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Recent problems solved by 'stanbon'
stanbon answered: 57178 problems
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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179, >>NextEquations/277911: Hi The question is find the equations for exponential functions that pass through the given oair of points . round the coefficeints to 4 decimal places if necessary. ( -2,1) ( 1,5) f(x) =
1 solutions
Answer 202293 by stanbon(57246)   on 2010-03-06 22:10:33 (Show Source):
You can put this solution on YOUR website!The question is find the equations for exponential functions that pass through the given pair of points . round the coefficeints to 4 decimal places if necessary. ( -2,1) ( 1,5) f(x) =
------------------------------------------------------
y = ab^x
5 = ab^1
1 = ab^-2
------------------
Divide the 1st equation by the 2nd to solve for "b":
5 = b^3
b = 5^(1/3)
------------
Substitute into 5 = ab^1 and solve for "a":
5 = a*5^(1/3)
a = 5^(2/3)
----------------------
Equation:
y = (5^(2/3))(5^(x/3)
===========================
Cheers,
stan H.
|
Exponents/277915: What is the solution to the problem '3x to the negative second power' ? Im not sure at all to do these equations when they involve a variable against the base.
1 solutions
Answer 202292 by stanbon(57246) on 2010-03-06 22:01:33 (Show Source):
You can put this solution on YOUR website!What is the solution to the problem '3x to the negative second power' ? Im not sure at all to do these equations when they involve a variable against the base.
------
(3x)^(-2)
The 2 means square
The negative means invert
----
You can perform these operation in any order.
----
If you invert 1st you get (1/3x)^2
If you then square you get (1/9x^2)
-----------------------------------------
If you square first and then invert you will get the same answer.
====================================================================
Cheers,
Stan H.
|
Travel_Word_Problems/277914: Driving his car at 50 mi/hr, jose can cover a certain distance in 20 min less than when he drives at 45 mi/hr . Find that distance.
1 solutions
Answer 202291 by stanbon(57246) on 2010-03-06 21:54:44 (Show Source):
You can put this solution on YOUR website!Driving his car at 50 mi/hr, jose can cover a certain distance in 20 min less than when he drives at 45 mi/hr . Find that distance.
--------------------------
Faster Rate DATA:
rate = 50 mph ; distance = x miles : time = d/r = x/50 hrs
----------------------------------------------
Slower Rate DATA:
rate = 45 mph ; distance = x miles ; time = d/r = x/45 hrs
--------------------------------------------------------
Equation:
slower time - faster time = 1/3 hr
x/45 - x/50 = 1/3
---
3*50x - 3*45x = 45*50
15x = 45*50
x = 150 miles
=====================================
Cheers,
Stan H.
|
Probability-and-statistics/277885: Healty people have body temperatures that are normally distributed with a mean of 98.20 degrees F and a standard deviation of 0.62 degrees F.
(a) If a healthy person is randomly selected, what is the probability that he or she has a temperature above 99.2 degrees F?
answer:
(b) A hospital wants to select a minimum temperature for requiring further medical tests. What should that temperature be, if we want only 0.5 % of healty people to exceed it?
answer:
1 solutions
Answer 202289 by stanbon(57246) on 2010-03-06 21:45:23 (Show Source):
You can put this solution on YOUR website!Healthy people have body temperatures that are normally distributed with a mean of 98.20 degrees F and a standard deviation of 0.62 degrees F.
-------------------------------------------
(a) If a healthy person is randomly selected, what is the probability that he or she has a temperature above 99.2 degrees F?
---
z(99.2) = (99.2-98.2)/0.62 = 1.6129
P(x > 00.2) = P(z> 1.6129) = 0.0534
----------------------------------------------
(b) A hospital wants to select a minimum temperature for requiring further medical tests. What should that temperature be, if we want only 0.5 % of healty people to exceed it?
-------
Find the z-score tht has a right tail of 5%: z = inv(0.95) = 1.645
-----
Find the temperature that corresponds to z = 1.645
x = zs + u
x = 1.645*0.62+98.2
x = 99.22 degrees
===========================================
Cheers,
Stan H.
|
Probability-and-statistics/277886: College students average 7 hours of sleep per night with a standard deviation of 40 minutes. If the amount of sleep is normally distributed, what proportion of college students sleep for more than 8.3 hours?
Probability =
1 solutions
Answer 202286 by stanbon(57246) on 2010-03-06 21:16:36 (Show Source):
You can put this solution on YOUR website!College students average 7 hours of sleep per night with a standard deviation of 40 minutes. If the amount of sleep is normally distributed, what proportion of college students sleep for more than 8.3 hours?
