It is estimated that 89% of senior citizens suffer from sleep disorders and 9% suffer from anxiety. Moreover, 5% of senior citizens suffer from both sleep disorders and anxiety.

(a)Find the probability that a senior citizen suffers from anxiety, given that he or she has a sleep disorder. Round your answer to the nearest hundredth.

(b)Given that a senior citizen suffers from anxiety, what is the probability that he or she also suffers from a sleep disorder? Round your answer to the nearest hundredth.

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Explanation

x = measure of angle 1

y = measure of angle 2

x = 2y+18, since angle 1 is 18 more than twice that of angle 2

Assuming this is a parallelogram, the adjacent angles are supplementary. So,

x+y = 180

2y+18+y = 180

3y+18 = 180

3y = 180-18

3y = 162

y = 162/3

y = 54

This leads to,

x = 2y+18

x = 2*54+18

x = 108+18

x = 126

Note that x+y = 126+54 = 180

Another useful fact about parallelograms is that the opposite angles are the same measure. So angle 1 = angle 3 = 126 degrees

The measure of angle 3, if The measure of ∠1 is 18 more than twice the measure of ∠2 is 126°

In geometry, a polygon is any closed curve made up of a collection of continuous line segments (sides) without any intersections. Triangles (three sides), quadrilaterals (four sides), and pentagons are the three simplest polygons (five sides).

Given:

The measure of angle 1 = 2 × The measure of the angle 2 + 18

Write an equation for the above statement,

x = 2y + 18

Here, x is a measure of angle 1 and y is the measure of angle 2,

As you can see from the figure it is a parallelogram then,

x + y = 180  (The sum of supplementary angle)

Solve the equation by elimination method,

y = 54, x = 2 × 54 + 18 = 126

The opposite angle of a parallelogram are equal,

Measure of angle 3 = Measure of angle 1 = 126

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Answer:

A line parallel to this one would have a slope of 3. where m is the slope and b is the y intercept. In this case, the equation y=3x+5 is already in slope intercept form, which means the slope is 3. Parellel lines have the same slope, so any other line with slope 3 is parallel to this line.

I think that's the answer

Answer: y = -3x - 3

Step-by-step explanation:

If you are looking for a line that is parallel, then it must have the same gradient

Therefore;

y= -3x +c

And because it passes through (0,3), substitute in the values to find c

3 = -3 x 0 + c

c = 3

So the equations would be y = -3x -3

Answer:

2,3,4

Step-by-step explanation:

Answer:

So Jennys Jean store charges the higher rate.

Step-by-step explanation:

Jeanys Jean store

Cost/pair = 20/1 = $20 per pair

Jeans warehouse

Cost/pairs = 36/2 = $18 per pair

So Jennys Jean store charges the higher rate.

Answer: The answer for the question is: 1 5/8

Step-by-step explanation:

Answer:

68

Step-by-step explanation:

The sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle

3x - 2 + 4x + 4 = 6x + 8 add like terms

7x - 2 = 6x + 8

7x - 6x = 8 + 2

x = 10

The measure of exterior angle

6x + 8 = 6*10 + 8

The measure of exterior angle is 68 degrees

Answer:

(9 ^ 3) x 0.04 (4/99)

Step-by-step explanation:

This seems overwhelming, but after simplifying, it will look much easier

Numerator (First Row)

First, we will combine like terms and simplify the top row

(9 ^ x + 1) x 8 - (9 ^ x - 1) x 81

(9 ^ x + 1) - (9 ^ x - 1) x (8 x 81)

(9 ^ 2x) x 648

Denominator (Second Row)

Next, we can combine like terms and simplify the second row

(9 ^ x) x 66 - (9 ^ x - 2) x 243

(9 ^ x) - (9 ^ x - 2) x (66 x 243)

(9 ^ 2x + 2) x 16,038

Simplify

Our expression is now

(9 ^ 2x) x 648

(9 ^ 2x + 2) x 16,038

We can simplify it as

(9 ^ 3) x 0.04 (4/99)

Answer:

Step-by-step explanation:

12 inches per foot

The floor is 9(12) = 108 inches by

12(12) = 144 inches

The floor area is 108(144) = 15552 sq. In.

Each tile is 4(6) = 24 sq. in.

Need 15552/24 = 648 tiles

Answer:

[tex]7x(4x-1)[/tex]

Step-by-step explanation:

First, find the largest integer that divides evenly into both numbers. In this case, 28 and 7 are both divisible by 7.

Next, find the highest degree of the variable that divides evenly into both. Here, that's just x. I'll show another example of that below.

Multiply those together, and you get 7x. That is what we need to factor out. Divide by that factor while multiplying by that factor at the same time to keep the value of the expression equal:

[tex]28x^2-7x\\\\7x(\frac{28x^2}{7x}-\frac{7x}{7x})\\\\7x(4x-1)[/tex]

Another example of what I said above would be this:

Take 4x + 2. The largest integer that divides these is 2, and the highest degree of x that divides them is 0. That is an x⁰, and that is equal to 1. Multiply those, and you just get 2.

[tex]4x+2\\\\2(\frac{4x}{2}+\frac{2}{2})\\\\2(2x+1)[/tex]

The expression which represents the total number of square yards of fabric she needs for both pillows is 3x + y = z

let

x = first pillow

y = second pillow

fabrics needed for first pillow = 3 yards

fabrics needed for second pillow = 1 yards

z = Total square yards needed

The equation:

3x + y = z

Therefore, the expression which represents the total number of square yards of fabric she needs for both pillows is 3x + y = z

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Answer:The expression which represents the total number of square yards of fabric she needs for both pillows is 3x + y = z

let

x = first pillow

y = second pillow

fabrics needed for first pillow = 3 yards

fabrics needed for second pillow = 1 yards

z = Total square yards needed

The equation:

3x + y = z

Therefore, the expression which represents the total number of square yards of fabric she needs for both pillows is 3x + y = z

Step-by-step explanation:

Answer:

4.7 kilograms

Step-by-step explanation:

[ 1000 g = 1 kg ]

Change 4700g into kg,

→ 4700 ÷ 1000

→ 4.7 kg

Answer:

C (5,4)

Step-by-step explanation:

(x,y)

fist number in the ordered pair is the X value

Second number in the ordered pair is the Y value

A (-3,0) means you go 3 spaces to the left in the negative direction and zero spaces in the Y axis

B(-2,1) means you go 2 spaces to the left on the x axis (negative) and 1 space up (positive) in the Y axis

C (5,4) means you go 5 spaces to the right on the x axis (positive) and 4 spaces up on the Y axis (positive)

After doing all of these we see that C does not end up on the line

Answer:

W= 2

Step-by-step explanation:

Answer:30 tacos and 70 burritos

Step-by-step explanation:

inequality 1: y≤110−x shade down

inequality 2:y≥80− 1/2x Shade up

Answer (30,70)

​

Answer:

your answer is the last option

Step-by-step explanation:

There is no way to prove what the length for line WU is. You can find the side lengths for VW and VU but not WU. Therefore the last option is the correct answer

Answers:

To reach the breakeven point, how many attendees will that take?     117  

What will be the company's total expenses and revenues?      $1755  for each  

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Explanation:

x = number of attendees

C(x) = cost function for the company

C(x) = 14x+117

This is because the company pays $14 per person, so x of them accounts for 14x dollars. Then we add on the flat fee of $117 to get 14x+117 dollars overall.

In contrast, the revenue is

R(x) = 15x

because each attendee brings in $15 for the company

The breakeven point is when the cost and revenue are the same. This produces a profit of $0.

R(x) = C(x)

15x = 14x+117

15x-14x = 117

x = 117

If 117 people attend the seminar, then the company breaks even.

To check this, we'll compute the cost and revenue

C(x) = 14x+117

C(117) = 14*117+117

C(117) = 1755

R(x) = 15x

R(117) = 15*117

R(117) =  1755

The cost and revenue is $1755 for each. Because we get the same value, this confirms the correct x value.

Since 117 people is the breakeven point, the company should aim for an attendee count above this, so they can get a positive profit. At some point, there is a max capacity so x can't go up forever.

