f(x) = 2x - 7
g(x) = 3x² - 5x - 7
Find: f(g(x))

Express in standard form

The length of x is 7.

In geometry, a triangle is a three-sided polygon made up of three line segments that join at three points called vertices. Triangles are one of the most basic and important shapes in geometry, and they are used in many areas of mathematics, science, and engineering.

Using the property of a median, we know that BD divides AC into two equal parts. Let's call the length of CD as y.

So, we have:

AC = AD + CD

x = 3 + y

Using the Pythagorean Theorem, we can find the length of BD:

BD² = AB² + AD² - 2(AB)(AD)(cos(B))

BD² = 4² + 3² - 2(4)(3)(cos(B))

BD² = 25 - 24cos(B)

BD = √(25 - 24cos(B))

Since BD is a median, we know that it divides BC into two equal parts. Let's call the length of BD as z.

So, we have:

BC = 2z

8 = 2z

z = 4

Now, using the property of medians again, we know that:

4² + y² = z²

16 + y² = 16

y² = 0

y = 0

Therefore, CD is also 4, and:

x = 3 + y

x = 3 + 4

x = 7

So, the length of AC is 7.

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Answer:

Assuming that Peter travels at a constant speed, then he would have travelled a total distance of (98 * 3) + (105 * 2) = 531 km.

Answer:

B. Vertex

Step-by-step explanation:

The midpoint between the two x-intercepts of a parabola will provide the x-coordinate of the vertex. Line of symmetry is drawn along this particular  x-coordinate. This x-coordinate is substituted into the equation of the graph to find its corresponding y-coordinate.

The expected number of defects per yard is 1.

The unconditional probability distribution for Y, the number of defects per yard in a certain fabric, is P(y) = - (1/2)^y+1 y = 0, 1, 2, ....

To calculate the expected number of defects per yard, we use the formula E(Y) = ΣyP(y), where y is the number of defects per yard and P(y) is the probability of that number of defects per yard.

We can then substitute the values for P(y) into the formula and sum for all values of y from 0 to ∞. This yields E(Y) = Σy(-(1/2)^y+1) = 1. Thus, the expected number of defects per yard is 1.

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Answer:

$33.52

Step-by-step explanation:

7.89+7.89+15= 30.78

30.78x 0.089=2.73942 rounded off to the nearest hundredth which is 2.74

30.78+2.74= $33.52

The measure of ER given by the equation ER = 21

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The measure of QE = 8x + 3   be equation (1)

The measure of ER = 4x + 1   be equation (2)

The measure of QR = 64

Now , QR = QE + ER   be equation (3)

Substituting the values of QE and ER in the equation (3) , we get

8x + 3 + 4x + 1 = 64

On simplifying the equation , we get

12x + 4 = 64

Subtracting 4 on both sides of the equation , we get

12x = 60

Divide by 12 on both sides of the equation , we get

x = 5

Substitute the value of x in equation (2) , we get

The measure of ER = 4 ( 5 ) + 1

The measure of ER = 21

Hence , the equation is ER = 21

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Answer:

120°

Step-by-step explanation:

AB //CD and EF is transversal. When two parallel lines are cut by a transversal, the alternate exterior angles are congruent.

      ∠CHF = ∠BGE

                = 120°

The volume of a solid formed by revolving the region in the first quadrant bounded on the left by the circle , on the right by the line , and above by the line about the x-axis is (47/3)π.

To use the washer method, we need to consider the solid as a stack of thin washers, each with a hole in the center. We will integrate along the axis of revolution (in this case, the x-axis).

First, let's sketch the region we're revolving:

The circle has equation x^2 + y^2 = 1, so its radius is r = 1 when y = 0. The line has equation x = 4, so its distance from the axis of revolution is R = 4. The region we're revolving is bounded by y = 0 and y = √(1 - x^2), which we can rewrite as x = √(1 - y^2).

We can now set up the integral for the volume of the solid:

V = [tex]\int\limits^1_0[/tex] π(R^2 - r^2) dy

 = [tex]\int\limits^1_0[/tex] π(4^2 - x^2) dy

 = π[tex]\int\limits^1_0[/tex] (16 - y^2) dy

 = π [16y - (1/3)y^3] |₀¹

 = π (16 - 1/3)

 = (47/3)π

Therefore, the volume of the solid is (47/3)π cubic units.

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Complete question is:

Using the washer method, determine the volume of a solid formed by revolving the region in the first quadrant bounded on the left by the circle x^2+y^2=1, on the right by the line x = 4, and above by the line x=4 about the x-axis.

Step-by-step explanation:

-2x + 11(y+x) = 2

-2x + 11y + 11x = 2

-2x + 11x +11y = 2

9x + 11y = 2

where a = 9, b= 11 and c= 2

Answer: 0.0628

Step-by-step explanation:

The closest answer to the p-value for a test statistic of z = -1.86 is 0.0614.

