Answer:
y = 2x - 12
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange 3 + 4x = 2y - 9 into this form
add 9 to both sides
12 + 4x = 2y ( divide all terms by 2 )
6 + 2x = y ← in slope- intercept form
with slope m = 2
• Parallel lines have equal slopes, hence
y = 2x + c ← is the partial equation of the parallel line
To find c substitute (4, - 4) into the partial equation
- 4 =8 + c ⇒ c = - 4 - 8 = - 12
y = 2x - 12 ← equation of parallel line
Answer:
f(g(-3))= 17.
Step-by-step explanation:
Start evaluating from the inside and work your way out. This means you start with (-3)²=9. Then go and plug that answer in to the equation f(x). f(9)=2(9)-1=17.
Answer:
0.750714286
Step-by-step explanation:
Question 1:
A = w * l
A = 5432m^2
l = 97
A / l = w
5432 / 97 = 56
w = 56
Question 2:
Perimeter of rectangle = 2w + 2l
P = 336
w = 79
P - 2w = 2l
336 - 158 = 178
178 / 2 = 89
l = 89
Cards are drawn, one at a time, from a standard deck; each card is replaced before the next one is drawn. Let X be the number of draws necessary to get an ace. Find E(X) is given in the following way
Step-by-step explanation:
- From a standard deck of cards, one card is drawn. What is the probability that the card is black and a
jack? P(Black and Jack) P(Black) = 26/52 or ½ , P(Jack) is 4/52 or 1/13 so P(Black and Jack) = ½ * 1/13 = 1/26
- A standard deck of cards is shuffled and one card is drawn. Find the probability that the card is a queen
or an ace.
P(Q or A) = P(Q) = 4/52 or 1/13 + P(A) = 4/52 or 1/13 = 1/13 + 1/13 = 2/13
- WITHOUT REPLACEMENT: If you draw two cards from the deck without replacement, what is the probability that they will both be aces?
P(AA) = (4/52)(3/51) = 1/221.
- WITHOUT REPLACEMENT: What is the probability that the second card will be an ace if the first card is a king?
P(A|K) = 4/51 since there are four aces in the deck but only 51 cards left after the king has been removed.
- WITH REPLACEMENT: Find the probability of drawing three queens in a row, with replacement. We pick a card, write down what it is, then put it back in the deck and draw again. To find the P(QQQ), we find the
probability of drawing the first queen which is 4/52.
- The probability of drawing the second queen is also 4/52 and the third is 4/52.
- We multiply these three individual probabilities together to get P(QQQ) =
- P(Q)P(Q)P(Q) = (4/52)(4/52)(4/52) = .00004 which is very small but not impossible.
- Probability of getting a royal flush = P(10 and Jack and Queen and King and Ace of the same suit)
