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Recent problems solved by 'edjones'

edjones answered: 3298 problems
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logarithm/241460: 3^(x^2+1)=243
solve for x. please explain
1 solutions

Answer 176849 by edjones(3298) on 2009-11-21 19:10:17 (Show Source):

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3^(x^2+1)=243
3^(x^2+1)=3^5
log[3](3^(x^2+1)=log[3](3^5)
x^2+1=5
x^2=4
x=2, x=-2
.
Ed

Radicals/241468: Simplify: (square root of 3y^2)^6
1 solutions

Answer 176837 by edjones(3298) on 2009-11-21 18:45:01 (Show Source):

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sqrt(3y^2)^6
(3^(1/2)y)^6
3^3y^6
27y^6
.
Ed

logarithm/241397: how to solve: 4^(3x-1)=3^(x-1)
i can't rember how to solve for x.
i am lost.
1 solutions

Answer 176789 by edjones(3298) on 2009-11-21 15:42:56 (Show Source):

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4^(3x-1)=3^(x-1)
log[4](4^3x-1)=log[3](3^(x-1))/log[3](4) Change of base formula from 3 to 4 on the right side.
3x-1=(x-1)/1.2619
3.7856x-1.2619=x-1
2.7856x=.2619
x=.094...
.
Ed

Probability-and-statistics/241382: Suppose that the probability that a new medication will cause a bad side effect is 0.03. If this medication is given to 150 people, what is the probability that more than three of them will experience a bad side effect? Round answer to 4 decimal places.
I think I know how to compute for "exactly three students," but I cannot figure out how to do "more than three students"
Here's how I approached "exactly three":
p = 0.03, q = 1 - p = 0.97, n = 150
P(r, n) = nCr (p)^r * (q)^(n - r)
P(3, 150) = 150C3 * 0.03^3 * 0.97^147 = 0.1691
Since I am trying to figure out how to do these types of problems on my own, please include the steps.
Thank you!

1 solutions

Answer 176783 by edjones(3298) on 2009-11-21 15:00:49 (Show Source):

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You are correct so far as you have gone.
Now do the same procedure for exactly 2, 1 and 0 students.
Find the sum of the 4 probabilities and subtract it from 1 and you have your answer.
.
Ed

Inequalities/241389: How do I solve:
7y-12 is less than 8y+5
1 solutions

Answer 176782 by edjones(3298) on 2009-11-21 14:47:11 (Show Source):

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7y-12 < 8y+5

add -7y-5 to each side.
y>-17
.
Ed

Linear-equations/241386: x + y =5
2x - y =4
-2x +-2y = -10 2x-y =4
2x - y = 4 2x -2 =4

3y -6
__ ___
3 = 3

y = -2 __

then lost - is this right so far and can you show me how to do problem?
1 solutions

Answer 176781 by edjones(3298) on 2009-11-21 14:39:28 (Show Source):

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x + y =5
2x - y =4
.
x=5-y
2(5-y)-y=4 Replace x with 5-y.
10-2y-y=4
-3y=-6
y=2
x=3
.
Ed

Mixture_Word_Problems/241234: Could someone please help me with this mixture problem? I have been pouring over it for two days (total of over 4 hours), and have tried various methods none of them yielding the correct answer.
A mechanic has 363 gallons of gasoline and 17 gallons of oil to make gas/oil mixtures. He wants one mixture to be 6% oil and the other mixture to be 2.5% oil. If he wants to use all of the gas and oil, how many gallons of gas and oil are in each of the resulting mixtures?
1 solutions

Answer 176699 by edjones(3298) on 2009-11-21 00:36:58 (Show Source):

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Let x=gals of gas required to make a .025 mixture.
Let y=gals of oil required to make a .025 mixture.
.
A) y/(x+y)=.025
B) (17-y)/(363-x+17-y)=.06
.
A)
y=.025x+.025y
.975y=.025x
y=.0256x
.
B)
(17-.0256x)/(380-x-.0256x)=.06
17-.0256x=22.8-.0615x
.0359x=5.8
x=161.56 gal
.
A)
y/(161.56+y)=.025
y=4.039+.025y
.975y=4.039
y=4.142 gal
It wont be exact because of rounding errors.
.
Ed

Permutations/241104: an octagon has 8 sides. How many diagnals does an octagon have??
my answer is 28 diagnals.
1 solutions

Answer 176612 by edjones(3298) on 2009-11-20 16:04:59 (Show Source):

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20
There are 5 diagonals for each point. 8*5=40.
Half are repetitions. 40/2=20
.
Ed

