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3 years ago

What is the sum of the first five terms of a geometric series with a1 = 20 and r = 1/4?

1 answer:

4 0

Sum of the first n terms of a geometric sequence is Sn = a(1 - r^n)/(1 - r)
Sn = 20(1 - (1/4)^5)/(1 - 1/4) = 20(1 - 1/1024)/(3/4) = 20(1023/1024)/(3/4) = 26 41/64

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MODELING WITH MATHEMATICS A farmer plants a garden that contains corn and pumpkins. The total area (in square

laiz [17]

Answer:

The equation in standard form that models area of pumpkins is:

$A_p = A_G - A_c$

and the area is: $x^2+8x+2$

Step-by-step explanation:

Given that the garden has corn and pumpkins

The expressions are:

Total area of garden: $A_G = 2x^2+5x+4$

Area of Corn: $A_c = x^2-3x+2$

Area of Pumpkins: $A_p = ?$

The sum of areas of corn and pumpkins is the total area of the garden.

It can be expressed mathematically as:

$A_G = A_c+A_p$

If we have to find the area of pumpkins,

$A_p = A_G - A_c$

Putting the values

$A_p = (2x^2+5x+4) - (x^2-3x+2)\\A_p = 2x^2+5x+4-x^2+3x-2\\A_p = 2x^2-x^2+5x+3x+4-2\\A_p = x^2+8x+2$

The equation in standard form that models area of pumpkins is:

$A_p = A_G - A_c$

and the area is: $x^2+8x+2$

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3 years ago

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A family smoothie recipe calls for strawberry juice and apple juice. This equation represents the proportional relationship betw

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Answer:number of juice and fruits

Step-by-step explanation:

juice and fruits

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what is the answer to this it takes sara 1/2 day to make birdhouse how much of birdhouse will be built after 2/5 day

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Step-by-step explanation:

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3 years ago

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Emily is 4 times as old as Tiffany. In ten years time, Emily will be twice as old as Tiffany . Find their ages.

Sholpan [36]

<h3><u>Question</u><u>:</u></h3>

Emily is 4 times as old as Tiffany. In ten years time, Emily will be twice as old as Tiffany. Find their ages.

<h3><u>Solution</u><u>:</u></h3>

Let the age of Tiffany be x years.
Then, the age of Emily = 4x years.
After 10 years, the age of Tiffany will be (x+10) years.
After 10 years, the age of Emily will be (4x+10) years.
Therefore, by the problem

$4x + 10 = 2(x + 10) \\ = 4x + 10 = 2x + 20 \\ = > 4x - 2x = 20 - 10 \\ = > 2x = 10 \\ = > x = \frac{10}{2} \\ = > x = 5$

So, Tiffany's present age = 5 years.
Emily's present age = (4×5) years = 20 years.

<h3><u>Answer:</u></h3>

Emily's age is 20 years and Tiffany's age is 5 years.

Hope it helps!

7 0

2 years ago

Read 2 more answers