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3 years ago

What is the sum of the series?

Mathematics

1 answer:

Sergeu [11.5K]3 years ago

5 0

Answer:

Sum

Step-by-step explanation:

An arithmetic series is the sum of the terms of an arithmetic sequence. A geometric series is the sum of the terms of a geometric sequence. ... The partial sum is the sum of a limited (that is to say, a finite) number of terms, like the first ten terms, or the fifth through the hundredth terms.

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The height of a triangle is 3cm less than twice the base. The area is 10cm2

Kamila [148]

Answer:

The base is 4cm and the height is 5cm.

Step-by-step explanation:

This is a solve the system question. Call H the height of the triangle and B the base. The question tells us:

$H=2B-3$

and

$\frac{B \times H}{2}=10$

Sub the first equation into the second (as H is already isolated). You will end up with a quadratic equation - solve that any way you wish (e.g. quadratic formula). I've provided the factored form below which shows you the roots:

$\frac{B(2B-3)}{2}=10\\\frac{2B^2-3B}{2}=10\\2B^2-3B=20\\2B^2-3B-20=0\\(2B+5)(B-4)=0\\B= - \frac{5}{2},4$

In this question, we take B=4. You can't have a negative side length so the other answer is eliminated. Now sub the value for B into either of the original equations. I'll use the first, again because H is already isolated:

$H=2(4)-3\\H=8-3\\H=5$

3 0

3 years ago

In a doctor's waiting room, there are 14 seats in a row. Eight people are waiting to be seated. There is someone with a very bad

diamong [38]

Answer: 12,972,960

Step-by-step explanation: There are 14 chairs and 8 people to be seated. But among the 8. three will be seated together:

So 5 people and (3) could be considered as 6 entities:

Since the order matters, we have to use permutation:

¹⁴P₆ = (14!)/(14-6)! = 2,162,160, But the family composed of 3 people can permute among them in 3! ways or 6 ways. So the total number of permutation will be ¹⁴P₆ x 3!

2,162,160 x 6 = 12,972,960 ways.

Another way to solve this problem is as follow:

5 + (3) people are considered (for the time being) as 6 entities:

The 1st has a choice among 14 ways

The 2nd has a choice among 13 ways

The 3rd has a choice among 12 ways

The 4th has a choice among 11 ways

The 5th has a choice among 10 ways

The 6th has a choice among 9ways

So far there are 14x13x12x11x10x9 = 2,162,160 ways

But the 3 (that formed one group) could seat among themselves in 3!

or 6 ways:

Total number of permutation = 2,162,160 x 6 = 12,972,960

5 0

3 years ago

Mrs. Bailey had 12 pieces of candy. She gave away some candy and has 3 pieces left. What is the percent decrease of candy? Pleas

atroni [7]

Answer:

75% decrease

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Help with #17 please

ohaa [14]

2 evens is an positive
1 odd,1 even is a odd
2 odd is an ofd

8 0

3 years ago

The radius of a circle is 6 in. Find the circumference to the nearest tenth.

ycow [4]

Answer:

37.7

Step-by-step explanation:

The orginal answer is 37.699

But you want to round the tenth

So 9 to the 6 you want to rasie the score

6 turns into a 7 and the numbers behind it (9 and the other 9) turn into a zero

37.7 or 37.700

8 0

3 years ago