Suppose that a customer is purchasing a car. He conducts an experiment in which he puts 10 gallons of gas in the car and drives it until it runs out of gas. He conducts this experiment 15 times on each car and records the number of miles driven.

Find the Sample standard deviation for Car 1 and Car 2

Image of point O(-2,-1) after two reflections , first across the line y=5 and then across the line x = 2 is (6,11) .

What do you mean by reflection in coordinate plane?

A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another. The reflected picture should have the same size and shape as the original, but it faces the opposite way. Changes in position during contemplation may also result in translation. Pre-image and image are terms used to refer to the same thing in this context.

Given point is O(-2,-1)

It is given that point O has reflected twice,

Firstly point O has reflected across the line y= 5

So, it become ,

(-2,11)

Secondly, it is reflected across the line x = 2

So, it become,

(6,11)

Hence, image of point O(-2,-1) after two reflections , first across the line y=5 and then across the line x = 2 is (6,11) .

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The value of x is 120.

70/100 shows 70% as a ratio. The ratio x : 84 compares 84 to the whole, x. Write an equation so that the first ratio is multiplied by the second ratio. Solve for x : x = 120.

Given, that 84 is 70% of the whole.

Let the whole be x,

According to the question,

(70/100) × x = 84

On multiplying both the sides by 100/70, we get

x = 84×100/70

Now, on solving the expression, we get

x = 120

Hence, 70/100 shows 70% as a ratio. The ratio x : 84 compares 84 to the whole, x. Write an equation so that the first ratio is multiplied by the second ratio. Solve for x : x = 120.

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Expression 2x²-(-1) - [7x-8] is equal to 2x² - 7x +9

Expression is combination of math operations , numbers and unknown variables.

Math operation can be subtraction , addition , multiplication or division.

There are two types of expression : numerical expression and algebraic expression . Expression consists of only numbers are numerical where expression containing numbers and variables are algebraic expression.

Subtract 7x-8 from 2x²-(-1)

2x²-(-1) - [7x-8]

product of two minus is plus

2x²+1 -[7x-8]

open the bracket and change the minus sign

2x²+1 - 7x + 8

there is no x² and x term so,

2x² - 7x +1+8

2x² - 7x +9 is our required expression

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Answer:

13

Step-by-step explanation:

.

Answer:

Alex is 14 years old.

Step-by-step explanation:

You can take William's age and divide it by 3, because William is 3 times the age of Alex:

31 divided by 3 = 10.33.

So, we will just say 10 for now.

Now, we add 4 to the 10 because WIlliam is 4 years older than three times his age.

So, in conclusion, Alex is 14 years old.

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Answer:

18 ft.

Step-by-step explanation:

By arranging similar terms, we have

since 13a minus a is 12a, the answer is

which corresponds to option 2 from top to bottom

It will take 9.21 minutes until 50 grams.

What is decay?

"Decay" means "decrease". If the rate of decrease of a quantity is proportional to its current value, then we say that it is subject to exponential decay.

Formula of decay,

f(t) = a(1-r)^t

f(t) is the value after decay.

r is rate

t is time and a is initial value

Given,

initial mass was 990.

rate = 0.278

after decay = 50 gram.

We get,

50 = 990(1-0.287)^t

50/990 = (0.723)^t

taking log on both side.

t = 9.21

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Answer:

Step-by-step explanation:

Let the cost of T-shirt is x.

The cost of pair of shoes is $49.95 and the total should be no more than $60.

This can be modeled as:

The matching choice is C.

Answer:

D

Step-by-step explanation:

even

4(-x^3) = 4x^3

-4x^3 = 4x^3 (false)

odd

-4x^3 = 4(-x^3)

-4x^3 = -4x^3

Question:

Solution:

Consider the following inequalities system :

Inequality 1:

or

Inequality 2:

Applying the distributive property in inequality 1, we obtain:

this is equivalent to:

that is:

this is equivalent to:

solving for x, we get:

that is:

Then inequality 1 is equivalent to the following solution

On the other hand, for inequality 2 solving for x, we get:

that is:

so that, the solution to the inequality system is

or

now, this is equivalent to say:

or in interval notation:

The characteristics of the vertical throw and Newton's second law allows finding the results for the questions about the motion of the ball with air resistance are:

For the upward movement.  The speed of the ball decreases with height of the ball.  The forces of gravity and friction go in the same direction.

For the point of maximum height, the velocity is zero and the net force is only the force of gravity.

The ball is in a downward movement. The speed increases as the height decreases. The friction force and gravity have the opposite direction, therefore the net force decreases until reaching zero, from this point the speed remains constant.

Kinematics analyzes the movement of bodies looking for relationships between the position, velocity, and acceleration of bodies.

Newton's second law relates the net force to the mass and the acceleration of the body.

In this case, there is a vertical launch where the ball is launched with an initial velocity and is subjected to an acceleration given by the acceleration of gravity with a vertically downward direction, therefore the speed of the ball must decrease with increasing height.

       v² = v₀² - 2g y

Where v and v₀ are the current and initial velocities, respectively, g is the acceleration of gravity, and y is the height of the body.

