The initial value stands at 20,300, decreasing annually by 9.5%.
Given that it decreases by 9.5% each year based on the preceding amount, we can apply an exponential decay model.
A 9.5% reduction means multiplying by 91.5% every year.
We express this mathematically. Plugging in 11 years for t yields.
$7,671.18
Answer:
50 Educators
Step-by-step explanation:
To tackle this question, the initial step is to calculate the amount of teachers prior to the addition of new staff. For this, I devised Model 1. In this model, teachers are positioned at the top of the ratio and students at the bottom. The variable X represents the number of teachers we are determining. Utilizing this model, I computed 2,100 multiplied by 1 (2,100) and then divided by 14 to conclude there were 150 teachers. Next, I formed a similar model with the updated student-teacher ratio (Model 2). This time, I multiplied 2,100 by 2 (which is 4,200) and divided by 21 to ascertain there are 200 teachers. Having established both the initial and the increased counts of educators, subtracting the original from the new gives you the tally of new teachers, which results in an increase of 50 teachers.
Step-by-step explanation:
Given are
Sides of the triangle measure 4 units, 6 units, and 7.21 units.
We need to compute the area of a circle whose circumference matches the triangle's perimeter.
The triangle's perimeter corresponds to the circle's circumference.
4 + 6 + 7.21 = 2πr, where r is the radius of the circle.
r = 2.73 units
Circle's area is:
or
A = 24 square units
Thus, the circle’s area is 24 square units.
To find the value of z in triangle XYZ, we can utilize the law of sines. We know the following:
1. The measure of angle XYZ is 51 degrees.
2. The measure of angle YZX is 76 degrees.
3. The length of side XZ is 2.6 units.
From these angles, angle XZY can be calculated, and then we can apply the law of sines to determine z.
Thus, we proceed to solve for z using the sine relationship in the triangle.
We will round the result to one decimal place.
