aahan has a job that guarantees him the same fixed salary increase every year. after 4 years, he makes $56,785; after 9 years, he makes $60,210. what is the equation of the line that would graph his salary over time?

The Area of the circle will be = is 144.87 [tex]cm^{2}[/tex]

Given in the question,

The sector of the circle has an area of = 121 [tex]cm^{2}[/tex]

The measure of an arc = is 36 inches.

According to the attached figure,

Let us consider the arc length = L

Let radius = r

As per the question L = 36'

Let the radius be

To calculate the length of the arc we need to use the formula,

L = r x θ

36 = r x θ

θ = [tex]\frac{36}{r}[/tex] degrees ------- equation 1

Now according to the area of the sector of the circle,

A = [tex]r^{2}[/tex] x θ / 2

121 = [tex]r^{2}[/tex] x θ / 2

[tex]r^{2}[/tex] = 2 x 121 / ( [tex]\frac{36}{r}[/tex] )

[tex]r^{2}[/tex] = [tex]\frac{2 * 121 * r}{36}[/tex]  ----- equation 2

r = [tex]\frac{2 * 121 }{36}[/tex]

r = 6.72 cm.

Now if the radius is = 6.72 cm

Diameter = 2 x radius

= 2 x 6.72

= 13.44 cm

Area of the circle = [tex]\pi r^{2}[/tex]

= [tex]\pi[/tex] x 6.72 x 6.72

= 144.87 [tex]cm^{2}[/tex]

Therefore, the area of the circle = is 144.87 [tex]cm^{2}[/tex]

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Step-by-step explanation:

A

for a linear function the slope ratio has to be the same between every pair of data points.

between (1, 4) and (2, 8) we have

x changes by +1 (from 1 to 2).

y changes by +4 (from 4 to 8).

the slope is

+4/+1 = 4

between e.g. (2, 8) and (3, 16) we have

x changes by +1 (from 2 to 3).

y changes by +8 (from 8 to 16).

the slope here is +8/+1 = 8.

which is not the same as 4.

so, it is not a linear function.

it is an exponential function.

B.

the function is actually

f(x) = y = 2^(x+1)

an exponential function is of the form

y = a^x

in our case we have

4 = a¹ = 2²

8 = a² = a¹×2 = 2² × 2 = 2^(2+1)

16 = a³ = a²×2 = a¹×2×2 = 2²×2×2

we see

f(n) = a1×2^(n-1) = 2²×2^(n-1) = 2^(n+1)

C.

the average rate of change is

(the difference of the function results at the interval ends) / (the difference of the interval ends).

so, in our case

(f(4) - f(2))/(4 - 2) = (32 - 8)/2 = 24/2 = 12

the average rate of change between stations 2 and 4 is 12 (or 12/1).

Answer:

Um in an old question of mine you said "its been forever". That was my elijahmiraclechild account. I don't really remember you but I would like to

Step-by-step explanation:

Using the roller coaster as an example, draw a right triangle.

Use h to symbolize the horizontal distance.

The following expression can be used to get h given that roller coaster serves as a representation of the hypotenuse side length.

30² = h² + 25².

Assemble similar phrases.

h² = 30² - 25².

horizontal separation

In (a), there is:

h² = 30² - 25².

This results:

h² = 275

Take both sides' roots.

h = 16.58

Consequently, 16.58 feet are the horizontal distance.

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Answer:

I tried as I can to solve it

One exponential function with the given features is y = 2^x - 3, and is graphed at the end of the answer.

An exponential function is defined as follows:

y = a(b)^x + c.

In which:

The graph of the function has a horizontal asymptote at y = -3, hence:

c = -3.

For a and b, they can assume any non-negative values, hence we attribute these following values:

a = 1, b = 2.

The graph is given at the end of the answer.

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The expression which has product of two binomials is (5-n)(n+7).

An expression is combination of variables, numbers and operators.

Binomials are expressions containing the sum (or difference) of two terms.

The expression (x + 3)(x + 2) is the product of two binomials.

(pq)(qp), (5-n)(n+7), 3x(2x+5), 6x-2y

(pq)(qp) is not the product of binomials because pq and qp are products.

3x(2x+5) is not the product of binomials because 3x is not a sum or difference.

6x-2y is also not because it is one binomial, not two multiplied together.

(5-n)(n+7) is the product of two binomials.

Hence, (5-n)(n+7) is the expression which has product of two binomials.

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It is approximately equal to 83.3%

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”

Given here, 5/6 thus in percentage terms it will be = 5/6 × 100

                                                                                    = 83.3%

Hence the answer is  83.3%

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Answer:

Step-by-step explanation:

Answer: 0.05

Step-by-step explanation:

The equation is k = y/x, which is a constant change rate

Take 5 divided by 100 = 0.05

5% = 0.05

So the constant of proportionality is 0.05

The linear functions defined in this problem are given as follows:

1. y = -x + 3.

