PLSSSS HEEEELPPP


A cone has a radius of 6 inches and a height of 16 1/2 inches. A cylinder
has a radius of 8.5 inches and a height of 25 inches. What is the sum of the
volumes, to the nearest tenth of a cubic inch, of the cone and the
cylinder? EXPLAIN YOUR ANSWER. *

Answer:

0.08

Step-by-step explanation:

5 ^-2 * cube root of 8

first of all, let us solve 5^-2

using the law of indices;

a^-2 = 1 / a ^2

following this law, we have;

5^-2 = 1 / 5^2

we know that 5^2 = 25

therefore,

5^-2 = 1 / 25

now, let is continue by solving the cube root of 8

now, there are three ways of solving this;

we could just simply think of any number that when multiplies itself three times times, it gives 8, or we could just simply use a calculator

regardless of what we use, we have to end up with the number 2 as the answer

leading is to our conclusion.

from all our solution, we have reduced our question to;

1 / 25 ( which is 5^-2) * 2 ( which is the cube root of 8 )

= 1 / 25 * 2 / 1

note that 2 is the same as 2 / 1. We put it like this when we want to carry out an operation on an integer ( e.g. 2) and and a fraction ( e.g. 1 / 25 )

so,

1 / 25 * 2 / 1 =

2 / 25 ( the two multiplies the 1 in 1 / 25 and the 25 multiplies the 1 in 2 / 1)

leaving our answer in decimal, we have;

0.08

hope this helps,

thanks!!!

the general solution of the given differential equation is:

y = [(1/3) x^3 + 2x^2 + 4x + C1] / |x^2 - 4|

To find the general solution of the given differential equation:

(x^2 - 4) dy/dx + 4y = (x + 2)^2

We can rearrange the equation to isolate the derivative term:

dy/dx = [(x + 2)^2 - 4y] / (x^2 - 4)

First, let's simplify the numerator:

[(x + 2)^2 - 4y] = (x^2 + 4x + 4) - 4y

= x^2 + 4x + 4 - 4y

= x^2 + 4x - 4y + 4

Now, substitute this simplified expression back into the differential equation:

dy/dx = (x^2 + 4x - 4y + 4) / (x^2 - 4)

This is a first-order linear homogeneous differential equation. To solve it, we can use the integrating factor method.

First, let's write the equation in the standard form: dy/dx + P(x)y = Q(x)

dy/dx + (4x / (x^2 - 4))y = (x^2 + 4x + 4) / (x^2 - 4)

The integrating factor is given by the exponential of the integral of P(x):

μ(x) = exp ∫ (4x / (x^2 - 4)) dx

To find the integral, we can use substitution. Let u = x^2 - 4, then du = 2x dx:

μ(x) = exp ∫ (2x dx) / (x^2 - 4)

= exp ∫ (du / u)

= exp(ln|u|)

= |u|

Substituting back u = x^2 - 4:

μ(x) = |x^2 - 4|

Now, multiply the entire differential equation by the integrating factor:

|x^2 - 4| dy/dx + (4x / (x^2 - 4)) |x^2 - 4|y = (x^2 + 4x + 4) |x^2 - 4| / (x^2 - 4)

The left side can be simplified using the product rule for differentiation:

d/dx [ |x^2 - 4|y ] = (x^2 + 4x + 4) |x^2 - 4| / (x^2 - 4)

Now, integrate both sides with respect to x:

∫ d/dx [ |x^2 - 4|y ] dx = ∫ (x^2 + 4x + 4) |x^2 - 4| / (x^2 - 4) dx

Integrating the left side gives:

|x^2 - 4|y = ∫ (x^2 + 4x + 4) dx

= (1/3) x^3 + 2x^2 + 4x + C1

where C1 is the constant of integration.

Finally, divide both sides by |x^2 - 4| to solve for y:

y = [(1/3) x^3 + 2x^2 + 4x + C1] / |x^2 - 4|

To know more about derivative visit:

brainly.com/question/29144258

#SPJ11

Answer:

x + x^2 = yx

not really sure if you are looking for this so comment if this is what you wanted

Considering the numeric values and the range concept, we have that:

The range of the function is given by: {f(0), f(1), f(2), f(3), f(4), f(5)}.

