What inverse operation should be used to isolate the variable in the equation p − 20 = 50?

Answer:

518.4 in³

Step-by-step explanation:

The ratio of the sides of the prisms = 5 : 6, hence

the ratio of their volumes = 5³ : 6³ = 125 : 216

let x be the volume of the larger prism then by proportion

[tex]\frac{125}{300}[/tex] = [tex]\frac{216}{x}[/tex] ( cross- multiply )

125x = 216 × 300 ( divide both sides by 125 )

x = [tex]\frac{216(300)}{125}[/tex] = 518.4

The volume of the larger prism is 518.4 in³

Answer: as·sume

verb

past tense: assumed; past participle: assumed

1.

suppose to be the case, without proof.

"it is reasonable to assume that such changes have significant social effects"

synonyms: presume, suppose, take it, take for granted, take as read, take it as given, presuppose, conjecture, surmise, conclude, come to the conclusion, deduce, infer, draw the inference, reckon, reason, guess, imagine, think, fancy, suspect, expect, accept, believe, be of the opinion, understand, be given to understand, gather, glean; More

2.

take or begin to have (power or responsibility).

"he assumed full responsibility for all organizational work"

synonyms: accept, shoulder, bear, undertake, take on, take up, take on oneself, manage, handle, deal with, get to grips with, turn one's hand to

"the children are to assume as much responsibility as possible"

seize (power or control).

"the rebels assumed control of the capital"

synonyms: seize, take, take possession of, take over, take away, appropriate, commandeer, expropriate, confiscate, requisition, hijack, wrest, usurp, preempt, arrogate to oneself, help oneself to, claim, lay claim to

"Edward I used the conflict to assume control of Scotland"

Step-by-step explanation:

suppose to be the case, without proof.

"I assumed you were done with the dishes"

For this case we have the following function:

[tex]c (f) = \frac {5} {9} (f-32)[/tex]

We must find the inverse function. For this we follow the steps below:

Replace c (f) with y:

[tex]y = \frac {5} {9} (f-32)[/tex]

We exchange variables:

[tex]\frac {5} {9} (y-32) = f[/tex]f = \frac {5} {9} (y-32)

We solve for "y":

[tex]\frac {5} {9} (y-32) = f[/tex]

We multiply by[tex]\frac {9} {5}[/tex]on both sides of the equation:

[tex]y-32 = \frac {9} {5} f[/tex]

We add 32 to both sides of the equation:

[tex]y = \frac {9} {5} f + 32[/tex]

We change y by[tex]c^{ -1} (f):[/tex]

[tex]c^{-1} (f) = \frac {9} {5} f + 32[/tex]

Answer:

[tex]c^{-1} (f) = \frac {9} {5} f + 32[/tex]

Answer:

[tex]f(c)=\frac{9}{5}c+32[/tex]

Step-by-step explanation:

Given function that is used to convert degrees to Fahrenheit to degrees Celsius,

[tex]c(f)=\frac{5}{9}(f-32)[/tex]

Let y represents the output value of the function and x represents the input value,

[tex]y=\frac{5}{9}(x-32)[/tex]

Switch x and y,

[tex]x=\frac{5}{9}(y-32)[/tex]

Isolate y,

[tex]9x=5(y-32)[/tex]

[tex]\frac{9}{5}x=y-32[/tex]

[tex]\implies y = \frac{9}{5}x+32[/tex]

[tex]\implies f(c)=\frac{9}{5}c+32[/tex]

Which is the required function.

Answer:

5/6

Step-by-step explanation:

Just plug in five where n is.

In this case, it would be:

5/(5+1) or 5/6

Answer:

C

Step-by-step explanation:

Expand the factors to obtain the product.

Each term in the second factor is multiplied by each term in the first factor

(3x + 2)(2x - 3)

= 3x(2x - 3) + 2(2x - 3) ← distribute both parenthesis

= 6x² - 9x + 4x - 6 ← collect like terms

= 6x² - 5x - 6 → C

Answer:

The area of the deck that surrounds the hot tub is 17.9 m².

