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ivanzaharov [21]
3 years ago
11

Find the area of a regular hexagon with an apothem 17.3 miles long and a side 20 miles long

Mathematics
1 answer:
Zinaida [17]3 years ago
4 0
The area of a hexagon is \frac{3 \sqrt{3} }{2} a^{2} where a = one side

\frac{3 \sqrt{3} }{2} 20^{2}

\frac{3*200 \sqrt{3} }{2}

\frac{600 \sqrt{3} }{2}

300 \sqrt{3} ≈ 1038 mi²

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In a race between 18 people, how many ways can the top 5 finishers be arranged?
snow_lady [41]

Answer:

Step-by-step explanation:

This is permutation, since order matters.  The formula for us is

₁₈P₅ = \frac{18!}{(18-5)!} which simplifies to

₁₈P₅ = \frac{18*17*16*15*14*13!}{13!}

The factorial of 13 cancels out on the top and bottom leaving you with

₁₈P₅ = 18 × 17 × 16 × 15 × 14

which comes to 1,028,160 ways

Another way to look at it is:  the first 5 people of 18 finish and the others you don't care about.  Once the first place person is first, there are only 4 of the 18 left to finish in second place.  Then there are only 3 left to finish in third place, etc.  So if we use that reasoning, we don't even need to use the formula, we can just say

18 * 17 * 16 * 15 * 14 and those are the first 5 people of 18 to finish.

8 0
3 years ago
What is the correct answer to this question?<br><br> F/2=5/8
ANTONII [103]

Answer:

F = 1.25

Step-by-step explanation:

All you would have to do is cross multiply, so our equations starts at \frac{F}{2} = \frac{5}{8}. We would now multiply F by 8 and 2 by 5. We now have 8F = 10. We can now divide both sides of the equation by 8 to get F = 1.25.

4 0
3 years ago
The number of members over time in an online music sharing club can be modeled by an exponential function. the club started with
Paraphin [41]

Answer:

a.) N(x) =  N_{0} e^{bx}

b.) therefore b = \ln \frac{2142}{2100}  =  \ln (1.02) = 0.0198

    b is the rate of increase of number of members

c.) The club will not be able to get more than 5000 members during its first year.

Step-by-step explanation:

i) the club started with 2100 members.

  so we can write N_{0} = 2100.

a.) so we can write the equation as an exponential function given by

  N(x) =  N_{0} e^{bx} where x is in months and b is a constant and N(x) is the number of members in the online music sharing club .

 therefore 2142 = 2100 \times (e^{b\times 1}) = 2100e^{b}

b.) therefore b = \ln \frac{2142}{2100}  =  \ln (1.02) = 0.0198

    b is the rate of increase of number of members

c.) Will the club have more than 5000 members during its first year? Justify your reasoning.

      5000 = 2100e^{0.0198x}

 therefore x  = \frac{1}{0.0198} \ln{(\frac{5000}{2100} )}  =  43.81 \hspace{0.1cm}months

The club will not be able to get more than 5000 members during its first year.

7 0
3 years ago
The length of a rectangle is 5 ft less than three times the width, and the area of the rectangle is 50 ft². Find the dimensions
Mariulka [41]

Answer

Length = 10 ft

Width = 5 ft

Explanation

Area of the rectangle given = 50 ft²

Let the width of the rectangle be x

So this means the length of the rectangle will be 3x - 5

What to find:

The dimensions of the rectangle.

Step-by-step solution:

Area of a rectangle = length x width

i.e A = L x W

Put A = 50, L = 3x - 5, W = x into the formula.

\begin{gathered} 50=(3x-5)x \\ 50=3x^2-5x \\ 3x^2-5x-50=0 \end{gathered}

The quadratic equation can now be solve using factorization method:

\begin{gathered} 3x^2-5x-50=0 \\ 3x^2-15x+10x-50=0 \\ 3x(x-5)+10(x-5)=0 \\ (3x+10)(x-5)=0 \\ 3x+10=0\text{ }or\text{ }x-5=0 \\ 3x=-10\text{ }or\text{ }x=5 \\ x=-\frac{10}{3}\text{ }or\text{ }x=5 \end{gathered}

Since the dimension can not be negative, hence the value of x will be = 5.

Therefore, the dimensions of the rectangle will be:

\begin{gathered} Length=3x-5=3(5)-5=15-5=10\text{ }ft \\  \\ Width=x=5\text{ }ft \end{gathered}

7 0
1 year ago
Ask Your Teacher Equal amounts are invested at 2%, 7%, and 9% annual interest. If the three investments yield a total of $828 an
Nookie1986 [14]

Answer:

$4600

Step-by-step explanation:

Write an equation to represent the problem.

Interest is calculated by multiplying the interest rate with the investment. <u>Multiplying each of the rates</u> (2%, 7% and 9%) <u>in decimal form with the investment amount is equal to the annual interest</u>, (828).

Convert a percentage to decimal form by dividing by 100:

2% ÷ 100 => 0.02

7% ÷ 100 => 0.07

9% ÷ 100 => 0.09

let "P" represent the amount of money for the total investment

0.02P + 0.07P + 0.09P = 828

Use the equation to solve for "P". Simplify by collecting like terms (numbers that have the same variable) then isolate "P" by moving the other numbers to the right side. To move a number to the other side, do it's reverse operation to both sides of the equation. (The reverse of multiplying is dividing).

0.02P + 0.07P + 0.09P = 828        Collect like terms

0.18P = 828        Isolate "P"

0.18P/0.18 = 828/0.18        Divide both sides by 0.18

P = 828/0.18         "P" is isolated because 0.18 cancelled out. Simplify.

P = 4600        Total investment

Therefore the total investment is $4600.

5 0
3 years ago
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