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3 years ago

WILL GIVE BRANLIEST!!!!!!!!!!!!!

Mathematics

1 answer:

Lunna [17]3 years ago

6 0

Answer:

D is the answer

Step-by-step explanation:

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Evaluate the sum of the following finite geometric series.

rjkz [21]

Answer:

$\large\boxed{\dfrac{156}{125}\approx1.2}$

Step-by-step explanation:

<h3>Method 1:</h3>

$\sum\limits_{n=1}^4\left(\dfrac{1}{5}\right)^{n-1}\\\\for\ n=1\\\\\left(\dfrac{1}{5}\right)^{1-1}=\left(\dfrac{1}{5}\right)^0=1\\\\for\ n=2\\\\\left(\dfrac{1}{5}\right)^{2-1}=\left(\dfrac{1}{5}\right)^1=\dfrac{1}{5}\\\\for\ n=3\\\\\left(\dfrac{1}{5}\right)^{3-1}=\left(\dfrac{1}{5}\right)^2=\dfrac{1}{25}\\\\for\ n=4\\\\\left(\dfrac{1}{5}\right)^{4-1}=\left(\dfrac{1}{5}\right)^3=\dfrac{1}{125}$

$\sum\limits_{n=1}^4\left(\dfrac{1}{5}\right)^{n-1}=1+\dfrac{1}{5}+\dfrac{1}{25}+\dfrac{1}{125}=\dfrac{125}{125}+\dfrac{25}{125}+\dfrac{5}{125}+\dfrac{1}{125}=\dfrac{156}{125}$

<h3>Method 2:</h3>

$\sum\limits_{n=1}^4\left(\dfrac{1}{5}\right)^{n-1}\to a_n=\left(\dfrac{1}{5}\right)^{n-1}\\\\\text{The formula of a sum of terms of a geometric series:}\\\\S_n=a_1\cdot\dfrac{1-r^n}{1-r}\\\\r-\text{common ratio}\to r=\dfrac{a_{n+1}}{a_n}\\\\a_{n+1}=\left(\dfrac{1}{5}\right)^{n+1-1}=\left(\dfrac{1}{5}\right)^n\\\\r=\dfrac{\left(\frac{1}{5}\right)^n}{\left(\frac{1}{5}\right)^{n-1}}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\r=\left(\dfrac{1}{5}\right)^{n-(n-1)}=\left(\dfrac{1}{5}\right)^{n-n+1}=\left(\dfrac{1}{5}\right)^1=\dfrac{1}{5}$

$a_1=\left(\dfrac{1}{5}\right)^{1-1}=\left(\dfrac{1}{5}\right)^0=1$

$\text{Substitute}\ a_1=1,\ n=4,\ r=\dfrac{1}{5}:\\\\S_4=1\cdot\dfrac{1-\left(\frac{1}{5}\right)^4}{1-\frac{1}{5}}=\dfrac{1-\frac{1}{625}}{\frac{4}{5}}=\dfrac{624}{625}\cdot\dfrac{5}{4}=\dfrac{156}{125}$

5 0

4 years ago

Determine the perimeter of the triangle.<br> 3x<br> x + 6<br> 5x – 7

Gekata [30.6K]

Answer:

9x-1

Step-by-step explanation:

The perimeter of the triangle is adding up all 3 sides.

(3x)+(x+6)+(5x-7)=P

9x-1 = perimeter

All I have done is combine like terms.

If there is a... x = something, replace x with the number.

8 0

3 years ago

I need help with this any one please help me

alexandr1967 [171]

Answer:

b. y = 1000x

Constant of proportionality = 1,000

Step-by-step explanation:

The equation that represents a proportional relationship between variable x and y usually takes the following form, y = kx.

Where,

k = constant of proportionality.

From the three given equations, the only equation that takes the form is b. y = 1000x.

The constant of proportionality (k) of the equation = 1,000.

5 0

3 years ago

3/4x = 3 I don't know how to solve

Stels [109]

Answer: It's not solvable.

Reason:

You need to ask for more information from your teacher, because x can be anything.

3 0

3 years ago

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Ari thinks the perfect milkshake has 3 ounces of caramel for every 5 scoops of ice cream. Freeze Zone makes batches of milkshake

aksik [14]

A. They have too much caramel

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3 years ago

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