Which rule explains why these triangles are congruent?

[tex] \large \boxed{ \boxed{ \mathrm{21.5 \: \: cm {}^{2}} }}[/tex]

By Observing the Above figure, we can conclude that the area of shaded region is equal to the Area of Square minus the sum areas of two equal semicircles (since their diameters are equal)

let's solve for area of square :

[tex]\longrightarrow \: \mathrm{side {}^{2} }[/tex]

[tex]\longrightarrow10 {}^{2} [/tex]

[tex]\longrightarrow \mathrm{100 \: cm {}^{2} }[/tex]

Now,

Radius of the both semicircles measure :

[tex]\longrightarrow \dfrac{10}{2} [/tex]

[tex]\longrightarrow5 \: cm[/tex]

now, let's solve for their area

[tex] \longmapsto 2 \times \dfrac{\pi {r}^{2} }{2} [/tex]

(Since, there are two semicircles)

[tex]\longrightarrow3.14 \times 5 \times 5[/tex]

[tex]\longrightarrow78.5 \: cm {}^{2} [/tex]

Area of Shaded region = Area of Square - Area of Semicircles, that is

[tex]\longrightarrow100 - 78.5[/tex]

[tex]\longrightarrow \mathrm{21.5 \: cm {}^{2} }[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{hope \: it \: helps \: you \: }}{\orange{.....}}}}}[/tex]

Answer:

0.9961

Step-by-step explanation:

Number of options per question = 2

P(success), p = 0.5

q = 1 - p = 0.5

Number of trials, n = 8

P(x ≥ 1) = p(x= 1) + p(x=2) +... + p(x = 8)

P(x = x) = nCx * p^x * q^(n-x)

Using a calculator to save computation time :

p(x ≥ 8) = 0.9961

Answer:

50

Step-by-step explanation:

6m-n

Let m = 9 and n = 4

6*9-4

Multiply first

54-4

Then subtract

50

Answer: the required sample size =1658944

Step-by-step explanation:

When the prior population proportion for the study is unknown , then the formula for sample size is [tex]Sample \ size = 0.25(\dfrac{z^*}{Margin\ of \ error})^2[/tex]

z-value for 99% confidence = 2.576

[tex]Sample \ size = 0.25(\dfrac{2.576}{0.001})^2\\\\=0.25(2576)^2\\\\=1658944[/tex]

Hence, the required sample size =1658944

Answer:

6.n/4

7.3/4time G or 0.75G

Step-by-step explanation:

6.3m+n/12-m-n/4=3m-3m+n+3n=4n/12=n/4

7.G=0.9a/1.2b G=3/4*a/b

Answer:

15/2 = 7 1/2

Step-by-step explanation:

3 1/3 * 2 1/4 =

= (3 * 3 + 1)/3 * (2 * 4 + 1)/4

= 10/3 * 9/4

= 90/12

= 45/6

= 15/2

= 7 1/2

[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]

See this attachment

Answer:

d

Step-by-step explanation:

180-149= 31.

31+ 122= 153

180-153= 27

a= 27

Answer:

Well just looking at the choices can lead you to the answer right away.

Well since the probability of boys and girls are equal, its 50/50. And since 125 in half well about is about 60-62 and the minimum amount of girls has to be 70. It can’t be higher then half and the choices remain to less then half not including 50%. So that eliminates all 3 choices except B.

The probability that out of 125 babies born, at least 70 will be girls is 10.5%. So, option B is correct.

Probability is defined as the chance for an event to occur. The value of probability is expressed from zero to one.

Here,

Let X be the number of girls born among the babies.

Let the number of babies born be n = 125

Let the probability of girls being born be P

Since, boys and girls are equally probable, P = 1/2 = 0.5

The probability that at least 70 girls will be born is P(X ≤ 70)

P(X ≤ 70) = P(70) + P(71) + P(72) + P(73) + P(74) +....P(125)

Applying the binomial probability equation,

P(X) = {n!/[X!(n - X)!} Pˣ (1 -P)ⁿ⁻ˣ

So,

P(70) = {125!/[70!(125-70)!]}x 0.5⁷x (1 - 0.5)⁵⁵

We get P(70) = 0.02913

Using cumulative probability function, we get the probability upto X=125.

By adding all the values, we get,

P(70) = 0.1051

Therefore probability that at least 70 girls are born = 0.1051 x 100 = 10.5%

Hence,

The probability that out of 125 babies born, at least 70 will be girls is 10.5%.

To learn more about probability, click:

https://brainly.com/question/14210034

#SPJ7

Answer:

x = -9

Step-by-step explanation:

ANGLES IN A TRIANGLE ADD UP TO 180°

50° + 80° = 130°

180° - 130° = 50

x+59 = 50

x = -9

Answer:

x = 13

Step-by-step explanation:

The sum of the exterior angles of a 4 sided polygon is 360

139+ 6x+9x+2x = 360

Combine like terms

139+17x=360

Subtract 139 from each side

17x = 360-139

17x = 221

Divide each side by 17

17x/17 = 221/17

x = 13

Answer:

The answer is option 1:  3

Step-by-step explanation:

Just took the test :)

Answer:

436.42 m

Step-by-step explanation:

We are to determine the perimeter of the field

perimeter = perimeter of rectangle + perimeter of the two semicircles

Perimeter of a rectangle = 2 x (length + breadth)

2 x (82 + 53) = 270m

Perimeter of a semicircle = 1/2πD

perimeter of the 2 semicircles = 2 x (1/2 x 3.14 x 53) = 166.42

Perimeter = 270 + 166.42 = 436.42 m

Answer:

Step-by-step explanation:

Answer:

3/10

Step-by-step explanation:

1/10 + 1/5 =          need to get common denominators to add.