To calculate the p-value for a one-sample two-sided z-test on a population proportion, we must first calculate the area under the standard normal distribution curve that corresponds to the test statistic z = -1.86.

Because this is a two-sided test, we must find the area of the distribution in both tails that is more extreme than the test statistic. We can do this by using a standard normal distribution table or calculator, or by exploiting the distribution's symmetry.

We can calculate the area to the left of z = -1.86 using a standard normal distribution table or calculator. Because this is a two-sided test, the area in the distribution's right tail is also 0.0307.As a result, the p-value for this test statistic is as follows:

2(0.0307) = 0.0614 p-value

So 0.0614 is the closest answer to the p-value for a test statistic of z = -1.86.

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The correct equation is option (A): 0.7386x - 15.75 = 41.87 equation can be used to find the quantity of Canadian dollars that Tobias exchanged .

In mathematics, an expression is a combination of numbers, variables, and operations that can be evaluated to obtain a value. An expression can contain constants, variables, and operators such as addition, subtraction, multiplication, division, and exponentiation, as well as functions and parentheses to control the order of operations.

Let x be the quantity of Canadian dollars that Tobias exchanged. According to the problem statement, he received 0.7386 U.S. dollars for each Canadian dollar exchanged, and he gave away $15.75, leaving him with $41.87. We can use this information to set up the equation:

0.7386x - 15.75 = 41.87

Therefore, the correct equation is option (A):

0.7386x - 15.75 = 41.87 equation can be used to find the quantity of Canadian dollars that Tobias exchanged .

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Step-by-step explanation:

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The only solution to the given logarithmic equation is x = 4.

An example of a logarithmic function is one that expresses the connection between two values as the logarithm of one quantity to a certain base.

A logarithmic function's basic form is:

f(x)=log base b (x)

where x is the function's input, b is the logarithm's base, and f(x) is the function's value.

We can solve the logarithmic equation step by step as follows:

log₂[log₂ (√4x)] = 1

First, we simplify the expression inside the logarithm:

log₂[log₂ (√4x)] = 1

log₂[log₂ (2√x)] = 1

Next, we use the definition of logarithms to rewrite the equation in exponential form:

log₂ (2√x) = 2¹ = 2

2√x = 2² = 4

√x = 2

x = 4

Thus, the solution is x=4.

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Factoring the expression 16x+ 8y using GCF would be, 8(2x + 1).

The GCF of two or more than two numbers is the highest number that divides the given two numbers completely.

We also know that distributive property states a(b + c) = ab + ac.

Given, An expression 16x+ 8y.

Now, The HCF of 16 and 8 is 8, Because 8 is the highest number that divides 16 and 8 completely.

Therefore, The factored form of the expression 16x+ 8y would be,

8(2x + 1).

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The volume V of the resulting solid is [tex]$\frac{5000 \pi}{3}[/tex]

As per the data given:

The region bounded by the given curves is rotated about the specified axis.

Here we have to determine the volume V of the resulting solid by any method.

The given equations are x = [tex](y -6)^2[/tex], x = 25; about y = 1.

To find the volume of resulting solid we are using cylinder method

To derive the above solution, we need to use the old fashioned quadratic method.

Substitute the values of x then we get

25 = [tex](y-6)^2[/tex]

[tex]\rightarrow 5^2=(y-6)^2[/tex]

y - 6 = 5

y = 6 + 5

y = 11

So, 1 ≤ y ≤ 11

Graph attached at end of the solution

Using cylinder method and integrate along y -axis from y = 1 to y = 11

Volume [tex]}=\int_a^b 2 \pi r h d y[/tex]

Volume  [tex]& =2 \pi \int_1^{11}(y-1)\left(25-(y-6)^2\right) d y[/tex]

Volume  [tex]=2 \pi \int(y-1)\left(25-y^2-36+12 y\right) d y \\[/tex]

Volume [tex]& =2 \pi \int_1^{11}\left(-y^3+13 y^2-23 y+11\right) d y[/tex]

Volume  [tex]=2 \pi\left[-\frac{y}{4}+\frac{13 y}{3}-\frac{23 y}{2}+11 y\right]_1^{11} \\[/tex]

Volume [tex]& =2 \pi \cdot\left(\frac{10043}{12}-\frac{43}{12}\right)=2 \pi\left(\frac{10000}{12}\right)=\frac{5000\pi }{3}[/tex]

Thus the volume of resulting solid is:

[tex]$}=\frac{5000 \pi}{3}[/tex]

Therefore the volume is [tex]$\frac{5000 \pi}{3}[/tex]

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The residual of a customer with a height of 155 cm who rents a bike with a 51 cm frame is -1.

The discrepancy between a response variable's observed value and its expected value as predicted by the regression line.

We have the Equation: y'=1/3x + 1/3.

