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2 years ago

What is the probability that another student has the same birthday as you?

Mathematics

1 answer:

Flura [38]2 years ago

5 0

There are 365 days in a year. So the answer is

1/365

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Pls help!!!<br><br> Question in the picture

Wewaii [24]

Answer:

-7, - $\pi$ - $\sqrt{3}$ , 9

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

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:

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

The first two equations are satisfied whenever $k\in\{0,\pm4,\pm8,\ldots\}$ , or more generally, when $k=4n$ and $n\in\mathbb Z$ (i.e. any multiple of 4).

The second two are satisfied whenever $k\in\left\{0,\pm\dfrac{10}7,\pm\dfrac{20}7,\ldots\right\}$ , and more generally when $k=\dfrac{10n}7$ with $n\in\mathbb Z$ (any multiple of 10/7).

It then follows that all four equations will be satisfied whenever the two sets above intersect. This happens when $k$ is any common multiple of 4 and 10/7. The least positive one would be 20, which means the period for your function is 20.

Let's verify:

$\sin\left(\dfrac\pi2(t+20)\right)=\sin\dfrac{\pi t}2\underbrace{\cos10\pi}_1+\cos\dfrac{\pi t}2\underbrace{\sin10\pi}_0=\sin\dfrac{\pi t}2$

$\cos\left(\dfrac{7\pi}5(t+20)\right)=\cos\dfrac{7\pi t}5\underbrace{\cos28\pi}_1-\sin\dfrac{7\pi t}5\underbrace{\sin28\pi}_0=\cos\dfrac{7\pi t}5$

More generally, it can be shown that

$f(t)=\displaystyle\sum_{i=1}^n(a_i\sin(b_it)+c_i\cos(d_it))$

is periodic with period $\mbox{lcm}(b_1,\ldots,b_n,d_1,\ldots,d_n)$ .

4 0

2 years ago

Please Help!! 10 Points! Brainliest Answer

Ivenika [448]

The correct answer is D because you already have one side and one angle that are equal so you need one more side

6 0

2 years ago

A customer purchases 10 m dade co. florida 7.50% g.o. bonds at a 9.50 basis. how much interest will she collect each year? $75 $

crimeas [40]

In the value of bonds, the symbol "M" means "thousands.
Therefore, 10 M = 10,000$

So, the customer bought a coupon with 10,000$ and the expected annual interest is 7.5% of the coupon's value.

Calculating the value of interest is simple, just multiply the interest rate (7.5%) by the original value of the coupon to know how much interest she will collect each year.

Interest collected each year = (7.5 / 100) x 1000 = 750$

5 0

2 years ago

3x+2y-5z=-1<br> 4x-3y+2z=-13<br> 2x-5y+4z=-9

Lina20 [59]

34252

I just guessed but here

5 0

2 years ago