--------------------------
z(8.3) = (8.3-7)/(2/3) = 1.95
P(x> 8.3) = P(z > 1.95) = 0.0256
Probability =0.0256
---------------------------------
Cheers,
Stan H.
|
Graphs/277866: 1. (20 points) In 1981, Vadimir Poliakov (USSR) set a world record of 19ft in for the pole vault (www.polevault.com). To reach that height, Poliakov obtained a speed of approximately 36 feet per second on the runway. The formula h = -16t2 + 36t gives his height t seconds after leaving the ground.
a. Does the graph of this equation open up or down? How did you determine this?
b. Describe what happens to his height as time passes, starting at t=0?
c. Use the method of your choice to find how long he was in the air.
d. Will his height peak or be at a low during the middle of the time he is in the air? How do you know?
e. After how many seconds will the peak or low occur?
f. How high will he be when the peak or low occurs?
g. What is the point of the vertex? How does this number relate to your answers in parts e and f?
h. How many solutions are there to the equation 0 = -16t2 + 36t? How do you know?
i. To use the quadratic formula to solve an equation like this, we need three values, represented in your text by a, b and c. In the equation in part h, what are a, b & c?
j. What do the solutions to 0 = -16t2 + 36t represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense?
1 solutions
Answer 202269 by stanbon(57246) on 2010-03-06 18:53:54 (Show Source):
You can put this solution on YOUR website!In 1981, Vadimir Poliakov (USSR) set a world record of 19ft in for the pole vault (www.polevault.com). To reach that height, Poliakov obtained a speed of approximately 36 feet per second on the runway. The formula h = -16t^2 + 36t gives his height t seconds after leaving the ground.
a. Does the graph of this equation open up or down? How did you determine this?
Ans: Down because of the -16t^2
------------------------------------------
b. Describe what happens to his height as time passes, starting at t=0?
Ans: h(0) = 0 means the height is zero when the time is zero.
--------------------------------
c. Use the method of your choice to find how long he was in the air.
Ans: Solve h=0 for two values of "t".
----------------------------------
d. Will his height peak or be at a low during the middle of the time he is in the air? How do you know?
Ans: peak because the parabola opens down and therefore has a peak at the vertex.
------------------------------------
e. After how many seconds will the peak or low occur?
Ans: Find the t-value of the peak at t = -b/2a
------
f. How high will he be when the peak or low occurs?
Ans: Find h at that t-value.
------------------
g. What is the point of the vertex? How does this number relate to your answers in parts e and f?
Ans: vertex has time of peak and height of peak.
-----------------------------------
h. How many solutions are there to the equation 0 = -16t2 + 36t? How do you know?
Ans: It is a quadratic
-----------------------------------------
i. To use the quadratic formula to solve an equation like this, we need three values, represented in your text by a, b and c. In the equation in part h, what are a, b & c?
Ans a = -16 ; b = 36 ; c = 0
--------------------------------------------
j. What do the solutions to 0 = -16t2 + 36t represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense?
Ans: They both tell the time when the vaulter is on the ground.
========================================
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/277839: Bob has twice as many hot dogs as Phil, while Phil has 5 less than 3 times as many hot dogs as Fred. Fred has two more than Nancy. They have 71 hot dogs altogether. If a hot dog costs $1.50, how much did each person spend?
1 solutions
Answer 202251 by stanbon(57246) on 2010-03-06 18:06:33 (Show Source):
You can put this solution on YOUR website!Bob has twice as many hot dogs as Phil, while Phil has 5 less than 3 times as many hot dogs as Fred. Fred has two more than Nancy. They have 71 hot dogs altogether. If a hot dog costs $1.50, how much did each person spend?
------------------------------------
Equations:
b + p + f + n = 71
b - 2p+ 0 + 0 = 0
0 + p -3f + 0 = -5
0 + 0 + f - n = + 2
-----------------
I used the matrix function on a TI calculator to get:
Bob has 38 dogs ; cost $57
Phil has 19 dogs ; cost = $28.50
Fred has 8 dogs ; $12
Nancy has 6 dogs; $9
==========================
Cheers,
Stan H.
|
Rational-functions/277841: How do I find the basic function of:
t(x)= -(-1-x)^2
What would this graph look like? Has it been shifted, reflected, stretched or compressed?
1 solutions
Answer 202230 by stanbon(57246) on 2010-03-06 16:40:52 (Show Source):
You can put this solution on YOUR website! How do I find the basic function of:
t(x)= -(-1-x)^2
What would this graph look like? Has it been shifted, reflected, stretched or compressed?