To find the numeric value of a function, we replace each instance of the variable by the desired value.

The range of a function is the set that contains all possible output values for the function. These outputs are the numeric values for the domain of the function, which compose the input values.

For this problem, we have that:

Hence:

The range of the function is given by: {f(0), f(1), f(2), f(3), f(4), f(5)}.

The function is not given, hence this problem was solved speaking in general terms. In your problem, you will mark the numeric values of the function given.

More can be learned about the numeric values of a function at brainly.com/question/28367050

#SPJ1

Answer:

Y axis is vertical the one running up and down in the middle x axis is the one going side to side

Step-by-step explanation:

Whatever it is your asking I hope this helps

Answer:

true or false

Step-by-step explanation:

Receiving a customer who has an appointment is a routine query

Answer:

300pi

Step-by-step explanation:

the formula for volume of a cylinder is pi3^2h

So pi * (25) * 12

300 pi.

If you forget the formula, remember circle area is pir^2 and multiplying that by the height will raise the circle's area, giving us volume.

The number of observations in a complete data set with 10 elements and 5 variables is a. data.

In the context of data analysis, a complete data set refers to a collection of data that includes all the required observations or cases. In this scenario, the data set consists of 10 elements, which represent the individual observations or data points. Each element is associated with 5 variables, which are the characteristics or attributes being measured or observed.

Therefore, the number of observations in this data set is determined by the number of elements, which is 10. The term "observations" refers to the individual data points or cases in the data set. The other options, such as "variables" and "elements," do not accurately represent the count of observations in this context.

Hence, the correct answer is a. data, indicating that the number of observations in the complete data set is determined by the number of elements, which in this case is 10

To know more about data sets, visit:
brainly.com/question/29011762

#SPJ11

Answer:

Step-by-step explanation:

they right it is 7

Answer:

c = 56.25

Step-by-step explanation:

Substitute the known values into the law of sines to find c.

good luck, i hope this helps :)

Answer:

a) The confidence interval for τA - τB is:

CI = (τA - τB) ± t* * SE(τA - τB)

b) the sum of squares: SSE = (11.3 - μA)² + (11.3 - μA)²

What is the confidence interval?

A confidence interval is a range of values that is likely to contain the true value of an unknown population parameter, such as the population mean or population proportion. It is based on a sample from the population and the level of confidence chosen by the researcher.

(a) To calculate the 95% confidence interval for τA - τB, we can use the formula:

CI = (τA - τB) ± t(α/2, df) * SE(τA - τB)

where t(α/2, df) is the t-score for the desired confidence level and degrees of freedom, and SE(τA - τB) is the standard error of the difference in means.

The degrees of freedom for the test can be calculated using the formula:

df = ∑(ni - 1)

Given the data:

nA = 12, nB = 8, and mean responses: μA = 11.3, μB = 8.4, μC = 10.2

We can calculate the standard error using the formula:

SE(τA - τB) = √((s²/nA) + (s²/nB))

where s² is the sample variance.

Calculating the degrees of freedom:

df = (nA - 1) + (nB - 1) = 11 + 7 = 18

Plugging in the values, we have:

SE(τA - τB) = √((4.9/12) + (4.9/8)) ≈ 1.313

The t-score for a 95% confidence interval with 18 degrees of freedom can be found using a t-table or statistical software. Let's assume the t-score is t*.

The confidence interval for τA - τB is:

CI = (τA - τB) ± t* * SE(τA - τB)

You would need to consult a t-table or use statistical software to find the t* value. The interval would be calculated by substituting the appropriate values.

(b) To calculate the F-test statistic for the hypothesis τA = τB = τC, we can use the formula:

F = (MSA / MSE)

where MSA is the mean square due to treatments and MSE is the mean square error.

The mean square due to treatments can be calculated as:

MSA = SSA / (k - 1)

where SSA is the sum of squares due to treatments and k is the number of groups (in this case, k = 3).

The mean square error can be calculated as:

MSE = SSE / (N - k)

where SSE is the sum of squares error and N is the total sample size.

