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Ket [755]
3 years ago
10

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?
You might be interested in
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}

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

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:

D

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
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