Find two acute angles that satisfy the equation sin(3x + 9) = cos(x + 5). check that your answers make sense.

The value of ∠APB = 180°. It is a straight line.

Given the information, we can deduce that the line passing through the center O of circle C2 and point A also passes through point B, as AB is the intersection of the two circles.

Now, consider the line segment AP. Since PAT is tangent to circle C1 at point A, we know that ∠APT = 90°. Additionally, since AB is a diameter of circle C1, we know that ∠ABP = 90°.

Using these angles, we can see that ∠APB is equal to the sum of ∠APT and ∠ABP. Therefore,

∠APB = ∠APT + ∠ABP = 90° + 90° = 180°.

So, we have shown that ∠APB is a straight line.

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The estimate for f(3.1, -3.01) using the linear approximation is approximately -54.28.

a. To find the linear approximation of f(x,y) at the point (3,-3), we need to find the gradient of the function at that point.

∇f(x,y) = [-8x, 4y]

So, at the point (3,-3), the gradient is ∇f(3,-3) = [-24, -12].

The linear approximation is given by:

L(x,y) = f(3,-3) + ∇f(3,-3)·(x-3,y+3)

Plugging in the values, we get:

L(x,y) = -4(3)^2 + 2(-3)^2 - 24(x-3) - 12(y+3)

Simplifying, we get:

L(x,y) = -12x - 4y - 36

b. To estimate f(3.1, -3.01) using the linear approximation, we plug in the values into the equation we found in part (a):

L(3.1, -3.01) = -12(3.1) - 4(-3.01) - 36

L(3.1, -3.01) ≈ -54.28

Therefore, the estimate for f(3.1, -3.01) using the linear approximation is approximately -54.28.

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The expected population proportion,  with 95% confidence, that prefers to shop at places with loyalty cards is between 54.6% and 61.4%.

Based on the survey results, we know that 58% of the sample respondents prefer to shop at places with loyalty cards. If the margin of error is 3.4%, we can calculate the expected range of the population proportion as follows:

Upper bound: 58% + 3.4% = 61.4%
Lower bound: 58% - 3.4% = 54.6%

Therefore, we can say with 95% confidence that the expected population proportion that prefers to shop at places with loyalty cards is between 54.6% and 61.4%.

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Answer: C

Step-by-step explanation:

4.20 cm² is the area of the triangle STU to the nearest 10th of a square centimeter.

Given, t = 3.4 cm, u = 6.9 cm and ∠S = 21°

We know that the formula for the area of the triangle = 1/2 * t*u *sin(S)

Substituting the values

Area = 1/2 × 3.4 × 6.9 × sin(21°)

Area = 11.73 × sin(21°)

Area = 11.73 ×  0.3583

Area = 4.2016

Rounding to the nearest 10th of a square centimeter .

Area = 4.20 cm²

Hence, 4.20 cm² is the area of the triangle STU to the nearest 10th of a square centimeter.

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The probability of selecting 2 silver rings or 2 gold rings is 3/28.

To find the probability of selecting 2 silver rings or 2 gold rings, we need to find the probability of each event separately and then add them.

Probability of selecting 2 silver rings:

There are 4 silver rings out of 9 total, so the probability of selecting a silver ring on the first draw is 4/9. After the first ring is selected, there are 3 silver rings left out of 8 total, so the probability of selecting a second silver ring is 3/8. Finally, after two silver rings have been selected, there are 2 silver rings left out of 7 total, so the probability of selecting a third silver ring is 2/7. Therefore, the probability of selecting 2 silver rings is:

(4/9) * (3/8) * (2/7) = 24/504 = 1/21

Probability of selecting 2 gold rings:

Similarly, there are 5 gold rings out of 9 total, so the probability of selecting a gold ring on the first draw is 5/9. After the first ring is selected, there are 4 gold rings left out of 8 total, so the probability of selecting a second gold ring is 4/8 = 1/2. Finally, after two gold rings have been selected, there are 3 gold rings left out of 7 total, so the probability of selecting a third gold ring is 3/7. Therefore, the probability of selecting 2 gold rings is:

(5/9) * (1/2) * (3/7) = 15/126 = 5/42

Adding the probabilities of selecting 2 silver rings or 2 gold rings, we get:

P(2 silver or 2 gold) = P(2 silver) + P(2 gold) = 1/21 + 5/42 = 3/28

Therefore, the probability of selecting 2 silver rings or 2 gold rings is 3/28.

