probability of selecting the first blue ball = 8/22.

Probability of selecting the second blue ball = 7/21.

Probability of selecting the third blue ball = 6/20.

Probability of selecting the yellow ball = 6/19.

Hence;

The probability of selecting 2 red balls, 3 blue balls, and 1 yellow ball in that order will be:

Probability = (10/24) * (9/23) * (8/22) * (7/21) * (6/20) * (6/19)

Probability = 0.000303

Therefore, the probability of selecting 2 red balls, 3 blue balls, and 1 yellow ball in that order without replacement is 0.000303.

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The x and y-intercepts of the equation, rounded to the nearest hundredth are:

Blank 1 = 1.60.

Blank 1 = -0.70.

In Mathematics and Geometry, the x-intercept is the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).

f(x) = log(5x + 2) - 1

0 = log(5x + 2) - 1

1 = log(5x + 2)

By applying log rule for base 10, we have the following:

10 = 5x + 2

5x = 8

x = 8/5

x = 1.60.

When the x-value = 0, the y-intercept can be calculated as follows;

f(x) = log(5x + 2) - 1

f(0) = log(5(0) + 2) - 1

f(0) = log(2) - 1

f(0) = 0.3010 - 1

f(0) = -0.70

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It is not possible to determine the missing dimension in Part B with the information provided.

To find the volume of Tank A, we can multiply the base area (24 x 96) by the height of the tank. So, the volume of Tank A is 24 x 96 x h, where h is the height of Tank A.

Similarly, the volume of Tank B can be found by multiplying the base area (45 x ?) by the height of the tank. So, the volume of Tank B is 45 x ? x h, where h is the height of Tank B and ? is the missing dimension of the base.

We are given that the total volume of the two tanks is 4,608 cubic feet. So, we can set up an equation:

24 x 96 x h + 45 x ? x h = 4,608

Simplifying the equation, we get:

2,304h + 45h? = 4,608

Dividing both sides by 9h, we get:

256 + 5? = 512/3

Solving for ?, we get:

? = (512/3 - 256)/5

? = 32/3

Therefore, the missing dimension of the base of Tank B is 32/3 feet, and the volume of Tank B is:

45 x 32/3 x h = 1,440h

Since the total volume of the two tanks is 4,608 cubic feet, we can set up another equation:

24 x 96 x h + 1,440h = 4,608

Solving for h, we get:

h = 2

Therefore, the height of each tank is 2 feet, and the missing dimension of the base of Tank B is 32/3 feet. The volume of each tank is:

Tank A: 24 x 96 x 2 = 4,608 cubic feet

Tank B: 45 x 32/3 x 2 = 1,440 cubic feet

So, the answer to Part B is indeed 2,304 for Tank A, but the answer for Tank B is 1,440

Answer:    570OC^2mFG

Step-by-step explanation: I did this in school! Trust Me! You can report if wrong!

Price without tax  is  $249.95.

A patio bench is a common piece of outdoor furniture for a patio or deck. To fit varied outdoor locations and seating requirements, it can be produced in a number of forms and sizes and is often made of wood, metal.

We can multiply the total cost by (1 + tax rate) to get the cost of the patio bench sans sales tax.

(1 + 0.065) = 1.065

Price without tax = $266.20 / 1.065 = $249.9

Therefore, the correct answer is D) $249.95.

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Let's use S to represent Sydney's age. According to the problem, Devaughn is 11 years younger than Sydney, so his age can be represented as S - 11. We also know that the sum of their ages is 73, so we can write an equation:

S + (S - 11) = 73

Simplifying this equation, we get:

2S - 11 = 73

Adding 11 to both sides, we get:

2S = 84

Dividing both sides by 2, we get:

S = 42

Therefore, Sydney is 42 years old.

Answer:

Where is the question?...

Answer: THE ANSWER IS Blank 1: 200, Black 2: 1000, Blank 3: 800, Blank 4: 30+0.50x, Blank 5: y=50=0.30x.

Step-by-step explanation: Please give Brainliest.

Hope this helps!!!!

I can answer more questions for Brainlist.

If the quadratic formula is used to solve 2x² - 3x - 1 = 0, the solutions include the following: C. [tex]x = [\frac{3\; + \;\sqrt{17}}{4}, \frac{3\; - \;\sqrt{17}}{4}][/tex]

In Mathematics and Geometry, a quadratic equation can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph.

In Mathematics, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Mathematically, the quadratic formula is represented by this mathematical equation:

x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}

For the given quadratic equation 2x² - 3x - 1 = 0, we have:

[tex]x = \frac{-(-3)\; \pm \;\sqrt{(-3)^2 - 4(2)(-1)}}{2(2)}\\\\x = \frac{3\; \pm \;\sqrt{9 +8}}{4}\\\\x = \frac{3\; \pm \;\sqrt{17}}{4}[/tex]

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Complete Question:

If the quadratic formula is used to solve 2x² - 3x - 1 = 0, what are the solutions?

For the humming bird X = 130m

For the monkey r= 2

For the trapezoid X = 110m

For the whale r = 7/2

To calculate the scale factor of a given shape or model, the formula that should be used would be;

Scale factor = dimensions of bigger model/smaller model

For hummingbird:

X = 585/4.5

= 130m

For monkey ;

r= 440/220

= 2

For the trapezoid;

X= 165×2/3

= 330/3

= 110m

For the whale;

r= 420/120

= 7/2

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Out of these events, the independent events are drawing a marble out of a bag, replacing it and drawing another and rolling a dice twice. So the correct option is 2 and 5.

Events that are independent are those in which the outcome of first event has no effect on the outcome of a second event. The independent event in each of the situations according to this definition are:

The outcome of the first event in either of these situations have no effect on the outcomes of the second event.

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Answer:

Step-by-step explanation: a mouse

The area of the shaded region will be 24 square units.

Given that:

AB = 4

BC = 12

Point E is located halfway between sides AB and CD of the rectangle ABCD and halfway between sides AD and BC.

The area of the shaded region will be given as,

A = 2 x (1/2 x 12 x 2

A = 2 x 6 x 2

A = 24 square units

The area of the shaded region will be 24 square units.

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The missing image is given below.

The length of shorter side is 2.8 inch.

We have,

A rectangular room is 28 feet by 32 feet.

The Perimeter of scale drawing of room is 12 inches.

So, the perimeter of room

= 2(l +w)

= 2(28+ 32)

= 2(60)

= 120 feet

So, the scale factor is

= 120 / 12

= 10 inches

Thus, the length of shorter side is

= 28/10

= 2.8 inch

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