----------------
The basic function is y = x^2
You could simplify t(x) as follows:
t(x) = -(-(x+1))^2
t(x) = -(x+1)^2
----
Now you can see the x+1 shifts y= x^2 one unit to the left.
---
The negative sign reflects y=(x+1)^2 in the x-axis.
-----
You end up with an upside-down parabola that was shifted one unit to the left:
===================================================
Cheers,
Stan H.
|
Mixture_Word_Problems/277812: Solution A is 25% acid and solution B is 40% acid. How much of each solution is needed to make 100 liters of 30% acid?
1 solutions
Answer 202214 by stanbon(57246) on 2010-03-06 14:58:30 (Show Source):
You can put this solution on YOUR website!Solution A is 25% acid and solution B is 40% acid. How much of each solution is needed to make 100 liters of 30% acid?
-------------
One variable solution:
0.25x + 0.40(100-x) = 0.30*100
Multiply thru by 100 to get:
25x + 40*100 - 40x = 30*100
-15x = -10*100
x = (2/3)100
x = 66.67 liters (amt of 25% solution needed in the mixture)
---
100-x = 33.3 liters (amt of 40% solution needed in the mixture)
==================================
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/277813: Use three or more sentences to describe the process you would follow to completely factor the polynomial 3x6+24?
1 solutions
Answer 202212 by stanbon(57246) on 2010-03-06 14:53:53 (Show Source):
You can put this solution on YOUR website!Use three or more sentences to describe the process you would follow to completely factor the polynomial 3x6+24?
----
Common Factor: 3
= 3(x^6 + 8)
---------
Rewrite:
= 3[(x^2)^3 + 2^3)
---
= 3[(x^2+2)(x^4 - 2x^2 + 4)
----------------------------------
Cheers,
Stan H.
|
Probability-and-statistics/277793: What is the t value for a 20% two-tailed test with degrees of freedom = 9
I do not just want an answer. I want to know step by step how to get the answer
1 solutions
Answer 202202 by stanbon(57246) on 2010-03-06 13:28:32 (Show Source):
You can put this solution on YOUR website!What is the t value for a 20% two-tailed test with degrees of freedom = 9
I do not just want an answer. I want to know step by step how to get the answer
------------
To get the answer you need a T-chart or a calculator that generates t-values,
such as a TI-84.
-------
Since the test is 2 tail, each tail has 10%
Check your T-chart for df=9 and left (or right) tail = 0.1000
---
Using a TI I get invT(0.9,9) = 1.3830
===================
Cheers,
Stan H.
|
Rational-functions/277792: Graph:
f(x) = -2x, x<=-2
f(x) = -3,-2
f(x) = 4x-6, x>1
On these types of problems I am used to being given an x-substitute, for example, graph problem one when x = 2, I would then sub in the number and solve. I am perplexed about how to do this without a substitute.
1 solutions
Answer 202201 by stanbon(57246) on 2010-03-06 13:23:41 (Show Source):
You can put this solution on YOUR website!
The second question was also messed up, it should have been
-3, when -2 < x <= 1
The way the problem is shown to me is
f(x) = {
and the three equations come within the single { which stretches to encompass all of them.
Graph:
f(x) = -2x, x<=-2
f(x) = -3, -2
f(x) = 4x-6, x>1
---------------------
So this is the graph of a semented function.
On the x-interval (-inf,-2] graph the line y = -2x
On the x-interval (-2,1} graph the line y = -3
On the x-interval (1,+inf) graph the line y = 4x-6
----------------------------------------------------------
To do each of these you need to determine two points
that are on each interval.
For example, on the (-inf,-2) interval you could have
(-5,10) and (-2,4)
Draw a line segment thru those points ending at (-2,4).
---
On the next interval you have points (-2,-3) and (1,-3)
Draw a line sement connecting those points.
------------------------
On the last interval you have points (1,-2) and arbitrary (4,10)
Draw a line segment that starts at (1,-2) and passes thru (4,10)
-----------------------------------------------------
Those three line segments comprise the graph of f(x)
======================================================
Cheers,
Stan H.
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Surface-area/277789: The depth of a rectangular pool is 2 feet. The volume is 16 cubic feet. What is the area in square feet of the bootom of the pool?
1 solutions
Answer 202200 by stanbon(57246) on 2010-03-06 13:18:55 (Show Source):
You can put this solution on YOUR website!The depth of a rectangular pool is 2 feet. The volume is 16 cubic feet. What is the area in square feet of the bottom of the pool?
-------------------
Volume = Bh where B is the area of the base and h is the height.
------------------------
16 = B*2
B = 8 sq. ft.