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The equation of the line that passes through (1, 2) and (a) having a slope of 2/3 is y = (2/3)x + 4/3, (b) Having an undefined slope is x = 1, (c) having slope m = 0 is y = 2 (d) point (2, 3) also lies on the line is y = x + 1.

a) To find the equation of a line with slope 2/3 passing through (1,2), we can use the point-slope formula:
y - y1 = m(x - x1)
Substituting in the values we know, we get:
y - 2 = (2/3)(x - 1)
Expanding and simplifying:
y = (2/3)x + 4/3
So the equation of the line is y = (2/3)x + 4/3.

b) To find the equation of a line with an undefined slope passing through (1,2), we know that this line must be vertical. The equation of a vertical line passing through (1,2) can be written as:
x = 1

So the equation of the line is x = 1.

c) To find the equation of a line with slope m=0 passing through (1,2), we know that this line must be horizontal. The equation of a horizontal line passing through (1,2) can be written as:
y = 2
So the equation of the line is y = 2.

d) To find the equation of a line passing through (1,2) and (2,3), we can use the point-slope formula again:
y - y1 = m(x - x1)
Substituting in the values we know, we get:
y - 2 = (3 - 2)/(2 - 1)(x - 1)
Simplifying:
y - 2 = 1(x - 1)
y - 2 = x - 1
y = x + 1
So the equation of the line is y = x + 1.

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Answer:

E,F,H

Step-by-step explanation:

Answer:

B = 2 (could be 4, like with this font)

E = 4

F = 3

H = 4

P = 0 (could be 3, like this this font)

R = 0 (could be 3, like with this font)

X = (could be 4)

Other right angles:

D = 0 (could be 2, like with this font)

L = 1

T = 2

Y = (could be 1)

Answer:  x = ± [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Equation:

4x² + 10 = 11         > bring everything over to other side

                            > first subtract 10 from both sides

4x² = 1                   > Divide by 4 on both sides

x² =  [tex]\frac{1}{4}[/tex]                    >Take square root of both sides

                             > When you take square root there is a ±

x = ±  [tex]\sqrt{(\frac{1}{4} )}[/tex]           > take the square root of both top and bottom

x = ± [tex]\frac{1}{2}[/tex]

The average amount of books read per student according to the histogram is given as follows:

1.27 books.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

The histogram shows the number of times for each observation, hence:

Hence the mean is calculated as follows:

M = (7 x 0 + 9 x 1 + 6 x 2 + 4 x 3)/(7 + 9 + 6 + 4) = 1.27 books.

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The value of x to the nearest tenth is 1.4

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

Sin(θ) = opp/hyp

cos(θ)= adj/hyp

tan( θ) = opp/adj

x is opposite side to angle F and 32 is adjascent to angle F.

therefore;

tan F = opp/adj

tan23 = x/3.2

x = tan23 × 3.2

x = 1.4

therefore the value of x to the nearest tenth is 1.4

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Kira planted 9/35 acres with corn.

To find out how many acres planted with corn, we first need to understand that the total amount of land she had was 3/5 acres. Then, we know that she planted 3/7 of her land with corn.

To calculate the area planted with corn, we multiply the total area of her land (3/5 acres) by the fraction that represents the portion she planted with corn (3/7). This gives us:

(3/5) x (3/7) = 9/35 acres

Therefore, Kira planted 9/35 acres of her land with corn.

We can simplify the fraction by dividing both the numerator and the denominator by their greatest common factor, which is 3 in this case. This gives us:

(9/3) / (35/3) = 3/11 acres

So, Kira planted approximately 0.26 acres with corn.

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Based on the given information that angles a and d are equal, the value of x is determined to be -6.

To find the value of x in the given scenario, we can equate the measures of the angles using the given information:

m< a = 3x

m< d = 4x + 6

Since angles a and d are stated to be equal, we can set up the equation:

3x = 4x + 6

To solve for x, we subtract 3x from both sides:

0 = x + 6

Next, we subtract 6 from both sides:

-6 = x

Therefore, the value of x is -6.

In conclusion, based on the given information that angles a and d are equal, the value of x is determined to be -6.

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You bought 8 stamps that cost 45 cents each and 2 stamps that cost 30 cents each.

Let's assume you bought x stamps that cost 45 cents each and y stamps that cost 30 cents each.

From the given information, we can create two equations:

The total number of stamps is 10: x + y = 10.

The total cost is $4.20: 45x + 30y = 420 (since the cost is given in cents).

