Find the slope of the line through each pair of points.
1. (4,-16), (7,18)
2. (2,1), (-9, -3)
3. (-11,2), (15,5)
4. (5,6), (10, -12)

A. The distributions of the periods is that using the five number summary is that

B. The box and whisker plot of the periods is attached

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

7th Period

66, 72, 77, 78, 78, 80, 82, 84, 84, 87, 88, 88, 89, 89, 90 92, 92, 93, 94, 94 96, 96

3rd Period

52, 60, 62, 64, 64, 65, 68, 71, 72, 74, 75, 76, 78, 79, 83, 84, 85, 88, 89, 93, 94, 97

The distributions of the periods will be compared using the five-number summaries

Using a graphing tool, the five-number summaries are:

7th Period

3rd Period

The box and whisker plot of the periods is added as an attachment

From the box and whisker plot attached, we can see the five-number summaries of the periods

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Answer:

\(\cos G=\dfrac{2}{3}\)

\(\csc E=\dfrac{3}{2}\)

\(\cot G=\dfrac{2}{\sqrt{5}}\)

Step-by-step explanation:

If the right angle of right triangle EFG is ∠F, then EG is the hypotenuse, and EF and FG are the legs of the triangle. (Refer to attached diagram).

Given ΔEFG is a right triangle, and EG = 6 and FG = 4, we can use Pythagoras Theorem to calculate the length of EF.

\(\begin{aligned}EF^2+FG^2&=EG^2\\EF^2+4^2&=6^2\\EF^2+16&=36\\EF^2&=20\\\sqrt{EF^2}&=\sqrt{20}\\EF&=2\sqrt{5}\end{aligned}\)

Therefore:

\(\hrulefill\)

To find cos G, use the cosine trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the hypotenuse is EG.

Therefore:

\(\cos G=\dfrac{FG}{EG}=\dfrac{4}{6}=\dfrac{2}{3}\)

\(\hrulefill\)

To find csc E, use the cosecant trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosecant trigonometric ratio} \\\\$\sf \csc(\theta)=\dfrac{H}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle E, the hypotenuse is EG and the opposite side is FG.

Therefore:

\(\csc E=\dfrac{EG}{FG}=\dfrac{6}{4}=\dfrac{3}{2}\)

\(\hrulefill\)

To find cot G, use the cotangent trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cotangent trigonometric ratio} \\\\$\sf \cot(\theta)=\dfrac{A}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the opposite side is EF.

Therefore:

\(\cot G=\dfrac{FG}{EF}=\dfrac{4}{2\sqrt{5}}=\dfrac{2}{\sqrt{5}}\)

Sleep hours per night is independent.

Given the data:

Hours of Sleep 39 or younger 40 or older

> 6 _____38 36

6 to 6.9 _ 61 58

7 to 7.9 __76 74

8 or more 65 92

The analysis will be conducted using the Chisquare statistic:

The supposition

H0: The amount of sleep each night is independent

H1: The amount of sleep each night is not independent

χ² = (observed - Expected) (observed - Expected)2 / Predicted

to speed up computation. To conduct the analysis, we might utilize a Chisquare calculator:

The evaluation statistic is 4.0061.

Row - 1 * The degree of freedom (column - 1)

Degree of freedom is equal to (4-1)*(2-1)=3*1=3.

Pvalue is 0.261.

Since Pvalue >, we are unable to reject the hypothesis that sleep duration is independent total %

> 6 _____38 36_ 74 _ 14.8

6 to 6.9 61 58 _ 119 23.8

7 to 7.9 __76 74 150 30

8 or higher 65 92 157 31.4

_______240 260 500 100

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Answer:

Step-by-step explanation:

At least 9 means more than 9 and includes 9

x ≥ 9     and    [9,  +∞)

At most 9 means numbers less than 9

x≤9       and  (-∞, 9]

more than 9 means bigger than 9 but not including 9

x > 9     and    (9,  +∞)

fewer than 9 means less than 9 but not including 9

x<9       and  (-∞, 9)

strictly between 7 and 9   means between 7 and 9 but not including

7<x<9      and    (7,9)       (This is the only one I'm unsure of.  Strictly, not sure if it includes or doesn't include, usually it just says include or doesn't include)

between 7 and 7 inclusive.   means it's just =7  There's no boundaries

x=7

no more than 7 means less than 7 and includes 7

x ≤ 7   and   (-∞, 7]

Answer:

1.05

Step-by-step explanation:

We start of with 100 * (1.7)^t

So the change in 100 is (1.7)^t(years). Well, that is in years, we need months. There are 12 months in a year, this is good to remember for several reasons ;). Since they ask for "Every month, the number of exercises increases by a factor of:", we must plug in 1/12 as t.

We can rewrite this as:

100 * (1.7)^1/12

Just plug the (1.7)^1/12 into a calculator, which is a cool device that can do boring math for you, and you should get 1.045... blah blah blah(a bunch of other useless numbers).

So now we have:

100*1.045

Well, the problem said "Round your answer to two decimal places."

So we need to round the 1.045.

5 is right in the middle, but if you know rounding, your probably know that the 5 goes up. So yay, your 1.045 is now 1.05.

