MATHEMATICS HIGH SCHOOL

Circle d has a radius of 21 millimeters and central angle, ∠edf, which measures 60°. find the exact length of . mm 7mm 14mm 42mm

Answers

Answer 1
Answer: the length of an arc length can be calculated using the formula:
s = ra
where s is the lenght of the arc
and r is the radius of the circle
a is the central angle in radians

first converts degrees to radians
a = 60 ( pi / 180)
a = pi /3 =1.05

s = 21(1.05)
s = 22 mm is the length of the arc
Answer 2
Answer:

Answer:

7π mm

Have a good day!

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The total cost for a bucket of popcorn and 4 movie tickets is $56. The total cost for the same size bucket of popcorn and 6 movie tickets is $80. Which equation represents the relationship between y, the total cost of the popcorn and movie tickets, and x, the number of movie tickets that are purchased

Answers

y+4x=56
y+6x=80

I think these are the two equations that should be used to solve for 'y' and 'x'!!

Answer:

y = 12x + 8y

Step-by-step explanation:

A certain bacteria population is known to quadruples every 150 minutes. Suppose that there are initially 200 bacteria. What is the size of the population after t hours?

Answers

This is a geometric progression
The size of the population afeter t hours will be=a₁*r^n

a₁= the first term =200
r=common ratio=4

150 minutes=150 minutes * (1 hour /60 minutes)=2.5 hours.

In this case:
the size of the populatation after t hours=200*4^t/2.5=200*4^0.4t

To check
 t=0⇒ the size will be=200*4⁰=200*1=200
t=2.5 hours=150 minutes; the size will be =200*4¹=800
t=5 hours; the size will be=200*4²=200*16=3200

Answer: the size will be= 200*4^(0.4t)

Final answer:

The growth of the bacteria is represented by the exponential growth equation. Given the initial population, the four-fold increase, and the time interval for the increase, we can find the population after any given time by using the equation P = 200 * 4^(t/2.5).

Explanation:

The problem given is an example of an exponential growth problem. For these types of problems, we use the formula P = P0 * e^(kt), where P is the final population, P0 is the initial population, k is the growth rate, and t is time. However, in this case, we were given that the bacteria quadruples, meaning 'quadrupling' is not a continuous rate, so we use a slightly different form of the equation: P = P0 * (b)^(t/t0), where b is the times increase and t0 is the time interval for the b-fold increase.

Given that the initial population P0 is 200 bacteria, b is 4 because the population quadruples every 150 minutes, and time t0 is 150 minutes or 2.5 hours. We need to find the population P after t hours. Substituting these values into our equation gives us: P = 200 * 4^(t/2.5).

So, after t hours, the population of the bacteria will be given by the equation P = 200 * 4^(t/2.5).

Learn more about Exponential Growth here:

brainly.com/question/12490064

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Which of the following statements contains a quotient? A. 7 + 6 = 13 B. 7 × 6 = 42 C. 42 ÷ 6 = 7 D. 7 – 6 = 1

Answers

Mathematically, quotient means the solution you get when solving a division problem.

The only reliable choice is C)

Choice A) is called "the sum or total"
Choice B) is called "the product."
Choice D) is called the "the difference"

The quotient is the answer to a division problem. Therefore, C is the correct answer.

A firm starts work with 110 employees for the 1st week. The number of employees rises by 6% per week. How many weeks will it take for 250 persons to be employed?

Answers

1 % of 110 = 1.1
x 6 = 6.6
round up because you can't have 0.6 of a person.
7 people a week.
250 - 110 = 140
140 divided by 7 = 20
20 weeks
110 x 1.06 = 116.6
Now if 116.6 is x repeat this step till you get 250 people
X x 1.06
, so it will take roughly 14-15 times to get 250 employees but 14 times is the closer one

Terrance and Lakendra are going to GameStop for new video game controller and some new games. Their grandmother gave them a $125 gift card for this purpose. If the controller they want is $45 and games are $20 each, what is the maximum number of games they can be purchase (their father will be paying the sales tax)?

Answers

125-40 = 85

Then if each game cost $20 they could get 4 games and have $5 left over

5/8 - 3/4 (8 - 1/3) + 1

Answers

Answer:

use a algebra caculator

Step-by-step explanation:

Answer:

-4.125

Step-by-step explanation:

5/8 - 3/4  (8-1/2 ) + 1 = - 33/8 = -4 1/8
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