Can someone help me with this please??
2 answers:
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Answer:
The warranty period should be of 32 months.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean time before failure of 40 months with a standard deviation of 6 months.
This means that
What should be the warranty period, in months, so that the manufacturer will not have more than 10% of the blenders returned?
The warranty period should be the 10th percentile, which is X when Z has a p-value of 0.1, so X when Z = -1.28.
The warranty period should be of 32 months.
4. To solve this problem, we divide the two expressions step by step:
Here we have inverted the second term since division is just multiplying the inverse of the term.
In this step we factor out the quadratic equation.
Then, we cancel out the like term which is x-1.
We then solve for the final combined expression:
For the restrictions, we just need to prevent the denominators of the two original terms to reach zero since this would make the expression undefined:
Therefore, x should not be equal to 1, -5, or -4.
Comparing these to the choices, we can tell the correct answer.
ANSWER:; 
5. To get the ratio of the volume of the candle to its surface area, we simply divide the two terms with the volume on the numerator and the surface area on the denominator:
We can simplify this expression by factoring out the denominator and cancelling like terms.
We then rationalize the denominator:
![\frac{rh(3r-3 \sqrt{ r^{2} + h^{2} })}{(3r)^{2}-(3 \sqrt{ r^{2} + h^{2} })^{2}}}=\frac{3 r^{2}h -3rh \sqrt{ r^{2} + h^{2} }}{9r^{2} -9 (r^{2} + h^{2} )}=\frac{3rh(r -\sqrt{ r^{2} + h^{2} })}{9[r^{2} -(r^{2} + h^{2} )]}=\frac{rh(r -\sqrt{ r^{2} + h^{2} })}{3[r^{2} -(r^{2} + h^{2} )]}](https://tex.z-dn.net/?f=%5Cfrac%7Brh%283r-3%20%5Csqrt%7B%20r%5E%7B2%7D%20%2B%20h%5E%7B2%7D%20%7D%29%7D%7B%283r%29%5E%7B2%7D-%283%20%5Csqrt%7B%20r%5E%7B2%7D%20%2B%20h%5E%7B2%7D%20%7D%29%5E%7B2%7D%7D%7D%3D%5Cfrac%7B3%20r%5E%7B2%7Dh%20-3rh%20%5Csqrt%7B%20r%5E%7B2%7D%20%2B%20h%5E%7B2%7D%20%7D%7D%7B9r%5E%7B2%7D%20-9%20%28r%5E%7B2%7D%20%2B%20h%5E%7B2%7D%20%29%7D%3D%5Cfrac%7B3rh%28r%20-%5Csqrt%7B%20r%5E%7B2%7D%20%2B%20h%5E%7B2%7D%20%7D%29%7D%7B9%5Br%5E%7B2%7D%20-%28r%5E%7B2%7D%20%2B%20h%5E%7B2%7D%20%29%5D%7D%3D%5Cfrac%7Brh%28r%20-%5Csqrt%7B%20r%5E%7B2%7D%20%2B%20h%5E%7B2%7D%20%7D%29%7D%7B3%5Br%5E%7B2%7D%20-%28r%5E%7B2%7D%20%2B%20h%5E%7B2%7D%20%29%5D%7D)
Since the height is equal to the length of the radius, we can replace h with r and further simplify the expression:
![\frac{r*r(r -\sqrt{ r^{2} + r^{2} })}{3[r^{2} -(r^{2} + r^{2} )]}=\frac{ r^{2} (r -\sqrt{2 r^{2} })}{3[r^{2} -(2r^{2} )]}=\frac{ r^{2} (r -r\sqrt{2 })}{-3r^{2} }=\frac{r -r\sqrt{2 }}{-3 }=\frac{r(1 -\sqrt{2 })}{-3 }](https://tex.z-dn.net/?f=%5Cfrac%7Br%2Ar%28r%20-%5Csqrt%7B%20r%5E%7B2%7D%20%2B%20r%5E%7B2%7D%20%7D%29%7D%7B3%5Br%5E%7B2%7D%20-%28r%5E%7B2%7D%20%2B%20r%5E%7B2%7D%20%29%5D%7D%3D%5Cfrac%7B%20r%5E%7B2%7D%20%28r%20-%5Csqrt%7B2%20r%5E%7B2%7D%20%7D%29%7D%7B3%5Br%5E%7B2%7D%20-%282r%5E%7B2%7D%20%29%5D%7D%3D%5Cfrac%7B%20r%5E%7B2%7D%20%28r%20-r%5Csqrt%7B2%20%7D%29%7D%7B-3r%5E%7B2%7D%20%7D%3D%5Cfrac%7Br%20-r%5Csqrt%7B2%20%7D%7D%7B-3%20%7D%3D%5Cfrac%7Br%281%20-%5Csqrt%7B2%20%7D%29%7D%7B-3%20%7D)
By examining the choices, we can see one option similar to the answer.
ANSWER:
Here we have inverted the second term since division is just multiplying the inverse of the term.
In this step we factor out the quadratic equation.
Then, we cancel out the like term which is x-1.
We then solve for the final combined expression:
For the restrictions, we just need to prevent the denominators of the two original terms to reach zero since this would make the expression undefined:
Therefore, x should not be equal to 1, -5, or -4.
Comparing these to the choices, we can tell the correct answer.
ANSWER:
5. To get the ratio of the volume of the candle to its surface area, we simply divide the two terms with the volume on the numerator and the surface area on the denominator:
We can simplify this expression by factoring out the denominator and cancelling like terms.
We then rationalize the denominator:
Since the height is equal to the length of the radius, we can replace h with r and further simplify the expression:
By examining the choices, we can see one option similar to the answer.
ANSWER: