Find value of cos75 degrees

What is the remainder of 10^2017 divided by 1001?

pashok25 [27]

Note: When I use the double equal sign, I mean the triple bar used with modular arithmetic

10^3 = 1000 == -1 (mod 1001)
10^3 == -1 (mod 1001)
(10^3)^672 == (-1)^672 (mod 1001)
(10^(3*672) == 1 (mod 1001)
10^2016 == 1 (mod 1001)
10*10^2016 == 10*1 (mod 1001)
10^2017 == 10 (mod 1001)

Final Answer: 10

5 0

3 years ago

Which statement explains how the lines 2x + y = 4 and y = one halfx + 4 are related?

KatRina [158]

Answer:

They are perpendicular

Step-by-step explanation:

To solve this problem .

we will convert the equations in slope intercept form.

Slope intercept form of equation is y = mx+c

where m is slope of line and c is y intercept.

________________________________

equation 1 is

2x+y = 4

=> y =4 - 2x or y = -2x + 4

comparing it with y = mx + c

m = -2 , c = 4

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equation 2 is y = one halfx + 4 ( one half is same as 1/2)

so equation is

y = x/2 +4

comparing it with y = mx + c

m = 1/2 , c = 4

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Now lets evaluate options

They are parallel. wrong option

For lines to be parallel slope should be same.

But here slope are different -2 and 1/2 .

Thus lines are not parallel.

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They are perpendicular. correct option

For lines to be perpendicular, product of slope should be equal to -1.

-2*1/2 = -1

we can see that product of slope should be equal to -1 .

Thus lines are perpendicular

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They are the same line. wrong option

For lines to be same both slope and y intercept should be same.

Y intercept is same but the slopes are different -2 and 1/2 .

Thus lines are not the same line.

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They are not related. wrong option

As we have found that the lines are perpendicular .

So this option is intuitively wrong

4 0

3 years ago

Two dance teams, the Roses and the Tulips, are perfectly matched so that their chances of winning are both set at 50%. What is t

shtirl [24]

Answer:

6%

Step-by-step explanation:

Step 1

The fist step is to define the probabilities.

The events are independent from each other. Each team wins with probability $\frac{1}{2}$ and looses with probability $\frac{1}{2}.$ Let $P(W_R)$ be probability that Roses win and $P(L_R)$ be the probability that Roses loose.

Step 2

The second step is to calculate the probabilities by multiplying the probabilities with the first 3 terms in the product being the probability of a win and the last term being the probability of a loss.

The calculation is shown below,

$P(W_R)\times P(W_R)\times P(W_R)\times P(L_R)=\frac{1}{2} \times \frac{1}{2} \times\frac{1}{2} \times\frac{1}{2} =\frac{1}{16}$