Determine the number of real solutions each quadratic equation has. y = 12x2 - 9x 4
2 answers:
ANSWER
The quadratic function,
has no real roots.
EXPLANATION
We use the discriminant,
to determine the nature of the roots of a quadratic equation.
If we compare
to
Then
We substitute these values in to the formula for the discriminant, to obtain,
This implies that,
Since the discriminant is zero, the quadratic function,
has no real roots.
The quadratic function,
has no real roots.
EXPLANATION
We use the discriminant,
to determine the nature of the roots of a quadratic equation.
If we compare
to
Then
We substitute these values in to the formula for the discriminant, to obtain,
This implies that,
Since the discriminant is zero, the quadratic function,
has no real roots.
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Answer:
5) 203.35
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The average service time for McDonald's is 203.21 seconds with a standard deviation of 5.67 seconds.
This means that
Sample of 90
This means that
There is a 51% chance that the average drive-thru service time is less than ________ seconds.
X when Z is in the 51st percentile, that is, has a p-value of 0.51, so X when Z = 0.025.
By the Central Limit Theorem
203.35 seconds.
Answer:
The original duration of the tour = 20 days
Step-by-step explanation:
Solution:
Total expenses for the tour = $360
Let the original tour duration be for days.
So, for days the total expense = $360
<em>Thus the daily expense in dollars can be given by</em> =
Tour extension and effect on daily expenses.
The tour is extended by 4 days.
<em>Tour duration now</em> = days
On extension, his daily expense is cut by $3
<em>New daily expense in dollars </em>=
Total expense in dollars can now be given as:
Simplifying by using distribution (FOIL).
We know total expense remains the same which is = $360.
So, we have the equation as:
Multiplying each term with to remove fractions.
Subtracting both sides
Dividing each term with -3.
Adding both sides.
Solving using quadratic formula.
For a quadratic equation:
Plugging in values from the equation we got.
So, we have
and
and
∴ and
Since number of days cannot be negative, so we take as the solution for the equation.
Thus, the original duration of the tour = 20 days