what is the volume of the cylinder below height 15 radius 11

Answer:

(8,5)(0,-3)

Step-by-step explanation:

-y=-x+3

y=x-3

Substitute for y:

(x-3)^2-2x=9

x^2-6x+9-2x=9

x^2-8x=0

x(x-8)=0

x=0,8

if x=0,

0-y=3

y=-3

if x=8

8-y=3

-y=-5

y=5

Answer :

x - y = 3

x = 3 + y

y^2 - 2x = 9

y^2 - 2(3+y) = 9

y^2 - 2y -6 -9 = 0

y^2 - 2y -15 = 0

Factorize

y = -3 y = 5

when y = -3

x -(-3) = 3

x = 0

when y = 5

x - 5 = 3

x = 8

Explanation:

Plug x = -2 into h(x)

h(x) = x+4

h(-2) = -2+4

h(-2) = 2

This means g[ h(-2) ] = g(2) after replacing h(-2) with 2.

g(x) = 5x

g(2) = 5*2

g(2) = 10

Therefore, g[ h(-2) ] = 10

The result of dividing (4x³ + 6x² + 20x + 9) by (2x + 1) using long polynomial division is 2x² + 2x + 9 with a remainder of 0.

To divide the polynomial (4x³ + 6x² + 20x + 9) by (2x + 1) using long polynomial division.

Arrange the terms of the dividend and the divisor in descending order of the degree of x:

      2x + 1 | 4x³ + 6x² + 20x + 9

Divide the first term of the dividend by the first term of the divisor and write the result on the top line:

             2x + 1 | 4x³ + 6x² + 20x + 9

                   | 2x²

Multiply the divisor (2x + 1) by the quotient obtained in the previous step (2x²) and write the result below the dividend:

             2x + 1 | 4x³ + 6x² + 20x + 9

           - (4x³ + 2x²)

           ---------------

                        4x² + 20x + 9

Subtract the result obtained in the previous step from the dividend and bring down the next term.

             2x + 1 | 4x³ + 6x² + 20x + 9

           - (4x³ + 2x²)

           ---------------

                        4x² + 20x + 9

                      - (4x² + 2x)

                      ---------------

                               18x + 9

Repeat the process by dividing the term brought down (18x) by the first term of the divisor (2x):

             2x + 1 | 4x³ + 6x² + 20x + 9

           - (4x³ + 2x²)

           ---------------

                        4x² + 20x + 9

                      - (4x² + 2x)

                      ---------------

                               18x + 9

                             - (18x + 9)

                             ---------------

                                         0

The division is complete when the degree of the term brought down becomes less than the degree of the divisor.

In this case, the degree of the term brought down is 0 (a constant term). Since we can no longer divide further, the remainder is 0.

Therefore, the result of the division is:

Quotient: 2x² + 2x + 9

Remainder: 0

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The calculated percentage error with the assumed answer of 10%

To find the percentage error in actual weights, we can use the formula:

Percentage Error = [(|Measured Value - Expected Value|) / Expected Value] * 100%

In this case, the expected weight is 4 ounces. Let's assume the measured value is 10% off from the expected value. So the measured value would be:

Measured Value = Expected Value + (10% of Expected Value)

              = 4 ounces + (10/100) * 4 ounces

              = 4 ounces + 0.4 ounces

              = 4.4 ounces

Now we can calculate the percentage error:

Percentage Error = [(|4.4 ounces - 4 ounces|) / 4 ounces] * 100%

               = [(0.4 ounces) / 4 ounces] * 100%

               = (0.4/4) * 100%

               = 0.1 * 100%

               = 10%

Comparing the calculated percentage error with the assumed answer of 10%, we can see that they are the same.

The percentage error represents the deviation from the expected value as a percentage of the expected value itself. In this case, it indicates that the actual weights deviate by 10% from the expected weight of 4 ounces. The calculated percentage error with the assumed answer of 10%

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Answer:

Yes

Step-by-step explanation:

Yes, it is a function. If you perform the vertical-line test, the line only touches a point once.

