She has totally 10+5+3=18 marbles, so the probability is 10/18=5/9. The complement is (9-5)/9=4/9.
Hope this helped!
Answer:
<h2>A) 3 cm</h2>
Step-by-step explanation:
The formula of a volume of a cylinder:
![V=\pi r^2H](https://tex.z-dn.net/?f=V%3D%5Cpi%20r%5E2H)
r - radius
H - height
We have r = 1cm and H = 21cm. Substitute:
![V=\pi(1^2)(21)=21\pi\ cm^3](https://tex.z-dn.net/?f=V%3D%5Cpi%281%5E2%29%2821%29%3D21%5Cpi%5C%20cm%5E3)
The formula of a cone:
![V=\dfrac{1}{3}\pi r^2H](https://tex.z-dn.net/?f=V%3D%5Cdfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2H)
r - radius
H - height
We have V = 21π cm³ and H = 7cm. Substitute:
<em>divide both sides by π</em>
<em>divide both sides by 7</em>
<em>multiply both sides by 3</em>
![r^2=9\to r=\sqrt9\\\\r=3\ cm](https://tex.z-dn.net/?f=r%5E2%3D9%5Cto%20r%3D%5Csqrt9%5C%5C%5C%5Cr%3D3%5C%20cm)
Answer:
Type I error: Concluding that mean mileage is less than 32 miles per hour when actually it is greater than or equal to 32 miles per gallon.
Step-by-step explanation:
We are given the following in the question:
Hypothesis:
Mean mileage for the Carter Motor Company's new sedan
We can design the null hypothesis and alternate hypothesis as:
![H_{0}: \mu \geq 32\text{ miles per gallon}\\H_A: \mu < 32\text{ miles per gallon}](https://tex.z-dn.net/?f=H_%7B0%7D%3A%20%5Cmu%20%5Cgeq%2032%5Ctext%7B%20miles%20per%20gallon%7D%5C%5CH_A%3A%20%5Cmu%20%3C%2032%5Ctext%7B%20miles%20per%20gallon%7D)
Type I error:
- It is the false positive error.
- It is the error of rejection a true hypothesis.
Type II error:
- It is the false negative error.
- It is the non rejection of a false null hypothesis.
Thus, type I error for the given hypothesis is concluding that mean mileage is less than 32 miles per hour when actually it is greater than or equal to 32 miles per gallon.
Type II error would be concluding that mean mileage is greater than or equal to 32 miles per gallon when actually it is less than 32 miles per gallon.