Suppose that you buy an exercise ball with diameter of 85 cm and your brother buys an exercise ball with diameter of 65 cm. What is the difference between the volume and surface area of both balls? Justify your answer and round to the nearest hundredth

Answer:

\(b = \sqrt{ \frac{ {c}^{2} }{2 {\pi}^{2} } - {a}^{2} } \)

Work Shown:

(5-8i)-(-6-11i)

5-8i+6+11i ....... distribute

(5+6) + (-8i+11i) .... group like terms

11 + 3i ..... combine like terms

Answer:

amount = £1415.57  

Step-by-step explanation:

given data

computer buy = £1600

depreciates rate = 4% per year

time = 3 year

solution  

we get here amount that is express here as

amount = P × \((1-r)^{t}\)    ...................................1                                    

here r is rate and t is time put here value

amount will  be              

amount = 1600 × \((1-0.04)^{3}\)  

solve it we get

amount = £1415.57  

Answer:

Step-by-step explanation:

(7/12) of 840 attended the concert:

(7/12)*(840) = 490 students attended the Spring Concert.

(840 - 490) = 350 did not attend

(350/840) is the fraction of students who did not attend.  This can be reduced to (35/84)

(350/840) = 0.4167 or 41.67% did not attend.  

Answer:

y=19.25x

Step-by-step explanation:

The function that represents the given equation is:

f(x) = 3x + 8

The equation is -12x + 4y = 32. To solve for y as a function of x, we need to isolate y on one side of the equation.

Adding 12x to both sides, we get 4y = 12x + 32.

To solve for y, we divide both sides of the equation by 4. This gives us y = 3x + 8.

Hence, the function that expresses y as a function of x is:

f(x) = 3x + 8.

Using this function, we can determine the value of y corresponding to any given x value. For example, if we substitute x = 5 into the function, we have f(5) = 3(5) + 8 = 15 + 8 = 23. Therefore, when x is 5, y is 23 according to the function f(x) = 3x + 8.

In summary, the function f(x) = 3x + 8 represents the relationship between x and y in the given equation, allowing us to calculate the corresponding y value for any given x value.

Therefore, the function that represents the given equation is:

f(x) = 3x + 8

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Answer:

d = 100t

Step-by-step explanation:

d = 100 * t

0 = 100 * 0

100 = 100 * 1

200 = 100 * 2

300 = 100 * 3

By elimination, the solution of the system of equations, x - y + z = -1, x + y + 3z = -3 and 2x - y + 2z = 0, is  (4 , 2 , -3).

Given:

x - y + z = -1     (equation 1)

x + y + 3z = -3     (equation 2)

2x - y + 2z = 0     (equation 3)

Using the elimination method, given the equations in x, y, and z, a variable should be eliminated by adding/subtracting the equations.

Subtracting equations 1 and 3 will eliminate the variable y.

2x - y + 2z = 0     (equation 3)

 x - y + z = -1   (equation 1)

x        + z = 1     (equation 4)

Adding equations 2 and 3 will eliminate the variable y.

x + y + 3z = -3     (equation 2)

2x - y + 2z = 0     (equation 3)

3x      + 5z = -3     (equation 5)

Multiply equation 4 by -5 and add with equation 5.

x + z = 1     (equation 4)

⇒ -5x - 5z = -5

+    3x + 5z = -3     (equation 5)

-2x             = -8

x = 4

Substitute the value of x to either equation 4 or 5 and solve for z.

x + z = 1     (equation 4)

4 + z = 1

z = 1 - 4

z = -3

Finally, substitute the value of x and z to any of the first three equations, and solve for y.

x - y + z = -1     (equation 1)

4 - y + (-3) = -1

-y = -1 - 4 + 3

-y = -2

y = 2

Checking if the values x = 4, y = 2, and z = -3 satisfies all the three equation.

x - y + z = -1     (equation 1)

4 - 2 + (-3) = -1

-1 = -1

x + y + 3z = -3     (equation 2)

4 + 2 + 3(-3) = -3

-3 = -3

2x - y + 2z = 0     (equation 3)

2(4) - 2 + 2(-3) = 0

0 = 0

Hence, the solution of the system of equations is (4 , 2 , -3).

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The image below shows a representation of a vertical number line.

The bigger number is below the smaller number.

Hence, by observation, the answer is option C

This is because 3.25 is smaller than 3.75, thus it will be above

Final answer: option C

The domain of the function is defined as 0 ≤  x ≤ 4.

option A is the correct answer.

A domain of a function refers to "all the values" that can go into a function without resulting in undefined values.

So the domain of a function is the set of x values, while the range of a function is the set of y values.

From the given statement, the range of the function is defined as;

y = vt

where;

y = 60 mph x 4 hr

y = 240 miles

From the given statement, the domain of the function is defined as;

0 ≤  x ≤ 4

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The area of the irregular figure will be equal to the sum of area of triangle and the area of the rectangle.

The required area can be determined as,

Thus, the required area of the irregular figure is 426 square feet.

Convert it to a decimal and multiply is the best way to describe rate in simple interest formula.

The real yearly cost of funds over the course of a loan is the annual rate that is charged for borrowing (or made by investing), expressed as a single percentage number. An interest rate indicates how expensive borrowing is or how lucrative saving is. Therefore, if you are a borrower, the interest rate is the sum you pay for borrowing money and is expressed as a percentage of the overall loan amount.

Given

The r in the simple interest formula stands for rate.

Convert it to a decimal and multiply is the best way to describe rate in formula.

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Answer:

I45

Step-by-step explanation:

Answer:

\(y = \frac{1}{2}x - 8\)

Step-by-step explanation:

1. Approach,

For this problem, the format of a line that will be used is, slope-intercept form;

\(y = mx + b\)

Where (\(m\)) is the slope of the line, also known as the change in the line and \((b)\) is the y-intercept, or where the graph of the line intersects the y-axis. Since, in this problem, the slope of the line is given, all one has to do is substitute in a point on the given line and solve.

2. Finding the equation,

In this problem, the slope of the line is given. Therefore, to solve this problem, all one has to do is substitute in a point on the given line and solve.

\(y = mx + b\)

Substitute in the slope,

\(y = \frac{1}{2}x + b\)

Substitute in the point,

\(-4 = \frac{1}{2}(8) + b\)

Simplify,

\(-4 = 4 + b\)

Inverse operations,

\(-4 = 4 + b\\-4\\\\-8 = b\)

3. Putting it all together,

Now, that one has y-intercept, (\(-8\)); use the given slope and the formula \(y = mx + b\),  substitute in all the information.

\(y = \frac{1}{2}x - 8\)

Subtract:

To perform this subtraction, since 4 is less than 6, borrow 1 from the top number on the left next to 4, we have:

DDR4 has several advantages over DDR3. Two of the key advantages are as follows:

Higher Data Transfer Rates: DDR4 offers higher data transfer rates compared to DDR3. It provides faster data transfer and improved overall system performance. DDR4 modules typically have higher clock speeds, allowing for faster data access and throughput.

Increased Memory Capacity: DDR4 supports higher memory capacities compared to DDR3. DDR4 modules can offer larger memory capacities, allowing for more memory to be installed in a system. This is beneficial for applications that require a large amount of memory, such as high-end gaming, video editing, and server applications.

Other advantages of DDR4 over DDR3 include improved power efficiency, lower operating voltage, and improved reliability. These factors contribute to better system performance, lower power consumption, and enhanced stability.

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Answer:

Step-by-step explanation:

Oh It is hard for me I do no know Whate is the answer is? Sorry about that

The mass dissolving power and volumetric dissolving power of HCl 15%, 28%, and formic acid are 50.4 g CaC\(O_3\) / g HCl and 11.2 L C\(O_2\) / g HCl, 44.3 g CaC\(O_3\) / g HCl and 10.6 L C\(O_2\) / g HCl and 82.2 g CaC\(O_3\) / g HCOOH and 22.4 L C\(O_2\) / g HCOOH, respectively.

