Factors and multiples Q&A: Get Expert Help and Learn from Real-World Examples

How many bit strings of length 10 have more 0s than 1s?

How many bit strings of length 10 have at least three 1s?

How many bit strings of length 10 have at least seven 1s?

let ${\displaystyle u=[2,-1,-4],v=[0,0,0]}$, and ${\displaystyle w=[-6,-9,8]}$. we want to determine by inspection (with minimal compulation) if ${\displaystyle \{u,v,w\}}$ is linearly dependent or independent. choose the best answer:
A. The set is linearly dependent because one of the vectors is a scalar multiple of another vector.
B. The set is linearly independent because we only have two vectors and they are not scalar multiples of each other.
C. The set is linearly dependent because the number of vectors in the set is greater than the dimension of the vector space.
D. The set is linearly dependent because two of the vectors are the same.
E. The set is linearly dependent because one of the vectors is the zero vector.
F. We cannot easily tell if the set is linearly dependent or linearly independent.

Thirteen people on a softball team show up for a game. How many ways are there to choose 10 players to take the field?

How many permutations of the letters ABCDEFG contain the strings CBA and BED?

How many permutations of the letters ABCDEFG contain the strings ABC and CDE?

Often new technology spreads exponentially. Between 1995 and 2005, each year the number of Internet domain hosts was 1.43 times the number of hosts in the preceding year. In 1995, the number of hosts was 8.2 million.
(a) Explain why the number of hosts is an exponential function of time. The number of hosts grows by a factor of __________ each year, this is an exponential function because the number is growing by constant multiples.
(b) Find a formula for the exponential function that gives the number N of hosts, in millions, as a function of the time t in years since 1995.
${\displaystyle N=}$
(c) According to this model, in what year did the number of hosts reach 35 million? (Round your answer to the nearest year.)

How many permutations of the letters ABCDEFG contain the strings BA and GF?

Consider the function ${\displaystyle f\left(x\right)=2\sin \left(\pi 2(x-3)\right)+4}$.
State the amplitude A, period P, and midline. State the phase shift and vertical translation. In the full period [0, P], state the maximum and minimum y-values and their corresponding x-values.
Hints for the maximum and minimum values of f(x):
The maximum value of ${\displaystyle y=\sin \left(x\right)}$ is ${\displaystyle y=1}$ and the corresponding x values are ${\displaystyle x=\pi 2}$ and multiples of ${\displaystyle 2\pi }$ less than and more than this x value. You may want to solve ${\displaystyle \pi 2(x-3)=\pi 2}$.
The minimum value of ${\displaystyle y=\sin \left(x\right)}$ is ${\displaystyle y=-1}$ and the corresponding x values are ${\displaystyle x=3\pi 2}$ and multiples of ${\displaystyle 2\pi }$ less than and more than this x value. You may want to solve ${\displaystyle \pi 2(x-3)=3\pi 2}$.
If you get a value for x that is less than 0, you could add multiples of P to get into the next cycles.
If you get a value for x that is more than P, you could subtract multiples of P to get into the previous cycles.
For x in the interval [0, P], the maximum y-value and corresponding x-value is at:
${\displaystyle x=}$
${\displaystyle y=}$
For x in the interval [0, P], the minimum y-value and corresponding x-value is at:
${\displaystyle x=}$
${\displaystyle y=}$

How many permutations of the letters ABCDEFG contain the strings ABC and DE?

A club has 25 members. a) How many ways are there to choose four members of the club to serve on an executive committee? b) How many ways are there to choose a president, vice president, secretary, and treasurer of the club, where no person can hold more than one office?

Consider the function ${\displaystyle f\left(x\right)=3\sin \left(\frac{\pi }{3}(x-4)\right)+5}$.
State the amplitude A, period P, and midline. State the phase shift and vertical translation. In the full period [0, P], state the maximum and minimum y-values and their corresponding x-values.
Enter the exact answers.
Amplitude: ${\displaystyle A=}$
Period: ${\displaystyle P=}$
Midline: ${\displaystyle y=}$
The phase shift is:
a. up 4 units
b. 4 units to the right
c. 4 units to the left
d. 5 units to the left
The vertical translation is:
a. up 4 units
b. down 5 units
c. up 5 units
d. down 4 units
Hints for the maximum and minimum values of f(x):
The maximum value of ${\displaystyle y=\sin \left(x\right)}$ is ${\displaystyle y=1}$ and the corresponding x values are ${\displaystyle x=\frac{\pi }{2}}$ and multiples of ${\displaystyle 2\pi }$ less than and more than this x value. You may want to solve ${\displaystyle \frac{\pi }{3}(x-4)=\frac{\pi }{2}}$.
The minimum value of ${\displaystyle y=\sin \left(x\right)}$ is ${\displaystyle y=-1}$ and the corresponding x values are ${\displaystyle x=\frac{3\pi }{2}}$ and multiples of ${\displaystyle 2\pi }$ less than and more than this x value. You may want to solve ${\displaystyle \frac{\pi }{3}(x-4)=\frac{3\pi }{2}}$.
If you get a value for x that is less than 0, you could add multiples of P to get into the next cycles.
If you get a value for x that is more than P, you could subtract multiples of P to get into the previous cycles.
For x in the interval [0, P], the maximum y-value and corresponding x-value is at:
x=
y=
For x in the interval [0, P], the minimum y-value and corresponding x-value is at:
${\displaystyle x=}$
${\displaystyle y=}$

How many permutations of the letters ABCDEFG contain the string CFGA?

How many permutations of the letters ABCDEFG contain the string BCD?

Determine the lowest common multiple of each of the following list of numbers
a) 9;6
b) 8; 14
c) 2; 9; 54;

For each topic, decide how a scatterplot of the data would likely look. Explain your reasoning.
Number of children living in a town and number of schools in the town