Lola bought a new chair for $299. The sales tax was 8.25% of the chair’s price. Which of these is closest to the amount of the s
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A quadratic equation is in the form of ax²+bx+c. The time at which the height of the ball is 16 feets is 0.717 seconds and 1.221 seconds.
<h3>What is a quadratic equation?</h3>A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
The complete question is:
A ball is thrown from an initial height of 2 feet with an initial upward velocity of 31 ft/s. The ball's height h (in feet) after 7 seconds is given by the following, h=2+31t-16t². Find all values of t for which the ball's height is 16 feet. Round your answer(s) to the nearest hundredth.
The time at which the height of the ball is 16 feet can be found by,
h = 2 + 31t - 16t²
16 = 2 + 31t - 16t²
16 - 2 - 31t + 16t² = 0
16t² - 31t + 14 = 0
t = 0.717 , 1.221
Hence, the time at which the height of the ball is 16 feets is 0.717 seconds and 1.221 seconds.
Learn more about Quadratic Equations:
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Answer:
a)
So the value of height that separates the bottom 75% of data from the top 25% is 236.121.
b)
c)
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".
2) Part a
Let X the random variable that represent the cuts of a population, and for this case we know the distribution for X is given by:
Where and
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 75% of data from the top 25% is 236.121.
Part b
For this case we know that the individual probability of select one wheel with a cutting rate higher than the calculated value in part a is 0.25, and we select n =10 so then we can use the binomial distribution for this case:
And we want this probability:
We can find the individual probabilities like this:
Part c
For this case we know that the distribution for the sample mean is given by:
And we want this probability:
And for this case we can use the complement rule and the z score given by:
And if we replace we got: