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3 years ago

True or False?

Mathematics

2 answers:

Natalka [10]3 years ago

7 0

I think it’s true. If I’m right give me brainiest plz!

bagirrra123 [75]3 years ago

6 0

Where is the problem?

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Dont really understand how to do this

bija089 [108]

Answers:

$t_{10} = -22 \ \text{ and } S_{10} = -85$

========================================================

Explanation:

$t_1 = \text{first term} = 5\\t_2 = \text{first term}-3 = t_1 - 3 = 5-3 = 2$

Note we subtract 3 off the previous term (t1) to get the next term (t2). Each new successive term is found this way

$t_3 = t_2 - 3 = 2-3 = -1\\t_4 = t_3 - 3 = -1-3 = -4$

and so on. This process may take a while to reach $t_{10}$

There's a shortcut. The nth term of any arithmetic sequence is

$t_n = t_1+d(n-1)$

We plug in $t_1 = 5 \text{ and } d = -3$ and simplify

$t_n = t_1+d(n-1)\\t_n = 5+(-3)(n-1)\\t_n = 5-3n+3\\t_n = -3n+8$

Then we can plug in various positive whole numbers for n to find the corresponding $t_n$ value. For example, plug in n = 2

$t_n = -3n+8\\t_2 = -3*2+8\\t_2 = -6+8\\t_2 = 2$

which matches with the second term we found earlier. And,

$tn = -3n+8\\t_{10} = -3*10+8\\t_{10} = -30+8\\t_{10} = \boldsymbol{-22} \ \textbf{ is the tenth term}$

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The notation $S_{10}$ refers to the sum of the first ten terms $t_1, t_2, \ldots, t_9, t_{10}$

We could use either the long way or the shortcut above to find all $t_1$ through $t_{10}$ . Then add those values up. Or we can take this shortcut below.

$Sn = \text{sum of the first n terms of an arithmetic sequence}\\S_n = (n/2)*(t_1+t_n)\\S_{10} = (10/2)*(t_1+t_{10})\\S_{10} = (10/2)*(5-22)\\S_{10} = 5*(-17)\\\boldsymbol{S_{10} = -85}$

The sum of the first ten terms is -85

-----------------------

As a check for $S_{10}$ , here are the first ten terms:

t1 = 5
t2 = 2
t3 = -1
t4 = -4
t5 = -7
t6 = -10
t7 = -13
t8 = -16
t9 = -19
t10 = -22

Then adding said terms gets us...

5 + 2 + (-1) + (-4) + (-7) + (-10) + (-13) + (-16) + (-19) + (-22) = -85

This confirms that $S_{10} = -85$ is correct.

6 0

2 years ago

Kevin and Randy Muise have a jar containing 92 coins, all of which are either quarters or nickels. The total value of the coins

Artemon [7]

<span>Let n = the number of nickles
Let q = the number of quarters
Then for your problem we have
(1) n + q = 43 and
(2) 5*n + 25*q = 100*6.95 (always work in cents to avoid decimal numbers) or
(3) 5*n + 25*q = 695
Now substitute n of (1) into (3) and get
(4) 5*(43 - q) + 25*q = 695 or
(5) 215 - 5*q + 25*q = 695 or
(6) 20*q = 695 - 215 or

(7) 20*q = 480 or
(8) q = 24
Then using (1) we get
(9) n + 24 = 43 or
(10) n = 19
Let's check these values.
Is (.05*19 + .25*24 = 6.95)?
Is (.95 + 6.00 = 6.95)?
Is (6.95 = 6.95)? Yes
Answer: Kevin and Randy have 19 nickles and 24 quarters in the jar.</span>

7 0

3 years ago

Is the equation 8 + 4= -5 + 7 true false or open and why

zysi [14]

This is false, because the equation is then 12=2, which is incorrect.

Hope this helps!

~ThePirc

4 0

3 years ago

Read 2 more answers

A rectangular garden is enclosed by 94 feet of fencing around its perimeter. The garden is 15 feet wide. How long is the garden?

mel-nik [20]

Answer:

Work:

94-15=79ft

Therefore, the answer would be 79ft.

Hope this helps,

Trey

8 0

3 years ago

Read 2 more answers

The ages of undergraduate students in a state

Elan Coil [88]

The percent of students that are aged 19 years or more is determined as 84%.

<h3>One standard deviation below the mean</h3>

In a normal distribution curve 1 standard deviation below the mean is defined as follows;

1 std below mean : M - d = 16%

M - d = 20.6 yrs - 1.3 yrs = 19.3 years ≈ 19 years

19 years or more will occur at (M - d) + (M) + (M + 2d) = 100% - (M - d)

= 100% - 16%

= 84%

Thus, the percent of students that are aged 19 years or more is determined as 84%.

Learn more about normal distribution here: brainly.com/question/4079902

#SPJ1

7 0

2 years ago