Answer:

Samuel = 21 orders

Nicole = 31 orders

Miguel = 63 orders

Step-by-step explanation:

Let N represent Nicole's orders, M represents Miguel's orders, and S represent Samuel's orders.

We know that the sum of their tree orders equals 115 as

N + M + S = 115

Since Miguel served 3 times as many orders as Samuel, we know that

M = 3S.

Since Nicole served 10 more orders than Samuel, we know that

N = S + 10

Samuel's Orders:

Now we can plug in 3S for M and S + 10 for N to find S, the number of Samuel's orders:

S + 10 + 3S + S = 115

5S + 10 = 115

5S = 105

S = 21

Thus, Samuel served 21 orders.

Nicole's Orders:

Now we can plug in 21 for S in N = S + 10 to determine how many orders Nicole served:

N = 21 + 10

N = 31

Thus, Nicole served 31 orders.

Miguel's Orders:

Now we plug in 19 for S in M  = 3S to determine how many orders Miguel served:

M = 3(21)

M = 63

Thus, Miguel served 63 orders.

The nth square number of the value given is the squared value of 19, which is 361

The nth square number , S is related by the formula :

Given that , n = 19

The nth square number , where n = 19 can be calculated thus:

S = -19² = 361

S = (-19) * (-19)

S = 361

Therefore, the 19th square number is 361

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Answer:

x = 10

Step-by-step explanation:

the figure inscribed in the circle is a cyclic quadrilateral , all 4 vertices lie on the circumference.

the opposite angles in a cyclic quadrilateral sum to 180° , that is

6x + 1 + 10x + 19 = 180

16x + 20 = 180 ( subtract 20 from both sides )

16x = 160 ( divide both sides by 16 )

x = 10

Answer: 21.15 ft²

Step-by-step explanation:

We can use the formula for the area of a triangle:

(b×h)/2

In this case, the base is 9 and the height is 4.7.

So, we substitute the variables with the numbers in this problem.

(9 × 4.7)/2

9 × 4.7 = 42.3

42.3/2 = 21.15

So, our final answer is 21.15 ft²

Answer:

Yes

Step-by-step explanation:

To know if a table is a function or not, we have to see if 1 input only has 1 output.

Looking at the table each input only has 1 output, so it is a function.

Answer:

a=55°

b=123°

c=55°

d=123°

Answer: 180 gallons needed

Step-by-step explanation:

Zykeith,

Assume x gallons of 50% antifreeze is needed

Final mixture is x + 60 gallons

Amount of antifreeze in mixture is 0.4*(x+60)

Amount of antifreeze added is .5x + .1*60 = .5x + 6

so .5x + 6 = .4(x + 60)

.5x -.4x = 24 -6

.1x = 18

x = 180

Let x be the number of gallons of the 50% antifreeze solution needed. We know that the resulting mixture will be 70 + x gallons. To get a 40% antifreeze mixture, we can set up the following equation:

[tex]{\implies 0.5x + 0.1(70) = 0.4(70 + x)}[/tex]

Simplifying the equation:

[tex]\qquad\implies 0.5x + 7 = 28 + 0.4x[/tex]

[tex]\qquad\quad\implies 0.1x = 21[/tex]

[tex]\qquad\qquad\implies \bold{x = 210}[/tex]

[tex]\therefore[/tex] We need 210 gallons of the 50% antifreeze solution to mix with 70 gallons of 10% antifreeze to get a mixture that is 40% antifreeze.

[tex]\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}[/tex]

a. The exact volume is V = π(9.5 ft)²(50 ft) = 225π ft³.

b. Rounding the answer to the nearest hundredth, the approximate volume of the silo is 706.50 ft³.

(a) The exact volume of the silo can be found using the formula for the volume of a cylinder, which is V = πr²h,

where r is the radius and h is the height.

Since the diameter is given, we can divide it by 2 to find the radius.

The radius of the silo is 19 ft / 2 = 9.5 ft.

The height of the silo is 50 ft.

