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blagie [28]
2 years ago
9

The side length of a regular hexagon is 11 cm.

Mathematics
1 answer:
Evgen [1.6K]2 years ago
8 0

Answer:

A)let x be the length of one side , 6 × x= peri.

B)6 × 11 = 66

You might be interested in
. A box in a certain supply room contains four 40-W lightbulbs, five 60-W bulbs, and six 75-W bulbs. Suppose that three bulbs ar
yaroslaw [1]

Answer:

a) 59.34%

b) 44.82%

c) 26.37%

d) 4.19%

Step-by-step explanation:

(a)

There are in total <em>4+5+6 = 15 bulbs</em>. If we want to select 3 randomly there are  K ways of doing this, where K is the<em> combination of 15 elements taken 3 at a time </em>

K=\binom{15}{3}=\frac{15!}{3!(15-3)!}=\frac{15!}{3!12!}=\frac{15.14.13}{6}=455

As there are 9 non 75-W bulbs, by the fundamental rule of counting, there are 6*5*9 = 270 ways of selecting 3 bulbs with exactly two 75-W bulbs.

So, the probability of selecting exactly 2 bulbs of 75 W is

\frac{270}{455}=0.5934=59.34\%

(b)

The probability of selecting three 40-W bulbs is

\frac{4*3*2}{455}=0.0527=5.27\%

The probability of selecting three 60-W bulbs is

\frac{5*4*3}{455}=0.1318=13.18\%

The probability of selecting three 75-W bulbs is

\frac{6*5*4}{455}=0.2637=26.37\%

Since <em>the events are disjoint</em>, the probability of taking 3 bulbs of the same kind is the sum 0.0527+0.1318+0.2637 = 0.4482 = 44.82%

(c)

There are 6*5*4 ways of selecting one bulb of each type, so the probability of selecting 3 bulbs of each type is

\frac{6*5*4}{455}=0.2637=26.37\%

(d)

The probability that it is necessary to examine at least six bulbs until a 75-W bulb is found, <em>supposing there is no replacement</em>, is the same as the probability of taking 5 bulbs one after another without replacement and none of them is 75-W.

As there are 15 bulbs and 9 of them are not 75-W, the probability a non 75-W bulb is \frac{9}{15}=0.6

Since there are no replacement, the probability of taking a second non 75-W bulb is now \frac{8}{14}=0.5714

Following this procedure 5 times, we find the probabilities

\frac{9}{15},\frac{8}{14},\frac{7}{13},\frac{6}{12},\frac{5}{11}

which are

0.6, 0.5714, 0.5384, 0.5, 0.4545

As the events are independent, the probability of choosing 5 non 75-W bulbs is the product

0.6*0.5714*0.5384*0.5*0.4545 = 0.0419 = 4.19%

3 0
3 years ago
Function Q gives a puppy's weight in pounds as function of its age in months. What does each expression represent in this situat
babymother [125]

Answer:

Q(18) is a mathematical representation of the weight in pounds of a puppy after 18 months.

Q(30) = 27.5 ; This means that the weight of puppy after 30 months will be 27.5 pounds

Step-by-step explanation:

Given the expressions :

Q(18)

Q(30) = 27.5

Function Q gives a puppy's weight in pounds as function of its age in months

What does each expression represent in this situation?

A function is generally represented in the form a(x) ;

Hence, Q(18) is a mathematical representation of the weight in pounds of a puppy after 17 months

Q(30) = 27.5 ; This means that the weight of puppy after 30 months will be 27.5 pounds. 27.5 is the result of working out the function Q at 30.

6 0
2 years ago
Evaluate to 212 base 3 - 121 base 3 + 222 base 3​
aksik [14]

Answer:

212 bp^3 (base pairs cubed) - 121 bp^3 (base pairs cubed) + 222 bp^3 (base pairs cubed) = 313 bp^3 (base pairs cubed

Step-by-step explanation:

5 0
3 years ago
Determine if the matrix is symmetric.
Amanda [17]

Answer:

because this is equal to the given matrix, the given matrix is symmetric.

Step-by-step explanation:

A symmetric matrix is a square matrix which has same number of rows and columns. Square matrix is equal to transpose. Equal matrices have equal dimensions. The given matrix is symmetric because the rows and columns are equally distributed.

4 0
3 years ago
Write the equation of the line of best fit using the slope-intercept formula $y = mx + b$. Show all your work, including the poi
Dennis_Churaev [7]

Answer:

y=\frac{5}{7}x+\frac{135}{7}

Step-by-step explanation:

You only need two points on a line to find the equation for that line.

We are going to use 2 points that cross that line or at least come close to. You don't have to use the green points... just any point on the line will work.  You might have to approximate a little.

I see ~(67.5,67.5) and ~(64,65).

Now once you have your points, we need to find the slope.

You may use \frac{y_2-y_1}{x_2-x_1} where (x_1,y_1) \text{ and } (x_2,y_2) are points on the line.

Or you can line up the points vertically and subtract then put 2nd difference over 1st difference.

Like this:

(  64  ,   65  )

-( 67.5, 67.5 )

--------------------

-3.5        -2.5

So the slope is -2.5/-3.5=2.5/3.5=25/35=5/7.

Now use point-slope form to find the equation:

y-y_1=m(x-x_1) where m is the slope and (x_1,y_1) is a point on the line.

y-65=\frac{5}{7}(x-64)

Distribute:

y-65=\frac{5}{7}x-\frac{5}{7}\cdot 64

Simplify:

y-65=\frac{5}{7}x-\frac{320}{7}

Add 65 on both sides:

y=\frac{5}{7}x-\frac{320}{7}+65

Simplify:

y=\frac{5}{7}x+\frac{135}{7}

6 0
3 years ago
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