An employee at a fireworks company is designing a rocket. The rocket will consist of a cardboard circular cylinder with a height that is seven times as large as the radius. On top of the cylinder will be a cone with a height of 5 in. and a radius equal to the radius of the base as shown in the figure. If the company wants to fill the cone and the cylinder with a total of 204 in.^3 of​ powder, then what should be the radius of the​ cylinder? Note that the volume of a right circular cylinder with radius r and height h is and the volume of a cone with a base of radius r and height h is .

Answer:

4

2

−

1

1

3

+

4

8

3

Step-by-step explanation:

The firm's federal income tax is $57,168.

To calculate the firm's federal income tax, we need to determine its taxable income first. Taxable income is calculated by subtracting deductions from the firm's total income.

In this case, the firm's total income consists of income from operations, interest income, and dividend income.

Total income:

Income from operations = $231,000

Interest income = $23,100

Dividend income = $29,700

Total income = $231,000 + $23,100 + $29,700 = $283,800

Next, we deduct expenses from the total income. In this case, the only relevant expense is the interest paid to bondholders:

Total expenses = Interest paid to bondholders = $11,000

Taxable income = Total income - Total expenses = $283,800 - $11,000 = $272,800

Now, we can calculate the federal income tax by applying the federal tax rate of 21% to the taxable income:

Federal income tax = Taxable income * Federal tax rate

Federal income tax = $272,800 * 0.21 = $57,168

Therefore, the firm's federal income tax is $57,168.

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Answer:

see below

Step-by-step explanation:

Part A

Notice that for each increase of 1 in x, there is an increase of 3 in y

There is a correlation between the amount of sunlight and the height of the plant

Part B

The slope in change in y over change in x

m = 3/1 = 3

y= mx+b

y = 3x+b

The y intercept is when x =0  so b = 4

y = 3x+4

Part C

With no sunlight the plant is 4 cm tall.  As the plant gets more sunlight, the plant grows at 3 cm per hour of sunlight.

Step-by-step explanation:

there is a direct correlation between the hours of sunlight and the height of the plant.

a delta of 1 hour sunlight results consistently in a growth of 3 cm. there is not a single point in the set of data that deviates from this.

therefore, the function for the height of the plant based on the number of sunlight received is

y = 3x + 4

as every hour of sunlight (x) results in an additional growth of 3cm. and we are starting with a plant that is already 4 cm tall at the beginning (x=0).

the y-intercept is the first data point (x=0) and shows y=4.

the slope is 3 (or 3/1 as y/x ratio) indicating that with one hour of sunlight the plant grows an additional 3 cm.

and as mentioned, we started with a plant already 4cm tall.

Answer:

x + x - 45 = 90

2x - 45 = 90

2x = 135

x = 67.5, so x - 45 = 22.5

The other two angles measure 22.5° and 67.5°.

Answer:

23.6

Step-by-step explanation:

Answer: 23.6

Step-by-step explanation:

Answer:

to find the least common multiple (LCM) of 18 and 22, you can use the following steps:

Prime factorize the numbers:

18 = 2 * 3^2

22 = 2 * 11

Identify the highest power of each prime factor that appears in either number:

The highest power of 2 is 2^1.

The highest power of 3 is 3^2.

The highest power of 11 is 11^1.

Multiply these highest powers together:

2^1 * 3^2 * 11^1 = 66.

Therefore, the least common multiple (LCM) of 18 and 22 is 66.

Step-by-step explanation:

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

dice:

6 sided

Step 02:

outcomes:

Event A (odd):

1 , 3 , 5

outcomes = 3

Event B (5 or more):

5 , 6

outcomes = 2

Event C (≤ 3):

1 , 2 , 3

outcomes = 3

Event D (4):

4

outcomes = 1

Answer:

1. 500 milligrams

2. 6450 grams

3. 50 oranges

4. 30 weeks

5. 1500 grams

To do this, all you basically need to do is convert grams, milligrams, etc.

