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Alik [6]
3 years ago
6

To the nearest hundredth, what is the sine of the acute angle formed by the line whose equation is y = 3x - 3 and the positive x

-axis?

Mathematics
1 answer:
Serhud [2]3 years ago
5 0

Answer:

The sine of the acute angle is 0.95

Step-by-step explanation:

using a graphing tool

see the attached figure

Let

A-----> the acute angle formed by the given line and the positive x-axis

In the right triangle XYZ

we know that

sin(A)=\frac{xy}{xz}

we have

xy=3\ units

yz=1\ units

Applying the Pythagoras Theorem find the value of xz

xz^{2}=3^{2}+1^{2}\\ \\xz^{2}=10\\ \\xz=\sqrt{10}\ units

substitute

sin(A)=\frac{3}{\sqrt{10}}=0.95

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It is the answer M: 1
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The sum of six number is 33. What is their mean?
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Answer:

mean = 33/6 =5.5

Step-by-step explanation:

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The temperature was x° F. It increased by 24°F and is now 6°F. What was the original
Nesterboy [21]

Answer:

The original temperature was -18°F

Step-by-step explanation:

x°F + 24°F = 6°F

or, x°F = 6°F - 24°F

so, x°F = -18°F

7 0
2 years ago
In a casino game, gamblers are allowed to roll n fair, 6-sided dice. If a 6 shows up on any of them, the gambler gets nothing. I
Soloha48 [4]

Answer:

a) \bf \boxed{W(n) = 3*n*\left( \frac{5}{6} \right)^n\;dollars}

the smallest n that maximizes the expected payoff is n=5.

b) 4

Step-by-step explanation:

a)

The expected amount of $ won for each die would be the average of 1, 2, 3, 4 and 5 which is $3.

Let W(n) the expected money won when rolling n dice.  

n =1

If the gambler rolls only one die, the expected money won would be $3 times the probability of not getting a 6, which is 5/6.

So  

\bf W(1) = 3*1*\frac{5}{6}

n=2

If the gambler rolls 2 dice, the expected money won would be $3 times the probability of not getting a 6 in any of the dice. Since the outcome of the rolling does not depend on the previous rollings, the probability is  

\bf \frac{5}{6}\times\frac{5}{6}=\left( \frac{5}{6} \right)^2

and

\bf W(2) = 3*2*\left( \frac{5}{6} \right)^2

n=3

Similarly, since the probability of not getting a 6 in 3 dice equals

\bf \left( \frac{5}{6} \right)^3

\bf W(3) = 3*3*\left( \frac{5}{6} \right)^3

and the formula for the expected money won with n dice would be

\bf \boxed{W(n) = 3*n*\left( \frac{5}{6} \right)^n\;dollars}

In the picture attached there is a plot of the values of the expected money won for n=1 to 20 (See picture)

For n=5 and n=6 we get the maximum profit expected of $6.02816=$6 rounded to the nearest integer.

Hence, the smallest n that maximizes the expected payoff is n=5.

b)

The probability that face k (k=1,2,...or 6) shows up is 1/6,

as this face can be in any of the 10 positions of the arrangement, there are 10 ways that face k can show up.

The probability that face k (k=1,2,...or 6) shows up twice is \bf \left( \frac{1}{6} \right)^2

as this face can be in any of the \bf C(10;2)=\binom{10}{2} (combinations of 10 taken 2 at a time) positions of the arrangement, there are C(10;2) ways that face k can show up twice.

The probability that face k (k=1,2,...or 6) shows up three times is \bf \left( \frac{1}{6} \right)^3

as this face can be in any of the \bf C(10;3)=\binom{10}{2} (combinations of 10 taken 2 at a time) positions of the arrangement, there are C(10;3) ways that face k can show up twice.

So, we infer that the expectation is  

\bf \sum_{k=1}^{10}\binom{10}{k}(1/6)^k=3.6716\approx 4

and the expected number of distinct dice values that show up is 4.

4 0
3 years ago
The slant asymptote of f(x)=(x^2-4x+1)/(2x-3)
ANEK [815]

Answer:

y=1/2x-5/4

I hope this helps you and I hope you do well on whatever you are working on.

3 0
3 years ago
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