What is the height, in meters, of a cylinder with surface area 104π m2 and radius 4 m?

The total cost of materials needed to build the house is $4374.75.

Calculate the area of the front and back of the house.

Area = Length x Width

Area = 3.5 m x 2.5 m = 8.75 m²

Calculate the area of the sides of the house.

Area = 2 x Length x Height

Area = 2 x 3.5 m x 5 m = 35 m²

Calculate the total cost of glass.

Cost of glass = Area x Cost per square meter

Cost of glass = 8.75 m² x $37 / m² = $323.75

Calculate the total cost of roof tiles.

Cost of roof tiles = Area x Cost per square meter

Cost of roof tiles = 35 m² x $95 / m² = $3325

Calculate the total cost of reinforcement metal.

Cost of reinforcement metal = Perimeter x Cost per meter

Cost of reinforcement metal = 2 x (Length + Width) x $54 / m = $726

Add the costs of glass, roof tiles, and reinforcement metal to get the total cost of materials.

Total cost = $323.75 + $3325 + $726 = $4374.75

Therefore, the total cost of materials needed to build the house is $4374.75.

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ANSWER: 100% of 2000000000 is 2000000000

What is 100 Percent of 2000000000?

100 percent *2000000000

= (100/100)*2000000000

= (100*2000000000)/100

= 200000000000/100 = 2000000000

Now we have: 100 percent of 2000000000 = 2000000000

Question: What is 100 percent of 2000000000?

We need to determine 100% of 2000000000 now and the procedure explaining it as such

Step 1: In the given case Output Value is 2000000000.

Step 2: Let us consider the unknown value as x.

Step 3: Consider the output value of 2000000000 = 100%.

Step 4: In the Same way, x = 100%.

Step 5: On dividing the pair of simple equations we got the equation as under

2000000000 = 100% (1).

x = 100% (2).

(2000000000%)/(x%) = 100/100

Step 6: Reciprocal of both the sides results in the following equation

x%/2000000000% = 100/100

Step 7: Simplifying the above obtained equation further will tell what is 100% of 2000000000

x = 2000000000%

Therefore, 100% of 2000000000 is 2000000000

The values of the angles a, b and c are 60°, 110° and 80° respectively.

Given is a figure we need to find the measure of the angles given,

a, b, c.

So,

70° + 50° + a = 180° [making linear pair angles]

120° + a = 180°

a = 60°

50° + a = b [corresponding angles between parallel lines]

b = 50° + 60°

b = 110°

a + 40° + ∠HFE = 180° [angle sum property of a triangle]

60° + 40° + ∠HFE = 180°

∠HFE = 80°

∠HFE = c [alternate angles between parallel lines]

c = 80°

Hence the values of the angles a, b and c are 60°, 110° and 80° respectively.

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Answer:

To determine the number of cards necessary to build a tower with 100 stories, let's analyze the pattern observed in the given information.

From the information provided, we know that building 5 stories of cards required 40 cards. Now, let's examine the relationship between the number of stories and the number of cards used:

Number of stories: 5

Number of cards used: 40

To find the number of cards needed for 100 stories, we can calculate the ratio of the number of stories to the number of cards used for the 5-story tower and then apply that ratio to the target number of stories (100).

Ratio = Number of stories / Number of cards used

Ratio = 5 / 40

Now, we can use this ratio to calculate the number of cards needed for 100 stories:

Number of cards for 100 stories = Ratio * Number of stories

Number of cards for 100 stories = (5 / 40) * 100

Calculating the result:

Number of cards for 100 stories = (0.125) * 100

Number of cards for 100 stories = 12.5

Since it is not possible to use a fraction of a card, we need to round up to the nearest whole number. Therefore, we would need a minimum of 13 cards to build a tower with 100 stories using a similar pattern.

Please note that the actual number of cards required may vary depending on the specific construction technique and stability of the tower.

Answer:

To calculate the future value (FV) of an investment with a given return on balance, monthly rate of return, monthly payment, and number of payments, you can use the future value of an ordinary annuity formula:

FV = P * ((1 + r)^n - 1) / r

Where:

FV = Future value

P = Monthly payment

r = Monthly rate of return (expressed as a decimal)

n = Number of payments

In this case, the return on balance and the monthly rate of return are provided separately. To incorporate the return on balance into the monthly rate of return, you can use the following formula:

Effective Monthly Rate of Return = (1 + Monthly Rate of Return) * (1 + Return on Balance) - 1

Let's calculate the effective monthly rate of return using the given values:

Return on Balance = 7.00% (expressed as a decimal) = 0.07

Monthly Rate of Return = 0.583% (expressed as a decimal) = 0.00583

Effective Monthly Rate of Return = (1 + 0.00583) * (1 + 0.07) - 1

= 1.00583 * 1.07 - 1

= 1.0761281 - 1

= 0.0761281

Now that we have the effective monthly rate of return, we can use the future value formula to calculate the future value:

FV = -$200 * ((1 + 0.0761281)^120 - 1) / 0.0761281

Please note that since the monthly payment is negative (-$200), it indicates that it is an outgoing payment or an investment with regular withdrawals.

Calculating the above formula will give you the future value of the investment.

I hope I was helpful

The ratio of technicians to all the helpers at the Harper Middle School fall play is 9 : 24.

The ratio of technicians to all helpers can be calculated by dividing the number of technicians by the total number of helpers.

Number of technicians = 9

Total number of helpers = 15 ushers + 9 technicians = 24

The ratio of technicians to all helpers = 9 / 24

The ratio will then be:

The ratio of technicians to all helpers =  9 : 24

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Complete question:

There are 15 ushers and 9 technicians helping at the Harper Middle School fall play. What is the ratio of technicians to all helpers?

The value of inequality :  x≤-9

Given,

Inequality 4(x-3) + 4 ≤ 10+ 6x

Firstly,

The distributive property: 4x-12 + 4 ≤ 10+ 6x

Then,

Combine like terms: 4x -8 ≤ 10+ 6x

Then,

The addition property of inequality: 4x ≤ 18 + 6x

Then,

The subtraction property of inequality: -2x ≤ 18

Then,

The division property of inequality:

Divide both sides of inequality by 2,

So,

x≤-9

Hence after last step the value of x is less than or equal to -9 .

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The best estimate of the number of centimeters (cm) in 1 yard is; Yard ⇒ feet ⇒ inches ⇒ centimeters

If we have to determine the number of centimeters in 1 yard, the best way is;

Here we convert  yard to feet = 1 yard = 3 ft

Then, we convert ft to inches = 1 ft = 12 inches

                                                  3 ft = 3 × 12 = 36 inches

Now, we convert inches to centimeters = 1 inch = 2.54 cm

                                            36 inches = 36 × 2.54 = 91.44 cm

Therefore, the best path is Yard to feet to inches to centimeters

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1260° is the sum of all interior angles of the given polygon.

Generally speaking, the measure of the angle at the center of a regular polygon is equal to 360 degrees.

The sum of the interior angles in a polygon can be calculated using the formula:

Sum of interior angles = (n - 2) * 180 degrees

In this formula, "n" represents the number of sides or vertices of the polygon.

In the given problem the number of sides is 9.

Thus,

Sum of all interior angle = (9-2)*180

The sum of all interior angles = 1260°

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The function y=x+3 has the greatest y intercept.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The given function is y=x, it has y intercept which is zero

The given function is y=-x, it has y intercept which is zero

Function is y=x+3, it has y intercept which is three

Function is y=2x, it has y intercept which is zero

Hence, the function y=x+3 has the greatest y intercept.

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Answer:

I estimate it is around 340 because 34 times 10 is 340 the product of 34 times 12 is 408

Step-by-step explanation:

Answer: 127

Step-by-step explanation:

360 - 70 - 36 = 254

254/2 = 127

D = 127

The variable that is contained in the given expression is y. Therefore, option C is the correct answer.

The given expression is 7y+2y² +3.

In the given expression there are 3 terms, so it is called trinomial.

In the term 7y, y is the coefficient of 7.

In the term 2y², y² is the coefficient of 2.

3 is the constant term.

Therefore, option C is the correct answer.

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Answer:

20 square feet

Step-by-step explanation:

area of a triangle = (1/2) base x height

The "base" for this one gigantic triangle is the 'top' of the diagram - - - - it's the entire 3+7 = 10 side. (We can calculate the area of the whole thing at once. We don't have to do the left and the right halves separately!!!)