So in the end, we get:

1.05

Ti⊂k∫∈s ω∅∅p :)

The number of exercises increases by a factor of approximately 14.17 each month.

To determine the monthly rate of change in the number of exercises, we need to find the factor by which the number of exercises increases each month.

The given function, Eyear(t) = 100 × \((1.7)^t\), represents the total number of exercises after t years. To convert this to a monthly rate, we need to divide the yearly rate by 12 (since there are 12 months in a year).

So, the monthly rate of change in the number of exercises is:

E_month(t) = Eyear(t)/12

Substituting the given function, we have:

Emonth(t) = 100 × \((1.7)^t\)/12

To find the factor by which the number of exercises increases each month, we can compare the value of E_month(t) at t = 1 to the value at t = 0:

E_month(1) = 100 × \((1.7)^t\)/12 = (100 × 1.7)/12 = 14.17

Therefore, the number of exercises increases by a factor of approximately 14.17 each month.

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Given a pair of points on a straight line

To Determine: The slope of the line

Solution:

The slope formula given two points is

The given points are

Substitute the given points into the formula to find the slope

The slope of the line is 0

Please note that a zero slope is just the slope of a horizontal line. The y-coordinate never changes no matter what the x-coordinate is.

Hence, the slope of the line is 0

The one way journey is 45 miles

Here, we want to get the number of miles for the one way trip

To calculate this, we have to look at the triangle formed on the left

By calculating this distance, we have the value of the number of miles traveled on a leg

We need the base and height of the triangle

The base is the x-axis change from the orgin while the height is the y-axis change from the origin

Looking at the graph, we can see that this value moves from 45 miles to 0 miles

So, the distance traveled is 45 miles on a leg of the journey

Answer:

  50√3 ≈ 86.6 m

Step-by-step explanation:

The geometry can be modeled by a right triangle with the height of the kite being the leg opposite the 60° angle. The hypotenuse has the given length of 100 m.

The mnemonic SOH CAH TOA reminds you that the relation between angles and the sides of interest here is ...

  Sin = Opposite/Hypotenuse

  sin(60°) = (kite height)/(100 m)

  kite height = (100 m)·sin(60°) = (100 m)(√3)/2

  kite height = 50√3 m ≈ 86.6 m

Answer:

74

Step-by-step explanation:

Answer:

24.5%

Step-by-step explanation:

Given

P(Off-Campus) = 0.30

P(Part-Time Job | Off-Campus) = 0.62

P(Part-Time Job | On-Campus) = 0.65

Inferred

P(On-Campus) = 0.70

P(No Part-Time Job | Off-Campus) = 0.38

P(No Part-Time Job | On-Campus) = 0.35

Calculation

P(No Part-Time Job | On-Campus) = P(No Part-Time Job ∩ On-Campus)/P(On-Campus)

0.35 = P(No Part-Time Job ∩ On-Campus)/0.70

0.245 = P(No Part-Time Job ∩ On-Campus)

Therefore, 24.5% of students that live on campus do not have a part-time job.

Answer:

Answer:

(0, 6)

Step-by-step explanation:

Point T has a coordinate pair of (3, 4). That is, at point T, x = 3, while y = 4.

3 points to the left of T would be a movement on the x-axis. This movement is a run across the x-axis. At T, x = 3. Therefore, 3 points to the left would be a decrease by 3 = 3 - 3 = 0.

3 points to the left of T would leave us with an x coordinate of 0.

2 points above T suggest a rise, which is on the y-axis.

Therefore, at T, y = 4. 2 points above 4 = 4 + 2 = 6. y coordinate would now be 6.

In conclusion, the ordered pair representing 3 points to the left, and 2 points above point T is (0, 6).

Answer:

(0, 6)

Step-by-step explanation:

The value of x that makes A parallel to B is 15.

Alternate exterior angles are a pair of angles that lie outside of two parallel lines and are on opposite sides of the transversal. In other words, they are a pair of non-adjacent angles that are formed when a transversal intersects two parallel lines. The angles are congruent, meaning that they have the same measure.

The term "alternate" refers to the fact that they are on opposite sides of the transversal and "exterior" indicates that they are outside of the parallel lines. Alternate exterior angles are important in geometry because they can be used to prove that two lines are parallel. If the alternate exterior angles are congruent, then the lines are parallel.

Since the alternate exterior angles are equal, we can set them equal to each other:

8x + 30 = 10x

Subtracting 8x from both sides, we get:

30 = 2x

Dividing both sides by 2, we get:

15 = x

So the value of x that makes A||B is 15.

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The answer is:

C. circumference

Work/explanation:

Here's the correct answer:

The distance around a circle is called the circumference.

How to find the circumference :

Answer:

2.) x=−3 and y=0

Step-by-step explanation:

im still tryna figure out answer to number 1. sorry

Answer:

i think C correct me if im wrong pls

Step-by-step explanation:

Answer:

(x+2) ^2 + (y-3)^2 = 25  

Step-by-step explanation:

The equation of a circle is given by

(x-h) ^2 + (y-k)^2 = r^2  where (h,k) is the center and r is the radius

(x--2) ^2 + (y-3)^2 = 5^2

(x+2) ^2 + (y-3)^2 = 25  

we have

6+6×8-5÷3+12​

so

Applying PEMDAS

P ----> Parentheses first

E -----> Exponents (Powers and Square Roots, etc.)