Step-by-step explanation:

Base of deck = 5 m

Height of deck = 5 m

Area of deck = base*height

= 5*5

= 25 m²

A circular hot tub is placed in the deck whose diameter is 3 m.

Radius = diameter/2

= 1.5 m

Area of the circular hot tub = πr²

= 3.14*(1.5*1.5)

= 7.07 m²

Area of the deck that surrounds the hot tub = Area of deck - Area of tub

= 25 - 7.07

= 17.93 m²

= 17.9 m²

Answer:

17.9

Step-by-step explanation:

A.3.3

B.7.1

C.17.9

D.18.8

To find out when Ava and Kelly will be 3/4 mile apart, we can set up a distance equation based on their average speeds. The time it takes for Ava and Kelly to be 3/4 mile apart is 22.5 minutes.

To find out when Ava and Kelly will be 3/4 mile apart, we can set up a distance equation based on their average speeds.

Let's assume that the time it takes for Ava and Kelly to be 3/4 mile apart is t. Ava's distance can be represented by the equation 6t, while Kelly's distance would be 8t. We can set up the equation:

6t - 8t = 3/4

Simplifying, we have -2t = 3/4. To solve for t, we can multiply both sides of the equation by -1/2 to eliminate the negative sign:

t = (3/4) * (-1/2) = -3/8

Since time cannot be negative, we can conclude that Ava and Kelly will be 3/4 mile apart after 3/8 of an hour or 22.5 minutes.

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Answer:

They will 3/4 miles apart after 3/8 hours.

Step-by-step explanation:

To find out when Ava and Kelly will be 3/4 miles apart, we can set up an equation.

[tex]d = 8t-6t=2t[/tex]

t is the time in hours and d is the distance between the two girls in miles. Kelly runs at 8 miles/hour (represented by 8t) and Ava runs at 6 miles/hour (represented by 6t), and the distance between them can be calculated by subtracting Ava's distance from Kelly's distance.

To find out when they will be 3/4 miles apart, set d to 3/4 and solve for t.

[tex]\frac{3}{4} =2t\\\frac{3}{8}=t[/tex]

So, they will 3/4 miles apart after 3/8 hours.

Answer: 24-11=a

Step-by-step explanation:

First, we need to find the area of both the tile and cardboard, so we can calculate how much tile will fit in the cardboard

Final answer:

Karl used a total of 42 square tiles to cover the piece of cardboard, with each tile weighing 3 ounces. Therefore, the combined weight of all the tiles is 126 ounces.

Explanation:

Karl used 2 inch by 2 inch square tiles to cover a 14 inch by 12 inch piece of cardboard. To find out how many tiles he used, we need to calculate the area of the cardboard and divide it by the area of a single tile. The area of the cardboard is 14 inches * 12 inches = 168 square inches. The area of one tile is 2 inches * 2 inches = 4 square inches. So, the number of tiles used is 168 divided by 4, which equals 42 tiles.

Now that we know Karl used 42 tiles, and each tile weighs 3 ounces, we can find the combined weight. The combined weight is 42 tiles * 3 ounces per tile = 126 ounces.

The answer is the third one because the answer to 4-4 is 0.

The Number line which shows the solution 4 + (-4) is the third number line.

The solution to the statement 4 + (-4) is correctly given by the third number line.

The solution given by plot 1 is : (-4) + (-4) as both arrows points 4 units to the left.

The solution given by plot 2 is : ( 4 + 4) as both arrows points 4 units to the right.

The solution given by plot 3 is (4) + (-4) as one arrow points 4 units to the left and the other points 4 units to the right.

The solution given by the plot 4 is (-4 + 8) as one arrow points 4 units to the left and the other points 8 units to the right.

Therefore, the Number line which shows the solution 4 + (-4) is the third number line.

