Solved on Sep 08, 2023

Find the minimum number of prizes that can be distributed from $\$800$ , where the prizes are powers of 2.

STEP 1

Assumptions1. The prizes are powers of. . The total amount to be distributed is $800.
3. We need to find the minimum number of prizes that can be distributed.

STEP 2

First, we need to understand that the powers of2 are1,2,4,8,16,32,64,128,256,512,1024, and so on.

STEP 3

We need to find the largest power of2 that is less than or equal to $800. In this case, it is$ 512.

STEP 4

Subtract the largest power of2 from the total amount to find the remaining amount.
$Remaining\, amount = Total\, amount - Largest\, power\, of\,2$

STEP 5

Plug in the values for the total amount and the largest power of2 to calculate the remaining amount.
$Remaining\, amount = \$800 - \$512$

STEP 6

Calculate the remaining amount.
$Remaining\, amount = \$800 - \$512 = \$288$

STEP 7

Now, repeat the process with the remaining amount. Find the largest power of2 that is less than or equal to $288. In this case, it is$ 256.

STEP 8

Subtract the largest power of2 from the remaining amount to find the new remaining amount.
$New\, remaining\, amount = Remaining\, amount - Largest\, power\, of\,2$

STEP 9

Plug in the values for the remaining amount and the largest power of2 to calculate the new remaining amount.
$New\, remaining\, amount = \$288 - \$256$

STEP 10

Calculate the new remaining amount.
$New\, remaining\, amount = \$288 - \$256 = \$32$

STEP 11

Now, notice that the new remaining amount is a power of. So, we can distribute this as a prize.

STEP 12

Count the number of prizes we have distributed. We have distributed one prize of $512, one prize of$ 256, and one prize of $32. So, the minimum number of prizes that can be distributed is.
The minimum number of prizes that could be distributed from $800 is.

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Find the minimum number of prizes that can be distributed from $\$800$ , where the prizes are powers of 2.

STEP 1

Assumptions1. The prizes are powers of. . The total amount to be distributed is $800.
3. We need to find the minimum number of prizes that can be distributed.

STEP 2

First, we need to understand that the powers of2 are1,2,4,8,16,32,64,128,256,512,1024, and so on.

STEP 3

We need to find the largest power of2 that is less than or equal to $800. In this case, it is$ 512.

STEP 4

Subtract the largest power of2 from the total amount to find the remaining amount.
$Remaining\, amount = Total\, amount - Largest\, power\, of\,2$

STEP 5

Plug in the values for the total amount and the largest power of2 to calculate the remaining amount.
$Remaining\, amount = \$800 - \$512$

STEP 6

Calculate the remaining amount.
$Remaining\, amount = \$800 - \$512 = \$288$

STEP 7

Now, repeat the process with the remaining amount. Find the largest power of2 that is less than or equal to $288. In this case, it is$ 256.

STEP 8

Subtract the largest power of2 from the remaining amount to find the new remaining amount.
$New\, remaining\, amount = Remaining\, amount - Largest\, power\, of\,2$

STEP 9

Plug in the values for the remaining amount and the largest power of2 to calculate the new remaining amount.
$New\, remaining\, amount = \$288 - \$256$

STEP 10

Calculate the new remaining amount.
$New\, remaining\, amount = \$288 - \$256 = \$32$

STEP 11

Now, notice that the new remaining amount is a power of. So, we can distribute this as a prize.

STEP 12

Count the number of prizes we have distributed. We have distributed one prize of $512, one prize of$ 256, and one prize of $32. So, the minimum number of prizes that can be distributed is.
The minimum number of prizes that could be distributed from $800 is.

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Find the minimum number of prizes that can be distributed from $800\$800$800, where the prizes are powers of 2.

STEP 1

Assumptions1. The prizes are powers of. . The total amount to be distributed is $800.3. We need to find the minimum number of prizes that can be distributed.

STEP 2

First, we need to understand that the powers of2 are1,2,4,8,16,32,64,128,256,512,1024, and so on.

STEP 3

We need to find the largest power of2 that is less than or equal to 800.Inthiscase,itis800. In this case, it is 800.Inthiscase,itis512.

STEP 4

Subtract the largest power of2 from the total amount to find the remaining amount.Remaining amount=Total amount−Largest power of 2Remaining\, amount = Total\, amount - Largest\, power\, of\,2Remainingamount=Totalamount−Largestpowerof2

STEP 5

Plug in the values for the total amount and the largest power of2 to calculate the remaining amount.Remaining amount=$800−$512Remaining\, amount = \$800 - \$512Remainingamount=$800−$512

STEP 6

Calculate the remaining amount.Remaining amount=$800−$512=$288Remaining\, amount = \$800 - \$512 = \$288Remainingamount=$800−$512=$288

STEP 7

Now, repeat the process with the remaining amount. Find the largest power of2 that is less than or equal to 288.Inthiscase,itis288. In this case, it is 288.Inthiscase,itis256.

STEP 8

Subtract the largest power of2 from the remaining amount to find the new remaining amount.New remaining amount=Remaining amount−Largest power of 2New\, remaining\, amount = Remaining\, amount - Largest\, power\, of\,2Newremainingamount=Remainingamount−Largestpowerof2

STEP 9

Plug in the values for the remaining amount and the largest power of2 to calculate the new remaining amount.New remaining amount=$288−$256New\, remaining\, amount = \$288 - \$256Newremainingamount=$288−$256

STEP 10

Calculate the new remaining amount.New remaining amount=$288−$256=$32New\, remaining\, amount = \$288 - \$256 = \$32Newremainingamount=$288−$256=$32

STEP 11

Now, notice that the new remaining amount is a power of. So, we can distribute this as a prize.

STEP 12

Count the number of prizes we have distributed. We have distributed one prize of 512,oneprizeof512, one prize of 512,oneprizeof256, and one prize of $32. So, the minimum number of prizes that can be distributed is.The minimum number of prizes that could be distributed from $800 is.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the minimum number of prizes that can be distributed from $\$800$ , where the prizes are powers of 2.

Assumptions1. The prizes are powers of. . The total amount to be distributed is $800.
3. We need to find the minimum number of prizes that can be distributed.

We need to find the largest power of2 that is less than or equal to $800. In this case, it is$ 512.

Subtract the largest power of2 from the total amount to find the remaining amount.
$Remaining\, amount = Total\, amount - Largest\, power\, of\,2$

Plug in the values for the total amount and the largest power of2 to calculate the remaining amount.
$Remaining\, amount = \$800 - \$512$

Calculate the remaining amount.
$Remaining\, amount = \$800 - \$512 = \$288$

Now, repeat the process with the remaining amount. Find the largest power of2 that is less than or equal to $288. In this case, it is$ 256.

Subtract the largest power of2 from the remaining amount to find the new remaining amount.
$New\, remaining\, amount = Remaining\, amount - Largest\, power\, of\,2$

Plug in the values for the remaining amount and the largest power of2 to calculate the new remaining amount.
$New\, remaining\, amount = \$288 - \$256$

Calculate the new remaining amount.
$New\, remaining\, amount = \$288 - \$256 = \$32$

Count the number of prizes we have distributed. We have distributed one prize of $512, one prize of$ 256, and one prize of $32. So, the minimum number of prizes that can be distributed is.
The minimum number of prizes that could be distributed from $800 is.