Answer: The proof is mentioned below.
Step-by-step explanation:
Here, Given : m∠AOC = 160° m∠AOD= (3x-10)° and m∠ DOC= (x+14)°
Prove: x= 39°
Statement Reason
1. m∠AOC = 160°, m∠AOD= (3x-10)° 1. Given
and m∠ DOC= (x+14)°
2. m∠AOD+m∠DOC=m∠AOC 2. Because OD divides ∠AOC
into ∠AOD and ∠DOC
3. (3x-10)° +(x+14)°= 160° 3. By substitution
4. 4x+4 = 160° 4. By equating like terms
5. 4x= 156° 5. By subtraction property
of equality
6. x= 39° 6. By division property of equality
Answer:
The correct answer has already been given (twice). I'd like to present two solutions that expand on (and explain more completely) the reasoning of the ones already given.
One is using the hypergeometric distribution, which is meant exactly for the type of problem you describe (sampling without replacement):
P(X=k)=(Kk)(N−Kn−k)(Nn)
where N is the total number of cards in the deck, K is the total number of ace cards in the deck, k is the number of ace cards you intend to select, and n is the number of cards overall that you intend to select.
P(X=2)=(42)(480)(522)
P(X=2)=61326=1221
In essence, this would give you the number of possible combinations of drawing two of the four ace cards in the deck (6, already enumerated by Ravish) over the number of possible combinations of drawing any two cards out of the 52 in the deck (1326). This is the way Ravish chose to solve the problem.
Another way is using simple probabilities and combinations:
P(X=2)=(4C1∗152)∗(3C1∗151)
P(X=2)=452∗351=1221
The chance of picking an ace for the first time (same as the chance of picking any card for the first time) is 1/52, multiplied by the number of ways you can pick one of the four aces in the deck, 4C1. This probability is multiplied by the probability of picking a card for the second time (1/51) times the number of ways to get one of the three remaining aces (3C1). This is the way Larry chose to solve the this.
Step-by-step explanation:
Answer: the second option !!!
Answer:
(4,11)
Step-by-step explanation:
y=2x+3
y=5x-9
the first equation is equal to the second equation so
2x+3=5x-9
put like terms together
2x-5x= -9-3
-3x= -12
divide both sides by -3
.•.x=4
now, use the value of x to find the value of y like this:
y=2x+3 (x=4)
y=2(4)+3
y=8+3
y=11
therefore, the two lines intersect at the point (4,11)
The equation that shows the relationship between x and y is:
y = 5x
A linear equation is in the form:
y = mx + b
where m is the rate of change and b is the initial value of y, y, x are variables.
Let x represent the number of nights knitting and y represent the length of the scarf.
The equation that shows the relationship between x and y is:
y = 5x
Find out more at: brainly.com/question/13911928