The height is 4.

So area = (1/2) base x height

= (1/2) * 10 * 4

= 20 square feet

Answer:

3/8 = (3 + AD)/20

8(3 + AD) = 60

24 + 8AD = 60

8AD = 36

A = 4 1/2

B is the correct answer.

Given statement solution :- The correct proportion to make the best estimate for the number of beats in 60 seconds is:

A. 48/40 = 60/x

To make the best estimate for the number of beats in 60 seconds, we need to find the proportion that relates the beats per second in the given scenario to the desired duration of 60 seconds.

Let's set up the proportion using the given information:

Heart beats per second (beats/sec) = 48 beats / 40 seconds

We want to find the number of beats in 60 seconds (x beats / 60 seconds).

The correct proportion would be:

48 beats / 40 seconds = x beats / 60 seconds

Therefore, the correct proportion to make the best estimate for the number of beats in 60 seconds is:

A. 48/40 = 60/x

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1. The proportion is; x/4 = 12/18

2. The height of the mailbox is 2.7 feet

In mathematics, a proportion is an equation that states that two ratios are equal. It expresses the relationship between the quantities in terms of their relative sizes or magnitudes. Proportions are used in various areas of mathematics and real-life applications, such as ratios

We have;

Length of the mail box shadow = 4 feet

Length of the tree shadow = 18 feet

Height of the mail box = x

Height of the tree = 12 feet

Thus;

x/4 = 12/18

x = 4 * 12/18

x = 2.7 feet

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The sales tax on the computer is $69.93.

To calculate the sales tax on the computer, we need to multiply the price of the computer by the sales tax rate. Here's how you can do it:

Price of the computer: $999.00

Sales tax rate: 7% (which can be expressed as 0.07)

Sales tax = Price of the computer * Sales tax rate

Sales tax = $999.00 * 0.07

To find the sales tax in dollars and cents, we can perform the calculation:

Sales tax = $999.00 * 0.07

Sales tax = $69.93

Therefore, the sales tax on the computer is $69.93.

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The amount of money that will produce Rs. 15000 at the end of 6 month for 10years at 16% is Rs. 3750

Compound interest is the interest you earn on interest.

For example, if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. At the end of the second year, you'll have $110.25.

Compound interest is expressed as;

A = P( 1+r/n) ^{nt}

where A is the amount

n is the number of time its compounded

t is time

A = 15000

r = 16/100 = 0.16

n = 6/12 = 0.5

t = 10 years

15000 = P( 1 + 0.16/0.5) ^{ 0.5× 10}

15000 = P( 1 + 0.32)⁵

15000 = P( 1.32)⁵

15000 = 4P

P = 15000/4

P = Rs. 3750

Therefore the amount that will be deposited to give Rs. 15000 is Rs. 3750.

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The interest rate for the first period is $287.22

To obtain the first period interest, we use simple interest formula;

Simple Interest = Principal * Rate * Time

Given:

Principal = $45,687.23

Annual interest rate = 7.555%

Interest period = Monthly

Convert the annual interest rate to a monthly interest rate.

Monthly interest = Annual interest/ 12 = 7.555/12 = 0.6295%

Interest = Principal * Monthly interest rate * Time

Since it's the first period, the time is 1 month:

Interest = $45,687.23 * 0.62958333% * 1

Interest = $45,687.23 * 0.0062958333

Interest ≈ $287.22

Therefore, the first period interest is $287.22.

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Answer:

-3x + 3

Step-by-step explanation:

To find the equation of a line perpendicular to the line passing through (-2, 1) and (4, 3), we need to determine the slope of the original line first. Then, we can use the negative reciprocal of that slope to find the slope of the perpendicular line. Finally, we can use the point-slope form to write the equation of the perpendicular line.

Step 1: Find the slope of the original line.

Slope (m) = (change in y) / (change in x)

m = (3 - 1) / (4 - (-2))

m = 2 / 6

m = 1/3

Step 2: Determine the slope of the perpendicular line.

The slope of the perpendicular line is the negative reciprocal of the original line's slope.

Perpendicular slope = -1 / (1/3)

Perpendicular slope = -3

Step 3: Use the point-slope form to write the equation.

The point-slope form is given by:

y - y1 = m(x - x1)

Using the point (-2, 9) and the perpendicular slope (-3), we can write the equation as:

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

y - 9 = -3(x + 2)

y - 9 = -3x - 6

y = -3x + 3

Therefore, the equation of the line perpendicular to the line passing through (-2, 1) and (4, 3) and passing through (-2, 9) is y = -3x + 3.

We have that Linda's net and expression incorrect

With the Expression of the surface area of attic

45 (40 + 25 + 25) + 1/2 (40 x 15)

Hence, Surface area is,

X = 4050 + 600

X = 4650 feet²

Hence, The answer is No, Because Her expression for the triangles are incorrect;

1/2(40 x 15)

Instead of,

1/2 x 40 x 15

Hence, Linda's net and expression incorrect,

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Linda is adding padding to all of the surfaces inside her attic for extra warmth in the winter.

She needs to find the approximate surface area of the attic, including the walls, floor, and

ceiling. The attic is in the shape of a triangular prism. Linda draws the net and writes

the expression below to represent the surface area of the attic. Are Linda's net and

expression correct?

The surface area of the cuboid that has length = 4 yd, width = 2 yd and height = 3 yd is 44 square yards.

To find the surface area of a cuboid, we need to add up the area of all six faces. The formula for the surface area of a cuboid is:

Surface Area = 2lw + 2lh + 2wh

where l, w, and h represent the length, width, and height of the cuboid, respectively.

Substituting the given values, we get:

Surface Area = 2(4 x 2) + 2(4 x 3) + 2(2 x 3)

Surface Area = 8 + 24 + 12

Surface Area = 44

This means that there are 44 square yards of material needed to cover all six faces of the cuboid.

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m/ABC=86° (because of the cyclic quadrilaterals). Hence, Option (B) is correct.

A cyclic quadrilateral is a four-sided polygon whose vertices all lie on a common circle.

The opposite angles of a cyclic quadrilateral have a total of 180°.

m/ABC +  m/ADC  = 180°

m/ABC + 94° = 180°

m/ABC = 180° - 94°

m/ABC = 86°

Similarly, one can find m/DCB

m/DAB +  m/DCB  = 180°

99° + m/DCB = 180°

m/DCB = 180° - 99°

m/DCB = 81°

Hence, m/ABC = 86°

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The equation of the graph in the required form is y = 5|x| - 5

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

The graph (see attachment)

The graph is an absolute value graph

And it can be expressed in the form of y = a|x – h| + k

Where

Vertex = (h, k)

The vertex of the graph is (0, -5)

So, we have

y = a|x| - 5

Using the point on the graph, we have

a|1| - 5 = 0

So, we have

a = 5

This means that the equation of the graph is y = 5|x| - 5

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The property that should be used to simplify the expression 1/t⁻³ is [tex]\frac{1}{a^-m}[/tex] = [tex]a^m[/tex] (where a ≠ 0). Option A

In the given scenario or expression, this property implies that 1/t⁻³ = t³. The negative exponent in the denominator becomes a positive exponent when moved to the numerator.

Here is the step-by-step solution

1/t⁻³ = 1/(t⁻³)

1/(t⁻³) = (t⁻³)⁻¹

(t⁻³)⁻¹ = t⁽⁻³⁾ˣ⁽⁻¹⁾

t⁽⁻³⁾ˣ⁽⁻¹⁾ = t³

Therefore, the simplified expression is t³.

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The  value of function f (α + β) is determined as  (3√3  +  1)/3,  (2√2 - 3)/3.

The value of f (α + β) is calculated by applying the following formula as follows;

The given functions;

for α:  x²  +  y² = 4

y is given as -1, the value of x is calculated as;

x²  +  (-1)² = 4

x²  +  1 = 4

x² = 3

x = √3

α = (√3, - 1)

for β:  x²  +  y² = 1

x is given as ¹/₃, the value of y is calculated as;

(¹/₃)² + y² = 1

¹/₉ + y² = 1

y² = 1 - ¹/₉

y² = ⁸/₉

y = √ (8/9)

y = 2√2/3

β = (¹/₃, 2√2/3)

The  value of function f (α + β) is calculated as;

f(α + β) =  (√3, - 1) + (¹/₃, 2√2/3)

f(α + β) = (3√3  +  1)/3,  (2√2 - 3)/3

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