Mass dissolving power (B) is defined as the mass of CaC\(O_3\)  that can be dissolved by 1 mole of HCl.

Volumetric dissolving power (X) is defined as the volume of C\(O_2\) that can be produced by 1 mole of HCl.

The mass dissolving power of HCl 15% is calculated as follows:

B = (1 mole CaC\(O_3\) ) / (2 moles HCl) * (100.1 g CaC\(O_3\) ) / (1.07 g HCl) = 50.4 g CaC\(O_3\)  / g HCl

The volumetric dissolving power of HCl 15% is calculated as follows:

X = (1 mole C\(O_2\)) / (2 moles HCl) * (22.4 L C\(O_2\)) / (1 mol C\(O_2\)) = 11.2 L C\(O_2\) / g HCl

The mass dissolving power of HCl 28% is calculated as follows:

B = (1 mole CaC\(O_3\) ) / (2 moles HCl) * (100.1 g CaC\(O_3\) ) / (1.14 g HCl) = 44.3 g CaC\(O_3\)  / g HCl

The volumetric dissolving power of HCl 28% is calculated as follows:

X = (1 mole C\(O_2\)) / (2 moles HCl) * (22.4 L C\(O_2\)) / (1 mol C\(O_2\)) = 10.6 L C\(O_2\) / g HCl

The mass dissolving power of formic acid is calculated as follows:

B = (1 mole CaC\(O_3\) ) / (1 mole HCOOH) * (100.1 g CaC\(O_3\) ) / (1.22 g HCOOH) = 82.2 g CaC\(O_3\)  / g HCOOH

The volumetric dissolving power of formic acid is calculated as follows:

X = (1 mole C\(O_2\) ) / (1 mole HCOOH) * (22.4 L C\(O_2\) ) / (1 mol C\(O_2\) ) = 22.4 L C\(O_2\) / g HCOOH

Therefore, the mass dissolving power and volumetric dissolving power of HCl 15%, 28%, and formic acid are as follows:

Acid Mass dissolving power (B) Volumetric dissolving power (X)

HCl 15% 50.4 g CaC\(O_3\)  / g HCl 11.2 L C\(O_2\) / g HCl

HCl 28% 44.3 g CaC\(O_3\)  / g HCl 10.6 L C\(O_2\) / g HCl

Formic acid 82.2 g CaC\(O_3\)  / g HCOOH 22.4 L C\(O_2\) / g HCOOH

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Prove of the given theorem is shown below by using definition of LU decomposition.

Now, For the given theorem, we need to show that the cost of computing the LU-decomposition of A is p³/3 - p/3 multiplications/divisions, and p/3 - p²/2 + p/6 additions/subtractions.

Since, in the LU-decomposition, we express A as the product of a permutation matrix P, a lower-triangular matrix L, and an upper-triangular matrix U.

That is, A = PLU.

The cost of computing the LU-decomposition involves the cost of computing P, L, and U, which we will consider separately.

Computing P:

Since P is a permutation matrix, computing P involves at most p(p-1)/2 row interchanges (swapping two rows of A).

Each row interchange requires p multiplications/divisions and p-1 additions/subtractions.

Therefore, the total cost of computing P is at most p(p-1)/2 × (p multiplications/divisions + (p-1) additions/subtractions).

Computing L:

Computing L involves computing p(p-1)/2 entries, which involve p-1 multiplications/divisions and p-1 additions/subtractions each.

This gives a total cost of p(p-1)/2 × (p-1 multiplications/divisions + (p-1) additions/subtractions).

Computing U:

Computing U involves computing p² entries, which involve p-1 multiplications/divisions and p-1 additions/subtractions each. This gives a total cost of p² × (p-1 multiplications/divisions + (p-1) additions/subtractions).

