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erastovalidia [21]
3 years ago
11

a baker has 80 rolls and 64 muffins to put into gift basket. He wants each gift basket to have the same number of rolls and the

same number of muffins. He also wants to use all of the rolls and all of the muffins. what is the greatest number of gift basket the baker can make?
Mathematics
2 answers:
GalinKa [24]3 years ago
6 0
16 baskets is the greatest number of baskets that could be made while using all the rolls and muffins. 80/64 reduces to 5/4
So if the baker puts 5 rolls and 4 muffins in each basket he would be able to make 16 baskets and use all the baked goods.
80/5=16
64/4=16
White raven [17]3 years ago
3 0
The greatest number of gift basket the baker can make is 8. Since there are 80 rolls and 64 muffins and he wants each gift basket to have the same amount of rolls and muffins and use all the rolls and muffins, there would be 10 rolls and 8 muffins in each gift basket. 
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A device produces random 64-bit integers at a rate of one billion per second. After how many years of running is it unavoidable
nikitadnepr [17]

Answer:

3171 × 10^(44) years

Step-by-step explanation:

For each bit, since we are looking how many years of running it is unavoidable that the device produces an output for the second time, the possible integers are from 0 to 9. This is 10 possible integers for each bit.

Thus, total number of possible 64 bit integers = 10^(64) integers

Now, we are told that the device produces random integers at a rate of one billion per second (10^(9) billion per second)

Let's calculate how many it can produce in a year.

1 year = 365 × 24 × 60 × 60 seconds = 31,536,000 seconds

Thus, per year it will produce;

(10^(9) billion per second) × 31,536,000 seconds = 3.1536 × 10^(16)

Thus;

Number of years of running is it unavoidable that the device produces an output for the second time is;

(10^(64))/(3.1536 × 10^(16)) = 3171 × 10^(44) years

6 0
3 years ago
Amanda teaches the art of quilling to four students these students each teach the art of quilling to four other students if this
il63 [147K]

Answer:

341

Step-by-step explanation:

The number of people who know the art of quilting in each successive generation is

1, 4, 16, …

These numbers represent a geometric sequence where each term has the form

aₙ = a₁rⁿ⁻¹

In your sequence, a₁ = 1 and r = 4.

Then, the formula for your sequence is

aₙ = 4ⁿ⁻¹

Sum over five generations

The formula for the sum of the first n terms of a geometric series is

Sum = a₁[(1 - rⁿ)/(1 - r)]

Sum = 1[(1 - 4⁵)/(1 - 4)

       = (1 - 1024)/(-3)

       = -1023/-3

       = 341

If the process continues for five generations, 341 people will know the art of quilting.

4 0
3 years ago
Read 2 more answers
the sum of 2 consecutive integers is at most the difference between nine times the smaller and 5 times the larger
Reil [10]
<h2>Answer:</h2>

x\geq 3 \ and \ x+1 \geq 4

<h2>Step-by-step explanation:</h2>

The question in this problem is:

<em>The sum of 2 consecutive integers is at most the difference between nine times the smaller and 5 times the larger. What are the numbers?</em>

<em />

First of all, let's name the first variable x which is the smaller number. Accordingly, the lager number will be x+1 given that those numbers are consecutive. On the other hand<em> at most </em>conveys the idea of an inequality, which is:

\leq \\ which \ means \ less \ than

So:

1. The sum of 2 consecutive integers can be written as:

v+(v+1)

2. Nine times the smaller and 5 times the larger can be written as:

9v-5(v+1)

Finally, the whole statement:

The sum of 2 consecutive integers is at most the difference between nine times the smaller and 5 times the larger:

x+(x+1) \leq 9x-5(x+1) \\ \\ x+x+1\leq 9x-5x-5 \\ \\ 2x+1 \leq 4x-5 \\ \\ 6 \leq 2x \\ \\

x+(x+1) \leq 9x-5(x+1) \\ \\ x+x+1\leq 9x-5x-5 \\ \\ 2x+1 \leq 4x-5 \\ \\ 6 \leq 2x \\ \\ \frac{6}{2} \leq \frac{2x}{2} \\ \\ 3 \leq x \\ \\ x\geq 3 \\ \\ and \\ \\ x+1 \geq 4

The two numbers are:

x\geq 3 \ and \ x+1 \geq 4

6 0
3 years ago
What is the length of BC⎯⎯⎯⎯⎯ ?<br><br><br> Enter your answer in the box.
Rudiy27

Answer:

  \overline{\text{BC}}=\boxed{22}

Step-by-step explanation:

The angle marks mean those angles have the same measure. That means the sides opposite them have the same measure, so ...

  2x -24 = x -2

  x = 22 . . . . . . . . . add 24-x

The length of BC is x, so is 22.

BC = 22

8 0
3 years ago
if a number is increased by 5 and the result is then divided by three,the result is seven. write an equation that models this ve
gregori [183]
A number (we don’t know the number so I’ll use X) plus five. So we can start the equation of with X+5 then divided by 3=7 so X+5➗3=7 so to solve what X is we can just go in reverse. 7 TIMES 3= 21-5=16 so X=16
6 0
3 years ago
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