A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window. Find the dimensions of a Norman window of maximum area when the total perimeter is 20 feet.

The volume of the container is 100 cubic inches.

The volume of a rectangular container is calculated by multiplying its base area by its height. Since the base of the container is square with an area of 25 square inches, the length of each side of the square base is the square root of 25, which is 5 inches.

Therefore, the volume of the container can be calculated as follows:

Volume = Base Area × Height

Volume = 25 square inches × 4 inches

Volume = 100 cubic inches

So, the volume of the container is 100 cubic inches.

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Answer:

a)3.68kg

b)900g

Step-by-step explanation:

a) First off we know that he weighs 4kg now and he weighed 8% less the next week. 8% of 4kg=0.32kg. We then have to subtract 0.32 kilograms from the original weight. 4-0.32=3.68

Your answer for A is 3.68 kg

b) If the baby gains 200g every two weeks, assuming it's a constant rate, he should gain 100g every week. 100*9weeks=900g.

The area and the perimeter of the given parallelogram are 36.792 mm² and 24.28 mm respectively.

In Euclidean geometry, a parallelogram is a simple quadrilateral having two sets of parallel sides.

The confronting or opposed sides and the opposing angles of a parallelogram are of equal length.

There are four distinct types of parallelograms, including three distinct types.

Rhombuses, parallelograms, squares, and rectangles are the four types.

So, the given image itself tells that the given figure is a parallelogram.

The area of the given parallelogram is:
A = b*h

A = 6.3*5.84

A = 36.792 mm²

The perimeter of the given parallelogram:

P = 2(a+b)

P = 2(6.3+5.84)

P = 24.28 mm

Therefore, the area and the perimeter of the given parallelogram are 36.792 mm² and 24.28 mm respectively.

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By using the partial sum of series is

[tex]a_{n} = 5^{(-n-1) } - (n+1)5^{(-(n+1))}[/tex]

and summation n=1 to infinity of [tex]a_{n}[/tex] is =6 .

To obtain the formula for the nth term of the series and its total, we must first discover the formula for the series' general term.

The formula for the series' nth partial sum is as follows:

[tex]sn = 6 - n*5^{-n}[/tex]

The nth term of the series can be obtained by subtracting the (n+1)th and nth partial sums, i.e.,

a = sn+1 - sn

When we substitute the formula for sn, we get:

[tex]a_{n} = [6 - (n+1)5^{(-(n+1))} ] - [6 - n5^{(-n)} ]\\a_{n} = 5^{(-n-1) } - (n+1)5^{(-(n+1))}[/tex]

As a result, the formula for the series' nth term is:

[tex]a_{n} = 5^{(-n-1) } - (n+1)5^{(-(n+1))}[/tex]

To calculate the series total, take the limit of the nth partial sum as n approaches infinity:

lim(n->inf) lim(n->inf) sn [6 - n*5^(-n)]

lim(n->inf) [n*5(-n)] = 6

= 6 - 0

= 6

As a result, the series' sum is 6.

As a result, the formula for the nth term in the series is:

[tex]a_{n} = 5^{(-n-1) } - (n+1)5^{(-(n+1))}[/tex]

And the series' total is:

a = sum(n=1 to inf) = 6

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Using a right-hand sum with three intervals, the approximate area under the curve of the function f(x) = x³ between the limits of integration a=0 and b=3 is 36 square units.

Numbers and their variants, equations and related structures, forms and their arrangements, and the places where they might be found are all topics covered in mathematics. The term "function" describes the relationship between a collection of inputs, each of which has a corresponding output.

To estimate the area under the curve of the function f(x) = x3 between the limits of integration a=0 and b=3, we must divide the interval [0, 3] into three subintervals of equal width.

Each subinterval's width, x, may be calculated as follows:

Δx = (b - a) / n = (3 - 0) / 3 = 1

So, the three subintervals are:

[0, 1], [1, 2], [2, 3]

To compute the right-hand total, we evaluate the function at each subinterval's right endpoint and multiply it by the breadth of the subinterval. Then we add these products together to calculate the area under the curve. The right-hand sum may be stated mathematically as follows:

RH = Δx * [f(1) + f(2) + f(3)]

where x represents the width of each subinterval, f(x) = x3 represents the function we are integrating, and f(i) represents the function's value at the right endpoint of the i-th subinterval.

RH = 1 * [f(1) + f(2) + f(3)]

= 1 * [(1³) + (2³) + (3³)]

= 1 * [1 + 8 + 27]

= 36

Using a right-hand sum with three intervals, the approximate area under the curve of the function f(x) = x³ between the limits of integration a=0 and b=3 is 36 square units.

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Answer:

-9.5.

Step-by-step explanation

To find a reasonable value for n, we need to use the given data points and the equation of the line. We can plug in any pair of x and y values into the equation and solve for m or b. For example, using (4, 2), we get:

2 = m(4) + b

Solving for b, we get:

b = 2 - 4m

Now we can plug in another pair of x and y values, such as (7, 4.5), and use the value of b we just found:

4.5 = m(7) + 2 - 4m

Solving for m, we get:

m = 0.5

Now we have the slope and the y-intercept of the line. The equation is:

y = 0.5x + 2 - 4(0.5)

Simplifying, we get:

y = -1.5x + 4

To find n, we need to plug in x = 9 and solve for y:

y = -1.5(9) + 4

y = -9.5

The cash payback period for the project is 4.7 years.

The cash payback period is a financial metric that calculates the amount of time it takes for a project to generate enough cash flows to recover the initial investment (cost). It is calculated by dividing the initial investment by the estimated annual net cash flows.

Decimal refers to a system of numbers based on the number 10, where each digit represents a different power of 10. It is a way of expressing numbers using a decimal point to separate the whole number from the fractional part.

Given:

Estimated annual net cash flows = $55,800

Initial investment (cost) = $262,260

Cash Payback Period = Initial Investment / Estimated Annual Net Cash Flows

Putting the values:

Cash Payback Period = $262,260 / $55,800

Calculating the cash payback period:

Cash Payback Period = 4.7 years (rounded to one decimal place)

Therefore, the cash payback period for the project is 4.7 years.

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The correct answer is a. True, b. False, c. True, d. True

The mean of Region 2 is 36+ 37+ 2x38+ (39+41)x3 +40x4+42/15 = 39.4°C

(The mean = all temperature of region divided by the number of states )

So,  39.4- 33.6 = 5.8 True

So False (variability is comparing the density)

The difference is 39.4 - 33.8= 5.6

The MAD of Region 3 is (32 - 33.8) +2 x (34 -33.8) + 2x (35 - 33.8) + 4x (36-33.8) + 2x (37-33.8) + 2x (38-33.8) + (39-33.8) + (40-33.8) ÷ 15 = 2.64

2-64 × 2 = 5.28, so true

33.8 is closest to 35.6, so true.

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The value of x is given as follows:

x = 21 cm.

The value of x is obtained applying the proportions in the context of the problem.

The ratio between the volumes is given as follows:

2430/90 = 27.

The side lengths are measured in units, while the volume is measured in cubic units, hence the proportion to obtain the value of x is given as follows:

x/7 = cubic root of 27

x/7 = 3

x = 21.

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Answer:

100 Minutes

Step-by-step explanation:

Step 1: Break it down-

3¢ can be expressed as 0.3

Step 2: Add monthly charge-

Since there is a 10$ monthly charge: 40-10=30

Step 3: Subtract-

Now divide: 30 ÷ 0.3

Step 4: Final Answer-

Hence the amount of minutes per month= 100