In the attached, we can see a free-body diagram of the ball, the interaction with the earth is constant and is directed towards the center of the earth, in a vertical direction. The friction force of the air is the opposition of the air to the movement of the ball and is directed opposite the direction of movement of the ball. In the case of the ascending ball, the friction force is directed downwards.

Write Newton's second law for upward motion

          -W- fr = m a

          -m g - fr = ma

Therefore, we see that the two forces go in the same direction, and therefore the net force increases and the acceleration in the opposite direction of the speed also increases.

At the point of maximum height, the speed of the ball is zero, therefore the friction forces of the air are also zero, at this point the acceleration is equal to the acceleration of gravity.

In the case of the ball lower.  Speed ​​increases as the ball descend.

Newton's second law is.

        -W + fr = ma

       - m g + fr = ma

In this case, we see that the forces go in the opposite direction, therefore the net force on the body decreases.

If the friction force with the air increases with the speed, the point where it is equal to the forces of gravity and the acceleration is zero, from this point the ball goes down with constant speed.

In conclusion with the characteristics of the vertical launch and Newton's second law, we can find the results for the questions about the motion of the ball with air resistance are:

The ball is in a downward movement. The speed increases as the height decreases. The friction force and gravity have the opposite direction, therefore the net force decreases until reaching zero, from this point the speed remains constant.

For the upward movement.  The speed of the ball decreases with height of the ball.  The forces of gravity and friction go in the same direction.

For the point of maximum height, the velocity is zero and the net force is only the force of gravity.

Answer:

x = 14

Explanation:

To get the value of x, we wll be using the SOH CAH TOA identity

Using sin theta = opposite/hypotenuse

h is the vertical height of the triangles.

Next is to get the value of x;

Similarly;

Hence the value of x required is 14

Given:

Monthly membersihp fee is, m = $19.

Initial enrollment fee is, i = $75.

The objective is to write a cost expression and to fnd the cost for 8 months of membership.

From the given data, the enrollment fee is an one time payment. But the monthly membership fee is a variable cost with respect to number of months x.

Then, the expression can be represented as,

Here, y stands for cost, x stands for number of months.

Thus, the required cost expression is obtained.

To find the cost for 8 months, substitute x = 8 in the cost expression.

Hence, the cost for 8 months is $227.

we ahve

110.4 ÷4

so

110.4/4

Multiply by 10/10 the expression

1104/40

simplify

1104/40=552/20=276/10=27.6

the answer is 27.6

Cost price = $44

mark up percent = 80% = 80/100 = 0.8

selling price = ?

The markup formula:

The distance between the points B (5 , -9) and D (-1 , 3) is 13.491 units.

Given, the coordinates of the vertices of a rectangle

A (5, 3), B (5,-9), C (-1,-9), and D (-1, 3)

Now we have to find the distance between B and D

On using the distance formula, we get

Distance = √((x1 - x2)² + (y1 - y2)²)

Distance = √(5 - (-1))² + (-9 - 3)²

Distance = √(6)² + (-12)²

Distance = √36 + 144

Distance = √180

Distance = 13.491 units

Hence, the distance between the points B (5 , -9) and D (-1 , 3) is 13.491 units.

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Answer:

The volume of air that is coming in and going out is 500 ml. A single respiratory cycle takes 4 seconds to complete. The residual volume of air left in the lungs after the completion of the cycle is 2000 ml.

Answer:   25

Step-by-step explanation:

Hello! First, let's remember what is Associative Property:

It is a mathematical rule who says that the order of the factors doesn't change the final result of a calculus.

We have the associative property in two mathematical operations, I'll show you some examples:

If we want to sum three numbers, 5, 10 and 15, how is the right way? We have some ways to do it:

(5+10)+15 = (15)+15 = 30

(5+15)+10 = (20)+10 = 30

5+(10+15) = 5+(25) = 30

So, no matter the order of the numbers, we will always get the same result.

An example with the other operation now:

If we want to multiply three numbers, 2, 3 and 5:

(2*3)*5 = (6)*5 = 30

(2*5)*3 = (10)*3 = 30

2*(3*5) = 2*(15) = 30

Also, no matter the order of the factors, we'll always obtain the same result.

However, in the subtraction and in the division we have to follow the right order, according to the precedence, so we can't use the Associative Property on these operations.

Right answer: C and D.

The unit rate per yard is 0.03yards per unit

The length of fence B is 0.3yards

A rate is a ratio that is used for comparing two different kinds of quantities which have different units. On the other hand, the unit rate illustrates how many units of quantity correspond to the single unit of another quantity. We say that when the denominator in rate is 1, it is called unit rate. In fact, unit rate is said to be the amount of something in each unit or per unit.

Fence A which is 1 1/2yards but 1 4/5inches on blueprint. 1 inch = 0.0278 yards

blueorint reading = 9/5×0.0278=0.05=5/100yards

therefore the scale is 3/2 : 5/100 = 3/2÷5/100

= 3/2×100/5= 1:30 = 0.03 :1

therefore the unit rate / yard = 0.03yardperunit

if a fence B is 10yards then on the blueprint it will be 10×0.03= 0.3yards

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Answer:

Step-by-step explanation:

1. Square root of 8 is not a rational number.

2. 1/4 is a rational number.

