Introduction to Interval Notation

What is the domain and range?

THERE YOU GO I HAVE TO TYPE WORDS

Answer:

[tex]y=\frac{15\sqrt{3} }{4}[/tex]

Step-by-step explanation:

Well what you have here are two right triangles within another right triangles created by an altitude. This results in 3 similar triangles (see attached for reference)

As a result , using the properties of similar triangles, and taking ratios of their sides of the medium triangle and the largest triangle, we can form the following relationship:

[tex]\frac{b}{z}=\frac{y}{x} = \frac{z}{a+b}[/tex]  (we know that a+b = 15), hence the equation becomes:

[tex]\frac{b}{z}=\frac{y}{x} = \frac{z}{15}[/tex]  ----------eq 1

If we consider the largest triangle, we will see that

cos 30° = z / 15

but from our special angles (see second attachment) we know that cos 30° = (√3)/2

hence

(√3)/2 = z / 15

z = (15√3) / 2 --------eq 2

from the same largest triangle, we will also see that

sin 30° = x / 15

similarly from our special angles, we know that sin 30° = 1/2

hence,

1/2 = x/15

x = 15/2 --------eq 3

now that we have values for x and z, we can neglect the first term of equation 1 and form an equality with x, y and z

[tex]\frac{y}{x} = \frac{z}{15}[/tex]

[tex]y = x\frac{z}{15}[/tex]  (substituting the values for x and z that we found above)

y = (15/2) · [ (15√3) / 2] / 15

y = (15√3) / 4

[tex]y=\frac{15\sqrt{3} }{4}[/tex]

Let as consider the complete ques is : Ray QS bisects ∠PQR. Solve for x and find m∠PQR. m∠PQS = 3x ; m∠SQR = 5x-20.

Given:

Ray QS bisects ∠PQR.

m∠PQS = 3x

m∠SQR = 5x-20

To find:

The value of x and m∠PQR

Solution:

Ray QS bisects ∠PQR. So,

[tex]m\angle PQS=m\angle SQR[/tex]

[tex]3x=5x-20[/tex]

[tex]3x-5x=-20[/tex]

[tex]-2x=-20[/tex]

[tex]x=10[/tex]

The value of x is 10.

Now,

[tex]m\angle PQR=m\angle PQS+m\angle SQR[/tex]

[tex]m\angle PQR=3x+5x-20[/tex]

[tex]m\angle PQR=8x-20[/tex]

Put x=10,

[tex]m\angle PQR=8(10)-20[/tex]

[tex]m\angle PQR=80-20[/tex]

[tex]m\angle PQR=60[/tex]

Therefore, the m∠PQR is 60 degrees.

Answer:

1/3

Step-by-step explanation:

We have 6 slices

2 are yellow

P ( yellow) = number of yellow / total

                 = 2/6

                  = 1/3

Answer:. 1/3 probability that it stops on yellow.

Step-by-step explanation:

There are 6 possible outcomes. 2 are the incidents that you are looking for.

Make a ratio 2:6 or a fraction 2/6

Then simplify or reduce the fraction. 2/6 = 1/3

Answer:

did anyone figure this out

The distance between two points on a plane can be found by Pythagoras's theorem.

The shortest route from her home to her workplace is the route that passes along the block in the middle of the graph ,which is approximately 2.5 blocks shorter, than the apparently next shortest route.

Reason:

The shortest distance between two points is a straight line.

The shortest route to her workplace are the routes that approximate a straight line the most.

Following the dotted lines, there are two routes, that are approximately direct and therefore short routes to her workplace which are;

Taking the route that passes close to the center of the map to her workplace ,gives;

Path 1 = √(2² + 4²) = 2·√5 (by Pythagoras's theorem)

Path 2 = √(1² + 2²) = √5

Path 3 = 1 + 1 = 2

Path 4 = √(2² + 3²) = √13

Path 5 = 3

Cumulative distance = 2·√5 + √5 + 2 + √13 + 3 ≈ 15.3

Taking the route to the left of the above route, gives;

Path 1 = √(2² + 4²) = 2·√5

Path 2 = 7 + 6 = 13

Cumulative distance = 2·√5 + 13 ≈ 17.5

Therefore, the shortest route is the route that heads to her workplace, through, close to the center of the map, which approximately 17.5 blocks - 15.3 blocks  = 2.5 blocks shorter

Learn more here:

https://brainly.com/question/20054245

Answer:

[tex]4a^{2} + 9b^{2} + 3b[/tex]

Step-by-step explanation:

Distributive Property

[tex]4a^2 - 3(2b - 3b^{2} + 3b)[/tex]

Distributive Property

[tex] {4a}^{2} - 6b + 9b^{2} + 9b[/tex]

Combine Like Terms

[tex]4a^{2} + 9b^{2} + 3b[/tex]

The missing part of the question is;

What is the projected number of people aged 65 and over with Alzheimer's disease in 2030 and in 2050

Answer:

In 2030, P(20) = 7.9536 (in millions)

In 2050, P(40) = 13.2688 (in millions)

Step-by-step explanation:

We are given that;

Number of people aged 65 and over in the U.S. population with Alzheimer's disease (in millions) as;

P(t) = −0.0002083t³ + 0.0157t² – 0.093t + 5.2 (4 ≤ t ≤ 40);

Where t is measured in years and t = 4 corresponds to the year 2014.

Now,

Since t = 4 represents 2014,therefore;

t = 20 would represent population in 2030

Thus in year 2030;

P(20) = −0.0002083(20)³ + 0.0157(20)² – 0.093(20) + 5.2

P(20) = 7.9536 (in millions)

Also, in year 2050, t will correspond to 40 years.

