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3 years ago

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Christine has always been weak in mathematics. Based on her performance prior to the final exam in Calculus, there is a 40% chan

ce that she will fail the course if she does not have a tutor. With a tutor, her probability of failing decreases to 10%. There is only a 50% chance that she will find a tutor at such short notice.

1 answer:

azamat3 years ago

6 0

Answer:

There are a 25% probability that Christine fails the course.

Step-by-step explanation:

We have these following probabilities:

A 50% probability that Christine finds a tutor.

With a tutor, she has a 10% probability of failling.

A 50% probability that Christine does not find a tutor.

Without a tutor, she has a 40% probability of failing.

Probability that she fails:

10% of 50%(fail with a tutor) plus 40% of 50%(fail without a tutor). So

$P = 0.1*0.5 + 0.4*0.5 = 0.25$

There are a 25% probability that Christine fails the course.

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Adam is going to cook a turkey for 14 people and wants to allow 3/4 lb of turkey for each person. 1lb = 450g

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(You forgot to add the question, but I guess you want to know the mass of the turkey for 14 people :p )
By hypothesis, 1 lb = 450g. Adam wants that each of the 14 person, get 3/4 lb. Let x be the mass of 3/4 lb in grams, using the rule of three:

1 lb --> 450g
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x = 3/4 * 450 = 337.5
So 3/4 lb = 337.5 g

Adam wants to cook for 14 people and wants to allow 3/4 lb of turkey for each person, so 337.5 for each.
So to know the total mass of the turkey, you multiply the mass for one person by the total number of people:
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Answer: 15y+50=x

Step-by-step explanation:

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3 years ago

How to know if a function is periodic without graphing it ?

zhenek [66]

A function $f(t)$ is periodic if there is some constant $k$ such that $f(t+k)=f(k)$ for all $t$ in the domain of $f(t)$ . Then $k$ is the "period" of $f(t)$ .

Example:

If $f(x)=\sin x$ , then we have $\sin(x+2\pi)=\sin x\cos2\pi+\cos x\sin2\pi=\sin x$ , and so $\sin x$ is periodic with period $2\pi$ .

It gets a bit more complicated for a function like yours. We're looking for $k$ such that

$\pi\sin\left(\dfrac\pi2(t+k)\right)+1.8\cos\left(\dfrac{7\pi}5(t+k)\right)=\pi\sin\dfrac{\pi t}2+1.8\cos\dfrac{7\pi t}5$

Expanding on the left, you have

$\pi\sin\dfrac{\pi t}2\cos\dfrac{k\pi}2+\pi\cos\dfrac{\pi t}2\sin\dfrac{k\pi}2$

and

$1.8\cos\dfrac{7\pi t}5\cos\dfrac{7k\pi}5-1.8\sin\dfrac{7\pi t}5\sin\dfrac{7k\pi}5$

It follows that the following must be satisfied:

$\begin{cases}\cos\dfrac{k\pi}2=1\\\\\sin\dfrac{k\pi}2=0\\\\\cos\dfrac{7k\pi}5=1\\\\\sin\dfrac{7k\pi}5=0\end{cases}$

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Let's verify:

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Answer:

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Step-by-step explanation:

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y=x+4

Since we know that y=x+4, we can put "x+4" into the first equation for "y", giving us:

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Simplifying gives us:

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---------

2x=70

--- ---

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x=35

Since we now know that x=35, and we know that y=x+4, we now know that:

y=(35)+4

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Now that we have both of the numbers, we should check our work to ensure it's correct:

Does 39+35=74? Yes it does.

Is 39 (the larger of the two numbers) four more than the smallest number (35)? Yes it is.

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