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mash [69]
3 years ago
12

WILL GIVE BRAINLIEST The sequence 7 21 63 189......shows the number of jumping jacks justin did each week, starting with the fir

st week of him working out.
A. is the sequence arithmetic or geometric? how do you know?
B. What is the recursive rule for the sequence?
C. what is the iterative (explicit) rule for the sequence.
Mathematics
1 answer:
vovangra [49]3 years ago
3 0

A

this is a geometric sequence since there exists a common ratio r between the terms

r = \frac{21}{7} = \frac{63}{21} = \frac{189}{63} = 3

B

to obtain the next term in the sequence multiply the previous term by 3

a_{n+1} = 3 a_{n} ← recursive rule

C

the n th term of a geometric sequence is

a_{n} = a_{1} r^{n-1}

where a_{1} is the first term in the sequence

a_{n} = 7 × 3^{n-1} ← explicit rule


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Ann is adding water to a swimming pool at a constant rate. The table below shows the amount of water in the pool after different
N76 [4]

Answer:

(a)  As time increases, the amount of water in the pool increases.

     11 gallons per minute

(b)  65 gallons

Step-by-step explanation:

From inspection of the table, we can see that <u>as time increases, the amount of water in the pool increases</u>.

We are told that Ann adds water at a constant rate.  Therefore, this can be modeled as a linear function.  

The rate at which the water is increasing is the <em>rate of change</em> (which is also the <em>slope </em>of a linear function).

Choose 2 ordered pairs from the table:

\textsf{let}\:(x_1,y_1)=(8, 153)

\textsf{let}\:(x_2,y_2)=(12,197)

Input these into the slope formula:

\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{197-153}{12-8}=\dfrac{44}{4}=11

Therefore, the rate at which the water in the pool is increasing is:

<u>11 gallons per minute</u>

To find the amount of water that was already in the pool when Ann started adding water, we need to create a linear equation using the found slope and one of the ordered pairs with the point-slope formula:

y-y_1=m(x-x_1)

\implies y-153=11(x-8)

\implies y-153=11x-88

\implies y=11x-88+153

\implies y=11x+65

When Ann had added no water, x = 0.  Therefore,

y=11(0)+65

y=65

So there was <u>65 gallons</u> of water in the pool before Ann starting adding water.

3 0
2 years ago
Read 2 more answers
According to a survey conducted by the U.S. Department of Health and Human Services, about 50% of U.S. adults age 18 and older a
liraira [26]

Using a confidence interval, we have that:

a) The range is from 48.8% to 51.2%.

b) Between 125,000 and 131,000 adults are registered organ donors.

<h3>What is a confidence interval?</h3>

A confidence interval is given by the <u>estimate plus/minus the margin of error</u>.

For this problem, we have that:

  • The estimate is of 50%.
  • The margin of error is of 1.2%.

The bounds of the range are given as follows:

  • 50% - 1.2% = 48.8%.
  • 50% + 1.2% = 51.2%.

Hence the range is from 48.8% to 51.2%.

<h3>What are the total numbers?</h3>

We have to find <u>48.8% and 51.2% of 255,200,373</u>, hence:

  • 0.488 x 255,200,373 = 124,537,782.
  • 0.512 x 255,200,373 = 130,662,591.

Rounded to hundredth thousand, between 125,000 and 131,000 adults are registered organ donors.

More can be learned about confidence intervals at brainly.com/question/25890103

#SPJ1

7 0
1 year ago
Please help!<br> Hard math.
Reil [10]

Answer:

the value of digit 3 in 156.32 =

3 x 0.1 = 0.3


The value of digit 3 in 13 =

3 x 1 = 3

3/0.3=10 times

The value of digit 3 in 13 is 10 ten times the value of digit 3 in 156.32

As long as the (digit in ones/single digit) of a number is equal to 3

The value of digit 3 of it is always 10 ten times the value of digit 3 in 156.32


5 0
2 years ago
A jar contains 99 large red​ marbles, 66 small red​ marbles, 88 large blue​ marbles, and 55 small blue marbles. if a marble is c
aliina [53]
I think it would be the first one
3 0
3 years ago
Which expression is equivalent to 3(x2 - 1) - (x2 - 7x + 10)?
alisha [4.7K]

Answer:

2. 2x² + 7x - 13

Step-by-step explanation:

3[x² - 1] - [x² - 7x + 10]

3x² - 3 - x² + 7x - 10

2x² - 13 + 7x

The above answer is a bit written in reverse, which is the exact same result.

So, after performing the Distributive Property, from there, you can combine all like-terms, as done above.

** Now, just in case you are wondering why that -7 has been altered to its opposite, it is because although -7x does not have another like-term to pair up with, IT IS STILL HOOKED UP TO ANOTHER NEGATIVE, so that -7x is REALLY 7x.

I am joyous to assist you anytime.

7 0
3 years ago
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