Now we can solve this system of equations to find the values of x and y.

We can multiply the first equation by 30 to eliminate y:

30x + 30y = 300.

Now we have a system of equations:

30x + 30y = 300,

45x + 30y = 420.

Subtracting the first equation from the second equation, we get:

45x + 30y - (30x + 30y) = 420 - 300,

15x = 120,

x = 120/15,

x = 8.

Substituting the value of x back into the first equation:

8 + y = 10,

y = 10 - 8,

y = 2.

Therefore, you bought 8 stamps that cost 45 cents each and 2 stamps that cost 30 cents each.

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1. An equation representing the number (N) of novels Deshaun needs to read in M months is N = 3M.

2. Based on the above equation, Deshaun needs to read 57 novels in 19 months.

An equation is a mathematical statement that shows the equality or equivalence of mathematical expressions.

While mathematical expressions combine variables with numbers, constants, and values using mathematical operands, equations use the equal symbol (=) in addition.

The number of novels Deshaun needs to read per month = 3

The number of months involved = 19 months

Let the number of novels Deshaun needs to read in M months = N

Let the number of months involved = M

N = 3M

N = 57 (3 x 19)

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The amount of money earned over a period of time is called 3. Income

Income refers to the money you receive from various sources such as salary, wages, investments, or any other means during a specific period of time.

Income is a fundamental concept in finance and accounting. It represents the inflow of money or economic benefits received by an individual, household, or organization.

It is typically measured and reported on a periodic basis, such as monthly, quarterly, or annually. Income can be derived from various sources, including salaries and wages, interest and dividends, rental income, profits from business activities, and capital gains.

It is an essential component in assessing an individual's or organization's financial health and is often used to calculate taxes, budgeting, and determining net worth. Understanding and effectively managing income is crucial for individuals and businesses to meet their financial goals and sustain their economic well-being.

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The table of values in a graph for fabian's income in expenses is

n            E(n)

0           825

1            828.25

2           831.5

4          838

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

The expenses E to make n cakes per month is given by the equation

E = 825 + 3.25n

Next, we assume values for n and calculate E

Using the above as a guide, we have the following:

E = 825 + 3.25(0) = 825

E = 825 + 3.25(1) = 828.25

E = 825 + 3.25(2) = 831.5

E = 825 + 3.25(4) = 838

So, we have

n            E(n)

0           825

1            828.25

2           831.5

4          838

This represents the table of values

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Let's denote the total distance traveled by the object as `d` and time as `t`.

We can use the given information to set up a system of equations:

When t = 10.0 seconds, d = 50.0 meters

50.0 = a(10.0)^2 + b(10.0) + c         (Equation 1)

When t = 20.0 seconds, d = 200.0 meters

200.0 = a(20.0)^2 + b(20.0) + c          (Equation 2)

When t = 0 seconds, d = 0 meters

0 = a(0)^2 + b(0) + c           (Equation 3)

Simplifying Equation 3, we get c = 0.

Substituting c = 0 in Equations 1 and 2, we get:

50.0 = 100a + 10b               (Equation 4)

200.0 = 400a + 20b              (Equation 5)

We can solve Equations 4 and 5 simultaneously to get the values of `a` and `b`:

From Equation 4, we get:

10b = 50 - 100a

b = 5 - 10a

Substituting this value of `b` in Equation 5, we get:

200.0 = 400a + 20(5 - 10a)

200.0 = 400a + 100 - 200a

200.0 = 200a + 100

100.0 = 200a

a = 0.5

Substituting this value of `a` in Equation 4, we get:

50.0 = 100(0.5) + 10b

50.0 = 50 + 10b

b = 0

Therefore, the quadratic function that models the total distance traveled by the object is:

[tex]d = 0.5t^2[/tex]

To find the total distance traveled by the object after 30.0 seconds, we can substitute `t = 30.0` in the above equation:

[tex]d = 0.5(30.0)^2[/tex]

d = 450.0 meters

Therefore, the object will travel a total distance of 450.0 meters after 30.0 seconds.

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A collection of information, such as numbers, measurements, or observations, is commonly referred to as data.

Data can be collected from a wide variety of sources, such as surveys, experiments, or observations, and can be analyzed to reveal patterns, trends, and relationships.

Data can be represented in many different ways, including tables, graphs, charts, or statistical summaries, and can be used to make informed decisions in a wide range of fields, including business, science, healthcare, and social sciences.

