Answer:
See below for answers and explanations
Step-by-step explanation:
<u>Problem 1:</u>
A standard deck of cards contains 52 cards, consisting of 13 spades. If you select only one randomly, the probability of that occurring would be 13/52 or 1/4. Since there are only 26 red cards in a standard deck, then the probability of selecting a red card would be 26/52 or 1/2. Because the two events are independent of each other, their probabilities are multiplied. Therefore, the probability of selecting a spade, and then replacing it in hopes of drawing a red card is (1/2)(1/4) = 1/8.
<u>Problem 2:</u>
We are selecting a spade and then another spade while NOT replacing the first spade (remember that these events are independent of each other also). This means that the total card count will change by picking up the second card. Therefore, the probability of selecting a spade, followed by another spade, is (13/52)(12/51) = 156/2652 = 1/17.
The quadratic formula is ![\frac{-b+-\sqrt[2]{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%2B-%5Csqrt%5B2%5D%7Bb%5E2-4ac%7D%7D%7B2a%7D)
and in the equation ax^2+bx+c=0
so now all you have to do is substitute the numbers into the quadratic formula
<span>Susanne is 16 years old.</span>
b = Bob's age
s = Susanne's age
d = Dakota's age
Bob's age is 4 times greater than Susanne's age:
b = 4s
Dakota is three years younger than Susanne:
d = s - 3
The sum of Bob's, Susanne's, and Dakota's ages is 93:
b + s + d = 93
solve these equations:
b = 4s
d = s - 3
b + s + d = 93
and get:
b = 64 years
s = 16 years
(remember that s = Susanne)
d = 13 years
46395 is greater than (>) 14906
Answer:
Step-by-step explanation:
The parent function of this graph is: y = sin(x)
The sine function is periodic, meaning it repeats forever.
Standard form of a sine function:
- A = amplitude (height from the mid-line to the peak)
- 2π/B = period (horizontal distance between consecutive peaks)
- C = phase shift (horizontal shift - positive is to the left)
- D = vertical shift
The parent function y = sin(x) has the following:
- Amplitude (A) = 1
- Period = 2π
- Phase shift (C) = 0
- Vertical shift (D) = 0
- Mid-line: y = 0
From inspection of the given graph:
- Amplitude (A) = 1
- Phase shift (C) = 0
- Vertical shift (D) = +3 (as mid-line is y = 3)
Substituting the values into the standard form:
Therefore, the equation of the given trigonometric graph is:
