Answer:
The length of the other leg of the triangle is units.
Step-by-step explanation:
The Pythagorean Theorem says that: <em>If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
</em>
This relationship is represented by the formula:
where <em>a</em> and <em>b</em> are the legs and <em>c</em> is the hypotenuse of the right triangle.
From the information given we know that one leg is 5 units and the hypotenuse is 8 units.
Applying the above formula and solving for <em>b</em> we get that
The expectation, E(3y +2) and variance, Var(3y+2) of the random variable are 13.4 and 19.44 respectively
<h3>How to determine the expectation and variance of a random variable?</h3>
The expectations or expected value E(y) of a random variable can be thought of as the “average” value of the random variable. It is also called its mean
By definition:
if y = ax + b
then E(y) = aE(x) + b
where a,b = constant
The variance V(y) of a random variable is the measure of spread for the distribution of a random variable that determines the degree to which the values of a random variable differ from the expected value
By definition
if y = ax + b
V(b) = 0
V(y) = V(ax) + V(b)
= a²V(x) + 0
where a,b = constant
Given: E(y)= 3.8 and Var(y)= 2.16
Calculate E( 3y +2) and Var( 3y+ 2)
E(3y +2) = 3E(y) + 2 since E(y) = 3.8
= 3×3.8 + 2
= 11.4+2
= 13.4
Var(3y+2) = 3²Var(y) + 0
= 9×2.16
= 19.44
Therefore, E(3y +2) is 13.4 and Var(3y+2) is 19.44
Learn more about expectations and variance on:
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Answer:
length = cm
Step-by-step explanation:
Perimeter is the sum of the length of all of the sides of a figure. A rectangle has 2 pairs of sides with equal length, which is a 4 sides. Two of those sides have the measure of the width and the other 2 sides have the measure of the length. Since we know the width is , we can multiply that value by 2 (since 2 of the sides are long) and subtract it from the perimeter, 13:
The sum of the 2 sides that have the measure of the length is cm. To find the length, divide the measure by amount of sides:
÷ 2 =
The length is cm.
Answer:
$620.
Step-by-step explanation:
$3,720/2 2/3 = 1395 = younger sister's amount of money
1395/2 1/4 = 620 = his amount of money