P = 52% = 0.52
SE = sqrt(p(1 - p)/n) = sqrt(0.52(1 - 0.52)/65) = sqrt((0.52 x 0.48) / 65) = sqrt(0.00384) = 0.0620
Let x be a random variable representing the percent of girls in the sample, then
P(x > 0.70) = 1 - P(x < 0.70) = 1 - P(z < (0.70 - 0.52) / 0.0620) = 1 - P(z < 2.905) = 1 - 0.99816 = 0.00184
The probability that there will be more than 70% of girls in the sample is 0.00184. Therefore, it will be unusual for more than 70% of them to be girls.
We know
![y=\sqrt[3]{x}](https://tex.z-dn.net/?f=y%3D%5Csqrt%5B3%5D%7Bx%7D)
is an increasing function as when the value of x increases the value of y increases
And when the value of x decreases , the value of y also decreases.
Now if we have (x+a) or (x-a) instead of x, the function shall have a horizontal shift.
So it shall either move left or right but shall not flip.
So
![y=\sqrt[3]{(x-8)}](https://tex.z-dn.net/?f=y%3D%5Csqrt%5B3%5D%7B%28x-8%29%7D)
and ![y=\sqrt[3]{(x-5)}](https://tex.z-dn.net/?f=y%3D%5Csqrt%5B3%5D%7B%28x-5%29%7D)
are increasing functions.
Only when x becomes -x, that the function shall flip & shall become a decreasing function.
But then it must be - (x-a) or -(x+a) inside.
So
![y=\sqrt[3]{-(5-x)}](https://tex.z-dn.net/?f=y%3D%5Csqrt%5B3%5D%7B-%285-x%29%7D)
is also increasing
Only
![y=- \sqrt[3]{(x+5)}](https://tex.z-dn.net/?f=y%3D-%20%5Csqrt%5B3%5D%7B%28x%2B5%29%7D)
is a decreasing function.
Option D) is the right answer.
Answer:
infinitely many
Step-by-step explanation:
You have the system
(1/2)x + 5y = 6
3x + 30y = 36
Multiplying the first equation by 6 results in 3x + 30y = 36, which is exactly the same as the second equation. The two graphs coincide, and so there are infinitely many solutions to this system
Answer:
The ratio of the areas = the ratio of the squares of the scale factor.
So the area of Z is 3^2 * 11 = 99 sq units.
