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You drove 56 miles on a service call for your company and it took 10 minutes longer than the return trip when you drove an average of 8 miles per hour faster. What was your average speed on the return trip?
---------
Service Call DATA:
distance = 56 miles ; rate = x mph ; time = d/r = 56/x hrs
================================
Return trip DATA:
distance = 56 miles ; rate = (x+8) mph ; time = 56/(x+8) hrs
------------------------------------
Equation:
go time - return time = 1/6 hr
56/x - 56/(x+8) = 1/6
1/x - 1/(x+8) = 1/336
Multiply thru by 336x(x+8) to get:
336(x+8) - 336x = x(x+8)
336*8 = x^2+8x
x^2 + 8x - 2688 = 0
(x-48)(x+56) = 0
Positive solution:
x = 48 mph (rate on the service call)
x+8 = 56 mph (rate on the return)
==============================================
Cheers,
Stan H.

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Compute the discriminant. Then determine the number and type of solutions for the given equation.
4x²-2x+1=0
a = 4 ; b = -2 ; c = 1
What is the discriminant?
----------------------------
discriminant = b^2-4ac
----------------------------
Your Problem:
D = (-2)^2 - 4*4*1 = 4-16 = -12
--------------
Since the discriminant is negative
the quadratic has two complex number solutions.
===================================================
Cheers,
Stan H.

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evaluate (-6c)^2 and 6c^2 when c = 10
-----
(-6c)^2 = (-6*10)^2 = (-60)^2 = 3600
-------------------------------
6c^2 = 6*(10)^2 = 6*100 = 600
================================
Cheers,
Stan H.

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That is not a trinomial.
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Stan H.

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how long would it take a car traveling 60 miles an hour to go 250 miles?
----
Time = distance/rate
time = 250/60 = 4 1/6 hrs or 4 hours 10 minutes
================================================
Cheers,
Stan H.

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(5/x)-(2/y)=7
---
Multiply thru by xy to get:
5y - 2x = 7xy
===================
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stan H.

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Factor the trinomial, or state that the trinomial is prime.
x²-3x-18
---------------
Think of two numbers whose product is -18 and whose sum is -3.
---
The numbers are -6 and 3
-----
Rewrite the problem making this substitution:
x^2 - 6x + 3x -18
---
Factor the 1st two and the last two terms separately:
x(x-6) + 3(x-6)
Factor again to get the solution:
(x-6)(x+3)
======================
Cheers,
stan H.

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Good Work.
Cheers,
Stan H.

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Is it possible to spend $30 for 100 stamps consisting of 20-cent stamps and 33-cent stamps?
---------------------
Equations:
Quantity: t + r = 100
Value::: 20t+33r = 3000
-----------------------------------------
Multiply thru the Quatity Eq. by 20 to get:
20t + 20r = 2000
----
Subtract that from the Value Eq. to get:
13r = 1000
r = 76.92
-----
Since r is the number of thirty cent stamps and is not
an integer the combination does not work.
============================================================
Cheers,
Stan H.

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log base 5 (x^2+x+4)=2
------------------
x^2+x+4 = 5^2
x^2 + x -21 = 0
x = [-1 +- sqrt(1 -4*-21)]/2
---
x = [-1 +sqrt(85)]/2 or x = [-1-sqrt(85)]/2
---------------------------------------------
Cheers,
Stan H.

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6e^(2x)-16e^x=6
solve for x. please explain
------------------------------------
This is a quadratic equation with e^x as it's variable:
Rewrite:
6(e^x)^2 - 16(e^x) - 6 = 0
----
Let m = e^x
----
6m^2 - 16m - 6 = 0
3m^2 - 8m - 3 = 0
---
3m^2 -9m+m - 3 = 0
3m(m-3)+(m-3) = 0
(m-3)(3m+1) = 0
m = 3 or m = -1/3
---------------------------
Substitute to solve for "x":
e^x = 3
x = ln(3) = 1.098612...
----------------------------------
e^x = (-1/3)
No solution because no value of e is negative.
================================================
Cheers,
Stan H.

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Find an equation of variation if the following conditions exist.
Suppose that y varies directly as z and y = 43 when z = 387.
-----------------------------------
y = kz
--------------------
43 = k*387
k = 43/387
k = 1/9
-------------------
Equation:
y = (1/9)/z
y = 1/(9z)
=========================
Cheers,
Stan H.

