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(a) The exponential growth model is given by the equation P(t) = P0 * r^t, where P(t) is the population t years after 2010, P0 is the population in 2010 (7420), and r is the annual growth rate (2.3%).

Substituting the given values into the equation gives us:

P(t) = 7420 * 1.023^t

This is the equation that estimates the population t years after 2010.

(b) To estimate the population of the town in 2022, we can substitute t = 12 into the equation:

P(12) = 7420 * 1.023^12

Calculating this gives us:

P(12) = 7420 * 1.023^12 = 7420 * 1.291891 = 9593.45

So the estimated population of the town in 2022 is approximately 9593

Happy to help!

Answer:

sqrt21 is real and irrational

Step-by-step explanation:

The other answers are a repeating decimal (rational), a terminating decimal (rational) and a perfect square (an integer--so also rational)

They are all real. Numbers that are not real have the imaginary number, i, in them or a square root of a negative number.

Yes, it is a proportional relationship. The relationship is distance (d) is directly proportional to time(t). The equation of the relationship is d= 65t

Direct Variation is said to be the relationship between two variables in which one is a constant multiple of the other. For example, when one variable changes the other, then they are said to be in proportion. If d( distance) is directly proportional to t( time) the equation is of the form d= kt (where k is a constant).

When d =65miles and t= 1hour, k =d/t

k= 65/1= 65

for other values of d and t, k = 65

Therefore the relationship between the distance and time is a proportional relationship. And the equation of the relationship is d= 65t

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Answer:

137.067

Step-by-step explanation:

1 percent = 15.41

0.1 percent = 1.541

8 x 15.41 = 123.28

7 x 1.541 = 10.787

123.28 + 10.787 = 137.067

The perimeter of the polygon is 57 meters.

A polygon is an enclosed two-dimensional shape with three or more straight sides that are connected together. It can be regular or irregular and can be made up of triangles, squares, rectangles, and other shapes. Polygons are classified by the number of sides they have, such as triangles (3 sides), quadrilaterals (4 sides), pentagons (5 sides), and hexagons (6 sides). Polygons can also be classified by their internal angles, such as acute (less than 90 degrees), right (90 degrees), obtuse (greater than 90 degrees), and reflex (greater than 180 degrees). Polygons are used in many mathematical problems and can be used to represent a variety of real-world objects, such as buildings, mountains, and stars.

The perimeter of the polygon is 57 meters.

The perimeter is calculated by adding up the lengths of each side. 7m + 16m + 9cm + 15m = 57m.

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Answer:

11.9988

Step-by-step explanation:

Use a calculator.

What percentage of $680 is 490? ANSWER: 138.78%

The price is reduced from $680 to $490. What is the percentage decrease? ANSWER: 72.06%

Step-by-step explanation:

ANSWER: 138.78%

690 & 490 can be written as a fraction

which would be 680/490, how do I find the percentage?

490 and 680 can be written as a fraction

which would be 490/680, how do I find the percentage?

If initial sample of 458 grams of a radioactive substance decays according to the function [tex]A(t)=458e^{-0.038t}[/tex] then the half-life of the substance is 0.

Half-life is the time required for a quantity (of substance) to reduce to half of its initial value.

Given,

An initial sample of 458 grams of a radioactive substance decays according to the function

[tex]A(t)=458e^{-0.038t}[/tex]

We need to find the half life

[tex]458=458e^{-0.038t}[/tex]

Divide both sides by 458

[tex]1=e^{-0.038t}[/tex]

Take log on both sides

[tex]log1=-0.038t[/tex]

0=-0.038t

t=0

Hence, the half-life of the substance is 0.

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Step-by-step explanation:

chances of rolling 1= 1/6

chances of rolling 2=1/6

chances of rolling anything else=2/3

Answer:

Ann must pay $800 in income tax for the first $8,000 of her taxable income because 8000 * .1 = 800

Ann must pay $4,600 in income tax for the amount of her taxable income over $8,000 because (35000 - 8000) * .16 = 4600

Therefore, Ann must pay a total of $800 + $4,600 = $<<800+4600=5400>>5,400 in income tax for last year.

Answer:

$5,120 in taxes, total

Step-by-step explanation:

Ann made $35,000 in taxable income last year. Suppose the income tax rate is 10% for the first $8,000 plus 16% for the amount over $8,000. How much must Ann pay in income tax for last year?

8,000 * 10% = 800 in taxes for first $8,000

remaining: 35,000 - 8,000 = $27,000 to be taxed at 16%

27,000 * 16% = $4,320

$800 + $4,320 = $5,120 in taxes, total

If the measure of the angle x is 116.89 degrees. Then the measure of the angle y will be 63.11 degrees.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

It is given that the angles x and y are supplementary angles. Then the equation is given as,

x + y = 180

If the measure of the angle x is 116.89 degrees. Then the measure of the angle y is calculated as,

x + y = 180

116.89 + y = 180

y = 180 - 116.89

y = 63.11 degrees

If the measure of the angle x is 116.89 degrees. Then the measure of the angle y will be 63.11 degrees.

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By solving the system of linear equations by elimination we get the value of x= 2 and y = 1.

What is the system of linear equations?

A grouping of one or more linear equation containing the same variables is known as a system of linear equations.

Here, we have

Given:  8x - 5y = 11....(1), 4x - 3y = 5...(2)

We solve equation(2) and find the value of x

4x = 5+ 3y

x = 5/4 + 3y/4

Now, we put the value of x in equation (1) and we get

8(5/4 + 3y/4) - 5y = 11

5×2 + 2×3y - 5y = 11

10 + y = 11

y = 1

Now, we put the value of y in equation(2) and we get

4x = 5+ 3(1)

4x = 8

x = 2

Hence, by solving the system of linear equations by elimination we get the value of x= 2 and y = 1.

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The value of y is 15.

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

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

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

Given:

87 + 87 y = 1218 + 174

Now, Solving

87+ 87y= 1392

87y= 1392- 87

87y= 1305

y= 1305/ 87

y= 15

Hence, the value of y is 15.

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We can substitute the number in the inequality to find if the inequality holds true. If the inequality holds true, it is a valid solution. This is very similar to substituting a number in an equation, in order to check if it holds.

The same holds true for others.

Change the equations to inequalities  to modify the graph and the solutions are (-1.871, 1.5) and (1.871, 1.5)

The graph is the given parameter

From the graph, we have the following equations

f(x) = x² - 2

g(x) = -x² + 5

To modify the graph, we simply change the equations to inequalities

After the modifications in (a), we have:

f(x) >  x² - 2

g(x) ≥  -x² + 5

From the graph of the inequalities, the curves of the inequalities intersect at (-1.871, 1.5) and (1.871, 1.5)

Hence, the solutions are (-1.871, 1.5) and (1.871, 1.5)

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The last boxplot is the one that displays the values of the distribution that is given.

The range of a function in mathematics can refer to one of two ideas that are connected in some way: Codomain for the function an illustration of the action If there is precisely one y in Y and there are two sets X and Y, then a binary relation f between X and Y is a function that connects x and y.

Here ,Given information:

6,7,9,9,20,22,26,28,29,30

N = 10 observations were made.

The base number is 6. ( least value)

Quartile lower= n+1(0.25)

term = 0.25(13) = 3.25term = 13

Median equals 0.5 (n + 1)

term = 0.5(13) = 6.5 term = (20 + 24) /2 = 22

Upper quartile: 0.75 (13)

A term equals 9.75 a term equals 26.5

Interquartile Range (IQR) is equal to= Q3 - Q1= (26.5 - 13) = 13.5

The highest value is 30. (highest value in the distribution)

As a result, the Last boxplot is the one that shows the distribution that is given.

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A) The vertex (h, k)=(9, 0) if  p(x)=[x-9]

B) The vertex (h, k)=(0, 9) if q(x)= [x]+9

The earliest known treatment of the idea of function can be found in the writings of the Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally merely a simplified illustration of the relationship between two varying quantities. The position of a planet is just one example of how time is used. The concept was historically developed towards the end of the 17th century with infinitesimal calculus, and the functions that were taken into consideration up until the 19th century. The concept of a function was formalised in terms of set theory at the end of the 19th century, greatly extending its range of applications.

Given,

A) p(x)=[x-9]

We have to compare with f(x)=a|x-h|+k

Therefore, the vertex (h, k)=(9, 0)

B) Given,

q(x)= [x]+9

We have to compare with the above equation we get,

The vertex (h, k)=(0, 9)

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The first function is an odd and the second one is neither even nor odd. The correct options are (1) and (2).

A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.

The given problem can be solved as follows,

(2) The graph of the given function shows the following,

The value of the function is positive for positive x and negative for negative x.

It can be mathematically written as,

f(-x) = -f(x).

Which shows the given graph is of an odd function.

(3) The given function is f(x) = 4x³ + 2x² - x⁵.

In order to check the type of the function, find its value at the same value of x with different signs as,

f(1) = 4 × 1³ + 2 × 1² - 1⁵ = 5

And, f(-1) = 4 × -1³ + 2 × -1² - -1⁵ = -1

Since, f(1) ≠ f(-1), the function is not even.

And f(-1)  ≠ -f(1), the function is not odd.

Thus, the given function is neither even nor odd.

Hence, the first and the second functions of the given problem are odd and neither even nor odd respectively.

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a) Histogram (figure attached)

b) The expected number of defective is equal to 0.4 syringes.

c) Probability that the batch will be accepted is equal to 0.94275.

d) The standard deviation is 0.6164.

It is a binomial distribution "DISCRETE probability distribution that encapsulates the likelihood that a value will take one of two independent values when a particular set of conditions is met. The assumptions for the binomial distribution are that each trial has a single possible outcome, each trial has an equal chance of success, and each trial is independent of the others or mutually exclusive ".

Let X be the number of syringes being defective as a binomial random variable.

We are given that in the batch, there can be assumed to be 5% defective syringes.

∴ n = 8

Probability of syringes being defective, p = 0.05

Probability of syringes being not defective , q = 1-p = 1-0.05 = 0.95

a) Histogram (figure attached)

b) We know that the formula for Expectation in binomial distribution is;

μ =n×p = 8×0.05

=0.4 syringes

Therefore, the inspector will find the expected number of defective is equal to 0.4 syringes.

c) We have to find binomial probability for that we will use the binomial probability distribution is given by:

P(X=x) = ⁿCₓpˣ (1-p)^n-x, x = 0,1,2,3 ..8

Therefore,

P(x<2) = P(X=0) + P(X=1)

= ⁸C₀(0.05)⁰(1-0.05)⁸ + ⁸C₁(0.05)¹(1-0.05)⁷

=  0.66342 + 8×0.05×0.6983

= 0.66342 + 0.27933

= 0.94275

Therefore, probability that the batch will be accepted is equal to 0.94275.

d) We first find the variance:

σ² = Var(X) = n×p×(1-p)

= 8 × 0.05 ×(1-0.05)

= 0.38

Thus, the standard deviation is

σ = [tex]\sqrt{0.38}[/tex] = 0.6164

Thus,

a) Histogram (figure attached)

b) The expected number of defective is equal to 0.4 syringes.

c) Probability that the batch will be accepted is equal to 0.94275.

d) The standard deviation is 0.6164.

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When the midpoint of GH is M at (-6,-3) and one endpoint is H at (-8,-10), the coordinates of endpoint G are (-8,-10) (-4,4).

A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y). a group of variables that accurately depict a stance. The first number on a graph represents the distance along, while the second number represents the distance up or down. For instance, the point (12,5) is located 12 units down and 5 units up.

Here,

let the points of G be (a,b)

mid point of GH =(-6,-3)

point of H =(-4,4)

for x coordinate,

-6=(a-4)/2

a-4 =-12

a=-8

for y coordinate,

-3=(b+4)/2

-6=b+4

b=-10

The coordinates of endpoint G is (-8,-10) when the midpoint of GH is M at (-6,-3) and one endpoint is H at (-4,4).

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Answer:

{red, orange , yellow}

Step-by-step explanation:

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Answer:

(0,-5) , (3, -6) , (6, -7) ,(9, -8)

Step-by-step explanation:

I apologize for being unable to graph, but here are some of the points.

(0,-5) <-- The "y intercept"

slope is y2-y1/x2-x1, so "-1" is added to the "y" of the coordinate, and 3 is added to the "x"

(3,-6)

(6,-7)

(9,-8)

Hope this helps :)

The vertex of the absolute function g(x) will be (0, -8). And the function opens up. Then the correct option is A.

The absolute function is also known as the mode function. The value of the absolute function is always positive.

If the vertex of the absolute function is at (h, k). Then the absolute function is given as

f(x) = | x - h| + k

The absolute function is given below.

g(x) = | x | - 8

Compare the function g(x) with the function f(x), then the vertex of the absolute function is as,

(h, k) = (0, -8)

The absolute function opens up because there is a positive sign before mode.

The vertex of the absolute function g(x) will be (0, -8). And the function opens up. Then the correct option is A.

The graph is given below.

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Answer:

4/3

Step-by-step explanation:

you use the slope formula y^1 - y^2 over x^1 over x^2, substitute the said values and are left with the slope of 4/3 in its improper form.

Hope this helps!!! :3

The required solution for the hypothesis testing is shown,

The T - statistic is the ratio of the predictive value of a parameter from its hypothesized value to its standard disputable values.

n = 16, ss = 960, and [tex]\bar x = 55,[/tex]
[tex]S.D, s = \sqrt{ \ [ss/n - 1]\\s = \sqrt{960/15} \\s = 8[/tex]

The test statistic is,
[tex]t = \bar x - mu / [s /\sqrt{n} ]\\t = 55 - 50 / [8/\sqrt{16} ]\\t = 2.5[/tex]

df = n - 1 = 15 , let α = 0.05
tcrp = 2.131 [from t - table]
Since t > 2.131
The result is significant

(b)

Cohen's d = mean difference /SD
                = 55 - 50 / 8 = 0625.

Thus, the required solution for the hypothesis testing is shown,

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The system of equations that Tristan needs to solve is:

x*0.05 + y*0.10 = 1.40

x = 2*y

Let's define the variables:

x = number of nickels.

y = number of dimes.

Knowing that the net is $1.40 and that he has twice as many nickels as dimes, we can write:

x*0.05 + y*0.10 = 1.40

x = 2*y

That is our system of equations that Tristan can use to find the numbers of nickels and dimes.

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Answer:

Line 2

Step-by-step explanation:

This would represent a negative slope.  A negative slope goes down if you start on the left side and go down.