============================
Cheers,
Stan H.
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Triangles/276959: You have a 15' ladder leaning against a wall.
It just touches the edge of a 5'x5' shed in the corner.
How high up the wall does the ladder touch and
how far out from the wall does it rest on the ground?
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I have tried using sin cos tan and a^2+b^2=c^2 but i can't seem to get it down to one variable that I can solve for or set them equal to.
1 solutions
Answer 202197 by stanbon(57246) on 2010-03-06 13:14:43 (Show Source):
You can put this solution on YOUR website!You have a 15' ladder leaning against a wall.
It just touches the edge of a 5'x5' shed in the corner.
How high up the wall does the ladder touch and
how far out from the wall does it rest on the ground?
-----------------
How high is the point where the ladder touches
the shed?
Cheers,
stan H.
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Miscellaneous_Word_Problems/277740: To build a set of book shelves, a carpenter needs 30 identical boards, each 2 feet 7 inches long. For this type of wood, the lumber yard sells only 12 foot long boards. How many 12 foot long boards must the carpenter purchase?
A.6 B.7 C.8 D.9 E.More than 9
1 solutions
Answer 202169 by stanbon(57246) on 2010-03-06 09:52:23 (Show Source):
You can put this solution on YOUR website!To build a set of book shelves, a carpenter needs 30 identical boards, each 2 feet 7 inches long. For this type of wood, the lumber yard sells only 12 foot long boards. How many 12 foot long boards must the carpenter purchase?
------------
# of shelves he gets from each 12' board: 12'/2'7" = 144"/31" = 4.65
Round down to get 4 shelves from each 12' board
---
# of boards needed = 30/4 = 7 1/2
Round up to get 8 boards
-----
He will need 8 12' boards.
===============================
Cheers,
Stan H.
A.6 B.7 C.8 D.9 E.More than 9
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Graphs/277749: Find the x- and y- intercepts
5x+y=15
1 solutions
Answer 202167 by stanbon(57246) on 2010-03-06 09:45:14 (Show Source):
You can put this solution on YOUR website!Find the x- and y- intercepts
5x+y=15
--------------
x-intercept?
Let y = 0 and solve for "x":
5x = 15
x = 3
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y-intercept?
Let x = 0 and solve for "y":
y = 15
====================
Cheers,
Stan H.
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Probability-and-statistics/277624: On a TV game show, the contestant is asked to select a
door and then is rewarded with the prize behind the door
selected. If the doors can be selected with equal probability,
what is the expected value of the selection if the
three doors have behind them a $40,000 foreign car, a $3
silly straw, and a $50 mathematics textbook?
1 solutions
Answer 202159 by stanbon(57246) on 2010-03-06 09:09:32 (Show Source):
You can put this solution on YOUR website!On a TV game show, the contestant is asked to select a
door and then is rewarded with the prize behind the door
selected. If the doors can be selected with equal probability,
what is the expected value of the selection if the
three doors have behind them a $40,000 foreign car, a $3
silly straw, and a $50 mathematics textbook?
-----
Random Number values: 40000,3,50
Probabilities: 1/3,1/3,1/3
---------------------------------
Expected Value: (1/3)(4053) = $1351
---------------------------------
Cheers,
Stan H.
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Mixture_Word_Problems/277746: A company makes pigments used to color fabrics, plastics and paints. To ensure the finished product matches the customers expectations, pigments of varying strength are blended to obtain what is called a 100% strength commercial standard. The plant has 5000 pounds of Pigment Red 1 with strength of 123% of the standard, and they also have 17,890 pounds of Pigment Red 1 at 87% strength versus the same commercial standard.
Your boss wants to know how much of the 87% material is needed to blend with the 5000 pounds of the 123% material so that the final strength of the blended material is 100% strength. What do you tell him?
1 solutions
Answer 202158 by stanbon(57246) on 2010-03-06 09:05:56 (Show Source):
You can put this solution on YOUR website!A company makes pigments used to color fabrics, plastics and paints. To ensure the finished product matches the customers expectations, pigments of varying strength are blended to obtain what is called a 100% strength commercial standard.
The plant has 5000 pounds of Pigment Red 1 with strength of 123% of the standard, and they also have 17,890 pounds of Pigment Red 1 at 87% strength versus the same commercial standard.
Your boss wants to know how much of the 87% material is needed to blend with the 5000 pounds of the 123% material so that the final strength of the blended material is 100% strength. What do you tell him?
