Without a diagram, one must make certain assumptions about this problem. If and only if these three angles are the interior angles of a triangle, then their sum must be 180 degrees, so that 18x+12 + 6y + 3x+4y = 180. Unfortunately, this is a single equation in 2 unknowns. Thus, we cannot solve for an explicit value for either x or y.
If there was a diagram, please share it; otherwise, describe the triangle in words as best you can.
To find the X intercept, make Y equal to 0. To find the Y intercept, make X equal to 0.
5x - 2(0) = 20
5x = 20
x = 4
5(0) - 2y = 20
-2y = 20
y = -10
Answer:
The probability is ![P( p < 0.9207) = 0.0012556](https://tex.z-dn.net/?f=P%28%20p%20%3C%20%200.9207%29%20%3D%200.0012556)
Step-by-step explanation:
From the question we are told
The population proportion is ![p = 0.96](https://tex.z-dn.net/?f=p%20%3D%200.96)
The sample size is ![n = 227](https://tex.z-dn.net/?f=n%20%20%3D%20%20227)
The number of graduate who had job is k = 209
Generally given that the sample size is large enough (i.e n > 30) then the mean of this sampling distribution is
![\mu_x = p = 0.96](https://tex.z-dn.net/?f=%5Cmu_x%20%3D%20p%20%3D%200.96)
Generally the standard deviation of this sampling distribution is
![\sigma = \sqrt{\frac{p (1 - p )}{n} }](https://tex.z-dn.net/?f=%5Csigma%20%20%3D%20%5Csqrt%7B%5Cfrac%7Bp%20%281%20-%20p%20%29%7D%7Bn%7D%20%7D)
=> ![\sigma = \sqrt{\frac{0.96 (1 - 0.96 )}{227} }](https://tex.z-dn.net/?f=%5Csigma%20%20%3D%20%5Csqrt%7B%5Cfrac%7B0.96%20%281%20-%200.96%20%29%7D%7B227%7D%20%7D)
=> ![\sigma = 0.0130](https://tex.z-dn.net/?f=%5Csigma%20%20%3D%200.0130)
Generally the sample proportion is mathematically represented as
![\^ p = \frac{k}{n}](https://tex.z-dn.net/?f=%5C%5E%20p%20%3D%20%20%5Cfrac%7Bk%7D%7Bn%7D)
=> ![\^ p = \frac{209}{227}](https://tex.z-dn.net/?f=%5C%5E%20p%20%3D%20%20%5Cfrac%7B209%7D%7B227%7D)
=> ![\^ p = 0.9207](https://tex.z-dn.net/?f=%5C%5E%20p%20%3D%20%200.9207)
Generally probability of obtaining a sample proportion as low as or lower than this, if the university’s claim is true, is mathematically represented as
![P( p < 0.9207) = P( \frac{\^ p - p }{\sigma } < \frac{0.9207 - 0.96}{0.0130 } )](https://tex.z-dn.net/?f=P%28%20p%20%3C%20%200.9207%29%20%3D%20P%28%20%5Cfrac%7B%5C%5E%20p%20-%20p%20%7D%7B%5Csigma%20%7D%20%3C%20%20%5Cfrac%7B0.9207%20-%200.96%7D%7B0.0130%20%7D%20%20%29)
![P( p < 0.9207) = P(Z< -3.022 )](https://tex.z-dn.net/?f=P%28%20p%20%3C%20%200.9207%29%20%3D%20P%28Z%3C%20-3.022%20%29)
From the z table the area under the normal curve to the left corresponding to -3.022 is
![P(Z< -3.022 ) = 0.0012556](https://tex.z-dn.net/?f=P%28Z%3C%20-3.022%20%29%20%3D%200.0012556)
=> ![P( p < 0.9207) = 0.0012556](https://tex.z-dn.net/?f=P%28%20p%20%3C%20%200.9207%29%20%3D%200.0012556)
Answer:
5/7 miles
Step-by-step explanation:
Gina travels a distance of 7 miles to reach home. The bus ride covers 5 Given data
Total distance traveled = 7 miles
Bus ride= 5 miles
Walk= 2 miles
Hence the fraction of miles traveled by bus is
=5/7 miles
Step-by-step explanation:
we cannot "solve" it, as we don't know anything about y or k, by we can "simplify" it.
as multiplication is commutative, we can split the whole expression into multiplication factors, simplify each factor, and then out the results back together as one large multiplication.
and remember for the simplification of exponents, multiplying terms with the same base means adding the exponents, dividing terms with the same base means subtracting the denominator exponent from the numerator exponent.
and a^-b = 1/(a^b).
so, we could see the main expression as
(-4/-8)×(y⁶/y⁹)×(k²/k⁵)
(-4/-8) = 1/2
(y⁶/y⁹) = y^-3 = 1/y³
(k²/k⁵) = k^-3 = 1/k³
because e.g.
y⁶/y⁹ = (y×y×y×y×y×y)/(y×y×y×y×y×y×y×y×y) = 1/(y×y×y)
putting the results back together gives us
1/2 × 1/y³ × 1/k³ = 1/(2y³k³)