Confused!! Please answer!!

A quadratic function f models the predicted population growth in Town F after x years. An exponential function g models the predicted population growth in Town G after x years. Use the table to compare the average rate of change for each function from x = 1 to x = 3. Which function has a greater average rate of change over this interval? Enter either f or g in the box.

mean marks of 100 students was 40.. It was discovered that 53 was misread as 83. Find the actual mean.

Total mean score = 40

\(mean \: = \frac{sum \: of \: observation}{number \: of \: observations} \)

sum of observations

= mean × no of observations

= 40×100

= 4000

After the replacement, sum of new observation will be

=4000-83+53

= 3970

mean of new the observation will be

\( = \frac{3970}{100} \)

\( = 39.7\)

[Hence, the actual mean is 39.7]

The probability the mean age at heart attack after using cocaine is greater than 42 is 0.9192. Hence, the correct option is D. 0.9192.

The standard deviation of the age of people who suffered heart attacks soon after using cocaine was 10 years. In a random sample of size 49, what is the probability the mean age at heart attack after using cocaine is greater than 42?We are given the following details:

The mean age of people in the study who suffered heart attacks soon after using cocaine was only 44.

Standard deviation = 10

Sample size = 49

Now we need to find the z-score using the formula:

z = (x - μ) / (σ / √n)

wherez is the z-score

x is the value to be standardized

μ is the mean

σ is the standard deviation

n is the sample size.

Substitute the values in the formula as given,

z = (42 - 44) / (10 / √49)z = -2 / (10/7)

z = -1.4

Probability of z > -1.4 can be found using the standard normal distribution table or calculator.

P(z > -1.4) = 0.9192

Therefore, the probability the mean age at heart attack after using cocaine is greater than 42 is 0.9192. Hence, the correct option is D. 0.9192.

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Answer:

0.50

Step-by-step explanation:

The individuals that do and do not wear glasses are evenly split, it is 2/4, therefore the probability that a teenager wears glasses AND watched TV is 0.50.

Answer:

Poem:

Function is binary relation of two sets

have a single output but

not Function is having no function

have multiple output.

Range is a function refer to two closely concepts

but

Domain is a set of possible input values with concepts.

All the function are relation but

not all relation are function.

Relation is a collection of ordered pair but

imaginary is a collection of complex number written in imaginary unit.

Vertical line is parallel to y-axis but

horizontal line is parallel to x-axis.

The calculated period of the function is 16

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

The graph

By definition, the period of the function is calculated as

Period = Difference between cycles or the length of one complete cycle

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

Period = 24 - 8

Evaluate

Period = 16

Hence, the period of the function is 16

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Answer:

Step-by-step explanation:

Since 40° is in the first quadrant, the reference angle is 40°

The sale price of an item that is regularly priced at $91 and is on sale for 35% off the regular price using the aleks calculator is $59.15.

To calculate the sale price of an item that is regularly priced at $91 and is on sale for 35% off the regular price using the aleks calculator we will follow these steps:

Step 1: Calculate the amount of discount = Regular Price × Discount rate

Discount rate = 35/100

Simplifying the value we have:

Discount rate = 0.35

Amount of discount = 91 × 0.35

Amount of discount = $31.85

Step 2: Calculate the sale price

Sale price = Regular price − Amount of discount

Sale price = $91 − $31.85

Sale price = $59.15

Hence, the sale price of an item that is regularly priced at $91 and is on sale for 35% off the regular price using the aleks calculator is $59.15.

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Answer:

Choice C    (1/3b)/7 = 25.50

Step-by-step explanation:

1/3 of budget b =(1/3)b

7 bills at $25.50 per bill = 7 x 25.50

Setting both equation to each other we get
(1/3)b = 7 x 25.50

Dividing by 7:
(1/3b)/7 = 25.50

For the given triangle FGH, ∠x is 36.4°.

What is the definition of a triangle?

Triangles are polygons with three sides and three vertices in geometry. This figure is two-dimensional and has three straight sides. A triangle is a polygon with three sides. The sum of a triangle's three angles equals 180°. The triangle is contained inside a single plane. Triangles are categorized into three types based on their sides.

Based on its sides, a triangle is classified into three types:

Scalene Triangle - Each side is different in length.