1/10 + 2/10 = 3/10

Answer:

54 square inches

Step-by-step explanation:

9 times 12 is 108. That is the area of a rectangle with the same length and width/height. A right triangle is half of that. So 108/2=54

Hi there!  

»»————-　★　————-««

I believe your answer is:  

Option B  

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Area of A Triangle:}}\\\\---------\\\frac{b*h}{2}\\\\\boxed{\text{Key:}}\\\\\text{b - base}\\\text{h - height}[/tex]

⸻⸻⸻⸻

[tex]\boxed{\text{Finding the area of the Triangle:}}\\\\-------------\\\ \frac{9*12}{2}\\\\\rightarrow\frac{108}{2}\\\\\rightarrow \boxed{54}\\\\\text{The area should be 54 square inches.}}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

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:

20%

Step-by-step explanation:

vrrggrgrhreah

Answer:

Length = 12 m, Width = 8 m

Step-by-step explanation:

Let the width of the rectangle is b.

Length, l = 4+b

The perimeter of the rectangle = 40 m

We know that,

Perimeter of rectangle = 2(l+b)

2(4+b+b) = 40

4+2b = 20

Subtract 2 from boths sides,

2b = 16

b = 8

Width = 8 m

Length = 4+8 = 12 m

Hence, the length and the width of the rectangle is 12 m and 8 m respectively.

9514 1404 393

Answer:

  a) 2π radians

  b) 10π inches

  c) 5/4π inches per minute

Step-by-step explanation:

The formulas are fairly straightforward. Use the given values in each.

a) θ = ωt

  θ = (π/4 radians/min)(8 min) = 2π radians

__

b) s = rθ

  s = (5 in)(2π radians) = 10π in

__

c) v = s/t

  v = (10π in)/(8 min) = 5/4π in/min

9514 1404 393

Answer:

  ∠A ≈ 72°

Step-by-step explanation:

Fill in the given numbers and do the arithmetic.

  cos A = (2.9² +2.5² -3.2²)/(2(2.9)(2.5)) = 4.42/14.5

The inverse cosine function is used to find the angle, given its cosine.

  A = arccos(4.42/14.5)

  ∠A ≈ 72°

Answer:

4

Step-by-step explanation:

in y=mx+b, the "b" is the y-intercept

Answer:

4

it's in y = mx + b form, where b is the y-intercept

Answer:

B. (1, 2)

D. (-10, 1)

Step-by-step explanation:

Both points land in the highlighted area.

Hope this helps! :)

Answer:

The correct answer would be

A. (–12, 0) & D. (–10, 1)

Answer:

d

Step-by-step explanation:

it is

Answer:

10%

Step-by-step explanation:

10% of the Male students have blonde hair

Answer:

its a geometric progression. r=1/5 or 0.2

Answer:

A

Step-by-step explanation:

Hi there!

The given equation of the line is in slope-point form, which is y-y1=m(x-x1), where (x1,y1) is a point and m is the slope

the given equation is y-5=-3(x - 17)

-3 is in the place of where m is, so -3 is the slope. Remember that the sign is part of the slope, so it can't be B (3). Therefore, the answer is A

Hope this helps!

Answer:

(-2) is the index of y make value 1/y².

Step-by-step explanation:

We need to find what index of y makes value 1/y².

Here, the numerator is 1 and the denominator is y².

We know that,

[tex]\dfrac{1}{a^x}=a^{-x}[/tex]

So, the given expression is :

[tex]\dfrac{1}{y^2}=y^{-2}[/tex]

Hence, (-2) is the index of y make value 1/y².

Answer:

n = 1

Step-by-step explanation:

Answer:

n = -4

Step-by-step explanation:

Let's solve your equation step-by-step.

−2(n − 6) = 20

Step 1: Simplify both sides of the equation.

−2(n − 6) = 20

(−2)(n) + (−2)(−6) = 20(Distribute)

−2n + 12 = 20

Step 2: Subtract 12 from both sides.

−2n + 12 − 12 = 20 − 12

−2n = 8

Step 3: Divide both sides by -2.

[tex]\frac{-2n}{-2} = \frac{8}{-2}[/tex]

n = -4

Hope this helps, please mark brainliest if possible. Have a great day.

Answer:

step one 1 ×3 = 4

Step-by-step explanation:

how first fo ther

Answer:

2 Function B

Step-by-step explanation:

Answer:

Function B is greater

Step-by-step explanation:

The gradient of Function B is of 3 = m

Though the gradient of Function A  is of 1 = m, obviously being of the smaller size

If you didn't know, gradient is the same as the slope

Hope this helps