For such more question on Number

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The input (-1/5 1/5 -7/5) without specified operations and unused variables a, b, and c, make it difficult to evaluate as a standard mathematical question. There may likely be a mistake in the original question.

Given the numbers a = -3, b = 4 and c = -5, the provided expression (-1/5 1/5 -7/5) appears to be a sequence of standalone fractions, not a standard mathematical operation or equation. To evaluate fractions, generally, we perform a calculation like addition, subtraction, multiplication, or division. However, the query lacks any specified mathematical operation to apply to these fractions. It seems there might be a mistake in the original question since the given values a, b, and c are also unused. To make it a valid mathematical question, we need to know what needs to be done with the fractions and variables given.

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Final answer:

The question appears to involve solving a quadratic equation using the quadratic formula, but there seems to be a typo in the provided figures. Nevertheless, the solution process entails substituting the given values into the quadratic formula and solving for x, which may result in two possible solutions depending on the discriminant.

Explanation:

The question involves solving a quadratic equation of the form ax² + bx + c = 0 using the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a). Based on the provided values of a, b, and c, we would substitute these into the quadratic formula to find the solutions to the equation. It seems there may be a typo in the original question, as the given values do not match any standard form of a quadratic equation nor the matrix form of a linear system. However, I will provide a general step-by-step solution for the quadratic equation based on the format provided in the reference information.

First, calculate the discriminant using the formula √(b² - 4ac). Then, use the values of a, b, and c to evaluate the positive and negative solutions of x using the quadratic formula. For example, if a = 1, b = 0.0211, and c = -0.0211, the solutions would be found as follows:

-0.0211 ± √(0.0211)² - 4(1)(–0.0211)

2(1)

It is important to note that this structure is indicative of the process and the actual computations will differ with the correct values provided for a, b, and c.

the set of 6 consecutive integers starting with -3:

{ -3,-2,-1,0,1,2 }

Answer:

Step-by-step explanation:

let :

x , x+1 , x +2 , x + 3 , x+4 , x+5 ....... ( 6  consecutive integers )

x +( x+1 ) + (x +2) + (x + 3)+ (x+4) + ( x+5) = - 3

6x+16 = - 3

6x = - 3 - 16

6x = - 18

x v= -18/6

x = - 3

6  consecutive integers  are : -3  ; - 2 ; - 1 ; 0 ; 1 ; 2

Answer:

Graph = Cardioid

Axis of symmetry = y-axis

Critical points= [tex]\frac{\pi}{2} , \frac{3\pi }{2}[/tex]

Step-by-step explanation:

General equation for this type of cardioid is:

a ± b sinθ

Condition for a cardioid = [tex]\frac{a}{b} = 1[/tex]

Axis of symmerty according to the graph of 2 + 2 sinθ is along y-axis.

Critical points:

r = 2 + 2 sinθ  ⇒ r = 2(1 + sinθ) ⇒ r' = 2 cosθ  

 ∵derivative of 1 + sinθ = cosθ

For finding critical point the derivative is equal to zero,

2 cosθ = 0    ⇒    cosθ = 0

the value of cosθ is equal to zero at intervals: [tex]\frac{\pi}{2} , \frac{3\pi }{2}[/tex]

So, critical points = [tex]\frac{\pi}{2} , \frac{3\pi }{2}[/tex]

Answer:

9 bottles of soda can be bought.

Step-by-step explanation:

Let chips represented by x

and soda represented by y

then

x + y = 14     eq(1)

and

5x + 3y = 52    eq(2)

Solving the equations simultaneously we can find the value of x and y

Multiplying eq(1) with 5 and subtracting from eq(2)

5x + 3y = 52

5x + 5y = 70

-     -        -

___________

-2y = -18

y = -18/-2

y = 9

Putting value of y in eq(1)

x + y =14

x + 9 = 14

x = 14 - 9

x = 5

As y represents the soda, so 9 bottles of soda can be bought.

