About 20% of the time you sleep is spent in rapid eye movement (REM) sleep, which is associated with dreaming. If an adult sleeps 7 to 8 hours, which inequality shows how much time, in hours, is spent in REM sleep?

1.4 < h < 1.6
35 < h < 40
0.35 < h < 0.4
14

Answer:

The correct option is D.

Step-by-step explanation:

Let the number of cars Zane washed on Saturday be x.

It is given that he gets paid $8 for every car he washes and made a total of $64 on Saturday.

We need to write an equation to show how many cars Zane washed on Saturday.

If he get $8 for one car, then the total amount he get for x cars is

Total amount = 8x

He made a total of $64 on Saturday, so

[tex]8x=64[/tex]

The required equation is 8x=64.Therefore the correct option is D.

Answer:

Look at the picture.

Step-by-step explanation:

A height  of a triangle is a line segment through a vertex and perpendicular to a line containing the base (the side opposite the vertex).

Answer:

t = 3.5c

Step-by-step explanation:

The correct table is attached in the image below. Since the papers are being folded at a constant rate, there is a linear relationship between c, the number of crane and t, the total time in minutes.

We can find the equation of this linear relation using any two pair of points from the table. Using the first two points: (5, 17.5) and (8, 28)

First we need to find the slope of the line which gives the relation between the two variables.

[tex]Slope=\frac{\text{Difference in y coordinates}}{\text{Difference in x coordinates}}[/tex]

y coordinates represents the dependent variable which is the time in this case and x coordinates represents the independent variable which is number of cranes in this case. Using the values from the two points we considered:

[tex]Slope=\frac{28-17.5}{8-5}=3.5[/tex]

Thus, the equation of the line will be of the form:

t = mc + b

m is the slope here. Using its values, we get:

t = 3.5c + b

b is known as y-intercept. We need the value of b to complete the equation. Substituting the value of t and c from any pair we can find the value of b.

Using the point (5, 17.5), we get:

17.5 = 3.5(5) + b

b = 0

This means, the equation of the line would be:

t = 3.5c

Answer:

t=3.5c

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

16/4 = 4

if 75% of equipment is iron then do the math.

So it would be 4(2) + 4 = 75% of 16

So if 75% of 16 is 12 you need that extra 4 to get you to 16

The number of woods are [tex]\fbox{\begin \\\math{4}\\\end{minispace}}[/tex].

Further explanation:

Consider the number of woods as [tex]x[/tex] and number of irons as [tex]y[/tex].

Since the number of irons is four more than two times the number of woods, the number of irons is calculated as follows:

[tex]y=2x+4[/tex]                                                      ......(1)

The number of equipment consists of the woods and irons, therefore, the number of equipment [tex]n[/tex] is written as the sum of number of woods [tex]x[/tex] and number of irons [tex]y[/tex] as follows:

[tex]n=x+y[/tex]                                                                  ......(2)

From equation (1), substitute [tex]2x+4[/tex] for [tex]y[/tex] in above equation.

[tex]n=x+2x+4\\n=3x+4[/tex]

Since the total equipment contains [tex]75\%[/tex] of irons, it can be written as follows:

[tex]y=0.75n[/tex]

From equation(1) and (2) substitute [tex]2x+4[/tex] for [tex]y[/tex] and [tex]3x+4[/tex] for [tex]n[/tex] in above equation.

[tex]2x+4=0.75(3x+4)\\\Leftrightarrow2x+4=2.25x+\\\Leftrightarrow4-3=2.25x-2x\\\Leftrightarrow1=0.25x\\\Leftrightarrow x=1/0.25\\\Leftrightarrow x=4[/tex]

Substitute 4 for [tex]x[/tex] in equation (1) to obtain the number of irons.

[tex]y=2(4)+4\\y=8+4\\y=12[/tex]

Thus, the number of woods are 4 and number of irons are 12.

Learn more:  

1. what is the y-intercept of the quadratic function f(x) = (x – 6)(x – 2)? (0,–6) (0,12) (–8,0) (2,0)  

https://brainly.com/question/1332667  

2. which is the graph of f(x) = (x – 1)(x + 4)?  

https://brainly.com/question/2334270  

Answer details:  

Grade: Middle school.  

Subjects: Mathematics.  

Chapter: Linear equation.  

Keywords: Linear equation, Function, Golf club, woods, y=2x+4, Variable, Middle term split method, Binomial, straight lines, Quadratic, Polynomial, Zeros, Zeros of a function, Expression, Equation, x, -x.

