An arithmetic series contains n terms. Show that if t1 = a−b and tn = a+b then the value of Sn is independent of b.[Arithmetic Sequences]

Answer:

69 m 70 cm

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

We can think in this situation as:

There is 10% (or a probability equal to 0.1) where the citrus grower's profit will be reduced by $15,000

There is 10% (or a probability equal to 0.1) where the citrus grower's profit will be reduced by $25,000

And in the remaining 80% (or a probability equal to 0.8), the profit does not change.

Then the expected value for the total profit can be written as:

EV = $100,000 + ( 0.1*(-$15,000) + 0.1*(-$25,000) + 0.8*$0)

     =  $96,000

In the case where the citrus grower spends $5000 to protect the fruits against possible bad weather, there is a 100% that is profit will not change, but he must pay $5,000

Then his profit will be:

P = $100,000 - $5,000 = $95,000

So in this case, the profit is $1000 less than the expected profit in the prior case. So the scenario where he does not buy the protection has a larger expected profit, which may mean that is better to not buy it (in a straight mathematical point of view)

One also could think that  the values are really close together, so buying the protection does not mean a big change, and increases the security

Answer: The first angle is 32 degrees

The second angle is 38 degrees

The third angle is 110 degrees.

Step-by-step explanation:

Let x represent the size of the first angle.

Let y represent the size of the second angle.

Let z represent the size of the third angle.

The second angle of the triangle is 6 more than the first angle. This means that

y = x + 6

The third angle is 14 more than three times the first angle. This means that.

z = 3x + 14

The sum of the angles in a triangle is 180 degrees. It means that

x + y + z = 180 - - - - - - - - - - - -2

Substituting y = x + 6 and z = 3x + 14 into equation 2, it becomes

x + x + 6 + 3x + 14 = 180

x + x + 3x = 180 - 14 - 6

5x = 160

x = 160/5 = 32

y = x + 6

y = 32 + 6 = 38

z = 3x + 14

z = 3×32 + 14 = 96 + 14

z = 110

Answer:

2.131

Step-by-step explanation:

Given :  Sample size = 16

             Sample mean is 4.2

             Sample standard deviation is 1.4.

             Level of significance is 0.05.

To Find : critical t value

Solution:

Sample size = 16

Since n < 30

So we will use t - test

We are supposed to find critical t value

Degree of freedom = n-1 = 16-1 = 15

Level of significance =α= 0.05

Now refer the t table for t critical

= = 2.131

Hence The critical t value for this problem is 2.131

If we are to write the pH range for the Jerry's Fizzy Cola as an inequality and label the substance as acidic or alkaline, given the data 4.1 through 4.3 (inclusive), this would be the result:

C. 4.1 ≤ h ≤ 4.3, acidic