New! Get regular updates about newly solved problems via algebra.com's RSS system.

Recent problems solved by 'robertb'

robertb answered: 4011 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019, >>Next

Probability-and-statistics/391769: A short-term insurance company receives 4 claims, on average, per day. What is the probability that over any two day period , at least 2 claims will be received?
1 solutions

Answer 278979 by robertb(4012) on 2011-01-10 22:41:53 (Show Source):

You can put this solution on YOUR website!
We use the Poisson distribution, with parameter alpha+=+8

(8 claims for 2 days!).

, to 3 decimal places.

Radicals/391749: what is the middle term in the expansion of
(x - 1/x)^6 ??
1 solutions

Answer 278978 by robertb(4012) on 2011-01-10 22:35:52 (Show Source):

You can put this solution on YOUR website!
The binomial expansion has 6 + 1 = 7terms, so the middle term is the fourth term.
From the binomial theorem, the fourth term is 6C3%2Ax%5E3%2A%28-1%2Fx%29%5E3+=+20%2Ax%5E3%2A%28-1%2Fx%5E3%29+=+-20

6C3%2Ax%5E3%2A%28-1%2Fx%29%5E3+=+20%2Ax%5E3%2A%28-1%2Fx%5E3%29+=+-20

Expressions-with-variables/392997: Blinn College in Bryan has 620 students. The difference between male students and female student is 20. How many female students are there?
1 solutions

Answer 278977 by robertb(4012) on 2011-01-10 22:29:11 (Show Source):

You can put this solution on YOUR website!
b + g = 620,
b - g = 20.
==> 2b = 640 (after adding corresponding sides of the 2 equations)
==> b = 320 ==> g = 300, the number of female students.

Trigonometry-basics/393007: 2sec(t)tan(t) + sec^(2)(t)
What (if any) are the zeros, holes, and vertical asymptotes?
1 solutions

Answer 278970 by robertb(4012) on 2011-01-10 22:19:21 (Show Source):

You can put this solution on YOUR website!
The expression could be written as %282sint%29%2F%28cost%29%5E2+%2B+1%2F%28cost%29%5E2+=+%282sint+%2B+1%29%2F%28cost%29%5E2

%282sint%29%2F%28cost%29%5E2+%2B+1%2F%28cost%29%5E2+=+%282sint+%2B+1%29%2F%28cost%29%5E2

.
Find out first the values of t where the top is equal to the bottom, i.e., 2sint++%2B+1+=+%28cost%29%5E2

==>

, or sint(2 + sint) = 0.
==> sint = 0 ==> t =0, +/- pi+

, +/-

, +/-

,...
At these t values the bottom, %28cost%29%5E2

is not equal to zero. The top, 2sint+%2B+1

is also not equal to 0 (it is equal to 1). Therefore there are no "holes" in the graph.
There are vertical asymptotes at t values where %28cos+t%29%5E2

= 0, namely
t = +/- pi%2F2

, +/-

, +/-

,...
The x-intercepts are located at t = 7pi%2F6

+/-

and t =

+/-

. (These are the t values where 2sint + 1 = 0).

logarithm/393005: Please help me in solving this problem
Q) Solve for x
log(x+1)+log(x-1)=log 8

1 solutions

Answer 278957 by robertb(4012) on 2011-01-10 21:55:19 (Show Source):

You can put this solution on YOUR website!
log(x+1)+log(x-1)=log 8
==> log((x+1)(x-1)) = log 8
==> log%28%28x%5E2+-+1%29%29+=+log+8

==>

, since the log function is one-to-one
<==> x%5E2+-+9+=+0

, or (x-3)(x+3) = 0, or x = -3, 3. Since -3 will not satisfy the original equation, the final answer is x =3.

Linear-equations/392903: an equation of the line that contains the origin and the point (1,2) is
1 solutions

Answer 278955 by robertb(4012) on 2011-01-10 21:26:32 (Show Source):

You can put this solution on YOUR website!
The slope is 2/1 = 2. The equation is y - 0 = 2(x-0) ==> y = 2x.

