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ra1l [238]
3 years ago
15

An archaeologist at a dig sets up a coordinate system using string. Two similar artifacts are found one at position (1, 4) and t

he other at (5, 2). How far apart were the two artifacts? Round to the nearest tenth of a unit if necessary
Mathematics
1 answer:
myrzilka [38]3 years ago
4 0

Given:

Positions of two artifacts are at points (1, 4) and (5, 2).

To find:

The distance between these two artifacts.

Solution:

Distance formula: The distance between two points is

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Using distance formula, the distance between two points (1, 4) and (5, 2) is

d=\sqrt{(5-1)^2+(2-4)^2}

d=\sqrt{(4)^2+(-2)^2}

d=\sqrt{16+4}

d=\sqrt{20}

d=4.4721359

Round to the nearest tenth of a unit.

d\approx 4.5

Therefore, the distance between two artifacts is 4.5 units.

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Find (a) the number of subsets and (b) the number of proper subsets of the set.
vaieri [72.5K]

Answer:

(a) Total No. of Subsets = 128

(b) Total No. of Proper Subsets = 127

Step-by-step explanation:

First we need to define the set of days of the week.

Set of Days of Week = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}

It is evident from the set of days of the week, that it contains 7 elements.

(a)

The total no. of subsets of a given set is given by the following formula:

Total No. of Subsets = 2^n

where,

n = no. of elements of the set = 7

Therefore,

Total No. of Subsets = 2^n

Total No. of Subsets = 2^7

<u>Total No. of Subsets = 128</u>

(b)

The total no. of proper subsets of a given set is given by the following formula:

Total No. of Proper Subsets = (2^n) - 1

where,

n = no. of elements of the set = 7

Therefore,

Total No. of Proper Subsets = (2^n) - 1

Total No. of Proper Subsets = (2^7) - 1 = 128 - 1

<u>Total No. of Proper Subsets = 127 </u>

3 0
3 years ago
Umberto buys a game for $7.89 and some batteries for $5.49. He pays with a $20 bill. Which is the best estimate of change he sho
Anika [276]

The change is the remaining money that is needed to take from the seller so a change of Umberto will be $6.62.

<h3>What is subtraction?</h3>

To subtract in mathematics is to take something away from a group or a number of objects.

The group's total number of items decreases or becomes lower when we subtract from it.

Given that,

Umberto buys a game for $7.89 and some batteries for $5.49.

Total money of buying = 7.89 + 5.49 = $13.38

Now he gives a $20 bill.

Remaining (change) = 20 - 13.38

⇒ $6.62

Hence "The change of Umberto will be $6.62".

For more about subtraction,

brainly.com/question/1927340

#SPJ1

6 0
1 year ago
How much material, in square inches, is needed to make the flag? square inches if the material costs $0.15 per square inch, how
lorasvet [3.4K]

The amount needed to purchase materials needed to cover the area of the triangular flag is: $54.

<h3>What is the Area of a Triangle?</h3>

Area of a triangle = 1/2(bh)

Given the dimensions of the flag as the following:

base (b) = 18 in.

height (h) = √(41² - 9²) = 40 in.

Area of the flag = 1/2(18)(40) = 360 in.²

Cost of material needed = (360)(0.15) = $54

Learn more about area of a triangle on:

brainly.com/question/9030437

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5 0
2 years ago
What is the grates common factor of 15 and 64??
Rashid [163]

Answer:

The gcf of 15 and 64 can be obtained like this: The factors of 15 are 15, 5, 3, 1. The factors of 64 are 64, 32, 16, 8, 4, 2, 1. The common factors of 15 and 64 are 1, intersecting the two sets above. In the intersection factors of 15 ∩ factors of 64 the greatest element is 1. Therefore, the greatest common factor of 15 and 64 is 1.

Hope this helped!

Good luck :p

~Emmy <3



7 0
3 years ago
Which describes the collection of all points in the same plane that are 8 1/2 inches from Point T?
lukranit [14]

Answer:

circle T with radius 8 and 1/ 2 inches

Step-by-step explanation:

 

5 0
3 years ago
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