What's the domain function for y=(x+1)(x-9)
2 answers:
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Answer:
And we can use the z score formula given by:
And using the z score we have:
And we can use the normal standard distribution table or excel in order to find the probabilities and we got:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the time it takes her to complete one review, and for this case we know the distribution for X is given by:
Where and
And we select a sample size of n =16. Since the dsitribution for X is normal then the distribution for the sample mean is also normal and given by:
For this case we want to find this probability:
And we can use the z score formula given by:
And using the z score we have:
And we can use the normal standard distribution table or excel in order to find the probabilities and we got:
The graph illustrating the problem is on the figure attached.
Answer:
The radius of the base of the cone is 2 units
The slant height of the cone is 4 units
The height of the cone is 2√3 units
The volume of the cone is units³
Step-by-step explanation:
* Lets revise the total surface area and the lateral area of a cone
- The lateral area of cone = π r l , where r is the radius of the base
and l is the slant height of the cone
- The surface area of the cone = π r l + π r², where π r l is the lateral
area and π r² is the base area
- The cone has three dimensions radius (r) , height (h) , slant height (l)
- r , h , l formed right triangle, r , h are its legs and l is its hypotenuse,
then l² = r² + h²
- The volume of the con = (π r² h)
* Now lets solve the problem
- We will use the total area to find the radius of the base
∵ TA = 12π
∵ TA = LA + πr²
∵ LA = 8π
- Substitute the value of the lateral area in the total area
∴ 12π = 8π + π r² ⇒ subtract 8π from both sides
∴ 12π - 8π = π r²
∴ 4π = π r² ⇒ divide both sides by π
∴ r² = 4 ⇒ take square root for both sides
∴ r = 2
* The radius of the base of the cone is 2 units
- We will use the lateral area to find the slant height
∵ LA = π r l
∵ LA = 8π
∵ r = 2
∴ π (2) l = 8π ⇒ divide both sides by π
∴ 2 l = 8 ⇒ divide both sides by 2
∴ l = 4
* The slant height of the cone is 4 units
- Use the rule l² = r² + h² to find the height of the cone
∵ r = 2 and l = 4
∵ l² = r² + h²
∴ (4)² = (2)² + h²
∴ 16 = 4 + h² ⇒ subtract 4 from both sides
∴ 12 = h² ⇒ take square root for both sides
∴ h = √12 = 2√3
* The height of the cone is 2√3 units
∵ The volume of the con = (π r² h)
∵ r = 2 and h = 2√3
∴ V = (π × 2² × 2√3) =
(π × 4 × 2√3) =
(π × 8√3)
∴ V =
* The volume of the cone is units³
