piece of wire
22 ft
long is cut into two pieces. One piece is used to form a square, and the remaining piece is used to form a circle. Where should the wire be cut so that the combined area of the two figures is a maximum? (Round your answers to two decimal places.)
length of wire used for the square ft
length of wire used for the circle ft
Where should the wire be cut so that the combined area of the two figures is a minimum? (Round your answers to two decimal places.)
length of wire used for the square ft
length of wire used for the circle ft

Answer:

1) (4x)² - (5)²

2) (4x + 5) (4x -5)

3) Zeros of b are \(\frac{5}{4}\) and \(\frac{-5}{4}\) (can also be 1.25 and -1.25)

Answer:

d. (600 - 81π) units ³

Step-by-step explanation:

Volume of the shaded portion = volume of triangular pyramid - volume of cone

= ⅓*A*h - ⅓πr²h

Where,

A = 15*10 = 150 units²

r = ½(9) = 4.5 units

h = 12

Plug in the values

Volume of the shaded portion = ⅓*150*12 - ⅓*π*4.5²*12

= (600 - 81π) units³

The volume of the given figure is 1176 cubic cm.

The value of the figure is calculated by multiplying all three side areas. Volume is a measure of the amount of space that an object or a substance occupies. It is typically expressed in cubic units such as cubic meters (m³), cubic centimetres (cm³), or cubic feet (ft³).

The volume of the figure is calculated as,

Volume = 2 ( 15 x 6 + 20 x 6 + 20 x 18 )

Volume = 1176 Cubic cm

Hence, the volume of the figure will be equal to 1176 Cubic cm.

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9514 1404 393

Answer:

  160 cm³

Step-by-step explanation:

The ratio of the linear dimensions is the square root of the ratio of areas:

  scale factor B/A= √(64/144) = 8/12 = 2/3

The ratio of volumes is the cube of the scale factor:

  (volume B)/(volume A) = (2/3)³ = 8/27

Then the volume of pyramid B is ...

  volume B = (volume A) × (volume B)/(volume A)

  = (540 cm³) × (8/27) = 160 cm³ . . . . volume of pyramid B

_____

Equivalently, the ratio of volumes is the 3/2 power of the ratio of areas.

 Vb = Va(64/144)^(3/2) = (540 cm³)(4/9)^(3/2) = (540)(8/27) cm³ = 160 cm³

Answer:

1. True

2. True

3. False

4. True

5. False

6. True

7. Jesus.

Answer:

B

Step-by-step explanation:

The square root of 448 rounded up to 6 decimal places is 21.166010. It is the positive solution of the equation x2 = 448. We can express the square root of 448 in its lowest radical form as 8 √7.

Answer:

43.6 has 3 significant figures.

well, let me not bore you to death on how we test it and test it.

\(\underline{\textit{testing for symmetry to the }\frac{\pi }{2}~line\qquad \qquad r=-r~~,~~\theta =-\theta } \\\\\\ r=5-sin(11\theta )\implies (-r)=5-sin[11(-\theta )]\implies -r=5-sin(-11\theta ) \\\\\\ \stackrel{symmetry~identity}{-r=5-\stackrel{\downarrow }{[-sin(11\theta )]}}\implies\implies r=-5-sin(11\theta )\impliedby \textit{no dice} \\\\[-0.35em] ~\dotfill\)

\(\underline{\textit{testing for symmetry to the polar axis}\qquad \qquad \theta =-\theta} \\\\\\ r=5-sin(11\theta )\implies r=5-sin[11(-\theta )]\implies r=5-sin(-11\theta ) \\\\\\ r=5-[-sin(11\theta )]\implies r=5+sin(11\theta )\impliedby \textit{no dice} \\\\[-0.35em] ~\dotfill\)

\(\underline{\textit{testing for symmetry to the pole}\qquad \qquad r=-r} \\\\\\ r=5-sin(11\theta )\implies -r=5-sin(11\theta )\implies r=-5+sin(11\theta )\qquad \textit{no dice}\)

so the symmetry tests didn't pass, notice the picture below though, looks a bit deceiving, it looks as if it'd have π/2 symmery, but it doesn't show in the test.

Answer:0.03125

Step-by-step explanation:

GOO*OOGLE

Step-by-step explanation:

(1/2)^5   = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 =   1/32

Answer:

tan = 12/5..............