You also need to do Multiplying, Dividing, Adding, and Subtratcing.

Please give me Brainliest!

Answer:

6 weeks.

Step-by-step explanation: Because if he answered 12 quizzes in 2 weeks then 12 times 3 equals 36 so then all you have to do is times the weeks by 3.

The value of x in the expression given is -7/6

(6x + 9)/2 =

First step is to cross multiply

6x + 9 = 2

Collect like terms

6x = 2 - 9

6x = -7

divide both sides by 6 to isolate x

x = -7/6

Therefore the value of x in the expression given is -7/6

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The measure of the central angle is 0.75 radians

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The area of a figure is the amount of space it occupies in its two dimensional state.

The length of an arc with an angle of Ф is given by:

Length of arc = (Ф/360) * (π * diameter)

The diameter is 16 cm and intercepted arc length is 6 cm, hence:

Length of arc = (Ф/360) * (π * diameter)

6 = (Ф/360) * (π * 16)

Ф = 42.97°

Ф = 42.97° * π/180 = 0.75 radian

The measure of the central angle is 0.75 radians

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Answer:

\({ \bf{area = \pi {r}^{2} }} \\ = 3.14 \times {11}^{2} \\ = 380.1 \: {cm}^{2} \)

Answer: 132

Step-by-step explanation:

1.

2.

3.

4.

5.

By adding the cost of 2 child passes to each expression, Leah includes the cost of 2 more children going on the trip.

We have,

To include the cost of 2 more child passes in the expressions 3(a + c) and 3a + 3c,

We can simply add the cost of 2 child passes to each expression.

Let's assume the cost of each child pass is represented by the variable "p".

To modify 3(a + c), we add the cost of 2 child passes to the expression:

3(a + c) + 2p

This represents the total cost of 3 passes for children, including the original "a" and "c" passes, as well as the additional 2 passes.

To modify 3a + 3c, we also add the cost of 2 child passes:

3a + 3c + 2p

This represents the total cost of 3 passes for children, including the original "a" and "c" passes, as well as the additional 2 passes.

Thus,

By adding the cost of 2 child passes to each expression, Leah includes the cost of 2 more children going on the trip.

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Answer:

The probability that the mean salary offer is of X or less is the p-value of \(Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\), in which \(\mu\) is the mean salary for the population, \(\sigma\) is the standard deviation for the population and n is the size of the sample.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Z-score with the Central Limit Theorem:

Z-is given by:

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

What is the probability that the mean salary offer for these students is X or less?

The probability that the mean salary offer is of X or less is the p-value of \(Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\), in which \(\mu\) is the mean salary for the population, \(\sigma\) is the standard deviation for the population and n is the size of the sample.

Answer:

118,000

Step-by-step explanation:

1.003M x (6,000/51,000) = 118,000

Answer:

Step-by-step explanation:

Sales Revenue:  $800.00

Cost of good sold:  $350,000.00

Subtract:                   $450,000.00

Sales Revenue:         $795,000.00

Cost of good sold:     $600,000.00

Subtract Sales             $195,000.00

Revenue from Cost

of goods sold.

Answer:

LCD = 30

3/10 = 9/30

2/3 = 20/30

Step-by-step explanation:

This is the answer because:

1) First, the least common denominator is 30 because 10 x 3 is 30 and 3 x 10 is 30

2) Next, multiply the numerators with the same number you multiplied with the denominator    

3 x 3 = 9

2 x 10 = 20  

3) Therefore, the answers are:

3/10 = 9/30

2/3 = 20/30

Hope this helps!

a) The equation for Bueller's height above the ground as a function of time is: h(t) = 9 cos(πt/8) + 1.5

b) When Bueller has been on the ride for 1 minute and 30 seconds, his height above the ground is approximately 10.5 m.

