Answer:
Part (a) The value of Z is 0.10396. Part (b) The value of Z is 0.410008.
Step-by-step explanation:
Consider the provided information.
Part (a)
In order to find the number z such that the proportion of observations that are less than z in a standard Normal distribution is 0.5414, simply find 0.5414 in the table and search for the appropriate Z-value.
Now, observing the table it can be concluded that the value of Z is 0.10396.
Part (b)
Consider the number 65.91%
The above number can be written as 0.6591.
Now, find 0.6591 in the table and search for the appropriate Z-value.
By, observing the table it can be concluded that the value of Z is 0.410008.
Answer:
1/6 for the number cube and 1/2 for coin
Step-by-step explanation:
If <em>x</em>² + <em>y</em>² = 1, then <em>y</em> = ±√(1 - <em>x</em>²).
Let <em>f(x)</em> = |<em>x</em>| + |±√(1 - <em>x</em>²)| = |<em>x</em>| + √(1 - <em>x</em>²).
If <em>x</em> < 0, we have |<em>x</em>| = -<em>x</em> ; otherwise, if <em>x</em> ≥ 0, then |<em>x</em>| = <em>x</em>.
• Case 1: suppose <em>x</em> < 0. Then
<em>f(x)</em> = -<em>x</em> + √(1 - <em>x</em>²)
<em>f'(x)</em> = -1 - <em>x</em>/√(1 - <em>x</em>²) = 0 → <em>x</em> = -1/√2 → <em>y</em> = ±1/√2
• Case 2: suppose <em>x</em> ≥ 0. Then
<em>f(x)</em> = <em>x</em> + √(1 - <em>x</em>²)
<em>f'(x)</em> = 1 - <em>x</em>/√(1 - <em>x</em>²) = 0 → <em>x</em> = 1/√2 → <em>y</em> = ±1/√2
In either case, |<em>x</em>| = |<em>y</em>| = 1/√2, so the maximum value of their sum is 2/√2 = √2.
An operation that is done to a value and it stays the same, it is called the "identity property".
Some quick examples:
Adding any number with zero will result in the same number.
Multiplying any number with one will result in the same number.
Hope this helps!
8xy-7xy-3xy-3y²-2y²+8y²+5x²+12x²
then simplify by combining like terms -2xy+3y²+17x²