3. Square root of 90 is not a rational number.

4. 2/3 is a rational number.

5. Square root of 4 is not a rational number.

6. /2 is not a rational number.

7. is not a rational number.

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The given expression:

Apply BODMAS Rule : Brackets, Of, Division, Multiplication, Addition, Subtraction

According to BODMAS rule, we first simplify division:

Simplify multiplication:

Simplify addition:

Answer: -40

Ava has 70 stickers.

Given that the ratio of the number of stickers Ava has to the number of stickers Cole has = 5:3 = 10:6

Also, the ratio of the number of stickers Cole has to the number of stickers Zane has = 2:3 = 6:9

Thus, the compounded ratio of the number of stickers Ava, Cole and Zane has is = 10:6:9

Let the numbers of stickers of Ava has be = 10x

The number of stickers of Cole has, is = 6x

The number of stickers of Zane has, is = 9x

According to question, the total number of stickers they have is 175. So,

10x+6x+9x = 175

25x = 175

x = 175/25

x = 7

Hence Ava has = 10x = 10*7 = 70 stickers.

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We need to first find the intersection between Q and R, which is the common elements between both groups. We have:

Now we need to determine the union between them:

To solve;

z/4=12

Multiply both-side of the equation by 4

That is;

At the left-hand side of the equation 4 will cancel-out 4 leaving us with just z

z = 48

Given two functions f(x) and g(x), its composition will be:

It is read g compound f or simply said to g we are going to fill it with f. So, you have

To expand the binomial, apply the binomial formula to the cube, that is:

So, you have

Finally, operate similar terms

To substract two fractions, we have to have common denominators.

For example, if we want to substract 1/3 from 1/2, we have to convert the fractions so they have a common denominator of 6.

The denominators are the ones that give sense to the fraction. In fact, when we substract whole numbers, we can consider we are substracting "fractions of one".

Then, for example, 5 - 4 could have been written as 5/1 -4/1.

If the numbers have different denominators, we can not perform additions or substractions until we express the fractions with the same denominator.

Trying to substract two fractions with different denominators is like substracting two things that are not expressed in the same units and it will yield an incorrect result.

Given equation is

[tex] \sqrt[3]{x {}^{2} - 7 } = \sqrt[3]{2x + 1} [/tex]

to solve this equation we first need to cube both the sides . As this would remove the cube root on both the sides ,

[tex]\longrightarrow (\sqrt[3]{x^2-7})^3 = (\sqrt[3]{2x+1})^3[/tex]

This would become ,

[tex]\longrightarrow x^2-7=2x+1 \\[/tex]

[tex]\longrightarrow x^2-2x-7-1=0\\[/tex]

[tex]\longrightarrow x^2-2x-8=0\\[/tex]

[tex]\longrightarrow x^2 -4x +2x -8=0\\[/tex]

[tex]\longrightarrow x(x-4)+2(x-4)=0\\ [/tex]

[tex]\longrightarrow (x+2)(x-4)=0\\[/tex]

[tex]\longrightarrow \underline{\underline{ x = 4,-2}} [/tex]

And we are done!

Answer:

[tex]\textsf{To solve the given equation, $\boxed{\sf cube}$ both sides}.[/tex]

Step-by-step explanation:

Given equation:

[tex]\sqrt[3]{x^2-7} =\sqrt[3]{2x+1}[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]

[tex]\implies (x^2-7)^{\frac{1}{3}}=(2x+1)^{\frac{1}{3}}[/tex]

Cube both sides of the equation:

[tex]\implies \left( (x^2-7)^{\frac{1}{3}}\right)^3= \left((2x+1)^{\frac{1}{3}}\right)^3[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies (x^2-7)^{\frac{3}{3}}=(2x+1)^{\frac{3}{3}}[/tex]

[tex]\implies (x^2-7)^{1}=(2x+1)^{1}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^1=a:[/tex]

[tex]\implies x^2-7=2x+1[/tex]

Subtract 2x from both sides:

[tex]\implies x^2-2x-7=1[/tex]

Subtract 1 from both sides:

[tex]\implies x^2-2x-8=0[/tex]

Rewrite -2x as (-4x + 2x):

[tex]\implies x^2-4x+2x-8=0[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x(x-4)+2(x-4)=0[/tex]

Therefore:

[tex]\implies (x+2)(x-4)=0[/tex]

Apply the zero-product property:

[tex]x+2=0 \implies x=-2[/tex]

[tex]x-4=0 \implies x=4[/tex]

Answer:

1. 1

2. 24

3. 1

4. 1 [ab]

5. 3

6. 1

Step-by-step explanation:

Every variable or alphabet's coefficient is the number on the left of it.

e. g coefficient of x is 1.

or coefficient of 83x is 83

To divide a number into a number with an exponent

So, factor the number then put it to the power of (how many will appear)

for example :

8 = 2 * 2 * 2

so, there are 3 of the number 2

So,

8 = 2^3