Using these values, the exact volume of the silo is:

V = π(9.5 ft)²(50 ft) = 225π ft³.

The approximate volume can be found using the ALEKS calculator, which is not available in this text-based interface.

However, you can use the exact volume calculated above to manually approximate the volume to the nearest hundredth by evaluating the expression using the value of π as approximately 3.14 or 22/7.

(b) Approximate volume using the ALEKS calculator: [Please use an online calculator or a scientific calculator to approximate the value to the nearest hundredth].

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The combinations of assembling these rectangles for which it is possible to create a rectangle with the length of 15 and the width 11 with no gaps or overlapping are:

A rectangle is a plane figure with four straight sides and four right angles, especially one with unequal adjacent sides.

Required

Which group forms a rectangle of

[tex]\text{Length}=15[/tex]

[tex]\text{Width}=11[/tex]

First, calculate the area of the big rectangle

[tex]\text{Area}=\text{Length}\times\text{Width}[/tex]

[tex]\text{A}_{\text{Big}}=15\times11[/tex]

[tex]\text{A}_{\text{Big}}=165[/tex]

Next, calculate the area of each rectangle A to E.

[tex]\text{A}_{\text{A}}=11\times7[/tex]

[tex]\text{A}_{\text{A}}=77[/tex]

[tex]\text{A}_{\text{B}}=2\times11[/tex]

[tex]\text{A}_{\text{B}}=22[/tex]

[tex]\text{A}_{\text{C}}=6\times6[/tex]

[tex]\text{A}_{\text{C}}=36[/tex]

[tex]\text{A}_{\text{D}}=6\times5[/tex]

[tex]\text{A}_{\text{D}}=30[/tex]

[tex]\text{A}_{\text{E}}=13\times4[/tex]

[tex]\text{A}_{\text{E}}=52[/tex]

Then consider each option.

(a) 2C + 2D + 2B

[tex]2\text{C}+2\text{D}+2\text{B}=(2\times36)+(2\times30)+(2\times22)[/tex]

[tex]2\text{C}+2\text{D}+2\text{B}=72+60+44[/tex]

[tex]2\text{C}+2\text{D}+2\text{B}=176[/tex]

(b) A + B + C + D

[tex]\text{A}+\text{B}+\text{C}+\text{D}=77+22+36+30[/tex]

[tex]\text{A}+\text{B}+\text{C}+\text{D}=165[/tex]

(c) A + 4B

[tex]\text{A} + 4\text{B}=77+(4\times22)[/tex]

[tex]\text{A} + 4\text{B}=77+88[/tex]

[tex]\text{A} + 4\text{B}=165[/tex]

(d) 3E + 2B

[tex]3\text{E}+2\text{B}=(3\times52)+(2\times22)[/tex]

[tex]3\text{E}+2\text{B}=156+44[/tex]

[tex]3\text{E}+2\text{B}=200[/tex]

(e) E + C + D + 3B

[tex]\text{E} + \text{C} + \text{D} + 3\text{B}=52+36+30+(3\times22)[/tex]

[tex]\text{E} + \text{C} + \text{D} + 3\text{B}=52+36+30+66[/tex]

[tex]\text{E} + \text{C} + \text{D} + 3\text{B}=184[/tex]

Recall that:

[tex]\text{A}_{\text{Big}}=165[/tex]

Only options (b) and (c) match this value.

[tex]\text{A}+\text{B}+\text{C}+\text{D}=165[/tex]

[tex]\text{A} + 4\text{B}=165[/tex]

Hence, options (b) and (c) are correct.

