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Recent problems solved by 'stanbon'
stanbon answered: 57214 problems
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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239, >>NextSequences-and-series/693435: What is the sum of the arithmetic series below?
2 + 5 + 8 + ... + 56
1 solutions
Answer 427389 by stanbon(57282)   on 2012-12-12 13:48:16 (Show Source):
You can put this solution on YOUR website!What is the sum of the arithmetic series below?
2 + 5 + 8 + ... + 56
-----
1st: What is the rank of the final term,i.e. 56?
Note: a(1) = 2 and d = 3
---
56 = 2 + (n-1)3
54 = (n-1)3
n-1 = 18
n = 19, so 56 is the 19th term.
------
2nd: Find the sum:
Sum = (19/2)(2+56) = 19(29) = 551
====================
Cheers,
Stan H.
====================
|
logarithm/693231: Use the log properties to write 7 log(4x+5)-2 log(x+2)+log(y+9) as a single log expression.
1 solutions
Answer 427363 by stanbon(57282) on 2012-12-12 09:47:28 (Show Source):
You can put this solution on YOUR website!write 7 log(4x+5)-2 log(x+2)+log(y+9) as a single log expression.
------
= log[(4x+5)^7*(y+9)/(x+2)^2]
----------
Cheers,
Stan H.
=============
|
logarithm/693278: How to solve the following equation log[9](5x-3)- log[3]2√x =0. Please help
1 solutions
Answer 427361 by stanbon(57282) on 2012-12-12 09:44:19 (Show Source):
You can put this solution on YOUR website!solve the following equation log[9](5x-3)- log[3]2√x = 0
---
log9(5x-3) - [log9[2sqrt(x)]]/log9(3) = 0
-----
log9(5x-3) - [log9(2sqrt(x)]/(1/2) = 0
-----
log9(5x-3) - log9(4x) = 0
----
log[(5x-3)/4x = 0
---
(5x-3)/4x = 1
----
5x-3 = 4x
x = 3
---------------
Cheers,
Stan H.
===========
|
Exponential-and-logarithmic-functions/691729: a sample of a radioactive substance was put in storage 6 years ago. It's half-life is 5.5 years. If 8.3 gm of the original substance remains in the sample now, what is the initial quantity of the substance (accurate to two significant figures)?
1 solutions
Answer 427353 by stanbon(57282) on 2012-12-12 08:56:54 (Show Source):
You can put this solution on YOUR website!a sample of a radioactive substance was put in storage 6 years ago. It's half-life is 5.5 years. If 8.3 gm of the original substance remains in the sample now, what is the initial quantity of the substance (accurate to two significant figures)?
-------
8.3 = A(1/2)^(6/5.5)
----
A = 8.3/(1/2)^(6/5.5)
---
A = 3.90 years
=================
Cheers,
Stan H.
===============
|
Money_Word_Problems/693308: Find the rate if the principal is $900, the time is 3 years, and the interest is $135.
1 solutions
Answer 427350 by stanbon(57282) on 2012-12-12 08:42:59 (Show Source):
You can put this solution on YOUR website!Find the rate if the principal is $900, the time is 3 years,
and the interest is $135.
---------------
I = Prt
135 = 900*r*3
----
r = 135/(2700)
----
r = 0.05 = 5%
================
Cheers,
Stan H.
================
|
Miscellaneous_Word_Problems/693303: Word problem: At Bake My Day, the owner decorates the day's cake orders three times as fast as her new assistant. If they can decorate all the cake orders working together in 75 min, how long would it take foreach of them to decorate the cakes working individually? Not sure how to set this up.
1 solutions
Answer 427349 by stanbon(57282) on 2012-12-12 08:36:06 (Show Source):
You can put this solution on YOUR website!Word problem: At Bake My Day, the owner decorates the day's cake orders three times as fast as her new assistant. If they can decorate all the cake orders working together in 75 min, how long would it take foreach of them to decorate the cakes working individually? Not sure how to set this up.
-----
Let the slower baker's time be 3x min/order ; rate = 1/(3x) order/min
The faster baker's time is x min/order ; rate = 1/x order/min
----
The together time is 75 min/order ; rate = 1/75 order/min
---------------------
Equation:
rate + rate = together rate
1/3x + 1/x = 1/75
Multiply thru by 75x to get
25 + 75 = x
x = 100 min (time for the faster baker alone)
3x = 300 min (time for the slower baker alone)
------------------
Cheers,
Stan H.
|
Linear-systems/693295: how many solutions the linear system has. this is for my algebra 2 class.
4x-2y=8
2x-y=7
1 solutions
Answer 427348 by stanbon(57282) on 2012-12-12 08:25:41 (Show Source):
You can put this solution on YOUR website!how many solutions the linear system has. this is for my algebra 2 class.
4x-2y=8
2x-y=7
-----
Find the slope of both equations:
y = 2x-4
y = 2x+7
----
Both have slope = 2 and they have different y-intercepts, so the lines are parallel.
Ans: No solutions
========================
cheers,
Stan H.
|
Linear-equations/693290: 300 apples r distributed equally among a certain no of stdudents had there been 10 more students each would have recd 1 apple less find number of students.
1 solutions
Answer 427347 by stanbon(57282) on 2012-12-12 08:21:40 (Show Source):
You can put this solution on YOUR website!300 apples r distributed equally among a certain no of stdudents had there been 10 more students each would have recd 1 apple less find number of students.
--------
Let the original # of students be "x";
300/x = k
300/(x+10) = k-1
------
Substitute for "k" and solve for "x":
---
300/(x+10) = (300/x)-1
----
300/(x+10) = (300-x)/x
----
300x = 300x-x^2+3000-10x
-------
-x^2-10x+3000 = 0
---
Positive solution:
x = 50 (original # of students)
==================================
Cheers,
Stan H.
======================
|
Travel_Word_Problems/693283: If the robbers rob into house somewhere, and leave that place at 3:15 a.m. on car with average speed of 65 Km/h..... Police runs after them at 4:05 a.m. with average speed of 79 km/h.... When will they catch the robbers???????
1 solutions
Answer 427346 by stanbon(57282) on 2012-12-12 08:03:25 (Show Source):
You can put this solution on YOUR website! If the robbers rob into house somewhere, and leave that place at 3:15 a.m. on car with average speed of 65 Km/h..... Police runs after them at 4:05 a.m. with average speed of 79 km/h.... When will they catch the robbers???????
------
Robber DATA:
rate = 65 km/h ; distance = x km ; time = x/65 hrs.
-----------------
Police DATA:
rate = 73 km/h ; distance = x km ; time = x/73 hrs
------
Equation:
robber time - police time = 5/6 hr
------
x/65 - x/73 = 5/6
-----
5*73x - 6*65x = 65*73*5
-----------------
8*5x = 65*73*5
x = 593 1/8 km
==================
Robber time: x/65 = 9 1/8 hr
3:15 + (9 1/8 hr) = 12:22.5 PM
-----------------------------------
Cheers,
Stan H.
|
Money_Word_Problems/693286: if a have $20,000.00 and it makes $4920.00 interest in a 12 month period what is the apr ( and is not compounded)
1 solutions
Answer 427344 by stanbon(57282) on 2012-12-12 07:50:36 (Show Source):
You can put this solution on YOUR website!if a have $20,000.00 and it makes $4920.00 interest in a 12 month period what is the apr
-----
I = Prt
4920 = 20000*r*1
-----
r = 4920/20,000
---
r = 0.246 = 24.6%
===================
Cheers,
Stan H.
===================
|
Linear-equations/693187: to solve this you can use any method for example multiplication with elimination method
using that method what is the answer to
3(x-y)=15
2x+y=7
thank you
1 solutions
Answer 427312 by stanbon(57282) on 2012-12-11 21:43:13 (Show Source):
You can put this solution on YOUR website!3(x-y)=15
2x+y=7
------
x-y = 5
2x+y = 7
----
Add to get:
3x = 12
x = 4
------
Solve for "y" using x-y = 5
---
4 -y = 5
y = -1
=============
Cheers,
Stan H.
================
|
Age_Word_Problems/693184: Tom is 3 years older than Mary and Jane is 5 years older than Tom. What is the average age?
1 solutions
Answer 427310 by stanbon(57282) on 2012-12-11 21:40:30 (Show Source):
You can put this solution on YOUR website!Tom is 3 years older than Mary and Jane is 5 years older than Tom. What is the average age?
------
Equations:
t = m+3
m = t + 5
j = t+5
-----
Average age = (t+m+j)/3 = (t + t-3 + t+5)/3 = (3t+3)/3 = t+1
----------------------
Cheers,
Stan H.
