Solve for x over the real numbers:
x^2 - 4 x = 5
Subtract 5 from both sides:
x^2 - 4 x - 5 = 0
x = (4 ± sqrt((-4)^2 - 4 (-5)))/2 = (4 ± sqrt(16 + 20))/2 = (4 ± sqrt(36))/2:
x = (4 + sqrt(36))/2 or x = (4 - sqrt(36))/2
sqrt(36) = sqrt(4×9) = sqrt(2^2×3^2) = 2×3 = 6:
x = (4 + 6)/2 or x = (4 - 6)/2
(4 + 6)/2 = 10/2 = 5:
x = 5 or x = (4 - 6)/2
(4 - 6)/2 = -2/2 = -1:
Answer: x = 5 or x = -1
We have that
(3√8)/(4√6)
we know that
√8---------> √(2³)-----> 2√2
so
(3√8)/(4√6)=(3*[2√2])/(4√6)---> 6√2/(4√6)
√6=√(2*3)---> √2*√3
6√2/(4√6)=6√2/(4√2*√3)----> 6/(4√3)----> 6/(4√3)*(√3/√3)-----> 6√3/(4*3)----> √3/2
the answer is
√3/2
We assume all employees are either full-time or part-time.
36 = 24 + 12
If the number of full-time employees is 24 or less, the number of part-time employees must be 12 or more. (Thinking, based on knowledge of sums.)
_____
You can write the inequality in two stages.
- First, write and solve an equation for the number of full-time employees in terms of the number of part-time employees.
- Then apply the given constraint on full-time employees. This gives an inequality you can solve for the number of part-time employees.
Let f and p represent the numbers of full-time and part-time employees, respectively.
... f + p = 36 . . . . . . given
... f = 36 - p . . . . . . . subtract p. This is our expression for f in terms of p.
... f ≤ 24 . . . . . . . . . given
... (36 -p) ≤ 24 . . . . substitute for f. Here's your inequality in p.
... 36 - 24 ≤ p . . . . add p-24
... p ≥ 12 . . . . . . . . the solution to the inequality
Answer:
h=48
Step-by-step explanation:
You should create an even proportion. So you could do seconds over heartbeats or the other way around. I decided to do the other way around. Since yu want to see h in m minutes and in a minute there are 60 seconds, I did 8/10 = h/60. Instead of cross multiplying, I saw that 10 times 6 is 60 so 8 x 6=h. 8 x 6 = 48 so h=48.
Answer:
The minimum height in the top 15% of heights is 76.2 inches.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean 
and standard deviation 
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
Find the minimum height in the top 15% of heights.
This is the value of X when Z has a pvalue of 0.85. So it is X when Z = 1.04.
The minimum height in the top 15% of heights is 76.2 inches.