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Answer:

Step-by-step explanation:

Let h(x) = y

The exponentail function is of the form :

[tex]y = ab^x[/tex]

We have :

[tex]y_{_1} = ab^{x_{_1}}\\y_{_2} = ab^{x_{_2}}\\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{ab^{x_{1}}}{ab^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{b^{x_{1}}}{b^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = b^{(x_1-x_2)}[/tex]

Given points : (4, 9) and (5, 34.2)

We have:

[tex]\frac{34.2}{9} = b^{(5-4)}\\\\\implies 3.8 = b[/tex]

Writing the equation with x, y and b:

[tex]y = ab^x\\\\\implies 9 = a(3.8^4)\\\\a = \frac{9}{3.8^4} \\\\a = 0.043[/tex]

a = 0.043

b = 3.8

When x = 6, y will be:

[tex]y = (0.043)(3.8^6)\\\\y = 128.47[/tex]

This is not the y value in the question y = 59.4

Therefore (6, 59.4) does not lie on the graph h(x)

i. The payback period for the project is 6 years.

ii. The accounting rate of return (ARR) using the average investment method is 21.18%.

iii. The net present value (NPV) of the project is -165,143.

iv. The internal rate of return (IRR) of the project is approximately 19.61%.

i. The payback period for the project:

To calculate the payback period, we need to determine how long it takes for the cumulative net cash flows to equal or exceed the initial investment of 350 million + 150 million.

Year 1: 70,000, Year 2: 70,000, Year 3: 80,000, Year 4: 100,000, Year 5: 100,000, Year 6: 120,000.

Cumulative Cash Flow:

Year 1: 70,000

Year 2: 70,000 + 70,000 = 140,000

Year 3: 140,000 + 80,000 = 220,000

Year 4: 220,000 + 100,000 = 320,000

Year 5: 320,000 + 100,000 = 420,000

Year 6: 420,000 + 120,000 = 540,000.

The cumulative cash flows exceed the initial investment of 500 million (350 million + 150 million) in Year 6.

So, the payback period for the project is 6 years.

ii. The accounting rate of return (ARR) using the average investment method:

ARR = Average Annual Profit / Average Investment

Average Annual Profit = Sum of Net Cash Flows / Number of Years

Average Annual Profit = (70,000 + 70,000 + 80,000 + 100,000 + 100,000 + 120,000) / 6

Average Annual Profit = 540,000 / 6

Average Annual Profit = 90,000

Average Investment = (Initial Investment + Residual Value) / 2

Average Investment = (500 million + 350 million) / 2

Average Investment = 425 million.

ARR = 90,000 / 425,000 = 0.2118 or 21.18%

iii. The net present value (NPV) of the project:

To calculate NPV, we discount each cash flow to its present value using the cost of capital of 12%.

NPV = (Net Cash Flow1 / [tex](1 + r)^1)[/tex]  + (Net Cash Flow2 / [tex](1 + r)^2)[/tex] + ... + (Net Cash Flow6 / (1 + r)^6) - Initial Investment.

[tex]NPV = (70,000 / (1 + 0.12)^1) + (70,000 / (1 + 0.12)^2) + (80,000 / (1 + 0.12)^3) + (100,000 / (1 + 0.12)^4) + (100,000 / (1 + 0.12)^5) + (120,000 / (1 + 0.12)^6) -[/tex] (350 million + 150 million)

Calculating each term and summing them up:

NPV = 54,017 + 48,234 + 54,497 + 62,313 + 55,631 + 60,165 - 500 million

NPV = -165,143

Therefore, the net present value (NPV) of the project is -165,143.

iv. The internal rate of return (IRR) of the project:

To calculate the IRR, we find the discount rate that makes the NPV equal to zero. Using a financial calculator or Excel, we can determine that the IRR for this project is approximately 19.61%.

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This means that she made a 20% return on the money she invested in the property. For every dollar she invested, she earned 20 cents in profit.

To calculate Jennifer Aniston's return on investment (ROI), we can use the formula:

ROI = (Net Profit / Initial Investment) * 100

First, let's calculate the net profit. The net profit is the selling price minus the initial investment:

Net Profit = Selling Price - Initial Investment

Net Profit = $2,200,000 - $2,000,000

Net Profit = $200,000

Next, we calculate the ROI:

ROI = (Net Profit / Initial Investment) * 100

ROI = ($200,000 / $1,000,000) * 100

ROI = 0.2 * 100

ROI = 20%

Jennifer Aniston's return on investment for this property is 20%.