2. y = x - 3.

3. y = 3x + 1.

4. y = -2x - 2.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

The coefficients and their meaning are given as follows:

From the second bullet point above,  the intercepts for each function in this problem are given as follows:

The slopes are given as follows:

The problem is incomplete, hence we just define the linear functions.

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The discount is $3.75 and the amount next week will be $21.25

This has to do with a percentage. A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this case, the pack of tomato plants costs $25. Next week, the plants are on sale for 15% off. Larissa wants to know the price of the tomato plants if she buys them next week.

The discount will be:

= 15% × $25

= $3.75

The amount next week will be:

= $25 - $3.75

= $21.25

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Answer:

554

Step-by-step explanation:

x + 2551 - 2551 = 3105 - 2551

x = 554

Answer:

[tex]x + 2551 = 3105 \\ x + 2551 - 2551 = 3105 - 2551 \\ x = 554[/tex]

Answer:

2(x+8)=126

Step-by-step explanation:

GD is the bisector of CGE and 126 and the angle CGE are equal

The solution is given as,
Two-digit  numbers                 Multiples of 3             Three-digit numbers
     30                                      3,30, 333,                            333    

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Place the given number in the appropriate place.
Numbers are 3, 30, 333, 3001,
Two digit number among the numbers = 30
Multiples of 3 among numbers = 30, 333, 3
Three-digit numbers among the numbers = 333

Thus, It is shown that the numbers are placed in their appropriate positions.

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Answer:

Yes, the lines are parallel. This is because the lines have the same slope. The slope of a line is a measure of how steep the line is, and it is calculated by taking the difference of the y-coordinates of two points on the line and dividing it by the difference of the x-coordinates of the same two points. In this case, the slope of line a is -1, and the slope of line b is also -1. Because the lines have the same slope, they are parallel to each other.

Answer:

t1/2=1m => 30days

A0=500g =0.5kg

t=8m = 240days

A=?

λ=ln2÷t1/2

λ=0.6931÷30

λ=0.0231033333

A=A0×e^-λ×t

A=0.5×e^-0.0231033333×240

A=1.953125grams

Answer:

Your answer should be [tex]\frac{\pi }{7}[/tex]

Step-by-step explanation:

Looking at the x-axis we can say that is our b.

Period Formula: 2π/b.

x-axis is from 0 to 20.

b = 14 because of the rise to rise.

2π/14 = π/7

When the spring is stretched and the distance from point a to point b is 5.3 feet, the value of θ is 53.13  degrees

The distance between point a to point b = 5.3 feet

The length of the top side = 3 feet

Therefore, it will form a right triangle

Here we have to use trigonometric function

Here adjacent side and the hypotenuse of the triangle is given

The trigonometric function that suitable for the given conditions is

cos θ = Adjacent side / Hypotenuse

Substitute the values in the equation

cos θ = 3 / 5

θ = cos^-1(3 / 5)

θ = cos^-1(0.6)

θ = 53.13 degrees

Therefore, the value of θ is 53.13  degrees

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Answer:

(8.25, 9.75)

Step-by-step explanation:

To find the point that is ¼ of the distance from A to D, we first need to find the coordinates of D. Since A is located at the point (3, 7) and D is located at the point (11, 11), we can use the distance formula to find the distance between these two points. The distance formula is given by:

distance = √((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, we have x1 = 3, y1 = 7, x2 = 11, and y2 = 11, so the distance between A and D is:

distance = √((11 - 3)^2 + (11 - 7)^2) = √(8^2 + 4^2) = √(64 + 16) = √80 = 8.944

Now that we know the distance between A and D, we can use this information to find the point that is ¼ of the distance from A to D. Since C is ¼ of the distance from A to D, it is located ¼ of the way along the line between A and D. This means that we can find the coordinates of C by taking the average of the coordinates of A and D, weighted by ¼ and ¾, respectively. In other words, the coordinates of C are given by:

C = ¼ * A + ¾ * D

where A and D are the coordinates of points A and D, respectively. Plugging in the coordinates of A and D, we get:

C = ¼ * (3, 7) + ¾ * (11, 11) = (0.75 * 3 + 2.25 * 11, 0.75 * 7 + 2.25 * 11) = (8.25, 9.75)

Therefore, the point C is located at the coordinates (8.25, 9.75).

there are 10 clubs on campus. how many ways are there if you want to choose 3 student clubs out of 10 to join is 120

A fractional factorial experiment utilizes subset of combinations that are gotten from the full factorial experiment. They are applicable when there are too many inputs to screen practically or cost or time would be excessive.

