
Math
There are no conditions as such that must be met when estimating the probability of any event that occurs when a die is rolled 20 times. Each of the rolls is independent of the others and the...

Math
`g(x)=1/3log_3(x1)+3` : (1) The vertical asymptote is at x=1 (you cannot take the logarithm of 0). (2) Some points to plot: (2,3) since `g(2)=1/3log_3(21)+3=1/3(0)+3=3` `(4,3 1/3)` since...

Math
After 13000 cars of a certain model are sold, it is discovered that about 0.04% of these cars contain a part that could lead to an accident. A recall would cost the company $18000 per vehicle. The...

Math
given y = (p+q+r) /4 multiply both sides by 4, we get 4y = (p+q+r)/4 * 4 = (p+q+r) that is 4y = p+q+r now to get q we have to eleminate p,q from the right side of the equation, so take pr on...

Math
According to the drug company their drug is effective in relieving flu symptoms in 95% of the people who take it. However, another study showed that 26 out of 250 patients who used this drug did...

Math
Let the time taken for B to pass A be t. Then when B passes A, has travelled 1000 m more than A. Therefore, Distance travelled by B = Distance travelled by A +1000 To find distance travelled by B,...

Math
We need the ztable to calculate this. `z = (xmu)/sigma` If you refer to a ztable you would find that 23rd percentile lies with the zvalue of 0.74. (you have to go backwards from the...

Math
The scores for a particular examination are normally distributed with a mean of 54.8% and a standard deviation of 16.3%. To determine the probability that a student who wrote the test gets 75%,...

Math
We will use formula for binomial probability: b(n, x; p) = nCx*p^x*(1p)^xwhere n = number of trial in a bonimial experiment (sample), x = number of successes that result from the binomial...

Math
When Lee saw the result of an exam he had given to his grade 2 class, Louise's score was 95%. Also, the standard deviation for the test was 0. As the standard deviation is 0, the square root of the...

Math
There are 7 places in the committee. The number of adults without children is 4. The probability that all of them are chosen to the committee can be found as below. There are 19 persons...

Math
In the 4th row there are 25 kids, 6 from grade 10, 8 from grade 11 and 11 from grade 12. The 3 CDs were won by students in the 4th row. The probability that the three winners were in the same grade...

Math
You should write the constant term 4 as 8  4 such that: `4x^2  8x + 8  4 = 0` You need to form 2 groups such that: `(4x^2  4)  (8x  8) = 0` You need to factor out 4 in the first group and 8...

Math
The identity `1/(sec^2x) = sin^2x*cos^2x + cos^4x` has to be proved. `sin^2x*cos^2x + cos^4x` => `(1  cos^2x)*cos^2x + cos^4x` => `cos^2x  cos^4x + cos^4x` => `cos^2x` =>...

Math
`f(x) = (e^x)/(x^21)` To find the critical points we have to find the derivative of f(x) `f'(x) = ((x^21)e^x  e^x(2x))/(x^21)^2` `f'(x) = (e^x((x^21)  (2x)))/(x^21)^2` `f'(x) =...

Math
You may use the function `f(x) = root(3) x` , and you should use Lagrange's theorem over interval [64,68] to prove the inequality such that: `f(68)  f(64) = f'(c)(68  64)` You need to evaluate...

Math
`sin A + sin B = 2 sin (A+B)/2*cos(AB)/2` You need to use double angle identity such that: `sinC = sin 2(C/2)=2sin(C/2)*cos(C/2)` Since, A,B,C are angles of triangle, then the sum of the measures...

Math
It has to be shown that `68^(1/3) 4 < 1/12` `4 + 1/12 = 49/12 ~~ (68.0839)^(1/3)` `(68.0839)^(1/3) > 68^(1/3)` => `4 + 1/12 > 68^(1/3)` => `68^(1/3)  4 < 1/12` This shows...

Math
The identity `sin y*cos (x  y) + cos y*sin(x  y) = sin x` has to be proved. Use the relation `sin a*cos b = (1/2)(sin (a  b)  sin(a + b))` `sin y*cos (x  y) + cos y*sin(x  y)` =>...

Math
For two perpendicular lines, the product of the slope is 1. For the equations of the lines given in the slopeintercept form: y=x+2 : slope = 1 y=(2/3)x +2 : slope = 2/3 y= (2/3)x5 : slope =...

Math
The disance between two points `A(x_1,y_1)` and `B(x_2,y_2)` is given by, `AB = sqrt((x_2x_1)^2+(y_2y_1)^2)` In the given two points, `A(k,0)` and `B(0,k).` `AB = sqrt((0k)^2+(k0)^2)` `AB =...

Math
The converse statement of the conditional statement is the following: "If the sum of the measures of two angles is 90 degrees, then they are complementary." The common biconditional statement is:...

Math
`a^12x^4  a^4x^12` `= a^4x^4(a^8x^8)` `= a^4x^4(a^4+x^4)(a^4x^4)` `= a^4x^4(a^4+x^4)(a^2+x^2)(a^2x^2)` `= a^4x^4(a^4+x^4)(a^2+x^2)(a+x)(ax)` Therefore, `a^12x^4  a^4x^12 =...

Math
The xintercept of the line is (6,0) and the yintercept of the line is (0,5) A line with x intercept a and y intercept b can be written in the interceptintercept form as `x/a + y/b = 1` Here a =...

Math
5 cards are drawn from a standard deck of 52. The probability distribution of the number of hearts drawn has to be determined. The number of hearts that are drawn can be 0, 1, 2, 3, 4 or 5. The...

