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Recent problems solved by 'mathitutor'

mathitutor answered: 25 problems

Linear-equations/382860: in a tour 2 adults and 5 students paid $77 and in other van 2 adults and 7 students paid $95 for the same tour.find adults price and student price?
1 solutions

Answer 271227 by mathitutor(25) on 2010-12-08 06:02:38 (Show Source):

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Say, adults price = x
and student price = y
Then
2x + 5y = 77 --- (1)
2x + 7y = 95 --- (2)
(2) - (1) =>
7y - 5y = 95 -77
2y = 18
y = $9 ---(3)
placing y's value in (1)
2x + 45 = 77
2x = 32
x = $16 ----(4)
(3) and (4) are the answers

Miscellaneous_Word_Problems/300237: What percent of all natural numbers from 1 to 10000 are perfect squares?
A) 1% B) 1.5% C) 2% D) 2.5% E) 5%
1 solutions

Answer 215473 by mathitutor(25) on 2010-05-04 05:28:41 (Show Source):

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A) 1%
100^2 = 10000
Hence there are 100 perfect squares.

Problems-with-consecutive-odd-even-integers/300236: If x denotes any negative integer number, which of the following expressions will always have the greatest value?
A) x+1 B) 2x C) –2x D) 6x+2 E) x-2
1 solutions

Answer 215472 by mathitutor(25) on 2010-05-04 05:26:27 (Show Source):

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C) -2x

Probability-and-statistics/299678: If two events are collectively exhaustive, what is the probability that one or the other occurs?
a. 0.25
b. 0.50
c. 1.00
d. Cannot be determined from the information given.
1 solutions

Answer 215258 by mathitutor(25) on 2010-05-03 05:29:42 (Show Source):

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B. 0.5

Problems-with-consecutive-odd-even-integers/299701: The sum of 4 consecutive integers is 26. What is the product of the 4 numbers?
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Answer 215257 by mathitutor(25) on 2010-05-03 05:26:39 (Show Source):

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Assume that the first number is x
x + x + 1 + x + 2 + x + 3 = 26
=> 4x + 6 = 26
=> 4x = 26 - 6
=> 4x = 20
=> x = 20/4
=> x = 5
Hence the numbers are: 5, 6, 7, 8
Product of these numbers = 5 x 6 x 7 x 8 = 1680

Linear_Algebra/299703: If f(x) = x - 1, what is the value of x that satisfies the equality f(x) - 1 = f(x^2)- x^2
1 solutions

Answer 215256 by mathitutor(25) on 2010-05-03 05:23:20 (Show Source):

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f(x) - 1 = f(x^2) - x^2
=> x - 1 - 1 = x^2 - 1 - x^2
=> x - 2 = -1
=> x = -1 + 2
=> x = 1

Miscellaneous_Word_Problems/252238: The pitch of a screw is the distance between threads. With each complete rotation of the screw, it goes in or out a distance equal to its pitch. How far will a screw with a pitch of 2/45 inches go into a piece of wood when it is turned 10 complete rotations clockwise?
a 1/225 in b 9/4 in c 4/9 in d 1/9 in e 9 in
1 solutions

Answer 184050 by mathitutor(25) on 2009-12-25 07:09:13 (Show Source):

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10 x 2/45 = 20/45 = 4/9
The answer is (C)

Numbers_Word_Problems/250412: what is Three more than twice a number x is fifteen
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Answer 182325 by mathitutor(25) on 2009-12-15 21:05:58 (Show Source):

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2x + 3 = 15
=> 2x = 15 - 3
=> 2x = 12
=> x = 12/2
=> x = 6

Functions/250253: Please help me help my daughter solve this homework problem.
For a car traveling at a constant rate of 60 mi/h, the distance traveled is a function of the time traveled.
a. Express this relation as a function
b Find the range of the function when the domain is [1,5,10]
c What do the domain and range represent?
I am thinking that the expressed function should be something like
f(d) = (60m)h
We can solve b. once we can figure out how to express it as a function.
Thank you for your help.
1 solutions

Answer 182324 by mathitutor(25) on 2009-12-15 21:01:27 (Show Source):

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(a)The distance travel when something is moving at a constant speed = speed x time
As the constant velocity is given = 60 mi/hr
The distance travel will be varying with time and it is a function of time as given below:
s(t) = 60t where t is in hours.

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Triangles/250392: The measure of each of the base angles of an isosceles triangle is 24 degrees less than the measure of the vertex angle. Find the measure of the vertex angle.
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Answer 182322 by mathitutor(25) on 2009-12-15 20:56:29 (Show Source):

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let the vertex angle = x
Hence the each of base angle = x - 24
Sum of all angles of a triangle = 180
=> x + x - 24 + x - 24 = 180
=> 3x - 48 = 180
=> 3x = 180 + 48
=> 3x = 228
=> x = 76 degree.

