MATHEMATICS COLLEGE

Select the correct answer from each drop-down menu. The table shows the heights of the 10 tallest buildings in San Francisco and Los Angeles.

The average height of the 10 tallest buildings in Los Angeles is than the average height of the tallest buildings in San Francisco. The mean absolute deviation for the 10 tallest buildings in San Francisco is

The answer:

Answers

Answer 1

Answer:

Answer with explanation:

$\text{Average}=\frac{\text{Sum of all the observation}}{\text{Total number of Observation}}$

Average Height of tallest Building in San Francisco

$=(260+237+212+197+184+183+183+175+174+173)/(10)\n\n=(1978)/(10)\n\n=197.8$

Average Height of tallest Building in Los Angeles

$=(310+262+229+228+224+221+220+219+213+213)/(10)\n\n=(2339)/(10)\n\n=233.9$

→→Difference between Height of tallest Building in Los Angeles and Height of tallest Building in San Francisco

=233.9-197.8

=36.1

⇒The average height of the 10 tallest buildings in Los Angeles is 36.1 more than the average height of the tallest buildings in San Francisco.

⇒Part B

Mean absolute deviation for the 10 tallest buildings in San Francisco

|260-197.8|=62.2

|237-197.8|=39.2

|212-197.8|=14.2

|197 -197.8|= 0.8

|184 -197.8|=13.8

|183-197.8|=14.8

|183-197.8|= 14.8

|175-197.8|=22.8

|174-197.8|=23.8

|173 -197.8|=24.8

Average of these numbers

$=(62.2+39.2+14.2+0.8+13.8+14.8+14.8+22.8+23.8+24.8)/(10)\n\n=(231.2)/(10)\n\n=23.12$

Mean absolute deviation=23.12

Answer 2

Answer:

1st -36.1 meters or more

2nd -23.12

Step-by-step explanation:

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Both the galapagos Islands and the island of naura are on the equator, but the galapagos Islands are at 90.30 degree West whereas the island of naura is at 166.56 degree east. How far is it from galapagos Islands to naura travelling over the pacific ocean along the equator, correct to the nearest km

Answers

Answer:

11481.4875 km

Step-by-step explanation:

Given the that :

Galapagos island and Island of Naura are on the equator

Galapagos = 90.30°W

Island of Naura = 166.56°E

Ensuring same bearing is used for both :

Island of Naura = 166.56°E = (360° - 166.56°) = 193.44°W

Hence, we can calculate the difference in the bearing of both locations :

(193.44 - 90.30)°W = 103.14°

Hence the distance between Galapagos and Island of Naura along the equator is :

(Difference in bearing / total bearing) * earth's Circumference

Earth's Circumference = 40,075km

(103.14 / 360) × 40,075

0.2865 × 40,075

= 11481.4875 km

25-foot long board is to be cut into two parts. The longer part is one foot more than twice the shorter part. How long is each part?

Answers

To solve this problem you must apply the following proccedure:

1. You have that 25-foot long board is to be cut into two parts. Then, the first equation is:

a+b=25

2. The longer part is one foot more than twice the shorter part:

a=1+2b

3. The system of equation is:

a+b=25
a=1+2b

4. When you solve it, you obtain:

a=25-b

25-b=1+2b
25-1=2b+b
24/3=b
b=8 ft

a=1+2(8)
a=17 ft

A set X is said to be closed under multiplication if for every X1, X2 E X we have X1X2 E X. Let A be the union of all bounded subsets X CR that are closed under multiplication. Does inf(A) exist? If it does, find it.

Answers

Answer:

inf(A) does not exist.

Step-by-step explanation:

As per the question:

We need to prove that A is closed under multiplication,

If for every $X_(1), X_(2)\in X$

$X_(1)X_(2)\in X$

Proof:

Suppose, x, y $\in A$

Since, both x and y are real numbers thus xy is also a real number.

Now, consider another set B such that:

B = {xy} has only a single element 'xy' and thus [B] is bounded.

Since, [A] represents the union of all the bounded sets, therefore,

$B\subset A$

⇒ xy $\in A$

Therefore, from x, y $\]in A$ , we have xy $\]in A$ .

Hence, set a is closed under multiplication.

Now, to prove whether inf(A) exist or not

Proof:

Let us assume that inf(A) exist and inf(A) = $\beta$

Thus $\beta$ is also a real number.

Let C be another set such that

C = { $\beta$ - 1}

Now, we know that C is a bounded set thus { $\beta$ - 1} is also an element of A

Also, we know:

inf(A) = $\beta$

Therefore,

$n(A)\geq \beta$

But

$\beta - 1$ is an element of A and $\beta - 1 \leq \beta$

This is contradictory, thus inf(A) does not exist.

Hence, proved.

This is a two-part question: A 12-pack of bottled mineral water sells for $3.85. For the following,state whether to use multiplication or division for the specified amount:
a) The cost of one bottle of water:
b) The cost of four 12-packs of water: