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Evaluating the composition of functions in x = 1 gives:

f(g(1)) = 28

Here we have the two functions:

f(x) = 4x

g(x) = 2x + 5

And we want to find to find the composition f(g(x)), we will get:

f(g(x)) = 4*g(x)

Replacing g(x) there we will get:

f(g(x)) = 4*(2x + 5)

         = 8x + 20

Now we can evaluate that in x = 1, then we will get:

f(g(1)) = 8*1 + 20 = 28

That is what we wanted to find.

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According to the linear equation given, it is found that the volume of each marble is of 0.05 liters.

A linear equation is modeled by:

\(y = mx + b\)

In which:

In this problem, the volume of water on a tank of 32 liters when n marbles are used is:

\(W = 32 - 0.05n\)

The slope is of \(m = 0.05\), which means that for each marble, there is 0.05 liters less available for water, meaning that the volume of each marble is of 0.05 liters.

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The probability that exactly 2 of the workers interviewed are union members is approximately 0.044.

To solve this problem, we can use the binomial probability formula, which is:

\(P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)\)

where:

n is the sample size (number of workers being interviewed)

k is the number of successes we are interested in (in this case, 2 of the workers being union members)

p is the probability of success (in this case, the probability that a worker is a union member)

(n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items (this can be calculated using the formula n! / (k! * (n - k)!))

Plugging in the values, we get:

\(P(X = 2) = (4 choose 2) * (0.96)^2 * (1 - 0.96)^(4 - 2)\)

\(= (6) * (0.96)^2 * (0.04)^2\)

= 0.04403136

Therefore, the probability that exactly 2 of the workers interviewed are union members is approximately 0.044.

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Answer:

The Answer Will Be D

Step-by-step explanation:
The fuel economy of a car is modeled by the function f(s) = -0.009s² +0.699s +12 where s represents the speed of the car, measured in miles per hour.We need to find the fuel economy of the car when it travels at an average of 20 miles an hour.f(20) = -0.009(20)² +0.699(20) +12f(20) = -0.009(400) +13.98f(20) = 9.6The fuel economy of the car when it travels at an average of 20 miles an hour is 9.6 miles per gallon.Therefore, the answer is option D. 22.38 miles per gallon.

Answer:

100,000,000/10^8

Step-by-step explanation:

10^3 = 1000

10^3 = 1000

10^2 = 100

Therefore,

= (1000) x (1000) x (100)

= (100,000) x (100)

= 100,000,000

or

= 10^8

(a) √2 · √8. The simplified surd expression is 4.

(b) √80. The simplified surd expression is  4√5.

(c) √5/√20. The simplified surd expression is  1/2.

(d) √20. The simplified surd expression is  2√5.

The given surd expression is simplified as follows;

(a) √2 · √8

we can simplify it as;

√2 · √8 = √(2 x 8) = √16 = 4

(b) √80

we can simplify it as;

√80 = √ (16 x 5) = √16  x √5 = 4√5

(c) √5/√20

we can simplify it as;

√5/√20  x  √20 / √20

= (√5  x √20 ) /(20)

= √100 / 20

= 10/20

= 1/2

(d) √20

we can simplify it as;

√20 = √4  x √5 = 2√5

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well, the profit is clearly just 490 - 350 = 140.

Now, if we take 350(origin amount) to be the 100%, what is 140 off of it in percentage?

\(\begin{array}{ccll} Amount&\%\\ \cline{1-2} 350 & 100\\ 140& x \end{array} \implies \cfrac{350}{140}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{5}{2} ~~=~~ \cfrac{100}{x}\implies 5x=200\implies x=\cfrac{200}{5}\implies x=40\)

Answer: 60m

Step-by-step explanation: V= b x h x l

Step-by-step explanation:

#G

enjoy. my son haha. lol

The dimensions of the rectangular page such that the least amount of paper is used are;

2.) (√30 + 4) inches by (√30 + 2) inches

A rectangle is a quadrilateral in which the four interior angles are right angles.

The area of the print contained in the page = 30 square inches

Length of the margin at the top of the page = 2 inches wide

Length of the margin at the bottom of the page = 2 inches

Length of the margin on each side = 1 inch

The dimensions of the rectangular page are therefore;

Length of the rectangle = The side length of the square + 2 × The margin at the top

Width of the rectangle = Side length of the square + 2 × The margin on the side

Area of a square, A = s²

Where;

s = The side length of the square

Therefore;

Side length of a square of area, A, is √(A)

The side length of area 30 square inches is thehttps://brainly.com/question/24158647refore;

s = √(30)

The dimensions of the rectangular page are therefore;

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\(6y^2(y^2+6y+9)\\\\=6y^2(y^2+2\cdot 3 \cdot y + 3^2)\\\\=6y^2(y+3)^2\\\\=6y^2(y+3)(y+3)\)

As a result, the roses and zinnias collectively occupy about 67.95% of the entire yard.

The area represents the size of a two-dimensional surface or territory in mathematics. It is measured in square measures, such as square inches (in2), square feet (ft2), or square metres (m2), and it refers to the volume of a closed figure. Depending on how the figure is shaped, a different method is required to calculate the area. For instance, you can calculate the area of a rectangle by multiplying its length by breadth, and you can calculate the area of a circle by multiplying (pi) by the square of its radius.

given

a. The formula for calculating the area of a rectangle must be used to determine the area of each variety of flower:

Area is equal to length times breadth.

Roses: The dimensions are 20 feet long and 16 feet wide.

