Solve the problem. Round as appropriate.
The gravitational attraction A between two masses varies inversely as the square of the distance between them.
The force of attraction is 9 lb when the masses are 2 ft apart, what is the attraction when the masses are 6 ft
apart?
A) 3 lb
B) 1 lb
0 2 lb
D) 4 lb

Answer:

Third one

Step-by-step explanation:

The circumference of a circle is given by the formula:

P= 20π ⇒ d*π = 20π ⇒ d= 20

The volume of a sphere is given by the formula:

V= \(\frac{4}{3}\)*π*10³

V= 1333.33*π

Answer: -8/21

Step-by-step explanation:

-5/7= -15/21

1/3=7/21

-15/21+7/21= -15+7=18

(15-7=8)

-8/21

Simplified Solution:

\(-\frac{8}{21}\)

Hope this helps!

The expression g(f(x)) means that we have to include the funcion f(x) inside g(x).

The given functions are

Then, we find g(f(x)).

If f(x) = x + 2, and g(x) = 1/x , then g(f(x)) = 1/(x+2). So, the correct answer to the given question is 1/(x+2).

Solution :

∵ f(x) = x + 2

& , g(x) = 1/x

So,  the Composition of Functions is :

   gof(x) = g(f(x))

⇒ g(f(x)) = g(x+2)

                = 1/(x+2)

∴g(f(x)) = 1/(x+2)

Learn more about Composition of Functions at :

https://brainly.com/question/17103299

Answer:

were is the pic I cant answer lik

An inequality that represents the situation is s > 140.

Let's use "s" to represent the number of milligrams of sodium in a serving.

Since a serving of food does not qualify as low sodium if it contains more than 140 milligrams of sodium, we can write the inequality:

s > 140

This inequality reads "s is greater than 140", indicating that any value of "s" that is greater than 140 milligrams of sodium per serving does not qualify as low sodium.

To graph this inequality, we can represent "s" on the vertical axis and mark the value of 140 with a dashed line.

Since the inequality is greater than 140, we shade the area above the line to represent all the possible values of "s" that do not qualify as low sodium.

The resulting graph would look like given in the attached image.

To learn more about inequality;

brainly.com/question/28823603

#SPJ1

The complete question:

Write and graph an inequality that represents the number of sodium 's' in a serving that does not qualify as low sodium.

For a food to be labeled low sodium, there must be no more than 140 milligrams of sodium per serving.

The mathematical model of an abstract syntax tree (AST) for a programming language's block (BL) statement typically involves representing the syntax of the statement using a tree structure.

This tree structure consists of nodes that correspond to different components of the statement, such as keywords, variables, operators, and expressions. The AST provides a way to parse and interpret the syntax of the statement, allowing for efficient compilation and execution of the code.

The model can be represented using various algorithms and data structures, such as recursive descent parsing or top-down parsing. Ultimately, the AST serves as a tool for developers to analyze, optimize, and debug their code, and is an essential component of many modern programming languages.

Learn more about syntax:

https://brainly.com/question/21926388

#SPJ11

Answer:

19.47

Step-by-step explanation:

if the radius Is 1 and height is 5.1

Answer:

It is a solution

Step-by-step explanation:

Given

\(2x - \frac{y}{2} = -8\)

Required

Determine if \((3,28)\) is a solution

\((3,28)\) implies that:

\(x = 3\)

\(y = 28\)

To check if it is a solution, we simply substitute values for x and y in the given equation;

\(2x - \frac{y}{2} = -8\)

\(2(3) - \frac{28}{2} = -8\)

\(6 - 14= -8\)

\(-8= -8\)

Since both sides of the equation are equal; then, Yes, it is a solution

The solution to this equation –3x + 1 + 10x = x + 4 include the following: A. x = 1/2.

In order to create a list of steps and determine the solution to the equation, we would have to rearrange the variables and constants, and then collect like terms as follows;

–3x + 1 + 10x = x + 4

-3x + 10x - x = 4 - 1

6x = 3

By dividing both sides of the equation by 6, we have the following:

6x = 3

x = 3/6

x = 1/2

In conclusion, we can reasonably infer and logically deduce that solution to this equation –3x + 1 + 10x = x + 4 is 1/2 or 0.5.

Read more on solution and equation here: brainly.com/question/25858757

#SPJ1

Complete Question:

Solve the equation.

–3x + 1 + 10x = x + 4

x = 1/2

x = 5/6

x = 12

x = 18

The length of the rectangle is 19 cm.

The formula for the area of a rectangle,

Area = Length x Width

Given that the area is 336 cm squared.

So, we can set up an equation,

⇒ 336 = (w + 5)w

where w represents the width of the rectangle.

Expanding this equation,

⇒ 336 = w² + 5w

Moving all terms to one side:

⇒ w² + 5w - 336 = 0

This is a quadratic equation that we can solve using the quadratic formula,

⇒ w = (-5 ± √(5² - 4(1)(-336))) / (2(1))

⇒ w = (-5 ± 23) / 2

We'll take the positive value,

⇒ w = 14

So, the width of the rectangle is 14 cm.

We also know that the length is 5 cm more than the width,

Therefore,

⇒ l = w + 5

⇒ l = 14 + 5

⇒ l = 19

Therefore, the length of the rectangle is 19 cm.

Learn more about the rectangle visit:

https://brainly.com/question/2607596

#SPJ12

Extrapolation is a useful tool for predicting future values based on past data

Bethany used a method of predicting future values from past values known as extrapolation. Extrapolation is a powerful tool for predicting future values, but it is important to remember that it only works if the underlying trend in the data does not change. In Bethany's case, she is making an assumption that her income over the next 10 years will follow the same trend as it did in the past 5 years.

In extrapolation, the assumption is that the data points that were observed in the past will continue in the same direction and with the same intensity into the future. Therefore, extrapolation can be used to make predictions about future values even when no new data points have been collected. It is important to remember, however, that any predictions made using extrapolation are only estimates and may not be accurate.

Extrapolation is used in many different fields, such as finance, economics, medicine, engineering, and even weather forecasting. For example, stock analysts may use extrapolation to make predictions about future stock prices based on past prices. Similarly, meteorologists may use extrapolation to make predictions about future weather conditions based on historical weather data.

Overall, extrapolation is a useful tool for predicting future values based on past data. However, it is important to remember that it only works when the underlying trend in the data does not change. Additionally, any predictions made using extrapolation are only estimates and may not be accurate.

See more about extrapolation at: https://brainly.com/question/18768845

#SPJ11

Answer:

Large boxes are 18.25 kg

Small boxes are 15.25 kg

Step-by-step explanation:

This is a system of equations. You need to set up each equation first.

I am assigning x to be big boxes and y to be small boxes.

5x + 3y = 137

2x + 6y = 128

To solve, you will need to eliminate a variable. That means you will have to multiply one of the equations by a number to make it so a variable will be eliminated. I will be multiplying the top equation by -2.

-2 ( 5x + 3y = 137)

    2x + 6y = 128

Distribute the -2 to everything in the parentheses in the first equation.

-10x - 6y = -274

2x + 6y = 128

Notice the 6y will go away because -6y + 6y = 0. Now add the equations together. The remaining equation is:

-8x = -146

Solve for x by dividing by -8.

x = 18.25

Now plug that into one of the original equations.

2(18.25) + 6y = 128.

36.5 + 6y = 128                Subtract 36.5 from each side

-36.5            -36.5

6y = 91.5                          Divide by 6 to solve

y = 15.25

Answer:

Juan said he made a better rate of pay because he was paid $14.80 an hour.

Step-by-step explanation:

Juan made more because he makes $14.80 an hour, whereas Lisa makes only $14 an hour.

Enjoy your day! :D

Answer:

Dolls missing value: 8

balls missing value: 18

Step-by-step explanation:

You would just add whatever the first number is.

Equivalent ratio for dolls: 4:8

equivalent ratio for balls: 6:18

Answer:

C

Step-by-step explanation:

Its straight and a straight line like that means your staying there for a long period of time.

