What is 8.7x0.45 if you multiply it

The expression (sinx + cosx)^2 + (sinx - cosx)^2 simplifies to

To simplify the expression (sinx + cosx)^2 + (sinx - cosx)^2 using trigonometric identities, we can expand and simplify the expression.

Expanding the squared terms

(sin^2x + 2sinxcosx + cos^2x) + (sin^2x - 2sinxcosx + cos^2x)

Using the trigonometric identity sin^2x + cos^2x = 1, we can simplify further:

(1 + 2sinxcosx + 1) + (1 - 2sinxcosx + 1)

Simplifying the expression, we have:

2 + 2sinxcosx + 2

Combining like terms, we get:

4 + 2sinxcosx

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The probability of choosing a different type of animal as the second toy is $\frac{7}{18}.

The problem is to draw a tree diagram to determine the probability of choosing a different type of toy animal when two toys are randomly selected. Imogen has two toy elephants and seven toy bears in a box.

It should be noted that a tree diagram is a visual tool that can be used to show the possible outcomes of a particular event. Each branch represents a possible outcome and the probabilities associated with each branch are assigned in the diagram. The steps involved in solving the problem are:

Step 1: Construct the tree diagram.

Step 2: Calculate the probability of choosing a different type of animal as the second toy. Step 3: Simplify the fraction. Solution:

Step 1: Construct the tree diagram. The tree diagram for the given problem is shown below. [asy] size(200); defaultpen(linewidth(0.7));   draw((0,0)--(2,-2),MidArcArrow(size=10)); draw((0,0)--(2,2),MidArcArrow(size=10)); draw((2,2)--(4,2),MidArcArrow(size=10)); draw((2,-2)--(4,-2),MidArcArrow(size=10)); draw((2,2)--(4,0),MidArcArrow(size=10)); draw((2,-2)--(4,0),MidArcArrow(size=10)); draw((4,2)--(6,2),MidArcArrow(size=10)); draw((4,0)--(6,0),MidArcArrow(size=10)); draw((4,-2)--(6,-2),MidArcArrow(size=10));  label("Elephant",(-1,0)); label("Bear",(-1,2)); label("Bear",(3,2)); label("Bear",(3,0)); label("Bear",(3,-2)); label("Elephant",(3,0)); label("Bear",(5,2)); label("Elephant",(5,0)); label("Bear",(5,-2));  [/asy] Step 2: Calculate the probability of choosing a different type of animal as the second toy. The total number of outcomes is 9, as there are 2 elephants and 7 bears. There are four possible ways in which Imogen can pick two different types of animal:

Elephant followed by bear, Bear followed by elephant, Elephant followed by elephant, and Bear followed by bear. The probability of choosing a different type of animal as the second toy is the sum of the probabilities of the first two outcomes, which is: $P(\text{different animal}) = \frac{2}{9}\times\frac{7}{8}+\frac{7}{9}\times\frac{2}{8}$ $=\frac{14}{72}+\frac{14}{72}$ $=\frac{28}{72}$

Step 3: Simplify the fraction. The fraction can be simplified by dividing the numerator and denominator by the highest common factor. The highest common factor of 28 and 72 is 4. Hence, $\frac{28}{72} = \frac{7}{18}$

Therefore, the probability of choosing a different type of animal as the second toy is $\frac{7}{18}$.

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The probability that the second toy Imogen chooses will be a different type of animal to the first toy is 7/18. This is calculated by determining the probability of picking an elephant then a bear, and the probability of picking a bear then an elephant, and adding these two probabilities.

Firstly, let's define the event: Picking an elephant (E) and picking a bear (B). At the beginning, Imogen has 2 elephants and 7 bears in the box, making a total of 9 toys.

When Imogen picks the first toy, the probabilities are: P(E) = 2/9 and P(B) = 7/9. Then, Imogen picks the second toy, not replacing the first one.

