Answer:
Width = 16(√5) - 1
Step-by-step explanation:
We are told that the golden rectangle is 32 cm long.
Thus, length = 32 cm
We are also told that the ratio of the length to the width is; (1 + √5):2
Thus;
If a length of (1 + √5) yields a width of 2
Then, a length of 32 cm would yield a width of; (32 x 2)/(1 + √5)
So corresponding width = 64/(1 + √5)
We want to reduce this width to it's simplest radical form which means the denominator should have no square root.
Thus, let's multiply top and bottom by (1 - √5);
Width = 64 x (1 - √5)/[(1 + √5) x (1 - √5)]
Width = 64(1 - √5)/(1 - 5)
Width = 64(1 - √5)/(-4)
Width = -16(1 - √5)
Width = 16(√5 - 1)
Width = 16√5 - 1
We use the Markov's inequality to solve for (a) and (b)
P(X > 18) = 16/18 = 8/9 or 0.8888 or 8.88%
P(X > 25) = 16/25 = 0.64 or 64%
For c, we use the z-score with the standard deviation as the square root of the variance
σ = √9 = 3
z = (X - μ) / σ
The limits are 10 and 22
For 10, the z-score is:
z = (10 - 16) / 3 = -2
For 22
z = (22 - 16) / 3 = 2
We use the z-score table to get the corresponding probability of the two limits and subtract the smaller probability from the bigger probability to get the actual probability. So, from the z-score table:
for z = -2, P = 0.0228
for z = 2, P = 0.9772
0.9772 - 0.0228 = 0.9544
The probability is 0.9544 or 95.44%
For (d), we do the same thing but we subtract the obtained probability from 1 since the condition is that the sales exceed 18
z = (18 - 16) / 3 = 0.67 which correspond to P = 0.7486
1 - 0.7486 = 0.2514
The probability is 0.2514 or 25.14%
Answer:
The value of x is 14.
Step-by-step explanation:
Given;
mid-segment of the trapezoid = 11
The mid-segment of trapezoid is calculated as;
Therefore, the value of x is 14.
Answer:
The critical value of chi-square for 20 degrees of freedom and 0.01 level of significance is 37.57.
Step-by-step explanation:
We have to find the value of chi-square for 20 degrees of freedom an area of 0.01 in the right tail of the chi-square.
As we know that in the chi-square table; there is one vertical column represented by 'P' (the level of significance and one horizontal column represented by '' which is degrees of freedom.
Here, the degrees of freedom given to us is 20.
and the level of significance is 0.01 or 1% for the right tail of chi-square.
By looking at the chi-square table, the critical value of chi-square for 20 degrees of freedom and 0.01 level of significance is 37.57.
No, because the relation passes the vertical line test