Rectangles/250396: The length of a rectangle is 7 centimeters less than twice its width.The perimeter of the rectangle is 34 cm. What are the demensions of the rectangle?
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Answer 182318 by mathitutor(25) on 2009-12-15 20:51:24 (Show Source):

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Let the width = x
Then the length = 2x - 7
Hence the perimeter = 2x + 2(2x-7) = 34
=> 2x + 4x - 14 = 34
=> 6x = 34 + 14
=> 6x = 48
=> x = 48/6
=> x = 8
Hence the width = 8 cm
length = 2x8 - 7 = 16 - 7 = 9 cm

Equations/250395: 2(x+1)=3x-1 Solve for x
1 solutions

Answer 182314 by mathitutor(25) on 2009-12-15 20:43:50 (Show Source):

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2(x+1)=3x-1
=> 2x + 2 = 3x - 1
=> 3x -2x = 2 + 1
=> x = 3

Quadratic_Equations/249999: a^2-11a+28=0
1 solutions

Answer 181984 by mathitutor(25) on 2009-12-14 21:30:14 (Show Source):

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a^2-11a+28= a^2-7a - 4a+28= a(a-7) -4(a-7)=(a-4)(a-7)=0 Hence a = 4 and 7

Quadratic_Equations/249184:
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Answer 181546 by mathitutor(25) on 2009-12-13 09:57:17 (Show Source):

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Solve equation by factoring
9x^2+5x-11=0
(3x)^2 + 2.3x.5/6 + (5/6)^2 - 11 - (5/6)^2 = 0
[3x + 5/6]^2 - [11 + 25/36] = 0
[3x + 5/6]^2 - [421/36] = 0
[3x + 5/6]^2 - [sqrt(421)/6]^2 = 0
[3x + 5/6 + sqrt(421)/6][3x + 5/6 - sqrt(421)/6]= 0
Equate each factor to 0 and that will give you two solutions.

Sequences-and-series/247854: Question: Find the sums of the following geometric series. 1 + 3 + 9 +...+2187.
What I've tried so far...
So: know:a=1
r=3
tn=2187
find:???
For this problem, wouldn't I have to find how many terms are in the sequence first? Then whatever n is, I plug that into another equation?
I'm so lost...please help!
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Answer 180736 by mathitutor(25) on 2009-12-09 17:41:35 (Show Source):

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This is a standard geometric progression,
3^0 + 3^1 + 3^2 + ... + 3^7
There is a standard formula for summation of terms of a geometric progression series. Use that to solve this.

Trigonometry-basics/247896: write the standard form of the equation of the circle that passes through the point (0,1) with its center at the origin.
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Answer 180734 by mathitutor(25) on 2009-12-09 17:34:47 (Show Source):

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radius = a = sqrt[(0-0)^2 + (1-0)^2] = 1
the equation of the circle is
x^2 + y^2 = 1^2
x^2 + y^2 = 1

Linear-systems/247895: 180=7x-15
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Answer 180733 by mathitutor(25) on 2009-12-09 17:32:37 (Show Source):

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180 = 7x -15
Add 15 to both side
180 + 15 = 7x -15 + 15
195 = 7x
x = 195/7

Linear_Algebra/245999: x + y=8 over x - y =-10
1 solutions

Answer 179686 by mathitutor(25) on 2009-12-04 21:38:36 (Show Source):

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x + y = 8 ---(1)
x - y = -10 ---(2)
(1) + (2) gives,
2x = -2 => x = -1
put the value of x in 1, -1 + y = 8
=> y = 8 + 1 = 9

Quadratic_Equations/244008: What is the quadratic equation of 4x^2-8x-9=0
(simplifiy your answer. type an exact answer using radicals as needed. Use integers or fractions for any number in the expression. Express complex numbers in the form of i.)
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Answer 178631 by mathitutor(25) on 2009-11-30 12:49:26 (Show Source):

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4x^2-8x-9=0
=> (2x)^2 - 2.2x.2 + 2^2 -9 -4 = 0
=> (2x -2)^2 = 13
=> 2x - 2 = +sqrt(13) or -sqrt(13)
=> 2x = 2 +sqrt(13) or 2-sqrt(13)
x = 1 + sqrt(13)/2 or 1 - sqrt(13)/2

Quadratic_Equations/244009: What is the quadratic equation of 4x^2-8x-9=0
(simplifiy your answer. type an exact answer using radicals as needed. Use integers or fractions for any number in the expression. Express complex numbers in the form of i.)
1 solutions

Answer 178629 by mathitutor(25) on 2009-11-30 12:46:25 (Show Source):

Graphs/243976: Find an equation of the line meeting the specified conditions. Write your final answer in slope-intercept form.
Containing the point (0, 4) and parallel to y = 7x - 6
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Answer 178627 by mathitutor(25) on 2009-11-30 12:39:57 (Show Source):

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slope = m = dy/dx = 7
y = 7x + c
put x =0, y = 4 to calculate c
4 = c
Hence the equation is
y = 7x + 4

logarithm/243984: Factorise:
25^2-64y^2
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Answer 178625 by mathitutor(25) on 2009-11-30 12:37:50 (Show Source):

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25^2-64y^2 = (5)^2 - (8y)^2 = (5+8y)(5-8y)

Rectangles/243971: The sum of 2numbers is 15. 1 less than 3 times the smaller is equal to the larger. Find the 2 numbers.
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Answer 178624 by mathitutor(25) on 2009-11-30 12:34:10 (Show Source):

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assume that the numbers are x and 15-x.
3x - 1 = 15 -x
=> 4x = 16
=> x = 4
The numbers are 4 and 11.

Age_Word_Problems/244005: If I add four times my age four years from now to five times my age five years from now, I get ten times my current age. How old will I be five years from now?
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Answer 178623 by mathitutor(25) on 2009-11-30 12:31:30 (Show Source):

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Assume my current age = x
4(x+4) + 5(x+5) = 10x
=> 4x + 16 + 5x + 25 = 10x
=> 9x + 41 = 10x
=> 10x-9x = 41
=> x = 41

Polynomials-and-rational-expressions/244006: What is the root of 49x^2-25=0?
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Answer 178622 by mathitutor(25) on 2009-11-30 12:28:30 (Show Source):

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49x^2-25=0 => (7x)^2 - 5^2 = 0 => (7x + 5)(7x-5) = 0
=> x = 5/7 and -5/7

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