To calculate the sum of squares:

SSA = ∑(ni * (μi - μ)²)

SSE = ∑∑((yij - μi)²)

Given the data, we can calculate the sum of squares:

SSA = (12 * (11.3 - ((11.3 + 8.4 + 10.2) / 3))^2) + (8 * (8.4 - ((11.3 + 8.4 + 10.2) / 3))²) + (16 * (10.2 - ((11.3 + 8.4 + 10.2) / 3))²)

SSE = (11.3 - μA)² + (11.3 - μA)²

Hence, a) The confidence interval for τA - τB is:

CI = (τA - τB) ± t* * SE(τA - τB)

b) the sum of squares: SSE = (11.3 - μA)² + (11.3 - μA)²

To Learn more about the confidence interval here:

https://brainly.com/question/20309162

#SPJ4

So we have shown that the largest possible area of the triangle is \(a^2,\)which occurs when the third side has length 3a and the height is a.

We can use the formula for the area of a triangle, which is A = (1/2)bh, where b is the length of the base and h is the height. In this case, we know that the base has length 2a, so we need to find the height.

Let's call the third side of the triangle, which is not given, b. We know that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, so we have:

a + 2a > b

3a > b

We can rearrange this to solve for b:

b < 3a

Now, let's use the formula for the area of a triangle:

A = (1/2)bh

We want to maximize A, so we want to maximize h. We know that h is the height of the triangle, which is perpendicular to the base, so it forms a right angle. We can use the Pythagorean theorem to find h in terms of a and b:

\(h^2 = b^2 - a^2\)

We can substitute our inequality for b:

\(h^2 < (3a)^2 - a^2\)

\(h^2 < 8a^2\)

h < √(8\(a^2\))

h < 2 √(2)a

Now we can use the formula for the area of the triangle again:

A = (1/2)bh

A < (1/2)(2 √(2)a)(a)

A < \(a^2\) √(2)

So we have shown that the largest possible area of the triangle is \(a^2,\)which occurs when the third side has length 3a and the height is a.

Learn more about  Pythagorean theorem

https://brainly.com/question/14930619

#SPJ4

The laws of exponents I will be using are:

\((x^y)^z = x^{yz}\), and \(x^y \cdot x^z = x^{y+z}\).

For the first part, \((15^3)^3 \cdot 15^{-6} = 15^9 \cdot 15^{-6} = 15^3\).

For the second part, \(15 \cdot (15^3)^2 \cdot (15^{-5})^2 = 15 \cdot (15^6) \cdot (15^{-10}) = 15^{1+6-10} = 15^{-3} = \frac{1}{15^3}\).

The domain of the function is from 0 to infinity or all positive numbers.

The domain of a function is the set of possible input values or the set of all values that x can take.

The range of a function is the set of possible output values or the set of all values that f(x) can take.

The car buyer considers the depreciation of a new car by creating a function to represent the car, f(x), based on the number of years after the car is purchased, x.

Therefore, the function is dependent on the number of years after the car is purchased and can be represented as:

f(x) = g(x) + p, where g(x) is the depreciation function and p is the purchase price of the car.

The best representation of the domain of this function is x ∈ [0,∞) or x ≥ 0. The car buyer considers the depreciation of a new car by creating a function to represent the car, f(x), based on the number of years after the car is purchased, x.

Thus, the best represents the domain of the function is "x ≥ 0".The statement means that the domain of the function is from 0 to infinity or all positive numbers.

To learn about the domain here:

https://brainly.com/question/2264373

#SPJ11

Answer:

To use the FOIL method to simplify the expression (2x - 1/2)^2, follow these steps:

F: Multiply the first terms in each set of parentheses:

(2x) * (2x) = 4x^2

O: Multiply the outer terms in each set of parentheses:

(2x) * (-1/2) = -x

I: Multiply the inner terms in each set of parentheses:

(-1/2) * (2x) = -x

L: Multiply the last terms in each set of parentheses:

(-1/2) * (-1/2) = 1/4

Now, combine the like terms:

4x^2 - x - x + 1/4

Simplify by combining like terms:

4x^2 - 2x + 1/4

Therefore, (2x - 1/2)^2 = 4x^2 - 2x + 1/4.

