What is the volumen of a sphere with a diameter of 32.5m

I need the answer of this with steps and solutions fast plz

Natali [406]

Answer:

$1 \dfrac{13}{15}$

Step-by-step explanation:

$2 \dfrac{1}{5} - \dfrac{1}{3} =$

$= \dfrac{11}{5} - \dfrac{1}{3}$

$= \dfrac{33}{15} - \dfrac{5}{15}$

$= \dfrac{28}{15}$

$= 1 \dfrac{13}{15}$

6 0

3 years ago

What is the equation of the line with a slope of -3 and passes through the point (-6,-3)

Taya2010 [7]

Answer:

f(x) = -3x - 21

Step-by-step explanation:

Graphed this equation and it passes through (-6, -3), also known as Point A.

7 0

2 years ago

If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple ar

Oksana_A [137]

Answer:

$n + 4 {n \choose 2} + 6 {n \choose 3} + 4 {n \choose 4} + {n \choose 5}$

Step-by-step explanation:

Lets divide it in cases, then sum everything

Case (1): All 5 numbers are different

In this case, the problem is reduced to count the number of subsets of cardinality 5 from a set of cardinality n. The order doesnt matter because once we have two different sets, we can order them descendently, and we obtain two different 5-tuples in decreasing order.

The total cardinality of this case therefore is the Combinatorial number of n with 5, in other words, the total amount of possibilities to pick 5 elements from a set of n.

${n \choose 5 } = \frac{n!}{5!(n-5)!}$

Case (2): 4 numbers are different

We start this case similarly to the previous one, we count how many subsets of 4 elements we can form from a set of n elements. The answer is the combinatorial number of n with 4 ${n \choose 4} .$

We still have to localize the other element, that forcibly, is one of the four chosen. Therefore, the total amount of possibilities for this case is multiplied by those 4 options.

The total cardinality of this case is $4 * {n \choose 4} .$

Case (3): 3 numbers are different

As we did before, we pick 3 elements from a set of n. The amount of possibilities is ${n \choose 3} .$

Then, we need to define the other 2 numbers. They can be the same number, in which case we have 3 possibilities, or they can be 2 different ones, in which case we have ${3 \choose 2 } = 3$ possibilities. Therefore, we have a total of 6 possibilities to define the other 2 numbers. That multiplies by 6 the total of cases for this part, giving a total of $6 * {n \choose 3}$

Case (4): 2 numbers are different

We pick 2 numbers from a set of n, with a total of ${n \choose 2}$ possibilities. We have 4 options to define the other 3 numbers, they can all three of them be equal to the biggest number, there can be 2 equal to the biggest number and 1 to the smallest one, there can be 1 equal to the biggest number and 2 to the smallest one, and they can all three of them be equal to the smallest number.

The total amount of possibilities for this case is

$4 * {n \choose 2}$

Case (5): All numbers are the same

This is easy, he have as many possibilities as numbers the set has. In other words, n

Conclussion

By summing over all 5 cases, the total amount of possibilities to form 5-tuples of integers from 1 through n is

$n + 4 {n \choose 2} + 6 {n \choose 3} + 4 {n \choose 4} + {n \choose 5}$

I hope that works for you!

4 0

3 years ago

8x=-4(x+3)<br> I would really appreciate some help

olganol [36]

Answer:

x = -1

Step-by-step explanation:

8x = - 4(x + 3)

8x = -4x - 12

+4x +4x

12 12

x = -1

Remember, a negative times a positive equals a negative
Remember, a negative divided by a positive equals a negative

Hope this helps you!!! :)

4 0

3 years ago

Read 2 more answers

Consider the following expression: (1 + x)^n. A) Use the Binomial Theorem to find the first four terms of this polynomial. B) Wh

sergiy2304 [10]

Given:

The expression: (1 + x)^n

The Binomial Theorem is used to predict the products of a binomial raised to a certain power, n, without multiplying the terms one by one.

The following formula is used:

(a + b)^n = nCk * a^(n-k) * b^k

we have (1 +x)^n,

where a = 1
b = x
let n = 4

First term, k = 1

4C1 = 4

first term: 4*(1^(4-1))*x^1

Therefore, the first term is 4x. Do the same for the next three terms.

2nd term: k =2
3rd term: k = 3
4th term: k = 4
<span />

3 0

3 years ago