Answer:

x=-2

Step-by-step explanation:

Answer:

x = - 2

y = 7

Step-by-step explanation:

4x - 2y = - 20

Now substitute - 3x for y.

4x - 2(-3x) = -20           combine the xs in the brackets

4x + 6x = - 20               Make the addition      

10x = - 20                      Divide by 10

x = - 20/10                     Do the division

x = - 2                            

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

3x - 2y = - 20                 Put - 2 in for x  

3(-2) - 2y = - 20              remove the brackets              

- 6 - 2y = - 20                 Add 6 to both sides

-2y = - 20 + 6                 Combine

-2y = - 14                         Divide by - 2

y = - 14/-2                        

y = 7

Hello!

Answer:

55mph

Step-by-step explanation:

car A distance, d1= 220

car b distance, d2= 260

speed of car A, s1= speed of car B- 10

let speed of car B be s2

s1= s2-10

speed = distance/time

time= distance/speed

As time of car A= time of car B

     distance of Car A/speed of Car A=distance of Car B/speed of Car B

220/s2-10= 260/s2

s2=(s2-10)260/220

s2=65

s1= s2- 10

  = 65-10

   =55

hence speed of first car is 55mph !

Answer: 55 mph

Step-by-step explanation:

Answer:

Choice D for Angle R

70 degrees for Angle P

Step-by-step explanation:

Google "central angles and inscribed angles geometry" for an explanation.

It's actually a poorly worded question.

Answer: $42

Step-by-step explanation:

Answer:

$0.50

Step-by-step explanation:

We have been given that Jack sold magazine subscriptions for $2 each receiving 25% commission on his sales. We are asked to find Jack's income for each subscription.

Jack's income for each subscription will be equal to 25% of $2.

[tex]\text{Jack's income}=\$2\times \frac{25}{100}[/tex]

[tex]\text{Jack's income}=\$2\times 0.25[/tex]

[tex]\text{Jack's income}=\$0.50[/tex]

Therefore, Jack's income for each subscription will be $0.50.

Answer:

The answer is 5 people.

Step-by-step explanation:

.25 * 20 people surveyed = 5.

Answer:

3/32

Step-by-step explanation:

Labels from 1 to 8:

The probability that he gets a number less than 4 (1, 2, 3) is 3/8

The probability to get a multiple of 4 (4, 8) is 2/8 = 1/4

So

The probability that he gets a number less than 4 or a multiple of 4:

= 3/8 x 1/4

= 3/32

Answer

3/32

Answer:

The answer is 5/8.

I saw an answer that gave 3/32, and since I knew that was wrong I wanted to give my answer to not lead others astray.

Step-by-step explanation:

There are 8 numbers john can pick.

Numbers less than 4 are (1, 2, 3)

Numbers that are a multiple of 4 are (4, 8)

The word "or" in the question implies addition, and adding 3/8 and 2/8 yields a result of 5/8. This is also the answer in the test that I took.

Answer:

parenthesis

Step-by-step explanation:

A common technique that is being used in solving with several arithmetic operations is the PEMDAS. It stands for "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction". It is the order to be followed when calculating involving more than one arithmetic operation.

The correct first operation to perform in a calculation involving multiple arithmetic operations is parentheses, as per the order of operations, known as PEMDAS or BEDMAS.

The correct operation that should be performed first for calculations involving more than one arithmetic operation is parentheses. According to order of operations, the sequence you would follow is: Parentheses (or grouping symbols), Exponents, Multiplication and Division (from left to right), and finally Addition and Subtraction (from left to right). This is also commonly remembered by the acronym PEMDAS in the American system or BEDMAS in the Canadian system, indicating the sequence: Parentheses/Brackets, Exponents, Multiplication/Division, and Addition/Subtraction.

Answer: C: 156 mi

Step-by-step explanation:

Driving north then east or west is 90 degrees rotation internally. Distance of Chad from his home to his final location is Option B: 130 mi

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]

A right angled triangle is a triangle having one of its angle with measure of 90 degrees.

