Segment be is the altitude of parallelogram abcd. Be is approximately 14. 5 units long. What is the area of the parallelogram rounded to the nearest unit? square units.

The value of the principal investment is:

$4,942.96

To determine the value of the principal investment, we can use the given compound interest formula:

\(A = P(1 + \frac{0.07}{4})^{4t}\)

Where:

A = the final amount after 15 years

P = the principal

0.07 = the interest rate (7%)

4 = the number of times the interest is compounded per year, in this case quarterly

t = the time period in years, 15

Substituting t and A into the formula, we can find P:

\(13,997.55 = P(1 + \frac{0.07}{4})^{4*15}\)

\(13,997.55 = P(1 + 0.0175)^{60}\)

\(13,997.55 = P(1.0175)^{60}\)

\(P = \frac{13,997.55}{(1.0175)^{60}}\)

P = $4,942.96

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Answer:

the correct answer is 9²

Answer:

9

Step-by-step explanation:

It is stating that 81 is equal to x², in which the variable x stands for a number.

Note the equal sign, what you do to one side, you do to the other. Isolate the variable, x, by rooting both sides:

√x² = √81

x = √81 = √(9 * 9) = 9

9 is your missing base.

~

1. The source of documents for:

2. Predetermined overhead rate = Manufacturing overhead cost/ Direct labor cost * 100

= 550/440* 100 = 125%

Therefore, the predetermined manufacturing overhead rate is 125% of the direct labor cost.

3. Total cost = Direct material + Direct labor + Manufacturing overhead

= 700 + 900 + 440 + 550 + 380 + 475 + 1600 +1500 + 540 + 675 = $7760

Unit cost =  Total cost/ Total Quantity = $7760/ 2500= $3.104

4. Finished goods inventory $7760

To Work in progress $7760

(To record the completion of job)

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The equation which can be used to find the amount of time Hiroshi spends on his math homework is 1/4(x + 30 + 60) = x

According to the question,

Let total time Hiroshi spent on his homework be "y"

Total time spent on history homework = 30 minutes

Total time spent on English homework = 60 minutes

It is given that the time spent on math homework is x

and Also that One fourth of his total homework time is spent on math

=> x = 1/4y

=> 4x = y ----------(1)

Also , Sum of time taken in different homework will be equal total time y

=> 30 + 60 + x = y --------(2)

Substituting the values of x from equation (1) in equation (2)

=> 30 + 60 + x = 4x

divide by 4

=> 1/4(x + 30 + 60) = x is equation

=> x + 30 + 60 = 4x

=> 3x = 90

=> x = 90/3

=> x = 30 minutes

Total time taken in doing homework is 120 minutes

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The method of algebraically increasing the power of sums of two or more binomials is known as the binomial theorem. Binomial coefficients are the coefficients of binomial terms in the expansion process.

The term "Binomial" refers to algebraic statements with two dissimilar terms. For instance, 8x + 5x^2 is a binomial expression because it combines the two dissimilar terms 8x and 5x^2.

Binomial Theorem for any positive integer n is expressed as:

(a + b)^n = nC0 a^n + nC1 a^(n–1)b +...+ nC(n – 1) a.b^(n–1) + nCn b^n

nCr are the binomial coefficients where r varies from 0 to n.

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The linear trend equation to predict monthly receipts is given by: $$Y_{t}=3,700+300t$$ where Y is the predicted monthly receipt and t is the time period in months where t=0 is July this year.

To forecast the receipt for October, we need to find the value of Y when t=3 (since t=0 corresponds to July, August would be t=1, September would be t=2, and October would be t=3).Therefore, we can substitute t=3 in the equation above to get: $$Y_{3}=3,700+300(3)$$$$Y_{3}=3,700+900$$$$Y_{3}=4,600$$

Therefore, the forecast for October of this year is $4,600. The linear trend equation to predict monthly receipts is given by: $$Y_{t}=3,700+300t$$ where Y is the predicted monthly receipt and t is the time period in months where t=0 is July this year. The answer to the given question is: The forecast for October of this year is $4,600.

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Answer:

See below.

Step-by-step explanation:

The x-intercept occurs when k(x) = 0.

3x - 6 = k(x) = 0

3x - 6 = 0

3x = 6

x = 2

The x-intercept occurs (2, 0).

The y-intercept occurs when x = 0.

k(x) = 3x - 6

k(x) = 3(0) - 6

k(x) = -6

The y-intercept occurs at (0, -6).

Answer:

486 ft²

Step-by-step explanation:

For this, you want to replace every w with 16.

This gives (16+2)(2×16-5) or 2×16²-16-10.

I'm going to show this with the first example because the numbers are a bit easier.

You want to begin by working out the brackets. 16+2=18, and 2×16=32, giving us 18(32-5).

32-5=27, giving 18×27 as the equation.

This equals to 486, so the area is 486 ft².

**This content involves polynomials and area, which you might want to revise. I'm always happy to help!

Answer:

.2 Cm

Step-by-step explanation:

Answer:

17×6=102 because he gave 2 boxes to his brother so he have 6 boxes

The expression for the power delivered to a resistance in terms of csc^2 2 pi ft is P = I^2_0 R (csc^2 2 pi ft).

According to the given information, the power delivered to a resistance R when an alternating current of frequency f and peak current I_0 passes through it is represented by the equation P = I^2_0 R sin^2 2 pi ft.

To express this equation in terms of csc^2 2 pi ft, we can use the trigonometric identity csc^2 x = 1/sin^2 x. Substituting this identity into the equation, we get P = I^2_0 R (1/sin^2 2 pi ft).

Since csc^2 x is the reciprocal of sin^2 x, we can rewrite the equation as P = I^2_0 R (csc^2 2 pi ft). This expression represents the power delivered to the resistance in terms of csc^2 2 pi ft.

Therefore, the correct expression for the power delivered to the resistance in terms of csc^2 2 pi ft is P = I^2_0 R (csc^2 2 pi ft).

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Answer:

x = 47

Step-by-step explanation:

3x - 2 + 41 = 180 {Supplementary}

3x   + 39 =  180

        3x   = 180 - 39

       3x  = 141

          x = 141/3

x = 47

The absolute value of y, and the square root of (xy to the power of z) is \(xy^{z}\)

Floats are a type of number representation that allows us to store very large or very small numbers with a high degree of precision. In computer programming, it is often used to represent real numbers, such as decimals.

In this problem, we are given three float numbers x, y, and z and asked to perform various mathematical operations with them.

Let's start with the first operation: x to the power of z. This means that we want to find x raised to the power of z. This can be written mathematically as xᵃ.

The next operation is x to the power of (y to the power of z). This means that we want to find x raised to the power of y raised to the power of z. This can be written mathematically as x(yᵃ).

The third operation is the absolute value of y. The absolute value of a number is its magnitude, or distance from zero, regardless of its sign. For example, the absolute value of -5 is 5 and the absolute value of 5 is 5. Mathematically, it can be written as |y|.

Finally, we have to find the square root of (xy to the power of a). The square root of a number is the value that, when multiplied by itself, gives the original number.

The square root of 25 is 5 because 5 * 5 = 25. This can be written mathematically as

=> √(xyᵃ).

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Answer:

√645^3=16,380.9. Mathematically correct

A real number b is a lower bound for the real zeros of f when no real zeros are less than b, and is an upper bound when no real zeros are greater than b.

A real number b is a lower bound for the real zeros of a function f when no real zeros are less than b. In other words, if a real number b is a lower bound, it means that all the real zeros of the function f are greater than or equal to b. So, b sets a limit or boundary below which no real zeros exist.

Similarly, a real number b is an upper bound for the real zeros of a function f when no real zeros are greater than b. If b is an upper bound, it means that all the real zeros of the function f are less than or equal to b. Therefore, b establishes a limit or boundary above which no real zeros exist.

These bounds help us understand the possible range of values for the real zeros of a function and provide information about where the real zeros may lie.

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\(a(1) = 240 \\ a(2) = a(1) + d = 240 + 24 = 264 \\ a(3) = a(2) + d = 264 + 24 = 288 \\ a(4) = a(3) + d = 288 + 24 = 312 \\ a(5) = a(4) + d = 312 + 24 = 336 \\ a(6) = a(5) + d = 336 + 24 = 360\)

Answer:

1,000 lightbulbs that day were tested

Step-by-step explanation:

The weight of the water within an apple is 6.4 ounces if the apple weighs 8 ounces.

