The scatter plot below shows the relationship between years of education and income for a representative sample of adults.
Which of the following is the best estimate of the average change in a person's income that is associated with going to school for an additional year?
Choose 1 answer:
Choose 1 answer:

(Choice A)
A
$
1
$1dollar sign, 1

(Choice B)
B
$
2
$2dollar sign, 2

(Choice C)
C
$
3000
$3000dollar sign, 3000

(Choice D)
D
$
7000
$7000dollar sign, 7000

2
2
4
4
6
6
8
8
10
10
12
12
14
14
16
16
18
18
20
20
22
22
24
24
20000
20000
40000
40000
60000
60000
80000
80000Annual income (dollars)Years of education

Answer:

Step-by-step explanation:

Remark

The cos(60) = 1/2

The radii marked 6 is the adjacent side. You have to solve for the hypotenuse.

Why?

Because the hypotenuse is the distance from the center of the circle to the point of intersection of the angle. Once you have the hypotenuse, you can find the length of the tangent, which will lead to the area of the kite. Then take away 1/3 the area of the circle.

Hypotenuse

Cos(60) = 1/2

cos(60) = adjacent / hypotenuse        Multiply both sides by the hypotenuse

hypotenuse * cos(60) = adjacent       Divide by Cos(60)

hypotenuse = adjacent / cos(60)  

adjacent = 6

hypotenuse = 6/0.5

hypotenuse = 12

Tangent

tangent^2 = 12^2 - 6^2

tangent^2 = 144 - 36

tangent^2 = 108

tangent = sqrt(108)

tangent = 6sqrt(3)

Triangles

The area of the triangle = 1/2 6sqrt(3) * 6

The area of the triangle = 18 sqrt(3)

There are two triangles so the area = 36 sqrt(3) That's the area of the kite.

Circle sector.

Area of the circle sector = 1/3 * pi * r^2

r = 6

Leave pi as it is.

Area of the circle sector = 1/3 * pi * 6^2

area of the circle sector = 12 pi

Answer

Area of the red part = area of the triangles - the area of circle sector

Area of the red part = 36*sqrt(3) - 12* pi            

Answer:

(0, -2)

(-3, 1)

(3, -4)

Step-by-step explanation:

The constraints given as;

x + y ≥ -2

3x - y ≤ 2

x - y ≥ -4

Since we want to find vertices of the feasible region, we will ignore the less than or greater than sign and use the equal to sign to some simultaneously.

Let's add first and third constraint together to get;

2x = -6

x = -6/2

x = - 3

Put - 3 for x in equation 1 to get;

-3 + y = -2

y = 3 - 2

y = 1

Thus, vertex here is; (-3, 1)

Lets add first and third equations to get;

4x + 0 = 0

Thus, x = 0

Putting this for x in eq 1;

0 + y = -2

y = -2

vertex here is; (0, -2)

Lets subtract eq 3 from eq 2 to get;

2x = 6

x = 6/2

x = 3

Put 3 for x in eq 3;

x - y = -4

vertex here is; (3, -4)

Answer: I'll solve A) since there is a lot of work to be shown.

Step-by-step explanation:

A)

(x−1)³+3x(x−4)+2=x³

Use binomial theorem to expand  (x−1)³

x³- 3x² + 3x - 1 + 3x(x-4) + 2=x³

Use distributive property on 3x(x-4)

x³- 3x² + 3x - 1 + 3x²-12x + 2=x³

Add like terms

x³ −9x + 1 =x³

Subtract x³ from both sides.

x³ −9x +1 -x³ = 0

Add x³ and -x³

−9x+1=0

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

−9x=−1

Divide both sides by -9.

x= 1/9

Answer: The student is not correct

To reflect over the y axis, you use this rule

[tex](x,y) \to (-x,y)[/tex]

The x coordinate swaps in sign (from positive to negative, or vice versa) while the y coordinate stays the same.

So for a point like A(1,1), it should move to A ' (-1, 1) and not (-2,1) like the diagram shows.

B(3,1) should move to B ' (-3, 1)

C(1,4) should move to C ' (-1, 4)

It appears that the student applied a reflection over the y axis, and then they shifted the triangle 1 unit to the left.

