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2 years ago

What is the 12th partial sum of the summation of negative 2i minus 10, from i equals 1 to infinity?

1 answer:

8 0

Ans: 12th partial sum = -276

Given :
$\sum_{i=1}^{12} (-2i-10)$

Find the values for i = 1 to 12:
x (1) = -2 – 10 = -12
x (2) = -4 – 10 = -14
x (3) = -6 – 10 = -16
x (4) = -8 – 10 = -18
x (5) = -10 – 10 = -20
x (6) = -12 – 10 = -22
x (7) = -14 – 10 = -24
x (8) = -16 – 10 = -26
x (9) = -18 – 10 = -28
x (10) = -20 – 10 = -30
x (11) = -22 – 10 = -32
x (12) = -24 - 10 = -34

Add all of them:
12th partial sum = -276

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Ella’s test grades in her history class are 89, 94, 82, 84, and 98. What score must Ella make on her next test to have a mean te

aksik [14]

Mean is same as average

to find average
add up terms
divided that sum by the number of terms you have
example

mean of x,y,z
x+y+z
3 terms
(x+y+z)/3=mean

so
represent next test score as x
89+94+82+84+98+x
count how many terms ther are (6 terms)

mean is 90
(89+94+82+84+98+x)/6=90
add the like terms
(447+x)/6=90
multiply both sides by 6 to clear fraction
447+x=540
subtract 447 from both sides
x=93

she needs a score of 93 on next test

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2 years ago

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David wants to rent a bicycle for a couple of hours to explore the city. The price of the bike rental, (P)(P)left parenthesis, P

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Answer:

The hourly charge is $4 per hour for the first 3 hours.

The rate then drops to $2 per hour until the end of the 6th hour.

The hourly rate drops further to $1 per hour between the 6th and 10th hours.

The maximum price of the bike rental is $30.

Step-by-step explanation:

The slope of the graph corresponds to the hourly rate for the bike rental.

During the first three hours of the bike rental, the price increases by $4 each hour.

Between the 3rd and 6 th hours, the slope of the graph is 2, which means the hourly rate of the bike rental is $2 per hour.

Between the 6th and 10th hours, the rate is $1 per hour.

After the 10th hour, the price, P, stops increasing. The maximum price of the bike rental is $30.

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2 years ago

Rameen’s heating bill is $5.42 per month plus $1.08 per therm. How many therms can Rameen use if he wants his heating bill to be

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Write and solve an inequality:

Total(t) = $5.42 + ($1.08/therm)(t) ≤ $87.50.

First, subtract $5.42 from $87.50: then ($1.08/therm)(t) ≤ $82.08

Next, divide both sides by $1.08 per therm:

t ≤ ($82.08) / ($1.08/therm) = 76 therms (maximum). Thus, Rameen's usage could be [0,76] (therms).

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2 years ago

A circle fits inside a semicircle of diameter 24mm

patriot [66]

Answer:

The shaded are is $113\ mm^{2}$

Step-by-step explanation:

we know that

The shaded area is equal to the area of the semicircle minus the area of the circle inside the semicircle

step 1

Find the area of semicircle

The area of semicircle is equal to

$A=\frac{1}{2}\pi r^{2}$

where

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substitute

$A=\frac{1}{2}\pi(12)^{2}=72\pi\ mm^{2}$

step 2

Find the area of the circle inside the semicircle

The area of circle is equal to

$A=\pi r^{2}$

where

$r=12/2=6\ mm$ ---> the radius of circle inside is half the radius of semicircle

substitute

$A=\pi(6)^{2}=36\pi\ mm^{2}$

step 3

Find the shaded area

$72\pi\ mm^{2}-36\pi\ mm^{2}=36\pi\ mm^{2}$

assume

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3 significant figures is

$113\ mm^{2}$

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