==========================
|
absolute-value/693181: write an equation of the line that passes through each pair of points (4,0) and (0,5)
1 solutions
Answer 427307 by stanbon(57282) on 2012-12-11 21:35:25 (Show Source):
You can put this solution on YOUR website!write an equation of the line that passes through each pair of points (4,0) and (0,5)
-----
x/4 + y/5 = 1
----
5x + 4y = 20
y = (-5/4)x + 5
==================
cheers,
stan H.
|
Probability-and-statistics/693174: Starting with the data values 70 and 100, add three data values to the sample so that the mean is 76, the median is 83, and the mode is 83. Please show all of your work.
1 solutions
Answer 427300 by stanbon(57282) on 2012-12-11 21:18:32 (Show Source):
You can put this solution on YOUR website!Starting with the data values 70 and 100, add three data values to the sample so that the mean is 76, the median is 83, and the mode is 83. Please show all of your work.
----
If the mode is 83, there must be at least 2 data values of 83,
---
So you have 70,100,83,83,and x
-----------------------------------
mean = (70+100+2*83+x)/5 = 76
-----
336+x = 380
x = 44
----
The Data set is 44,70,83,83,100
=================================
Cheers,
Stan H.
|
test/693170: Sarah and Rachel are sisters. They leave a park at the same time on their bycicle and ride home along the same bycicle path. Sarah is in a hurry, so she cycles at 15km/h. Rachel has time to spare, so she cycles at 11km/h. Sarah gets home at 12 min before Rachel. How long did Sarah take to ride home from the park?
1 solutions
Answer 427297 by stanbon(57282) on 2012-12-11 21:11:43 (Show Source):
You can put this solution on YOUR website!Sarah and Rachel are sisters. They leave a park at the same time on their bycicle and ride home along the same bycicle path. Sarah is in a hurry, so she cycles at 15km/h. Rachel has time to spare, so she cycles at 11km/h. Sarah gets home at 12 min before Rachel. How long did Sarah take to ride home from the park?
-------
Sarah DATA:
rate = 15 km/h ; distance = x km ; time = x/15 hrs
----
Rachel DATA:
rate = 11 km/h ; distance = x km ; time = x/11 hrs
-----
Equation:
rachel time - sarah time = 12 min = 1/5 hr
-----
x/11 - x/15 = 1/5
-----
75x - 55x = 11*15
20x = 156
x = 7.8 km
--------
Sarah time = x/15 = 7.8/15 = 0.52 hr = 31.2 min = 31min 12sec
=================================================================
Cheers,
Stan H.
==============
|
Percentage-and-ratio-word-problems/693171: how do you answer the question?
if 50 students answered the survey, how many chose apple juice?
grape juice-35%
orange juice- 15%
fruit punch-25%
apple juice-25%
1 solutions
Answer 427296 by stanbon(57282) on 2012-12-11 21:04:56 (Show Source):
You can put this solution on YOUR website!how do you answer the question?
if 50 students answered the survey, how many chose apple juice?
grape juice-35%
orange juice- 15%
fruit punch-25%
apple juice-25%
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ans: 0.25*50 = 12.5
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Rounding up you get 13 students
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Cheers,
Stan H.
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Age_Word_Problems/693151: Mr. Munch is twice as old as his daughter. In two years, he will be four times as old as his daughter was fifteen years ago. How old are they now?
1 solutions
Answer 427282 by stanbon(57282) on 2012-12-11 20:32:24 (Show Source):
You can put this solution on YOUR website!Mr. Munch is twice as old as his daughter. In two years, he will be four times as old as his daughter was fifteen years ago. How old are they now?
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Equations:
m = 2d
m+2 = 4(d-15))
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Substitute for "m" and solve for "d"
2d+2 = 4d-60
2d = 62
daughter = 31 yrs
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Solve for "m":
m = 2d
Mr. Munch = 2*31 = 62 yrs
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Cheers,
Stan H.
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Exponential-and-logarithmic-functions/691819: How long will it take for the population of a certain country to double if its annual growth rate is 5%? Round to the nearest year.
1 solutions
Answer 427276 by stanbon(57282) on 2012-12-11 20:26:38 (Show Source):
You can put this solution on YOUR website! How long will it take for the population of a certain country to double if its annual growth rate is 5%? Round to the nearest year.
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Solve:
2P = P(1.05)^x
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(1.05)^x = 2
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x*log(1.05) = log(2)
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x = log(2)/log(1.05)
x = 14 when rounded down to the nearest year
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Cheers,
Stan H.
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