Isosceles Triangle - A triangle with two sides that are equal in length and one side that is not.

Equilateral Triangle - A triangle with three equal-length sides.

Now,

For triangle FGH,

perpendicular=5

Hypotenuse=8.8

then, sin x=P/H=5/8.8

x=sin⁻¹(0.5681)

x=36.4°

Hence,

           ∠x is 36.4°.

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The dimensions of the rectangle are length = 13.38 cm, width = 13.38 cm and height = 13.4 cm.

Given that,

A closed rectangular container must have a volume of 2400 cubic centimeters and a square base without a top. The bottom is three times more expensive per square centimeter than the sides.

We have to calculate the size of the container with the lowest cost.

We know that,

Volume V = 2400 cm³

Let us take the base of the square length as x and height is h

Volume of the rectangle is length × width ×height

Length and width are same x and height is h

Then,

x × x × h = 2400

h = \(\frac{2400}{x^2}\)

Area of the sides \(A_s\)= length ×height = hx + hx + hx + hx = 4(\(\frac{2400}{x^2}\))x = \(\frac{9600}{x}\)

Let cost is $1 for 1 cm²

Cost of the sides \(C_s\) = \(\frac{9600}{x}\) × 1 = \(\frac{9600}{x}\)

Area of the top and bottom is area of square \(A_t\) = x² + x² = 2x²

Cost of the sides \(C_t\) = 2x²

Total cost = \(C_s +C_t\)

C =  \(\frac{9600}{x}\) + 2x²

By differentiating on both the sides

\(\frac{dC}{dx}\) = 4x - \(\frac{9600}{x^2}\)

Taking \(\frac{dC}{dx}\) = 0

0 = 4x - \(\frac{9600}{x^2}\)

4x =  \(\frac{9600}{x^2}\)

4x³ = 9600

x³ = \(\frac{9600}{4}\)

x³ = 2400

Taking cube root on both the sides,

x = 13.38 cm

Then h = \(\frac{2400}{x^2}\) = \(\frac{2400}{(13.38)^2}\) = \(\frac{2400}{179.02}\) = 13.4 cm

Therefore, The dimensions of the rectangle are length = 13.38 cm, width = 13.38 cm and height = 13.4 cm.

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Hope this helps :)

need more help just comment :) :)

To solve for the sum and difference of complex numbers in polar form, we can add or subtract their magnitudes and their angles separately.

Given:

a = 3.1∠63.2°

b = 6.6∠26.2°

To find a + b:

We can use the formula for adding complex numbers in polar form:

(a + b) = (3.1∠63.2°) + (6.6∠26.2°)

       = (3.1 cos 63.2° + 6.6 cos 26.2°) + j(3.1 sin 63.2° + 6.6 sin 26.2°)

       ≈ 6.94∠37.4°

Therefore, a + b = 6.94∠37.4°.

To find a - b:

We can use the formula for subtracting complex numbers in polar form:

(a - b) = (3.1∠63.2°) - (6.6∠26.2°)

       = (3.1 cos 63.2° - 6.6 cos 26.2°) + j(3.1 sin 63.2° - 6.6 sin 26.2°)

       ≈ -3.78∠141.5°

Therefore, a - b = -3.78∠141.5°.

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The decrease in diameter of the bar due to the applied load is -0.005434905d and the final diameter of the bar is 1.005434905d.

A compressive load of 80,000 lb is applied to a bar with a circular section of 0.75 in diameter and a length of 10 in.

if the modulus of elasticity of the bar material is 10,000 ksi and the Poisson's ratio is 0.3.

We have to determine the decrease in diameter of the bar due to the applied load.

Let d be the initial diameter of the bar and ∆d be the decrease in diameter of the bar due to the applied load, then the final diameter of the bar is d - ∆d.

Length of the bar, L = 10 in

Cross-sectional area of the bar, A = πd²/4 = π(0.75)²/4 = 0.4418 in²

Stress produced by the applied load,σ = P/A

= 80,000/0.4418

= 181163.5 psi

Young's modulus of elasticity, E = 10,000 ksi

Poisson's ratio, ν = 0.3

The longitudinal strain produced in the bar, ɛ = σ/E

= 181163.5/10,000,000

= 0.01811635

The lateral strain produced in the bar, υ = νɛ

= 0.3 × 0.01811635

= 0.005434905'

The decrease in diameter of the bar due to the applied load, ∆d/d = -υ

= -0.005434905∆d

= -0.005434905d

The final diameter of the bar,

d - ∆d = d + 0.005434905d

= 1.005434905d

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Step-by-step explanation:

draw the last one by yourself.

im sure you can do it buddy.

good luck♥️♥️♥️♥️♥️.

