If the amount of air in a spherical balloon is 288π cu. in.,what is the radius of the balloon?

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 9000\\ P=\textit{original amount deposited}\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}\)

\(9000 = P\left(1+\frac{0.04}{4}\right)^{4\cdot 4} \implies 9000=P(1.01)^{16} \\\\\\ \cfrac{9000}{(1.01)^{16}}=P\implies \boxed{7675.39\approx P}\)

Answer:  x= y

Step-by-step explanation:

3x + y =5x -y         Subtract 5x from both sides

-5x         -5x

-2x + y = -y         Now subtract  y from both sides

       -y    -y

-2x = -2y      Now divide both sides by -2

x = y

Answer:

the product of the decimal equivalents of all discount in the series

Answer:

-118 feet

Step-by-step explanation:

\(-342+224=-118\)

Answer: I believe it can be a right triangle

Step-by-step explanation:

Answer:

In mathematics, the extrema of a function refer to the maximum and minimum values that the function can take on. These values can be local extrema, which occur within a certain range of the function, or global extrema, which are the maximum and minimum values over the entire domain of the function.

To find the extrema of a function, one can use a variety of techniques, such as taking the derivative of the function and setting it equal to zero to find the points of stationary values, or using the second derivative test to determine whether a stationary point is a local maximum or minimum.

Interpreting the extrema of a function can provide valuable information about the behavior of the function. For example, the global maximum of a function might represent the highest possible value that the function can attain, while the global minimum might represent the lowest possible value. Local extrema can also be important, as they can indicate changes in the slope or concavity of the function, which can have important implications for applications such as optimization or modeling real-world phenomena.

Answer:

\(A=502.4\ \text{inches}^2\)

Step-by-step explanation:

The radius of the ball, r = 2 inches

We need to find how many square inches of plastic does the company  need to make 10 beach balls.

Let A be the area of 1 ball. Balls are in the form of spheres. The area of a sphere is given by :

\(A=4\pi r^2\)

For 10 balls,

\(A=10\times 4\pi r^2\\\\=10\times 4 \times 3.14\times (2)^2\\\\=502.4\ \text{inches}^2\)

Hence, the area of 10 beach balls is \(502.4\ \text{inches}^2\).

Answer:☠️☠️☠️☠️do ur hw lil bro u actually need to learn this fr fr dont let me catch u slippin on foenem

Step-by-step explanation:

b. 650 because in the directions it says for groups of more than ( > ) 8 people they charge a FIXED fee of 650 so it's not 75 times 9 which would have been 675

Step-by-step explanation:

C(n) = {

75n, if n <= 8

650, if n > 8 and n <= 12

}

This function states that for groups of 8 people or fewer, the total cost is 75n, while for groups of 9 to 12 people, the total cost is a fixed $650.

b. To determine the total cost of a 1-hour private guided tour with 9 people, we can simply plug n = 9 into the equation we derived in part a:

C(9) = {

75*9, if 9 <= 8

650, if 9 > 8 and 9 <= 12

}

Since 9 is greater than 8 but less than or equal to 12, we use the second case:

C(9) = 650

Therefore, the total cost of a 1-hour private guided tour with 9 people is $650.

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Answer:

x = 20

Step-by-step explanation:

Original Equation:

1/2x - 3 = 7

(1/2x can be written as 0.5x)

0.5x - 3 = 7

Add 3 to both sides.

0.5x = 10

Divide both sides by 0.5

x = 20

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The functions are f(x) = 600 - 10x & g(x) = 20/3x, and the graphs are added as attachments

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

The table of values

For the membership application, we have the following features

So, the function is

f(x) = 600 - 10x

For the membership available, we have the following features

So, the function is

g(x) = 20/3x

So, the functions are f(x) = 600 - 10x & g(x) = 20/3x

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Answer:

$29765.50

Step-by-step explanation:

Median is the middlemost value (or the average of the 2 middlemost value if there are even number of values) in an ascending order.

First, arrange the salary list in an ascending order.

$21,971 , $25,997 , $27,512 , $32,019 , $38,860 , $43,702

As we can see here, there are even number of values (6), so the median will be the average of the 2 middlemost value, which will be:

Median = \(\frac{27512 + 32019}{2}\)

= \(\frac{59531}{2}\)

= $29765.50

Answer:

$29,765.50 is the median salary

Step-by-step explanation:

To find the median of the following salary list $32,019, $21,971, $27,512, $43,702, $38,860, $25,997

The steps to do this is:

Doing the steps:

This means take the average of $27,512 and $32,019

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Answer:

Top and bottom graphs on the right.

Step-by-step explanation:

When reading the question it says data rather than line or function. So, the Top and bottom graphs on the right have continuous data points. The Top and bottom graphs on the left have continuous linear functions. I am not 100% on this, but I think the top and bottom graphs on the right are correct.

