Answer:
0 and -2
Step-by-step explanation:
(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:
y = 4x
Step-by-step explanation:
When two lines are parallel, their slopes are equal. The slope in this equation is 4. Therefore, any line with slope 4 will suffice.
Split up the interval [2, 5] into
equally spaced subintervals, then consider the value of
at the right endpoint of each subinterval.
The length of the interval is
, so the length of each subinterval would be
. This means the first rectangle's height would be taken to be
when
, so that the height is
, and its base would have length
. So the area under
over the first subinterval is
.
Continuing in this fashion, the area under
over the
th subinterval is approximated by
, and so the Riemann approximation to the definite integral is
and its value is given exactly by taking
. So the answer is D (and the value of the integral is exactly 39).
Answer:
20%
Step-by-step explanation:
1/5 as a percent is 20%
The 1 in 1/5 is equal to 10.
The 5 in 1/5 is equal to 50.
Therefore you would multiply 50 x 2 to get 100.
Then, you would multiply 10 x 2 to get 20/100 or 20%
