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Scrat [10]
3 years ago
12

A spinner used in a board game is divided into 12 equally sized sectors. Seven of these sectors indicate that the player should

move his token forward on the board, three of these sectors indicate that the player should move his token backward, and the remaining sectors award the player bonus points but do not move his token on the board. The total area of the sectors that do not allow the player to move his token is 45.1 inches squared. What is the radius of the spinner
Mathematics
1 answer:
forsale [732]3 years ago
3 0

Answer:

9.3 inches

Step-by-step explanation:

The computation of the radius of the spinner be given below:

Let us assume the same be x

So

We know that

Total area of the sector = one-sixth of the total area of the spinner

Given that

45.1 =  1 ÷ 6 × π × r^2

r^2 = 45.1 × 6 ÷ π

r^2 = 86.1

r = 9.279

= 9.3 inches

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A person invests 7000 dollars in a bank. The bank pays 5.5% interest compounded
kotykmax [81]

The time required to get a total amount of $13,200.00 with compounded interest on a principal of $7,000.00 at an interest rate of 5.5% per year and compounded 12 times per year is 11.559 years. (about 11 years 7 months)

Answer:

t = 11.559 years

<h3>Compound Interest </h3>

Given Data

  • Principal P= $7000
  • Rate r= 5.5%
  • Final Amount A = $13200
  • Time t = ??

(about 11 years 7 months)

Calculation Steps:

First, convert R as a percent to r as a decimal

r = R/100

r = 5.5/100

r = 0.055 per year,

Then, solve the equation for t

t = ln(A/P) / n[ln(1 + r/n)]

t = ln(13,200.00/7,000.00) / ( 12 × [ln(1 + 0.055/12)] )

t = ln(13,200.00/7,000.00) / ( 12 × [ln(1 + 0.0045833333333333)] )

t = 11.559 years

Learn more about compound interest here:

brainly.com/question/24924853

6 0
2 years ago
Using the Principle of Mathematical Induction, prove that . n ^2 − n is even for n ≥ 1​
Tamiku [17]

Base case: if <em>n</em> = 1, then

1² - 1 = 0

which is even.

Induction hypothesis: assume the statement is true for <em>n</em> = <em>k</em>, namely that <em>k</em> ² - <em>k</em> is even. This means that <em>k</em> ² - <em>k</em> = 2<em>m</em> for some integer <em>m</em>.

Induction step: show that the assumption implies (<em>k</em> + 1)² - (<em>k</em> + 1) is also even. We have

(<em>k</em> + 1)² - (<em>k</em> + 1) = <em>k</em> ² + 2<em>k</em> + 1 - <em>k</em> - 1

… = (<em>k</em> ² - <em>k</em>) + 2<em>k</em>

… = 2<em>m</em> + 2<em>k</em>

… = 2 (<em>m</em> + <em>k</em>)

which is clearly even. QED

8 0
3 years ago
Help solve for r algebra
bija089 [108]

Answer:

\frac{20}{7}

Step-by-step explanation:

Multiply both sides by 7 to get rid of the denominator on the Right Side (RS). Do the same for the left side (LS) by multiplying both sides by 5 to get:

7r=4(5)

Simplify: 7r=20

Divide both sides of the equation by 7 to get: r=\frac{20}{7}

6 0
3 years ago
Sam is delivering two refrigerators that each weigh 105 kilograms there is an elevator with a weight limit of 1,00 pounds
rosijanka [135]

Question:

Sam is delivering two refrigerators that each weigh 105 kilograms. There is an

elevator with a weight limit of 1,000 pounds. Can he take both refrigerators on the

elevator in one trip? (1 kilogram 2.2 pounds)

Answer: yes he can

Step-by-step explanation:

Yes he can.

He can if the total weight of the 2 refrigerator didn't exceed the weight limit of the elevator.

Therefore:

Since 1 refrigerator weigh 105kg

2 refrigerator = 2 x 105kg = 210kg

The weight limit of the elevator 1000pounds convert to kg.

Since

2.2 pounds = 1kg

1000 pounds = 1000/2.2 kg

=454.55kg

Weight limit of the elevator = 454.55kg.

Since Weight of the 2 refrigerator is less than

weight limit of the elevator, he can take both refrigerators on the elevator in one trip

5 0
2 years ago
A concrete pillar has the shape of a cylinder. It has a radius of 6 meters and a height of 4 meters. If concrete costs $82 per c
wel

Answer: $37077.12

Step-by-step explanation:

Please see the attachment below

7 0
3 years ago
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