For this case we must reduce the following fraction:

[tex]\frac {130xy} {50x}[/tex]

Canceling similar terms in the numerator and denominator:

[tex]\frac {130y} {50}[/tex]

Dividing by 10 the numerator and denominator we have:

[tex]\frac {13y} {5}[/tex]

Finally, the expression is reduced to:

[tex]\frac {13y} {5}[/tex]

Answer:

[tex]\frac {13y} {5}[/tex]

Answer: D. 0.8125

Step-by-step explanation: His expenses is $975, and his salary is $1200. Divide the expenses by the salary to find the debt-to-income ratio.

975/1200 = 0.8125

The debt-to-income ratio is 0.8125.

Answer:

d) 0.8125

Step-by-step explanation:

Malcolm’s debt-to-income ratio is 0.8125 if his monthly expenses are $975 and his monthly salary is $1200.

All you have to do is divide monthly expenses by the monthly salary.

975 ÷ 1200 = 0.8125

Answer:

x = 6, x = -5, x = 9

if f(x)=(x-6)(x+5)(x-9)

Step-by-step explanation:

The zeros of a polynomial in factored form can be found by setting the polynomial equal to zero and then realizing if a product is zero, then at least one of it's factors is zero.

So we have the zero's are the x's that satisfy

(x-6)(x+5)(x-9)=0.

We just need to solve three equations:

x-6=0

           This can be solved by adding 6 on both sides:  x=6

x+5=0

         This can be solved by subtracting 5 on both sides: x=-5

x-9=0

         This can be solved by adding 9 on both sides: x=9

The solutions are in { 6,-5,9 }.

Answer:

x = 6, x = -5, x = 9

Step-by-step explanation:

If the polynomial f(x) is written in factored form, f(x) = (x − 6)(x + 5)(x − 9), the zeros of the polynomial function are x = 6, x = -5, x = 9.

x-6=0  x = 6

x+5=0  x = -5

x-9=0  x = 9

Therefore, x = 6, x = -5, x = 9 would be the correct answer.

Answer:

[tex]f^{-1}(x)=\frac{1}{2}+\sqrt{x-\frac{3}{4}}[/tex]

Step-by-step explanation:

y=x^2-x+1

We want to solve for x.

I'm going to use completing the square.

Subtract 1 on both sides:

y-1=x^2-x

Add (-1/2)^2 on both sides:

y-1+(-1/2)^2=x^2-x+(-1/2)^2

This allows me to write the right hand side as a square.

y-1+1/4=(x-1/2)^2

y-3/4=(x-1/2)^2

Now remember we are solving for x so now we square root both sides:

[tex]\pm \sqrt{y-3/4}=x-1/2[/tex]

The problem said the domain was 1/2 to infinity and the range was 3/4 to infinity.

This is only the right side of the parabola because of the domain restriction. We want x-1/2 to be positive.

That is we want:

[tex]\sqrt{y-3/4}=x-1/2[/tex]

Add 1/2 on both sides:

[tex]1/2+\sqrt{y-3/4}=x[/tex]

The last step is to switch x and y:

[tex]1/2+\sqrt{x-3/4}=y[/tex]

[tex]y=1/2+\sqrt{x-3/4}[/tex]

[tex]f^{-1}(x)=1/2+\sqrt{x-3/4}[/tex]

Answer:

y+1 = 2/5(x+3)

Step-by-step explanation:

We have a point and a slope so we can use point slope form

y-y1 = m(x-x1) where m is the slope and (x1,y1) is the point

y--1 = 2/5 (x--3)

y+1 = 2/5(x+3)

Answer: y=-6/7x

Step-by-step explanation: A perpendicular slope is opposite reciprocal. The opposite reciprocal of 7/6 is -6/7. The equation of the perpendicular line is y=-6/7x.

Answer:

I. 45.

Step-by-step explanation:

3 green peppers      g green peppers

--------------------     =  --------------------------

4 red peppers           60 red peppers

Using cross products

3 * 60 = 4 * g

180 = 4g

Divide each side by 4

180/4 =4g/4

45 = g

There are 45 green peppers

Answer:

Step-by-step explanation:

We know: measures of angles in a triangle add up to 180°.

Therefore we have the equation:

[tex]\gamma+\gamma+72^o=180^o[/tex]      subtract 72° from both sides

[tex]2\gamma=108^o[/tex]       divide both sides by 2

[tex]\gamma=54^o[/tex]

Answer:

The answer is 9

Step-by-step explanation:

When you divide 54 by 6 you get 9 because 10 times 6 equals 60 so if you minus 6 you get 54 which equals 6 times 9. :)

Answer:

9 or 9/1

Step-by-step explanation:

To convert improper fractions to whole numbers, you have to divide the numerator by the denominator.

So, 54 divided by 6 is 9

So 54/6 as a whole number 9

If you want to keep as a fraction it would be 9/1

Answer:

C

Step-by-step explanation:

When we set the numerator equal to 0 and solve for x, that value is the horizontal asymptote (a line the graph come towards, but never crosses).