Also, using the fractional factorial experiment makes running the experiments faster and cheaper.

10C3 = 10! / (7!*3!)

        = 10*9*8/6

        = 120

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Answer:

The value of n in this equation is 5.

Step-by-step explanation:

This can be determined by using the property of exponents that states that x^n * x^m = x^(n+m). In this case, 10^n * 10^5 = 14,521, so 10^(n+5) = 14,521. Solving for n, we get n = 5.

A sampling error is the difference between a population parameter and a sample statistic.

Parameters are numbers that describe the properties of entire populations. Statistics are numbers that describe the properties of samples. For example, the average income for the United States is a population parameter. Conversely, the average income for a sample drawn from the U.S. is a sample statistic. The difference between a parameter vs a statistic is that a parameter is a fixed measure describing the whole population, while a statistic is a characteristic of a sample, a portion of the target population.

Thus, the difference is defined as sampling error.

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The range of the given function in the figure is R - {0, 1, 2, 3}.

The given mapping shows a function f(x).

There are 4 inputs to the function and 5 outputs.

So, the domain set for the given function is written as D = {0, 5, 10, 15}

And the range set for the given function is written as R = {0, 1, 2, 3}

(Since the 5th output is repeating, in the range it is considered only once).

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if there are 720 different classes in one quarter at time, each in its own room, different rooms will be required 720 rooms.

To answer this question, we need to understand that each class needs its own room. Therefore, the number of rooms required will be equal to the number of classes. In this case, there are 720 different classes in one quarter, so 720 different rooms will be required. Each room can accommodate one class at a time, so the total number of rooms needed is 720.

Number of Classes = 720

Number of Rooms Required = Number of Classes = 720

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Answer:

70.5%

Step-by-step explanation:

If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:

[tex]\large\boxed{X \sim\text{N}(\mu,\sigma^2)}[/tex]

Given:

Therefore, if the weights of the 12-month-old baby boys are normally distributed:

[tex]\boxed{X \sim\text{N} \left(22.5,2.2^2 \right)}[/tex]

where X is the weight of the baby boy.

To find the percentage to the nearest tenth of 12-month-old baby boys who weigh between 19.7 and 24.4 pounds find P(19.7 ≤ X ≤ 24.4).

Calculator input for "normal cumulative distribution function (cdf)":

[tex]\implies \text{P}(19.7 \leq X \leq 24.4)=0.704548741[/tex]

[tex]\implies \text{P}(19.7 \leq X \leq 24.4)=70.5\%[/tex]

Therefore, the percentage of 12-month-old baby boys who weigh between 19.7 and 24.4 pounds is 70.5% (nearest tenth).

The fit statistic that can be used across different series that are in fact measured in different units is; MAPE

There are different statistics models in this regards such as;

Mean Absolute Error (MAE)

Mean Absolute Scaled Error (MASE)

Accuracy Percent (Accuracy %)

Mean Squared Error (MSE)

Root Mean Squared Error (RMSE)

Mean Absolute Percent Error (MAPE)

Now, we are told that we need the fit statistic that can be used across different series that are in fact measured in different units.

The correct one will be Mean Absolute Percent Error (MAPE) because the average absolute percent difference between the values that are fitted by the model and the observed data values.

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Answer:

29=n/3

Step-by-step explanation:

Answer:

29 = n/3

Step-by-step explanation:

[tex]29 = \frac{1}{3} of \: n \\ 29 = \frac{1}{3} \times n \\ 29 = \frac{n}{3} [/tex]

Probability of the person has the diseases and the test result is positive = 1/90 = 0.011

Probability  refers to the possibility of occurring a certain event. It is expressed by the ratio of the number of favorable outcome to the total possible outcome.

Given, percentage of people who have disease and test result positive =90

percentage of people who has not disease but test result positive =3.1

Suppose 6.0 percent of population are infected

Now, probability of a  randomly selected person  who has diseases and test positive

                          = 1/90

                       =   0.011

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The time presently is 8:15 a.m, and the rocket will launch in 3.75 hours, at 11:20 a.m.

Subtraction (represented by the minus sign) is one of four mathematical operations, the others being addition, multiplication, and division. Subtraction is the procedure of removing items from a collection. Subtraction may be thought of as the inverse of addition. Counting forwards helps children learn to add. To subtract, they just count backwards.

Here,

launch time=11:20 am

time left to launch=3.75 hour

=0.75*60

=45 minutes

= 3 hours 45 minutes

=11 hours 20 minutes-3 hours 45 minutes

=8 hours 15 minutes

=8:15 AM

The time right now is 8:15 AM when rocket will launch in 3. 75 hour and the launch time is 11:20 am.

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