However, it is important to ensure that the data is accurate, reliable, and unbiased, and that appropriate statistical methods are used to analyze and interpret it.

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Full Question: What is a collection of information such as number measurement or observation called?

A graph of polygon GREAT and its image after a counterclockwise rotation of 90° around the origin is shown in the image attached below.

In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

By applying a rotation of 90° counterclockwise around the origin to vertices W, the coordinates of the vertices of the image ΔA'B'C' are as follows:

(x, y)                               →            (-y, x)

Ordered pair G = (-3, -2) → Ordered pair G' = (2, -3)

Ordered pair R = (-4, 4) → Ordered pair R' = (-4, -4)

Ordered pair E = (0, 1) → Ordered pair E' = (-1, 0)

Ordered pair A = (1, -2) → Ordered pair A' = (2, 1)

Ordered pair T = (-1, -3) → Ordered pair T' = (3, -1)

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The equation y=1/2x can be graphed using either number graph or the slope-intercept form. In either case, the result is a straight line that passes through the same points.

In mathematics, a graph is a visual representation of a mathematical relationship. The equation y=1/2x ​is a linear equation, which means that it describes a straight line. This equation can be graphed using the number graph.

To graph the equation y=1/2x, one must first plot points on the graph. To do this, one can use the given equation to calculate the x and y values of the points. For example, if x is equal to 1, then y is equal to 1/2. Therefore, the point (1, 1/2) can be plotted on the graph. This process can be repeated for other values of x, such as 2, 3, and 4. The result is a straight line that passes through the points (1, 1/2), (2, 1), (3, 1 1/2), and (4,2).

The equation y=1/2x can also be graphed using the slope-intercept form of the equation. This form of the equation is written as y=mx + b, where m is the slope of the line and b is the y-intercept. For the equation y=1/2x, the slope is 1/2 and the y-intercept is 0. To graph the line, one must first plot the y-intercept, which is the point (0,0). Then, one must calculate the slope and draw a line through (0,0) in the direction of the slope. The result is a straight line that passes through the points (0, 0), (1, 1/2), (2,1), (3, 1 1/2), and (4, 2).

In conclusion, the equation y=1/2x can be graphed using either number graph or the slope-intercept form. In either case, the result is a straight line that passes through the same points.

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The slope-intercept form or a number graph can both be used to visualise the equation y=1/2x. The outcome is a straight line that goes through the same spots in both scenarios.

A graph in mathematics is a picture of a mathematical connection. A linear equation is one that describes a straight line, such as y=1/2x. The number graph can be used to graph this equation.

The graph must first have points drawn on it before the equation y=1/2x can be graphed. To do this, one can compute the x and y values of the points using the above equation. For instance, y is equal to 1/2 if x is equal to 1. As a result, the graph's point (1, 1/2) can be drawn. You can repeat this procedure for x values of 2, 3, and 4. Consequently, a straight line that traverses the coordinates (1, 1/2), (2, 1), (3, 1 1/2),and (4,2).

The slope-intercept form of the equation can also be used to graph the equation y=1/2x. Y=mx + b, where m is the line's slope and b is its y-intercept, is how this form of the equation is expressed. The slope and y-intercept of the equation y=1/2x are 1/2 and 0, respectively.

Plotting the y-intercept, or the point, is required before the line can be graphed. (0,0). The next step is to determine the slope and draw a line through (0,0) in the slope's direction. A straight line is created as a result, passing through the points (0, 0), (1, 1/2), (2, 1), (3, 1 1/2), and (4, 2).

In conclusion, the slope-intercept form or a number graph can both be used to graph the equation y=1/2x. The outcome is a straight line that goes through the same spots in both scenarios.

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Hello!

In this question, we are asked to find which set of points are solutions to our equation: 7x + 4y = -23

In order to find which points are solutions to our equation, we will plug the values into our equation and solve. If both sides of the equation are equal, the point will be a solution.

Note: Our coordinate point is in the format of (x,y), so we will plug in the values according to its variable.

Solve:

(-1,-4):

Plug in coordinate.

7(-1) + 4(-4) = -23

Simplify.

-7 - 16 = -23

-23 = -23

Since it is equal, (-1,-4) is a solution.

(2,6):

Plug in coordinate.

7(2) + 4(6) = -23

Simplify.

14 + 24 = -23

38 = -23

Since it is not equal, making it false, (2,6) is not a solution.

(-5,3):

Plug in coordinate.

