Use factoring to solve the quadratic equation. Check by substitution or by using a graphing utility and identifying x-intercepts
1 answer:
9514 1404 393
Answer:
x = -1/2, x = 7
Step-by-step explanation:
Written in standard form, the equation is ...
2x² -13x -7 = 0
We observe that factors of (2)(-7) that have a sum of -13 are -14 and +1. Rewriting the middle term using these numbers, we have ...
2x² -14x +x -7 = 0
2x(x -7) +1(x -7) = 0 . . . . . factor pairs of terms
(2x +1)(x -7) = 0 . . . . . . . . factored form
The solutions are the values of x that make these factors zero.
2x +1 = 0 ⇒ x = -1/2
x -7 = 0 ⇒ x = 7
The solutions to the quadratic are x = -1/2 and x = 7.
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Answer:
Probability that their mean credit card balance is less than $2500 is 0.0073.
Step-by-step explanation:
We are given that a bank auditor claims that credit card balances are normally distributed, with a mean of $3570 and a standard deviation of $980.
You randomly select 5 credit card holders.
Let<em> </em><em> = </em><u><em>sample mean credit card balance</em></u>
The z score probability distribution for sample mean is given by;
Z = ~ N(0,1)
where, = population mean credit card balance = $3570
= standard deviation = $980
n = sample of credit card holders = 5
Now, the probability that their mean credit card balance is less than $2500 is given by = P(<em> </em>< $2500)
P(<em> </em>< $2500) = P(
<
) = P(Z < -2.44) = 1 - P(Z
2.44)
= 1 - 0.9927 = 0.0073
The above probability is calculated by looking at the value of x = 2.44 in the z table which has an area of 0.9927.
Therefore, probability that their mean credit card balance is less than $2500 is 0.0073.