Answer:
In that one week, his commision was $896, over all 52 weeks, he made $46592
Step-by-step explanation:
So, he makes 14% commision on any stock he sells. This week, he sold $6,400 worth of stocks, and, hes going to make 14% on it. So, take 6400 and divide that by 14%, and what do you get? $896! So, he made $896 that week. Now, say he made that amount EVERY WEEK. so, all you have to do is know how many weeks are in a year (52) and multiply that by 896, which gives you 46592.
Answer:
Given the equation: ![3x^2+10x+c =0](https://tex.z-dn.net/?f=3x%5E2%2B10x%2Bc%20%3D0)
A quadratic equation is in the form:
where a, b ,c are the coefficient and a≠0 then the solution is given by :
......[1]
On comparing with given equation we get;
a =3 , b = 10
then, substitute these in equation [1] to solve for c;
![x_{1,2} = \frac{-10\pm \sqrt{10^2-4\cdot 3 \cdot c}}{2 \cdot 3}](https://tex.z-dn.net/?f=x_%7B1%2C2%7D%20%3D%20%5Cfrac%7B-10%5Cpm%20%5Csqrt%7B10%5E2-4%5Ccdot%203%20%5Ccdot%20c%7D%7D%7B2%20%5Ccdot%203%7D)
Simplify:
![x_{1,2} = \frac{-10\pm \sqrt{100- 12c}}{6}](https://tex.z-dn.net/?f=x_%7B1%2C2%7D%20%3D%20%5Cfrac%7B-10%5Cpm%20%5Csqrt%7B100-%2012c%7D%7D%7B6%7D)
Also, it is given that the difference of two roots of the given equation is
i.e,
![x_1 -x_2 = \frac{14}{3}](https://tex.z-dn.net/?f=x_1%20-x_2%20%3D%20%5Cfrac%7B14%7D%7B3%7D)
Here,
, ......[2]
.....[3]
then;
![\frac{-10 + \sqrt{100- 12c}}{6} - (\frac{-10 + \sqrt{100- 12c}}{6}) = \frac{14}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B-10%20%2B%20%5Csqrt%7B100-%2012c%7D%7D%7B6%7D%20-%20%28%5Cfrac%7B-10%20%2B%20%5Csqrt%7B100-%2012c%7D%7D%7B6%7D%29%20%3D%20%5Cfrac%7B14%7D%7B3%7D)
simplify:
![\frac{2 \sqrt{100- 12c} }{6} = \frac{14}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B2%20%5Csqrt%7B100-%2012c%7D%20%7D%7B6%7D%20%3D%20%5Cfrac%7B14%7D%7B3%7D)
or
![\sqrt{100- 12c} = 14](https://tex.z-dn.net/?f=%5Csqrt%7B100-%2012c%7D%20%3D%2014)
Squaring both sides we get;
![100-12c = 196](https://tex.z-dn.net/?f=100-12c%20%3D%20196)
Subtract 100 from both sides, we get
![100-12c -100= 196-100](https://tex.z-dn.net/?f=100-12c%20-100%3D%20196-100)
Simplify:
-12c = -96
Divide both sides by -12 we get;
c = 8
Substitute the value of c in equation [2] and [3]; to solve ![x_1 , x_2](https://tex.z-dn.net/?f=x_1%20%2C%20x_2)
![x_1 = \frac{-10 + \sqrt{100- 12\cdot 8}}{6}](https://tex.z-dn.net/?f=x_1%20%3D%20%5Cfrac%7B-10%20%2B%20%5Csqrt%7B100-%2012%5Ccdot%208%7D%7D%7B6%7D)
or
or
![x_1 = \frac{-10 + \sqrt{4}}{6}](https://tex.z-dn.net/?f=x_1%20%3D%20%5Cfrac%7B-10%20%2B%20%5Csqrt%7B4%7D%7D%7B6%7D)
Simplify:
![x_1 = \frac{-4}{3}](https://tex.z-dn.net/?f=x_1%20%3D%20%5Cfrac%7B-4%7D%7B3%7D)
Now, to solve for
;
![x_2 = \frac{-10 - \sqrt{100- 12\cdot 8}}{6}](https://tex.z-dn.net/?f=x_2%20%3D%20%5Cfrac%7B-10%20-%20%5Csqrt%7B100-%2012%5Ccdot%208%7D%7D%7B6%7D)
or
or
![x_2 = \frac{-10 - \sqrt{4}}{6}](https://tex.z-dn.net/?f=x_2%20%3D%20%5Cfrac%7B-10%20-%20%5Csqrt%7B4%7D%7D%7B6%7D)
Simplify:
![x_2 = -2](https://tex.z-dn.net/?f=x_2%20%3D%20-2)
therefore, the solution for the given equation is:
and -2.
By definition, the formula of the period of a pendulum is given by:
From here, we must clear the value of l.
We have then:
Raising both members to the square we have:
Then, passing gravity to multiply, we have:
Answer:
When clearing we have:
Answer:
300 miles / 6 hours = 50 miles/hour
Choice a) is correct
Step-by-step explanation:
Using it's concept, the experimental probability that in a group of 4 students, at least one of them has green eyes is of 0.45 = 45%.
<h3>What is a probability?</h3>
A probability is given by the <u>number of desired outcomes divided by the number of total outcomes</u>. An experimental probability is calculated considering the results of previous trials.
In this problem, there were 20 trials. The digit 9, which represents a student with green eyes, appears at least once in 9 of the the trials, hence the probability is:
p = 9/20 = 0.45 = 45%.
More can be learned about probabilities at brainly.com/question/14398287
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