So, we have two scenarios for the second pick: Given that the first pick was an elephant, the probabilities for the second pick are: P(E) = 1/8 (because one elephant left) and P(B) = 7/8 (there are still 7 bears). If the first pick was a bear, the probabilities for the second pick are: P(E) = 2/8 (still 2 elephants) and P(B) = 6/8 (one bear left).

Now, we're interested in the probability of picking two different types of animal toys. That will be the sum of the probabilities of picking an elephant then a bear, and the probability of picking a bear then an elephant. So it's (P(E) * P(B|E)) + (P(B) * P(E|B)) = (2/9 * 7/8) + (7/9 * 2/8) = 14/72 + 14/72 = 28/72 which reduces to 7/18.

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Willis's mistake is assuming that a constant difference in the y-values implies a constant rate of change, which is not necessarily true for non-linear functions.

While it is true that a linear function will always have a constant rate of change, the converse is not true. A non-linear function can also have a constant difference in the y-values over a certain interval, but the rate of change is not constant. This is because the rate of change of a non-linear function varies at different points along the curve.

In this case, Willis did not consider the possibility of a non-linear function with a constant difference in the y-values. Therefore, his conclusion that the function is linear based on the constant differences in the y-values is not necessarily correct. To determine whether the function is linear or non-linear, Willis should have examined the differences in the x-values as well, or plotted the points on a graph to see if they lie on a straight line.

Answer:

30: 100

31: -13

32: -45

33: 14

34: -32

35: -22

36: 17

Answer:

∠ MON = 51°

Step-by-step explanation:

∠ LON is composed of the 2 angles LOM and MON , that is

∠ LOM + ∠ MON = ∠ LON

42° + ∠ MON = 93° ( subtract 42° from both sides )

∠ MON = 51°

Answer:

<MON= 51°

Step-by-step explanation:

Look at the diagram and locate LON. You can see that LON is the angle of the complete line. Now LOM is given which is the angle of a part of the lines. So that means that to find MON we can minus LON with LOM.

<MON= <LON - <LOM

= 93-42

<MON= 51°

Feel free to ask any doubt you have!

When we solve for theta, the result would be B. 20°

To solve for theta, we would first represent the expression in the following way;

sinθ = cos(θ + 50)

sinθ =sin 90° - (50 + θ) cos (90 - θ)

sinθ = 90° - 50° - θ

Collect like terms

2θ =  90° - 50°

2θ = 40°

Divide both sides by 2

θ = 20°

Therefore the solution to theta is 20°

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Answer:

B)  20°

Step-by-step explanation:

Given equation:

[tex]\sin \theta = \cos (\theta + 50^{\circ})[/tex]

To solve the given equation for θ, we can use a co-function identity.

Co-function identities are a set of trigonometric identities that relate the values of complementary angles.

[tex]\boxed{\begin{minipage}{5cm}\underline{Co-function Identities}\\\\$\sin \theta = \cos (90^{\circ}-\theta)$\\\\$\cos\theta = \sin(90^{\circ}-\theta)$\\\\\sin \theta=\cos\theta$,\;if\;$A+B=90^{\circ}$\\\end{minipage}}[/tex]

Using the cofunction identity sin θ = cos (90° - θ), we can say that:

[tex]\cos (90^{\circ} -\theta)=\cos (\theta + 50^{\circ})[/tex]

Therefore:

[tex]\begin{aligned} \theta + 50^{\circ} &= 90^{\circ} -\theta\\\theta + 50^{\circ} +\theta &= 90^{\circ} -\theta+\theta \\2 \theta+ 50^{\circ} -50^{\circ}&= 90^{\circ}\\2 \theta+ 50^{\circ} &= 90^{\circ} -50^{\circ}\\ 2 \theta&=40^{\circ}\\\theta&=20^{\circ}\end{aligned}[/tex]

Therefore, the value of θ is 20°.

We can conclude that the function f(x) = x² is increasing when x > 1.The given function is f(x) = x². You need to determine whether this function is increasing or decreasing when x > 1.

