The house Trevor's family lives in has 6 people (including Trevor) and 3 bathrooms. In the past month, each
person showered for an average of 480 minutes and used an average 72 liters of shower water (over the
entire month). Water costs 0.20 dollars per liter.
How much did Trevor's family pay per minute on shower water?

Answer:

9.16

Step-by-step explanation:

We know that

Total expense = price of sugar * consumption

let price of sugar was 100

So total expense = 100*10=1000

But now new expense =1100 (I,e.10% more than 1000)

and new price =120(i,e. 20% more than 100)

So new consumption = new expense/ new price=

1100/120

=110/12

=9.16

HOPE IT HELPS :)

PLEASE MARK IT THE BRAINLIEST!

Answer:

16 2/3 %   or approx. 16.67%

Step-by-step explanation:

Original price = 100%

New price = 100+20% = 120%

To reduce back to 100%

we need to reduce 20% from 120 % = 20/120 = 1/6 = 16 2/3 % = 16.7% approx.

Answer:

3x+7=10x+17

Step-by-step explanation:

1.9

10x

27x

Answers:

Equation is  3x+7 + 10x+17 = 180 (there are infinitely many other ways to write the equation)

x = 12

Angles are 43 and 137

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

Explanation:

The horizontal lines are parallel, so the same side interior angles marked are supplementary. The angles add to 180

(3x+7) + (10x+17) = 180 is the equation, or one variation of such

13x+24 = 180

13x = 180-24

13x = 156

x = 156/13

x = 12 is the value of x

Use this x value to find the measure of each angle

3x+7 = 3*12+7 = 43

10x+17 = 10*12+17 = 137

The two angles are 43 and 137 degrees

Note how 43 and 137 add to 180.

Answer:

The coordinates of point P are (-7/2, 5/4)

Step-by-step explanation:

Here, we want to give the coordinates of the point P that divide CD in the given ratio

To do this , we shall be making use of a mathematical formula;

Let’s say the ratio 1:3 represents a:b, our formula those becomes

{(bx1 + ax2)/(a + b) ,( by1+ay2)/a+b}

From the question, we can identify that

(x1,y1) = (-6,-1)

(x2,y2) = (4,8)

a = 1 and b = 3

Plugging these values into the formula we have

3(-6) + 1(4)/(1+3) , 3(-1) + 1(8)/(1+3)

= (-18 + 4)/4 , (-3+ 8)/4

=-14/4, 5/4

= (-7/2, 5/4)

Answer:

60 cents or $0.60

Step-by-step explanation:

9.00/15 = 0.6

Answer:

$.60

Step-by-step explanation:

This is just 9 divided by 15 which is $.60

Answer:

2(cos30°+isin30°)

Step-by-step explanation:

Complex value z is written in a rectangular form as z = x+iy where (x, y) is the rectangular coordinates.

On converting the rectangluar to polar form of the complex number;

x = rcosθ and y = rsinθ

Substituting in the rectangular form of the comlex number above;

z = rcosθ + irsinθ

z = r(cosθ+isinθ)

r is the modulus of the complex number and θ is the argument

r =√x²+y² and θ = tan⁻¹y/x

Given the complex number in rectangular form z = -(3)^1/2 - i

z = -√3 - i

x = -√3 and y = -1

r = √(-√3)²+(-1)²

r = √3+1

r = √4

r = 2

θ = tan⁻¹ (-1/-√3)

θ = tan⁻¹ (1/√3)

θ = 30°

Hence the complex number in polar form will be z = 2(cos30°+isin30°)

Answer:

[tex]\huge\boxed{\sqrt[4]{16a^{-12}}=2a^{-3}=\dfrac{2}{a^3}}[/tex]

Step-by-step explanation:

[tex]16=2^4\\\\a^{-12}=a^{(-3)(4)}=\left(a^{-3}\right)^4\qquad\text{used}\ (a^n)^m=a^{nm}\\\\\sqrt[4]{16a^{-12}}=\bigg(16a^{-12}\bigg)^\frac{1}{4}\qquad\text{used}\ a^\frac{1}{n}=\sqrt[n]{a}\\\\=\bigg(2^4(a^{-3})^4\bigg)^\frac{1}{4}\qquad\text{use}\ (ab)^n=a^nb^n\\\\=\bigg(2^4\bigg)^\frac{1}{4}\bigg[(a^{-3})^4\bigg]^\frac{1}{4}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=2^{(4)(\frac{1}{4})}(a^{-3})^{(4)(\frac{1}{4})}=2^1(a^{-3})^1=2a^{-3}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}[/tex]

[tex]=2\left(\dfrac{1}{a^3}\right)=\dfrac{2}{a^3}[/tex]

Answer: It is option 2 or B

Step-by-step explanation: Simple and easy, the test said it was right too.

Answer:

25

Step-by-step explanation:

let his age be x, then

5 years ago his age was x - 5 and in 5 years will be x + 5 , thus

(x - 5)(x + 5) = 600 ← expand factors using FOIL

x² - 25 = 600 ( add 25 to both sides )

x² = 625 ( take the square root of both sides )

x = [tex]\sqrt{625}[/tex] = 25

Answer:

[tex]\boxed{Age \ of \ man = 25 \ years}[/tex]

Step-by-step explanation:

Let the age be x

Then, the given condition is:

(x-5)(x+5) = 600     [ x-5 for age 5 years ago and x+5 for age 5 years after ]

Using Formula [tex](a+b)(a-b) = a^2-b^2[/tex]

[tex]x^2-25 = 600[/tex]

Adding 25 to both sides

[tex]x^2 = 600+25[/tex]

[tex]x^2 = 625[/tex]

Taking sqrt on both sides

[tex]x = 25[/tex] years

Answer:

Step-by-step explanation:

Multiply $9500 by .05 (5%) to get 475. That is 5% of $9500. Now subtract 475 from 9500 to get 9025. That is your answer!  

The value of car in month of January is, [tex]\$ 9975[/tex]

It is given that, At the end of any year a car is worth 5% less than what it was worth at the beginning of the year.

Since, car was worth $9 500 in December 2016.

Then, the value of car in month of January is, 105 % of value of car in moth of December.

So that, value of car in month of January is,

                                     [tex]=9500*\frac{105}{100}\\ \\=9500*1.05=9975[/tex]

The value of car in month of January is, [tex]\$ 9975[/tex]

Learn more about percentage here:

https://brainly.com/question/24304697

Answer:

[tex] s = 5.8 [/tex]

Step-by-step Explanation:

Given:

∆RST,

m < T = 17°

t = RS = 5

m < S = 20°

s = RT = ?

Apply the Law of Sines to find s

[tex] \frac{s}{sin(S)} = \frac{t}{sin(T)} [/tex]

[tex] \frac{s}{sin(20)} = \frac{5}{sin(17)} [/tex]

Multiply both sides by sin(20) to make s the subject of formula.

[tex] \frac{s}{sin(20)}*sin(20) = \frac{5}{sin(17)}*sin(20) [/tex]

[tex] s = \frac{5*sin(20)}{sin(17)} [/tex]

[tex] s = 5.8 [/tex] (to nearest tenth)

Answer:

$17,028.06

Step-by-step explanation:

Given that :

Kaylee's down payment = $4500

monthly payment = $300

If he can finance a vehicle with a 7%, 4-year loan (assume a 0% tax rate).

the  maximum amount Kaylee can afford to spend on the car is being calculated as the present value for all the payments.

