an auto dealer would like to determine if there is a difference in the braking distance (the number of feet required to go from 60mph to 0mph) of two different models of a high-end sedan. six drivers are randomly selected and asked to drive both models and brake once they have reached exactly 60mph. the distance required to come to a complete halt is then measured in feet. the results of the test are as follows. can the auto dealer conclude that there is a significant difference in the braking distances of the two models? use α

The co-ordinate of B ( -3 , 2 )

Its x value lies in the middle of the two x values.

Its y value lies in the middle of the two y values.

To figure it out:

Add the two "x" coordinates, then divide by two.

n order to divide by two, add the two "y" coordinates.  

Mid point  (X , Y) formula

X = ( x₁ + x₂ ) ÷ 2

Y = ( y₂ + y₂ ) ÷ 2

where ( x₁ , y₁)  co- ordinate of A ( 7 , -2 )

(x₂ , y₂ ) co- ordinate of B

 2 = ( 7 + x₂ ) ÷ 2

x₂ = -3

0 = ( -2 + y₂ ) ÷ 2

y₂ = 2

co- ordinate of B ( -3 , 2 )

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Based on the number of teachers who voted for the skating rink and those who voted for the bowling alley, the ratio of votes for skating to bowling is 30 : 13

The ratio can be found by taking a ratio of those who voted for the skating rink against those who voted for the bowling alley. This ratio should then be taken to its simplest form.

Number of votes for bowling alley = 13 votes

Number of votes for skating rink = 30 votes

The ratio of votes for the skating rink to those of the bowling alley is:

30 : 13

This is the simplest form.

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The value of the expression is 13 that is formed by subtraction .

A mathematical expression that uses integer variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, multiplication, division, and exponentiation by a rational exponent).

now we use subtraction:

y-7

= 20-7

= 13

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We need to apply the Pythagorean Theorem, which says that the square of the Hypothenuse is equal to the sum of the squares of the cathetus. So we have:

The missing side is equal to 40.

The quadratic function's domain for a given function is -2<x>2.

What is the Domain of a quadratic function?

Function given [tex]x=-2(y-2)^2+2[/tex]

The vertices are represented by the vertex form, y = an (x-h)^2+ k, and (h,k).

h=-2

k=+2

It is clear that this parabola has a minimum value of y = -2 and a maximum value of y=+2.

The quadratic function's domain for a given function is -2<x>2.

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Using it's concept, the y-intercept for each table in this problem is given as follows:

2) y = 4.

3) y = -3.

In the context of this problem, we are given two tables with pairs of values (x,y), hence the y-intercept for each case is given by the value of y when x = 0.

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Graph:

x intercept = where it crosses the x axis = 5

asymptote = never touches it = 4

Answer:

The x-intercept is 5, and the asymptote is located at x = 4.

Answer:

A. Total area of Alaska is considerable larger than total area of Connecticut.

B. Population of California is considerably larger that population of Alaska.

Step-by-step explanation:

A. What is the difference in total area of Alaska and Connecticut?

According to the US government, total areas of Alaska and Connecticut are 663,268 square miles and 5,567 square miles, respectively.

The difference between both quantities is:

[tex]x=6.633 \times 10^{5} mi^{2} -5.567 \times 10^{3} mi^2\\x=6.577 \times 10^{5} mi^2[/tex]

Which means that total area of Alaska is considerable larger than total area of Connecticut.

B. What is the difference in total population of California and Alaska?

According to the US government, total populations of California and Alaska are 39,512,223 people and 710,249 people, respectively.

The difference between both quantities is:

[tex]x=3.951 \times 10^7 people - 7.103 \times 10^5 people\\x=3.880 \times 10^7 people[/tex]

Which means that population of California is considerably larger that population of Alaska.

Slope = 2

The slope of coordinates ( 20 , 15 ) and (30 , 35) = 2

Here given two points (20, 15) and (30 , 35)

Formula to find slope = y2 - y1 / x2 - x1

                                    = 35 - 15 / 30 - 20

                                    = 20 / 10

                                    = 2 / 1

                                    = 2

∴ Slope of (20 , 15) (30 , 35) = 2 .

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Given that the start time is 5:15 am. It can be represented as,

Also given that the end time is 12:04 pm. It can be represented as.

The elapsed time (e) is equal to the difference between the end time and start time as given below,

Substitute the values,

Note that 04 minutes is greater than 15 minutes, so we have to borrow 1 hour from 12 hours and add it to the minutes,

Replace the value and perform the subtraction,

Thus, the required elapsed time is 6:49, that is, 6 hours and 49 minutes.

The relation is a function if every ordered pair has one value of x, which means x does not repeat

Let us study each relation

a) {(5, 1), (-2, 4), (1, 1), (5, 2)}

Since each ordered pair has a different value of x

There are 2 ordered pairs that have x = 5

This relation is not a function

b) {(1, 4), (-2, 2), (5, 1), (-6, 2)}

Since no repeated x in the ordered pairs

Then the relation is a function

c) There are 2 ordered pairs with x = -2

It is not a function

d) There are 2 ordered pairs with x = 1

It is not a function

The answer is b

The coefficient of the first term of the polynomial is 1.