We need to simplify the following expression:

We will need to sum all the numbers that have an "x" together, we will also need to sum all the ones that don't. When we are doing this we need to check for the signals on each number. If the signals are the same, we add the values and mantain the signal, if they are different we subtract the value and maintain the signal of the greater one. We have:

Answer:

39.864

Step-by-step explanation:

24*4=96

1827/96

=39.864

Answer:

290 dollars

Step-by-step explanation:

$44(to rent the car) x 5 = $220

$7( for insurance) x 5 = $35

35$ for gas

Add all those prices up:

220 + 35 + 35= 290

I hope this helps...

Answer:

thise day is

Tuesday

February 17 2022

Saturday

To find the distance above the ground at which the tack is, we need to calculate the vertical displacement of the front wheel when the tack was picked up.

First, let's determine the circumference of the front wheel. The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter. Given that the diameter is 26 inches, we can calculate the circumference:

C = π × 26

C ≈ 81.64 inches

This means that for every complete revolution of the wheel, Devon travels a distance of approximately 81.64 inches.

Next, we need to determine how many complete revolutions the front wheel made as Devon rolled another 100 feet (1200 inches). Since the circumference of the wheel is 81.64 inches, we can divide 1200 inches by 81.64 inches to find the number of revolutions:

1200 / 81.64 ≈ 14.68 revolutions

Now, we know that the tack was picked up after one full revolution. Therefore, out of the 14.68 revolutions, 13 complete revolutions have occurred. The tack is located at the point where the 14th revolution starts.

Since each revolution covers a distance equal to the circumference of the wheel, the vertical displacement of the tack is the height of the wheel, which is the radius of the wheel. The radius is half the diameter, so in this case, it is 26 / 2 = 13 inches.

Therefore, the tack is located 13 inches above the ground.

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Explanation:

When we reflect any point (x,y) over the line y = x, the x and y coordinates swap. So for instance, we have K = (5, -9) turn into K ' = (-9, 5).

Consider a point like (1,2). We can move it down 1 unit to have it land on the line y = x, then we can move it one unit to the right to move it to (2,1). These two translations effectively move the original point to its reflected location. The distance from (1,2) to y = x, is the same as the distance from (2,1) to y = x. Furthermore, the line connecting (1,2) to (2,1) is perpendicular to y = x.

Answer:

show the top plzzz

Step-by-step explanation:

Answer:

the last one

Step-by-step explanation:

the last one goes up in a linear sequence(the same amount each time)

The value of c in the triangle is (b) 5 units

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

The right triangle

The length c is the hypotenuse of one of the triangles and can be calculated using the following Pythagoras theorem

c² = sum of squares of the legs

Using the above as a guide, we have the following:

c² = 3² + 4²

Evaluate

c² = 25

Take the square roots

c = 5

Hence, the hypotenuse of the right triangle is 5

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Answer:

The mean distance to his friends' house is between 2 -3 blocks.

Step-by-step explanation:

1. Mean = Average.

Average = (n1+n2+n3....nx)/x

2. The average = 1+2+5+3+2+2+5+3/8

3. Therefore, the answer is 2.875, making the mean between 2 and 3

Answer:

The statement that supports the data is the mean distance to his friends' houses is in between 2 and 3 blocks.

Step-by-step explanation:

What is mean, median and mode?

Mean: The average of the given data points.

Median: The central point of the whole data set.

Mode: The number that occurs for the maximum times in the data set.

Given:

Karl records the number of city blocks from his house to each of his friends houses.

Data set for the number of city blocks to eight friends houses:

{1, 2, 5, 3, 2, 2, 5, 3}

The first option: it is given that the maximum number of blocks the Karl lives from his friend is 4, but according to the data set, the maximum number of house blocks should be 5.

Hence, this option is incorrect.

The second option: It is given that the mode shows that Karl has 3 friends who live 3 blocks from him, but according to the given data set Karl has 3 friends who lives 2 blocks from him. Hence the mode is 2.

Hence, this option is incorrect.

The third option: It is given that the minimum distance from Karl's house to a friend's is 2 blocks, but according to the given data set the minimum distance from Karl's house to a friend's is 1 block.

Hence, this option is incorrect.

The fourth option:  It is given that the mean distance to his friend's houses is in between 2 and 3 blocks.

We will find the mean for the given data set.

⇒ Mean = (Sum of all the data points) / (Total number of data points)

⇒ Mean = (1 + 2 + 5 + 3 + 2 + 2 + 5 + 3)/8

⇒ Mean = 23/8

⇒ Mean = 2.875

∴ The mean distance from Karl to his friend's houses is 2.875 which is in between 2 and 3.

Hence, this option is correct.

Therefore, the fourth option which says the mean distance between Karl and his friend's houses is in between 2 and 3 is correct.

The equation that can be used to find the number of pieces of candy Joey has is j = (315 - 18) / 3 .

Number of candies Sal has = 3(number of candies that Joey has) + 18

315 = 3(j) + 18

Where j represents the number of candies that Joey has.

Given this equation, 315 = 3(j) + 18 , we are to make j the subject of the formula. To do this, take the following steps.

Combine similar terms :

(315 - 18) = 3j

Divide both sides by j

j = (315 - 18) / 3

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Answer: 15/2

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