Charlie is helping refill ketchup bottles at his uncle's diner. He has a huge container with 2 gallons of ketchup, which he distributes evenly among 15 bottles. How much ketchup goes in each bottle? Write your answer as a proper fraction or mixed number.

Answer:

f⁻¹(-2)=3

f⁻¹(1)=0

Step-by-step explanation:

inverse function flips x any coordinate into y and x

Answer:

10 minutes

Step-by-step explanation:

5/6 of an hours is 50 min. Assume x is the time she spends on each skill.

5x=50

x=10

She spent 1/6 of an hour i.e. 10 minutes on each skill.

In area model for multiplication a rectangle is used to represent multiplication between two quantities. Width and Length of the rectangle are assigned the numerical value of the two quantities being multiplied.

Let the number of skills be represented by the length of the rectangle in the figure.

Let the time spent(in hours), which is same for all skills, on each skill be represented by the width of the rectangle in the figure.

The area of the rectangle = length × width = 5 × t = 5t hours.

This area represents total time spent on five skills, which is 5/6 hours.

The smaller rectangles into which the whole rectangle is divided have area 1 × t = t hours. This represents time spent on one skill.

From the figure, such five smaller and equal rectangles constitutes the whole rectangle.

So, area of one smaller rectangle = Area of big rectangle / number of small rectangles = (5/6)/5 = 1/6 hours.

Since, this represents time spent on one skill. So, the required time is 1/6 hours.

She practice each skill for 1/6 of an hour.

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Answer:

Question 1:

The sum of interior angles of a polygon can be found by the following formula:

(n-2) × 180

Where n is the no. of sides

A pentagon has 5 sides

So,

= (5-2) × 180

= (3) × 180

= 540 degrees

Question 2:

Since The sum of interior angles of a regular octagon is 1080 and the total interior angle are 8

So, Measure of interior angle = [tex]\frac{1080}{8}[/tex]

Measure of interior angle = 135 degrees

Question 3:

Since, one interior angle in a hexagon measures 120 degrees.

So,

The interior angle should be subtracted by 180 to get the exterior angle.

Exterior angle = 180-120

Exterior Angle = 60 degrees

Answer:

Step-by-step explanation:

10,12,13,20, 21,

Answer: U = 600 m/s

Step-by-step explanation:

Given that an aeroplane covers a distance of 1500km in a certain time t at a certain speed U.

After increasing the speed by 100km/hr, that is, V = U + 100 it covers the same distance in a time which is half an hour less than the previous time. That is t2 = t - 0.5.

From the first statement

Speed = distance/ time

Distance = speed × time

1500 = Ut

Make t the subject of the formula

t = 1500/U ..... (1)

From the second statement

Distance = speed × time

1500 = (U + 100) × ( t - 0.5 )

Open the bracket

1500 = Ut - 0.5U + 100t - 50

Collect the like terms

1550 = Ut - 0.5U + 100t .... (2)

Substitutes equation 1 into 2

1550 = 1500U/U - 0.5U + 100(1500/U)

1550 = 1500 - 0.5U + 150000/U

1550 - 1500 = (150000 - 0.5U^2)/U

Cross multiply

50U = 150000 - 0.5U^2

0.5U^2 + 50U - 150000 = 0

Divide all by 0.5

U^2 + 100U - 300000 = 0

Using completing the square method

U^2 + 100U = 300000

U^2 + 100U + 50^2 = 300000 + 50^2

(U + 50)^2 = 302500

U + 50 = sqrt(302500)

U + 50 = +/-(550)

U = 50 + 550 or 50 - 550

U = 600 or - 500

Since U is of the same direction, it is

positive. Therefore, the previous speed of the aeroplane is 600 m/s

Answer:

500km/hr

Step-by-step explanation:

The formula for Speed (km/hr) = Distance / Time

Where S = Speed

D = Distance

T = Time

S = D/T

From the question, the aeroplane covered a distance of 1500 km

S = 1500/ T

ST = 1500

Time taken( T ) = 1500/S ......... Equation 1

We are told from the question that speed was increases by 100km/hr, it covers the same distance in a time which is half an hour less than the previous time

This is expressed mathematically as:

The new speed =S + 100km/hr

The new Time taken = 1500/ S - 1/2....... Equation 2

Also since Time = Distance / Speed

The new Time taken also = 1500/ S + 100 ......... Equation 3

Step 1

We would simplify Equation 2:

Time = 1500/S - 1/2

Find the Lowest common multiple = 2

Time = (2 × 1500 - S )/ 2S

Time = 3000 - S / 2S ......... Equation 4

Step 2

Equate Equation 4 and 3 together since they are both equal to time taken

1500/ S + 100 = 3000 - S / 2S

We cross multiply

2S × 1500 = (S + 100) ( 3000 - S)

3000S = 3000S - S² + 300000 - 100S

3000S - 3000S + S² - 300000 + 100S = 0

S² + 100S - 300000 = 0

Step 3

We solve for S = Speed by using factorisation method.

S² + 100x - 300000 = 0

S² - 500S + 600S - 300000 = 0

(S² - 500S) + (600S - 300000) = 0

S(S - 500) + 600(S - 500) = 0

(S - 500) (S + 600) = 0

S - 500 = 0, S = 500

S + 600 = 0 , S = -600

Our answer cannot be in negative form, hence, the previous speed of the aeroplane = 500km/hr

Answer: The equation is 45-10=x the answer is 35

Step-by-step explanation: To make the equation you need to have and = sign so, we can do what he has (45) and subtract what he gives away (10) which would equal what he has left (x)

Answer:

45 (initial amount) - 10 (given to brother) = x (number of cd's left)

Equation:

    45 - 10 = x

Answer:

    35 CDs

Answer:

-1

Step-by-step explanation:

Parallel lines have the same slope

If the green line has a slope of -1, the red line has a slope of -1

Answer:

5:00 pm -> 1700 hours

6:45 pm -> 1845 hours

8:05 am ->  0805 hours

12:59 am -> 0059 hours

0400 hours -> 4:00 am

1500 hours -> 3:00 pm

0010 hours -> 12:10 am

0240 hours -> 2:40 am

Step-by-step explanation:

12:xx am -> 00xx

all times from 1:00 am to 9:59 am stay nearly the same 0100 to 0959

all times 10:00 am to 12:59 pm stay nearly the same 1000 to 1259

all times 01:00pm to 12:00pm + 12 -> 1300 to 2400

Answer:

-39,063

Step-by-step explanation:

In this geometric, sequence, you are multiplying by -5. So, we can continue the sequence by mulitplying 375(your last value) by -5 and so on, until we have 7 total terms.

Now we add the terms together:

-3+15+-75+375+-1875+9375+-46875

=-3+15-75+375-1875+9375-46875

=-39063

Hope this helps :)

Answer:

Speed from NY to LA is 172 mph

Step-by-step explanation:

Let the jet’s speed from NY to LA be x mph.The speed form NY to LA would be (x-140) mph

Mathematically, we know that distance = speed * time

The total speed will x + x -140 = 2x-140

Now;

12(2x-140) = 2450

24x - 1680 = 2450

24x = 2450 + 1680

24x = 4130

x = 4130/24

x = 172.1 which is approximately 172 mph

Answer:

explained below

Step-by-step explanation:

Because the electro has a smaller mass than the mass of the proton, scientific notation is usually used so that the numbers are on the same "scale" but if we see the scientific notation we may be able to identify which is greater and which is less, due to that the exponent is less the number is smaller and on the contrary if the number is greater, it is a larger number.

In the image I leave an example of the use of scientific notation in this area

Since angle A and angle C forms side AC, AC is included between: A. ∠A and ∠C.

An included side is a side that is in between two angles in a triangle, where the rays of the angles overlap.

Thus, in triangle ABC, side AC lies in between angle A and angle C.

Therefore, since angle A and angle C forms side AC, AC is included between: A. ∠A and ∠C.

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Answer: A

Step-by-step explanation:

Answer:

The probability that the outcome of the roll is an even sum or a sum that is a multiple of 3

P( E∪F)  [tex]= \frac{24}{36}[/tex]

Step-by-step explanation:

Given Each number cube has sides numbered 1 through 6

Two distinct number cubes are rolled together

Total number of exhaustive cases n(S) = 36

Let 'E' be the event of getting sum is even

n(E) = {(1,3),(1,5), (2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(4,2),(4,4), (4,6),(5,1),(5,3),(5,5),(6,2),(6,4),(6,6)} = 17

[tex]P(E) = \frac{n(E)}{n(S)} = \frac{17}{36}[/tex]

Let 'F' be the event of getting sum that is a multiple of '3'

n(F) = {(1,2),(1,5),(2,1),(2,4),(3,3),(3,6),(4,2),(4,5),(5,1),(5,4),(6,3),(6,6) = 12

[tex]P(F) = \frac{n(E)}{n(S)} = \frac{12}{36}[/tex]

n((E∩F) = {(2,4),(3,3),((4,2),(5,1),(6,6)} =5

[tex]P(En F) = \frac{n(En F)}{n(S)} = \frac{5}{36}[/tex]

The probability that the outcome of the roll is an even sum or a sum that is a multiple of 3

P( E∪F) = P(E) + P(F) - P( E∩F)

            [tex]\frac{17}{36} +\frac{12}{36} - \frac{5}{36} = \frac{24}{36}[/tex]

Answer:

(2,17)

Step-by-step explanation:

This is because x is the input and y is the output. All you have to do is create a value for x the substitute it in the equation. Next solve for y 0.5 times 2 is 1, plus 16 is 17. Then just put your values in an order pair.

