Answer:
Option E is correct.
The expected number of meals expected to be served on Wednesday in week 5 = 74.2
Step-by-step Explanation:
We will use the data from the four weeks to obtain the fraction of total days that number of meals served at lunch on a Wednesday take and then subsequently check the expected number of meals served at lunch the next Wednesday.
Week
Day 1 2 3 4 | Total
Sunday 40 35 39 43 | 157
Monday 54 55 51 59 | 219
Tuesday 61 60 65 64 | 250
Wednesday 72 77 78 69 | 296
Thursday 89 80 81 79 | 329
Friday 91 90 99 95 | 375
Saturday 80 82 81 83 | 326
Total number of meals served at lunch over the 4 weeks = (157+219+250+296+329+375+326) = 1952
Total number of meals served at lunch on Wednesdays over the 4 weeks = 296
Fraction of total number of meals served at lunch over four weeks that were served on Wednesdays = (296/1952) = 0.1516393443
Total number of meals expected to be served in week 5 = 490
Number of meals expected to be served on Wednesday in week 5 = 0.1516393443 × 490 = 74.3
Checking the options,
74.3 ≈ 74.2
Hence, the expected number of meals expected to be served on Wednesday in week 5 = 74.2
Hope this Helps!!!
Here are a few things you'll need to know for this question:
- Domain: <u>The list of x-values that are possible on a line.</u>
- Range: <u>The list of y-values that are possible on a line.</u>
- Interval Notation: <u>Shows the domain/range using the endpoints</u>. Brackets mean that the endpoint is included, parentheses mean the endpoint is excluded. Ex: (2,10]. 2 is excluded, 10 is included.
- Closed Circles: <u>The endpoint is included.</u>
- Open Circles: <u>The endpoint is excluded.</u>
So firstly, let's look at the domain. We see that there is a closed circle at x = -2 and an open circle at x = 5. Using what we know, <u>the interval notation of the domain is [-2,5).</u>
Next, let's look at the range. We see that there is a closed circle at y = -5 and an open circle at y = 2. Using what we know, <u>the interval notation of the range is [-5,2).</u>
Answer:
proof below
Step-by-step explanation:
Remember that a number is even if it is expressed so n = 2k. It is odd if it is in the form 2k + 1 (k is just an integer)
Let's say we have to odd numbers, 2a + 1, and 2b + 1. We are after the sum of their squares, so we have (2a + 1)^2 + (2b + 1)^2. Now let's expand this;
(2a + 1)^2 + (2b + 1)^2 = 4a^2 + 4a + 4b + 4b^2 + 4b + 2
= 2(2a^2 + 2a + 2b^2 + 2b + 1)
Now the sum in the parenthesis, 2a^2 + 2a + 2b^2 + 2b + 1, is just another integer, which we can pose as k. Remember that 2 times any random integer, either odd or even, is always even. Therefore the sum of the squares of any two odd numbers is always even.
Answer:
A is the correct answer.
Step-by-step explanation:
Thus, option A is the correct answer.
Answer:
Angular velocity: 
(
)
Linear velocity: 
(
)
Step-by-step explanation:
The gear experiments a pure rotation with axis passing through its center, the angular (
), in radians per second, and linear velocities (
), in inches per second, of a point on the outer edge of the element are, respectively:
(1)
(2)
Where:
- Rotation rate, in revolutions per minute.
- Radius of the gear, in inches.
If we know that 
and 
, then the linear and angular velocities of the gear are, respectively:
()
()
