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1 year ago

What is the area of the shaded part?

Mathematics

1 answer:

makvit [3.9K]1 year ago

4 0

C) 225m

Explanation:
Looking at the board we see each side is 25m in length. Each side has 5 squares, therefore the length of one side of each square is 5m (25m/5=5).

Let’s count how many full squares there are. There’s 5 completely full squares (one in the middle, and one on each of the four edges).

There’s also half-full squares which we COULD calculate separately using the area of a triangle. However, we know that two halves make one full square so let’s count how many full blocks these make up. There’s 8 triangles (or half full squares), therefore there are 4 full squares.

Adding this to the clearly full blocks shows 4+5=9. There are 9 fully shaded squares. The area of a square is A=s x s (Area = length of side x length of side). Therefore, one square’s area is 5x5=25m^2. The area of 9 squares is 25 x 9 = 225m^2.

Therefore the answer is C

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Answer:

A sample size of 79 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$\pi = 0.21$

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

What sample size is needed if the research firm's goal is to estimate the current proportion of homes with a stay-at-home parent in which the father is the stay-at-home parent with a margin of error of 0.09?

A sample size of n is needed.

n is found when M = 0.09. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.09 = 1.96\sqrt{\frac{0.21*0.79}{n}}$

$0.09\sqrt{n} = 1.96\sqrt{0.21*0.79}$

$\sqrt{n} = \frac{1.96\sqrt{0.21*0.79}}{0.09}$

$(\sqrt{n})^{2} = (\frac{1.96\sqrt{0.21*0.79}}{0.09})^{2}$

$n = 78.68$

Rounding up to the nearest whole number.

A sample size of 79 is needed.

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3 years ago

Suppose you roll a regular 6-faced die. What is the probability of rolling: a 6?, a 2?, and a 4?

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3 years ago

3600 dollars is placed in an account with an annual interest rate of 9%. How much will be in the account after 25 years, to the

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Answer:

31043.09

Step-by-step explanation:

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3 years ago

Just number 9 would be fine please but also if you could number 10 would help

topjm [15]

Answer:

9. a = -7

10. x = 1

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Step-by-step explanation:

Step 1: Define equation

a + 6a - 14 = 3a + 6a

Step 2: Solve for a

Combine like terms: 7a - 14 = 9a
Subtract 7a on both sides: -14 = 2a
Divide 2 on both sides: -7 = a
Rewrite: a = -7

Step 3: Check

Plug in a into the original equation to verify it's a solution.

Substitute in a: -7 + 6(-7) - 14 = 3(-7) + 6(-7)
Multiply: -7 - 42 - 14 = -21 - 42
Subtract: -49 - 14 = -63
Subtract: -63 = -63

Here we see that -63 is equal to -63.

∴ a = -7 is a solution of the equation.

Step 4: Define equation

-12 - 4x = 8x + 4(1 - 7x)

Step 5: Solve for x

Distribute 4: -12 - 4x = 8x + 4 - 28x
Combine like terms: -12 - 4x = -20x + 4
Add 20x on both sides: -12 + 16x = 4
Add 12 on both sides: 16x = 16
Divide 16 on both sides: x = 1

Step 6: Check

Plug in x into the original equation to verify it's a solution.

Substitute in x: -12 - 4(1) = 8(1) + 4(1 - 7(1))
Multiply: -12 - 4 = 8 + 4(1 - 7)
Subtract: -16 = 8 + 4(-6)
Multiply: -16 = 8 - 24
Subtract: -16 = -16

Here we see that -16 does indeed equal -16.

∴ x = 1 is a solution of the equation.

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Answer:

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Step-by-step explanation:

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3 years ago