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The value of b in the Problem given is 0.5

The given problem can be represented mathematically as below :

We can find be in the expression thus :

4 = 8b

divide both sides by 8 in other to isolate b

4/8 = 8b/8

0.5 = b

Therefore, value of b in the expression is 1/2.

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Answer: Step-by-step work:

40,328

77

3,105 (Carry the 3)

27,468

302,976

1,609,432

Add the numbers horizontally:

2,943,941

So, 40,328 * 77 = 2,943,941

The remainder when divided by 10 is:

2,943,941 % 10 = 1

Therefore, the remainder is 1.

More concisely:

40,328 * 77 = 2,943,941

2,943,941 % 10 = 1

So the remainder when 2,943,941 is divided by 10 is 1.

Hope this helps! Let me know if you have any other questions

Step-by-step explanation:

When x = 3, the expression 2x - 50 evaluates to -44.

To demonstrate an example using the expression 2(x + 5) - 5 × 12, let's simplify it step by step:

Start with the given expression.

2(x + 5) - 5 × 12

Apply the distributive property.

2x + 2(5) - 5 × 12

Simplify within parentheses and perform multiplication.

2x + 10 - 60

Combine like terms.

2x - 50

The simplified form of the expression 2(x + 5) - 5 × 12 is 2x - 50.

Let's consider an example for substituting a value for the variable x:

Suppose we want to evaluate the expression when x = 3. We substitute x = 3 into the simplified expression:

2(3) - 50

Now, perform the calculations:

6 - 50

The result is -44.

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Question

evaluate the expression 2(x+5)-5 x 12.

Type the expressions as radicals y^5/2.

[tex] \sqrt{ {y}^{5} } [/tex]

Radical:- The ( √ ) symbol that is used to denote square root or nth roots...

It can be rewritten as rational exponents ( exponents which are fractions ) using the formula:-

[tex] \sqrt[n]{x} = {x}^{ \frac{1}{n} } [/tex]

Generally, using the power rule of exponents:

[tex] \sqrt[n]{ {x}^{m} } = {( {x}^{m)} }^{ \frac{1}{n} } = {x}^{ \frac{m}{n} } [/tex]

Let's take an example to understand better:

• convertion between radicals and rational exponents:

[tex] \sqrt[7]{ {8}^{4} } = {8}^{ \frac{4}{7} } [/tex]

Since the type of radical corresponds with the denominator of a rational exponent, we know the denominator of the exponent will be 7 ..

[tex] {y}^{ \frac{5}{2} } = \sqrt{ {y}^{5} } [/tex]

As , √ denotes ½ ..

The expression "y 5/2" can be written as the fifth root of y squared: √[[tex]y^{2}[/tex]]^(1/5).

The expression "y 5/2" can be written as the fifth root of y squared: √([tex]y^{2}[/tex])^(1/5).

To explain this, let's break it down:

The numerator, [tex]y^{2}[/tex], represents y raised to the power of 2.

Taking the square root of [tex]y^{2}[/tex] simplifies it to √([tex]y^{2}[/tex]).

Finally, raising the result to the power of 1/5 gives us the fifth root of y squared: √([tex]y^{2}[/tex])^(1/5).

In other words, the expression "y 5/2" represents the operation of first squaring y, then taking the fifth root of the resulting value. This is equivalent to finding the value that, when raised to the power of 5, yields [tex]y^{2}[/tex].

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,Alice, Raul, and Maria can make 1 whole batch of a dozen cookies together using the ingredients they brought.

To determine how many whole batches of a dozen cookies they can make, we need to compare the amount of flour and butter they have with the required amounts for each batch of cookies.

Let's calculate the total amount of flour and butter each student brought:

Alice:

Flour: 2 cups

Butter: 1/4 cup

Maria:

Flour: 1 1/4 cups

Butter: 3/4 cup

Now let's compare the amounts with the required ingredients for a batch of cookies:

Required amount per batch:

Flour: 3/4 cup

Butter: 1/3 cup

First, let's see how many batches of cookies Alice can make:

Flour: Alice has 2 cups, and each batch requires 3/4 cup. So she can make 2 cups / (3/4 cup) = 8/3 = 2 and 2/3 batches of cookies.

Butter: Alice has 1/4 cup, and each batch requires 1/3 cup. Since she doesn't have enough butter for a full batch, she can't make any batches of cookies with the butter she brought.

Next, let's see how many batches of cookies Maria can make:

Flour: Maria has 1 1/4 cups, and each batch requires 3/4 cup. So she canmake (5/4 cups) / (3/4 cup) = 5/3 = 1 and 2/3 batches of cookies.

Butter: Maria has 3/4 cup, and each batch requires 1/3 cup. So she can make (3/4 cup) / (1/3 cup) = 9/4 = 2 and 1/4 batches of cookies.

Now, to find the maximum number of whole batches they can make together, we take the minimum of the number of batches each student can make:

Alice: 2 and 2/3 batches

Maria: 1 and 2/3 batches

Raul: Not mentioned, so we assume he brought the required ingredients.

The minimum value is 1 and 2/3 batches, which means they can make 1 whole batch of a dozen cookies together.

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Savings accounts and CDs are good options for people who want to save money without taking on a lot of risk.

If Anita and Miguel do not take any money from their accounts, Anita's account will grow faster than Miguel's.

This is because the interest rate for Anita's account is 6%, while Miguel's is 5%.

The interest rate is the percentage of the principal that a bank or other financial institution pays for the use of money.

It can be thought of as a fee charged for borrowing money.

The higher the interest rate, the more money a person can earn on their investment.

Anita and Miguel's accounts are probably savings accounts or CDs, which are low-risk investments that pay a fixed interest rate.

Savings accounts and CDs are good options for people who want to save money without taking on a lot of risk.

Anita and Miguel's accounts are probably savings accounts or CDs, which are low-risk investments that pay a fixed interest rate.

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The correct matches are:

-1: 0

-2: 0

X: 14/3

0: 0

6: Not used

= 2² + 2x - 5: Not used

To match the representations with their respective average rates of change, we need to calculate the average rate of change for each function over the interval (0, 3) and compare it to the given values.

Let's calculate the average rate of change for each function:

Function: 2² + 2x - 5

To find the average rate of change, we need to calculate the difference in function values divided by the difference in x-values:

Average rate of change = (f(3) - f(0)) / (3 - 0)

Average rate of change = ((2² + 2(3) - 5) - (2² + 2(0) - 5)) / 3

Average rate of change = (13 - (-1)) / 3

Average rate of change = 14 / 3

Match: X = 14/3

Function: -1

Since the function is constant, the average rate of change is 0.

Match: 0

Function: 2

Since the function is constant, the average rate of change is 0.

Match: 0

Function: 3

Since the function is constant, the average rate of change is 0.

Match: 0

Function: -2

Since the function is constant, the average rate of change is 0.

Match: 0

Function: -3

Since the function is constant, the average rate of change is 0.

Match: 0

Therefore, the correct matches are:

-1: 0

-2: 0

X: 14/3

0: 0

6: Not used

= 2² + 2x - 5: Not used

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Answer:

The total surface area is given by: base area + 4 * triangular face area

Substituting the values we calculated: 52441 + 4 * 10424.4 ≈ 91588.4 square meters.

Therefore, the surface area of the square pyramid is approximately 91588.4 square meters.

Answer:

Step-by-step explanation:

144*33/

The correct range for the piecewise graph is [-4, 2].

We need to find the minimum and maximum values of the y-coordinates.

The first segment goes from (-3, 2) to (0, 1), so the range for this segment is from 1 to 2.

The second segment goes from (0, 1) to (5, -4), so the range for this segment is from -4 to 1.

We must take into account the minimum and maximum values from each segments in order to determine the overall range. The minimum and highest values are -4 and 2, respectively.

Therefore, the correct range for the piecewise graph is [-4, 2].

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