Which expressions are equivalent to 3 1/4

Find the area of the shaded region. Round your answer to the nearest hundredth.

PilotLPTM [1.2K]

Answer:

4.56

Step-by-step explanation:

i see a sector hosting 2 semi circles.

this sector area will be .25 of area of circle with radius 4ft.

area of sector = .25*π*16= 4π ft^2

area of semi circle of radius 2ft = .5π*4= 2πft^2

area of 2 semicircles = 4π

the total area of sector = area of 2 semicircles - intersection area + area not covered by semi circles

4π = 4π - intersection area+area not covered by semi circles

intersection area = area not covered by semi circles

now draw a square starting from the intersection point of 2 semi circles at their upper portion. the side will be 2ft

the area of intersection will be covered in the square.

area of intersection = 2*quarter area of circle of radius 2ft - area of square

= 2*(.25π4) - 4

2π-4 = 2.28

area of intersection = area not covered by semicircle

so area of shaded region = 4.56

4 0

2 years ago

The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.11 millimeters and a standard deviat

____ [38]

Answer:

The diameter that separates the bottom 9% is 5.02 millimeters.

The diameter that separates the top 9% is 5.2 millimeters.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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 of 5.11 millimeters and a standard deviation of 0.07 millimeters.

This means that $\mu = 5.11, \sigma = 0.07$

Bottom 9%:

The 9th percentile, which is X when Z has a pvalue of 0.09. So X when Z = -1.34.

$Z = \frac{X - \mu}{\sigma}$

$-1.34 = \frac{X - 5.11}{0.07}$

$X - 5.11 = -1.34*0.07$

$X = 5.02$

The diameter that separates the bottom 9% is 5.02 millimeters.

Top 9%:

The 100 - 9 = 91th percentile, which is X when Z has a pvalue of 0.91. So X when Z = 1.34.

$Z = \frac{X - \mu}{\sigma}$

$1.34 = \frac{X - 5.11}{0.07}$

$X - 5.11 = 1.34*0.07$

$X = 5.2$

The diameter that separates the top 9% is 5.2 millimeters.

6 0

2 years ago

USA Today reported that about 20% of all people in the United States are illiterate. Suppose you take eight people at random off

Law Incorporation [45]

Answer:

a) Figure and code attached

b) $E(X)=\mu = np = 8*0.2= 1.6$

$Var(X) =\sigma^2= np(1-p) = 8*0.2*(1-0.2) = 1.28$

$Sd(X)=\sigma= \sqrt{1.28}= 1.131$

c) $P(X\geq 7) =0.97$

And we can calculate this with the complement rule.

$P(X \geq 7) = 1-P(X$

So then we have:

$P(X \leq 6) = 0.03$

And we are interested on the valueof n who satisfy this expression.

And for this we can verify this with the following code:

"=BINOM.DIST(6,E54,0.2,TRUE)"

And as we can see on the second figure attached the value who satisfy the condition would be n = 60.

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".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=8, p=0.2)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Part a

We can use the following R code to generate the histogram for this case:

> x <- seq(0,8,by = 1)

> y <- dbinom(x,8,0.2)

> plot(x,y,type = "h",main="Histogram")

And as we can see we got the result on the figure attached. And the distribution seems to be skewed to the right.

Part b

For this case the expected value is given by:

$E(X)=\mu = np = 8*0.2= 1.6$

The variance is given by:

$Var(X) =\sigma^2= np(1-p) = 8*0.2*(1-0.2) = 1.28$

And the standard deviation would be:

$Sd(X)=\sigma= \sqrt{1.28}= 1.131$

Part c

For this case we have the following inequality:

$P(X\geq 7) =0.97$

And we can calculate this with the complement rule.

$P(X \geq 7) = 1-P(X$

So then we have:

$P(X \leq 6) = 0.03$

And we are interested on the valueof n who satisfy this expression.

And for this we can verify this with the following code:

"=BINOM.DIST(6,E54,0.2,TRUE)"

And as we can see on the second figure attached the value who satisfy the condition would be n = 60.

5 0

3 years ago

Ill give brainliest help me out

dusya [7]

Answer:

A

Step-by-step explanation:

In the graphing calculator, I tried out the different answers, and I think this graph matches yours pretty closely. x is multiplied by a number greater than one, and it looks like instead of expanding/stretching open, it folded in more, which is compressing.

5 0

2 years ago

Which transformation can be used to prove Similarity and why?

lyudmila [28]

A similarity transformation is one or more rigid transformations (reflection, rotation, translation) followed by a dilation. When a figure is transformed by a similarity transformation, an image is created that is similar to the original figure. In other words, two figures are similar if a similarity transformation will carry the first figure to the second figure.

7 0

2 years ago