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Solve using the elimination method.
x + y = 6,
-x + 3y = -2
----------------------
Add the two equations to get:
4y = 4
y = 1
----
Substitute into x+y=6 to solve for "x":
x + 1 = 6
x = 5
-------------------
Cheers,
Stan H.

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write an equation that expresses the distance you travel, d kilometers, as a function of the time, t hours
------
distance = rate*time
d(t)
Cheers,
stan H. = rt
================

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Solve using the substitution method. First, solve one equation for one variable.
s + t = - 4,
s - t = 2
--------------------
solve the 2nd for "s":
s = t+2
-------------------
Substitute into to 1st and solve for "t":
t+2 + t = -4
2t + 2 = -4
2t = -6
t = -3
------
Since s = t+2, s = -3+2 = -1
================================================
Solution:
t = -3
s = -1
==========================
Cheers,
Stan H.

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What are the three consecutive odd integers whose sum is 521?
------------------------
1st 2x-1
2nd 2x+1
3rd 2x+3
------------------
Equation:
6x+3 = 521
6x = 518
x = 56 1/3
-------------------
1st: 2x-1 = 3(56 1/3)-1 is not an integer
================================================
Cheers,
Stan H.

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How do you find an equation in slop-intercept form of the line satisfying the specified conditions? through (-6,-9), perpendicular to -7x-5y=-3
----------
Find the slope of the given line:
y = (-7/5)x+(3/5)
That slope is -7/5
------------------------------
A perpendicular line must have slope = 5/7
------------------------------------------------
Form of the equation you want:
y = mx +b
You know m = 5/7 and you know y = -9 when x = -6:
-9 = (5/7)(-6) + b
-63/7 = -30/7 + b
b = -33/7
==================
Equation:
y = (5/7)x - (33/7)
===========================
Cheers,
Stan H.

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The perimeter P of a regular pentagon is 5 times the length of a side s.
-----
Since you do know the perimeter and you do not know the side the best
you can say is P = 5s
=============================
Cheers,
Stan H.

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At what angle, or slope in degrees will the hypotenus of this triangle ly?
The vertical leg measures 29"
The hypotenuse measures 63"
One angle of the triangle is 90 degree
-------------
Draw the picture of the triangle.
slope = rise/run
------------------
run = sqrt(63^2-29^2) = 55.93 inches
----------------------
slope = 29/55.93 = 0.5185
=====================================
Cheers,
Stan H.

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Two cars leave town at the same time going in the same direction. One travels at 45 mph and the other travels at 68 mph. In how many hours will they be 138 miles apart.
---------------------
1st car:
rate = 45 mph ; time = x hrs ; distance = 45x miles
-------------------
2nd car :
rate = 68 mph ; time = x hrs ; distance = 68x miles
---------------------------
Equation:
distance 2 - distance 1 = 138 miles
68x - 45x = 138
23x = 138
x = 6 hours
======================
Cheers,
Stan H.

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The director of a summer day camp estimates that 100 children will join if the camp fee is $250, but for each $20 decrease in the fee, ten more children will enroll.
A.)Determine the linear equation that will represent the number of children who will enroll at a given fee.
N(x) = 100+10(250-x)/20
-----------------------------------------------------

B.)Approximately how many students will enroll if the camp fee is $180? Round to the nearest child.
N(180) = 100+10(250-180)/20
N(180) = 100 + 10(7/2)
N(180) = 135
------------------------------

C.) How many students will enroll if the camp is free? Round to the nearest child.
N(0) = 100 + 10(250-0)/20
N(0) = 100 + 10(12.5)
N(0) = 100 + 125
N(0) = 225
=====================
Cheers,
Stan H.

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I rolled a pair of number cubes 30 times. Heres a google spreadsheet webpage that shows what numbers I got:
http://spreadsheets.google.com/pub?key=tTcZez2zPqpi6D1a7RHTOcQ&output=html
----------------
What numbers are on your cubes?
What "result" are you looking at from each roll?
Are you looking for the sum of the upward faces?, the product of the
up ward faces? or what?
----
I'm asking this so I can understand how you would get P(36)?
Cheers,
Stan H.
=========================
There were many questions, but the ones I don't get are: Use your data to find the following experimental probabilities P(5)

P(6) P(12) and P(36)
Make a chart to find the "SAMPLE SPACE" which I don't know how to do...
The other 5 questions I could understand.

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Develop a 90 percent confidence interval for the population mean. Interpret the results.
The Greater Pittsburgh Area Chamber of Commerce wants to estimate the mean time workers who are employed in the downtown area spend getting to work. A sample of the 15 workers reveals the following number of minutes spent traveling.
29 38 38 33 38 21 45 34
40 37 37 42 30 29 35
------------
sample mean = 35.067
sample std = 6.017
-------
standard error = z*s/sqrt(n)
standard error = 1.645*6.017/sqrt(15) = 2.556
-------------------------------------------------------
90% CI: 35.067-2.556 < u < 35.067+2.556
90% CI: 32.511 u < 37.62
======================================================
Develop a 98 percent confidence interval for the population mean. Interpret the results.
Use the z-value for 98%: z = 2.3263
sample mean is the same as above
standard error = 2.3263*6.017/sqrt(15)=3.614
---
98% CI: 35.067 - 3.614 < u < 35.067 + 3.614
98% CI: 31.45 < u < 38.68
---------------------------------
Meaning: We have 98% confidence the population mean is between
31.45 and 38.68
==============================================
Cheers,
Stan H.

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Cos(x) + 2 = -sec(x)
cos(x) + sec(x) + 2 = 0
----
Multiply thru by cos(x) to get this quadratic:
cos^2(x) + 1 + 2cos(x) = 0
Rearrange:
cos^2(x) + 2cos(x) + 1 = 0
Factor:
(cos(x) + 1)^2 = 0
cos(x) = -1
x = pi+2npi where n = 0,1,2,...
======================
Cheers,
Stan H.

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Solve the system of equations.
2x - 5y = 6
4x - 10y = 30
-----------------------
Multiply thru the 1st equation by 2 to get:
4x - 10y = 12
4x - 10y = 30
------------------
Subtract the 1st from the 2nd and you get this contradiction:
0 = 18
-----------------
This means the lines are parallel; there is no point common
to the two lines. There is no solution.
=============================================
Cheers,
Stan H.

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I need to find the name and degree of this polynomial. I think it is a trinomial but don't know the degree could you please hekp?
7x^3+6x^2-2
-------------------
Type: trinomial because it has 3 terms
Degree: 3 because the highest powere of the variable is 3.
==============================================================
Cheers,
Stan H.

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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"
---------------------
You should have or you need a cumulative binomial chart or a calculators
with a Stat function.
------
Your problem:
Binomial with n = 150, p = 0.03, 4 <= x <= 150
------------------
Your problem:
P(4 <= x <= 150) = 1 - P(0 <= x <= 3)
= 1 - [P(x= 0) + P(x=1) + P(x=2) + P(x=3)]
= 1 - [0.01037 + 0.048106..+ 0.110843 + 0.16912...)
= 1 - [0.33844
= 0.66156...
========================
Stan H.

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9x^2-16y^2+36x+64y=172
What type of conic?
Standard Form?
---------------------
Since the squared terms have opposite signs
the conic is a hyperbola.
----------------------------------
Form:
Complete the square on the x and on the y terms:
9(x^2 + 4x) - 16(y^2-4y) = 172
Complete the two squares:
9(x^2 + 4x + 4) - 16(y^2 - 4y + 4) = 172 + 9*4 -16*4
9(x+2)^2 - 16(y-2)^2 = 144
Divide thru by 144 to get:
(x+2)^2/16 - (y-2)^2/9 = 1
=================================
Cheers,
Stan H.

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find the vertex, the line of symmetry,
the maximum or minimum value of the quadratic
function and graph the function
f(x)=7-x2 and find zeros
You have a quadratic with a = -1, b = 0, c = 7
-----------------
Max or min occurs when x = -b/2a = -0/-2 = 0
f(0) = 7
So the vertex is (0,7)
------------------------------
Axis of symmetry is x=0
-------------------------------
Zeroes: 7-x^2 = 0
x^2 = 7
x = +sqrt(7) ; x = -sqrt(7)
====================================
Graph:

=====================================
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Stan H.

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(42k^3 + 12^k2 + 18k) ÷ (6k)
----------------
= 7k^2 + 2k + 3
=======================
Cheers,
Stan H.