Answer:

28 weeks

Step-by-step explanation:

She starts with $500.

She adds $40 per week. In w weeks, she adds 40w.

After w weeks, she has 500 + 40w.

The total must equal $1620.

500 + 4w = 1620

Subtract 500 from both sides.

4w = 1120

Divide both sides by 40.

w = 1120/40 = 28

Answer: 28 weeks

Step-by-step explanation:

Step-by-step explanation:

Area of triangle = base × height ×½

triangle = 9×8×½=36cm²

rectangle = length×width

rectangle = 15×26=390cm²

area of irregular fig= 390+36 =426cm²

Answer:

19.40 dollars is equal to rs4400

Answer:

9 is c

10 is b

i think the last one is a but not too sure

Step-by-step explanation:

The smallest positive integer x for which the product of 140 and x is a perfect square is 140.

To find the smallest positive integer value of x for which the product of 140 and x is a perfect square, let's break down the problem step by step.

First, let's factorize 140 to find its prime factors:

\(140 = 2 \times 2 \times 5 \times 7\)

Next, we need to determine the prime factors of a perfect square that will cancel out the odd powers of the prime factors of 140.

In this case, the odd power is 1 (since all the prime factors of 140 have an exponent of 1).

To cancel out the odd powers, we need to find a perfect square with prime factors that include 2, 5, and 7.

The smallest such perfect square is:

\(2 \times 2 \times 5 \times 5 \times 7 \times 7 = 19600\)

Now, we can calculate the value of x by dividing the perfect square by 140:

x = 19600 / 140 = 140

Therefore, the value of x is 140.

For similar question on smallest positive integer.

https://brainly.com/question/30076540  

#SPJ11

Therefore, the preceding equation, which states that Brittany will be twice as old as Steve in 9 years, is proven when Brittany is 54 years old and Steve is 18 years old.

Equations are mathematical statements with the equals (=) sign on each side and two algebraic expressions in the center.

Coefficients, variables, operators, constants, terms, and the equal to sign are just a few of the components that make up an equation. The "=" symbol and terms on both sides are always needed when writing an equation.

calculation

Let s = brittany 's age now

Let t = steve's age now

s = 3t

s + 9 = 2 (t+9)

s + 9 = 2t + 27

s = 2t + 27 - 9

s = 2t + 18

Substitute 3t for s and find t

3t = 2t + 18

3t - 2t = 18

t = 18 yrs is steve's age

then

s = 3(18)

s = 54 yrs is brittany's age

Therefore, the preceding equation, which states that Brittany will be twice as old as Steve in 9 years, is proven when Brittany is 54 years old and Steve is 18 years old.

To know more about equations visit :-

https://brainly.com/question/29657992

#SPJ4

So, the average speed of the train is 54.09 miles per hour.

To calculate the average speed of the train for the entire trip, you need to find the total distance traveled and the total time traveled.

First, you can convert the time traveled at each speed to hours. 40 minutes is equal to 40/60=0.67 hours. So the total time traveled is 1+0.67=1.67 hours.

To find the total distance traveled, you can use the formula: distance = speed x time. At 45 mph, the distance traveled is 45 x 0.67 = 30.15 miles. At 60 mph, the distance traveled is 60 x 1 = 60 miles. Therefore, the total distance traveled is 30.15 + 60 = 90.15 miles.

Finally, you can use the formula: average speed = total distance / total time.

Average speed = 90.15 miles / 1.67 hours = 54.09 miles per hour.

To learn more about Average Speed

Visit; brainly.com/question/12322912

#SPJ4

Pythagorean theorem tells us how the side lengths of right triangles are related.

The Pythagorean theorem, also known as the Pythagorean identity, states that the sum of the squares of the lengths of the two sides forming the right angle is equal to the square of the length of the hypotenuse in any right triangle (the side opposite the right angle). In other words, the Pythagorean theorem can be used to calculate the length of the hypotenuse given the lengths of the two sides of a right triangle.