MD ----> Multiplication and Division (left-to-right)

AS ----> Addition and Subtraction (left-to-right)

step 1

Multiplication

6x8=48

substitute

6+48-5÷3+12​

step 2

Division

5÷3=5/3

substitute

6+48-(5/3)+12

step 3

Addition

6+48=54

54-5/3+12

step 4

S

Answer:

64.33 is the answer.

The single power that is equivalent (4³)² to is 4^6.

This is a term in mathematics to refer to the exponents. The given expression is four to the power of three all to the power of two. Exponents helps to represent equations and makes it easier to remember  and handle.

Given data

(4³)²

This could be solved using the laws of indices

(4³)² =  4³ * 4²

4³ * 4² = 4³ *² = 4^6

Hence we can say that the single power that is equivalent (4³)² to is 4^6.

base = 4

power = 6

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Answer:

Is g(x)

Step-by-step explanation:

We search the roots of the function on this way

(x-1)^2 (x+2) =0

(x-1)^2 =0

x-1=\(\sqrt{0}\)

x=1  ////

(x+2)=0

x=-2 ////

So (1,0) and (-2,0) are the roots of the function (as the image)

0 and 2.

These numbers will make the rational expression undefined.

basically the denominator will be 0 which is undefined.

Answer:

8 months

Step-by-step explanation:

if you can get 120 per month then 950/120 = ~8

Answer:

She needs $350.

Step-by-step explanation:

120 x 5 = 600

$950 - $600 = $350

In order to find the sign of the product, we need to know that the product of two equal signs will be a positive sign, and two different signs will be a negative sign.

Also, we can consider just the sign of each number in order to find the final sign.

So we have that:

The sign of the product is negative, if A is a positive number, and is positive, if A is a negative number.

The actual distance represented by 23.7 cm on the map is 355.5 km.

To find the ratio of the amount of money Mabaso has to the amount of money Thabo has and the amount of money Ally has, we can divide each amount by the smallest amount (which is R35) to simplify the ratio.

Mabaso has R140, Thabo has R70, and Ally has R35.

The ratio of Mabaso's money to Thabo's money is:

R140 ÷ R35 = 4

The ratio of Mabaso's money to Ally's money is:

R140 ÷ R35 = 4

Therefore, the ratio of the amount of money Mabaso has to the amount of money Thabo has and to the amount of money Ally has is 4:1:1.

To calculate the percentage discount of a steel table, we need to find the difference between the original price and the discounted price, and then divide it by the original price. Finally, we multiply the result by 100 to get the percentage.

Original price: R750

Discounted price: R600

Discount: R750 - R600 = R150

Percentage discount: (R150 ÷ R750) × 100 = 20%

So, the table has a 20% discount on Black Friday.

To convert 125 grams to kilograms, we divide the amount in grams by 1,000 (since there are 1,000 grams in a kilogram).

125 g ÷ 1,000 = 0.125 kg

Therefore, 125 grams is equal to 0.125 kilograms.

If a green grocer packs 12 apples in a plastic bag and has 285 apples, we divide the total number of apples by the number of apples per bag to determine the number of bags needed.

Number of bags needed: 285 apples ÷ 12 apples/bag = 23.75 bags

Since we can't have a fraction of a bag, we round up to the nearest whole number. Therefore, the green grocer would need 24 bags.

If the scale of a map is 1,500,000 and the measurement on the map is 23.7 cm, we can use the scale to determine the actual distance.

1 cm on the map represents 1,500,000 cm in reality.

23.7 cm on the map represents x cm in reality.

x = 23.7 cm × 1,500,000 cm = 35,550,000 cm

To convert cm to km, we divide by 100,000 (since there are 100,000 cm in a kilometer).

35,550,000 cm ÷ 100,000 = 355.5 km

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Answer:

x=3

Step-by-step explanation:

A vertical line is an up and down line

It is of the form

x =

The x coordinate is 3

x=3

Answer:

The geometric mean growth rate of sales is 1.4422.

Step-by-step explanation:

We have two sales values, one from 6 years ago and the other from now.

We have to calculate the geometric growth rate of sales.

We have:

\(y(-6)=1,000,000\\\\y(0)=9,000,000\)

We can write the relation between these two values as:

\(y(0)=y(-6)k^{0-(-6)}\\\\9,000,000=1,000,000k^6\\\\k^6=9\\\\k=9^{1/6}= 1.4422\)

The geometric mean growth rate of sales is 1.4422.

Answer:

4y^12+9 over y^12

Step-by-step explanation:

hope it helps

Answer:

300 + 15x = 500

15x = 200

x = 200/15

x=13.333

14 pair of shoes

Step-by-step explanation:

Answer:

one

Step-by-step explanation:

Answer:

-3/-2 is the correct answer

Step-by-step explanation:

i have done this stuff before so it is that because the two negatives becomes one