Answer:
98 yd²
Step-by-step explanation:
From the diagram attached, The polygon is a square with the distance from the edge of the square to the center of the square = 7 yd.
The distance from the edge of the square to the center of the square is half of the diagonal. Therefore length of the diagonal = (7 yd * 2) = 14 yd
The diagonal and two sides of the triangle form a right angle triangle. Let the side of the triangle be a. Therefore the hypotenuse is the diagonal, using Pythagoras theorem:
a² + a² = 14²
2a² = 196
a² = 98
a = √98 = 7√2
The length of the side of the triangle = a = 7√2 yd
The area of the rectangle = length × length = 7√2 × 7√2 = 98 yd²
Answer:
A. 12.3%
Step-by-step explanation:
Model this as a binomial distribution
where X is the random variable, n is the number of trials, and p is the probability of success.
Therefore,
- X = lambs born male
- n = 60
- p = 0.5
(If the probability of lambs being male and female is equal, then the probability of males being born = 0.5)
The probability that at least 35 lambs will be born male:
This one can besolved using system of equations. From the first statement we can assume that
length = 2 * width. The area of rectange equals product of it's width and length. By knowing that and following to the second statement we get the second equation:
(3 * width) * (length - 5) = width * length + 4. Let's mark the
width as
x and the
length as
y and write down our equations system:
Using substituion method, lets replace every
y with
2x within second equation and solve it:
Now lets find the discriminant in order to solve this quadratic equation:
The second root is negative, so we ignore it as
x represents width which can't be negative.
Now, using found root, let's find
y value from the first equation:
So,
the width is equal 4 (and the length is equal 8).
<u>Given</u>:
Given that the figure is a triangular prism.
The length of the prism is 4 m.
The base of the triangle is 2.5 m.
The height of the triangle is 2.25 m.
We need to determine the volume of the triangular prism.
<u>Volume of the triangular prism:</u>
The volume of the triangular prism can be determined using the formula,
where b is the base of the triangle,
h is the height of the triangle and
l is the length of the prism.
Substituting b = 2.5, h = 2.25 and l = 4 in the above formula, we get;
Thus, the volume of the triangular prism is 11.25 m³