All categories

3 years ago

If an arithmetic sequence has a4 = 107 and a8 = 191, what is a₁?PLEASE HELP ME

Mathematics

1 answer:

katen-ka-za [31]3 years ago

3 0

$\text{nth term of an arithmetic sequence,}\\\\a_n = a_1 + (n-1)d\\\\a_4 = a_1 +3d=107~~~......(i)\\ \\a_8=a_1+7d = 191~~~......(ii)\\\\\\\text{(ii) -(i):}\\\\~~~~~~a_1+7d-a_1-3d = 191 -107\\\\\implies 4d = 84\\\\\implies d = \dfrac{84}4\\\\\implies d= 21\\\\\text{Substitute d= 21 in eq~(i):}\\ \\~~~~~ a_1 +3(21) = 107\\\\\implies a_1 + 63 = 107\\\\\implies a_1 = 107-63\\\\\implies a_1 =44$

You might be interested in

Adam is training a group of cyclists. Each cyclist completes a 10-kilometer time trial during training. Adam records the times,

nydimaria [60]

The histogram which shows the results of the time trial is option B

<h3>Histogram</h3>

Given data:

12:32, 12:46, 13:30, 15:03, 13:43, 13:46, 14:20, 14:29, 12:34, 14:43, 15:26, 16:02, 16:16, 14:38, 16:55, 17:10, 14:26, 17:21, 17:58, 13:30

Grouping of data,:

12:00 - 12:59 = 3

13:00 - 13:59 = 4

14:00 - 14:59 = 5

15:00 - 15:59 = 2

16:00 - 16:59 = 3

17:00 - 17:59 = 3

The frequency is represented on the y-axis(number of cyclist)
The time is represented on the x-axis

Learn more about histogram:

brainly.com/question/9388601

#SPJ1

7 0

2 years ago

The numbers of students in the four sixth-grade classes at Northside school are 26,19,34 and 21. Use properties to find the tota

san4es73 [151]

Basically there are 3 addition properties and they are associative property, identity property, and commutative property.

Commutative property is just changing the order of the addends. Example: 26+19+34+21= 21+34+19+26

Identity Property is just adding a 0 to the number that doesnt change anything. Example: 26+19+34+21 +0 = 100

Associative property is just changing the grouping of the addends. Example: (26+19) + (34+21)

6 0

3 years ago

Joe flips the disc shown below 15 times:

vfiekz [6]

Whatever the number of times you flip the disc, as long as the disc has uniformly distributed mass throughout the body, then

The probability will always be 50%

7 0

3 years ago

Read 2 more answers

A number is equal to twice a smaller number plus 3. Yhe same number is equal to twice the sum of smaller number and 1. How many

allsm [11]

Answer:

There is no solution to the problem

Step-by-step explanation:

In order to find the solutions to the problem you can write the situation in an algebraic form.

You have that a number is equal to twice a smaller number plus 3. This can be written as follow:

$x=2y+3$ (1)

where x is the number and y is the smaller number

Furthermore, the same number x is equal to twice the sum of the smaller number and 1, which can be written as follow:

$x=2(y+1)$ (2)

To find the solution you equal the equation (1) with (2), and you solve for y:

$2y+3=2y+1$

$3=1$

You obtain an inconsistency, hence, the situation of the problem does not have solution

5 0

3 years ago

4. The following intervals were plausible population proportions for a given sample. Find the margin of error in each case.

Vedmedyk [2.9K]

Answer: a. 0.15 b. 0.03 c. 0.055 d. 0.05

Step-by-step explanation:

For plausible intervals of population proportions , the margin of error is basically half of the difference between upper limit and lower limit.

a. Interval = From 0.35 to 0.65

Upper limit = 0.65

Lower limit = 0.35

Difference = Upper limit- Lower limit

= 0.65-0.35=0.30

Margin of error = (Difference)÷2 =(0.30)÷2=0.15

b. Interval = From 0.72 to 0.78

Upper limit = 0.78

Lower limit = 0.72

Difference = 0.78-0.72 = 0.06

Margin of error =(0.06)÷2=0.03

c. Interval = From 0.84 to 0.95

Upper limit = 0.95

Lower limit = 0.84

Difference =0.95-0.84= 0.11

Margin of error = (0.11)÷2 = 0.055

d.Interval = From 0.47 to 0.57

Upper limit = 0.57

Lower limit = 0.47

Difference = 0.57-0.47=0.10

Margin of error = (0.10)÷2=0.05

3 0

3 years ago

If an arithmetic sequence has a4 = 107 and a8 = 191, what is a₁?PLEASE HELP ME​

If an arithmetic sequence has a4 = 107 and a8 = 191, what is a₁?PLEASE HELP ME