Answer:

58%

Step-by-step explanation:

10*5=50

7*3=21

21/50 chance to choose inside small rectangle

21/50*2 = 42/100 chance to choose inside small rectangle

100-42=58%

Multiply x and y by 2:

A. (-6, 4)

B. (2, 2)

C. (-2, -2)

Answer:

B. slope 1/4, y-intercept at ( 0, 5)

Step-by-step explanation:

slope m = change in y /chance in x = 5-4 / 0-(-4) = 1 / 4

the y-intercept is the point where the graph of the line intersects the y-axis so will have the coordinates (0 because x will be 0 if the point is on the y-axis, and y is a number) so is (0, a number)

we are given that one of the points is (x=0, y=5) so this is our y-intercept

OR

the slope intercept form equation of a line y= mx+b, where b is the y-intercept

y = (1/4)x +b, for the point (0, 5) we substitute x=0, and y=5

5 = (1/4)*0 +b

5 = b

Answer:

3

Step-by-step explanation:

Easy pythagorean theorum question.

The law states that "A squared plus B squared, equals C squared."

A and B are the two sides that border the 90 degree mark.

C is the hypotenuse or the longest side/diagonal.

Since we know C and A (I chose to use A because why not) we can fill in the equation with what we know

2^2 + ?^2 = [tex]\sqrt{13^{2} }[/tex]

So

4 + ?^2 = [tex]\sqrt{13^{2} }[/tex]

Since the 13 is already squared in side of a root, it stays as 13

4 + x^2 = 13

4 - 4 + x^2 = 13 - 4

x^2 = 9

x^2 root = root of 9

x = 3

The missing side is 3.

Or you could use an online calculator xD

Answer:

A. 18

Step-by-step explanation:

the equation :

RF×RS = PR×RQ

16×9 = PR × 8

144 = PR×8

PR = 144/8

PR = 18

If the length of FR is 16 units then the length of PR is 18 units which is option A.

Circle is a figure whcih is having an arc showing points which are at equidistant from the centre point. The distance of arc from the centre point is known as radius.

From the rule of tangents and point outside the circle we can say that,

RF×RS = PR×RQ

16×9 = PR × 8

144 = PR×8

PR = 144/8

PR = 18 units

Hence if the length of FR is 16 units then the length of PR is 10 units.

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Answer:

A

Step-by-step explanation:

Cuz that’s the only graph that goes with the statement.

on this graph it’s saying the cost of 3 hair accessories is $10.

X = 3

Y = 10

Respuesta:

9 años

Explicación paso a paso:

Dado :

Capital = Principal, P = 8500 €

Rendimiento, tasa, r = 3,75%

Intereses, i = 2868,75 €

Para obtener el plazo, número de años que se necesitarán para devengar un interés de 2868,75 € sobre un capital de 8500 € al tipo del 3,75%;

Interés = principal * tasa * tiempo

2868,75 € = 8500 € * 0,0375 * t

2868,75 € = 318,75 billones €

t = 2868,75 € / 318,75 €

t = 9

Por lo tanto, tomará un período de 9 años.

Answer:

is it 4.2626

Step-by-step explanation:

let me know if it right

Answer:

2.7 kilometers

Step-by-step explanation:

Distance per run = 50 meters

Number of run per day = 6

Distance run per day = Distance per run * Number of run per day

= 50 meters * 6

= 300 meters

Last week he ran 4 day

Total distance run last week = Distance run per day * number of days

= 300 meters * 4

= 1200 meters

this week he ran 5 days

Total distance run this week = Distance run per day * number of days

= 300 meters * 5

= 1500 meters

Total distance for two weeks = Total distance run last week + Total distance run this week

= 1200 meters + 1500 meters

= 2700 meters

1000 meters = 1 kilometer

2700 meters = 2700/1000

= 2.7 kilometers

Total distance for two weeks = 2.7 kilometers

Answer:

There are 104 nickels and 33 quarters

Step-by-step explanation:

Start of with the equation N = 3Q + 5. q is the amt of quarters n is the nickels. Then substitute Q with 33 since that is the amount of quarters and solve the equation for the amount of nickels that there are.

Answer:

4th option, 5 5/6

Step-by-step explanation:

8 1/2 - 2 2/3

= 17/2 - 8/3

= (51-16)/6

= 35/6

= 5 5/6

Answered by GAUTHMATH

Answer:

a/9 - 4

Step-by-step explanation:

The expression will be (x/9) - 4.

