Divide 127 and 13. The quotient will give the number of boxes and the remainder will give the number of leftover brownies:

9/127

\(-117/10\)

Therefore \(127 \div13=9R10\) so she packed 9 boxes and had 10 leftover brownies.

Question

asked 2021-07-30

Exercise 1: Counting binary strings.

Count the number of binary strings of length 10 subject to each of the following restrictions.

There is only one binary string of length ten with no 1's: 00000000000. There are \(\displaystyle{2}^{{{10}}}\) binary strings of length ten. Therefore the number of binary strings of length ten with at least one 1 is \(\displaystyle{2}^{{{10}}}-{1}\).

(b)

The string has at least one 1 and at least one 0.

(c)

The string contains exactly five 1's or it begins with a 0.

Exercise 2: Counting integer multiples.

(b)

How many integers in the range 1 through 140 are integer multiples of 2, 5, or 7?

Count the number of binary strings of length 10 subject to each of the following restrictions.

There is only one binary string of length ten with no 1's: 00000000000. There are \(\displaystyle{2}^{{{10}}}\) binary strings of length ten. Therefore the number of binary strings of length ten with at least one 1 is \(\displaystyle{2}^{{{10}}}-{1}\).

(b)

The string has at least one 1 and at least one 0.

(c)

The string contains exactly five 1's or it begins with a 0.

Exercise 2: Counting integer multiples.

(b)

How many integers in the range 1 through 140 are integer multiples of 2, 5, or 7?

asked 2021-05-05

The photograph shows a workman struggling to keep a stack of boxes balanced on a dolly. The man's right foot is on the axle of the dolly. Assuming that the boxes are identical, which one creates the greatest torque with respect to the axle?

a) the highest box

b) the lowest box

c) the box farthest to the right

d) the box farthest to the left

a) the highest box

b) the lowest box

c) the box farthest to the right

d) the box farthest to the left

asked 2021-06-01

Some friends were playing darts decided to impose a 4-point penalty for each dart that missed the dart board completely. During the evening, a boy had 3 darts in the 20-point section, 6 darts in the triple-15-point section, and 2 darts in the double-10-point section. He missed the dart board completely 4 times. How many points did the boy score?

asked 2021-08-08

Determine if you should find the LCM or GCF Boxes that are 12 inches tall are being stacked next to boxes that are 18 inches tall. What is the shortest height at which the two stacks will be the same height? Do it right LCM- least common multiple GCF- greatest common factor.

1) GCF NS 2) LCM

1) GCF NS 2) LCM