Lashonda runs 12 miles in 92 minutes.<br> How many miles does she run per minute?

Use Pascal's triangle to find 6C3

katrin2010 [14]

Ignore tht pascal triangle its way too inefficient
Formula nCr = n! /r! (n-r)!
So 6C3= 6!/3!(6-3)!=20

5 0

3 years ago

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What are the coefficients for the binomial expansion of (a + b)^3?

sashaice [31]

Answer:

Required coefficient :coefficient of 1st, 2nd, 3rd and 4th term are 1, 3,3,1 respectively.

Explanation:

Formula for binomial expansion is $(a+b)^n=^nC_0\cdot a^n\cdot b^0+^nC_1\cdota^(n-1)\cdot b^1+------b^n$

We will substitute the values a=a, b=b and n=3 in the formula for binomial expansion we will get

$^3C_0\cdot a^3\cdot b^0+^3C_1\cdot a^2\cdot b^1+^3C_2\cdot a^1\cdot b^2+^3C_3\cdot a^0\cdot b^3$

After simplification of the terms we will get

$a^3+3\cdot a^2\cdot b+3\cdot a\cdot b^2+b^3$

Since, $^nC_r=\frac{n!}{(r!)(n-r)!}$

Therefore the required coefficient : coefficients of 1st, 2nd, 3rd and 4th term are 1, 3,3,1 respectively.

5 0

3 years ago

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The range of the function y=secx-2 is all reals except<br><br> -1 1 -3 -2

Umnica [9.8K]

Answer:

For a function y = f(x), the range is the set of all the possible values of y.

In the question you wrote:

y = secx - 2

This can be interpreted as:

y = sec(x - 2)

or

y = sec(x) - 2

So let's see each case (these are kinda the same)

If the function is:

y = sec(x - 2)

Firs remember that:

sec(x) = 1/cos(x)

then we can rewrite:

y = 1/cos(x - 2)

notice that the function cos(x) has the range -1 ≤ y ≤ 1

Then for the two extremes we have:

y = 1/1 = 1

y = 1/-1 = -1

Notice that for:

y = 1/cos(x - 2)

y can never be in the range -1 < x < 1

As the denominator cant be larger, in absolute value, than 1.

Then we can conclude that the range is all reals except the interval:

-1 < y < 1

If instead the function was:

y = sec(x) - 2

y = 1/cos(x) - 2

Then with the same reasoning, the range will be the set of all real values except:

-1 - 2 < y < 1 - 2

-3 < y < -1

6 0

3 years ago

Which statement best explains ?

Tems11 [23]

A is the correct answer. Hope this helps. I need brainliest so if you can I really appreciate it!

5 0

3 years ago

Identify all the sets to which the number belongs. Choose from Rational Number, Irrational number, whole number, and integer. 1.

Allushta [10]

Answer:

The number 1.256 is A)rational number.

Step-by-step explanation:

A whole number is a non-negative number without any digits behind the decimal.

An integer is a set of negative and non negative numbers that don't have any digits behind the decimal.

A number that can be shown as a fraction of two whole numbers is a rational number.And the numbers that are not rational are irrational numbers.

Here, 1.256 is a fraction of whole numbers 1256 and 1000 , so it is a rational no.

$\frac{1256}{1000} =1.256$

But since it has digits behind the decimal it is neither a whole number, or an integer.

4 0

3 years ago

Lashonda runs 12 miles in 92 minutes. How many miles does she run per minute?