The slant side of that triangle is called Hypotenuse and it is the longest side in that triangle.

Referring to the diagram attached below, as Chad moved from north driving to east driving, thus, he made a 90 degrees angle internally as perpendiculars are with 90 degrees. Then joining his first and final position, we get a right angled triangle. Thus,

Distance of Chad from final point to his home = length of AC = |AC|

A is the starting point of Chad. His speed was 60 mph for the first travel in the north direction. He traveled 2 hours. Since each hour he travels 60 miles(from his speed), and he spent 2 hours so 60 + 60 = 120 miles covered.

Thus, |AB| = distance traveled in north direction is 120 miles.

Similarly, as he traveled in east for 1 hour with speed 50 mph, thus, he traveled 50 miles. Thus,

Length of BC = |BC| = 50 miles.

His distance from his home A to his final position C is calculated as follows.

Using Pythagoras theorem, we get:

[tex]|AC|^2 = |AB|^2 + |BC|^2\\|AC| = \sqrt{120^2 + 50^2} = \sqrt{16900} = 130 \: \rm miles\\\\[/tex]

(we took positive root since |AC| is length's measure., which is a non-negative quantity)

Thus,

Distance of Chad from his home to his final location is Option B: 130 mi

Learn more about Pythagoras theorem here:

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Answer:

"B" represents the area of the base so if the base is a square than a capital "B" means to find the area of the base (square). To find the area of a square it would be length x width.

Step-by-step explanation:

It’s important to keep PEMDAS in mind (order of operations) when solving this.

PEMDAS stands for: Parentheses, exponents, multiplication, division, addition, subtraction.

So when doing this problem we can see that there are two multiplication problems (8 • 9) and (2 • 5) so let’s put those to the side and solve those.

8 • 9 = 72

2 • 5 = 10

Now we can put the problem back together as 72-10

So ... 72-10=62

rolling a 5= 11/100

getting tails=71/29

i’m pretty sure you times the fractions together to get an overall probability

The probability of rolling a 5 on number cube and tail on coin is:

            [tex]P(A\bigcap B)=\dfrac{781}{10000}[/tex]

                                      or

          [tex]P(A\bigcap B)=0.0781[/tex]      

Let A denote the event of rolling a 5 on the number cube.

and B denote the event of coin landing on tails.

Let P denote the probability of an event.

Also, event A is independent of event B.

( Since, both the events are not affected by happening of each other )

We are asked to find the probability:  P(A∩B)

We know that:

[tex]P(A\bigcap B)=P(A)\cdot P(B)[/tex]

( Since, both the events are independent )

Also,

[tex]P(A)=\dfrac{11}{100}[/tex]

( Since, 5 occurs 11 times out of a total of 100 times on the number cube )

and

[tex]P(B)=\dfrac{71}{100}[/tex]

Hence, we have:

[tex]P(A\bigcap B)=\dfrac{11}{100}\times \dfrac{71}{100}[/tex]

i.e.

[tex]P(A\bigcap B)=\dfrac{781}{10000}[/tex]

i.e.

[tex]P(A\bigcap B)=0.0781[/tex]

Answer:

D

Step-by-step explanation:

Well, we know that for every 2 strawberries are 5 grapes.

What times 2 is 16? 8.

so, it would be 40 grapes.

(This is now making me hungry.)

Answer: 51 feet

Since we know George's height, the length of George's shadow, and the length of the flagpole's shadow we have all the information we need

Now we can set up a relationship between George and the flagpole:

[tex] \frac{6}{10} = \frac{x}{85} [/tex]

6 represents George's height

10 represents the length of George's shadow

x is the unknown height of the flagpole

85 is the length of the flagpole's shadow

Now you solve for x:

[tex]x = \frac{85 \times 6}{10} \\ x = \frac{510}{10} \\ x = 51[/tex]

So, the height of the flagpole is 51 feet