Answer:
- a)
- b)
- c)
- d)
Step-by-step explanation:
We will use the product rule from combinatorics.
- a) There are 26 letters in the English alphabet, so there are 26 possible choices for the first character and 26 possible choices for the last one. Each one of the remaining eight characters of the string has 36 choices (letters or digits). By the product rule, there are
strings.
- b) We have 5 possible choices for the first character, it must be some vowel a,e,i,o,u. The second character can be chosen in 21 ways, selecting some consonant. There are 10 possibilities for the last character because only of the digits are allowed. The other seven characters have no restrictions, so each one can be chosen in 36 ways. By the product rule there are
strings.
- c) The third character has 5 possibilities. Repetition of vowels is allowed, so the sixth and eighth characters have each one 5 possible choices. There are seven characters left. None of them are a vowel, but they are allowed to take any other letter or digit, so each one of them can be chosen in 36-5=31 ways. Therefore there are strings.
- d) Remember that the binomial coefficient
is the number of ways of choosing k elements from a set of n elements. In this case, to count all the possible strings, we first need to count in how many ways we can select the four positions that will have the digits. This can be done in 
ways, since we are choosing four elements from the set of the ten positions of the string. Now, for the first position, we can choose any digit so it has 10 possibilities. The second position has 9 possibilities, because we can't repeat the digit used on the first position. Similarly, there are 8 choices for the third position and there are 7 choices for the fourth. Now, these are the only digits on the string, so the remaining 6 characters must be letters, then each one of them has 26 possibilities. By the product rule, there are strings.
X< 5 and (- infinity, 5 )
I'll give you an example:
Find the first and third quartiles using this set of data - 3, 5, 7, 8, 9, 11, 15, 16, 20, 21.
Step 1: Put the numbers in order.
3, 5, 7, 8, 9, 11, 15, 16, 20, 21.
Step 2: Make a mark in the center of the data:
3, 5, 7, 8, 9, | 11, 15, 16, 20, 21.
Step 3: Place parentheses around the numbers above and below the mark you made in Step 2–it makes Q1 and Q3 easier to spot.
(3, 5, 7, 8, 9), | (11, 15, 16, 20, 21).
Step 4: Find Q1 and Q3
Q1 is the median (the middle) of the lower half of the data, and Q3 is the median (the middle) of the upper half of the data.
(3, 5, 7, 8, 9), | (11, 15, 16, 20, 21). Q1 = 7 and Q3 = 16.
The measure of the angle created by the car's turning is 105°
Step-by-step explanation:
Given : a car is traveling east on 4th Street and turns onto King Avenue heading northeast.
We have to calculate the measure of the angle created by the car's turning.
Since, car is travelling in east direction on 4th street that is from A to D as shown below in image by arrow.
Then at point B, the car turns toward King Avenue heading northeast. that is B to C as shown below in image
Since, we need to calculate the measure of the angle created by the car's turning that is measure of ∠ABC.
AD is a straight line, thus measure of any angle at line segment AD is 180° as angles on one side of a straight line always add to 180 degrees
Therefore, at B,
∠ABC + ∠CBD = 180°
Aldo given , ∠CBD = 75°
Thus, the measure of ∠ABC is ,
⇒ ∠ABC = 180° -∠CBD
⇒ ∠ABC = 180° - 75°
⇒ ∠ABC = 105°
Thus, the measure of the angle created by the car's turning is 105°
Answer: The number of pieces of the ribbon she can cut = 
yards
Step-by-step explanation:
Given: The length of the ribbon = 
yards
yards
Length of each piece = 
yards
The number of identical pieces can be cut from the entire ribbon = (Length of the ribbon ) ÷ (Length of each piece )
Hence, the number of pieces of the ribbon she can cut = yards