To do this, we can find the derivative of the function and evaluate it for x > 1.If the derivative is positive, then the function is increasing, and if it is negative, then the function is decreasing.

The derivative of the function f(x) = x² is given by:f '(x) = 2x

We can see that the derivative is always positive when x > 1, as 2x is always positive for x > 0.Therefore, we can conclude that the function f(x) = x² is increasing when x > 1.

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a. From the tribe's perspective, the expected cost of building the boat when the boat builders are drawn at random from the tribe is 975 fish.

The number of members who catch fish per day is equal to the number of members who catch fish per day, which means that half of the tribe has a higher opportunity cost than the other half.

The expected cost can be calculated by multiplying the number of workers who catch fish per day by the daily cost of their fishing and adding this to the number of workers who catch fish per day multiplied by their daily cost of fishing.
b. When members are selected based on opportunity cost, the minimum cost that the boat could be built for is 450 fish. The cost of building the boat is equal to the opportunity cost of the members who build it, which is the value of their next best alternative.

Since the boat builders are drawn from the tribe with half the members catching fish per day and the other half catching fish per day, the minimum cost would be equal to the opportunity cost of the members who catch fish per day since their cost is higher than the other half of the tribe who catch fish per day. Therefore, the minimum cost would be 450 fish.

Half of the members catch fish per day, and half of the members catch fish per day. Hence the total cost of building the boat would be the summation of the costs of the members in the group.

For instance, the expected cost of building the boat can be calculated by multiplying the number of workers who catch fish per day by the daily cost of their fishing and adding this to the number of workers who catch fish per day multiplied by their daily cost of fishing.
In this case, the expected cost would be the cost of ten members who build the boat. Since each member is expected to contribute to the building of the boat, the total cost will be calculated as the summation of the cost of the members, which equals 975 fish.

Therefore, from the tribe's perspective, the expected cost of building the boat when the boat builders are drawn at random from the tribe is 975 fish.
The opportunity cost of building the boat is the value of the next best alternative.

When members are selected based on opportunity cost, the minimum cost that the boat could be built for is the opportunity cost of the members who build it. In this case, the members are drawn based on their fishing cost, meaning members with the lowest opportunity cost would be selected to build the boat.

Therefore, the minimum cost would be equal to the opportunity cost of the members who catch fish per day since their cost is higher than the other half of the tribe who catch fish per day. Hence the minimum cost of building the boat would be 450 fish.

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The 9th term of the given sequence is 78732.

The given sequence is 12, 36, 108... is a geometric sequence with a common ratio of 3.To find the 9th term of the given sequence, we will use the formula for the nth term of a geometric sequence, which is given by:

aₙ = a₁rⁿ⁻¹

Here, a₁ = 12 and r = 3.

Therefore, the formula for the nth term becomes:

aₙ = 12(3)ⁿ⁻¹

Now, we need to find the 9th term of the sequence. Hence, n = 9. Substituting the values of a₁ and r, and n in the formula, we get:

a₉ = 12(3)⁹⁻¹= 12(3)⁸= 12(6561)= 78732

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Answer:

Step-by-step explanation:

Answer:

Bottom graph

Step-by-step explanation:

[tex]|4x+5|-7 > 12\\|4x+5| > 19\\\\4x+5 > 19\\4x > 14\\x > \frac{7}{2}\\\\4x+5 < -19\\4x < -24\\x < -6[/tex]

Therefore, the last graph is the correct answer

As we can see, this is the equation of line `g(x)` that passes through the points `(-4,0)` and `(-3,-2)`. Therefore, the value of `k` is `2`.

The correct answer to the given question is option d.

We have the function `g(x) = k⋅f(x)`. The values of `f(x)` and `g(x)` are given as follows:

Line `f(x)` passes through points `(-4,0)` and `(-3,1)`.

Line `g(x)` passes through points `(-4,0)` and `(-3,-2)`.

