How do u figure out the rise and run without a graph

2(1-k), k-1, k+8 are the first three terms of a geometrical sequence. Find the value of k.

Galina-37 [17]

If these are terms of a geometric sequence, they have a common ratio. That is, ...

... (k -1)/(2(1 -k)) = (k +8)/(k -1)

... (k -1)² = 2(1 -k)(k +8) . . . . . multiply by the product of the denominators.

... k² -2k +1 = -2k² -14k +16 . . . eliminate parentheses

... 3k² +12k -15 = 0 . . . . . . . . put in standard form (subtract the right side)

... 3(k +5)(k -1) = 0 . . . . . . . . . factor

Possible values of k are ... -5, +1. The solution k=1 is extraneous, as it makes the first two terms 0 and the third term 8. (It doesn't work.)

The value of k is -5.

_____

The three terms are 12, -6, 3. The common ratio is -1/2.

8 0

4 years ago

Help, hurry pleaseee.

Vlad [161]

Answer:

3.5 and -3.5

Step-by-step explanation:

The lines on the outside of n mean the absolute value (the distance from 0)

8 0

4 years ago

Read 2 more answers

Suppose you pay a dollar to roll two dice. if you roll 5 or a 6 you Get your dollar back +2 more just like it the goal will be t

LiRa [457]

Answer:

(a)$67

(b)You are expected to win 56 Times

(c)You are expected to lose 44 Times

Step-by-step explanation:

The sample space for the event of rolling two dice is presented below

$(1,1), (2,1), (3,1), (4,1), (5,1), (6,1)\\(1,2), (2,2), (3,2), (4,2), (5,2), (6,2)\\(1,3), (2,3), (3,3), (4,3), (5,3), (6,3)\\(1,4), (2,4), (3,4), (4,4), (5,4), (6,4)\\(1,5), (2,5), (3,5), (4,5), (5,5), (6,5)\\(1,6), (2,6), (3,6), (4,6), (5,6), (6,6)$

Total number of outcomes =36

The event of rolling a 5 or a 6 are:

$(5,1), (6,1)\\ (5,2), (6,2)\\( (5,3), (6,3)\\ (5,4), (6,4)\\(1,5), (2,5), (3,5), (4,5), (5,5), (6,5)\\(1,6), (2,6), (3,6), (4,6), (5,6), (6,6)$

Number of outcomes =20

Therefore:

P(rolling a 5 or a 6) $=\dfrac{20}{36}$

The probability distribution of this event is given as follows.

$\left|\begin{array}{c|c|c}$Amount Won(x)&-\$1&\$2\\&\\P(x)&\dfrac{16}{36}&\dfrac{20}{36}\end{array}\right|$

First, we determine the expected Value of this event.

Expected Value

$=(-\$1\times \frac{16}{36})+ (\$2\times \frac{20}{36})\\=\$0.67$

Therefore, if the game is played 100 times,

Expected Profit =$0.67 X 100 =$67

If you play the game 100 times, you can expect to win $67.

(b)

Probability of Winning $=\dfrac{20}{36}$

If the game is played 100 times

Number of times expected to win

$=\dfrac{20}{36} \times 100\\=56$ times$

Therefore, number of times expected to loose

= 100-56

=44 times

8 0

4 years ago

A researcher wishes to determine whether there is a difference in the average age of middle school, high school, and college tea

MakcuM [25]

The correct statement that can be made about the means is a. There is not enough evidence to suggest that the means are different.

<h3>What is true about the means?</h3><h3 />

Given that α = 0.01, we can use an ANOVA analysis to determine the p-value of the means.

When we run the means through an ANOVA software, the p-value can be found to be 0.1142.

This figure is greater than α = 0.01.

This means that we do not have the evidence to reject the null hypothesis that the means are different.

Options for this question:

a. There is not enough evidence to suggest that the means are different.
b. The mean age of middle school teachers is different from the mean age of high school teachers.
c. The mean age of middle school teachers is different from the mean age of college teachers.
d. The mean age of high school teachers is different from the mean age of college teachers.

Find out more on the p-value at brainly.com/question/4621112

#SPJ1

7 0

2 years ago

Shawna buys 2 1/2 gallons of paint. If she uses 1/3 of it on the first day, how much does she have left?

Stolb23 [73]

Answer:

2 and 1/2 = 2.5

2.5 divided by 3 = 0.83

0.83 x 2 = 1.66 or 1 and 2/3 gallons of paint left

Step-by-step explanation:

Hope this helps! Have a nice day!

4 0

3 years ago