Sequences-and-series/392971: What is the 12th term and rule of 2,-6,18,-54,162
1 solutions

Answer 278949 by robertb(4012) on 2011-01-10 20:57:35 (Show Source):

You can put this solution on YOUR website!
a%28n%29+=+2%2A%28-3%29%5E%28n-1%29

. It is a geometric sequence with first term 2 and common ratio -3.

Probability-and-statistics/392953: boundries of each value
42.8 miles
1.6 millilliters
5.36 ounces
18tons
93.8 ounces
40 inches
1 solutions

Answer 278947 by robertb(4012) on 2011-01-10 20:55:18 (Show Source):

You can put this solution on YOUR website!
(42.75, 42.85)
(1.55, 1.65)
(5.355, 5.365)
(17.5, 18.5)
(93.75, 93.85)
(39.5, 40.5)
Note my use of the OPEN interval, and not the closed interval.

Functions/392959: a(x)=5x-1
Give the domain of each function. Is it all numbers except 0?
1 solutions

Answer 278944 by robertb(4012) on 2011-01-10 20:51:21 (Show Source):

You can put this solution on YOUR website!
No. The domain is the set of all real numbers. (There are no restrictions on the expression defining the function.)

Points-lines-and-rays/392960: two lines are parrallel one passes through the points (-3,4)and (5,k)and the other has slope -2.what is the value of k?
1 solutions

Answer 278941 by robertb(4012) on 2011-01-10 20:47:58 (Show Source):

You can put this solution on YOUR website!
%28k-4%29%2F%285--3%29+=+%28k-4%29%2F8++=+-2

==> k-4 = -16 ==> k = -12.

Functions/392952: My question says:
Graph the function. Is the domain discrete or continuous?
Input
Length, x (inches)
2
4
6
Output
Area, y (square inches)
12
24
36
Then It has a graph.
I dont know what to do.
1 solutions

Answer 278936 by robertb(4012) on 2011-01-10 20:38:42 (Show Source):

You can put this solution on YOUR website!
If you want the given x-values to be part of a MUCH larger set of real numbers (because it is LENGTH, which in general is a CONTINUOUS variable), the domain is (0, infinity

). The graph is the positive part of the line y = 6x .

Linear-systems/392937: Pablo's Pizza pays $8/hour for their delivery persons. Pedro's Pizza pays $6/hour and $1.25 per delivery for their delivery persons. How many deliveries must be made at Pedro's Pizza in order to be paid more for an 8-hour shift?
1 solutions

Answer 278934 by robertb(4012) on 2011-01-10 20:29:21 (Show Source):

You can put this solution on YOUR website!
Let d = # deliveries in Pedro's pizza.
Then 8*8 < 6*8 + 1.25d ==> 64 < 48 + 1.25d ==> 16 < 1.25d ==> 12.8 < d. Therefore there must be at least 13 deliveries.

test/392913: if y varies directly as x and y = 10 when x = 1/2, what is the value of y when x = 2?
1 solutions

Answer 278933 by robertb(4012) on 2011-01-10 20:24:10 (Show Source):

You can put this solution on YOUR website!
10%2F%281%2F2%29+=+y%2F2

==> 20 = y/2 ==> y = 40.