Size: 20 feet by 16 feet

≈ 320 square feet

As a result, each flower type's size is as follows:

Roses: 320 square feet

Zinnia: 528 square feet

Qualcomms: 0 square feet

A square foot of petunias. The total area of the roses and zinnias must be added, divided by the total area of the garden, and multiplied by 100 to obtain the proportion of the entire garden that each takes up:

320 square feet of roses and 528 square feet of zinnias equal 848 square feet.

(Area of Roses Plus Area of Zinnias) / Total Area x 100% is the percentage of the entire garden.

Garden percentage equals (848 square feet / 1248 square feet) times 100%

67.95% of the garden's overall area

As a result, the roses and zinnias collectively occupy about 67.95% of the entire yard.

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The complete question is:-  

a. Find the area of all the different flower types (Show ALL Work). Hint: You will have to subtract out the previous one to find the next one. For example, to find the Zinnias, you will have to find the area of it and then subtract out the area of the Roses.

b. What percent of the total garden does the Roses and Zinnias take up? Hint: Find the area of the total and then divide it with the area of the Roses and Zinnias.

Answer: 178 4/5 or as an improper fraction 894/5

Hope this helps!

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Answer:

\(y+1=\frac{1}{2}(x-6)\)

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals, so the slope of the line to be found is 1/2.

Substituting into point-slope form, the equation is

\(y+1=\frac{1}{2}(x-6)\)

Answer: 75%

We know that 1/4 of 24 (25%) is 6, 6 fits into 18 three times and 25 times 3 is 75. So the answer is 75%

Answer:

62°

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

I think it is A because if you do the math when your double her time she has way more distance.

The ratio of the strawberries to the blueberries is 32 strawberries: 30 blueberries (option d).

Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s). The sign that is used to represent ratio is :.

The ratio of strawberries to blueberries - total number of strawberries : total number of blueberries.

(8 x 4) : 30

32 : 30

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Answer: A. 8 strawberries: 30 blueberries

Step-by-step explanation:

Answer:

B. Over the past few months, Cesar's cell phone bill has doubled from the previous month.

Step-by-step explanation:

Answer:

look attachment below

Step-by-step explanation:

We find the midpoints of AC and BD and the corresponding coordinates for quadrilateral ABCD.

Midpoint of AC: ( (x₁ + x₃) / 2 , (y₁ + y₃) / 2 )

Midpoint of BD: ( (x₂ + x₄) / 2 , (y₂ + y₄) / 2 )

Then we can measure and record the slopes of each side.

Slope = (y₂ - y₁) / (x₂ - x₁)

Here,

To draw quadrilateral ABCD with the midpoints of AC and BD coinciding, we first need to find the midpoints of AC and BD.

The midpoint of a line segment is the average of the coordinates of its endpoints.

Given points A(x₁, y₁), B(x₂, y₂), C(x₃, y₃), and D(x₄, y₄), we can find the midpoints as follows:

Midpoint of AC: ( (x₁ + x₃) / 2 , (y₁ + y₃) / 2 )

Midpoint of BD: ( (x₂ + x₄) / 2 , (y₂ + y₄) / 2 )

Once we have the coordinates of the midpoints, we can connect them to form quadrilateral ABCD.

To measure the slope of each side of quadrilateral ABCD, we need to find the slope of each line segment formed by connecting points A, B, B, C, C, D, and D, A.

The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by:

Slope = (y₂ - y₁) / (x₂ - x₁)

Let's assume we find the midpoints of AC and BD and the corresponding coordinates for quadrilateral ABCD. Then we can measure and record the slopes of each side.

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Answer:

7/2

Step-by-step explanation:

notice that if you substitute x by five you get 0/0 wich a non-defined form

The trick is to simplify by x-5

Hey there! :)

Answer:

\(\lim_{x \to 5} = 7/2\)

Step-by-step explanation:

We are given the equation:

\(\frac{x^{2}-3x-10 }{2x-10}\)

Factor the numerator and denominator:

\(\frac{(x - 5)(x+2) }{2(x-5)}\)

'x - 5' is on both the numerator and denominator, so it gets cancelled out and becomes a "hole".

This means that at x = 5, there is a hole. There is a limit at x ⇒ 5. Find the hole by plugging 5 into the simplified equation:

\(\frac{((5)+2) }{2}\) = 7/2

Therefore:

\(\lim_{x \to 5} = 7/2\)

Answer:

d. slope: -3; y-intercept: -2

Step-by-step explanation:

The equation of the line is given to us in slope-intercept form. The slope-intercept form of a line is:

y = mx + b

where m is the slope and b is the y-intercept.

The equation given to us is:

y = -3x - 2

Since the equation is in slope-intercept form, we can see that -3 is the slope and -2 is the y-intercept.

Answer choice d is correct.

I hope you find my answer and explanation to be helpful. Happy studying.

Answer:

B

Step-by-step explanation:

i got it right

Answers:

Step-by-step explanation:

I solved the problem.

Answer:

16 blocks

Step-by-step explanation:

equation: 0.8x = 12.8

if each block is 0.8oz and the total weight is 12.8oz then divide 12.8 by 0.8 and get 16! in other words, 0.8oz goes into 12.8oz 16 times, meaning there are 16 blocks that each weigh 0.8oz

Answer:

c(3a) = 2(3a)^2 - 4(3a) + 3 = 18a^2 - 12a + 3.

Step-by-step explanation:

c(3a) = 18a^2 - 12a + 3

Note: this is the simplified form of the expression.

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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