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taurus [48]
3 years ago
15

The length of a side of a regular hexagon is 6.8 cm, correct to one decimal place. Find the smallest possible perimeter of the l

ength
Mathematics
1 answer:
marysya [2.9K]3 years ago
7 0

Answer: 40.8cm

Step-by-step explanation:

A hexagon is a polygon that is made up of 6 sides. The perimeter of a regular hexagon is calculated by multiplying the side given by 6

Since the length of a side of a regular hexagon is 6.8 cm, the perimeter will be:

= 6 × 6.8

= 40.8cm

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The graph of was shifted 5 units down and 4 units to the left. What is the equation of the resulting graph?
marysya [2.9K]

Answer:

5x+4

Step-by-step explanation:

use the equation mx+b I think this is right but I really dunno

8 0
3 years ago
Five men and 5 women are ranked according to their scores on an examination. Assume that no two scores are alike and all possibl
serg [7]

Answer:

P(X=i) where i = 1,2,3,4,5,6,7,8,9,10 = 1/2, 5/18, 5/36, 5/84, 5/252, 1/252, 0, 0, 0, 0.

Step-by-step explanation:

X denotes the highest ranking achieved by the woman.

When X=1, the top ranked person is a female.

When X=2, the first person is a male and the second ranked person is a female.

Similarly, when X=3, the first two ranked persons are male and the third one is a female.

When X=4, the first three persons are male and the fourth one is a female.

When X=5, the first four persons are males and the fifth person is a female.

When X=6, the first five people are males and the sixth person is a female. The rest of the four people are also females since there are only five men in a sample space.

The probability for X=7, 8, 9, 10 is zero because there are only five men who can achieve the first five positions and the last highest rank that can be achieved by a woman is 6.

To compute the probabilities, we will use the formula:

<u>No. of ways a female can be ranked X/Total number of ways to rank 10 people</u>

Note that the total number of ways of ranking 10 different people is 10P10 or 10!

For X=1, the first position can be taken by any of the 5 women. The possible ways of the first person being a woman is 5C1. The rest of the 9 people can take any of the ranks. They can be ordered in 9P9 ways.

So, P(X=1) = (5C1)(9P9)/(10P10) = (5 x 362880)/(3628800) = 1/2

For X=2, the first rank must be taken by a male. The number of ways to arrange the first person as a male out of the 5 men can be calculated by 5P1. The second position must be taken by a female and rest of the 8 positions can be taken by any of the 8 people in 8P8 ways.

So, P(X=2) = (5P1)(5C1)(8P8)/(10P10) = (5 x 5 x 40320)/(3628800) = 5/18

For X=3, first two people must be men and the number of ways to arrange 2 out of 5 males at the first two positions is 5P2. The third position is a female. The rest of the 7 people can be ordered in 7P7 ways.

P(X=3) = (5P2)(5C1)(7P7)/(10P10) = (20 x 5 x 5040)/(3628800) = 5/36

P(X=4) = (5P3)(5C1)(6P6)/(10P10) = (60 x 5 x 720)/(3628800) = 5/84

P(X=5) = (5P4)(5C1)(5P5)/(10P10) = (120 x 5 x 120)/(3628800) = 5/252

P(X=6) = (5P5)(5C1)(4P4)/(10P10) = (120 x 5 x 24)/(3628800) = 1/252

P(X=7) = 0

P(X=8) = 0

P(X=9) = 0

P(X=10) = 0

7 0
3 years ago
A rectangle is 20 meters long and 20 meters wide. If the length is increased by 10% and the width is decreased by 10%, what is t
Solnce55 [7]

Consider that the initial length and width of the rectangle are given as,

\begin{gathered} l=20 \\ b=20 \end{gathered}

After the length is increased by 10%, the new length (L) of the rectangle is calculated as,

\begin{gathered} L=(1+\frac{10}{100})\cdot l \\ L=(\frac{110}{100})\cdot20 \\ L=22 \end{gathered}

After the width is decreased by 10%, the new width (B) of the rectangle is calculated as,

\begin{gathered} B=(1-\frac{10}{100})\cdot b \\ B=(\frac{90}{100})\cdot20 \\ B=18 \end{gathered}

Then the area (A) of the new rectangle is calculated as,

\begin{gathered} A=L\times B \\ A=22\times18 \\ A=396 \end{gathered}

Thus, the new area of the rectangle is 396 square meters.

7 0
1 year ago
1. What is the constant of proportionality, k,<br><br><br> of Kevin's wage? Greg's? Savannah's?
Gala2k [10]

Answer:

Part a) The constant of proportionality of Kevin's wage is k=\$8.25\ per\ hour

Part b) The constant of proportionality of Greg's wage is k=\$9.00\ per\ hour

Part c) The constant of proportionality of Savannah's wage is k=\$9.50\ per\ hour

Step-by-step explanation:

See the attached figure to better understand the problem

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y/x=k or y=kx

To find out the constant of proportionality k , divide the variable y (total earned) by the variable x (number of hours)

<em>Kevin's wage</em>

Take any point from the table

I take the point (2,16.50)

k=\frac{16.50}{2}=\$8.25\ per\ hour

<em>Greg's wage</em>

Take any point from the table

I take the point (3,27.00)

k=\frac{27.00}{3}=\$9.00\ per\ hour

<em>Savannah's wage</em>

Take any point from the table

I take the point (2,19.00)

k=\frac{19.00}{2}=\$9.50\ per\ hour

3 0
3 years ago
A pound of popcorn is popped for a class party. The popped corn is put into small popcorn boxes that each hold 120 popped kernel
V125BC [204]
Let x be the no of boxes.

120x = 14501
x = 14501/120

Upon division the quotient +1 = The no of boxes required and 
The remainder is the amount of popcorn in the last box

No of boxes = 121 boxes
Kernels in the last box = 101 kernels
6 0
3 years ago
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