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djverab [1.8K]
2 years ago
5

Frederick designed an experiment in which he spun a spinner 20 times and recorded the results of each spin.He spun a 4 five time

s. Which statements are true? Choose all that apply.
A.For the experimental outcomes to be closer to the predicted outcome, the number of trials should be increased.
B.For the experimental outcomes to be closer to the predicted outcome, the number of trials should be decreased.
C.If the number of trials is changed, the experimental probability also changes.
D.If the number of trials is changed, the theoretical probability also changes.
E.If the number of trials is changed, the number of experimental outcomes also changes.

Mathematics
1 answer:
kogti [31]2 years ago
6 0
If the number of trials is changed the number of experimental outcomes also changes
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To graph it, just graph y=-3^{-x}-6 and y=-3^x+10 and see where they intersect

I would like to solve it by using math and not graphing
if you don't want to see the math, just don't scroll down
the graphical meathod is above, first line, just read it

hmm
multiply both sides by -1
3^{-x}+6=3^x-10
multiply both sides by 3^x
3^0+6(3^x)=3^{2x}-10(3^x)
1+6(3^x)=3^{2x}-10(3^x)
minus 1 from both sides and minus 6(3^x) from both sides
0=3^{2x}-16(3^x)-1
use u subsitution
u=3^x
we can rewrite it as
0=u^2-16u-1
now factor
I mean use quadratic formula
for ax^2+bx+c=0 x=\frac{-b+/-\sqrt{b^2-4ac}}{2a}
so for 0=u^2-16u-1, a=1, b=-16, c=-1
u=\frac{-(-16)+/-\sqrt{(-16)^2-4(1)(-1)}{2(1)}
u=8+/-\sqrt{65}
remember that u=3^x so u>0
if we have u=8+√65, it's fine, but u=8-√65 is negative and not allowed
so therfor
u=8+\sqrt{65}=3^x
8+\sqrt{65}=3^x
if you take the log base 3 of both sides you get
log_3(8+\sqrt{65})=x
if you use ln then
ln(8+\sqrt{65})=xln(3)
then
\frac{ln(8+\sqrt{65})}{ln(3)}=x

8 0
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Answer: B
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Answer:

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Step-by-step explanation:

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At the beginning of the business day, a bank's vault held $575,900. By the end of the day, $(3.5 103) had been added to the vaul
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