The total cost of bedsheets will be 200x and the total cost of pillowcases will be 50y. According to the problem, she needs to make at least ₱6000, so we have the equation 200x + 50y ≥ 6000.

To help Beth determine the number of bedsheets and pillowcases she needs to sell to make at least ₱6000, we can set up an equation based on the cost of each item. Let's assume she sells x bedsheets and y pillowcases.

To find the number of bedsheets and pillowcases, we can explore different combinations that satisfy the equation. For example, if we assume she sells 20 bedsheets, the cost would be 200 * 20 = ₱4000. To reach a total of ₱6000, she would need to sell additional pillowcases. By trying different combinations, we can find a solution that satisfies the equation.

For the advertisement, we can create a printed ad that highlights the quality and affordability of the products. We can include attractive visuals of the bedsheets and pillowcases, along with the prices and any special offers. The ad should emphasize the benefits of purchasing from Beth, such as the reasonable prices and the opportunity to support a local business. Additionally, providing contact information and a clear call-to-action can help potential customers easily reach out and make a purchase.

Learn more about bedsheets here:

brainly.com/question/30958604

#SPJ11

Any function whose graph is NOT a line is said to be nonlinear. It has the equation f(x) = ax + b. With the exception of the form f(x) = ax + b, its equation can take any form. Any two points on the curve have the same slope.

To ascertain whether a table of values is a linear function, follow these steps:

Learn more about graph Visit: brainly.com/question/19040584

#SPJ4

Answer:

7 x - 8 y = 5

x - 8 y = -13

6 x = 18      subtract equations

x = 3

7 (3)  - 8 y = 5

8 y = 16     solve for y

y = 2

Solution :   (3, 2)

Check:

3 - 8 * 2 = -13     agrees with second equation

Answer:

x=11

Step-by-step explanation:

These add up to 180 since a straight line = 180 degrees

Your equation is: 4x+15+11x=180

15x+15=180

15x=165

x=11

Answer:

X=11

HOPE THIS HELPS

- Todo ❤️

Step-by-step explanation:

4x+15+11x=180

15x+15=180

180-15=165

165/15=11

X=11

Answer:

The answer is

C. The mapping represents y as a function of x, because each x-value corresponds to exactly one y-value.

Step-by-step explanation:

In mathematics, mapping is used synonymously to a function, and a function is basically a relation between two values or expressions say y and x

like the difference equation relating y and x.

In a function, for every value of x plugged into the function there is always a corresponding value of y.

Example.

Given the function

y=2x+5.

find the value of y when x=0

we are going to substitute x=0 and solve

y=2(0)+5

y=5

so for x=0 y=5

Answer:

B. Two

I did this on Edge

The distribution of X follows the characteristics of a normal distribution with a mean of 106 and a standard deviation of 18, reflecting the IQ distribution of the ruling species on the faraway planet. This can be denoted as X ~ N(106, 18), where "N" represents the normal distribution.

The distribution of X, representing the IQ of an individual from the ruling species on the faraway planet, is a normal distribution with a mean (μ) of 106 and a standard deviation (σ) of 18. This can be denoted as X ~ N(106, 18), where "N" represents the normal distribution.

In this distribution, the majority of IQ values will cluster around the mean of 106. The standard deviation of 18 indicates the average amount of variation or dispersion from the mean. The normal distribution is symmetric, which means that the probabilities of IQ values being above or below the mean are equal.

The shape of the normal distribution is bell-shaped, with the highest point being at the mean. As we move away from the mean, the probability of observing extreme values decreases. The spread of the distribution is determined by the standard deviation, where a larger standard deviation indicates a wider spread of IQ values.

the distribution of X follows the characteristics of a normal distribution with a mean of 106 and a standard deviation of 18, reflecting the IQ distribution of the ruling species on the faraway planet.

Learn more about standard deviation here:

https://brainly.com/question/13498201

#SPJ11

On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 106 and a standard deviation of 18. Suppose one individual is randomly chosen. Let X = IQ of an individual.  What is the distribution of X? X ~ N( 106 , 18 )