Sequences-and-series/392911: Write an algebraic expression for the following sequence 2, 4, 8, 14, 22, 32, ....
1 solutions

Answer 278932 by robertb(4012) on 2011-01-10 20:22:10 (Show Source):

You can put this solution on YOUR website!
The recursion formula is a(n) = a(n-1) + 2*(n-1) = a(n-2) + 2*(n-2) + 2*(n-1) = a(n-3) + 2*(n-3) + 2*(n-2) + 2*(n-1) = ... = a(1) + 2*1 + 2*2 + ... + 2*(n-2) + 2*(n-1) = 2 + 2(1 + 2 + ..+ (n-2) + (n - 1)) = 2 + (n - 1)n = n%5E2+-+n+%2B+2

.
Therefore +a%28n%29+=+n%5E2-+n+%2B+2

Polynomials-and-rational-expressions/392942: solve by factoring
2w(4w+1)=1
1 solutions

Answer 278922 by robertb(4012) on 2011-01-10 20:07:36 (Show Source):

You can put this solution on YOUR website!
8w%5E2+%2B2w+-+1+=0

==> (4w - 1)(2w + 1 ) = 0 ==> w = 1/4, -1/2.

Polynomials-and-rational-expressions/392941: solve by factoring
2h^2-h-3=0
1 solutions

Answer 278921 by robertb(4012) on 2011-01-10 20:04:53 (Show Source):

You can put this solution on YOUR website!
(2h - 3)(h + 1) = 0 ==> h = 3/2, -1.

Geometry_Word_Problems/392922: make a table of all possible whole-number pairs of length and width values for a rectangle with a perimeter of 18 meters
1 solutions

Answer 278920 by robertb(4012) on 2011-01-10 20:03:40 (Show Source):

You can put this solution on YOUR website!
Let (L, W) be the ordered pair of positive integers. Assume that neither L nor W can be 0, for no rectangle will be formed in that case, and that L%3E=W

.
Then L + W = 9, and easily the ordered pairs are (8,1), (7,2), (6,3), and (5,4).

Matrices-and-determiminant/392357: Which matrix equation should be used to find the intersection of these two lines? 3x = 2 + 4y 2y = 6 -5x
1 solutions

Answer 278524 by robertb(4012) on 2011-01-09 19:57:01 (Show Source):

You can put this solution on YOUR website!

Quadratic_Equations/392420: Solve for y, where y is a real number.
+sqrt+%28y+%2B+20+=+y%29+

If there is more than one solution, separate them with commas
1 solutions

Answer 278519 by robertb(4012) on 2011-01-09 19:47:22 (Show Source):

You can put this solution on YOUR website!
sqrt%28y%2B20%29+=+y

Square both sides:
y+%2B+20+=+y%5E2

,
==>

==> (y-5)(y+4) = 0 ==> y = 5, -4.
Y = 5 satisfies the original equation, while y = -4 does not.
Therefore the final answer is only y = 5.

Money_Word_Problems/392158: at what time will 2000 amount to 3650 at 4% compounded semi-annually.
1 solutions

Answer 278334 by robertb(4012) on 2011-01-09 07:22:26 (Show Source):

You can put this solution on YOUR website!
3650+=+2000%281%2B0.04%2F2%29%5E%282t%29

<==>

<==>

<==>

years. (To 2 decimal places)

Miscellaneous_Word_Problems/392142: I have 3 exam scores 44, 84, and 71 for total exam points of 199. My term paper score is 37 and homework score is 33 total points 269. In this class there are possible 400 points. What is my semester agerage?
1 solutions

Answer 278333 by robertb(4012) on 2011-01-09 07:17:12 (Show Source):

You can put this solution on YOUR website!
%28269%2F400%29%2A100+=+67.25

Miscellaneous_Word_Problems/392146: Maria bought seven boxes. A week later half of her boxes were destroyed ina fire.There are now only 22 boxes left. With how many did she start with?
1 solutions

Answer 278332 by robertb(4012) on 2011-01-09 07:15:16 (Show Source):

You can put this solution on YOUR website!
%287%2Bx%29%2F2+=+22

==>

==> x = 37 boxes, the original number of boxes she had.

