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2 years ago

Find the 20th term in the sequence, where the first term is -2 and the common ratio is-2.

Mathematics

1 answer:

geniusboy [140]2 years ago

6 0

Answer:

Step-by-step explanation:

(1)

a1=-2

r=-2

$a_{20}=(-2)(-2)^{20-1}=-2(-2)^{19}=2^{20}=1048576\\(2)\\a_{1}=1000\\r=\frac{200}{1000} =\frac{1}{5} \\a_{8}=1000(\frac{1}{5} )^{8-1}=1000(.2)^7=0.0128\\(3)\\a_{1}=2\\a_{3}=50\\a_{2}=\sqrt{2*50} =10\\r=\frac{10}{2} =5$

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Find the midpoint of the segment with the given endpoints.<br> (-4,-5) and (10,- 9)

Elanso [62]

Answer:

(3, -7)

Step-by-step explanation:

$\left(\frac{-4+10}{2}, \frac{-5-9}{2} \right)=(3, -7)$

6 0

1 year ago

5. Priya mixes 2..5 cups of water with 1/3 cup or orange juice concentrate. Diego mixes 1 2/3 cups of water with 1/4 cup or oran

Snowcat [4.5K]

Priya needs 13⅓ cups of orange juice

Diego 15 cups

Step-by-step explanation:

......................................................................................................................

Priya

......................................................................................................................

Cup of water = 2½

Cup of orange = ⅓

If 2½ cups of water requires ½ cup of orange juice concentrate

Then 100 cups of water would require x cup of orange

Representing the above statement mathematically

2½ : ⅓ = 100 : x

5/2 : 1/3 = 100 : x ------------------Convert ratio sign to division

5/2 ÷⅓ = 100/x

5/2 * 3 = 100/x

15/2 = 100/x ---------------Multiply both sides by x

15/2 * x = 100/x * x

15x/2 = 100 ------------------ Multiply both sides by 2

2 * 15x/2 = 2 * 100

15x = 200 --------------- Divide both sides by 15

x = 200/15

x = 13⅓

So, 13⅓ cups of orange is needed by Priya

......................................................................................................................

Diego

......................................................................................................................

Cup of water = 1⅔

Cup of orange = ¼

If 1⅔ cups of water requires ¼ cup of orange juice concentrate

Then 100 cups of water would require x cup of orange

Representing the above statement mathematically

1⅔:¼ = 100:x

5/3 : ¼ = 100:x

5/3 ÷¼ = 100 ÷ x

5/3 * 4/1 = 100 ÷ x

20/3 =100/x----------------------- Multiply x to both sides

20/3 * x = 100/x * x

20x/3 = 100 ------------------------ Multiply 3 to sides by 3

3 * 20x/3 = 100 * 3

20x = 300 ------------- Divide both sides by 2

20x/20 = 300/20

x = 15

So, 15 cups of orange is needed by Diego

6 0

3 years ago

The owner of a cattle ranch would like to fence in a rectangular area of 3000000 m^2 and then divide it in half with a fence dow

Reika [66]

If you notice the picture below, the amount of fencing, or perimeter, that will be used will be 3w + 2l

now $\bf \begin{cases}
A=l\cdot w\\\\\
A=3000000\\
----------\\
3000000=l\cdot w\\\\
\frac{3000000}{w}=l
\end{cases}\qquad thus
\\\\\\
P=3w+2l\implies P=3w+2\left( \cfrac{3000000}{w} \right)\implies P=3w+\cfrac{6000000}{w}
\\\\\\
P=3w+6000000w^{-1}\\\\
-----------------------------\\\\
now\qquad \cfrac{dP}{dw}=3-\cfrac{6000000}{w^2}\implies \cfrac{dP}{dw}=\cfrac{3w^2-6000000}{w^2}
\\\\\\
\textit{so the critical points are at }
\begin{cases}
0=w^2\\\\
0=\frac{3w^2-6000000}{w^2}
\end{cases}$

solve for "w", to see what critical points you get, and then run a first-derivative test on them, for the minimum

notice the $0=w^2\implies 0=w$ so. you can pretty much skip that one, though is a valid critical point, the width can't clearly be 0

so.. check the critical points on the other

8 0

3 years ago

How can the Associative, Commutative, and Distributive Properties be applied when performing operations on complex numbers and p

ozzi

By using Associative, Commutative, and Distributive Properties in performing operations on complex numbers and polynomials, you would be able to simplify correctly and simply. To combine complex numbers, you must distribute any coefficients in front of the parentheses. Then identify and<span>combine like terms by combining the real number parts and the imaginary number parts separately.</span>

8 0

3 years ago

Read 2 more answers

In a lottery game, a player picks six numbers from 1 to 22. If the player matches all six numbers, they win 20,000 dollars. Othe

Angelina_Jolie [31]

Answer:

Total possible number of outcomes = C(24,6) [24 choose 6]

=24!/(6!18!)

= 134596

Out of which there is only one winning combination.

Therefore we conclude:

P(win 20000)=1/134596

P(lose 1)=134595/134596

and hence the expected value is:

20000*(1/134596)+(-1)*(134595/134596)

=-114595/134596

=-0.8514 (rounded to four places after decimal)

Step-by-step explanation:

Hope this helped!

8 0

3 years ago