It is given that a number x is the quotient of a number and 9 decreased by 4.

We have to find the variable expression for this.

What will be the expression for , 2 times of a number minus 4 ?

The expression will be 2x -4.

Quotient of a number and 9

= x / 9

Decrease this by 4 ; we get

= (x / 9 ) - 4

Thus , the expression will be (x/9) - 4.

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Answer:

Step-by-step explanation:

Answer:

a^2 + b^2 = c^2

4+16 = c^2

20 = c^2

c = [tex]\sqrt{20}[/tex] = [tex]2\sqrt{5}[/tex]

Step-by-step explanation:

Answer:

x = 4 and y = 8

Step-by-step explanation:

This is a special right triangle with angle measures 90-60-30 degrees

The side lengths are like the following :

The side length that sees 90 degrees is represented with a

The side length that sees 60 degrees is represented with a[tex]\sqrt{3}[/tex]

The side length that sees 30 degrees is represented with 2a

now, the angle measure that sees 60 degrees is given as 4[tex]\sqrt{3}[/tex] so we understand that a is = 4 that's how we find the value of x and y

Answer:

B

Step-by-step explanation:

The correct answer is B

Answer:

216

Step-by-step explanation:

π=3

r=3

h=8

so,

πr²h

= 3×3²×8

= 216

Answered by GAUTHMATH

Answer:

51

Step-by-step explanation:

$\sf\underline\bold{Question:1-}$

A ball is thrown upwards and it goes to the height of 100meter and comes down. What is the net displacement?

$\sf\underline\bold{Solution}$

$\sf{According \: to\:the\: question,}$

Displacement for the above situation is 0. As we know, that displacement is the shortest path from the initial to the final point. Here, the initial and the final points are the same, and henceforth, it takes no time to travel. So the displacement is 0.

$\sf\underline\bold{Question:2-}$

An athlete completes one round of a circular track of diameter 200m in 30 seconds. Find the distance covered by the athlete at the end of 30 second.

$\sf\underline\bold{Solution:}$

$\sf\bold{Given\:parameters:}$

$\sf\small{☆The\:diameter\:of\:the\:circular\:track:200m}$

$\sf{Radius=}$ $\sf\dfrac{200}{2}$ → $\sf\underline{Radius = 100m}$

☆Time taken by an athlete to complete one round : 30 seconds.

$\space$

$\sf\bold{To\:find:}$

❍Distance travelled by an athlete in 30 seconds.

$\space$

❍ AND,Distance travelled by the athlete will be equal to the cumference of the circle.

$\space$

$\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\sf{So,}$

$\mapsto$ $\sf{Circumference\:of\:the\:circle: 2 πr}$

$\space$

$\mapsto$ $\sf{Circumference=2\times}$ $\sf\dfrac{22}{7}$ $\sf{\times 100}$

$\space$

$\mapsto$ Circumference of the circle : $\sf\dfrac{4400}{7}$

$\space$

[tex]\sf\underline\bold{∴Circumference = 628.57m}[/tex]

$\space$

||Therefore,The distance travelled in 30 seconds, by the athlete is 628.57m.||

0 = 1st answer

628.57 m = Question 2 answer.

Answer:

[tex]3\left(8-4x\right)<6\left(x-5\right)[/tex]

[tex]3(8-4x)=241-2x[/tex]

[tex]6(x-5)=6x-30[/tex]

[tex]24-12x<6x-30[/tex]

Subtract 24 from both sides

[tex]-12x<6x-54[/tex]

Now, subtract 6x from both sides

[tex]-18x<-54[/tex]

Multiply both sides by -1

[tex]18x>54[/tex]

Divide 18 from both sides

[tex]x>3[/tex]

OAmalOHopeO

Answer:

96 ounces each day

Step-by-step explanation:

Divide the 24 bottles by 3

24/3 = 8

8bottles per day

8 bottles *12 ounces per bottle

96 ounces each day

Answer:

Step-by-step explanation:

Triangle ABC is a 45-45-90 right triangle. That means that segment BC also measures 10.

The big triangle as a whole is a 30-60-90. The side length across from the 30 degree angle is 10, so the whole length of BD is 10√3. However, since we already have the length of BC as 10, then segment CD measures

10√3 -10 which is 7.32