Length-and-distance/392141: There is a square with each of it’s side is of 2m. An octagonal is cut-of from this square by cutting it’s edge such that the octagonal has all it’s sides equal. Find out the length of each side of the octagonal?
1 solutions

Answer 278331 by robertb(4012) on 2011-01-09 07:13:13 (Show Source):

You can put this solution on YOUR website!
Let x = side of the regular octagon. By symmetry, each figure cut from the corners must be an isosceles right (45-45-90) triangle,
and all four of them must be congruent. Then the leg of each isosceles triangle must have measure x%2Fsqrt%282%29

.
Then we must have x%2Fsqrt%282%29+%2B+x+%2B+x%2Fsqrt%282%29+=+2

, or

after simplification, or
%281%2Bsqrt%282%29%29x+=+2

, or

meter.

Linear-equations/392152: find the slope and y intercept y=4.2x-7
1 solutions

Answer 278330 by robertb(4012) on 2011-01-09 07:02:04 (Show Source):

You can put this solution on YOUR website!
The equation is written already in slope-intercept form y = mx + b. Therefore the slope is 4.2, while the y-intercept is the point (0, -7).

Rate-of-work-word-problems/392150: the difference between a positive number and its reciprocal is 99/10. find the number.

1 solutions

Answer 278329 by robertb(4012) on 2011-01-09 06:58:39 (Show Source):

You can put this solution on YOUR website!
x+-+1%2Fx+=+99%2F10

<==>

<==>

<==> (10x + 1)(x - 10) = 0.
==> x = -1/10, 10.
Therefore the final answer is 10.

Percentage-and-ratio-word-problems/392153: the ratio of the number of boys to the number of girls in a class was 2:3 at first. after 4 girls left the class, the ratio became 4:5. how many boys were there in the class
1 solutions

Answer 278328 by robertb(4012) on 2011-01-09 06:53:40 (Show Source):

You can put this solution on YOUR website!
b%2Fg+=+2%2F3

and

==>

and

==>

==> 5g = 6g - 24
==>g = 24, the number of girls, and
b = 16, the number of boys.

Permutations/392151: prove that P(n,n) = 2P(n,n – 2)
and prove that C(2n,2) = 2C(n,2) + n^2 .

1 solutions

Answer 278327 by robertb(4012) on 2011-01-09 06:41:45 (Show Source):

You can put this solution on YOUR website!

P%28n%2C+n-2%29+=+n%21%2F2%21+=+n%21%2F2

==>

Probability-and-statistics/392129: A die rolled 3 time. Find probability
P(three even numbers)
P(no 4s)
thank you so much
1 solutions

Answer 278326 by robertb(4012) on 2011-01-09 06:13:31 (Show Source):

You can put this solution on YOUR website!
P(3 even numbers) = .5*.5*.5 = 0.125
P(no 4's) = %285%2F6%29%2A%285%2F6%29%2A%285%2F6%29+=+125%2F216

Probability-and-statistics/392133: Two cards drawn from standar deck of cards.Find probability
P(2 aces)
Thank you so much
1 solutions

Answer 278325 by robertb(4012) on 2011-01-09 05:53:22 (Show Source):

You can put this solution on YOUR website!
4C2/52C2 = 6/1326 = 1/221

Sequences-and-series/392147: 150,30,6,.....
in the sequence above , each term after the 1st term is 1/5 of the term preceding it.what is the 5th term of this sequence ?
1 solutions

Answer 278324 by robertb(4012) on 2011-01-09 05:48:30 (Show Source):

You can put this solution on YOUR website!
The 4th term is 6/5, and so the 5th term is 6/25.

Divisibility_and_Prime_Numbers/392149: if p,r,and s are three different prime numbers greater than 2, and n= p x r x s, how many positive factors, including 1 and n, does n have?
1 solutions

Answer 278323 by robertb(4012) on 2011-01-09 05:46:22 (Show Source):

You can put this solution on YOUR website!
The power of p is 1, the power of r is 1, and the power of s is 1, so the total number of divisors, or factors, of n, is (1+1)(1+1)(1+1) = 2*2*2 = 8.

See tutors' answers!

Recent problems solved by 'robertb'