This relationship can be written as the equation:

\(a^2 + b^2 = c^2\)

where a and b are the lengths of the legs, and c is the length of the hypotenuse. The Pythagorean Theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery.

For more question on Pythagorean theorem click on

https://brainly.com/question/343682

#SPJ4

The graph of g is Transformation up 7 units.

what is Transformation?

A graph transformation is a method for altering an existing graph or graphed equation to create a different version of the graph that follows. The modification of algebraic equations is a typical form of algebraic issue.

solution:

From the question, we have the following parameters that can be used in our computation:

g(x) = f(x) + k

Also, we have the value of k to be

k = 7

From the question, we can interpret g(x) = f(x) + k as f(x) is shifted up by k units

This means that

g(x) = f(x) + k

So, we have

g(x) = f(x) + 7

Hence, the transformation is (a) translated up 7 units

To learn more about Transformation from the given link

https://brainly.com/question/1620969

#SPJ1

According to given -

5p = 140

Dividing by 5 on both sides we get,

\( \frac{5p}{5} = \frac{140}{5} \)

Now,

By the cancelling the factors we get,

\(p = \frac{28 \times 5}{5} \)

\(p = 28\)

Therefore,

a) 28 is the correct option.

What are factors?

We know that,

Factors are the numbers that can divide a number exactly. Hence, after division, there is no remainder left. Factors are the numbers you multiply together to get another number. Thus, a factor is the divisor of another number.

A prime number has only two factors, i.e., 1 and the number itself. But the composite numbers have more than two factors.

Some of the important properties of factors of a number are listed below:

How to find factors?

There are two possible methods to find factors of any number, such as:

Disclaimer : The complete question is attached

Learn more about factors at : https://brainly.com/question/24182713?referrer=searchResults

#SPJ4

We get that the value of h is option (a) 28 for the equation 5 p = 140

We are given an equation:

5 p = 140

An equation is an expression that has an equality sign in between.

For example: 3 x + 5 y = 6 or 7 x + 4 y = 9 or 4 x + 16 y = 0

We have to solve the equation to find the value of p.

First, we will divide both the sides of the equation by 5:

5 p / 5 = 140 / 5

Now simplifying the expression, we get that:

p = 140 / 5

Solving the expression to get the value of p:

p = 28

So, option (a) 28 is correct.

Therefore, we get that the value of p is option (a) 28.

Learn more about equation here:

brainly.com/question/1214333

#SPJ4

Answer:

Max

Step-by-step explanation:

the function given that h = -16t³+64t+10

the general function Equation:

h = at²+bt+c

=> t at the highest point is defined by t = -b/2a

= -64/2(-16) = -64/-32 = 2 second

the total times that the ball hits the ground

= 2× 2 seconds = 4 seconds.

so, Max is right

Answer:

Solution given:

Let h=0=when the ball hit the ground,the height=0.

h= -16t^2 + 64t + 10.

0=16t²-64t-10

8t²-32t-5=0

∆=\( \frac{32±\sqrt{32²+4*5*8}}{2*8}=\frac{8±\sqrt{74}}{4}\)

taking positive

t1=\( \frac{8+\sqrt{74}}{4}=4.15seconds\)

t2=\( \frac{8-\sqrt{74}}{4}(t2<O)(neglected)\)

So

t=4.15seconds closer to 4seconds.So

Max is closer.

Answer:

x = -2

-2(-2^2) + 4(-2)

-2(4) + -8

Yes, this is a binomial distribution because we are flipping the same coin ten times and the probability of a head is constant at 1/2 for each flip.

The number of heads, X, is a count of successes in a fixed number of trials, making it a binomial random variable.
Your question asks whether X is a binomial random variable or not. X represents the number of heads obtained from flipping the same coin ten times, with the probability of a head being ½.

Your answer: Yes, X is a binomial random variable. This is because there are a fixed number of trials (10 coin flips), each trial has only two outcomes (head or tail), the trials are independent, and the probability of success (a head) remains constant at ½.

Visit here to learn more about binomial distribution  : https://brainly.com/question/14565246
#SPJ11