Answer and Step-by-step explanation:
Solve for x.
Distribute the 2.
4x - 5 = 4x - 2 - 3
Combine like terms
4x - 5 = 4x - 5
Add 5, and subtract 4x.
0 = 0
There are infinitely many solutions, meaning any value plugged in for x will result in the equation being true.
<em><u>#teamtrees #PAW (Plant And Water)</u></em>
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:
There is not any solid evidence provided by Patrice to reject the fast food chain's claim.
Step-by-step explanation:
As Patrice weighs the next 16 random orders of onion rings before she eats them and finds the sample mean is 112.4 grams and the standard deviation is 7.63 grams so here
sample size = 16
sample mean = 112.4
standard deviation = 7.63
Formula for test statistic:
t = ( sample mean - weight ) / standard error of mean
Formula for standard error of mean:
standard error of mean = standard deviation / sqrt (sample size)
therefore by putting the values in the above formula, we get
standard error of mean = 7.63 / sqrt(16)
Now
t = ( 112.4-114 ) / ( 7.63 / sqrt(16) )
= -0.84
p-value = P (z < -0.84) = 0.201
Therefore it fails to reject null hypothesis because p-value > 0.1
Hence, there is not any solid evidence provided by Patrice to reject the fast food chain's claim.