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tekilochka [14]
3 years ago
10

Find the perimeter and the area of each shape. Give your answer as a completely simplified exact value in terms of π (no approxi

mations).

Mathematics
1 answer:
nydimaria [60]3 years ago
3 0

Answer:

Circumference: 12π + 8 cm,

Area: 48 ( cm )^2

Step-by-step explanation:

This figure is composed of circles, squares, and semicircles. As you can see, the squares indicate that each semicircle should have ( 1 ) the same area, and ( 2 ) the same length ( circumference ). It would be easier to take the circumference of the figure first, as it is composed of arcs part of semicircles the same length.

Circumference of 1 semicircle = \frac{1}{2}( πd ) =  \frac{1}{2}π( 4 ) = 2π ( cm )

Circumference of Figure (composed of 6 semicircles + 2 sides of a square),

We know that 6 semicircles should be 6 * 2π, and as the sides of a square are equal - if one side is 4 cm, the other 3 are 4 cm as well. Therefore the " 2 sides of a square " should be 2

Circumference of Figure = 6 * 2π + 2 = 12π + 8 ( cm )

_____________

The area of this figure is our next target. As you can see, it is composed of 3 semicircles, and the area of 3 semicircles subtracted from the area of 3 squares. Therefore, let us calculate the area of 1 semicircle, and the area of 1 square first.

Area of 1 semicircle = 1/2πr^2 = 1/2π(2)^2 = 2π ( cm ),

Area of 1 square = ( 4 cm )( 4 cm ) = 16 ( cm^2 )

So, the area of the figure should be the following -

Area of Figure = 3 * 2π + 3( 16 - 2π ) = 48 ( cm )^2

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vivado [14]

Answer:

Step-by-step explanation:

1. There is a total of 16 outcomes

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2+4, 3+3, 3+4, 4+2, 4+3, 4+4 for a total of 6 outcomes.

3. To spin the same number twice, the possible outcomes are

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7 0
3 years ago
Simplify: √8x^5+ x√18x^3<br>÷x^2√50x​
Sergeu [11.5K]

Answer:

10x^2 √2x

Step-by-step explanation:

hope this helps

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7 0
2 years ago
Identify intervals on which the function is increasing, decreasing, or constant.
tigry1 [53]
G ( x ) = 2 - ( x - 7 )²
g ( x ) = 2 - ( x² - 14 x + 49 )
g ( x ) = 2 - x² + 14 x - 49
g ( x ) = - x² + 14 x - 47
The maximum of the function is at:
x= - b / 2 a
x = - 14 / ( - 2 ) = 7
Therefore the function is increasing form x ∈ ( - ∞, 7 ) and decreasing for x ∈ ( 7, +∞ ).
Answer:
C.   increasing, x < 7; decreasing x > 7.
3 0
3 years ago
A small business owner estimates his mean daily profit as $970 with a standard deviation of $129. His shop is open 102 days a ye
Katena32 [7]

Answer:

The probability that the shopkeeper's annual profit will not exceed $100,000 is 0.2090.

Step-by-step explanation:

According to the Central Limit Theorem if we have a population with mean <em>μ</em> and standard deviation <em>σ</em> and we select appropriately huge random samples (<em>n</em> ≥ 30) from the population with replacement, then the distribution of the sum of values of <em>X</em>, i.e ∑<em>X</em>, will be approximately normally distributed.  

Then, the mean of the distribution of the sum of values of X is given by,  

 \mu_{x}=n\mu

And the standard deviation of the distribution of the sum of values of X is given by,  

 \sigma_{x}=\sqrt{n}\sigma

The information provided is:

<em>μ</em> = $970

<em>σ</em> = $129

<em>n</em> = 102

Since the sample size is quite large, i.e. <em>n</em> = 102 > 30, the Central Limit Theorem can be used to approximate the distribution of the shopkeeper's annual profit.

Then,

\sum X\sim N(\mu_{x}=98940,\ \sigma_{x}=1302.84)

Compute the probability that the shopkeeper's annual profit will not exceed $100,000 as follows:

P (\sum X \leq  100,000) =P(\frac{\sum X-\mu_{x}}{\sigma_{x}}

                              =P(Z

*Use a <em>z</em>-table for the probability.

Thus, the probability that the shopkeeper's annual profit will not exceed $100,000 is 0.2090.

6 0
3 years ago
Function g is a transformation of the parent function f(x) = x2. The graph of g is a translation right 5 units
Allisa [31]

Answer:

  C.  y = x^2 -10x +26

Step-by-step explanation:

The translated function is ...

  g(x) = f(x - right) + up

  g(x) = f(x -5) +1

  g(x) = (x -5)^2 +1

  g(x) = x^2 -10x +26

In "y =" form, this is ...

  y = x^2 -10x +26 . . . . matches choice C

6 0
3 years ago
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