In mathematics, a function is a rule that assigns a unique output value to each input value in a specified set. More precisely, a function is a set of ordered pairs (x, y) where each x-value (the input) corresponds to exactly one y-value (the output).

In mathematics, an equation is a statement that asserts the equality of two expressions, typically containing one or more variables. An equation consists of two sides, the left-hand side, and the right-hand side, separated by an equal sign (=).

According to the given information,

a) To determine an equation for Bueller's height above the ground as a function of time, we can use the equation for the height of a point on a Ferris wheel:

h(t) = r cos(ωt) + h0

where:

1) h(t) is the height of the point above the ground at time t

2) r is the radius of the Ferris wheel

3) ω is the angular velocity of the Ferris wheel (in radians per second)

4) t is the time elapsed since the point was at its lowest position

5) h0 is the initial height of the point above the ground

In this case, we know that Bueller boards the Ferris wheel at a height of 1.5 m off the ground, so h0 = 1.5 m. The radius of the Ferris wheel is 9 m, and it rotates once every 16 seconds, so the angular velocity is:

ω = 2π / T = 2π / 16 = π / 8 radians per second

Therefore, the equation for Bueller's height above the ground as a function of time is:

h(t) = 9 cos(πt/8) + 1.5

b) To find Bueller's height off the ground when he has been on the ride for 1 minute and 30 seconds (or 90 seconds), we can substitute t = 90 into the equation for h(t):

h(90) = 9 cos(π(90)/8) + 1.5

h(90) = 9 cos(11.25π) + 1.5

Using a calculator, we get:

h(90) ≈ -6.3 m

Note that the negative sign means that Bueller is below ground level, which is not physically possible. This occurs because we started counting time from the bottom of the wheel, so 90 seconds corresponds to the bottom position plus 5 and a half rotations. To fix this, we can add a multiple of the period T = 16 seconds to t to bring it back to the correct range:

h(t) = 9 cos(πt/8) + 1.5

h(90 + 5T/2) = 9 cos(π(90 + 5T/2)/8) + 1.5

h(90 + 5T/2) = 9 cos(π(2 + 5/16)) + 1.5

h(90 + 5T/2) ≈ 10.5 m

Therefore, when Bueller has been on the ride for 1 minute and 30 seconds, his height above the ground is approximately 10.5 m.

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Answer:

B or C

hope this helps :)

Both planes have the same normal vector:

\(6x-y-z=6\implies\mathbf n=\langle6,-1,-1\rangle\)

The plane we want must contain the point (4, -3, -1), so its equation would be

\(\mathbf n\cdot\langle x-4,y+3,z+1\rangle=0\)

\(\implies 6(x-4)-(y+3)-(z+1)=0\)

\(\implies\boxed{6x-y-z=28}\)

Amount of $150,000 represents 42.86% of $350,000.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have Danny’s home cost $350,000. The federal government program for flood damage insurance covers only $150,000.

Assume that it represents [x%] percent of the total value. Then, we can write -

x = (150000/350000) x 100

x = 42.86%

Therefore, $150,000 represents 42.86% of $350,000.

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Answer:

\(\left(x^2+1\right)\left(x+1\right)\left(x-1\right)\left(x^2+x+1\right)\left(x^2-x+1\right)\left(x^4-x^2+1\right)\)

Step-by-step explanation:

Factor of \(x^{12}-1\) is

\(\left(x^2+1\right)\left(x+1\right)\left(x-1\right)\left(x^2+x+1\right)\left(x^2-x+1\right)\left(x^4-x^2+1\right)\)

Answer: True

Explanation: The domain of a quadratic function in standard format is always all real numbers, meaning you can substitute any real number for x. The range of a function is the set of all real values of y that you can get by plugging real numbers into x.

Linear function is almost always going to be all real numbers. The range of a non-horizontal linear function is all real numbers no matter how flat the slope might look.

Answer: The answer is 43000

Step-by-step: Adding a number under 500 to get 43000 makes it rounded up and not down.