The amounts of water in an apple in ounces, given only that it contains 80% water. Yet, it is well known that an average apple contains 84% to 86% water by weight.

We need to know the apple's weight in ounces to translate the water content to 80%. 

Assume for the moment that the apple weighs 8 ounces. 80% is listed as the water content percentage. We may use the following formula to determine how much water is in an apple:

Weight of water = (water content percentage / 100) x weight of the apple

By entering the specified values, we obtain:

Weight of water = (80 / 100) x 8 ounces = 6.4 ounces.

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I searched your question and here is what I found:

Step-by-step explanation:

L = 4 + 3W  (from the second condition)

L2 = 66 + LW (combining the first and third condition)

L2 = 66 + L(L-4)/3

3L2 = 198 + L2 -4L

2L2 + 4L -198 = 0

(2L - 18)(L + 11) = 0; discarding the negative root for lack of practicality , L = 9

from the first equation W = (L - 4)/3 = 5/3 = 1 2/3; 1.67

Hence the length of the rectangle is 9 cm and the width is 1.67 cm

check;        

2nd condition; L = 4 + 3*1.67 = 9 (proven)

1st and 3rd condition; 92 = 66 + 9*1.67 = 81 (proven)

The length of the rectangle is 9 cm.

The width of the rectangle is 5/3 cm.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

Rectangle:

Length = 3w + 4

Width = w

Area = (3w + 4)w

Square:

Side = 3w + 4

Area = (3w + 4)²

Now,

The area of the square is 66 more than the area of the rectangle.

This means,

(3w + 4)² =  (3w + 4)w + 66

9w² + 16 + 24w = 3w² + 4w + 66

9w² - 3w² + 24w - 4w + 16 - 66 = 0

6w² + 20w - 50 = 0

2 (3w² + 10w - 25) = 0

3w² + 10w - 25 = 0

3w² + (15 - 5)w - 25 = 0

3w² + 15w - 5w - 25 = 0

3w(w + 5) - 5(w + 5) = 0

(3w - 5)(w + 5) = 0

w + 5 = 0 and 3w - 5 = 0

w + 5 = 0

w = -5 (rejected since its negative)

3w - 5 = 0

3w = 5

w = 5/3

Now,

Length.

= 3w + 4
= 3 x 5/3 + 4

= 5 + 4

= 9

Width = 5/3

Thus,

The length and width of the rectangle are 9 and 5/3.

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Answer:

B

Step-by-step explanation:

Figure A

2(8*4 + 4*4 + 4*8)

160

Figure B

6*4^2

96

Answer:

B

Step-by-step explanation:

On a coordinate plane, parallel lines have the same slope as geometric figures are true. Thus option B is correct.

Marks, splines, spheres, and curved are used to build enclosed geometric shapes. We can see these shapes all around us. Illustrations of geometric shapes include circles, rectangles, triangles, and others. Any configuration of points, columns, or angles is a geometry figure.

A point is the most fundamental algebraic concept because it has no boundaries. Simply put, a point upon that plane is a location. A dot is used to symbolize it. A plane can be identified by three non-straight-line points.

As two or much more vectors seldom cross each other and are located on the same dimension, these are said to be parallel. The slope of these lines is constant. Coplanar lines that seem to be parallel are the ones that don't cross. Therefore, option B is the correct option.

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The temperature was 48° at least once throughout the day as the temperature rises from 43° to 56° and 43° < 48° < 56° .  

The temperature was 43° at 3 PM and it rises to 56°  at 7.30 PM.

So we know that the rise of temperature in linear , hence the temperature will follow the rule of real numbers. Hence the temperature will increase through all the possible numbers between 43 and 56

Again 43° < 48° < 56°  , so at least once the temperature will be 48 ° .

You can think about integers as either independent objects or as a tool for problem-solving. The study of analytical objects (such as the Riemann zeta function) that somehow encode features of integers, primes, or any other number-theoretic objects is often the best method for understanding number theory issues (analytic number theory).

Most people refer to number theory as arithmetic. By the turn of the 20th century, "numerical theory" had taken its place.  (The term "arithmetic" is usually used to refer to "elementary computations," but it has come to signify more concepts in mathematical logic and computer technology, such as floating-point arithmetic.)

