josh wanted to buy a bicycle but didn't have enough money. After josh told his troubles to sam slick, sam said,"I can fix that. see that fence? each time you jump that fence, i'll double your money. There's one small thing though: you must give me $32 each time for the priviledge of jumping." Josh agreed, jumped the fence, received his payment from sam slick, and paid sam $32. Repeating the routine twice more, josh was distressed to find that, on the last jump,after sam had made his payment to josh, josh had only $32, with which to pay sam and so had nothing left. Sam, of course, went merrily on his way, leaving josh wishing that he had known a little more about mathematics.

Answers

Answer 1
Answer: If he had less than 32 he couldn't jump. If he had 64 he would have not lost nor won on each jump -- he gets 64 in total after each jump. If he had more than 64 he would have won.
Now, 3 jumps give him a result of 32. After 2 jumps he had 32(pay)+16(doubled)=48. After the first jump he had 32+24=56. Before that he had 32+28=$60. 5 more dollars and he could have build his way to richness!
Answer 2
Answer:

Answer:If he had less than 32 he couldn't jump. If he had 64 he would have not lost nor won on each jump -- he gets 64 in total after each jump. If he had more than 64 he would have won.

Now, 3 jumps give him a result of 32. After 2 jumps he had 32(pay)+16(doubled)=48. After the first jump he had 32+24=56. Before that he had 32+28=$60. 5 more dollars and he could have build his way to richness!

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Step-by-step explanation:


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Y''+2y'+y=2e^(-t)
find the general solution of the giving nonhomogenous differential equation

Answers

The general solution of the differential equation y'' + 2y' + y = 2e^(-t) is (c1 + c2 x) e^-x

The simple interest earned by an account varies jointly as the time and the principal. In 2 years, a principal of $5000 earns $650 interest. How much would $1000 earn in 1 year?

Answers

Final answer:

To find the simple interest $1000 would earn in 1 year, we first calculate the interest rate from the provided example, which is 6.5%. Using this rate, the simple interest formula (Principal x Rate x Time) gives us an interest of $65.

Explanation:

The subject of this question regards the calculation of simple interest, a fundamental concept in Mathematics and Finance. First, we'll need to determine the interest rate used in the initial scenario where a $5000 deposit earns $650 interest in 2 years. In this case, using the simple interest formula which is Principal x Rate x Time(PRT), we have:

$650 = $5000 x Rate x 2 years

Solving for Rate, we get: Rate = $650 / ($5000 * 2) = 0.065, or 6.5%.

Now that we know the interest rate is 6.5%, we can calculate the interest $1000 would earn in 1 year. Again using the simple interest formula, we have: Interest = Principal x Rate x Time = $1000 * 6.5% * 1 year = $65.

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Mr. Hann is trying to decide how many new copies of a book to order for his students. Each book weighs 6 ounces.Which ordered pair is a viable solution if x represents the number of books he orders and y represents the total weight of the books, in ounces?

Answers

The answer that only made sense to me is (0,0)
x + 6y x being the number of books he orders, considering you have no idea how many books he need this remains x. the information you do know is every book weighs 6oz. this is your y value. 

Jemma has 24 balls. Out of the 24 balls, 12 are yellow, 4 are pink, and the rest are red. What is the ratio of the number of red balls to the number of balls that are either yellow or pink?

Answers

12+4+8=24.The ratio of the red balls is 8.

The ratio of the number of red balls to the number of balls that are yellow will be 2/3 and with pink will be 2.

What are ratio and proportion?

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

Jemma has 24 balls. Out of the 24 balls, 12 are yellow, 4 are pink, and the rest are red.

Then the number of red balls will be

⇒ 24 - 12 - 4

⇒ 24 - 16

⇒ 8

The ratio of the number of red balls to the number of balls that are yellow will be

⇒ 8 / 12

⇒ 2/3

The ratio of the number of red balls to the number of balls that are pink will be

⇒ 8 / 4

⇒ 2

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Find the area of a regular octagon with apothem K and side of 10.40K
60K
80K

????

Answers

Answer: 40K

Step-by-step explanation:

We know that the area of a regular polygon is given by :-

A=(1)/(2)*Apothem*Perimeter

Given: The side of regular octagon = 10

Then, the perimeter of the regular octagon =8(side)=8(10)=80

Now, the area of given regular octagon is given by :-

A=(1)/(2)*K*80\n\Rightarrow\ A=40K

Mr Taylor brought back 180 Euros to the UK. The exchange rate was €1.2 to £1. How much did he get in £ sterling?

Answers

The answer is £150.

This could be calculated using proportion. If £1 is €1.2, how many £ is €180:
£1 : €1.2 = x : €180
x = £1 ÷ €1.2 × €180
x = £150