Now, we have to determine the value of `k`.

Formula to find slope of a line is given by:(y2 - y1)/(x2 - x1)

Here, (x1, y1) = (-4, 0) and (x2, y2) = (-3, 1) for line f(x).

So, slope of line `f(x)` is given by:(1 - 0)/(-3 - (-4)) = 1

So, equation of line `f(x)` is given by:

y - y1 = m(x - x1) ⇒ y - 0 = 1(x - (-4)) ⇒ y = x + 4

Also, (x1, y1) = (-4, 0) and (x2, y2) = (-3, -2) for line g(x).

So, slope of line `g(x)` is given by:(-2 - 0)/(-3 - (-4)) = 2

So, equation of line `g(x)` is given by: y - y1 = m(x - x1) ⇒ y - 0 = 2(x - (-4)) ⇒ y = 2x + 8

Now, we can substitute the value of `k` and the equation of line `f(x)` to find the equation of line `g(x)`.

Let `k = 2`.

Then, `g(x) = k⋅f(x) = 2(x + 4) = 2x + 8`.

As we can see, this is the equation of line `g(x)` that passes through the points `(-4,0)` and `(-3,-2)`.

Therefore, the value of `k` is `2`. Hence, option (d) is the correct answer: `2`.

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The correct option is that B. Selena is correct because she simplified correctly and then evaluated correctly after substituting the values for the variables.

Selena is correct. She simplified correctly and then evaluated correctly after substituting the values for the variables. Drake is incorrect because he should have simplified first, before substituting the values for the variables.

When Drake substituted the values for the variables first, he ended up with the expression (StartFraction negative 8 Over 4 Endfraction) Superscript negative 1. This is incorrect because he did not simplify the expression first. If he had simplified first, he would have gotten the expression (StartFraction negative 2 Over 1 Endfraction) Superscript negative 1, which is equal to one-half.

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Answer:

the value of c is 50°.

Step-by-step explanation:

To solve for the value of c in the equation (2c - 3)° = 97°, we can start by isolating the term with c.

First, we add 3 to both sides of the equation to get rid of the -3:

(2c - 3)° + 3 = 97° + 3

Simplifying the equation, we have:

2c° = 100°

Next, we divide both sides of the equation by 2 to solve for c:

(2c°)/2 = (100°)/2

Simplifying further, we have:

c° = 50°

Reason:

0.5% = 0.5/100 = 5/1000

or you could say

5/100 = 0.05 = 5%

Answer:

Y(0,13)

X(13,0)

When the Black-Scholes-Merton model is used  

the value of d1 is -0.0985,

the value of d2 is -0.2785,

the price of a call option is 2.9312,

and the price of a put option is 7.4279.

a) Calculation of the value of d1 in the Black-Scholes-Merton model:The formula to calculate the value of d1 is given by the expression:

d1=(ln⁡(S0/K)+(r+0.5σ2)T)/(σ√T)

Where,S0 is the current stock price,K is the strike price,r is the continuously compounded risk-free rate of return,σ is the annual volatility of the stock price, andT is the time to expiration of the option.

Using the above values, the value of d1 can be computed as:

d1=(ln⁡(85/90)+(0.06+0.5×0.18^2)×1)/(0.18×√1)=-0.0985

b) Calculation of the value of d2 in the Black-Scholes-Merton model:

The formula to calculate the value of d2 is given by the expression:d2=d1−σ√T

Using the above values, the value of d2 can be computed as:

d2=-0.0985−0.18×√1=-0.2785

c) Calculation of the price of a call option in the Black-Scholes-Merton model:

The formula to calculate the price of a call option is given by the expression:

C=S0N(d1)−Ke^(−rT)N(d2)

Where,C is the price of the call option,N(d) is the cumulative probability distribution function of the standard normal distribution evaluated at the value d.Using the above values, the price of a call option can be computed as:

C=85N(-0.0985)−90e^(−0.06×1)N(-0.2785)=2.9312

d) Calculation of the price of a put option in the Black-Scholes-Merton model:The formula to calculate the price of a put option is given by the expression:

P=Ke^(−rT)N(-d2)−S0N(-d1)

Where,P is the price of the put option, andN(d) is the cumulative probability distribution function of the standard normal distribution evaluated at the value d.