The distance from Southville to Westfield is 95 miles.

How to find the distance?

Let's say that Portland is the origin of the coordinate axis, East is the positive x-axis and North is the positive y-axis.

Westfield is 76 mi due west of Portland, then Westfield's position is:

(76mi, 0mi).

Southville is 57 mi due south of Portland, then its position is:

(0mi, 76mi)

The distance between these two points is given by:

\(D=\sqrt{(76mi-0mi)^2+(0mi-(-57mi)^2}\) = 95 miles.

So the distance from Southville to Westfield is 95 miles.

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Answer:

If you multiply the 7 by 15 using the AZB formula you will get the asnwer^5 to divide the answer by .05

Step-by-step explanation:

The method of induction is a mathematical proof technique that involves showing that a statement holds for a base case, and then showing that if it holds for n, it also holds for n+1. This process is repeated until the statement is shown to hold for all positive integers.

This statement can be proven by induction.

Base Case:

For n = 1, there are 3 airports. Let the 3 airports be A, B, and C. If an airplane from airport A is heading towards airport B, then the airplane from airport B must be heading towards airport C, and the airplane from airport C must be heading towards airport A. Hence, there is no airport that none of the airplanes are heading towards.

Inductive Step:

Assume that the statement holds for n = k, where k is a positive integer.

We need to prove that the statement holds for n = k + 1, where there are 2(k + 1) + 1 = 2k + 3 airports.

Let the 2k + 3 airports be A1, A2, ..., A2k + 3. Without loss of generality, let the airplane from airport A1 be heading toward airport A2.

Since the distances between any two airports are all different, we have two cases to consider:

If there exists an airport Ai, such that Ai is the closest airport to A1, then airplanes from Ai must be heading towards A1.

If there is no airport Ai that is closest to A1, then there must be the closest pair of airports, say Ai and Aj, such that Ai is the closest to A1 and Aj is the closest to Ai.

In the first case, none of the airplanes are heading towards Ai, and in the second case, neither Ai nor Aj is the closest airport to any other airport. Hence, in both cases, there is an airport that none of the airplanes are heading towards.

By induction, the statement holds for all positive integers n.

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Answer:

a

Step-by-step explanation:

The discriminant D(x, y) of the function f(x, y) = x³ + y4 - 6x-2y² + 2 has been computed, the point (√2, 0) is a saddle point and the points (√2, 0) and (√2, 1) have been identified correctly as a saddle point and a local minimum, respectively.

To compute the discriminant D(x, y) of the function f(x, y) = x³ + y⁴ - 6x - 2y² + 2, we need to calculate the second partial derivatives and then evaluate them at each critical point.

First, let's find the partial derivatives:

fₓ = ∂f/∂x = 3x² - 6

f_y = ∂f/∂y = 4y³ - 4y

Next, we need to find the critical points by setting both partial derivatives equal to zero and solving the resulting system of equations:

3x² - 6 = 0

4y³ - 4y = 0

From the first equation, we have:

3x² = 6

x² = 2

x = ±√2

From the second equation, we can factor out 4y:

4y(y² - 1) = 0

This gives us two possibilities:

y = 0 or y² - 1 = 0

For y = 0, we have a critical point at (±√2, 0).

For y² - 1 = 0, we have two more critical points:

y = ±1, which gives us (-√2, -1) and (√2, 1).

To determine the nature of each critical point, we need to calculate the discriminant at each point.

The discriminant D(x, y) is given by:

D(x, y) = fₓₓ * f_yy - (f_xy)²

Calculating the second partial derivatives:

fₓₓ = ∂²f/∂x² = 6x

f_yy = ∂²f/∂y² = 12y² - 4

f_xy = ∂²f/∂x∂y = 0 (since the order of differentiation does not matter)

Substituting these values into the discriminant formula, we have:

D(x, y) = (6x)(12y² - 4) - 0²

= 72xy² - 24x

Evaluating the discriminant at each critical point:

D(√2, 0) = 72(√2)(0) - 24(√2) = -24√2

D(-√2, -1) = 72(-√2)(1) - 24(-√2) = 96√2

D(√2, 1) = 72(√2)(1) - 24(√2) = 48√2

Now we can determine the nature of each critical point based on the sign of the discriminant.

