The nine members of an academy league have an gpa of 3.7 . a new member joins who has a 4.0 gpa . what is the league’s new average?

3.73

Step-by-step explanation:

To solve this, we simply need to find the mean (or the average) with the addition of the new member. To find an average, we simply add all the values and then divide by the total amount of values. The work is shown below...

(3.7) + (3.7) + (3.7) + (3.7) + (3.7) + (3.7) + (3.7) + (3.7) + (3.7) + (4.0) = 37.3

Now we divide 37.3 by the amount of members, which is 10.

37.3 / 10 = 3.73

The league's new average is 3.73

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°