Add the fractions and simplify the answer 1/2+2/3

PLEASE HELP ILL MARK BRAINLIEST !!!

Alexus [3.1K]

Answer:

a) the common difference is 20

b) $x_8=115 , x_{12}=195$

c) the common difference is -13

d) $a_{12}=52, a_{15}=13$

Step-by-step explanation:

a) what is the common difference of the sequence xn

Looking at the table, we get x_3=16, x_4=36 and x_5= 56

Deterring the common difference by subtracting x_4 from x_3 we get

36-16 =20

So, the common difference is 20

b) what is x_8? what is x_12

The formula used is: $x_n=x_1+(n-1)d$

We know common difference d= 20, we need to find $x_1$

Using $x_3=16$ we can find $x_1$

$x_n=x_1+(n-1)d\\x_3=x_1+(3-1)d\\15=x_1+2(20)\\15=x_1+40\\x_1=15-40\\x_1=-25$

So, We have $x_1 = -25$

Now finding $x_8$

$x_n=x_1+(n-1)d\\x_8=x_1+(8-1)d\\x_8=-25+7(20)\\x_8=-25+140\\x_8=115$

So, $\mathbf{x_8=115}$

Now finding $x_{12}$

$x_n=x_1+(n-1)d\\x_{12}=x_1+(12-1)d\\x_{12}=-25+11(20)\\x_{12}=-25+220\\x_{12}=195$

So, $\mathbf{x_{12}=195}$

c) what is the common difference of the sequence $a_m$

Looking at the table, we get a_7=104, a_8=91 and a_9= 78

Deterring the common difference by subtracting a_7 from a_8 we get

91-104 =-13

So, the common difference is -13

d) what is a_12? what is a_15?

The formula used is: $a_n=a_1+(n-1)d$

We know common difference d= -13, we need to find $a_1$

Using $a_7=104$ we can find $x_1$

$a_n=a_1+(n-1)d\\a_7=a_1+(7-1)d\\104=a_1+7(-13)\\104=a_1-91\\a_1=104+91\\a_1=195$

So, We have $a_1 = 195$

Now finding $a_{12}$ , put n=12

$a_n=a_1+(n-1)d\\a_{12}=a_1+(12-1)d\\a_{12}=195+11(-13)\\a_{12}=195-143\\a_{12}=52$

So, $\mathbf{a_{12}=52}$

Now finding $a_{15}$ , put n=15

$a_n=a_1+(n-1)d\\a_{15}=a_1+(15-1)d\\a_{15}=195+14(-13)\\a_{15}=195-182\\a_{15}=13$

So, $\mathbf{a_{15}=13}$

5 0

3 years ago

Square root of 13+29

Ugo [173]

The square root of 13+29 is <span>6.48074069841 but, you can simply put 6.4</span>

5 0

3 years ago

Find the slope of the line that passes through the pair of points

BlackZzzverrR [31]

Answer:

undefined

Step-by-step explanation:

To find the slope through 2 points

m = ( y2-y1)/(x2-x1)

= ( -4 - -3)/(3 - 3)

= ( -4+3)/(3-3)

= -1/0

Since it is a number divided by zero, the slope is undefined

7 0

2 years ago

Urgent ! <br>i can't seem to solve this :(

Archy [21]

Answer: 15 cm to the highest total ; amount of triangles: 25

Step-by-step explanation: for the height just add 3 cm until you reach the top, which will give you 15 cm

for the amount just count them and for the top top layer count up to 9, which will give you 25 triangles.

3 0

3 years ago

The following data were collected by counting the number of operating rooms in use atTampa general Hospital over a 20-day period

arlik [135]

Answer:

a)

Operating room x 1 2 3 4

P(x) 0.15 0.25 0.4 0.2

b)

The graph of probability distribution is in attached image.

c)

All the probabilities lies in the range (0 to 1) and the probabilities add up to 1 so, the computed probability distribution is the valid probability distribution.

Step-by-step explanation:

Number of operating rooms Days

1 3

2 5

3 8

4 4

a)

Sum of frequencies=1+2+3+4=10

Operating rooms x frequency f Relative frequency

1 3 3/20=0.15

2 5 5/20=0.25

3 8 8/20=0.4

4 4 4/20=0.2

So, using the relative frequency approach, a discrete probability distribution for number of operating rooms in use on any given day is

Operating room x 1 2 3 4

P(x) 0.15 0.25 0.4 0.2

b)

The graph of probability distribution is in attached image.

c)

There are two conditions for a probability distribution to be valid

1. All probability must ranges from 0 to 1.

2. All probabilities must add up to 1.

We can see that all the probabilities lies in the range (0 to 1), so, condition 1 is satisfied.

For condition 2,

sum[p(x)]= 0.15+0.25+0.4+0.2=0.4+0.6=1.

As the probabilities add up to 1, so the condition 2 is also satisfied.

Thus, the computed probability distribution is the valid probability distribution.

7 0

3 years ago