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Rufina [12.5K]
2 years ago
9

A series contains 18 numbers and has a sum of 4,185. The last number of the series is 275. What is the first number?

Mathematics
1 answer:
dusya [7]2 years ago
3 0
The sum of arithmetic series is given by:
Sn=n/2(a1+an)
where:
n=number of terms
a1=first term
an=nth term
but
n=18, an=275, Sn=4185
plugging the values in the formula we get:
4185=18/2(a1+275)
simplifying this we get:
4185=9(a1+275)
dividing through by 9 we get:
465=a1+275
thus
a1=465-275
a1=190

Answer: first number is 190
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tia_tia [17]

Answer:

The lateral area is equal to

LA=64\sqrt{3}\ m^{2}

Step-by-step explanation:

In this problem the lateral area is equal to the area of one equilateral triangle multiplied by 4

To find the area of one equilateral triangle calculate the height

The area of the triangle is equal to

A=\frac{1}{2}bh

we have

b=8\ m

Applying the Pythagoras theorem

h^{2}=8^{2} -4^{2} \\h^{2}=64-16\\ h=\sqrt{48} \\ h=4\sqrt{3}\ m

The area of one triangle is equal to

A=\frac{1}{2}(8)(4\sqrt{3})\ m^{2}

so

The lateral area is equal to

LA=4\frac{1}{2}(8)(4\sqrt{3})=64\sqrt{3}\ m^{2}

3 0
1 year ago
A satellite makes 4 revolutions of the earth in one day. How many revolutions would it make in 6 1/2 days?
koban [17]
26. 
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8 0
2 years ago
The population of a Midwestern city decays exponentially. If the population decreased from 900,000 to 800,000 from 2003 to 2005,
olga55 [171]
Hello.<span><span>   </span><span>
<span><span>
-------
Let 2003 be the zero year; then 2005 is the three year, and 2008 the 5 year.
---------------
P = ab^x
---
P(3) = ab^3 = 800000
P(0) = ab^0 = 900000

---
a = 900000
Solve for "b"::
b^3 = 8/9 
b = 2/cbrt(9) 
----
Equation::
P(x) = 900000^x
----
Ans: P(5) = 900000


Have a nice day</span></span></span></span>
4 0
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. Over the next two days, Clinton Employment Agency is interviewing clients who wish to find jobs. On the first day, the agency
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Answer:

4

Step-by-step explanation:

Given that :

Clients are interviewed in groups of 2 on the first day; meaning two persons at a time

Second day, clients are interviewed in groups of 4; meaning 4 persons at a time.

Therefore, if the same number of clients are to be interviewed on each day, the smallest number of clients that could be interviewed each day could be obtained by getting the Least Common Multiple of both numbers: 2 and 4

- - - - 2 - - - 4

2 - - - 1 - - - 2

2 - - - 1 - - - 1

Therefore, the Least common multiple is (2 * 2) = 4

Therefore, the smallest number of clients that could be interviewed each day is 4.

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4 0
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