----------------------
Equation:
red + red = red
1.23x + 0.87(5000-x) = 1.00(5000)
Multiply thru by 100 to get:
123x + 87*5000 - 87x = 100*5000
36x = 13*5000
x = 1805.56 lbs (amt of 123% pigment needed for the mixture)
5000-1805.56 = 3194.44 lbs (amt of 87% pigment needed for the mixture)
===================================
Cheers,
Stan H.
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Probability-and-statistics/277742: A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were
3.087 3.131 3.241 3.241 3.270 3.353 3.400 3.411 3.437 3.477
(a) Construct a 90 percent confidence interval for the true mean weight.
(b) What sample size would be necessary to estimate the true weight with an error of } 0.03 grams with 90 percent confidence?
(c) Discuss the factors which might cause variation in the weight of Tootsie Rolls during manufacture.
1 solutions
Answer 202157 by stanbon(57246) on 2010-03-06 08:58:58 (Show Source):
You can put this solution on YOUR website!A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on
a very accurate scale. The results in grams were
3.087 3.131 3.3.241 3.270 3.353 3.400 3.411 3.437 3.477
(a) Construct a 90 percent confidence interval for the true mean weight.
E = z*sigma/sqrt(n)
E = 1.645*0.13199/sqrt(10)
E = 0.06866
--------------
x-bar = 3.3048
-----------------
90% CI = (3.3048-0.06866 , 3.3048+0.06866)
-----------------------------------------------
(b) What sample size would be necessary to estimate the true weight with an error of 0.03 grams with 90 percent confidence?
E = z*sigma/sqrt(n)
n = [z*sigma/E]^2
z* for 90% confidence = 1.645
sigma = 0.13199
E = 0.03
------------
n = [1.645*0.13199/0.03]^2 = 52.38
rounded up: n = 53
========================
(c) Discuss the factors which might cause variation in the weight of Tootsie Rolls during manufacture.
Temperature; consistency of batches; machine tolerances
=========================
cheers,
Stan H.
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Probability-and-statistics/277743: In 1992, the FAA conducted 86,991 pre-employment drug tests on job applicants who were to be engaged in safety and security-related jobs, and found that 1,143 were positive.
(a) Construct a 95 percent confidence interval for the population proportion of positive drug tests.
(b) Why is the normality assumption not a problem, despite the very small value of p?
1 solutions
Answer 202155 by stanbon(57246) on 2010-03-06 08:55:40 (Show Source):
You can put this solution on YOUR website!In 1992, the FAA conducted 86,991 pre-employment drug tests on job applicants who were to be engaged in safety and security-related jobs, and found that 1,143 were positive.
---
sample proportion = 1143/86991 = 0.013
standard error = E = 1.96sqrt(0.013*0.987/86991) = 0.000753
-------------------
(a) Construct a 95 percent confidence interval for the population proportion of positive drug tests.
95% CI: 0.013-0.000753 < p < 0.013+0.000753
95% CI: 0.01222 < p < 0.013753
====================================
(b) Why is the normality assumption not a problem, despite the very small value of p?
I'll leave that to you.
Cheers,
Stan H.
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Probability-and-statistics/277629: The number of accidents that occur at the intersection
of Pine and Linden streets between 3 p.m. and
6 p.m. on Friday afternoons is 0, 1, 2, or 3, with probabilities
of 0.84, 0.13, 0.02, and 0.01, respectively.
Graph this probability distribution. What is the
expected value for the random variable given the
number of accidents?
1 solutions
Answer 202153 by stanbon(57246) on 2010-03-06 08:36:02 (Show Source):
You can put this solution on YOUR website! The number of accidents that occur at the intersection
of Pine and Linden streets between 3 p.m. and
6 p.m. on Friday afternoons is 0, 1, 2, or 3, with probabilities
of 0.84, 0.13, 0.02, and 0.01, respectively.
Graph this probability distribution. What is the
expected value for the random variable given the
number of accidents?
----------------------
The Graph.
Put 0,1,2,3 on the horizontal axis
Plot the probabilities as the y-values associated with 0,1,2,3
-------------------------------------------
E(x) = 0*0.84+1*0.13+2*0.02 + 3*0.01
= 0 + 0.13 + 0.04 + 0.03
= 0.21
=============
Cheers,
Stan H.
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Probability-and-statistics/277673: 1.Estimate the probability that a randomly selected person in the U.S. will be afflicted with
ashtma in 2003. Use this probability to estimate the number of Americans afflicted in 2004.
2. Using data from 2003, estimate the probability a newborn baby will be female. Locate the necessary data on the World Wide Web and submit the relevant URLs along with your answer.
1 solutions
Answer 202151 by stanbon(57246) on 2010-03-06 07:49:54 (Show Source):
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