7(-5) + 4(3) = -23

Simplify.

-35 + 12 = -23

-23 = -23

Since it is equal, (-5,3) is a solution.

(6,-7):

Plug in coordinate.

7(6) + 4(-7) = -23

Simplify.

42 - 28 = -23

14 = -23

Since it is not equal, making it false, (6,-7) is not a solution.

Answer:

The solutions to the equation are: (-1,-4) and (-5,3).

The z scοre is negative the actual probability would be

1-0.7995 = 0.2005

What is the probability?

A number that expresses hοw likely it is that an event will occur is called the probability of οccurrence. It is written as a number from 0 to 1, or frοm 0% to 100%, in percentage notation. The probability of an event occurring increases with probability.

here,

mean = 20.20

standard deviatiοn = 2.60

we knοw that,

Z scοre = (X-mean)/standard deviation

fοr X = 18:

Z scοre = (18-20.20)/2.6 = -0.8461

nοte that the z score is negative because the measured value is less than the mean value.

fοr Z score 0.8461 probability is 0.7995

and since the z scοre is negative the actual probability would be

1-0.7995 = 0.2005

a. For nοt within 1 hour of the population mean

We apply the formula here and we get the value οf P.

P(19.20>x>21.20) = P(19.20-20.20/2.60√18) > X-μ/σ√n >21.20-20.20/2.60√18

P(19.20>x>21.20) = P(-1.63>z>1.63)

Now, we find the value οf z.

P(19.20>x>21.20) = P(z>1.63) + P(z<-1.63)

P(19.20>x>21.20) = 0.0516 + 0.0516

P(19.20>x>21.20) = 0.1032

b. Fοr 20. 0 to 20. 5 hours

P(20<x<20.5) = P(20-20.20/2.60√18) < X-μ/σ√n<20.50-20.20/2.60√18

P(20<x<20.5) = P(-0.33<z<0.49)

Nοw, we find the value of the z-score and we get

P(20<x<20.5) = P(z<0.49) - P(z<-0.33)

P(20<x<20.5)  = 0.6879 - 0.2707

P(20<x<20.5)  = 0.3172

c. Fοr at least 22 hours

We apply the t-test fοrmula here and we get

P(x≥22) = P(X-μ/σ√n≥22-20.20/2.60√18)

Nοw, we find the value of z.

P(x≥22) = P(z≥2.94)

P(x≥22) = 0.0016

d. Fοr not more than 21 hours.

P(x<21) = P(X-μ/σ√n<21-20.20/2.60√18)

We find here the value οf P for x<21 and we get

P(x<21) = P(z<1.31)

Now, we find the value οf the z- score.

P(x<21) = 0.9049

Hence, a. 0.1032

b.  0.3172

c. 0.0016

d. 0.9049

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Complete question is,

Among college students who hold part-time jobs during the school year, the distribution of the time spent working per week is approximately normally distributed with a mean of 20.20 hours and a standard deviation of 2.60 hours. Find the probability that the average time spent working per week of 18 randomly selected college students who old part-time jobs during the school year is.

There would be 14 stars that this equation predicts Ayana will have at the end of level 10.

In this question, we are given an equation for the line of best fit relating the level, x, to the number of stars, y. The equation is y = (3/2)x - 1.

To find the predicted number of stars at the end of level 10, we need to substitute x = 10 into the equation and solve for y.

y = (3/2)x - 1

y = (3/2)(10) - 1

y = 15 - 1

y = 14

Therefore, the equation predicts that Ayana will have 14 stars at the end of level 10.

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If you let z be a random variable with a standard normal distribution, the indicated probability is 0.0793. So, the probability P(z ≥ 1.41) = 0.0793

To find the probability P(z ≥ 1.41) for a standard normal distribution, you can use a Z-table or calculator to find the area to the right of z = 1.41.

Using a Z-table or calculator, you will find the value of P(z ≥ 1.41) is approximately 0.0793. So, the probability P(z ≥ 1.41) = 0.0793. Remember to round your answer to four decimal places.

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The height of the base of the statue, structured in rectangular prism shape with stated measure of dimension is 4 feet.

The volume of the rectangular prism will be given by the formula -

Volume = length × width × height

Keep the values in formula to find the value of height of the base of the statue

60 = 5 × 3 × height

Rearranging the equation in terms of height

Height = 60 × (5 × 3)

Multiplying the denominator on Right Hand Side

Height = 60/15

Divide the values

Height = 4

Hence the height is 4 feet.