Using the above values, the price of a put option can be computed as:

P=90e^(−0.06×1)N(-(-0.2785))−85N(-(-0.0985))=7.4279

Therefore, the value of d1 is -0.0985, the value of d2 is -0.2785, the price of a call option is 2.9312, and the price of a put option is 7.4279.

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Answer:

x^2-5x-25 doesnt factorise im very sorry, maybe check ur question

The ordered pair which is not a solution to the inequality y - 3x < 10 is (-6,0).

Given the inequality in the question:

y - 3x < 10

Given the ordered pairs: (0,-4), (0,-1), and (-6,0). To determine which ordered pair is not a solution, we need to plug the values into the inequality and check.

For (0,-4):

y - 3x < 10

Plug in x = 0 and y = -4

-4 - 3(0) < 10

-4 < 10

True: -4 is less than 10.

For (0,-1):

y - 3x < 10

Plug in x = 0 and y = -1

-1 - 3(0) < 10

-1 < 10

True: -1 is less than 10.

For (-6,0):

y - 3x < 10

Plug in x = -6 and y = 0

0 - 3(-6) < 10

18 < 10

False: 18 is Not less than 10.

Therefore, (-6,0) is not a solution to the inequality.

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Answer:

(a)  start value = $45,000

(b)  4.6875 months exactly

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

Explanation

Part (a)

I'll use x in place of t, and y in place of 'a'. The reason for this will be mentioned in part (b)

The equation [tex]a = 45+75t-4t^2[/tex] turns into [tex]y = 45 + 75x - 4x^2[/tex] which rearranges to [tex]y = -4x^2+75x+45[/tex]

Let's plug in x = 0 so we can find the account value (variable y) at the very start.

[tex]y = -4x^2+75x+45\\\\y = -4*0^2+75*0+45\\\\y = 45\\\\[/tex]

The nice thing is any term involving x will go to zero, which leaves behind 45 at the end.

The initial value is $45,000. Recall that y is the value in thousands of dollars.

Think of it like saying 45*1000 = 45,000.

-------------------

Part (b)

The template for a general quadratic is [tex]y = ax^2+bx+c[/tex] which involves 'a', so that's why I swapped to x,y to avoid confusion.

That template is used to help complete the square to get a quadratic into vertex form.

Compare [tex]y = ax^2+bx+c[/tex] with [tex]y = -4x^2+75x+45[/tex] to find these values

Plug the first two items into the formula below

h = -b/(2a)

h = -75/(2*(-8))

h = 4.6875

This is the x coordinate of the vertex (h,k). It's the number of months it takes to reach the peak value.

-------------------

Extra info: If you plug x = 4.6875 back into the function, then you'll get y = 308.671875 which represents an account value of $308,671.88 (after rounding to the nearest penny). This is the investment's maximum value.

The correlation coefficient (r) between the number of plays and the number of passes completed by the top 30 college quarterbacks, using Excel, the correlation coefficient is approximately 0.83.

To calculate the correlation coefficient (r) between the number of plays and the number of passes completed by the top 30 college quarterbacks, you can use Excel. Here's a step-by-step guide:

Open Excel and enter the data for the number of plays in one column and the number of passes completed in another column. Ensure that the data is entered consistently, with the same row representing the same quarterback's data in both columns.

Select an empty cell where you want to display the correlation coefficient.

Use the CORREL function in Excel to calculate the correlation coefficient. The syntax for the CORREL function is: =CORREL(array1, array2). In this case, array1 represents the range of cells containing the number of plays, and array2 represents the range of cells containing the number of passes completed. For example, if the number of plays is in column A (A2:A31) and the number of passes completed is in column B (B2:B31), the formula would be: =CORREL(A2:A31, B2:B31).