Square-cubic-other-roots/241151: the square root of 49 is how much less than four squared?
1 solutions

Answer 176609 by edjones(3298) on 2009-11-20 16:00:27 (Show Source):

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sqrt(49)=7
4^2=16
16-7=9
.
Ed

Miscellaneous_Word_Problems/241163: 4 more than 3
how would i right that
4+3?
1 solutions

Answer 176608 by edjones(3298) on 2009-11-20 15:58:14 (Show Source):

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3+4

Geometry_Word_Problems/241053: The ratio of the diameters of two circles is 1:4. The ratio of their radii is
A) 1:2 B) 1:4 C) 1:8 D) 1:16
1 solutions

Answer 176536 by edjones(3298) on 2009-11-20 04:24:58 (Show Source):

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B

Systems-of-equations/240941: solve
y=x+3
y=2x+4
1 solutions

Answer 176502 by edjones(3298) on 2009-11-19 20:03:05 (Show Source):

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y=x+3
y=2x+4
2x+4=x+3
x=-1
y=2
.
Ed

Quadratic_Equations/240939: Polynomials
(y^3)^2

Please help me
Thank you
1 solutions

Answer 176499 by edjones(3298) on 2009-11-19 19:58:19 (Show Source):

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(y^3)^2
=y^6 because 3*2=6
.
Ed

Number-Line/240943: what are the 2 numbers that are equal distance from zero
1 solutions

Answer 176498 by edjones(3298) on 2009-11-19 19:54:09 (Show Source):

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2 and -2

Radicals/240945: simplify the square root of 56 divided by the square root of 3
1 solutions

Answer 176494 by edjones(3298) on 2009-11-19 19:51:20 (Show Source):

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sqrt(56)/sqrt(3)
=sqrt(4*14)/sqrt(3)
=2sqrt(14)/sqrt(3) * sqrt(3)/sqrt(3)
=2sqrt(42)/3
.
Ed

Quadratic_Equations/240936: How do you solve the following quadratic equations:
-6(u+5)^2=120

3s^2-1=7s^2
1 solutions

Answer 176489 by edjones(3298) on 2009-11-19 19:34:21 (Show Source):

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-6(u+5)^2=120
(u+5)^2=-20
u^2+10u+25=-20
u^2+10u+45=0
u^2+10u =-45
u^2+10u+25=-45+25 Completing the square
(u+5)^2=-20
u+5=+-sqrt(-20) Take sqrt of each side.
u=-5+-2sqrt(-5)
u=-5+2sqrt(5)i, u=-5-2sqrt(5)i
.
Ed

expressions/240905: (M + 11) + (N + 44)
1 solutions

Answer 176482 by edjones(3298) on 2009-11-19 19:20:43 (Show Source):

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m+11+n+44
=m+n+55
.
Ed

Polynomials-and-rational-expressions/240914: Factor.
x^2 –3xy -18y^2
1 solutions

Answer 176479 by edjones(3298) on 2009-11-19 19:18:20 (Show Source):

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x^2 –3xy -18y^2
=(x-6)(x+3)
.
Ed

Miscellaneous_Word_Problems/240918: Give an example of the sum of two binomials that is a trinomial.
1 solutions

Answer 176476 by edjones(3298) on 2009-11-19 19:17:10 (Show Source):

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(a+b)+(b+c)=a+2b+c

Linear-systems/240926: i need help on solving for elmination, i get confused.
Problem: 2x+6y=17
2x-10y=9
break it down for me step by step, if you can..thank you! :)
1 solutions

Answer 176474 by edjones(3298) on 2009-11-19 19:13:53 (Show Source):

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2x+6y=17
2x-10y=9
----------------subtract
==>16y=8
y=1/2
.
2x+3=17 replace y with 1/2
2x=14
x=7
.
Ed

Triangles/240911: what is the heigth of an equalateral triangle that is 30 ft wide by 30 ft on each side and formula to solve this problem?
1 solutions

Answer 176471 by edjones(3298) on 2009-11-19 19:07:09 (Show Source):

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The height bisects the base of an equilateral triangle.
b=15 c=30
a^2+b^2=c^2
a^2+225=900
a^2=675
a=sqrt(3^3*5^2) prime factors of 675.
=15sqrt(3)'
.
Ed

Geometry_Word_Problems/240740: The length of a certain rectangle is 3 cm greater than its width. If the width were doubled and the length were decreased by 1 cm, the new rectangle would have the same perimeter as the original. Find the dimensions of the original rectangle.
1 solutions

Answer 176412 by edjones(3298) on 2009-11-19 16:00:48 (Show Source):

