We can start solving this problem by first identifying what the elements of the sets really are.
R is composed of real numbers. This means that all numbers, whether rational or not, are included in this set.
Z is composed of integers. Integers include all negative and positive numbers as well as zero (it is essentially a set of whole numbers as well as their negated values).
W on the other hand has 0,1,2, and onward as its elements. These numbers are known as whole numbers.
W ⊂ Z: TRUE. As mentioned earlier, Z includes all whole numbers thus W is a subset of it.
R ⊂ W: FALSE. Not all real numbers are whole numbers. Whole numbers must be rational and expressed without fractions. Some real numbers do not meet this criteria.
0 ∈ Z: TRUE. Zero is indeed an integer thus it is an element of Z.
∅ ⊂ R: TRUE. A null set is a subset of R, and in fact every set in general. There are no elements in a null set thus making it automatically a subset of any non-empty set by definition (since NONE of its elements are <u>not</u> an element of R).
{0,1,2,...} ⊆ W: TRUE. The set on the left is exactly what is defined on the problem statement for W. (The bar below the subset symbol just means that the subset is not strict, therefore the set on the left can be <u>equal</u> to the set on the right. Without it, the statement would be false since a strict subset requires that the two sets should not be equal).
-2 ∈ W: FALSE. W is just composed of whole numbers and not of its negated counterparts.
Answer:
11 boxed lunches
Step-by-step explanation:
Full question
Janie ordered boxed lunches for a student advisory committee meeting. Each lunch cost 4.25. The total cost of the lunches is 53.75, including a 7$ delivery fee. Write and solve an equation to find x the number of boxed lunches Janie ordered
First of all subtract the delivery feesince it was inckuded in the total cost, this will now be the total cost of all the noxed lunches ordered by Janie, then divide the balance of the total cost by the cost of one boxed lunch to get thd total boxed kunches
X= 53.75-7/4.25
X= 53.75-7= 46.75/4.25
X=11
<span>The answer is c. 1.5r + 2.5(5 – r) = 10.50. Let r be the number of raisins and p be the number of peanuts. Raisins cost $1.50 per pound: 1.5r. Peanuts cost $2.50 per pound: 2.5p. Jeremy spends $10.50: 1.50r + 2.50p = 10.50. Jeremy makes 5 pounds of trail mix: r + p = 5. So, we have the system of two equations: 1.5r + 2.5p = 10.50 and r + p = 5. Use the second equation to express p: p = 5 - r. Now, substitute p in the first equation: 1.5r + 2.5(5 - r) = 10.50. Therefore, the correct choice is c. 1.5r + 2.5(5 – r) = 10.50.</span>
Answer:
-95.78
Step-by-step explanation:
As the researcher decided to make the number of parties attended per week the explanatory variable, this would be variable x in the regression line, and of course, the variable y would be the number of text messages sent per day.
After constructing the linear regression equation, the researcher found that an approximate value 
for the actual value of y could be represented by the line
Since this is an approximate value, it is not expected that it coincides with the actual value of y. We define then the residual for each value of x as the difference between the actual value of y and the approximation for the given x.
For the value x = 2 (the student attended 2 parties that week) the actual value of y is 20 (the student sent 20 text messages per day that week).
The approximate value of y would be according to the regression line
Hence, the residual value for x=2 would be
24,000/8= 3,000 balls
The machine produce 3,000 balls per hour.
Hope that helps!