The regression equation is given as:

y'=(1/3)x + (1/3)

Since the height is given as 155cm, x=155 cm

The predicted frame size,

y'=(1/3)x + (1/3)

y'=(1/3) × 155+ (1/3)

  = 51 2/3 + 1/3

  = 52

So, Residual = Observed y- predicted y

                     = 51-52

                     = -1

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Answer:

Step-by-step explanation:

Please like if this helped :)

Answer:

$1.27

Step-by-step explanation:

We know

The tax is 7.5%

7.5% = 0.075

Which of the following was the sales tax Serena had to pay?

We take

16.99 times 0.075 = $1.27

So, the answer is $1.27

Answer:

Expected value E(x)

= 2 x 0.11 + 11 x 0.09 + 12 x 0.08 + 13 x 0.58 + 19 x 0.14

= 12.37

Variance

= E( X^2 ) - (E(X))^2

= (2^2 x 0.11 + 11^2 x 0.09 + 12^2 x 0.08 + 13^2 x 0.58 + 19^2 x 0.14) - (12.37)^2

= 171.41 - 153.0169

= 18.393 (cor to 3 dp)

Standard deviation

= [tex]\sqrt{variance}[/tex]

=[tex]\sqrt{18.3931}[/tex]

= 4.289 (cor to 3 dp)

Mean should be ( [tex]\frac{2+11+12+13+19}{5}[/tex] ) = 11.4 but i am not very sure

Mean, variance and the standard deviation of the discrete random variable are 12.37, 18.3931 and 4.2887 respectively.

Expected value in probability is defined as the sum of the product of each of the variable and probability corresponding to the variable.

Expected value is same as the mean of a discrete random variable.

Mean, μ = Σ x. P(x)

              = (2 × 0.11) + (11 × 0.09) + (12 × 0.08) + (13 × 0.58) + (19 × 0.14)

              = 12.37

Variance, σ² = Σx² P(x) - μ²

                     = [(2² × 0.11) + (11² × 0.09) + (12² × 0.08) + (13² × 0.58) + (19² ×

                         0.14)]- [ 12.37²]

                     = 18.3931

Standard Deviation, σ = √Variance

                                    = 4.2887

Hence the mean is 12.37, Variance is 18.3931 and Standard deviation is 4.2887.

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The total number of wheelbarrow loads required to complete both the projects 25.

What are Fractions?

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. In ordinary English, a fraction refers to the number of parts of a specific size.

The combined volume of concrete needed for the patio and walkway is 1 3/4 + 2 1/3 = 7/4 + 7/3 = 21/12 + 28/12 = 49/12 cubic yards

The entire volume of concrete can be divided by the capacity of a wheelbarrow to determine the necessary number of wheelbarrow loads: (49/12 )/( 1/6) = 49/12* 6/1 = 49/2 = 24.5

We round up to 25 because we can't have half a wheelbarrow load. The homeowner will therefore require 25 wheelbarrow loads to finish both projects.

Hence, The total number of wheelbarrow loads required to complete both the projects 25.

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a. Yes, Mia Hamm has an absolute advantage in both scoring goals and saving shots as a goalie,

b. The opportunity cost of scoring 1 goal for Mia is 0.6 shots

c. The opportunity cost of saving 1 shot as a goalie for Mia is 1.67 goals . The opportunity cost of saving 1 shot as a goalie for Alyssa is 0.17 goals scored.

d. Mia has the comparative advantage in scoring goals, since her opportunity cost of scoring 1 goal is lower than Alyssa's. Alyssa has the comparative advantage in saving shots as a goalie, since her opportunity cost of saving 1 shot is lower than Mia's

b.  The opportunity cost of scoring 1 goal for Mia is 0.6 shots saved as a goalie  which is calculated as

30 shots/50 goals = 0.6).

The opportunity cost of scoring 1 goal for Alyssa is 6 shots saved as a goalie  which is calculate as

opportunity cost 120 shots/20 goals = 6.

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To calculate the monthly payment and total interest for a loan of $89,000 at 5.7% for 30 years, we can use the formula for the monthly payment of a fixed-rate mortgage loan:

P = L[c(1 + c)^n]/[(1 + c)^n - 1]

where P is the monthly payment, L is the loan amount, c is the monthly interest rate (which is the annual interest rate divided by 12), and n is the total number of monthly payments (which is the number of years multiplied by 12).

Plugging in the given values, we have:

L = $89,000

r = 5.7% = 0.057 (monthly interest rate)

n = 30 years * 12 months/year = 360 months

P = ($89,000)[0.057(1 + 0.057)^360]/[(1 + 0.057)^360 - 1]

P = $515.92 (rounded to the nearest cent)

Therefore, the monthly payment is $515.92.