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The  function f(x)=500[tex]x^2[/tex] +10,000  can  be  used  to  model  the  food  vendor's  annual  revenue. The  food  vendor  would expect  to  bring  in  $ 60,000  in  annual  revenue by 10 years from now.

To find out when the mobile food vendor should expect to bring in $60,000 in annual revenue using the function f(x) = 500x^2 + 10,000, follow these steps:

1. Set the function equal to 60,000: 500[tex]x^2[/tex]+ 10,000 = 60,000
2. Subtract 60,000 from both sides of the equation: 500[tex]x^2[/tex]+ 10,000 - 60,000 = 0
3. Simplify the equation: 500[tex]x^2[/tex]- 50,000 = 0
4. Divide both sides by 500:[tex]x^2[/tex] - 100 = 0
5. Add 100 to both sides: [tex]x^2[/tex] = 100
6. Find the square root of both sides: x = ±10

Since it doesn't make sense to have a negative number of years, the food vendor should expect to bring in $60,000 in annual revenue 10 years from now.

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All of the unit rates that are equivalent to the speed of the model airplane are 22 feet per second, 1320 feet per minute, and 0.25 miles per minute.

To calculate the speed of the model airplane, we need to use the formula:

Speed = Distance / Time

Given that the distance covered by the model airplane is 330 feet, and the time taken is 15 seconds, we can substitute these values in the above formula to get:

Speed = 330 feet / 15 seconds

Simplifying this, we get:

Speed = 22 feet per second

To convert this unit rate to other equivalent unit rates, we need to use conversion factors. For example, to convert feet per second to feet per minute, we can multiply the unit rate by 60 (since there are 60 seconds in a minute):

22 feet per second x 60 seconds per minute = 1320 feet per minute

Similarly, to convert feet per minute to miles per minute, we can use the conversion factor 1 mile = 5280 feet:

1320 feet per minute / 5280 feet per mile = 0.25 miles per minute

Therefore, all of the unit rates that are equivalent to the speed of the model airplane are 22 feet per second, 1320 feet per minute, and 0.25 miles per minute.

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The average rate of change of g(x) from x = 1 to x = 6 is 7

The average rate of change of a function over an interval is given by the difference in the values of the function at the endpoints of the interval, divided by the length of the interval.

In this case, we want to find the average rate of change of g(x) = 2x² - 7x from x = 1 to x = 6.

The value of g(x) at x = 1 is:

g(1) = 2(1)² - 7(1) = -5

The value of g(x) at x = 6 is:

g(6) = 2(6)² - 7(6) = 30

So the difference in the values of g(x) is:

g(6) - g(1) = 30 - (-5) = 35

The length of the interval is:

6 - 1 = 5

Therefore, the average rate of change of g(x) from x = 1 to x = 6 is:

Rate = 35/5

Evaluate

Rate = 7

So, the rate is 7

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The average rate of change is 7.

We know that,

The average rate of change = (final value - initial value)/change in the value of x.

Now,

The given function is,

g(x)=2x²-7x

The initial value of x is 1 (given)

∴ The initial value of the function g(x), at x=1,

g(1)=2(1)²-7(1)=2-7

or, g(1)= -5

Now, the final value of x is 6,

∴ Finding the final value of the function g(x) at x=6,

i.e, g(6)=2(6)²-7(6)

or,  g(6)=72-42 = 30

∴ The change in the value of function g(x), from x= to x=6,

= g(6)-g(1)

= 30-(-5)

= 35

Now, change in the value of x = 6-1=5

∴ The average rate of change = 35/5 = 7

Hence the average rate of change is 7.

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Carl pays his broker a total of $200 in fees for the 40 trades he made during the year.

To calculate how much Carl pays his broker, we need to first determine how many trades he made in a year. Looking at the table, we can see that Carl made a total of 40 trades - 20 buys and 20 sells. Since each trade incurs a $5 charge, we can multiply the number of trades by the cost per trade to get the total amount paid to the broker.

40 trades x $5 per trade = $200 paid to the broker in a year

It's important to note that transaction costs can have a significant impact on investment returns, especially for small accounts, so it's important to consider these costs when making investment decisions. Some brokers may offer lower transaction fees or other incentives to attract clients, so it's worth shopping around and comparing fees before choosing a broker. Additionally, it may be more cost-effective to use a robo-advisor or invest in index funds or exchange-traded funds (ETFs) that have lower fees compared to actively managed funds.

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