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3 years ago

The observations 56, 58, 63 x-5 x+1 75 81, 85 have been

Mathematics

1 answer:

motikmotik3 years ago

5 0

Answer:

The value of x is 66.

Step-by-step explanation:

The median of a data set is the term that separates the lower half of the set from the upper half.

In a set with even cardinality, the median is given by the mean of it's two middle terms.

In this question:

Cardinality: 8

Middle terms: 4th and 5th, which are x - 5 and x + 1.

The median is 64.

This means that:

$\frac{x - 5 + x + 1}{2} = 64$

$2x - 4 = 128$

$2x = 132$

$x = \frac{132}{2}$

$x = 66$

The value of x is 66.

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How to solve this system of equal: x+y+z=1;x^2+y^2+z^2=1

swat32

There are infinitely many solutions.

Algebraically, we can eliminate $z$ and try to solve for $x,y$ :

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$\implies x^2+y^2+1-2x+x^2-2y+y^2+2xy=1$

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3 years ago

Explain how to determine if something is a vector space or not

nlexa [21]

All you do is referring to the following definition:

Definition: A vector space is a set V on which two operations + and · are defined, called vector addition and scalar multiplication.

The operation + (vector addition) must satisfy the following conditions:

Closure: If u and v are any vectors in V, then the sum u + v belongs to V.

(1) Commutative law: For all vectors u and v in V, u + v = v + u

(2) Associative law: For all vectors u, v, w in V, u + (v + w) = (u + v) + w

(3) Additive identity: The set V contains an additive identity element, denoted by 0, such that for any vector v in V, 0 + v = v and v + 0 = v.

(4) Additive inverses: For each vector v in V, the equations v + x = 0 and x + v = 0 have a solution x in V, called an additive inverse of v, and denoted by - v.

The operation · (scalar multiplication) is defined between real numbers (or scalars) and vectors, and must satisfy the following conditions:

Closure: If v in any vector in V, and c is any real number, then the product c · v belongs to V.

(5) Distributive law: For all real numbers c and all vectors u, v in V, c · (u + v) = c · u + c · v

(6) Distributive law: For all real numbers c, d and all vectors v in V, (c+d) · v = c · v + d · v

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3 years ago

Could a circle be circumscribed around this?

djyliett [7]

Answer:

Step-by-step explanation:

4 0

2 years ago

Let A = {1,2,3,..., 8, 9, 10} B = {4, 7, 10}

Dovator [93]

The answers to the questions are

(i) B - A = Ф / null set

(ii) A - B = {1, 2, 3, 5, 6, 8, 9}

(iii) (A - B) ∩ (B - A) = Ф / null set

(iv) (A - B) ∪ (B - A) = {1, 2, 3, 5, 6, 8, 9}

A set contains different elements which are mathematical objects of any kind such as numbers, points, spaces, lines e.t.c.

Different types of set are -singleton setsfinite and infinite setsempty or null sets equal sets unequal sets equivalent sets overlapping sets disjoint sets subsets super sets power sets universal sets

According to question,

i ] B - A = 0/null set

ii ] A - B = [ 1,2,3,5,6,8,9 ]

iii ] (A-B) n (B-A) = 0/ null set

iv ] (A-B) u ( B-A) = [ 1,2,3,5,6,8,9 ]

Hence, the answers to the questions are

(i) B - A = Ф / null set

(ii) A - B = {1, 2, 3, 5, 6, 8, 9}

(iii) (A - B) ∩ (B - A) = Ф / null set

(iv) (A - B) ∪ (B - A) = {1, 2, 3, 5, 6, 8, 9}

To understand more about Set Theory refer - brainly.com/question/13458417#SPJ9

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1 year ago

What is this answer please help

Burka [1]

Answer:

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Step-by-step explanation:

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8 0

3 years ago