(e) Each license has the formABcxyz;whereC6=A; Bandx; y; zare pair-wise distinct. There are 26-2=24 possibilities forcand 10;9 and 8 possibilitiesfor each digitx; yandz;respectively, so that there are 241098 dierentlicense plates satisfying the condition of the question.3:A combination lock requires three selections of numbers, each from 1 through39:Suppose that lock is constructed in such a way that no number can be usedtwice in a row, but the same number may occur both rst and third. How manydierent combinations are possible?Solution.We can choose a combination of the formabcwherea; b; carepair-wise distinct and we get 393837 = 54834 combinations or we can choosea combination of typeabawherea6=b:There are 3938 = 1482 combinations.As two types give two disjoint sets of combinations, by addition principle, thenumber of combinations is 54834 + 1482 = 56316:4:(a) How many integers from 1 to 100;000 contain the digit 6 exactly once?(b) How many integers from 1 to 100;000 contain the digit 6 at least once?(a) How many integers from 1 to 100;000 contain two or more occurrencesof the digit 6?Solutions.(a) We identify the integers from 1 through to 100;000 by astring of length 5:(100,000 is the only string of length 6 but it does not contain6:) Also not that the rst digit could be zero but all of the digit cannot be zeroat the same time. As 6 appear exactly once, one of the following cases hold:a= 6 andb; c; d; e6= 6 and so there are 194possibilities.b= 6 anda; c; d; e6= 6;there are 194possibilities. And so on.There are 5 such possibilities and hence there are 594= 32805 such integers.(b) LetU=f1;2;;100;000g:LetAUbe the integers that DO NOTcontain 6:Every number inShas the formabcdeor 100000;where each digitcan take any value in the setf0;1;2;3;4;5;7;8;9gbut all of the digits cannot bezero since 00000 is not allowed. SojAj= 9<span>5</span>
Answer:
V = 882pi units^3
or approximately
2769.48 units^3
Step-by-step explanation:
The column of a cylinder is given by
V = pi * r^2 * h
We know the radius is 7 and the height is 18
V = pi * 7^2 *18
V =pi *49 *18
V =882 pi
If we want an approximate answer, we can approximate pi by 3.14
V = 3.14 * 882
V =2769.48
Answer:
22.4
Step-by-step explanation:
using altitude theorem, the height of the triangle is 20
let y = height
10/y = y/40
y² = 400
y = 
or 20
Now we can us the Pythagorean Theorem to find 'x':
10² + 20² = x²
100 + 400 = x²
x=
≈ 22.4
<span><span><span><span><span><span><span><span><span><span><span><span>(</span></span><span><span><span><span><span><span>1</span></span><span><span>⋅</span></span><span><span>3</span></span></span><span><span>+</span></span><span><span><span>1</span></span><span><span><span>(</span></span><span><span><span><span>5</span></span><span><span>i</span></span></span></span><span><span>)</span></span></span></span></span><span><span><span><span><span>−</span></span><span><span>2</span></span></span><span><span>i</span></span></span><span><span><span>(</span></span><span><span><span><span>3</span></span><span><span>+</span></span><span><span><span>5</span></span><span><span>i</span></span></span></span></span><span><span>)</span></span></span></span></span></span><span><span>)</span></span></span><span><span><span>(</span></span><span><span><span><span>3</span></span><span><span><span>−</span></span><span><span>i</span></span></span></span></span><span><span>)</span></span></span></span></span></span><span><span><span><span>5</span></span></span></span><span /></span><span /></span></span></span></span></span><span>1⋅3+15i-2i3+5i3-i5</span>
