Answer:
187.96
Step-by-step explanation:
yeah
The measure of angle theta is 30 degrees.
This is a 30-60-90 triangle where the short leg is half that of the hypotenuse. The short leg is opposite the smallest angle 30 degrees.
You can use trig to find that
sin(angle) = opposite/hypotenuse
sin(theta) = 5/10
sin(theta) = 0.5
theta = arcsin(0.5)
theta = 30 degrees
Ratio triangle height to square side 7:8
ratio triangle base to square side 1:2
Area of the square is 64 in² then the sides = 8 in
ratios give
h = 7(8)/8
h = 7
b = 8/2
b = 4
Area Triangle = 0.5(7)(4)
= 14
Then shaded region is the Area of the square minus the Area of the triangle.
A = 64 - 14
A = 50 in²
Answer:
The probability of flipping a coin 10 times and it landing on heads exactly seven times is about 0.1172 or 11.72%.
Step-by-step explanation:
We can use basic binomial distribution, which is given by the formula:

Where <em>n</em> represent the number of trials, <em>x</em> represent the number of successes desired, <em>p</em> represent the chance of success, and <em>q</em> represent the chance of failure.
Since we are flipping a coin 10 times, we are conducting 10 trials. So, <em>n</em> = 10.
We want to probability that it lands on heads exactly 7 out of 10 times. So, the number of desired successes <em>x</em> is 7.
The probability of success <em>p</em> is 1/2.
And the probability of failure <em>q</em> is also 1/2.
Substituting:

The probability of flipping a coin 10 times and it landing on heads exactly seven times is about 0.1172 or 11.72%.
Answer:
A = 18 cm²
Step-by-step explanation:
The volume (V) of a prism is calculated as
V = area of base (A) × height
Here V = 216 cm³ and h = 12 cm , then
A × 12 = 216 ( divide both sides by 12 )
A = 18 cm² ← area of base