For a point to be a saddle point, the discriminant must be negative:

D(√2, 0) = -24√2 (saddle point)

D(-√2, -1) = 96√2 (not a saddle point)

D(√2, 1) = 48√2 (not a saddle point)

Therefore, the point (√2, 0) is a saddle point.

To determine local minima and a local maximum, we need to consider the second partial derivatives.

At (√2, 0):

fₓₓ = 6(√2) > 0

f_yy = 12(0) - 4 < 0

Since fₓₓ > 0 and f_yy < 0, the point (√2, 0) is a local maximum.

At (√2, 1):

fₓₓ = 6(√2) > 0

f_yy = 12(1) - 4 > 0

Since fₓₓ > 0 and f_yy > 0, the point (√2, 1) is a local minimum.

Therefore, the points (√2, 0) and (√2, 1) have been identified correctly as a saddle point and a local minimum, respectively.

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Answer:

-6<x≥-1

Step-by-step explanation:

-6<x≥-1

The expression is written as;

-6 < x ≤ -1

What is Inequality?

To compare two or more mathematical expression in a relation is called an inequality.

Given that;

The expression is;

A number x is more than -6 and at most -1.

Now, The number x is more than -6.

It can be written as;

-6 < x

And, The number x is at most -1.

It can be written as;

x ≤ -1

After combine both inequality, we get;

- 6 < x ≤ -1.

Thus, The expression is written as;

-6 < x ≤ -1

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Bryant Industries uses forecasting to estimate the number of orders that will be placed by their customers. The table below gives the sales figures for the last four months.Month2345Sales92491942004There are different forecasting techniques used by companies like Bryant Industries to predict future sales.

One of the most widely used methods is the time-series method. This method is particularly useful when the demand for a product or service changes over time and when there are no external factors that affect the sales. In this case, we can use a time-series method called the moving average to estimate future sales. The moving average is a time-series method that uses the average of past sales data to estimate future sales. It is particularly useful when there are no external factors that affect the sales. In this case, we can use a 3-month moving average to estimate future sales. The 3-month moving average is calculated as follows: (924 + 919 + 420) / 3 = 754.33. This means that we can expect sales of around 754 units next month. The moving average method is easy to use and is a good way to get a quick estimate of future sales. However, it has some limitations. For example, it does not take into account external factors that may affect sales, such as changes in the economy or in consumer behavior.

In conclusion, Bryant Industries can use the moving average method to estimate future sales. However, they should also consider other factors that may affect sales, such as changes in the economy or in consumer behavior. By doing so, they can make more accurate forecasts and improve their overall performance.

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Answer:

The slope is 10

The y - intercept is 20

Step-by-step explanation:

The equations are written as:

y = ?x + ?

The first ? is the slope of the equation, every time y increases by that amount, x increases by one, the slope here is 10

The second ? is the y-intercept, or the place where x is 0. Here, when x is 0, y is 20, so it is the y-intercept

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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Answer:

sorrry but i need points

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

half of 10 is 5

Answer:10

Step-by-step explanation:

Answer:

Statement 4 is correct

Step-by-step explanation:

Here, we want to select which statement is true based on the given diagram;

The statement that must be true is that Y is the midpoint of XV

This is because, by bisection , we mean dividing into 2 equal parts

The line UW has divided the line XV into two equal parts

So this mean that Y is the midpoint of the line XV

Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

Equation of the line

The equation of a line in slope-intercept form is:

y = mx + b

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

We are required to find the equation of a line that is perpendicular to the line

y = 5x + 4

and passes through the point (-5,2)

The first thing we need to do is to calculate the slope of the required line.

The slope of the given line is m1=5. Two lines are perpendicular if their slopes satisfy the equation:

m1 * m2 = -1

Solving for m2:

The equation of the required line is:

To find the value of b, we substitute the given point (-5,2):

Operating:

Solving for b:

b = 1

Finally, our equation is: