Question 5
Use technology to find the line of best fit for the following data.
(1,4), (2, 3), (3,5), (4,4), (5,5)
When the equation of the line is in the form y=mx+b, what is the value of **m**?
Enter your answer as a decimal rounded to the nearest tenths place, like this: 42.5
Click on the following link to use the GeoGebra graphing calculator .

The formula for exponential growth is expressed as

y = a(1 + r)^t

where

y is the population after t years

ais the initial population

r is the growth rate

t is the number of years

From the information given,

a = 350

r = 14% = 14/100 = 0.14

By substituting these values into the equation, the function to model th growth rate is

y = 350(1 + 0.14)^t

y = 350(1.14)^t

We would substitute values of t into the equation to determine corresponding values of y. We have

For t = 2, y = 350(1.14)^2 = 454.86

For t = 6, y = 350(1.14)^6 = 768.24

For t = 10, y = 350(1.14)^10 = 1297.52

We would plot these values of y on the y axis and the corresponding values of t on the x axis. The graph is shown below

The time when the population will reach 20000 would be the value of x at the point where y = 20000 on the graph. It is around y = 30.87

Thus, the population will reach 20000 in approximately 31 years

We can confirm this by solving the equation. We have

20000 = 350(1.14)^t

20000/350 = 1.14^t

57.14 = 1.14^t

Taking natural log of both sides, we have

ln 57.14 = ln1.14^t = tln1.14

t = ln 57.14/ln1.14

t = 30.87505

we can make a relation

where x is the missing value

if she bikes 2/3km in 4 minutes how much kilometers she bike on 1 minute?

we solv using cross multiplication

we multiply 1 and 2/3 and the divide by 4

she will bike 1/6km in one minute

The problem can be expressed in the following system of linear equations:

A total of 120 adults (a) and students (s) attended a school:

a + s = 120

Each adult paid $2.50, mathematically, that is 2.5a

Each student paid $1, mathematically, that is 1s

and the total paid by adults and students attending the game was $189

then, we have:

2.5a + 1s = 189

then, we can conclude that the problem can be expressed as follows:

a + s = 120

2.5a + 1s = 189

or equivalently:

a + s = 120

2.5a + s = 189

so, the correct answer is D.

see the figure below to better understand the problem

we have that

Answer:

3/4 inches

Explanation:

The most number of cross symbols (vertical line) is on the length 6/8 inches, that is, 3/4 inches.

So, the most common button is of length 3/4 inches.

The polygon EFGH is a polygon.

What is polygon?

A polygon is a form of planar figure in geometry and is defined as a closed polygonal chain made up of a finite number of straight line segments. A region that is enclosed by a bounding plane, a bounding circuit, or both is referred to as a polygon. The portions of a polygonal circuit are referred to as its edges or sides.

To check the polygon EFGH is a square or not, first to find the length of each side of polygon.

If the length of each side is equal then the polygon EFGH is a square.

(Since length of each side of square is equal).

We know,

[tex]d \sqrt{(x_2-x_1)^2 + (y_2 - y_1)^2}[/tex]

where,

d = distance

[tex](x_1, x_2)[/tex] = Coordinates of the first point.

[tex](x_2, y_2)[/tex] = Coordinates of the second point.

So,

[tex]EF = \sqrt{(3-(-2))^2 + (3.5-3.5)^2} = \sqrt{25 + 0} = 5[/tex]

[tex]FG = \sqrt{(3-3)^2 + (-1.5-3.5)^2 } = \sqrt{0 + 25} = 5[/tex]

[tex]GH = \sqrt{(-2-3)^2 + (-1.5-(-1.5))^2} = \sqrt{25 + 0} = 5[/tex]

[tex]EH = \sqrt{(-2-(-2))^2 + (-1.5-3.5)^2} = \sqrt{0 + 25} = 5[/tex]

From above the length of each side is equal.

Therefore, given polygon EFGH is a square.

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The solution is option C.

Answer:  0.77

Step-by-step explanation:

Equation is -(x+4)² +4.

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line. The vertex form of a quadratic equation is y = a (x h) 2 + k as opposed to the regular quadratic form, which is an x 2 + b x + c = y. In both cases, the variables that indicate whether the parabola is facing up (+ a) or down ( a) are y, the y-coordinate, x, and a.

Given Data

Solutions (-6, 0) and (-2,0)

y = a(x - (-6)) (x-(-2))

y  = a(x+6) (x+2)

Vertex (-4,4)

at x = -4 and y = 4

4 = a(-4+6)(-4+2)

4 = a (2)(-2)

a = -1

y = -1(x+6)(x+2)

y = -(x²+8x+12)

y = =(x² + 3x +4x+4²-4²+12)

y = -(x+4)² +4

Equation is -(x+4)² +4.

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PROBLEM:

To find the point-slope form of the equation of the line passing through points (0, 0) and (-4, 7)

METHOD:

The point-slope form of the equation of a line is given to be:

Step 1: Find the slope of the line.

The formula to calculate the slope of a line is given to be:

We can use the two points provided to find the slope of the line such that:

Therefore, the slope is given to be:

Step 2: Pick a point on the line to use for the equation.

Step 3: Use the values gotten from Steps 1 and 2 to write out the equation of the line in the point-slope form:

ANSWER:

The slope-intercept form of the line is given to be:

SOLUTION

This becomes

Hence the answer is option D

Probability of drawing 3 green marbles in a row with replacement is 0.059

The probability that you draw 7 blue marbles in a row without replacement is 0

Probability is used to determine the odds in favor or against a random event happening. The probability that the random event happens lie between 0 and 1. The more likely it is that an event would happen the closer the probability value would be to 1.

Probability of drawing 3 green marbles in a row with replacement = (7/18) x (7/18) x (7/18) = 0.059

The probability that you draw 7 blue marbles in a row without replacement = (6/18) x (5/17) x (4/16) x (3/15) x (2/14) x (1/13) x 0 = 0

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You should jot down any new ideas you have while you revise.

Revision is the process of rearrangement, addition, or deletion of paragraphs, sentences, or words in writing. Writers are free to edit their work both during and after the writing process. Many of the techniques associated with editing are used in revision, but it can also require more significant changes to the goal, target audience, and content.

To ensure proper memorization, revise by reading or writing the material again. A must-do before each exam is revision. Additionally, it allows you to check for errors and reorganize your work.

During revision, you should write down additional thoughts.

The correct option is (c).

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the inverse function = f^-1(x) is option C

First let's state what we are given:

f(x) = x^3 - 5

We are to find the inverse of f(x).

To do this, first let's represent f(x) with y

y = = x^3 - 5

Then, we would interchange x and y

From the answer we got, the inverse function = f^-1(x) is option C

Answer:

Step-by-step explanation:

Comment

The question is since f(x) really means y, then when y = 9 what's x?

Solution

y = 2x - 4

y = 9

9 = 2x - 4                Add 4 to both sides

9+4 = 2x                 Combine

13 = 2x                    Divide both sides by 2

13/2 = 2x/2              

6.5 = x

Do you mean what is f(X) when x is 3. f(3) = 2x - 4. So what is y when x = 3

y = 2x - 4                   Substitute 3 for x

y = 2*3 - 4                  Combine

y = 6 - 4

y = 2

Let that number be variable x

MATHEMATICALLY THE STATEMENT IS SAYING

[tex]8x + 3 = 19 \\ 8x = 19 - 3 \\ 8x = 16 \\ \frac{8x}{8} = \frac{16}{8} \\ x = 2 [/tex]

ATTACHED IS THE SOLUTION

we have

m=-2

point (1,2)

step 1

find the equation of the line in point slope form

y-3=-2(x-1)

convert to slope intercept form

y-3=-2x+2

y=-2x+2+3

y=-2x+5

To graph the line we need two points

Find the y-intercept (value of y when the value of x is equal to zero)

For x=0

y=5

so

the y-intercept is (0,5)

Find the x-intercept

Value of x when the value of y is equal to zero

For y=0

0=-2x+5

2x=5

x=2.5

the xintercept is (2.5,0)

Plot the points (0,5) and (2.5,0), join them and graph the line

using a graphing tool

see the attached figure

please wait a minute

It takes 400 years for $600 to earn $72 at the rate of 0.03 percent annual

"Simple" interest refers to the straightforward crediting of cash flows associated with some investment or deposit.

The formula for calculating Simple interest

I=PRT

Where I is the Interest

P=Principle amount

I is interest Amount

R is rate of interest per year as a percent

T is time period involved

P=600

I=72

r=0.03%

t=?

I=PRT

Plug in the values P, R and I

72=600×(0.03%)×T

72=600×0.0003×T

72=0.18×T

400=T

Hence it takes 400 years, for amount  $600 to earn $72 at the rate of 0.03 percent annual.

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The predicted temperature of the substance after 3.5 minutes implies that x =3.5, and we are to find y.

Therefore,

Therefore, the predicted temperature of the substance, 3.5 minutes after the start of the experiment is 40.5 degrees Celsius

Answer:

Explanation:

Step 1. The function we have is:

And we are asked to find the derivative of the function. The rule to find the derivative for this type of function is:

Step 2. Before we apply the derivative rule, remember the following:

This means that we need to derivate each part or term of the function and combine them for the total derivative.

Step 3. Apply the derivative rule from step 1 to the given function.

First we rewrite the function as follows:

Apply the derivative rule:

Step 4. The last step is to simplify the expression:

Answer:

The given information is:

- Tim needs to be at work at 8:00 A.M.

- He needs 30 minutes to get ready in the morning

- It takes him 15 minutes to drive to the work

The total time Tim needs to get ready and drive to work is:

So, he needs at least 45 minutes to be on time at work. So, the latest time Tim can get up in the morning is 45 minutes earlier than 8:00 A.M., and it is equal to:

The answer is 7:15 A.M.

Given

The function,

To find the type of function, domain, range, x-intercept, y-intercept, one minimum or maximum, intervals where the function is positive, intervals where the function is negative.

Explanation:

It is given that,

Since the function is related to modulus value.

Then, the type of the function is Absolute value function.

Also, Since

Then, the domain of the function is,

Set h(x)=z,

The range of the absolute function c | a x + b | + k is f(x) is greater than equal to k.

Then,

Therefore, the range is,

From, the graph

From the figure there is no x-intercept.

Also, the y-intercept is 6.

Now, to find the critical points

Answer:   -11

Step-by-step explanation:

5⁶ is the simplified form of the expression ( 5⁶/5³ )².

Given the expression in the question;

( 5⁶/5³ )²

To simplify the expression; us the law of indices.

xᵃ ÷ xᵇ = xᵃ⁻ᵇ

Hence, perform the operation inside the parenthesis

( 5⁶/5³ )²

( 5⁶ ÷  5³ )²

( 5⁶⁻³ )²

( 5³ )²

To remove the parenthesis, apply the law of indices.

( xᵃ )ᵇ = xᵃ ˣ ᵇ

( 5³ )²

5³ ˣ ²

5⁶

Therefore, the simplified form of the expression is 5⁶.

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ANSWERS

(a) 0.420

(b) 0.400

(c) With a large number of spins, there might be a difference between the experimental and theoretical probabilities, but the difference should be small

EXPLANATION

(a) The experimental probability is given by,

In this case, Donna spun the dial 1000 times and 420 times it landed on yellow,

Hence, the experimental probability of landing on yellow is 0.420.

(b) The theoretical probability is given by the geometry of the spinner and, if it is fair, the number of yellow sections,

In this case, the spinner is divided into 10 equally sized slices, and 4 of them are yellow,

Hence, the theoretical probability of landing on yellow is 0.400.

(c) As we can see in parts a and b, for 1000 trials, the experimental and theoretical probabilities are almost the same - i.e. there is a small difference. This is known as the law of large numbers which states that if the number of trials of an experiment is large, the experimental probability of each event should be close to the theoretical probability.

Hence, the true statement is the first one: with a large number of spins, there might be a difference between the experimental and theoretical probabilities, but the difference should be small.

Answer:

x=12

Step-by-step explanation:

(4x + 7) + 35 = 90

(4x+7)=90-35
4x+7=55
4x=55-7
4x=48

x=12

Answer:

x=12

Step-by-step explanation:

it just is.,...........

Correct answer is C, For the given figure, ∠2 = ∠3, as they are corresponding angles of parallel lines.

The angles created when a transversal intersects two parallel lines are known as corresponding angles.

Typical examples of equivalent angles include opening and closing a lunchbox, resolving a Rubik's cube, and endless parallel railroad tracks.

Two congruent or identical triangles' corresponding angles are those of a congruent pair of their sides in a triangle. As a result, these angles are equivalent or have the same value.

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Complete Question -

In the figure, lines a and b are intersected by line t. Which of these statements proves that lines a and

b are parallel?

The end behavior of the given function will be given by Down on the left down on the right.

A function may be defined as the expression in which for one value of input variable there is only one value of output variable. The input variable or the independent variable is x, and the output variable or the dependent variable is y. In the given function f(x) = -3x⁴ + 7x² - x + 13 we will use the Power and Polynomial Functions features. For final behavior of power functions of the form f(x) = axⁿ where n is represented as a non-negative integer depends on the power and the constant. Here, the leading coefficient is -3x⁴. So, when x → ∞ the value of f(x) → -∞ and when x → -∞ then the value of f(x) → -∞. So, the final answer for the behavior will be given by "Down on the left, down on the right".

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The function of the total money raised from both donors after walking d kilometers is T(d) = 12d + d^2

From the question, the given parameters are:

Also, from the question, T is the total money raised from both donors at d kilometers

This means that the equation of the total money can be represented a

T(d) = A(d) + B(d)

Substitute the known values in the above equation

So, we have the following equation

So, we have

T(d) = 10d + 2d + d^2

Evaluate the like terms in the above equation

T(d) = 12d + d^2

The equation cannot be further simplified

Hence, the composite function is T(d) = 12d + d^2

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Complete question

Onur is participating in a walkathon fundraiser. Two donors promised to donate money based on the total distance he walks. The money, A, in dollars, that he receives from the first donor given that he walks d kilometers is given by the formula A(d)=10d

The money, B, in dollars, that he receives from the second donor given that he walks d kilometers is given by the formula B(d)=2d+d^2

Let T be the total money that Onur raises from those donors by walking d kilometers in the walkathon.

Write a formula for T(d) in terms of A(d) and B(d)