Answer:
Height = 5
Step-by-step explanation:
![Solution,\\Volume(V)=45\pi \\Radius(r)=3\\Height(h)=?\\As,\\V=\pi r^{2} h\\45\pi =\pi (3)^{2} h\\\frac{45\pi }{9\pi } =h\\h=5](https://tex.z-dn.net/?f=Solution%2C%5C%5CVolume%28V%29%3D45%5Cpi%20%5C%5CRadius%28r%29%3D3%5C%5CHeight%28h%29%3D%3F%5C%5CAs%2C%5C%5CV%3D%5Cpi%20r%5E%7B2%7D%20h%5C%5C45%5Cpi%20%3D%5Cpi%20%283%29%5E%7B2%7D%20h%5C%5C%5Cfrac%7B45%5Cpi%20%7D%7B9%5Cpi%20%7D%20%3Dh%5C%5Ch%3D5)
Answer: 10.5 miles
Step-by-step explanation: If she runs 7 miles for 50 minutes, if you half it, she runs 3.5 miles in 25 minutes. This means if you add 7 and 3.5 miles, you would add 50 and 25 minutes,
So 10.5 miles in 75 minutes in your answer
SOLUTION
This is a binomial probability. For i, we will apply the Binomial probability formula
i. Exactly 2 are defective
Using the formula, we have
![\begin{gathered} P_x=^nC_x\left(p^x\right?\left(q^{n-x}\right) \\ Where\text{ } \\ P_x=binomial\text{ probability} \\ x=number\text{ of times for a specific outcome with n trials =2} \\ p=\text{ probability of success = }\frac{4}{24}=\frac{1}{6} \\ q=probability\text{ of failure =1-}\frac{1}{6}=\frac{5}{6} \\ ^nC_x=\text{ number of combinations = }^4C_2 \\ n=\text{ number of trials = 4} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20P_x%3D%5EnC_x%5Cleft%28p%5Ex%5Cright%3F%5Cleft%28q%5E%7Bn-x%7D%5Cright%29%20%5C%5C%20Where%5Ctext%7B%20%7D%20%5C%5C%20P_x%3Dbinomial%5Ctext%7B%20probability%7D%20%5C%5C%20x%3Dnumber%5Ctext%7B%20of%20times%20for%20a%20specific%20outcome%20with%20n%20trials%20%3D2%7D%20%5C%5C%20p%3D%5Ctext%7B%20probability%20of%20success%20%3D%20%7D%5Cfrac%7B4%7D%7B24%7D%3D%5Cfrac%7B1%7D%7B6%7D%20%5C%5C%20q%3Dprobability%5Ctext%7B%20of%20failure%20%3D1-%7D%5Cfrac%7B1%7D%7B6%7D%3D%5Cfrac%7B5%7D%7B6%7D%20%5C%5C%20%5EnC_x%3D%5Ctext%7B%20number%20of%20combinations%20%3D%20%7D%5E4C_2%20%5C%5C%20n%3D%5Ctext%7B%20number%20of%20trials%20%3D%204%7D%20%5Cend%7Bgathered%7D)
Note that I made the probability of being defective as the probability of success = p
and probability of none defective as probability of failure = q
Exactly 2 are defective becomes the binomial probability
![\begin{gathered} P_x=^4C_2\times\lparen\frac{1}{6})^2\times\lparen\frac{5}{6})^{4-2} \\ P_x=6\times\frac{1}{36}\times\frac{25}{36} \\ P_x=\frac{25}{216} \\ =0.1157 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20P_x%3D%5E4C_2%5Ctimes%5Clparen%5Cfrac%7B1%7D%7B6%7D%29%5E2%5Ctimes%5Clparen%5Cfrac%7B5%7D%7B6%7D%29%5E%7B4-2%7D%20%5C%5C%20P_x%3D6%5Ctimes%5Cfrac%7B1%7D%7B36%7D%5Ctimes%5Cfrac%7B25%7D%7B36%7D%20%5C%5C%20P_x%3D%5Cfrac%7B25%7D%7B216%7D%20%5C%5C%20%3D0.1157%20%5Cend%7Bgathered%7D)
Hence the answer is 0.1157
(ii) None is defective becomes
![\begin{gathered} \lparen\frac{5}{6})^4=\frac{625}{1296} \\ =0.4823 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Clparen%5Cfrac%7B5%7D%7B6%7D%29%5E4%3D%5Cfrac%7B625%7D%7B1296%7D%20%5C%5C%20%3D0.4823%20%5Cend%7Bgathered%7D)
hence the answer is 0.4823
(iii) All are defective
![\begin{gathered} \lparen\frac{1}{6})^4=\frac{1}{1296} \\ =0.00077 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Clparen%5Cfrac%7B1%7D%7B6%7D%29%5E4%3D%5Cfrac%7B1%7D%7B1296%7D%20%5C%5C%20%3D0.00077%20%5Cend%7Bgathered%7D)
(iv) At least one is defective
This is 1 - probability that none is defective
![\begin{gathered} 1-\lparen\frac{5}{6})^4 \\ =1-\frac{625}{1296} \\ =\frac{671}{1296} \\ =0.5177 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%201-%5Clparen%5Cfrac%7B5%7D%7B6%7D%29%5E4%20%5C%5C%20%3D1-%5Cfrac%7B625%7D%7B1296%7D%20%5C%5C%20%3D%5Cfrac%7B671%7D%7B1296%7D%20%5C%5C%20%3D0.5177%20%5Cend%7Bgathered%7D)
Hence the answer is 0.5177
Answer:
The product of the other two zeros is c
Step-by-step explanation:
Let α, β and γ be the zeros of the polynomial x³ + ax² + bx + c. Since one of the zeros is -1, therefore let γ = -1. Hence:
sum of the roots = α + β + γ = -a
-1 + β + γ = -a
β + γ = -a + 1
αβ + αγ + βγ = b
-1(β) + (-1)γ + βγ = b
-β -γ + βγ = b
Also, the product of the zeros is equal to -c, hence:
αβγ = -c
-1(βγ) = -c
βγ = c
Hence the product of the other two zeros is c
Yup, that right there is a math.