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FromTheMoon [43]
3 years ago
12

Part 1: Create a scenario for an arithmetic sequence. For example, Jasmine practices the piano for ______ minutes on Monday. Eve

ry day she ___________ her practice time by _________.
If she continues this pattern, how many minutes will she practice on the 7th day? Be sure to fill in the blanks with the words that will create an arithmetic sequence.

Use your scenario to write the function for the 7th term in your sequence using sequence notation.

Part 2: Create a scenario for a geometric sequence. For example, Anthony goes to the gym for ______ minutes on Monday. Every day he _________his gym time by ____________.

If he continues this pattern, how many minutes will he spend at the gym on the 5th day? Be sure to fill in the blanks with the words that will create a geometric sequence.

Use your scenario to write the formula for the 5th term in your sequence using sequence notation.

Part 3: Use your scenario from part 2 to write a question that will lead to using the geometric series formula. Use the formula to solve for Sn in your scenario.
Mathematics
1 answer:
mr Goodwill [35]3 years ago
6 0
Let a_n be the n'th term of a sequence, 

for example a_1 is the first term, a_2 is the second term and so on.
----------------------------------------------------------------------------------------------------
a sequence is arithmetic if the difference between any 2 terms is equal:

so an arithmetic sequence, for the first term = t, and the common difference = d, has the following form:

a_1=t

a_2=t+d

a_3=t+d+d

a_4=t+d+d+d

so clearly a_n=t+d*(n-1)
---------------------------------------------------------------------------------------------------
A sequence is geometric, if the ratio between any 2 consecutive terms is the same, and it is called the common ratio.

a geometric ratio with first term = t, and common ratio = r is:

a_1=t

a_2=t*r

a_3=t*r*r

a_4=t*r*r*r

thus clearly a_n=t* r^{n-1}
--------------------------------------------------------------------------------------------------

Part 1:

"<span>Jasmine practices the piano for  __30___ minutes on Monday. Every day she ____increases_______ her practice time by ____5 minutes_____. </span>"


let a_n be the number of hours Jasmine practices the n'th day, 

for n=7, t=30, d=5 we have

a_7=30+5*(7-1)=30+5*6=30+30=60,
 
minutes is the time Jasmine practices on the 7the day.


Part 2

 "<span>Anthony goes to the gym for ___60___ minutes on Monday. Every day he ___increases______his gym time by ____1/10_of the previous day_____. </span>"

if S_n represents the minutes that Anthony goes to gym on the n'th day, 

then

S_1=60

S_2=60+1/10*60=10/10*60+1/10*60=11/10*60=1.1*60

S_3=1.1*1.1*60

S_4=1.1*1.1*1.1*60

S_5=1.1*1.1*1.1*1.1*60= (1.1)^{4}*60= 1.4641*60=87.85
 (minutes)

Part 3: it is clear that the formula that can be derived in Part 2 is:

S_n=60*(1.1)^{n-1}

so assume we want to find how many hours does Anthony spend in the gym on the 10th day,

then we calculate S_10=60*(1.1)^{9}=60*2.358=141.5  (minutes)





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Anuta_ua [19.1K]

Answer:

The probability of a big storm is 40%.

Now, you can find a D10 (a die with 10 faces)

You can assign 4 numbers (0, 1, 2, 3) to the event "there is a major storm"

in this way, you have 40% of having a storm.

and the other 6 numbers (4, 5, 6, 7, 8, 9) to the event "there is not a major storm". This means that we have 60% of not having a storm.

now, when you roll the dice you can see if a year there will be a storm or not.

Now, you roll the dice 5 times (for the 5 years) and take note of the results and the number of storms in those 5 rolls.

Now do the same thing a bunch of times, at least 25 times.

Now, you recorded the results in each set of rolls, now see the number of sets that have at least years with storms.

Take that number and divide it by the total number of sets of data (in this case 25, for example)

The result is the probability that we are looking for.

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3 years ago
Please help me on this one I’m stuck
crimeas [40]
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7 0
3 years ago
Given (x – 1)2 = 50, select the values of x.
nexus9112 [7]

Answer:

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6 0
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Slav-nsk [51]

Answer:

Step-by-step explanation: Hey for the second one I got y = -3/4x -0.5 I'm not sure if its correct though sorry if not
ill try my best to explain my solution though
1. From the parallel equation (3x + 4y = 12) all we need to do is find the slope

So the easiest way to do so is to put the said equation in <u>y-intercept </u>form

y=mx +b
m= slope

b= y intercept

so 1. 3x + 4y = 12

=

4y = 12-3x

divide that by 4 to get only y

y=3-3/4x

-3/4 is our slope

y=-3/4x+b

than we have a point -2, -2

if we put -2 for y

-2=-3/4x+b

and then we put our -2 for x
-2 = -3/4 * -2 + b

=

-2  = -1.5 +b
b=-0.5

Answer : y=-3/4x-0.5

4 0
2 years ago
Please help with math (30 points)
ikadub [295]

Here we have some problems about circles, the solutions are:

  • a) 490.6 yd^2
  • b) x = 15
  • c) x = 27

<h3>How to find the area of a circle?</h3>

We know that for a circle of diameter D, the area is given by:

A = pi*(D/2)^2

where pi = 3.14

In the image we can see that the diameter of the circle is 25 yd, replacing that in the area equation we get:

A = 3.14*(25yd/2)^2 = 490.6 yd^2

<h3>How to find the value of x?</h3>

<u>For the second image</u>, each line creates two 180° angles. So, if we look at the tilted line, we can see that it is divided in two angles, one of 37° and the other that depends of x, so we can write:

180° = 37° + (9x + 8)°

180° - 37° - 8°  = (9x)°

135°/9° = x = 15

So the value of x is 15.

For the last image:

Notice that we have a 90° angle denoted, then <u>the other 3 sections must add up to 270°.</u>

270° = 54° + (2x + 21)° + (5x + 6)°

Now we solve this for x:

270 - 54 - 21 - 6 = 2x + 5x

189 = 7x

189/7 = x = 27

x is equal to 27

If you want to learn more about circles, you can read:

brainly.com/question/25306774

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