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3 years ago

Find Sn for the given arithmetic series. a1= -100, d = –2, n = 21

Mathematics

1 answer:

labwork [276]3 years ago

5 0

Answer:

$-2520$

Step-by-step explanation:

For arithmetic series, $S_n$ means that sum of first n terms.

The formula is:

$S_n=\frac{n}{2}[2a_1+(n-1)d]$

Where

$a_1$ is the first term (given as -100)

n is the number of terms (given as 21)

d is the common difference (given as -2)

So, we can plug in the values we know and find the sum of first 21 terms:

$S_n=\frac{n}{2}[2a_1+(n-1)d]\\S_{21}=\frac{21}{2}[2(-100)+(21-1)(-2)]\\S_{21}=10.5[-200+20(-2)]\\S_{21}=10.5[-240]\\S_{21}=-2520$

So the sum is -2520

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A bird population is decreasing by 3 percent each year. Find the bird population after 6 years.

QveST [7]

Hello!

If it is decreasing by 3% each year, 18% of its population will have decreased after 6 years. As we do not have an original number, we will just say that the population is 18% less than the original.

If you want to find the exact number, multiply the original population by 0.18. Subtract the number from the original population.

I hope this helps!

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4 years ago

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Solve. -5 3/4 - 3 1/2 =

zepelin [54]

Answer:

-9 $\frac{1}{4}$

-9.25

Step-by-step explanation:

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3 years ago

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X=3y-4 2x-y=7 use substitution method. pls explain :)

Nesterboy [21]

Answer:

the sustitucion metod is easy x=5 y=3

Step-by-step explanation:

x-3y=-4 (-2)

2x-y=7 (1)

-2x+6y=8

2x-y=7

5y=15

y=3

2x-3=7

2x=10

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3 years ago

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The graph of $y=ax^2+bx+c$ passes through points $(0,5)$, $(1,10)$, and $(2,19)$. Find $a+b+c$.

MAVERICK [17]

Answer:

$a+b+c=10$

Step-by-step explanation:

We are given that the graph of the equation:

$y=ax^2+bx+c$

Passes through the three points (0, 5), (1, 10), and (2, 19).

And we want to find the value of (a + b + c).

First, since the graph passes through (0, 5), its y-intercept or c is 5. Hence:

$y=ax^2+bx+5$

Next, since the graph passes through (1, 10), when x = 1, y = 10. Substitute:

$(10)=a(1)^2+b(1)+5$

Simplify:

$5=a+b$

The point (2, 19) tells us that when x = 2, y = 19. Substitute:

$(19)=a(2)^2+b(2)+5$

Simplify:

$14=4a+2b$

This yields a system of equations:

$\begin{cases} 5 = a + b \\ 14 = 4a + 2b\end{cases}$

Solve the system. We can do so using elimination (or any other method you prefer). Multiply the first equation by negative two:

$-10=-2a-2b$

Add the two equations together:

$(-10)+(14)=(-2a+4a)+(-2b+2b)$

Combine like terms:

$4 = 2a$

Hence:

$a=2$

Using the first equation:

$5=(2)+b\Rightarrow b=3$

Therefore, our equation is:

$y=2x^2+3x+5$

Thus, the value of (a + b + c) will be:

$a+b+c = (2) + (3) + (5) = 10$

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3 years ago

This graph compares shoe sizes for a group of 80 two-year-old boys and a group of 60 three-year-old boys. Two box and whisker pl

Ivanshal [37]

To determine about how many more boys have a shoes size of 6 or less, you need to understand that a box and whisker plot takes a data set and show it in quarters (25% of the data is represented in each section).

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For the 3 year olds, the closest point to 6 is 6.5, and it is located after the line on the left. This means that only 25% of the boys have shoe sizes of 6.5 or under. 25% of the 60 three-year olds they collected data on is 15.

The difference is 40-15= 25.
There are about 25 more two-year olds wearing a size 6 or under.

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3 years ago

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