= [tex]=\$4,500 +\dfrac{\$300}{(1+\frac{0.07}{12})} + \dfrac{\$300}{(1+\frac{0.07}{12})^2} +\dfrac{\$300}{(1+\frac{0.07}{12})^3} + ....+ \dfrac{\$300}{(1+\frac{0.07}{12})^{46}}+ \dfrac{\$300}{(1+\frac{0.07}{12})^{47}}+ \dfrac{\$300}{(1+\frac{0.07}{12})^{48}}[/tex]

Using the online desmos calculator to determine the maximum amount Kaylee can afford to spend on the car; we have:

= $17,028.06

Answer:

slope of the line containing the given points (6,-1) AND (5,-7) is 6

point- slope form of the equation is

(y+1)= 6(x-6)  ( because, i'm choosing the point (6,-1)

Step-by-step explanation:

slope = (-7 + 1) / (5 - 6 ) = -6/-1 = 6

(y-y1) = m ( x - x1)

(y+1 ) = 6 ( x-6)

Answer:175

Step-by-step explanation:

1. Turn 28% into a decima: 0.28

2. Multiply 1250 by 0.28 to get the amount of ninth grade students:350

3. Half the amount of ninth grade students:175

Answer:

The answer is 175

Step-by-step explanation:

Because I read the problem carefully and identified that the explanation is way too long so I am gonna make this short and easy for you. I am correct, just Trust me :)

Answer:

The last option

Step-by-step explanation:

The centroid is the point that is equidistant from all the vertices, not the incenter. Furthermore, the incenter is formed by finding the point of concurrency (intersection) of the angle bisectors.

Answer:

3,896 have signed up from other countries

Step-by-step explanation:

In this problem we are required to calculate the number of signups from other countries.

well, since we know the total sign ups to be 3,922

And also we know that 26 out of the total signed up from the USA

This means that the sign ups from other countries will be

3,922-26=3,896

Answer:

Dimensions of square shaped pit = 6m [tex]\times[/tex] 6m

Dimensions of rectangular pit = 1m [tex]\times[/tex] 36m or 2m [tex]\times[/tex] 18m or 3m [tex]\times[/tex] 12m or 4m [tex]\times[/tex] 9m

Step-by-step explanation:

Given:

Two pits in the school playground area (one square shaped and one rectangular shaped).

Each pit must have an area = 36 [tex]m^2[/tex]

To find:

Dimensions of each pit = ?

Solution:

First of all, let us have a look at the formula for area of a square and a rectangle:

[tex]Area_{square} = (Side)^2[/tex]

[tex]Area_{Rectangle} = Length\times Width[/tex]

Now, let us try to find out dimensions of square:

[tex]36 = Side^2\\\Rightarrow Side = 6\ m[/tex]

So, dimensions of Square will be 6m [tex]\times[/tex] 6m.

Now, let us try to find out dimensions of rectangle.

[tex]36 = Length\times Width[/tex]

We are not given any restrictions on the Length and Width of the rectangle.

So, let us explore all the possibilities by factorizing 36:

[tex]36 = 1 \times 36\\36 = 2 \times 18\\36 = 3 \times 12\\36 = 4 \times 9[/tex]

6 [tex]\times[/tex] 6 factors not considered because then it will become a square and which is not the required case.

Dimensions of rectangular pit = 1m [tex]\times[/tex] 36m or 2m [tex]\times[/tex] 18m or 3m [tex]\times[/tex] 12m or 4m [tex]\times[/tex] 9m

Answer:

The height of the cylinder is 4 x units.

The area of the cylinder’s base is One-fourthπx2 square units

Step-by-step explanation:

Formula for volume of the cylinder:

V = r² π h

Volume of the cylinder=

πx^3

Diameter=x

Radius (r)=diameter/2

=x/2

V = r² π h

πx^3=(x/2)^2πh

πx^3=(x^2/4)πh

Divide both sides by π

x^3=(x^2/4)h

Make h the subject of the formula

h=x^3÷x^2/4

=x^3×4 / x^2

=4x^3 / x^2

=4*x*x*x / x*x

h=4x

Area of the base:

B = r² π

Recall, r=x/2

B=(x/2)^2 * π

=(x^2/4)π

=πx^2/4

=1/4(πx^2)

The area of the cylinder’s base is One-fourthπx2 square units.

Answer:

B & E

Step-by-step explanation:

Edge 2020

Answer:

A) [tex]1<x<\infty[/tex]

Step-by-step explanation:

Given:

A graph of a function.

When we analyze the given graph, it is of a parabola.

To find:

The interval of values of [tex]x[/tex] where the function is increasing.

Solution:

First of all, let us learn about the meaning of increasing and decreasing functions.

1. A function [tex]y=f(x)[/tex] is known as increasing  in an interval [tex]a<x<b[/tex] when

Value of y keeps on increasing when we move from the value of x from a to b.

2. A function [tex]y=f(x)[/tex] is known as decreasing  in an interval [tex]a<x<b[/tex] when

Value of y keeps on decreasing when we move from the value of x from a to b.

On analyzing the given graph , we can see that the graph is decreasing on the interval: [tex]-\infty<x<1[/tex]

and is increasing on the interval: [tex]1<x<\infty[/tex]

When we choose from the options,

The correct answer is option A) [tex]1<x<\infty[/tex]

Answer:

Jackson's distance from the finish line after x minutes will be given as;

since from the statements we know that x represents the number of minutes he had run, for us to be able to calculate his  distance from the finish line we simply solve the problem mathematically as follows;

x=80-8y

Step-by-step explanation:

from the initial representation we have x+8y=80,

from the preliminary statement we know x to be the number of minutes from the start of the race to the current point Jackson.

so we assume that y in the equation represents the number of distance covered by the x minutes in miles.

that is how we end up with ;

x=80-8y.

Answer:

The correct option is;

(0, -3), (-1, 0) and (3, 0)

Step-by-step explanation:

From the given graph of the function we have the following observations;

There are two x-intercepts which are;

1) To the left of the vertical y-axis having coordinates (-1, 0)

2) To the the right of the y-axis having coordinates (3, 0)

There is only one y-intercept  having coordinates, (0, -3)

Therefore, all the intercepts of the function are, (0, -3), (-1, 0) and (3, 0).

Answer:

(0, -3), (-1, 0) and (3, 0)

Step-by-step explanation:

Answer:

On a coordinate plane, a parabola opens down

has a vertex at (negative 0.5, 6.75)

The vertex is the maximum value. The axis of symmetry is x = negative one-half.

The domain is all real numbers

Step-by-step explanation:

Answer:

The vertex is the maximum value.

The axis of symmetry is x = negative one-half.

The domain is all real numbers.  

Step-by-step explanation:

The answer above is correct.

Answer: A

Step-by-step explanation

2.167x10^4 = 21,670

                   = 9,978

1.1x10^6      = 1100,000

                   = 56,344,000

2.468x10^5 =  246,800

Answer: A. 9,978

Based on the power, move the decimal point that many spaces to the right. (E.g., If it's 4.2 × 10^3, then move the decimal three spaces to the right, and you'd get 4200.)

2.167 × 10^4 = 21670

1.1 × 10^6 = 1100000

2.468 × 10^5 = 246800

Out of all the numbers mentioned in the question, 9,978 is the only one that's less than 2.167 × 10^4 = 21670.

Part A

Answer:  33.2 degrees F

Explanation: Adding on a negative is the same as subtracting. So 72.3 + (-39.1) = 72.3 - 39.1 = 33.2

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

Part B

Answer: 70 +  2   +  0.3    + (-30) + (-9) + (   -0.1   )

Explanation:

Think of 72 as 70+2. Furthermore, think of 72.3 as 70+2+0.3; we just break the number up into its corresponding digits (adding zeros when needed). The 7 is in the tens place, the 2 is in the units or ones place, and the 3 is in the tenths place.

Similarly, we have 39.1 break down into 30+9+0.1, in which all three terms are made negative to represent -39.1

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

Part C

Answer:   70 + (-30) + 2 + (-9) + 0.3 + ( -0.1  )  

Explanation: Arrange the tens place value items to be next to each other. Same goes for the units place value, and also the tenths place value.

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

Part D

Answer:  [70 + (-30)] +  [ 2 + (-9) ] + [ 0.3 + ( -0.1  ) ]

Explanation: Take the result of part C and surround each pair of terms in square brackets to show how the terms pair up.

Answer:

B

Step-by-step explanation:

The inscribed angle's arc measures 36°, and central angle's arc measures 72°.

Answer:

the answer is B

Step-by-step explanation:

Answer:

a) 4.236 x 10^2

b) 7.194548 x 10^6

c) 5.0023 x 10^2

d) 7.123884 x 10^1

e) 5.62 x 10^-1

f) 3.48 x 10^-2

g) 1.23 x 10^-4

h)  5.603002 x 10^-1

Hopefully this helps :)

Answer:

a) 423.6=4.236*10^2

b) 7,194,548=7.194548*10^6

c) 500.23=5.0023*10^2

d) 71.23884=7.123884*10^1

e) 0.562=5.62*10^-1

f) 0.348=3.48*10^-1

g) 0.000123=1.23*10^-3

h) 0.5603002=5.603002*10^-1

Step-by-step explanation:

The numbers in which the point lies must be between 0 and 10

Hope this helps ;) ❤❤❤

Answer:

The center is ( 1,-3) and the radius is 3

Step-by-step explanation:

The equation of a circle can be written in the form

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

(x-1)^2 + (y+3)^2= 9

(x-1)^2 + (- -3)^2= 3^2

The center is ( 1,-3) and the radius is 3

Answer:

$186.89

Step-by-step explanation:

Let's start by finding the area of the floor.

Area of a trapezium can be found with the formula:

A=(a+b)/2*h

Let's plug our values in.

A=(10+16)/2*7.6

Simplify.

A=26/2*7.6

A=13*7.6

A=98.8

The area of the floor is 98.8 square meters.

Find how many litres of paint are needed.

98.8/1.9=52

He needs 52 liters of paint.

52/5=10.4

He needs 11 5 liter cans of paint.

Each one costs %16.99.

16.99*11=186.89

It would cost $186.89 to buy all the paint he needs.

Answer:Let PQRS to be the rhombus where PQ=12cm and RS = 16cm

step 1:let,PQ and RS intersect each other at O.Now, diagonals of rhombus bisect each other at right angles.

STEP 2:Since POQ is a right angled triangle, by pythagoras theoram.

STEP 3:After applying formula , PQ =10cm .length of each side of rhombus is 10cm.

Step-by-step explanation:

Answer:

10cm

Step-by-step explanation:

As you can see in the first image is a rhombus with its diagonals 12cm and 16cm

You can see that the diagonals divide the rhombus into four right triangles and that the hypotenuse of each triangle is one side of the rhombus.

In the second image I picked out one triangle from the rhombus and slashed the length of the diagonals of the rhombus in half to get the sides of the triangle.

Now all you have to do is use the Pythagorean theorem to find the hypotenuse of the triangle which will give you the length of side of rhombus

6² + 8² = hypotenuse²

36 + 64 = h²

100 = h²

h = √100

h = 10

All the side of the rhombus are equal so all the sides of the rhombus are 10cm

Answer:

h=−6, k=−30

Step-by-step explanation:

did on edge

Considering the equation of the parabola, the coefficients of the vertex are:

h=−6, k=−30

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The vertex is given by:

[tex](h,k)[/tex]

In which:

[tex]h = -\frac{b}{2a}[/tex]

[tex]k = -\frac{b^2 - 4ac}{4a}[/tex]

In this problem, the equation is:

[tex]f(x) = x^2 + 12x + 6[/tex]

Hence the coefficients are a = 1, b = 12, c = 6, thus:

[tex]h = -\frac{12}{2} = -6[/tex]

[tex]k = -\frac{120}{4} = -30[/tex]

More can be learned about the equation of a parabola at https://brainly.com/question/24737967

Answer:

y = 250

Step 1:

To solve, we plug in 50x for y.

[tex]50x=200+10x[/tex]

Then, we subtract the 10x from the right side. Our goal is to get the x by itself first.

[tex]40x=200[/tex]

Then, we divide both sides by 40, since we have to get the x by itself.

[tex]\frac{40x}{40}=x\\\\\frac{200}{40} =5[/tex]

x = 5

Step 2:

Now that we found x, we plug in 5 to the original equation and solve from there.

[tex]y=200+10(5)\\y=200+50\\y=250[/tex]

y = 250