3 years ago

Restaurants A, B, C, and D lie on a circular lake. Restaurants A and Care near the

Mathematics

1 answer:

DaniilM [7]3 years ago

6 0

Answer:

Step-by-step explanation:

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The angles below are supplementary. What is the value of x?

AVprozaik [17]

Answer:

the angle of x measures 16.6

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3 years ago

The population of a local species of bees can be found using an infinite geometric series where a1=860 and the common ratio is 1

erma4kov [3.2K]

$a_1=860$
$a_2=\dfrac{a_1}5$
$a_3=\dfrac{a_2}5=\dfrac{a_1}{5^2}$
$\vdots$
$a_n=\dfrac{a_{n-1}}5=\dfrac{a_{n-2}}{5^2}=\cdots=\dfrac{a_1}{5^{n-1}}$

The $k$ th partial sum is

$\displaystyle S_k=\sum_{n=1}^ka_n=\sum_{n=1}^k\frac{a_1}{5^{n-1}}$
$S_k=a_1\left(1+\dfrac15+\dfrac1{5^2}+\cdots+\dfrac1{5^{k-2}}+\dfrac1{5^{k-1}}$
$\dfrac15S_k=a_1\left(\dfrac15+\dfrac1{5^2}+\dfrac1{5^3}+\cdots+\dfrac1{5^{k-1}}+\dfrac1{5^k}\right)$

$\implies S_k-\dfrac15S_k=a_1\left(1-\dfrac1{5^k}\right)$
$\dfrac45 S_k=860\left(1-\dfrac1{5^k}\right)$
$S_k=1075-\dfrac{1075}{5^k}$

As $k\to\infty$ , we're left with

$\displaystyle\sum_{n=1}^\infty a_n=\lim_{k\to\infty}\left(1075-\frac{1075}{5^k}\right)=1075$

which is the upper limit to the population of the bees.

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3 years ago

Peppers cost $17.00 for 51 pounds. How much for 1 pound?

Gala2k [10]

Lets set up a ratio!

17.00USD per 51 pounds and 1 pound per x dollars.

$\frac{17}{51} = \frac{1}{x}
$

next step. cross multiply for the answer :)

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4 years ago

Two airplanes leave an airport at the same time and travel in opposite directions. One plane travels 60km\h slower than the othe

DanielleElmas [232]

Answer:

4 V + 4 (V - 60) = D where D is distance apart after 4 hrs

8 V - 240 = 7304

V = 943 km/hr

and V2 = 943 - 60 = 883 km/hr where second plane is 60 km/hr slower

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2 years ago

Jackson is playing a game of chance where he must randomly draw a marble out of a jar. He calculates the probability of drawing

madam [21]

Answer:

12/15

Step-by-step explanation:

If the probability of drawing a read marble is 3/15

Then that would just make the probability of NOT drawing a red marble 12/5

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3 years ago