Polynomials are algebraic expressions of the following form:

f = Σ (cₙ · xₙⁿ)

Where:

The order of the terms of a polynomial is usually from the left to the right. Then, the first term of the polynomial x + 9 · y³ + 4 is x = 1 · x, whose coefficient is equal to 1.

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The cups of flour that is needed for 2 1/2 cups of flour is 6 2/3 cups.

A mixed number is a fraction that has a whole number, a numerator and a denominator. The numerator usually has a smaller value when compared with the denominator. An example of a mixed number is 2 1/2.

In order to determine the cups of flour that is needed for 2 1/2 batches of pancakes, multiply 2 1/2 by 2 2/3. Multiplication is the mathematical operation that is used to determine the product of a number. The sign that represents multiplication is x.

Flour needed = batches to be made x amount of flour needed for one batch

2 2/3 x 2 1/2

8/3 x 5/2 = 20 / 3 = 6 2/3 cups

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In order to find the quadratic equation, let's use the vertex form below:

Where the vertex is located at (h, k).

So, if the vertex is (h, k) = (-4, 2) and using the point (x, y) = (-4, 0), we have:

Since the final statement is false, it's not possible to have a quadratic function with vertex (-4, 2) and with the point (-4, 0).

If we use the point (4, 0) instead, we would have:

So the equation in this case would be:

The empty spaces would be filled with the values -1/32, -4 and 2.

Answer:

[tex]f(x)=x+2[/tex]

Step-by-step explanation:

Given parameters:

Therefore, there are two points on the line:

The linear relationship between the x and y values is:

[tex]\implies f(x)=x+2[/tex]

To prove this algebraically, define the points:

Find the slope of the linear function by substituting the defined points into the slope formula:

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{4-2}{2-0}=\dfrac{2}{2}=1[/tex]

Substitute the found slope and one of the points into the point-slope formula to create a linear function that satisfies the given parameters:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-2=1(x-0)[/tex]

[tex]\implies y-2=x[/tex]

[tex]\implies y=x+2[/tex]

Hence proving that the linear function is:

[tex]f(x)=x+2[/tex]

Answer:

It meant that the results were more reliable and the average makes it more reliable.

Step-by-step explanation:

The researchers used data from ten trials and averaged them, rather than data from a single trial because the data from single trials are more likely to include errors.

Research the issue utilizing data from a number of sources. It is critical to understand what one is attempting to achieve while designing an experiment.

The first method is to average identical successive trials, in which the researcher simply compares mean values across groups of patients or treatment effects. Averaging, to some extent, presume that the behavior is random. This premise is often ignored. If there is something systematic going on, such as a trial-by-trial change in response owing to adaptation/learning or weariness, this is potentially highly significant clinical information that is lost when the trials are averaged.

Thus, the data from single trials are more likely to include errors

Hence, the researchers used data from ten trials and averaged them, rather than data from a single trial.

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From the given parameters using Pythagoras theorem, we can say that No, the ladder will not reach a window that is 21.5 feet above the ground.

We are told that the ladder is 25 ft and leans against the wall and so this will be the hypotenuse of the right angle triangle formed with the building.

The horizontal distance from the base of the ladder to the building is 15 ft. Thus, this will be the base or adjacent side of the triangle.

I have drawn a triangle to show this measurements and so we can use Pythagoras theorem to find the vertical height from the top of the ladder to the ground.

BC² = AB² +  AC²

25² = 15² +  AC²

AC² = 25² - 15²

AC = √(25² - 15²)

AC = 20 feet

Since the ladder is a vertical height of 20 ft from the ground which is less than the height of the window from the ground then we cans ay that the ladder will not reach the window.

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The slope and y-intercept of 2y = 6x - 12 are 3 and (-6) respectively.

What is the slope intercept form of a line?
The line with m as the slope, and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.
The slope, m, is a measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, c, denotes the y-coordinate of the location where the line's graph crosses the y-axis.

Given, the equation of the line is 2y = 6x - 12
Dividing the given equation by 2 we get, y = 3x - 6 ⇒ y = 3x + (-6)
Comparing the equation with the standard form of slope intercept form of a line as established in literature, we have:
Slope = m = 3 and y-intercept = c = -6
Thus, the slope and y-intercept of 2y = 6x - 12 are 3 and (-6) respectively.

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Answer:

-3/4÷5= -3/4*1/5

-3/20

-3/20 is the answer

The equation of the volume function is V(x) = 1/3(x + 4)²(x - 1)

The given parameters are

Radius, r = x + 4

Height, h = 5 units less than the radius

This means that

h = r - 5

So, we have

h = x + 4 - 5

Evaluate

h = x - 1

The volume of a cone is calculated as

V = 1/3πr²h

Substitute the known values in the above equation

V = 1/3 * (x + 4)² * (x - 1)

This gives

V = 1/3(x + 4)²(x - 1)

Express as a function

V(x) = 1/3(x + 4)²(x - 1)

Hence, the function is V(x) = 1/3(x + 4)²(x - 1)

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Answer:

it is per 1

Step-by-step explanation:

The rate of change of the area is -80.5 [tex]inches^{2}[/tex]/sec.

Given:

A right triangle has legs of 21 inches and 28 inches whose sides are changing.The short leg is decreasing by 2 in/sec and the long leg is shrinking at 5 in/sec.

Let's set the two legs as a and b, so the lengths are:

a = 21 - 2t

b = 28 - 5t

The area is:

area a = ab /2

= (21 - 2t) (28 - 5t)/2

= (588 - 105t - 56t + 10[tex]t^{2}[/tex]/2

a = 5[tex]t^{2}[/tex] - 161t/2 - 299

The rate of change of the area is:

da/dt = d(5[tex]t^{2}[/tex] - 161t/2 - 299)/dt

da/dt = 10t -161/2

And at t=0,

= 10(0) - 161/2

= - 80.5

so the  rate of change of the area is -80.5 [tex]inches^{2}[/tex]/sec.

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Answer:

4

Step-by-step explanation:

the prime factors for each is

220 = 2 ×2×5×11

8 = 2×2×2

so the HCF =2×2 = 4

For any line, if you draw two right triangles using the line as the hypotenuse, we can say that; Yes, the triangles have to be similar because the sides of both triangles will have the same ratio.

From the attached diagram, we will assume any two right triangles are drawn on the line OP, and AB and A'B' as the hypotenuse on the same line OP.

Now, due to the fact that the slope of the line OP is constant and assume that it makes x° with the positive x-axis, then we can say that;

tan x = AC/BC = A'C'/B'C'

Thus;

AC/A'C' = BC/B'C'

Therefore, we can say that the sides of the two right triangles are in the same ratio and as such, Δ ABC and Δ A'B'C' are similar.

Therefore, all the right triangles will be similar.

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Equation of line in ordinary form: y = 2x+0

Equation of  line  in standard (general) form: 2x - y = 3

What is Slope?

The ratio of how much y grows as x grows by a certain amount is known as a line's slope. The slope of a line indicates how steep it is, or how much y rises as x rises. Anywhere along the line, the slope remains constant (the same).

a) Ordinary form =>

Slope Intercept Form:

y = mx+b

where m is the slope of the line

(Δy/Δx)

and b is the y-intercept.

For a line with slope 2 and point (-3,-6), plug 2 in for m, -3 for x, -6 for y, and solve for b.

-6 = 2(-3) + b

-6 = -6 + b

6 - 6 = b

b = 0

The equation in slope intercept form is

y = 2x+0

b) Standard form =>

Point Slope Form:

(y - y1) = m(x - x1)

Where m is the slope of the line

(Δy/Δx), y1 is the y coordinate of a point, and x1 is the x coordinate of a point.

For a line with slope 2 and point (-3,-6), plug 2 in for m, -3 for x1, -6for y1,

(y - (-6)) = 2(x - (-3))

Standard Form:

Ax + By = C

Where A, B, and C are integers. To write an equation in standard form, rewrite the equation in point slope form so that it fits the formula for standard form.

(y - (-6)) = 2(x - (-3))

(y + 6) = 2(x + 3)

y + 6 = 2x + 3

2x - y = 6 - 3

2x - y = 3

Hence, Equation of line in ordinary form is y = 2x+0

Equation of  line  in standard (general) form is 2x - y = 3

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The amount of money   Justin would have in his account than Aaron, to the nearest dollar is $0

What is the future value formula for continuous compounding cash flow?

The future value, which is used to determine the worth of this investment of $740 made now in 18 years is as shown below:

FV=PV*e^(rt)

FV=the worth of the investment in 18 years=unknown

PV=the amount invested today=$740

e=mathematical exponential value=2.7182818

r=rate of interest which compounded continuously=5%

t=time of investment in years=18

FV=$740*2.7182818^(5%*18)

FV=$740*2.7182818^(0.90)

FV=$740*2.459603087981220

FV=$1,820.11

Justin:

FV=PV*(1+r/m)^(n*m)

PV=$740

r=5%

m=number of times in a year that interest is compounded=365

m=number of years=18

FV=$740*(1+5%/365)^(18*365)

FV=$1,819.99

difference=$1,820.11-$1,819.99

difference=$0.12($0 to the nearest dollar)

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The variable x has a value of 3 in the triangle

The given parameter represents the triangle(s) in the figure

In the triangle, we can see that:

The above means that:

The sides of the triangle are in equivalent ratio

This is represented as

4 : 5x - 4 = 4 : 3x + 2

This also means that

5x - 4 = 3x + 2

Collect the like terms

5x - 3x = 4 + 2

Evaluae

2x = 6

Divide

x = 3

Hence, the value of x is 3

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Apply the compound interest formula:

A= P (1+r/n)^nt

Where:

A: future value of the investment

P: Principal amount

r: interest rate (in decimal form)

n: number of compounding periods in each year

t: years

Replacing:

A= 20,000 (1+0.08/12)^12x40

A = 20,000 (1.0067)^480

A= 485,467.7116