The factors of the quadratic equation are (x+3) and (x-15).
<h2 /><h2>Given to us</h2>The factors of .
As we can see in the quadratic equation the value of ac is -45x². therefore, we need to divide -12x into two parts such that their sum must give -12x and their product gives us -45x².
therefore, dividing -12x into -15x and 3x,
Taking common out,
Hence, the factors of the quadratic equation are (x+3) and (x-15).
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Answer:
5040,56
Step-by-step explanation:
We have to construct pass words of 4 digits
a) None of the digits can be repeated
We have total digits as 0 to 9.
4 digits can be selected form these 10 in 10P4 ways (since order matters in numbers)
No of passwords = 10P4
=
b) start with 5 and end in even digit
Here we restrain the choices by putting conditions
I digit is compulsorily 5 and hence only one way
Last digit can be any one of 0,2,4,6,8 hence 5 ways
Once first and last selected remaining 2 digits can be selected from remaining 8 digits in 8P2 ways (order counts here)
=56
Answer:
We conclude that 50.
Step-by-step explanation:
We are given that x bar = 60, s = 12, n = 30, and alpha = 0.10
Also, Null Hypothesis, :
= 50
Alternate Hypothesis, :
50
The test statistics we will use here is;
T.S. = ~
where, X bar = sample mean = 60
s = sample standard deviation = 12
n = sample size = 30
So, Test statistics = ~
= 4.564
At 10% significance level, t table gives critical value of 1.311 at 29 degree of freedom. Since our test statistics is more than the critical value as 4.564 > 1.311 so we have sufficient evidence to reject null hypothesis as our test statistics will fall in the rejection region.
P-value is given by, P( > 4.564) = less than 0.05% {using t table}
Here also, P-value is less than the significance level as 0.05% < 10% , so we will reject null hypothesis.
Therefore, we conclude that 50.