For this case we must find the quotient of the following expression:
![\frac {-8x ^ 6} {4x ^ {- 3}} =](https://tex.z-dn.net/?f=%5Cfrac%20%7B-8x%20%5E%206%7D%20%7B4x%20%5E%20%7B-%203%7D%7D%20%3D)
By definition of power properties we have:
![a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}](https://tex.z-dn.net/?f=a%20%5E%20%7B-%201%7D%20%3D%20%5Cfrac%20%7B1%7D%20%7Ba%20%5E%201%7D%20%3D%20%5Cfrac%20%7B1%7D%20%7Ba%7D)
Rewriting the expression we have:
![\frac{-8}{4}*x^6*x^3](https://tex.z-dn.net/?f=%5Cfrac%7B-8%7D%7B4%7D%2Ax%5E6%2Ax%5E3)
By definition of multiplication of powers of the same base we have to put the same base and add the exponents:
![-2x^{6+3}](https://tex.z-dn.net/?f=-2x%5E%7B6%2B3%7D)
Answer:
![-2x ^ 9](https://tex.z-dn.net/?f=-2x%20%5E%209)
The correct answer is: 27 .
________________________________
Explanation:
_________________________________
9^(3/2) = (√9)³ = 3³ = 3 * 3 * 3 = 27 .
____________________________________
Answer:
![s(t) = \frac{t^4}{12} - \frac{4t^3}{3} + \frac{7t^2}{2} + v_0t + s_0](https://tex.z-dn.net/?f=s%28t%29%20%3D%20%5Cfrac%7Bt%5E4%7D%7B12%7D%20-%20%5Cfrac%7B4t%5E3%7D%7B3%7D%20%2B%20%5Cfrac%7B7t%5E2%7D%7B2%7D%20%2B%20v_0t%20%2B%20s_0)
Step-by-step explanation:
We can first integrate the acceleration to find the velocity with respect to time
![v(t) = \int {a(t)} \, dt= \int {t^2 - 8t + 7} \, dt = \frac{t^3}{3} - 4t^2 + 7t +v_0](https://tex.z-dn.net/?f=v%28t%29%20%3D%20%5Cint%20%7Ba%28t%29%7D%20%5C%2C%20dt%3D%20%5Cint%20%7Bt%5E2%20-%208t%20%2B%207%7D%20%5C%2C%20dt%20%3D%20%5Cfrac%7Bt%5E3%7D%7B3%7D%20-%204t%5E2%20%2B%207t%20%2Bv_0)
Then we can integrate the velocity to find the position of the particle with respect to time:
![s(t) = \int {v(t)} \, dt = \int {(\frac{t^3}{3} - 4t^2 +7t + v_0)} \, dt = \frac{t^4}{12} - \frac{4t^3}{3} + \frac{7t^2}{2} + v_0t + s_0](https://tex.z-dn.net/?f=s%28t%29%20%3D%20%5Cint%20%7Bv%28t%29%7D%20%5C%2C%20dt%20%3D%20%5Cint%20%7B%28%5Cfrac%7Bt%5E3%7D%7B3%7D%20-%204t%5E2%20%2B7t%20%2B%20v_0%29%7D%20%5C%2C%20dt%20%3D%20%5Cfrac%7Bt%5E4%7D%7B12%7D%20-%20%5Cfrac%7B4t%5E3%7D%7B3%7D%20%2B%20%5Cfrac%7B7t%5E2%7D%7B2%7D%20%2B%20v_0t%20%2B%20s_0)
Answer:
The mean is 0.32 and the standard deviation is 0.0122.
Step-by-step explanation:
Given that the Tampa Times polled 1,457 adults in the city to determine whether they put on their shirt before they put on their pants.
Of the respondents, 48% said they put their shirt on first.
32% of all adults actually put their shirt on first
i.e. sample proportion is 48% while population proportion is 32%
Hence sampling distribution follows a distribution with mean = population proportion p
Hence here mean = 0.32
Std deviation of sampling distribution = ![\sqrt{\frac{pq}{n} } =\sqrt{\frac{0.32(0.68)}{1457} } \\=0.0122](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7Bpq%7D%7Bn%7D%20%7D%20%3D%5Csqrt%7B%5Cfrac%7B0.32%280.68%29%7D%7B1457%7D%20%7D%20%5C%5C%3D0.0122)
Hence option 3) The mean is 0.32 and the standard deviation is 0.0122.
is right
Answer:
1750
Step-by-step explanation:
We first find the rate
70/4
= 17.5
We know 17.5 is 1% of the people that read newspaper, we will multiply 17.5 by 100 as it would represent 100% of the people
17.5 * 100
= 1750