Adding up the costs of computing P, L, and U, we get:

p(p-1)/2 (p multiplications/divisions + (p-1) additions/subtractions) + p(p-1)/2 (p-1 multiplications/divisions + (p-1) additions/subtractions) + p²(p-1 multiplications/divisions + (p-1) additions/subtractions)

Simplifying this expression, we get:

p³/3 - p/3 multiplications/divisions + p/3 - p²/2 + p/6 additions/subtractions

which is the desired result.

To obtain the expressions 1 + 2 + ... + n = n(n+1)/2 and

1² + 2²+ ... + n² = n(n+1)(2n+1)/6, w

e can use the formulas for the sum of an arithmetic series and the sum of a series of squares, respectively.

These formulas are well-known and can be proved by induction or other methods.

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Answer:

1) 15x+10=130 (corresponding angles)

15x=120

x=120/15

x=8

2) 60+128+x=180 (angle to straight line)

188+x=180

x=180-188

x=-8

3) 12x+8=13x+2

12x-13x=2-8

-x=-6

x=6

4) 115+16x+1=180 (co interior angles)

116+16x=180

16x=180-116

16x=64

x=64/16

x=4

Answer:

90°

Step-by-step explanation:

as a straight line is 180°

and the angle 4 is 90 degrees it must mean that the other side is 90 degrees too

The probability that four or less adults exercise regularly out of 11 randomly selected adults is approximately 0.9824.

This problem can be solved using the binomial distribution, since we are interested in the probability of a certain number of successes (adults who exercise regularly) in a fixed number of trials (selecting 11 adults randomly).

Let X be the number of adults who exercise regularly out of 11. Then X has a binomial distribution with parameters n = 11 and p = 0.25, since the probability of success (an adult who exercises regularly) is 0.25.

We want to find the probability that four or less adults exercise regularly, which is equivalent to finding the probability of X ≤ 4. We can use the binomial cumulative distribution function to calculate this probability:

P(X ≤ 4) = Σ P(X = k), for k = 0, 1, 2, 3, 4

Using a calculator, spreadsheet software, or a binomial probability table, we can find the probabilities for each value of k, and then add them up to get the cumulative probability:

P(X = 0) = (11 choose 0) * (0.25)^0 * (0.75)^11 = 0.0563

P(X = 1) = (11 choose 1) * (0.25)^1 * (0.75)^10 = 0.2015

P(X = 2) = (11 choose 2) * (0.25)^2 * (0.75)^9 = 0.3159

P(X = 3) = (11 choose 3) * (0.25)^3 * (0.75)^8 = 0.2747

P(X = 4) = (11 choose 4) * (0.25)^4 * (0.75)^7 = 0.1340

P(X ≤ 4) = 0.0563 + 0.2015 + 0.3159 + 0.2747 + 0.1340 = 0.9824

Therefore, the probability that four or less adults exercise regularly out of 11 randomly selected adults is approximately 0.9824.

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Answer:

39.4 or 40 % depending on which place you round it to

Step-by-step explanation:

18 * 1.10= 19.8      

(19.8  - 12) / 19.8 = 0.39393939...

so 39.4 or 40 % depending on which place you round it to

Step-by-step explanation:

6x - 8 = 4x

6x- 4x = 8

2x = 8

x = 8/2

x = 4

\(...\)

Answer:    x=4

Step-by-step explanation:

6x-8=4x   subtract 4x from both sides

-4x   -4x

2x-8=0     isolate x by adding 8 on both sides

+8    +8

2x=8     divide by 2 on both sides

/2    /2

x=4

The Solution.

The correct answer is 2 right angles.

Answer:

20

Step-by-step explanation:

C(6,3) = 6!/[3!(6-3)!]

= 20

Answer:

Direction: Opens Up

Vertex:(3,−14)

Focus:(3

Step-by-step explanation:

hope this help if not let me know have a blessed day