Thomas invested $8,500 for one year. Part of the money was invested at6% and the rest at 9%. The total interest earned was $667.
1 answer:
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If there are real roots to be found for this polynomial, the Rational Root Theorem and synthetic division are the best way to find them. I teach from a book that uses c and d for the possible roots of the polynomial. C is our constant, 2, and d is the leading coefficient, 1. The factors of 2 are +/- 1 and +/-2. The factors for 1 are +/-1 only. Meaning, in all, there are 4 possibilities as roots for this polynomial. But there are only 3 total (because our polynomial is a third degree), so we have to find the first one, at least, from our possibilities above. Let's try x = -1, factor form (x + 1). If there is no remainder when we do the synthetic division, then -1 is a root. Put -1 outside the "box" and the coefficients from the polynomial inside: -1 (1 2 -1 -2). Bring down the first coefficient of 1 and multiply it by the -1 outside to get -1. Put that -1 up under the 2 and add to get 1. Multiply 1 times the -1 to get -1 and put that -1 up under the -1 and add to get -2. -1 times -2 is 2, and -2 + 2 = 0. So we have our first root of (x+1). The numbers we get when we do the addition along the way are the coefficients of our new polynomial, the depressed polynomial (NOT a sad one cuz it hates math, but a new polynomial that is one degree less than that of which we started!). The new polynomial is 
. That can also be factored to find the remaining 2 roots. Use standard factoring to find that the other 2 solutions are (x+2) and (x-1). Our solutions then are x = -2, -1, 1, choice B from above.
Answer:
P(6) = 0.6217
Step-by-step explanation:
To find P(6), which is the probability of getting a 6 or less, we will need to first calculate two things: the mean of the sample (also known as the "expected value") and the standard deviation of the sample.
Mean = np
Here, "n" is the sample size and "p" is the probability of the outcome of interest, which could be getting a heads when a tossing a coin, for instanc
So, Mean = n × p = (18) ×(0.30) = 5.4
Next we we will find the standard deviation:
Standard Deviation =
n = 18 and p = 0.3 "q" is simply the probability of the other possible outcome (maybe getting a tails when flipping a coin), so q = 1 - p
Standard Deviation =
= 1.944
Now calculate the Z score for 6 successes.
Z = ( of successes we're interested in - Mean) ÷ (Standard Deviation)
=(6-5.4) ÷ (1.944) = 0.309
we have our Z-score, we look on the normal distribution and find the area of the curve to the left of a Z value of 0.309. This is basically adding up all of the possibilities for getting less than or equal to 6 successes. So, we get 0.6217.