The key to solving this problem is to represent the four consecutive numbers correctly. They are x, x+1, x+2 and x+3. Add them up and equate the sum to 86.
Compare both sides,
x² - x - 1 = 2 - 3x
x² + 2x - 3 = 0
x² -x + 3x - 3 = 0
x(x - 1) 3(x - 1) = 0
(x - 1)(x+3) = 0
x = 1 or - 3
In short, Your Answers would be 1 & -3
Hope this helps!
Answer:
The p-value for this hypothesis test is P=0.015.
Step-by-step explanation:
In this case we have hypothesis test for the mean, with standard deviation of the population unknown.
The null hypothesis we want to test is
To work with this test we have a sample of size n=20, sample mean=91 and sample standard deviation=21.
First, we estimate the standard deviation of the population
Then, because we have an estimated standard deviation, we have to calculate the statistics t.
We can look up this value of t in a t-table to know the probability of this value, taking into account 19 degrees of freedom:
The p-value or the probability of P(t>2.342) is 0.01511.
This value P=0.0151 is compared to the significance level (0.05). Since the probability value (0.0151) is less than the significance level (0.05) the effect is statistically significant. Since the effect is significant, the null hypothesis is rejected.
Answer:
To prove:
X+Y.Z=(X+Y).(X+Z)
Taking R.H.S
= (X+Y).(X+Z)
By distributive law
= X.X+X.Z+X.Y+Y.Z --- (1)
From Boolean algebra
X.X = X
X.Y+X.Z = X.(Y+Z)
Using these in (1)
=X+X(Y+Z)+Y.Z
=X(1+(Y+Z)+Y.Z --- (2)
As we know (1+X) = 1
Then (2) becomes
=X.1+Y.Z
=X+Y.Z
Which is equal to R.H.S
Hence proved,
X+Y.Z=(X+Y).(X+Z)