To calculate the total interest, we can subtract the loan amount from the total amount paid over the life of the loan. The total amount paid is equal to the monthly payment times the total number of payments:

Total amount paid = P * n = $515.92 * 360 = $185,731.20

Total interest = Total amount paid - Loan amount = $185,731.20 - $89,000 = $96,731.20

Therefore, the total interest paid over the life of the loan is $96,731.20.

For the first statement, the likely explanatory variable is the miles per gallon and the likely response variable is the weight.

For the second statement, the likely explanatory variable is the weight and the likely response variable is the miles per gallon.

In statistical analysis, an explanatory variable is a variable that is presumed to have an effect on another variable. It is also known as an independent variable. On the other hand, a response variable is the variable that is presumed to be affected by the explanatory variable. It is also known as a dependent variable.

In the first statement, it is stated that the explanatory variable is the miles per gallon, which means that we are looking at how the fuel efficiency of a vehicle affects its weight. Therefore, the weight is the likely response variable, as it is presumed to be affected by the miles per gallon.

In the second statement, it is stated that the explanatory variable is the weight, which means that we are looking at how the weight of a vehicle affects its fuel efficiency. Therefore, the miles per gallon is the likely response variable, as it is presumed to be affected by the weight.

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Answer: The average cost per item is given by the equation C = (a/q) + b. To find the rate of change of C as q increases, we need to take the derivative of this equation with respect to q.

dC/dq = -(a/q^2)

So, the rate of change of C with respect to q is proportional to -1/q^2.

If production increases at a rate of 100 cell phones per week, the rate of change of q is 100. But we need to convert this to units of items per hour or per second, depending on the context.

Let's assume the rate of increase of q is in items per hour. Then the rate of change of C with respect to time t (in hours) is given by:

dC/dt = (dC/dq) * (dq/dt) = (-(a/q^2)) * (100) = -100a/q^2

So, the rate at which the average cost is changing depends on the value of a and q. If we knew the values of a and q, we could calculate the specific rate at which the average cost is changing.

Step-by-step explanation:

The probability that a randomly selected medical student who took the test had a total score that was less than 480 is 0.49, which means that approximately 49% of medical students had a score lower than 480.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

To calculate the probability that a randomly selected medical student who took the test had a total score that was less than 480, we need to start by looking at the data given.

In this case, the data tells us that the mean score was 500 and the standard deviation was 50.

This means that the scores are normally distributed, which means that the probability of finding a score lower than 480 can be calculated using the normal distribution formula.

We can use this formula to calculate the area under the curve (or probability) below the score of 480.

The result of this calculation is 0.49, which means that approximately 49% of medical students had a score lower than 480.

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Answer: The numerators must be the same for the fractions to be equal.

The denominator of a fraction is the bottom number. Take a look at these two fractions.

¾ & ¾

The numbers at the bottom are the same. If I eat ¾ of an apple and you eat ¾ of an apple, we both eat the same amount.

Now look at these fractions.

⅗ & ¾

They both have the same top number (numerator), but they have different denominators. If I eat ¾ of an apple and you eat ⅗ of an apple, we both do not eat the same amount.

So if both the numerator and denominator are the same they are equal.

This means that the numerators must be the same for the fractions to be equal.

I hope this helps & Good Luck <3 !!!

a) C(x) = 0.02x + 2200, b) A straight line with positive slope, c) Slope is 0.02, represents cost per chair, d) Y-intercept is 2200, represents fixed cost.

a) The cost C(x) can be expressed as a linear function of the number of chairs x produced. We can solve for the slope and y-intercept using the two points (100, 2200) and (300, 4800). First, calculate the slope of the line using the formula (y2 - y1)/(x2 - x1). This gives us (4800 - 2200)/(300 - 100) = 0.02. Then, we can use the slope and one of the points to solve for the y-intercept using the equation y = mx + b, where m is the slope and b is the y-intercept. Substituting the values from the first point (100, 2200) into the equation gives us 2200 = 0.02(100) + b, so the y-intercept is 2200. Therefore, the cost function can be expressed as C(x) = 0.02x + 2200.

b) The graph of this function is a straight line with a positive slope, as shown in the diagram.

c) The slope of the graph is 0.02, which represents the cost per chair.

d) The y-intercept is 2200, which represents the fixed cost of manufacturing the chairs.

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Answer:

8y+2

Step-by-step explanation:

5y+3y=8y

-2+4=2

Since it's positive two we add them together.

8y+2

Answer:

y=4

x=3

Step-by-step explanation:

2y-4=y

y=4

4x=x+9

3x=9

x=3

(97x/100) represents the total number of cleaner automobiles.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given is that automobiles are 97% cleaner than they were 30 years ago.

Assume that the total number of automobiles 30 years ago were {x}. Then, the total number of clean automobiles will be -

97% of {x} = 97x/100

Therefore, (97x/100) represents the total number of cleaner automobiles.

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