Answer:
See below.
Step-by-step explanation:
(a) Because the solution led to a square root of a negative number:
x^2 -10x+40=0
x^2 - 10x = -40 Completing the square:
(x - 5)^2 - 25 = -40
(x - 5)^2 = -15
x = 5 +/-√(-15)
There is no real square root of -15.
(b) A solution was found by introducing the operator i which stands for the square root of -1.
So the solution is
= 5 +/- √(15) i.
These are called complex roots.
(c) Substituting in the original equation:
x^2 - 10 + 40:
((5 + √(-15)i)^2 - 10(5 + √(-15)i) + 40
= 25 + 10√(-15)i - 15 - 50 - 10√(-15)i + 40
= 25 - 15 - 50 + 40
= 0. So this checks out.
Now substitute 5 - √(-15)i
= 25 - 10√(-15)i - 15 - 50 + 10√(-15)i + 40
= 25 - 15 - 50 + 40
= 0. This checks out also.
ANSWER:
3 jjjjjjjjjjjjjjjlkkn buy4fref7g8f7f3g87egf87ewdc7cc wc68efce ewtedg67cccf6cw6f6cfefecec c e6ve6 ev fve
Answer:
$18
Step-by-step explanation:
Buying the jeans for $27 leaves you with ($60 - $27), or $33.
Buying the shirt for s dollar leaves you with $15. To find s, the price of the shirt, you subtract $15 from $33: $18.
The shirt cost you $18.
Answer:
0.00621
Step-by-step explanation:
To solve for this question: we would be making use of the z score formula.
z = (x - μ)/σ
where
x is the raw score
μ is the population mean
σ is the population standard deviation
Step 1
Find the Standard Error
From the above question, we are given number of samples, hence, the standard deviation we would use for our z score is Standard error.
Standard error = Standard deviation/√n
Where n = number of samples = 25
Standard deviation = 4
Standard error = 4/√25
= 4/5
= 0.8
Step 2
Calculate the z score
Since we are given number of samples in the question,
z score = z = (x - μ)/σ
where
x is the raw score = 14
μ is the population mean = 12
σ is the standard error = 0.8
z score = 14 - 12/0.8
z score = 2.5
Step 3
We find the Probability.
The probability that a randomly selected sample of 25 students will consume on average more than 14 pizzas per month is calculated as:
We find the Probability of the Z score 2.5 using a Z table.
P(z = 2.5) = P(x ≤ 14) = 0.99379
P(x > 14) = 1 - P(x<14)
= 1 - 0.99379
= 0.0062097
Approximately ≈ 0.00621
Therefore, the probability that a randomly selected sample of 25 students will consume on average more than 14 pizzas per month is
0.00621
