Angelina factored (x - 4)8 and wrote that it was equal to (x2 - 42)2(x2 + 42). Use complete sentences to explain how you could c
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Answer:
And we can find this probability with this difference:
And we can find the real value with the following excel code using the binomial distribution:
"=BINOM.DIST(110,400,0.2,TRUE)-BINOM.DIST(89,400,0.2,TRUE)"
And we got 0.118 a very close value from the value obtained using the normal approximation
Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Let X the random variable of interest, on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
We need to check the conditions in order to use the normal approximation.
So we see that we satisfy the conditions and then we can apply the approximation.
If we appply the approximation the new mean and standard deviation are:
So then we can approximate the random variable as
And we want this probability:
We can use the z score formula given by:
And replacing we got:
And we can find this probability with this difference:
And we can find the real value with the following excel code using the binomial distribution:
"=BINOM.DIST(110,400,0.2,TRUE)-BINOM.DIST(89,400,0.2,TRUE)"
And we got 0.118 a very close value from the value obtained using the normal approximation
Answer:
<h3>- The ratio of the measure of central angle PQR to the measure of the entire circle is One-eighth. </h3><h3>- The area of the shaded sector depends on the length of the radius. </h3><h3>- The area of the shaded sector depends on the area of the circle</h3>Step-by-step explanation:
Given central angle PQR = 45°
Total angle in a circle = 360°
Ratio of the measure of central angle PQR to the measure of the entire circle is . This shows ratio that <u>the measure of central angle PQR to the measure of the entire circle is one-eighth</u>.
Area of a sector =
= central angle (in degree) = 45°
r = radius of the circle = 6
Area of the sector
<u>The ratio of the shaded sector is 4.5πunits² not 4units²</u>
From the formula, it can be seen that the ratio of the central angle to that of the circle is multiplied by area of the circle, this shows <u>that area of the shaded sector depends on the length of the radius and the area of the circle.</u>
Since Area of the circle = πr²
Area of the circle = 36πunits²
The ratio of the area of the shaded sector to the area of the circle =
For length of an arc
ratio of the length of the arc to the area of the circle =
It is therefore seen that the ratio of the area of the shaded sector to the area of the circle IS NOT equal to the ratio of the length of the arc to the area of the circle