2x+4y=1 3x-5y=7 solve the simultaneous equations
1 answer:
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Answer:
Probability that next week's show will have between 30 and 37 million viewers is 0.2248.
Step-by-step explanation:
We are given that the distribution of the number of viewers for the American Idol television show follows a normal distribution with a mean of 26 million with a standard deviation of 8 million.
<em>Let X = number of viewers for the American Idol television show</em>
So, X ~ N()
Now, the z score probability distribution is given by;
Z = ~ N(0,1)
where, = population mean = 26 million
= standard deviation = 8 million
So, probability that next week's show will have between 30 and 37 million viewers is given by = P(30 < X < 37) = P(X < 37) - P(X 30)
P(X < 37) = P( <
) = P(Z < 1.38) = 0.91621
P(X 30) = P(
) = P(Z
0.50) = 0.69146
<em>Therefore, P(30 < X < 37) = 0.91621 - 0.69146 = 0.2248</em>
Hence, probability that next week's show will have between 30 and 37 million viewers is 0.2248.
Tow rates are equivalent if tow initial investments over a the same time, produce the same final value using different interest rates.
For the annually rate we have that:
Where
= initial investment.
= annually interest rate in decimal form.
And the exponent (1) represents the full year.
For the quarterly interest rate we have that:
Where
= initial investment.
= quarterly interest rate in decimal form.
And the exponent (4) the 4 quarters in the full year.
Since the rates are equivalent if tow initial investments over a the same time, produce the same final value, then
Notice that we are not using the initial investment
since they are the same.
The first thin we are going to to calculate the equivalent quarterly rate of the 7% annually rate is converting 7% to decimal form
7%/100 = 0.07
Now, we can replace the value in our equation to get:
![\sqrt[4]{1.07} =1+ i_{q}](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%7B1.07%7D%20%3D1%2B%20i_%7Bq%7D%20)
![i_{q} = \sqrt[4]{1.07} -1](https://tex.z-dn.net/?f=%20i_%7Bq%7D%20%3D%20%5Csqrt%5B4%5D%7B1.07%7D%20-1)
Finally, we multiply the quarterly interest rate in decimal form by 100% to get:
(0.017)(100%) = 1.7%
We can conclude that Alexander is wrong, the equivalent quarterly rate of an annually rate of 7% is 1.7% and not 2%.
For the annually rate we have that:
Where
And the exponent (1) represents the full year.
For the quarterly interest rate we have that:
Where
And the exponent (4) the 4 quarters in the full year.
Since the rates are equivalent if tow initial investments over a the same time, produce the same final value, then
Notice that we are not using the initial investment
The first thin we are going to to calculate the equivalent quarterly rate of the 7% annually rate is converting 7% to decimal form
7%/100 = 0.07
Now, we can replace the value in our equation to get:
Finally, we multiply the quarterly interest rate in decimal form by 100% to get:
(0.017)(100%) = 1.7%
We can conclude that Alexander is wrong, the equivalent quarterly rate of an annually rate of 7% is 1.7% and not 2%.