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L=w+3
P=2(w+w+3)=4w+6 replace L with w+3
.
2nd rectangle:
2w
L-1=w+2
2(2w+w+2)=4w+6
6w+4=4w+6
2w=2
w=1 cm, L=4 cm
.
Ed

Probability-and-statistics/240758: how many different arrangements can be made using two of theletters of the word texas if no letter is to be used more than once?
1 solutions

Answer 176405 by edjones(3298) on 2009-11-19 15:41:54 (Show Source):

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2

Complex_Numbers/240798: my question is what is the square root of -12 divided by the square root of -3? im in pre calc and it has been a long time since i had to do this so if you could also provide a good explanation of complex numbers that would be great my teacher gave me notes but she didnt give any explanation because she wasnt there so they dont make any sense to me
1 solutions

Answer 176402 by edjones(3298) on 2009-11-19 15:36:08 (Show Source):

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sqrt(-12)/sqrt(-3)
=sqrt(4*-3)/sqrt(-3)
=2sqrt(-3)/sqrt(-3)
=2
.
Ed

Equations/240759: 3(x+2)=x-18. What does x equal?
1 solutions

Answer 176399 by edjones(3298) on 2009-11-19 15:30:43 (Show Source):

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3(x+2)=x-18
3x+6=x-18
2x=-24
x=-12
.
Ed

Probability-and-statistics/240765: accordin to goverment data, the probability that an adult was never married is 15%, in a random survey of 10 adults, what is the probability that at least 8 were married?
1 solutions

Answer 176396 by edjones(3298) on 2009-11-19 15:28:15 (Show Source):

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Let m=married and n=never married
.85+.15=1
m^10+10m^9n+45m^8n^2 (derived from (m+n)^10)
.85^10 + 10*.85^9*.15 + 45*.85^8*.15^2
=.82
.
Ed

Age_Word_Problems/240776: How do I write this problem into an equation:
Sean is 20 and his brother is 12. How many years ago was Sean three times as old as his brother?
1 solutions

Answer 176385 by edjones(3298) on 2009-11-19 15:08:52 (Show Source):

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Let x be the number of years past.
(20-x) / (12-x) = 3
.
Ed

Probability-and-statistics/240767: six cards are to be drawn or delt, without replacement, from a deck of 52 cards. In how many ways can this be done if
A. all of the cards to be drawn are clubs?
B. All are to be jacks or queens?
C. None are to be aces?
D. All are to be spades or all not spades?
1 solutions

Answer 176382 by edjones(3298) on 2009-11-19 15:00:08 (Show Source):

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nCr=n!/((n-r)!r!)
.
A) 13C6/52C6=1716 / 20358520=.00008429 (13 clubs)
.
B) 8C6/52C6=28 / 20358520=.000001375 (8 Jacks or Queens)
.
C) 48C6/52C6=12271512 / 20358520=.6028
.
D) I changed this question to what I thought you meant.
(13C6 + 39C6) / 52C6 = (1716 + 3262623)/20358520 =.1603
.
Ed

Numbers_Word_Problems/240772: There were 82 people at a family reunion.
There were 4 more men than women.
There were 10 more children than adults.
How many childern were there?
1 solutions

Answer 176377 by edjones(3298) on 2009-11-19 14:35:20 (Show Source):

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w=number of women, w+4=numb of men, w+w+4+10=numb of kids
w+w+4+w+w+4+10=82
4w+18=82
4w=64
w=16
w+w+4+10=46
.
Ed

Functions/240769: i'm confused as to how to do these problems. for example : what is 80% of 14? or 15 is what percent of 45?
1 solutions

Answer 176375 by edjones(3298) on 2009-11-19 14:29:27 (Show Source):

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14*.8=11.2
.
Let the percent = 100x
45x=15
x=15/45=1/3
1/3 * 100=100/3 % = 33 1/3 %
.
Ed

Radicals/240743: For the problem below, 1 is an extraneous solution and the solution is 2 and 9. True or false? why?
square root of 2x+9-square root of x+1=2
1 solutions

Answer 176372 by edjones(3298) on 2009-11-19 14:20:56 (Show Source):

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sqrt(2x+9)-sqrt(x+1)=2
3x-(2sqrt(2x+9)*sqrt(x+1))+10=4 square each side
-(2sqrt(2x+9)*sqrt(x+1))=-3x-6
8x^2+44x+36=9x^2+36x+36 square each side
x^2-8x=0 Subtract the left side from the right.
x(x-8)=0
x=8, x=0
.
Ed