Thus;

P(40) = −0.0002083(40)³ + 0.0157(40)² – 0.093(40) + 5.2

P(40) = 13.2688 (in millions)

Answer:

Is there anything else to add onto the question? What are you trying to find :)?

Answer:

Step-by-step explanation:the first one is 8

Second 3 3- 6

1) There are total 16 possible outcomes.

2) There are 6 possible outcomes for spinning two numbers that have sum greater than 5.

3) There are 4 possible outcomes for spinning the same number twice.

" Probability is a branch of mathematics which represents the all possibilities. It is defined as the ratio of total number of favourable outcomes to the total number of outcomes of the particular event."

According to the question,

A spinner is divided into 4 equal sections that is 1 to 4.

As per the diagram,

All possible outcomes are as follow:

{ (1 ,1), ), (1,2), (1,3), (1,4), (2,1),  (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4),(4,1),(4,2),(4,3), (4,4) }

1)  Total possible outcomes = 16

2) Possible outcomes for spinning two numbers that have sum greater than 5 are (2,4), (3,3), (3,4), (4,2), (4,3), (4,4)

Therefore,

Total Possible outcomes for spinning two numbers that have sum greater than 5 = 6

3) Possible outcomes for spinning the same number twice are (1,1), (2,2), (3,3), (4,4)

Therefore,

Total Possible outcomes for spinning the same number twice = 4

Hence,

1) There are total 16 possible outcomes.

2) There are 6 possible outcomes for spinning two numbers that have sum greater than 5.

3) There are 4 possible outcomes for spinning the same number twice.

Learn more about probability here

https://brainly.com/question/23044118

#SPJ2

Answer:

(h°h)(10) = 10

Step-by-step explanation:

(h°h) = 6-(6-x) = x

h(10) = x

x = 10

the answer is c

i already done it

Answer:

1/3 would be your answer

Step-by-step explanation:

anyway have a great day

The inverse of f (×) =2× + 3 is

yes it is true

Answer:

Slope of it is 6

Step-by-step explanation:

Slope is on the graph going up to the 6 and then to the 4

Answer:

$6.05 for each burrito bowl

Step-by-step explanation:

12.96+12.96=25.92

45.42-25.92= 19.5

19.5/3= 6.5

Answer:

The possible number of CDs she could buy is 1, 2, and 3.

Step-by-step explanation:

First, you have to make an equation to solve to find the answer(s):

1.) 80 - (18 · 1) ≥ 20

80 - 18 · 1 ≥ 20

80 - 18 ≥ 20

62 ≥ 20

Since 62 ≥ 20 is always true, there are infinitely many solutions.

2.) 80 - (18 · 2) ≥ 20

80 - 18 · 2 ≥ 20

80 - 36 ≥ 20

44 ≥ 20

Since 44 ≥ 20 is always true, there are infinitely many solutions.

3.) 80 - (18 · 3) ≥ 20

80 - 18 · 3 ≥ 20

80 - 54 ≥ 20

26 ≥ 20

Since 26 ≥ 20 is always true, there are infinitely many solutions.

4.) 80 - (18 · 4) ≥ 20

80 - 18 · 4 ≥ 20

80 - 72 ≥ 20

8 ≥ 20

Since 8 ≥ 20 is false, there is no solution.

5.) 80 - (18 · 5) ≥ 20

80 - 18 · 5 ≥ 20

80 - 90 ≥ 20

- 10 ≥ 20

Since - 10 ≥ 20 is false, there is no solution.

Answer:

1,2,3

Step-by-step explanation:

Answer:

x⁴ - 3x² - 2x - 2

Step-by-step explanation:

Step 1: Write out expression

(-3x² + 4x⁴ - 8x) - (-6x + 3x⁴ + 2)

Step 2: Distribute negative

-3x² + 4x⁴ - 8x + 6x - 3x⁴ - 2

Step 3: Combine like terms (x⁴)

x⁴ - 3x² - 8x + 6x - 2

Step 4: Combine like terms (x)

x⁴ - 3x² - 2x - 2

Answer:

S=46.6

Step-by-step explanation:

x is the number of years :

from 1998 to 2020 = 22 years

S-1.9x=4.8

S-(1.9)(22)=4.8

S=4.8+41.8

S=46.6

S = (HR(Wi - Wn)) / 1000.

First, multiply both sides by 1000.

1000S = HR(Wi - Wn)

Divide bot sides by H(Wi - Wn)

(1000S) / H(Wi - Wn) = R

Answer:

domain = x

range = y

Answer:

Step-by-step explanation:

3

it would equal -19.92

Answer:

= −19.92

Step-by-step explanation:

Answer:

im pretty sure its the 2nd or 3rd one

Answer:

-79

Step-by-step explanation:

Set up the composite function and simplify.

Answer:

each person should get 1/24th or 0.0417

Step-by-step explanation:

Answer:

x = -1

Step-by-step explanation:

Step 1: Write equation

-4(-5x + 2) - 3x - 5 = -30

Step 2: Solve for x

Distribute -4: 20x - 8 - 3x - 5 = -30

Combine like terms: 17x - 13 = -30

Add 13 on both sides: 17x = -17

Divide both sides by 17: x = -1

Answer:

x = -1

Step-by-step explanation:

invere operation

−4(−5x+2)−3x−5= -30

20x - 8 -3x - 5 = -30

17x -13 = -30

17x = -17

x = -1