Find the explicit form of the arithmetic function of p if the first term is 12 and the common difference is 2. Then find the seventh term.​

Answer:

Step-by-step explanation:

From the information given:

The probability distribution at the end of 6 months is determined as follows:

After 6 months;

Mean of probability distribution =  value of Initial cash  + [tex]\alpha[/tex]T  

=2.0 +(0.1 × 6)

=2.6

After 6 months;

The probability distribution's standard deviation is estimated by using the following formula:

Standard deviation:

[tex]= b\sqrt{T}[/tex]

[tex]= 0.4 \times \sqrt{6}[/tex]

= 0.9798

Hence, after 6 months;

The company's cash position is supposed to be allocated monthly, with the following expenses.

Mean                            2.6

Standard deviation     0.9798

Variance                      0.96

After 12 months, the probability distribution is as follows:

Mean = value of Initial cash  + [tex]\alpha[/tex]T

= 2.0 +(0.1 × 12)

= 3.2

The standard deviation is:

The standard deviation of probability distribution = [tex]b \sqrt{T}[/tex]

[tex]= 0.4 \times \sqrt{12}[/tex]

= 1.3856

Hence, after 6 months;

The company's cash position is supposed to be allocated monthly, with the following expenses.

Mean                            3.2

Sandard deviation      1.3856

Variance                      1.92

b)  

in 6-month distribution, the probability of the negative value of the cash position is as follows.

Now, for us to find the negative cash distribution;

We need to estimate the z -scores value.

The z-score inform us greatly on the concept of how far a particular data point is from the mean.

For a normal distribution;

[tex]z = \dfrac{x-\mu}{\sigma}[/tex]

Here;

the value of x = zero as a result that if it exceeds zero. the cash position will be negative.

∴

[tex]z = \dfrac{x-\mu}{\sigma}[/tex]

[tex]z = \dfrac{0 - 2.6}{0.9798}[/tex]

[tex]z = -2.6536[/tex]

Using the standard distribution tables, it is now possible to calculate that the likelihood N(-2.65) equals 0.004 or 0.4 percent.

As a result, there's a 0.4 percent chance of getting a negative cash balance after six months.

For 12 months distribution:

The Probability of negative cash position is calculated as follows:

[tex]z = \dfrac{x-\mu}{\sigma} \\ \\ z = \dfrac{0-3.2}{1.3856} \\ \\ z = -2.3094[/tex]

Using the standard distribution tables,

N(-2.31) equals 0.0104 or 1.04 percent.

As a result, there's a 1.04 percent chance of getting a negative cash balance after 1 year  

c) To determine the time period over which the likelihood of achieving a negative cash condition is highest, it's necessary to examine the z-score more closely. Essentially, the z-score measures the difference between a given value(x) and the mean of all potential values [tex](\mu)[/tex], expressed in terms of the total set's standard deviation [tex](\sigma)[/tex]

This suggests that the higher the z-score, the greater the difference occurring between x and [tex]\mu[/tex], and thus the likelihood of receiving x is minimal. As a result, the best chance of finding a certain value is when the z-score is the lowest.

To do so, calculate the derivative of the z-score in relation to the time interval. The point where the derivative is equivalent to zero is where the z-scores are at their lowest.

The first step is to go over the z-score formula in more detail, as seen below.;

[tex]z = \dfrac{x-\mu}{\sigma} \\ \\ z = \dfrac{0-(initial \ value + \alpha T)}{b \sqrt{T}} \\ \\ z = \dfrac{-initial \ value }{b\sqrt{T}}-\dfrac{a \sqrt{T}}{b} \\ \\[/tex]

Now, compute the derivative of this equation with respect to T as follows:

[tex]\dfrac{dz}{dT}= \dfrac{initial \ value \times T^{-\dfrac{3}{2}}}{2b} - \dfrac{aT^{-\dfrac{1}{2}}}{2b}[/tex]

Now, figure out the value of T at which this derivative is equal to zero by substituting all values as follows:

[tex]0 = \dfrac{2.0 \times T^{-\dfrac{3}{2}}}{2\times 0.4}- \dfrac{0.1 \times T^{-\dfrac{1}{2}}}{2 \times 0.4} \\ \\ \\ 0.1 \times T^{-\dfrac{1}{2}}= 2.0 \times T^{-\dfrac{3}{2}} \\ \\ \\T = \dfrac{2}{0.1} \\ \\ \\ T = 20[/tex]

As a result, the time period in which achieving a negative cash condition is = 20 months.

Answer:

Step-by-step explanation:

0: -2

1: -4

2: -6

Answer:

∠4 = 22

Step-by-step explanation:

Hello There!

The angles shown are consecutive interior angles

If you didn't know consecutive interior angles are supplementary angles meaning that the sum of the two angles is 180

So we can find the missing angle by subtracting the given angle (158 in this case) from 180

180 - 158 = 22

so we can conclude that ∠4 = 22

180.timr3fzgncvdfccfxdfdxxfhk

180-158=22

the measure is 44

Answer: false

Step-by-step explanation: that’s what my teacher told me sorry if it’s wrong

Answer:

It is false

Definetely false

Answer:

$135

Step-by-step explanation:

Answer:

Equation 1 would be: 3a+2C

Equation 2 would be: 5a+3C

Step-by-step explanation:

Answer:

12.50

Step-by-step explanation:

Answer:

she will see 108 humming birds

Step-by-step explanation:

30x6= 180

so mutiply how many times she sees one in a month by 6

Answer:

3240

Step-by-step explanation:

Answer:

C. 150

Step-by-step explanation:

It's right on Plato.

Answer:

A

Step-by-step explanation:

Answer:

x= -6 ,1

Step-by-step explanation:

B is the answer

x= -6 ,1

Answer:

x = 21

Step-by-step explanation:

Based on the inscribed angle theorem, we would have:

120° = 2(3x - 3)°

Solve for x

120 = 2*3x - 2*3

120 = 6x - 6

Add 6 to both sides

120 + 6 = 6x

126 = 6x

Divide both sides by 6

126/6 = x

21 = x

x = 21

Answer:

You take 1,000 because it's in the thousandths place of 1,255. The value of that one is 1,000 so you multiply that times 100, which is the value of 1 in 82,175.

Answer:

71 is 10% of 710

52 is 97% of 5200/97

Step-by-step explanation:

Let’s start with 71 is 10% of what number.

basically, what this is saying, is that 71 = 10% times and unknown valu. We can set this as x.

so, 71=0.1x

divide on both sides,

710=x

now the second one.

repeat the same process.

52=0.97x

divide

5200/97 =x

Answer:

13/20

Step-by-step explanation:

you count up all the marbles together, which is 20 and then count up all the other marbles besides blue, which would be 13 of the 20 marbles are not blue

Answer:

D. 11

Step-by-step explanation:

Midsegment theorem:

The length of the midsegment of a triangle is half the length of it's third side.

In this question:

Third side: 3x - 5

Midsegment: 14m

So

[tex]\frac{3x - 5}{2} = 14[/tex]

[tex]3x - 5 = 28[/tex]

[tex]3x = 33[/tex]

[tex]x = \frac{33}{3}[/tex]

[tex]x = 11[/tex]

The correct answer is given by option D.

Answer:

Step-by-step explanation:

Given two similar triangles.

Corresponding parts of similar figures have same ratio.

Use ratios to find the value of x:

Find the value of FG:

tan²(x) - sin²(x) = sin²(x)/cos²(x) - sin²(x)

… = sin²(x) (1/cos²(x) - 1)

… = sin²(x) (sec²(x) - 1)

… = sin²(x) tan²(x)

Answer:

4/10, 6/15, 8/20, 10/25

Step-by-step explanation:

Answer:

4.7 · 10^7

Step-by-step explanation:

Answer:

30 tables

Step-by-step explanation:

1/10 of 300 is 30

Answer:

30 tables were reserved

Step-by-step explanation:

1/10 × 300 = 30

Answer:

24 square inches

Step-by-step explanation:

Based on the diagram or figure given, The  area of the figure is known to be 24 square inches.

The area of a figure is known to be the rate or the number of unit squares that is said to have cover the surface of a closed figure.

Note that the area is often measured in square units such as (cm²) and in the case above, the Based on the diagram or figure given, The  area of the figure is known to be 24 square inches.

Learn more about area  from

https://brainly.com/question/25292087

#SPJ2

Step-by-step explanation:

1. 51-x-5

= 46-x Answer

2. 21-24

= -3 Answer

9514 1404 393

Answer:

  $12 for each shirt

Step-by-step explanation:

If we let 's' and 't' represent the costs of a shirt and tie, respectively, then we can write the general form equations ...

  6s +3t -79.50 = 0

  3s +2t -41.00 = 0

The solution for s can be found using the "cross multiplication" technique.

Differences of products can be formed:

  d1 = (6)(2) -(3)(3) = 3

  d2 = (3)(-41) -(2)(-79.50) = 36

Then we have ...

  1/d1 = s/d2   ⇒   s = d2/d1 = 36/3 = 12

The cost of each shirt is $12.00.

___

2 ties cost 41-36 = 5, so each one is $2.50.

_____

Additional comment

The use of simple elimination on this set of equations would eliminate the s-variable, so would mean additional work to find s after finding t. The t-variable could be eliminated by multiplying one equation by one coefficient, and the other by a different coefficient. As long as we're doing that amount of work, we may as well do just enough cross-multiplication to get the one answer we need. This is where the "cross-multiplication" method of solution comes in handy.

This method solves the general-form equations ...

by considering the two rows of coefficients:

Then differences of cross-products are formed in adjacent columns:

  d1 = ae -db

  d2 = bg -ec

  d3 = cd -ga

The solutions are ...

  1/d1 = x/d2 = y/d3   ⇒   x = d2/d1, y = d3/d1

Answer:

65°

Step-by-step explanation:

All angles in a triangle added up make 180° so you have to add 68° and 47° whih equals 115° and then simply subtract it from 180° so 180°-115°=65°

Answer:

(-4,-4)

Step-by-step explanation:

Anytime you reflect a coordinate point across the x-axis, the y-coordinate becomes its opposite and the x-coordinate stays the same.

In this coordinate: (-4,4)

Reflecting (-4,4) across the x-axis means the x-coordinate (-4) would stay the same and the y-coordinate (4) would become its opposite (-4).

The new coordinates after being reflected across the x-axis are (-4,-4).

Answer:

obtuse

Step-by-step explanation:

When c, the hypotenuse, is greater than the legs (a and b), it's an obtuse triangle