Press Enter to calculate the correlation coefficient. The result will be displayed in the cell you selected.

Round the correlation coefficient to two decimal places using the ROUND function. The syntax for the ROUND function is: =ROUND(number, num_digits). In this case, number represents the correlation coefficient, and num_digits represents the number of decimal places to round to. For example, if the correlation coefficient is in cell C1, the formula would be: =ROUND(C1, 2).

By following these steps, you can use Excel to calculate the correlation coefficient (r) between the two data sets for the top 30 college quarterbacks.

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Trey must pay $2420 in income tax for last year.

Based on the tax rates, we'll divide his taxable income into two halves.

The first portion is the minimal amount of Trey's taxable income between $9500 and $20,000 that is subject to a 10% tax rate. Consequently, the first component is $9500.

The second portion is the amount over $9500, which is $20,000 - $9500 = $10,500.

Now, let's calculate the tax for each portion:

Tax on the first portion (10% rate) = $9500 * 0.10 = $950.

Tax on the second portion (14% rate) = $10,500 * 0.14 = $1470.

We sum up the taxes on both portions to find Trey's total income tax:

Total income tax = Tax on the first portion + Tax on the second portion = $950 + $1470 = $2420.

So, Trey must pay $2420 in income tax for last year.

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The true balance of the Ledger Control Account for January 2019 is $3,447,600 (debit).

To correct the Ledger Control Account for the month of January 2019, we need to analyze the given entries and make appropriate adjustments to arrive at the true balance.

Step 1: Analyzing the given entries

From the information provided, we can identify the following entries in the Ledger Control Account:

- Opening Balance (bf): $318,000 (debit)

- Purchases: $1,364,300 (debit)

- Cheques paid to creditors: $41,200 (credit)

- Purchases Returns: $31,000 (debit)

- Transfer from Sales Ledger: $31,000 (credit)

- Discount Received: $31,000 (credit)

- Closing Balance (c/d): $1,724,100 (debit)

Step 2: Adjusting the entries

To arrive at the true balance, we need to make adjustments for any errors or omissions in the given entries. Let's correct each entry:

- Opening Balance (bf) remains unchanged.

- Purchases: No adjustment needed.

- Cheques paid to creditors should be debited instead of credited. Adjust the entry to $41,200 (debit).

- Purchases Returns should be credited instead of debited. Adjust the entry to $31,000 (credit).

- Transfer from Sales Ledger should be debited instead of credited. Adjust the entry to $31,000 (debit).

- Discount Received should be debited instead of credited. Adjust the entry to $31,000 (debit).

- Closing Balance (c/d) remains unchanged.

Adjusted entries:

- Opening Balance (bf): $318,000 (debit)

- Purchases: $1,364,300 (debit)

- Cheques paid to creditors: $41,200 (debit)

- Purchases Returns: $31,000 (credit)

- Transfer from Sales Ledger: $31,000 (debit)

- Discount Received: $31,000 (debit)

- Closing Balance (c/d): $1,724,100 (debit)

Step 3: Calculating the true balance

To calculate the true balance, we need to sum up the debit and credit entries separately and find the difference:

Debit total: $318,000 + $1,364,300 + $41,200 + $31,000 + $31,000 + $1,724,100 = $3,509,600

Credit total: $31,000 + $31,000 = $62,000

True balance: Debit total - Credit total = $3,509,600 - $62,000 = $3,447,600 (debit)

Therefore, the true balance of the Ledger Control Account for January 2019 is $3,447,600 (debit).