Answer:

  $39,227.50

Step-by-step explanation:

Vika's income will be ...

  $35,500 + 10.5%×35,500 = $35,500(1 +0.105) = $39,227.50

Vika's adjusted income is $39,227.50.

Answer:

The ladder reaches [tex]15ft[/tex]

Step-by-step explanation:

In the first case we have

[tex]cos\theta =\frac{12}{15}[/tex]

In second case let the height be [tex]x[/tex]

We have

[tex]sin\theta =\frac{x}{25}[/tex]

We know that

[tex]cos\theta =\frac{12}{15}\\\\sin\theta =\sqrt{1-\frac{12^{2}}{15^{2}} } \\\\sin\theta =\sqrt{\frac{81}{225} } \\\\sin\theta =\frac{9}{15} }[/tex]

Substituting

[tex]\frac{9}{15} =\frac{x}{25}\\\\x=\frac{25\times9}{15} =15[/tex]

The ladder reaches [tex]15ft[/tex]

Answer:

2 more

Step-by-step explanation:

you can only get 1 of everything 2 times

this is - the outfit she already made

3 - 1 = 2   - 1 = 1

7 - 1 = 6   - 1 = 5

4 - 1 = 3   - 1 = 2

2 - 1 = 1    - 1 = 0

Answer:

n

Step-by-step explanation:

In algebra, like terms are terms that have the same variables and powers.

Answer:

Step-by-step explanation:

We assume the graph is a plot of Sean's distance from home as he drives to work, works 8 hours, then drives home with a 2-hour stop along the way. It also appears that t is measured in hours after midnight.

The graph shows Sean's distance from home between 9 a.m. and 5 p.m. (t=17) is 20 km. Based on our assumptions, ...

  Sean's workplace is located 20 km from his home.

__

Speed is the change in distance divided by the change in time. Between 8 a.m. and 9 a.m. Sean's position changes by 20 km. His speed is then ...

  (20 km)/(1 h) = 20 km/h

  Sean's speed driving to work was 20 km/h.

__

Between 5 p.m. (t=17) and 7 p.m. (t=19), Sean's position changes from 20 km to 10 km from home. That change took 2 hours, so his speed was ...

  (10 km)/(2 h) = 5 km/h

  Sean's speed between 5 p.m. and 7 p.m. was 5 km/h.

_____

Additional comment

The units of speed (kilometers per hour) tell you it is computed by dividing kilometers by hours. ("Per" in this context means "divided by".)

While the slope of the line on the graph between 5 p.m. and 7 p.m. is negative, the speed is positive. The negative sign means Sean's speed is not away from home, but is toward home. When the direction (toward, away) is included, the result is a vector called "velocity." Speed is just the magnitude of the velocity vector. It ignores direction.

No.

To find the rate for how many miles Greg drove for 5 hours, we need to divide 300 by 5:

300 / 5 = 60.

60 miles represents the speed for 1 hour.

60<70.

The inequality indicates that his rate (60 miles per hour) is less than the speed limit.

Answer:1. (1,2)    2.(-1,0)

Step-by-step explanation:

1.  5x-4(-3x+5)=3  x=1             2. 3(2y-1)-2y=-3    y=0                                                  

y=-3x1+5    y=2 Plug them in                       X=2x0-1            x=-1       plug them in                

Answer:

a.7/4x

b.2/3c

Step-by-step explanation:

Step-by-step explanation:

similar means that (with all angles being the same) the side lengths of one triangle all correlate to the corresponding side lengths of the second triangle by the same factor.

and so, because AD = 2 is 1/3 of AB = 4+2 = 6, we need to apply the same factor 1/3 to x compared to 12.

12 × 1/3 = 4.

so, A is correct.

Answer:

it becomes a 12 by 20

Step-by-step explanation:

Answer:

Linear functions are equations where the greatest power of the variable (typically x) is 1;

They are graphed as straight lines;

So, any function that has the following format:

f(x) = ax + b;

Nonlinear functions would be any equation that has a variable to a power greater than 1;

This could be a quadratic equation or an exponential equation

Answer:

So the answer would be 21 because the side is longer than 12 but not longer than 21