Answer: $14.40
Step-by-step explanation:
Firstly, I noticed that there are fractions, decimals, and percents. I will change everything to percents, so it’s more easy for me to compare each of them.
List 1. 140%, 25%, 14%. This is from greatest to least, not least to greatest.
List 2. 25%, 14%, 14%. This is not from least to greatest, either.
List 3. 14%, 25%, 140%. This is from least to greatest.
List 4. 140%, 14%, 25%. This is not from least to greatest.
List 3 is from least to greatest. I got this answer by converting all of the fractions and decimals to percentages.
We are given the following information:
the sum of the first number cubed and the second number is 500
their product is a maximum
We are looking for the 2 missing numbers.
To answer this, let's represent the two numbers as x and w.
From the given, we can form the following equation:
We can then express y as:
We can express their product as:
To find the maximum value of x, let's solve for the derivative of -x^4 + 500 x.
Then we solve for the value of x where f'(x) = 0.
Then we use x = 5 to solve for the second number, w.
Therefore, the two numbers are 5 and 375.
Answer:
8/13
Step-by-step explanation:
In a standard deck there are 52 cards. Let A denote the event of drawing a black card and B denote the event of drawing face card. We have to find P(A or B) or P(A∪B).
P(A∪B)=P(A)+P(B)-P(A∩B)
There are 26 black cards in a standard deck so,
P(A)=26/52.
There are 12 face cards in a standard deck so,
P(B)=12/52.
There are 6 cards that are black face cards.
P(A∩B)=6/52.
P(A∪B)=P(A)+P(B)-P(A∩B)
P(A∪B)=26/52+12/52-6/52
P(A∪B)=38/52-6/52
P(A∪B)=32/52
P(A∪B)=8/13
Thus, probability of drawing a black card or a face card is 8/13.
Answer:
See proof below
Step-by-step explanation:
In trigonometry identity
tan^2 theta = sin^2 theta /cos^2 theta
cot^2 theta = cos^2 theta/sin^2 theta
csc^2 theta = 1/sin^2 theta
Substitute into the expression
(sin^2 theta /cos^2 theta )+ (cos^2 theta/sin^2 theta)/1/sin^2 theta
= [sin^4theta + cos^4theta/cos^2 theta sin^2 theta]÷(1/sin^2 theta)
= 1/cos^2 theta sin^2 theta÷(1/sin^2 theta)
= 1/cos^2 theta sin^2 theta * sin^2 theta/1
= 1/cos^2theta
= sec^2theta (Proved!)
