# How to find the ima of a wedge

## Answers

b

Explanation:

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1) This occurs during the rising action. This decision begins to drive the plot toward its climax and eventual resolution. It sets the first domino in motion for the rest of the story.

2) The author's voice in this passage can best be described as Informal and Humorous.

The author seems to be poking some fun at himself, and also changes streams of thought and interjects his own voice often.

3) The best answer is suspense. The passage provides a sense of excitement and anticipation of what the fire escape will lead Jason to.

[tex]P(90< X< 110)= P(\frac{90-80}{8} <z<\frac{110-80}{8}) =P(1.25<z<3.75)[/tex]

And we can find this probability with this difference:

[tex]P(90< X< 110)=P(z<3.75) -P(z<1.25)= 0.999-0.894= 0.106[/tex]

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:

[tex]X \sim Binom(n=400, p=0.2)[/tex]

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

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]

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

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]

We need to check the conditions in order to use the normal approximation.

[tex]np=400*0.2=80 \geq 10[/tex]

[tex]n(1-p)=400*(1-0.2)=320 \geq 10[/tex]

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:

[tex]E(X)=np=400*0.2=80[/tex]

[tex]\sigma=\sqrt{np(1-p)}=\sqrt{400*0.2(1-0.2)}=8[/tex]

So then we can approximate the random variable as [tex]X \sim N(\mu = 80, \sigma = 8)[/tex]

And we want this probability:

[tex]P(90< X< 110)[/tex]

We can use the z score formula given by:

[tex]z = \frac{x -\mu}{\sigma}[/tex]

And replacing we got:

[tex]P(90< X< 110)= P(\frac{90-80}{8} <z<\frac{110-80}{8}) =P(1.25<z<3.75)[/tex]

And we can find this probability with this difference:

[tex]P(90< X< 110)=P(z<3.75) -P(z<1.25)= 0.999-0.894= 0.106[/tex]

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

A. The surface area of the cheese is 24·π in.² or 75.4 in.² B. The surface area of the remaining cheese after the wedge is removed is about 72 in.² 2. The surface area decreased

Step-by-step explanation:

It's 75.4 instead of 75.40, thank me please.

A. The surface area of the cheese is 24·π in.² or 75.40 in.²

B. The surface area of the remaining cheese after the wedge is removed is about 72 in.²

2. The surface area decreased

Step-by-step explanation:

From the figure attached to a similar question, we have;

Radius, r of cheese = 3 in.

Height, h of the cheese = 1 in.

A. The surface area of the cheese is equal to the area of two circles, one on top and the other underneath added to the surface area of the sides which is equivalent to the surface area of a cylinder given by the relation

Surface area of the cheese = 2×π×r² + 2×π×r×h

∴ Surface area of the cheese = 2×π×3² + 2×π×3×1 = 24·π in.²

Surface area of the cheese = 24·π = 75.398 ≈ 75.40 in.² to the nearest 10th

B. The surface area of the remaining cheese after the wedge is removed is found by first subtracting the cut wedge from the total surface area as follow

Outer surface area of cut wedge = 24·π÷8 = 3·π

New outer surface area = Total surface area - Removed outer surface area

∴ New outer surface area = 24·π - 3·π = 21·π

New total surface area = New outer surface area + Area of newly exposed segment

Area of newly exposed segment = 3 × 1 × 2 = 6 in.²

∴ New total surface area = (21·π + 6) in.² = 71.9734 in.² ≈ 72 in.²

The surface area of the remaining cheese after the wedge is removed is about 72 in.²

2. The surface area decreased.

D. encourage the audience to find reality in the moment

Explanation:

He talks about time and eternity as a concept and mentions how "be it life or death, we crave only reality".

Step-by-step explanation:

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The lesson one can expect to find from reading Aron's story is, Where there is a will, there is a way.

Option C.

Explanation:

Aron Lee Ralston who is an American outdoorsman and an engineer is widely known for how he survived the canyoneering accident. From the excerpt, we can figure out that when all his attempts to survive failed, he committed one of the most extreme act of cutting off his own arm. His story teach us a lesson that if a person's will to live and survive is strong enough, then he can overcome can hurdle, no matter how difficult and impossible it might seem. Aron's will to survive was so strong that he overcame even his death.

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have a good day :)

Explanation: