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3 years ago

Let us say there are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. we can have three scoops. how m

any variations will there be?

Mathematics

1 answer:

Morgarella [4.7K]3 years ago

6 0

$C(5,3)=\dfrac{5!}{3!2!}=\dfrac{4\cdot5}{2}=10$

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Using principle of mathematical induction prove that 6^-1 divisble by 5 .

salantis [7]

I suppose the claim is $5 \mid 6^n - 1$ for $n\in\Bbb N$ .

When $n=1$ , we have $6^1 - 1 = 6 - 1 = 5$ , and of course 5 divides 5.

Assume the claim holds for $n=k$ , that $5 \mid 6^k - 1$ . We want to use this to show it holds for $n=k+1$ , that $5 \mid 6^{k+1} - 1$ .

We have

$6^{k+1} - 1 = \left(6^{k+1} - 6\right) + \left(6 - 1) = 6\left(6^k - 1\right) + 5$

Since $5 \mid 6^k - 1$ , we can write $6^k - 1 = 5\ell$ for some integer $\ell$ . Then

$6^{k+1} - 1 = 6\cdot5\ell + 5 = 5(6\ell + 1)$

which is clearly divisible by 5. QED

5 0

1 year ago

The 7th-grade class took a survey on their favorite ice cream. 58 people said they prefer vanilla, while 28 people said they pre

MA_775_DIABLO [31]

Since 58 for vanilla and 28 for chocolate
The ratio would be 28:58
You can simplify it even further
to 14:29

6 0

2 years ago

The number of typing errors made by a typist has a Poisson distribution with an average of two errors per page. If more than two

wlad13 [49]

Answer: 0.6767

Step-by-step explanation:

Given : Mean = $\lambda=2$ errors per page

Let X be the number of errors in a particular page.

The formula to calculate the Poisson distribution is given by :_

$P(X=x)=\dfrac{e^{-\lambda}\lambda^x}{x!}$

Now, the probability that a randomly selected page does not need to be retyped is given by :-

$P(X\leq2)=P(0)+P(1)+P(2)\\\\=(\dfrac{e^{-2}2^0}{0!}+\dfrac{e^{-2}2^1}{1!}+\dfrac{e^{-2}2^2}{2!})\\\\=0.135335283237+0.270670566473+0.270670566473\\\\=0.676676416183\approx0.6767$

Hence, the required probability :- 0.6767

6 0

3 years ago

A patient has 0.0000075 gram of iron in 1 liter of blood. The normal level is between 6* 10^-7 grams and 1.6*10^-5 grams. Is the

Vinil7 [7]

0.0000075 = 7.5 x 10^6 --- Patients Blood

and it has to be between 0.0000006 and 0.000016

so Yes it is normal

4 0

3 years ago

Find the absolute value. 1 -31=___ -1 121=___ -1 -221=___

Veseljchak [2.6K]

I guess we will never know

5 0

2 years ago

Read 2 more answers