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Answer:

30 Percent

Step-by-step explanation:

Use the percent change formula.

The probability that either event will occur is 0.83

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

Event A = 18

Event B = 12

Other Events = 6

Using the above as a guide, we have the following:

Total = A + B + C

So, we have

Total = 18 + 12 + 6

Evaluate

Total = 36

So, we have

P(A) = 18/36

P(B) = 12/36

For either events, we have

P(A or B) = 30/36 = 0.83

Hence, the probability that either event will occur is 0.83

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The required value of y for the unit circle is: 2/3

The circle is defined as the locus of a point whose distance from a fixed point is constant i.e center (h, k).

The equation of the circle is given by:

(x - h)² + (y - k)² = r²

where:

h, k is the coordinate of the center of the circle on coordinate plane.

r is the radius of the circle.

Here,

Equation of the unit circle is given as,

x² + y² = 1

Now substitute the given value in the equation,

5/9 + y² = 1

y² = 1 - 5/9

y² = 4/ 9

y = √(4/9)

y = 2/3

Thus, the required value of y for the unit circle is 2/3

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So the probability, rounded to the nearest thousandth, of getting at least 2 fours in 5 rolls of a fair die is 0.194.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

The probability of getting at least 2 fours is the sum of the probabilities of getting exactly 2, 3, 4, or 5 fours:

P(X ≥ 2) = P(X=2) + P(X=3) + P(X=4) + P(X=5)

Using the binomial formula, we can calculate each of these probabilities:

P(X=k) = (n choose k) p^k (1-p)^(n-k)

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from n distinct items.

P(X=2) = (5 choose 2) (1/6)² (5/6)³ = 0.1608

P(X=3) = (5 choose 3) (1/6)³ (5/6)² = 0.0322

P(X=4) = (5 choose 4) (1/6)⁴ (5/6)¹ = 0.0013

P(X=5) = (5 choose 5) (1/6)⁵ (5/6)⁰ = 0.00003

Therefore,

P(X ≥ 2) = 0.1608 + 0.0322 + 0.0013 + 0.00003 = 0.1943

So the probability, rounded to the nearest thousandth, of getting at least 2 fours in 5 rolls of a fair die is 0.194.

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Therefore, the circumference of the triangle is 2r, which is equal to the diameter of the circle.

To find the circumference of the triangle, we need to first find the lengths of its sides. Let the three sides be x, y, and z, such that x:y:z is the given ratio. Without loss of generality, we can assume that x is the shortest side.

Let k be a constant such that y = kx and z = lx, where k and l are constants. Then, we have:

x + kx + lx = 2r

Simplifying this equation, we get:

x(1 + k + l) = 2r

So, we have:

x = (2r)/(1 + k + l)

y = kx = k(2r)/(1 + k + l)

z = lx = l(2r)/(1 + k + l)

The circumference of the triangle is the sum of its three sides:

C = x + y + z

Substituting the expressions for x, y, and z, we get:

C = (2r)/(1 + k + l) + k(2r)/(1 + k + l) + l(2r)/(1 + k + l)

Simplifying this expression, we get:

C = (2r(1 + k + l))/(1 + k + l)

C = 2r

Therefore, the circumference of the triangle is 2r, which is equal to the diameter of the circle.

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The area of the triangle is equal to A) 8.64. The Correct option is A) 8.64.

Let the lengths of the triangle be, 3x,4x,5x

Square of largest side = \(25x^{2}\)

Sum of square of other sides = \(3x^{2} + 4x^{2} = 25x^{2}\)

It is a right-angled triangle because the square of the greatest side equals the sum of the squares of the other sides.

The circumference of a right-angled triangle has a diameter equal to its hypotenuse.

hence, 5x=6 or x= \(\frac{6}{5}\)

Now, two perpendicular sides are then,  \(\frac{18 }{5} , \frac{24}{5}\)

\(Area = \frac{1}{2} \times \frac{18}{5} \times \frac{24}{5} = 8.64\)

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Question

A triangle with side lengths in the ratio 3 : 4 : 5 is inscribed in a circle of radius 3. The area of the triangle is equal to

A. 8.64

B. 12

C. 6

D. 10.5