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OleMash [197]
2 years ago
7

Five light bulbs that are either on or off are lined up in a row. A certain code uses different combinations of lights turned on

to represent
different words. If exactly 2 lights must be turned on to represent a word, how many different words can be formed using the 5 light
bulbs? (1 point)
Mathematics
1 answer:
Paraphin [41]2 years ago
7 0

Answer:

10

Step-by-step explanation:

The number of different ways that 2 lights can be chosen from 5 is ₅C₂.  Use a calculator or find the value manually:

₅C₂ = 5! / (2! (5−2)!)

₅C₂ = 5! / (2! 3!)

₅C₂ = 5×4×3×2×1 / (2×1 × 3×2×1)

₅C₂ = 5×4 / 2

₅C₂ = 10

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If s is Julian’s savings, evaluate the expression when s = $125. First, write the expression . Second, 125 in for the variable s
Shkiper50 [21]

Answer:

Hey just took this and got it right.

s/2

substitute

simplifying/ dividing

$62.50

100%

Step-by-step explanation:

6 0
2 years ago
What is the multiplicative inverse of 5 in z11, z12, and z13? you can do a trial-and-error search using a calculator or a pc?
grin007 [14]

A multiplicative inverse of an integer a is an integer x such that the product ax is congruent to 1 with respect to the modulus m.  

1. Z_{11}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10}\}.

Check:

  • 5\cdot 0=\overline{0};
  • 5\cdot 1=\overline{5};
  • 5\cdot 2=\overline{10};
  • 5\cdot 3=15=\overline{4};
  • 5\cdot 4=20=\overline{9};
  • 5\cdot 5=25=\overline{3};
  • 5\cdot 6=30=\overline{8};
  • 5\cdot 7=35=\overline{2};
  • 5\cdot 8=40=\overline{7};
  • 5\cdot 9=45=\overline{1};
  • 5\cdot 10=50=\overline{6}.

The multiplicative inverse of 5 in Z_{11} is 9.

2.   Z_{12}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10},\overline{11}\}.

Check:

  • 5\cdot 0=\overline{0};
  • 5\cdot 1=\overline{5};
  • 5\cdot 2=\overline{10};
  • 5\cdot 3=15=\overline{3};
  • 5\cdot 4=20=\overline{8};
  • 5\cdot 5=25=\overline{1};
  • 5\cdot 6=30=\overline{6};
  • 5\cdot 7=35=\overline{11};
  • 5\cdot 8=40=\overline{4};
  • 5\cdot 9=45=\overline{9};
  • 5\cdot 10=50=\overline{2};
  • 5\cdot 11=55=\overline{7}.

The multiplicative inverse of 5 in Z_{12} is 5.

3.  Z_{13}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10},\overline{11},\overline{12}\}.

Check:

  • 5\cdot 0=\overline{0};
  • 5\cdot 1=\overline{5};
  • 5\cdot 2=\overline{10};
  • 5\cdot 3=15=\overline{2};
  • 5\cdot 4=20=\overline{7};
  • 5\cdot 5=25=\overline{12};
  • 5\cdot 6=30=\overline{4};
  • 5\cdot 7=35=\overline{9};
  • 5\cdot 8=40=\overline{1};
  • 5\cdot 9=45=\overline{6};
  • 5\cdot 10=50=\overline{11};
  • 5\cdot 11=55=\overline{3};
  • 5\cdot 12=60=\overline{8}.

The multiplicative inverse of 5 in Z_{13} is 8.

8 0
2 years ago
Mr. jovanovski is having wood flooring put in his rectangular living room. the area of the room is 234 square feet. the length o
OlgaM077 [116]
By definition the area of a rectangle is:
 A = l * w
 Where,
 l: long
 w: width
 So we have to clear the width:
 w = A / l
 Substituting the values:
 w = (234) / (18) = 13
 w = 13 feets
 answer
 the width, in feet, of the room is 13
5 0
2 years ago
Read 2 more answers
Choose the algebraic expression that represents the area of a triangle that has a base 8 inches less than 2 times wider than the
loris [4]

Answer:

B. (1/2)(2h-8)(h)

Step-by-step explanation:

Area of a triangle = 1/2 × base × height

Let

Height = h

Base = 8 inches less than 2 times wider than the hight

= 2h-8

Substituting the values of base and height into the formula

We have,

Area of a triangle = 1/2 × base × height

= 1/2 × (2h-8) × h

= (1/2)(2h-8)(h)

The correct answer is option

B. (1/2)(2h-8)(h)

7 0
2 years ago
Ernie earned $121.50 more than Kaylin. Tria earned $35 less than 3 times the amount Kaylin earned. Ernie, Tria, and Kaylin earne
Dvinal [7]
X - Ernie, y - Kaylin, z - Tria
x = y + 121.50
z = 3y - 35
x + y + z = 579
-------------------------
z = 3 y - 35      =>   - 3 y + z = -35
y + 121.50 + y + z = 579
---------------------------------
- 3 y + z = - 35        / · ( -1 )
 2 y + z = 457.50     (we will use the elimination method) 
---------------------------------
3 y - z = 35
2 y + z = 457.50
----------------------
5 y = 492.5,            y = 492.5 : 5 = 98.5
z = 3 · 98.5 - 35
z = 260.5
Tria earned $260.5 
8 0
2 years ago
Read 2 more answers
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