Answer:

8,20

Step-by-step explanation:

Answer:

if i counted correctly its 15

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Ok, so on this chart, each blue dot represents one person, so add up all the dots, and we get 15.

Answer:

[tex]m=A-\frac{2n}{Z}[/tex]

Step-by-step explanation:

Multiply by 2:

2n = Z(A - m)

Divide by Z:

[tex]\frac{2n}{Z} =A-m[/tex]

Subtract A:

[tex]-m=\frac{2n}{Z}-A[/tex]

Multiply by -1:

[tex]m=A-\frac{2n}{Z}[/tex]

Answer:

Brainelist goes to me!

Step-by-step explanation:

-6/3 = -2

Answer:

B

Step-by-step explanation:

Given

[tex]\frac{3-x}{x-6}[/tex] ← substitute x = 9 into the expression

= [tex]\frac{3-9}{9-6}[/tex]

= [tex]\frac{-6}{3}[/tex]

= - 2 → B

Answer:

B)

D)

Step-by-step explanation:

B) 1 and 13 are x intercepts so true

D) greatest profit is when price is 7; after that profit is getting smaller because function is decreasing

Answer:36/52, simplified to 9/13 or 69.23%

Step-by-step explanation:

Need to pick 6, 7, 8, 9, 10, J, Q, K, A (9 cards per suit)

4 suits x 9 cards

36 cards

Answer:

uhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh sorry needed the points lol

Answer:

the middle one is the correct answer

Step-by-step explanation:

Answer:

the answer is (1,R)

Step-by-step explanation:

Answer:

-1/2

Step-by-step explanation:

Slope is change in x over change in y

so..

2-(-4)

over

-1-11

so...

-6/12 or -1/2

Answer:

Step-by-step explanation:

The surface area of the sides of the cylinder is A = 2πrh, where r is the radius and h is the height.  

Here this comes out to A = 2π(4)(7) = 56 π units^2

If you also want the combined area of the two ends (top and bottom of the cylinder), here's the calculation:

A = 2πr² = 2π(4 units)² = 32π units²

Answer:

its 88 pi

Step-by-step explanation:

i did it on khan

Answer:

2n+21

Step-by-step explanation:

rule = 2 so 2n

if n=1, 1x2=2     23-2=21

so +21

10%+50%=60%

60% of 6000=3600

a)3600 people had left the match when it ended

b)6000-3600=2400

40% of the crowd was still there

Answer:2,3,4

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The formula for the volume of a cylinder is [tex]\pi r^2 h[/tex], since you are multiplying the area of the base (a circle) by the height of the cylinder to find the volume. Therefore, the volume of this cylinder is:

[tex]\pi r^2 h= \\\\3.14 \cdot 8^2 \cdot 15=\\\\3.14 \cdot 960=\\\\3014.4[/tex]

Hope this helps!

Answer:

[tex]3014.4ft^3[/tex]

even though this is not the most precise answer, ths is the answer you will be looking for

Step-by-step explanation:

To find the volume of a cylinder you use the formula [tex]V=\pi r^2h\\=\pi *8^2*15\\=3015.93ft^3[/tex]

Answer:

(a-b)^3 = [tex]\left(a-b\right)^3=a^3-3a^2b+3ab^2-b^3[/tex]

Step-by-step explanation:

(a-b)^3 = (a-b)(a-b)(a-b)

According to the perfect cube formula (a-b)^3 = [tex]\left(a-b\right)^3=a^3-3a^2b+3ab^2-b^3[/tex]

And there you have it! The perfect cube formula already solved your equation!

Answer:

A

Step-by-step explanation:

We can see that the two triangles are similar, and are in a 17:1 ration since 51/3 = 17

Now we can set up the equation

144-x = 17x

adding x to both sides we get

144 = 18x

dividing by 18 we get

x = 8

Now we plug x = 8 back in and get

144-8 = 136

Answer: 65π

Step-by-step explanation:

you can draw the cone to make it easier for you to understand.

to find the curved surface area of a cone, you multiply the base radius of the cone by pie. Then multiply your answer by the length of the side of the cone.

to do this you need the length of the side and the radius of the cone.

to find radius, divide the diameter by 2.

[tex]\frac{10}{2}[/tex] = 5

then use the right angle triangle in the cone to find the length of the side

use Pythagoras theorem which  states that a² + b²= c²

a= 5, b= 12, c= x (length of side)

∴[tex]x^{2} 5^{2} + 12^2 =x^{2} \\25 + 144 = x^{2} \\169= x^{2} \\x=\sqrt{169} \\x= 13[/tex]

no that you have found the length

multiply the base radius by pie

which is:

5 ×π = 5π

then multiply this by the length of the side

5π × 13 = 65π

there you go!

hope it helps!