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-BARSIC- [3]
3 years ago
10

Find the 78th term of the arithmetic sequence 14, 5, -4, ...14,5,−4

Mathematics
1 answer:
o-na [289]3 years ago
3 0

\bf 14~~,~~\stackrel{14-9}{5}~~,~~\stackrel{5-9}{-4}~~,~~...~\hspace{10em}\stackrel{\textit{common difference}}{d = -9} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=14\\ d= -9\\ n= 78 \end{cases} \\\\\\ a_{78}=14+(78-1)(-9)\implies a_{78}=14+(77)(-9) \\\\\\ a_{78}=14-693\implies a_{78}=-679

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2√5 (√3+3√5 ) Simplify step by step
nataly862011 [7]
2√5(√3+3√5) (1.73+3+2.23)= (6.96) 2√5= 4.23 4.23(6.96)= 29.44
5 0
3 years ago
Tammy buys a 4-gigabyte memory card for her camera. Dijonea buys a memory card with twice as much storage as Tammy’s. One gigaby
tigry1 [53]

Answer:

Dijonea have 8192  megabytes on her memory card

Step-by-step explanation:

Capacity of Tammy's memory card =  4-gigabyte

given that Dijonea buys a memory card with twice as much storage as Tammy’s

Thus,

Capacity of Dijonea's memory card =  2*Capacity of Tammy's memory card

Capacity of Dijonea's memory card =  2*4-gigabyte = 8-gigabyte

Given that

1 gigabyte = 1,024 megabytes

we have to find value of 8 gigabyte in terms of megabytes

for that we multiple both side in above equation by 8

1 *8 gigabyte = 1,024 *8 megabytes

8 gigabyte = 8192  megabytes

Thus, Dijonea have 8192  megabytes on her memory card

6 0
3 years ago
Henry wants to buy the same number of gift bags and bows. Gift bags are sold in packs of 6. Bows are sold in packs of 9. What is
Lynna [10]

Answer:

<em>Henry will buy 18 gift bags and 18 bows in 3 packs of gift bags and 2 packs of bows.</em>

Step-by-step explanation:

<u>Least Common Multiple (LCM)</u>

Is the smallest positive number that is a multiple of two or more numbers. To find the least common multiple of two numbers is to first list the prime factors of each number. Then multiply each factor the greatest number of times it occurs in either number.

Since Henry wants to buy the same number of gift bags and bows and they are sold in packs with different quantities, we must find the LCM between those numbers.

Gift bags are sold in packs of 6. Bows are sold in packs of 9.

List the prime factors of 6: 2,3

List the prime factors of 9: 3,3

Multiply: 2*3*3=18

The  LCM is 18. This means Henry will buy 18 gift bags and 18 bows in 3 packs of gift bags and 2 packs of bows.

3 0
4 years ago
The principal represents an amount of money deposited in a savings account subject to
Nataliya [291]

Compound interest is the adding of interest to the principle sum of a loan or deposit. The amount of money in the account after 2 years is $7426.30, while the interest earned in 2 years is $426.30.

<h3>What is compound interest?</h3>

Interest on interest, or compound interest, is the adding of interest to the principle sum of a loan or deposit. It's the outcome of reinvesting interest rather than paying it out, so that interest is received on the principal plus previously collected interest in the next quarter.,

A = P(1+ \dfrac{r}{n})^{nt}

where A is the final amount

P is the principal amount

r is the rate of interest

n is the number of times interest is charged in a year

t is the number of years

Given the principal amount is $7,000 while the rate of interest is 3% which is compounded annually.

A. The amount of money in the account after 2 years will be,

A = $7000(1 + 0.03)² = $7426.30

B. The amount of interest earned is will be,

The amount of interest earned = $7426.30 - $7000 = $426.30

Hence, the amount of money in the account after 2 years is $7426.30, while the interest earned in 2 years is $426.30.

Learn more about Compound Interest:

brainly.com/question/25857212

#SPJ1

4 0
2 years ago
Pls help I’m so confused
gavmur [86]

Answer:

its a

Step-by-step explanation:

7 0
3 years ago
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