Answer: 
Step-by-step explanation:
The given geometric series are:
a)
on simplifying in decimals, we get
b) 
on simplifying in decimals, we get
c)
on simplifying in decimals, we get
Thus, this geometric series represent 0.4444.
d)
on simplifying in decimals, we get
Answer: We have two solutions:
1000 - 998 = 2
1001 - 999 = 2
Step-by-step explanation:
So we have the problem:
****-*** = 2
where each star is a different digit, so in this case, we have a 4 digit number minus a 3 digit number, and the difference is 2.
we know that if we have a number like 99*, we can add a number between 1 and 9 and we will have a 4-digit as a result:
So we could write this as:
1000 - 998 = 2
now, if we add one to each number, the difference will be the same, and the number of digits in each number will remain equal:
1000 - 998 + 1 - 1 = 2
(1000 + 1) - (998 + 1) = 2
1001 - 999 = 2
now, there is a trivial case where we can find other solutions where the digits can be zero, like:
0004 - 0002 = 2
But this is trivial, so we can ignore this case.
Then we have two different solutions.
Work the information to set inequalities that represent each condition or restriction.
2) Name the
variables.
c: number of color copies
b: number of black-and-white copies
3)
Model each restriction:
i) <span>It
takes 3 minutes to print a color copy and 1 minute to print a
black-and-white copy.
</span><span>
</span><span>
3c + b</span><span>
</span><span>
</span><span>ii) He needs to print
at least 6 copies ⇒
c + b ≥ 6</span><span>
</span><span>
</span><span>iv) And must have
the copies completed in
no more than 12 minutes ⇒</span>
3c + b ≤ 12<span />
4) Additional restrictions are
c ≥ 0, and
b ≥ 0 (i.e.
only positive values for the number of each kind of copies are acceptable)
5) This is how you
graph that:
i) 3c + b ≤ 12: draw the line 3c + b = 12 and shade the region up and to the right of the line.
ii) c + b ≥ 6: draw the line c + b = 6 and shade the region down and to the left of the line.
iii) since c ≥ 0 and b ≥ 0, the region is in the
first quadrant.
iv) The final region is the
intersection of the above mentioned shaded regions.v) You can see such graph in the attached figure.
Answer: Answer is 3
BC 6
------ = ------
XY 3
Step-by-step explanation:
The statements below can be used to prove that the triangles are similar.
On a coordinate plane, right triangles A B C and X Y Z are shown. Y Z is 3 units long and B C is 6 units long.
A B Over X Y = 4 Over 2
?
A C Over X Z = 52 Over 13
△ABC ~ △XYZ by the SSS similarity theorem.
Which mathematical statement is missing?
1. Y Z Over B C = 6 Over 3
2. ∠B ≅ ∠Y
3. B C Over Y Z = 6 Over 3
4. ∠B ≅ ∠Z
Answer:
18.25
Step-by-step explanation:
just divide the total cost of scarves by the number of scarves:
91.25 / 5 = 18.25