Looking at the graph, the horizontal asymptote is x = 2, so which one of the 4 functions has a horizontal asymptote of 2? Let's check.

A) 2x - 1 = 0

x = 1/2

B) same, x = 1/2

C) 2x -4 = 0

x = 2

D) same as A,B, x = 1/2

As we can see, option C has the right horizontal asymptote and A,B,D are eliminated. So answer is C.

Answer:

[tex]x \geq\frac{2}{3}[/tex]

Step-by-step explanation:

The question is  [tex]3x+5 \geq 7[/tex]

We simply take the numbers to one side and variables to one side and solve via algebra (shown below):

[tex]3x+5 \geq 7\\3x \geq 7-5\\3x \geq 2\\x \geq\frac{2}{3}[/tex]

This range of values is the solutions of the inequality.

Answer:

A

Step-by-step explanation:

3x-5≥19

Add 5 to each side

3x-5+5≥19+5

3x ≥ 24

Divide each side by 3

3x/3 ≥24/3

x ≥8

Since this is greater than or equal to there is a closed circle at 8

greater than means the line goes to the right

Answer:

[tex]\large\boxed{\$10,999}[/tex]

Step-by-step explanation:

In this question, we're trying to find the value of Tom's car after 3 years.

From the question, we know that:

With the information above, we can solve the question.

We can do the simplest way by multiplying 250 by 36, since there's 36 months in 3 years, and then we would subtract that from our starting value.

Solve:

[tex]250*36=9000\\\\\text{We would then subtract 9000 from 19,999}\\\\19,999=10,999\\\\\text{Cars value after 3 years is}\, \bf\$10,999[/tex]

When you're done solving, you should get 10,999.

This means that Tom's car worth in 3 years is $10,999.

Answer:

10,999

Step-by-step explanation:

250 x 36 = 9,000

9,000 is how much the car went down in value it went down 3,000 a year for three years

19,999 - 9,000 = 10,999

10,999 is how much the car is worth after 3 years

Answer:

four thousand one hundred

Step-by-step explanation:

expand the form

The answer to the question is A

Answer:

Option B

Step-by-step explanation:

As per the contract

"The Buyer shall make each monthly payment by the first day of the month it is due."

this makes option a :"Pay the monthly payment on time." responsibility of the buyer.

"A payment not received by the fifteenth day of the month it is due will be subject to a late charge of $75.00."

this makes option c :"Pay an additional $75.00 with a payment made after the 15th day of the month it was due." responsibility of the buyer.

"Notification of the Buyer’s intent to do so must be made by written letter or phone call to the phone number and address listed below within one business week of delinquency.”

this makes option d :"Notify the bank of his or her intent to split a late payment into three partial payments." responsibility of the buyer.

So,buyer needs to only notify the bank about the monthly payments in case of delinquency and not about if payment is going to be late or not.  

Hence Option B is correct  

Notify the bank if a payment is going to be late!

The option that is not a responsibility of the buyer is notify the bank if a payment is going to be late.

A contract is an agreement that is enforceable legally between two or more parties to give something or render a services.

To learn more about contracts, please check: brainly.com/question/12991600

Answer:

[tex]\large\boxed{for\ (-3,\ 2):\ y-2=-\dfrac{1}{5}(x+3)}\\\boxed{for\ (2,\ 1):\ y-1=-\dfrac{1}{5}(x-2)}[/tex]

Step-by-step explanation:

The point-slope form of an equation of a line:

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

m - slope

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

========================================

We have the points (-3, 2) and (2, 1).

Substitute:

[tex]m=\dfrac{1-2}{2-(-3)}=\dfrac{-1}{5}=-\dfrac{1}{5}[/tex]

for (-3, 2)

[tex]y-2=-\dfrac{1}{5}(x-(-3))\\\\y-2=-\dfrac{1}{5}(x+3)[/tex]

for (2, 1)

[tex]y-1=-\dfrac{1}{5}(x-2)[/tex]

Answer:

[tex]\large\boxed{d.\ (-4,\ 0)}[/tex]

Step-by-step explanation:

The formula of a midpoint of a segment AB with endpoints at A(x₁, y₁) and B(x₂, y₂):

[tex]M_{AB}\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)[/tex]

We have the points F(-5, -3) and G(-3, 3).

Substitute:

[tex]M_{FG}(x,\ y)\\\\x=\dfrac{-5+(-3)}{2}=\dfrac{-8}{2}=-4\\\\y=\dfrac{-3+3}{2}=\dfrac{0}{2}=0[/tex]

Answer:

$1.80

Step-by-step explanation:

Based on the ratio shown in the double number line, the cost for 1 pound of avocados is $1.80.

5 pounds = 9$

9 divided by 5 = 1.8$/pound

Answer:

$1.80

Step-by-step explanation:

Note this:

5 lbs of avocado/$9

So, how much for 1 lb?

Remember units!!! They REALLY are important!!

1_lb_ x $9____ = (1 x 9)/5 = 1.8

5 lbs

**where are the numbers in our conversion coming from? Our notes!

We must now convert our answer to $'s, so $1.80 is our answer!

Answer:

2.45 or 2 9/20

Step-by-step explanation

Answer:

The correct answer is last option 362.9 ft

Step-by-step explanation:

Points to remember

Sin θ = Opposite side/Hypotenuse

To find the value of x

It is given that length of slope = 1500 ft

From the figure we can get,

Sin 14 =  Opposite side/Hypotenuse

 =  x/1500

x = 1500 * sin(14)

 = 1500 * 0.2419

 = 362.88 ft ≈ 362.9 ft

The correct answer is last option 362.9 ft

first off, let's notice something, the graph seems a bit misleading, since the height of the nut is 0.5 cm, whilst the side of the base is 0.6 cm, however in the picture 0.5 appears longer.  That said

1)

the volume of the nut itself is simply the volume of a hexagonal prism, which will just be the product of the area of the hexagon and the height.

[tex]\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap~~ \begin{cases} a=apothem\\ p=perimeter\\ \cline{1-1} a=0.5\\ p=\stackrel{0.6\times 6}{3.6} \end{cases}\implies A=\cfrac{(0.5)(3.6)}{2}\implies A=0.9 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{volume of the hexagonal prism}}{\stackrel{\textit{hexagon's area}}{(0.9)}~~\stackrel{\textit{height}}{(0.5)}\implies 0.45}[/tex]

2)

[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=0.4\\ h=0.5 \end{cases}\implies V=\pi (0.4)^2(0.5)\implies V\approx 0.25[/tex]

3)

well, the composite figure is just a hexagonal nut with a cylindrical hole, so if we simply get the volume of the prism and subtract the volume of the cylindrical hole, what's leftover, is the volume of the nut alone without the hole.

[tex]\bf \stackrel{\textit{from 1)}}{0.45}~~-~~\stackrel{\textit{from 2)}}{0.25}\implies 0.20[/tex]

4)

in short, dividing the mass of 3.03 by our result from 3)

3.03 ÷ 0.2 = 1.515.

Answer:

x = 2, y = -6, and z = 9

Step-by-step explanation:

This question can be solved using multiple ways. I will use the Gauss Jordan Method.

Step 1: Convert the system into the augmented matrix form:

•  3  -4   1      |  39

•  -3   1  -2     |  -30

•  2  -2  3      |  43

Step 2: Add row 1 it into row 2:

•  3 -4   1 |  39

•  0  -3  -1 |   9

•  2 -2  3 |  43

Step 3: Multiply row 1 with -2/3 and add it in row 3 and then multiply row 3 with 3:

•  3 -4   1   |  39

•  0  -3  -1   |   9

•  0  2    7  |  51

Step 4: Multiply row 2 with 2/3 and add it in row 3 and then multiply row 3 with 3:

•  3 -4     1       |  39

•  0 -3    -1       |   9

•  0 0   19/3     |  57

Step 5: It can be seen that when this updated augmented matrix is converted into a system, it comes out to be:

• 3x - 4y + z = 39  

• -3y - z = 9

• (19/3)z = 57 (This implies that z = 9.)

Step 6: Since we have calculated z = 9, put this value in equation 2:

• -3y - 9 = 9

• -3y = 18

• y = -6.

Step 8: Put z = 9 and y = -6 in equation 1:

• 3x - 4(-6) + 9 = 39

• 3x + 24 + 9 = 39

• 3x = 6.

• x = 2.

So final answer is x = 2, y = -6, and z = 9!!!

Answer:

x^2y^2 +9xy^2-xy-27y-6

Step-by-step explanation:

(xy+9y+2) (xy-3)

Each term of second bracket will be multiplied with the terms of first bracket

= xy(xy+9y+2) -3(xy+9y+2)

= x^2y^2+9xy^2+2xy-3xy-27y-6

=x^2y^2+9xy^2-xy-27y-6

38<4x+3+7-3x

38<x+10

28<x

Ans: x>28

For this case we must solve the following inequality:

[tex]38 <4x + 3 + 7-3x[/tex]

We add similar terms to the right side of inequality:

[tex]38 <4x-3x + 3 + 7\\38 <x + 10[/tex]

We subtract 10 from both sides of the inequality:

[tex]38-10 <x\\28 <x[/tex]

Thus, the solution will be given by all values of "x" greater strict to 28.

Answer:

[tex]x> 28[/tex]