All you have to do is substitute the y value from the 1st equation into the second equation and solve...
a) y= 2-x
5x + 4y = 5
Substitute (2-x) into the second equation anywhere there is a y...
5x + 4y = 5
5x + 4(2-x) = 5
Now solve
5x + 8 - 4x = 5
5x - 4x + 8 = 5
x + 8 = 5
x = -3
Now that you have a solution for x, substitute -3 into either of the original equations anywhere there is an x then solve for y...
y = 2 - x
y = 2 - (-3)
y = 2+3 = 5
You solved for x and got -3 and solved for y and got 5, so your solution set is
(-3, 5).
Now check it by substituting both numbers into one of the original equations and you should have a true statement if it is correct...
y = 2 - x
5 = 2 - (-3)
5 = 2+3
5 = 5
True statement... it checks!
note* during the check, if the equation would have worked out to something like 2 = 5, then that is a false statement therefore the solution set would be wrong and you'd have to go back and find the mistake.
Answer:
9.2
Step-by-step explanation:
Since it is a right triangle, you can use the Pythagorean theorem to find the third side which is the hypotenuse.
a^2 + b^2 = c^2
7^2 + 6^2 = c^2
49 + 36 = c^2
85 = c^2
9.219 = C
So, the answer rounded to the nearest tenth would be: 9.2
Answer:
answe is 1+i
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Binomial distribution will be used to model situation because all following criteria are satisfied:
1. Bernoulli trials, i.e. exactly two possible outcomes (show up or not)2. Number of trials is known before and constant throughout the experiment, i.e. independent of outcomes (150 booked)3. All trials are independent of each other. (assumed from context)4. Probability of success is known, and remain constant throughout trials. (85%)Since all criteria are satisfied, we can model with binomial distribution, where the probability of x successes out of N trials each with probability of success p is given byP(x)=C(N,x)(p^x)(1-p)^(N-x)and,C(N,x) is number of combinations of selecting x objects out of N.
P(>140)=P(141)+P(142)+...+P(150)
=.00035620+0.00012783+0.00004056+0.00001117+0.00000262+0.00000051+0.00000008+0.00000001+0.00000000
=0.00053907
The above calculation is not very practical unless we have a statistical calculator or a software.
For practical hand calculations, we usually use the binomial approximation.
mean=np=150*0.85=127.5
variance = np(1-p)=150*.85*.15=19.125 (>10, possible to use binomial approximation, but accuracy is marginal).
We also need to use the continuity correction, which means that the portion above 140 is counted as 140.5 to 150 passengers. Then we calculate
Z=(140.5-127.5)/sqrt(19.125)=2.973
P(x>=140.5)
=P(z>=Z)
=1-P(z<Z)
=1-P(z<2.973)
=1-0.99852
=0.00148
The answer is quite a bit off from the exact value of 0.000539, but an approximation is an approximation especially for skew distribution like in the present case (p=0.85 far from 0.5, and x=140 far from mean).
Answer:
$100
Step-by-step explanation:
$100 because, you are showing that you can pay of what you spent, quickly and responsibly, this will increase your credit and you will likely be able to take loans more often from that same place because they "trust" you.
