Answer:
$10.19
Step-by-step explanation:
We are told:
If the mean of 20 prices is $10.39
We have to find the total price
= Mean × number of prices
= 20 × $10.39
= $207.8
5 of the items with a mean of $10.99 are sampled
We would also find the total price
Mean × Number of samples
$10.99 × 5
= $54.95
what is the mean of the other 15 prices?
We find the total prices of the 15 prices
= Total 20 prices - Total of 5 prices
= $207.8 - $54.95
= $152.85
The mean of the other 15 prices
= $152.85/15
= $10.19
Answer:
8x⁴ - 7x³ + 12x
Step-by-step explanation:
=(4x⁴ + 7x + 5x³) + (8x⁴ + 6x³ - 3x)- (4x⁴ + 4x³ - 8x)
=4x⁴ + 7x + 5x³ + 8x⁴ + 6x³ - 3x - 4x⁴ - 4x³ + 8x
=4x⁴ + 8x⁴ - 4x⁴+ <em>5x³ + 6x³ - 4x³</em> + <u>7x - 3x + 8x</u>
=8x⁴ + 7x³ + 12x
Answer: The required probability is 22.5%.
Step-by-step explanation:
Since we have given that
Probability of radio listeners live in Waterville = 0.75
Probability of radio listeners live in Newport = 0.25
Probability of radio station KTBC in Waterville = 0.20
Probability of radio station KTBC in Newport = 0.30
So, using "Multiplication rule of Probability":
Probability that the listener will be tuned in to station KTBC is given by
![0.75\times 0.20+0.25\times 0.30\\\\=0.15+0.075\\\\=0.225\\\\=22.5\%](https://tex.z-dn.net/?f=0.75%5Ctimes%200.20%2B0.25%5Ctimes%200.30%5C%5C%5C%5C%3D0.15%2B0.075%5C%5C%5C%5C%3D0.225%5C%5C%5C%5C%3D22.5%5C%25)
Hence, the required probability is 22.5%.
Personally, I would recommend reading this as a fraction, and splitting up mantissa from the power of 10. (Mantissa refers to the number 1.23 in
.)
![\left(3.6 \times 10^{-5}\right) \div \left(9 \times 10^{-7}\right) = \dfrac{3.6 \times 10^{-5}}{9 \times 10^{-7}} = \dfrac{3.6}9 \times \dfrac{10^{-5}}{10^{-7}}](https://tex.z-dn.net/?f=%5Cleft%283.6%20%5Ctimes%2010%5E%7B-5%7D%5Cright%29%20%5Cdiv%20%5Cleft%289%20%5Ctimes%2010%5E%7B-7%7D%5Cright%29%20%3D%20%5Cdfrac%7B3.6%20%5Ctimes%2010%5E%7B-5%7D%7D%7B9%20%5Ctimes%2010%5E%7B-7%7D%7D%20%3D%20%5Cdfrac%7B3.6%7D9%20%5Ctimes%20%5Cdfrac%7B10%5E%7B-5%7D%7D%7B10%5E%7B-7%7D%7D)
Now just reduce each fraction:
![\dfrac{3.6}9 = \dfrac{36}{90} = \dfrac25 = 0.4](https://tex.z-dn.net/?f=%5Cdfrac%7B3.6%7D9%20%3D%20%5Cdfrac%7B36%7D%7B90%7D%20%3D%20%5Cdfrac25%20%3D%200.4)
![\dfrac{10^{-5}}{10^{-7}} = 10^{-5-(-7)} = 10^{-5+7} = 10^2](https://tex.z-dn.net/?f=%5Cdfrac%7B10%5E%7B-5%7D%7D%7B10%5E%7B-7%7D%7D%20%3D%2010%5E%7B-5-%28-7%29%7D%20%3D%2010%5E%7B-5%2B7%7D%20%3D%2010%5E2)
So
![\left(3.6 \times 10^{-5}\right) \div \left(9 \times 10^{-7}\right) = 0.4 \times 10^2 = \boxed{4 \times 10^1}](https://tex.z-dn.net/?f=%5Cleft%283.6%20%5Ctimes%2010%5E%7B-5%7D%5Cright%29%20%5Cdiv%20%5Cleft%289%20%5Ctimes%2010%5E%7B-7%7D%5Cright%29%20%3D%200.4%20%5Ctimes%2010%5E2%20%3D%20%5Cboxed%7B4%20%5Ctimes%2010%5E1%7D)
since
.
Sum of two sides of triangle always greater than third side, so third side (x) could be:
14 < x < 32