Answer: No, they are not equivalent. They arent equivalent because 28$/56 days= 0.5/day

18$/24 days= 0.75/day

Step-by-step explanation:

Answer:

no they are not equivalent.

Step-by-step explanation:

to start, the question has mias saving rate at weekly and we need to convert that to days so we can compare to her sister. we multiply 8*7 to find the number of days which is 56. we then divide $28 by 56. mias daily saving rate is y= .5x.

for mias sister we divide 18/24 which is .75. her sisters daily saving rate is y=.75x.

this shows that the saving rates for the sisters are not equivalent

Answer:

10x7x5=350. Your answer is B! heart it if it was good!

Step-by-step explanation:

Answer:

to find the volume of a prism you need to multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.

Step-by-step explanation:

Answer:

the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes is 0.4215

Step-by-step explanation:

Let consider Q to be the opening altitude.

The mean μ = 135 m

The standard deviation = 35 m

The probability that the equipment damage will occur if the parachute opens at an altitude of less than 100 m can be computed as follows:

\(P(Q<100) = P(\dfrac{X- 135}{\sigma} < \dfrac{100 - 135}{35}})\)

\(P(Q<100) = P(z< \dfrac{-35}{35}})\)

\(P(Q<100) = P(z<-1)\)

\(P(Q<100) = 0.1587\)

If we represent R to be the number of parachutes which have equipment damage to the payload out of 5 parachutes dropped.

The probability of success = 0.1587

the number of independent parachute n = 5

the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes can be computed as:

P(R ≥ 1) = 1 - P(R < 1)

P(R ≥ 1) = 1 - P(R = 0)

The probability mass function of the binomial expression is:

P(R ≥ 1) = \(1 - (^5_0)(0.1587)^0(1-0.1587)^{5-0}\)

P(R ≥ 1) =\(1 - (\dfrac{5!}{(5-0)!})(0.1587)^0(1-0.1587)^{5-0}\)

P(R ≥ 1) = 1 - 0.5785

P(R ≥ 1) = 0.4215

Hence, the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes is 0.4215

The Length is 5 inches and the Breadth is 15 inches

What is Perimeter?

A perimeter is a closed route that covers, surrounds, or outlines a two-dimensional form or length. The circumference of a circle or an ellipse is its perimeter. There are various practical applications for calculating the perimeter.

Solution:

Perimeter of Rectangle = 2*(Length + Breadth)

According to the question

Breadth = 3*Length

Perimeter = 40

40 = 2*(Length + 3*Length)

20 = 4*Length

Length = 5 inch

Breadth = 15 inch

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a. The 25th percentile of X is 2/3.The median of X is 1/√2. b. the probability density function f(x) is given by f(x) = ⎩⎨⎧​0, for x<01/2x3​, for 0≤x<20, for x≥2. c. the expected value of X is 3/8.

a. To find the 25th percentile, we need to find the value x for which F(x) = 0.25.

Since F(x) is given by different formulas for different intervals, we need to consider each interval separately.

For x < 0, F(x) = 0. So this interval does not contribute to the percentile we are interested in.

For 0 ≤ x < 2, F(x) = ∫0x f(t) dt = ∫0x (1/4t²) dt = -1/(4x) + 1/4.

Solving -1/(4x) + 1/4 = 0.25 for x, we get x = 2/3.

For x ≥ 2, F(x) = 1. So this interval does not contribute to the percentile we are interested in.

Therefore, the 25th percentile of X is 2/3.

To find the median, we need to find the value x for which F(x) = 0.5.

For x < 0, F(x) = 0. So this interval does not contribute to the median we are interested in.

For 0 ≤ x < 2, F(x) = ∫0x f(t) dt = ∫0x (1/4t²) dt = -1/(4x) + 1/4.

Solving -1/(4x) + 1/4 = 0.5 for x, we get x = 1/√2.

For x ≥ 2, F(x) = 1. So this interval does not contribute to the median we are interested in.

Therefore, the median of X is 1/√2.

b. To find the probability density function f(x), we take the derivative of F(x) in each interval where it is defined:

For x < 0, f(x) = 0.

For 0 ≤ x < 2, f(x) = d/dx F(x) = 1/2x³.

For x ≥ 2, f(x) = d/dx F(x) = 0.

Therefore, the probability density function f(x) is given by f(x) = ⎩⎨⎧​0, for x<01/2x3​, for 0≤x<20, for x≥2​

c. To compute E[X], we use the formula E[X] = ∫x f(x) dx over the entire range of X:

E[X] = ∫0∞ x f(x) dx = ∫0² x (1/2x³) dx = [(-1/4)\(x^{-2}\)]0² = 1/2.

To compute E[X²], we use the formula E[X²] = ∫x² f(x) dx over the entire range of X:

E[X²] = ∫0∞ x² f(x) dx = ∫0² x² (1/2x³) dx = [(-1/4)\(x^{-1}\)]0² = 1/2.

Finally, to compute V[X], we use the formula V[X] = E[X²] - (E[X])²:

V[X] = E[X²] - (E[X])² = 1/2 - (1/2)² = 3/8.

Therefore, the expected value of X is 3/8.

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The equivalent decimal and mixed number for given letter C is,

⇒ C = 8.2 ; 8 2/10

We have to given that,

A number line is shown in image.

Since,

A number lines are the horizontal straight lines in which the integers are placed in equal intervals.

And, All the numbers in a sequence can be represented in a number line. This line extends indefinitely at both ends.

Now, By given number line,

Point C is two point left from point 8.

Hence, The point C is denoted as,

⇒ C = 8.2

⇒ C = 82/10

⇒ C = 8 2/10

Therefore, the equivalent decimal and mixed number for given letter C is,

⇒ C = 8.2 ; 8 2/10

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By finding all the four slopes, we can see that the word is ECHA.

We know that the general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

We know that if the line passes through (x₁, y₁) and (x₂, y₂) then the slope is:

s = (y₂ - y₁)/(x₂ - x₁)

With that formula we can get the slopes.

1) Using the points (0, 3) and (2, 4).

m = (4 - 3)/(2 - 0) = 1/2, so the letter is E.

2)Using (-1, -12) and (1, -8)

m = (-8 + 12)/(1 + 1) = 4/2 = 2, so the letter is C.

3) We have (2, -6) and (-4, -3) so:

m = (-3 + 6)/(-4 - 2) = 3/-6 = -1/2, so the letter is H

4)we can use the points (0, 3) and (1, 1), so:

m = (1 - 3)/(1 - 0) = -2, so the letter is A

Then the word is ECHA

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Answer: 20%

Step-by-step explanation: Annual depreciation = $2,600 * 12 = $31,200

Annual depreciation rate = Annual depreciation /Depreciable costs

= $31,200 / ($188,000 - $32,000)

= 20%

Answer:

☆<《HOPE IT WILL HELP YOU 》>☆

Step-by-step explanation:

capital of Peru is Lima

Answer:

4.15932686862 Exact Form:

√

17.3

Step-by-step explanation:

Answer:

4 17/24

Step-by-step explanation:

7/8 + 3 5/6

= 7/8 + 23/6

= 21/24 + 92/24

= 113/24

= 4 17/24

Answer:

-4, -9/4, 0.5, 2.2 (the last one) , 3.7

Step-by-step explanation:

I hope you have a great day and LEAVE ME ALONE! <3

Answer:

simplified: 4x−28

Step-by-step explanation:

The product of 4 and the difference of a number and 7 can be written as 4(x-7) where x is the number you are looking for.

9 is the equivalent value of x from the given triangle.

The angle bisector theorem is concerned with the proportions of the two segments that a line that bisects the opposite angle divides a triangle's side into.

Applying the rule to solve the given question, we will have:

3x-7/12 = 3x +3/18

Cross multiply

12(3x+3) = 18(3x-7)36x + 36 = 54x - 126

Collect the like terms

36x-54x = -126 - 36

-18x = -162

x = 162/18

x = 9

Hence the value of x from the given figure is 9.

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1. selection of index number: during the construction of index number it is to be kept in mind that the selection of the index number should be correct accordingly.

2. selection of formula: while the construction of index numbers it is compulsory to select the correct formula for the given question.

3. selection of price: selection of prices should be done accordingly while constructing the index numbers.`

construction of index number is also available in two parts:

1. simple

2. weighted

1. simple: the simple method is classified into simple aggregative and simple relative.

2. weighted: the weighted method is classified into a weighted aggregative and weighted average.

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Answer: infinite solutions

Step-by-step explanation:

Answer:

21/4 :3/4=  21/4 *4/3= 7/1 *1/1 = 7

7 bookcases

Step-by-step explanation:

Answer:

hdkskxxlsmna

Step-by-step explanation:

cusaksmxd