Math
You need to write down the original function `y = x/(3x+2)` and then you should solve for x the equation `y = x/(3x+2)` such that: `3xy + 2y = x =gt x  3xy = 2y ` You need to factor out x such...

Math
The football kicker has a field goal conversion rate of 56.7% for kicks longer than 50 yards. The probability that 5 field goals are made in a row is `(0.567)^5 = 0.0586` If 25 field goals of this...

Math
The survey shows that of the 785 randomly selected subjects that have completed 4 years of college, 18.3% smoke and 81.7% do not smoke. The confidence interval with a 0.01 significance level is...

Math
Of the 5000 households with a TV set that were monitored 15% had tuned in to watch the show. The percentage not tuned in was 85%. The confidence interval with a 0.01 significance level is given by...

Math
When the zscore is given, the pvalue can be estimated using the formula `int_(oo)^z 1/sqrt (2*pi)*e^(u^2/2) du` For a zscore of 2.5, the corresponding pvalue is 0.0062 This is a very small...

Math
When the zscore is given, the pvalue can be estimated using the formula `int_(oo)^z int 1/sqrt 2*pi)*e^(u^2/2) du` For a zscore of 1.25, the corresponding pvalue is 0.1056 This is a...

Math
Given `p(t)=5000/(1+e^((2t)/3))` : This is a logisitics function in the form `y=a/(1+e^(kt))` . In this form, 0 is a lower bound for the function and a is an upper bound. The function approaches...

Math
If you're looking for orthogonal vectors (and not orthonormal vectors), you have quite a bit of freedom, because you can scale them however you need. Thus, you really only care about whether your...

Math
The identity `(1 + csc x)/sec x  cot x = cos x` has to be proved. `(1 + csc x)/sec x  cot x` => `(1 + 1/sin x)/(1/cos x)  (cos x)/(sin x)` => `(cos x + cos x/sin x)  (cos x)/(sin x)`...

Math
The integral roots of x^3  x = 0 has to be determined. x^3  x = 0 => x(x^2  1) = 0 Use the relation a^2  b^2 = (a  b)(a + b) => x(x  1)(x + 1) = 0 => x = 0, x = 1 and x = 1 The...

Math
The series given has the terms 4, 10, 16, 22... It is seen that 22 16 = 16  10 = 10  4 = 6. This is an arithmetic series with the first term equal to 4 and the common difference equal to 6. The...

Math
The integral `int (3x^24)/x^2 dx` has to be determined. `int (3x^24)/x^2 dx` =>` int 3  4/x^2 dx` => `int 3  4*x^2 dx` => `3x  4*x^1/1 + C` => `3x + 4/x + C` The integral...

Math
You should remember how to evaluate the antiderivative of irrational function `sqrt(x^2+a^2) ` such that: `int sqrt(x^2+a^2) dx = (1/2)(xsqrt(x^2+a^2) + a^2*ln(x+sqrt(x^2+a^2))) + c` You need to...

Math
x has to be determined given that `log_x(1/4) = 2/3 ` `log_x(1/4) = 2/3` => `(1/4) = x^(2/3)` => `(1/8)^(2/3) = x^(2/3)` => `8^(2/3) = x^(2/3)` As the base is the same equate the...

Math
The given probability distribution is a binomial distribution with having a ticket is the favorable incident and let's assume its probability is P. The probability density function of a binomial...

Math
In the town 74% of the homes have satellite dishes. The percentage of homes without a satellite dish is 26%. Of the 50 people selected at least 42 of them should have a satellite dish. This is...

Math
`f(x) = x+7` `g(x) = 2x5` `h(x) = 2x+4` What you have asked is just the simple arithmetic involved with functions. `f(x) + h(x) xx g(x)  12` `= (x+7)+(2x+4)xx(2x5)  12` `=x+7 +...

Math
The expression 12c^2 + cd  6d^2 has to be factorized. 12c^2 + cd  6d^2 => 12c^2 + 9cd  8cd  6d^2 => 3c(4c + 3d)  2d(4c + 3d) => (3c  2d)(4c + 3d) The factorized form of 12c^2 + cd ...

Math
The equation of the line is 3x + 4y = 8. This can be rewritten in the slopeintercept form as `y = (3/4)x + 2` . The line has a slope of `3/4` . As the slope of a line is the tan of the angle it...

Math
The slope of a tangent drawn to the graph of any function y = f(x) at a point where x = c is given by the value of f'(c). If a line makes an angle of 45 degrees with the positive xaxis the slope...

Math
Statistics can be used to determine the affect on literary scores of the number of books read by a student. The study would involve choosing a large number of students that makes up a meaningful...

Math
You should write `sin x = sin(3x  2x)` and `sin 5x = sin(3x + 2x)` such that: `sin(3x  2x) + sin 3x + sin(3x + 2x)= (1+2cos2x)sin3x ` You need to use the following formulas such that: `sin(a ...

Math
Five cards are drawn from a standard deck of 52 cards. A deck of cards has 13 hearts. The probability that there are 4 hearts in the 5 cards drawn is given by `(C(13, 4) + C(13, 5))/(C(52, 5)) ~~...

Math
(1)One possibility is to divide a circle into 7 congruent sectors. Color any two of them red, and the rest blue. Then attach a spinner; every spin should be random. If the spinner lands on red,...

Math
Determine the 8th term of the expansion of `(x/44/x)^10` : We use the binomial theorem: the nth term of `(ab)^k` is given by `((n),(k))(1)^(nk)a^(nk)b^k` where `((n),(k)) =. _nC_k` , the...