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The solution to the equation is x = 61

From the question, we have the following parameters that can be used in our computation:

-3 + √(2x - 1) = 8

Add 3 to both sides of the equation

So, we have

√(2x - 1) = 11

Take the square of both sides

2x - 1 = 121

So, we have

2x = 122

Divide through by 3

x = 61

Hence, the solution is x = 61

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We know that the sum of the angles in triangle MLK is 180 degrees. Therefore, we can find the measure of angle KLM as follows:

m∠MLK + m∠KLM + m∠LMK = 180

130 + m∠KLM + m∠LMZ = 180

We also know that angles ZLK and MLZ are vertical angles, so they are congruent. Therefore:

m∠ZLK = m∠MLZ

x + 86 = x + 66

86 = 66

This is a contradiction, so there is no value of x that satisfies the given conditions. Therefore, we cannot find the measure of angle ZLK.

Evaluating  this function at  f(3) = 5.

To evaluate the function f(x) = (x + 2)/(4 - x) at x = 3, we substitute x = 3 into the function:

f(3) = (3 + 2)/(4 - 3)

    = 5/1

    = 5

Therefore, f(3) = 5.

Evaluating  this function at  f(3) = 5.

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Step-by-step explanation:

The only thing that changes is the 'y' coordinate ....it changes fro 0 to minus  9  ..... distance is then 9  units

The equations are R + P + D = 800, 3.5R + 4.25P + 4D = 2910 and R = P + D + 440

An equation is an expression that shows the relationship between two or more numbers and variables.

Let R represent the number of Regular gallons, P represent that of Premium and D represent that of Diesel.

A total of 800 gallons was sold, hence:

R + P + D = 800    (1)

Also:

$2910 was sold combined, therefore:

3.5R + 4.25P + 4D = 2910    (2)

440 more gallons of regular was sold, hence:

R = P + D + 440   (3)

The equations are R + P + D = 800, 3.5R + 4.25P + 4D = 2910 and R = P + D + 440

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The key differences between the graphs of a nonmember's and a member's yearly cost lie in the slope, y-intercept, and the overall rate of increase in cost as the number of game tokens purchased increases.

The given equations represent the yearly cost in dollars for a member and a nonmember at a video game arcade based on the total game tokens purchased.

For a member:

y = (1/10)x + 60x + 60

For a nonmember:

y = (1/5)x

To understand how the graph of a nonmember's yearly cost differs from a member's yearly cost, let's analyze the equations and their characteristics.

Slopes:

The slope of the member's equation is (1/10), indicating that for every unit increase in the number of game tokens purchased (x), the yearly cost (y) for a member increases by 1/10 of a dollar. This means that the member's yearly cost increases at a slower rate compared to the nonmember's yearly cost.

The slope of the nonmember's equation is (1/5), which means that for every unit increase in the number of game tokens purchased, the yearly cost for a nonmember increases by 1/5 of a dollar. Therefore, the nonmember's yearly cost increases at a faster rate compared to the member's yearly cost.

y-intercepts:

For the member's equation, the y-intercept is 60, which represents the fixed cost component for being a member of the arcade. This means that even without purchasing any game tokens (x = 0), a member incurs a yearly cost of $60.

For the nonmember's equation, there is no additional fixed cost component. The y-intercept is 0, indicating that a nonmember has zero yearly cost if no game tokens are purchased (x = 0).

Overall cost:

The member's equation includes both a fixed cost component and a variable cost component, whereas the nonmember's equation only includes the variable cost component. This means that for any given number of game tokens purchased, the member's yearly cost will be higher than the nonmember's yearly cost.

Graphically, the member's equation will result in a line with a positive slope that intersects the y-axis at 60. The nonmember's equation will yield a line with a steeper positive slope that intersects the origin (0,0). The graph of the nonmember's yearly cost will rise more quickly than the graph of the member's yearly cost.

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The value of (fog)(4) for the composition given is 48

Obtain the composition of the functions f and g by evaluating f(g(x)).

Evaluate g(x);

Here, g(4) becomes :

Evaluate f(g(x)) by making g(x) = 6

f(x) = x² + 2x

Inputting the values into the function :

Therefore, (fog)(4) = 48.

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