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Equations/44573: Sally bought three chocolate bars and a pack of gum and paid $1.75. Jake bought two chocolate bars and four packs of gum and paid $2.00. Find the cost of chocolate bar and the cost of a pack of gum.
1 solutions

Answer 29471 by Nate(3500) on 2006-07-02 00:20:07 (Show Source):

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Cost of Chocolate Bar: b
Cost of Pack of Gum: p
Equation:
3b+%2B+p+=+1.75

Combine:

Plug:

Bar of Chocolate: $0.50
Pack of Gum: $0.25

Equations/44576: Angus invested $18,000, part at 3% and part at 5%. If the total interest at the end of the year is $660, how much did he invest at each rate?
1 solutions

Answer 29470 by Nate(3500) on 2006-07-02 00:13:54 (Show Source):

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0.03%28x%29+%2B+0.05%2818000+-+x%29+=+660

$12,000 in 3%
$6,000 in 5%

logarithm/44584: This question is from textbook College Algebra
If a bank returned to us/me $15,000 with the bank compounding continously when using logarithms how long would we have to leave the money in the bank?
And how long will it take to double my money at 10% interest rate and continous compounding?
If a computer scientist needs a logarithm she uses a log to the base 2.How can I find the log of a number to any base,use a conversion formula but will use log210000 rounded to the hundredths place?
1 solutions

Answer 29469 by Nate(3500) on 2006-07-02 00:08:20 (Show Source):

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For your first questions, I do not know the initial amount placed in the bank.
If a computer scientist needs a logarithm she uses a log to the base 2.How can I find the log of a number to any base,use a conversion formula but will use log210000 rounded to the hundredths place?
log%282%2C10000%29

log%2810%2C10000%29+=+log%2810%2C2%5Ex%29

log%2810%2C10000%29+=+x%2Alog%2810%2C2%29

log%2810%2C10000%29%2Flog%2810%2C2%29+=+x

About 13.29

real-numbers/44588: I need help with this question:
Helen has 1/5 of her portfolio in US stocks, 1/8 in European stocks, and 1/10 in Japanese stocks. The remainder is in municipal bonds. What FRACTION of of her portfolio is in Municipal bonds? What PERCENT is invested in municipal bonds?
1 solutions

Answer 29468 by Nate(3500) on 2006-07-02 00:02:53 (Show Source):

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1 - 1/5 - 1/8 - 1/10
40/40 - 8/40 - 5/40 - 4/40
(40 - 8 - 5 - 4)/40
23/40 in municipal bonds
23/40 = 0.575 = 57.5%

Graphs/44559: the national cost C in billions of dollars for
dental service can be modeled by the linear equation
C=2.85n+30.52
where n is the number of years since 1990
A)Find and interpret the C-intercept for the line
B)Find and interpret teh n-intercept for the line
C)Graph teh line for n ranging from 0 through 20
D If this trenad continues, tehn in what year will the
cost of dental services reach 100 billion?
1 solutions

Answer 29463 by Nate(3500) on 2006-07-01 19:43:40 (Show Source):

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A) Find and interpret the C-intercept for the line
C = 2.85n + 30.52
C = 2.85(0) + 30.52
C = 30.52
At zero years, the C-intercept is at $30.52 billion.
B)Find and interpret the n-intercept for the line
C = 2.85n + 30.52
0 = 2.85n + 30.52
-30.52 = 2.85n
-3052/285 = n
-10 202/285 = n
Before 1990, the cost was zero.
C)Graph the line for n ranging from 0 through 20
+graph%28+800%2C+600%2C+-2%2C+20%2C+-5%2C+90%2C+2.85x+%2B+30.52+%29+

+graph%28+800%2C+600%2C+-2%2C+20%2C+-5%2C+90%2C+2.85x+%2B+30.52+%29+

D If this trend continues, then in what year will the
cost of dental services reach 100 billion?
C = 2.85n + 30.52
100 = 2.85n + 30.52
69.48 = 2.85n
About 24 years later:
1990 + 24
Year: 2014

Graphs/44558: graph the following inequality?
y-x>-3

1 solutions

Answer 29462 by Nate(3500) on 2006-07-01 19:34:49 (Show Source):

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Just Did This One

Graphs/44560: Graph the following inequality.
y-x>-3

1 solutions

Answer 29461 by Nate(3500) on 2006-07-01 19:34:23 (Show Source):

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y - x > -3
y > x - 3
Since 'y' is greater than, you would shade above the dotted line.
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x-3+%29+

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x-3+%29+

Equations/44561:

1 solutions

Answer 29460 by Nate(3500) on 2006-07-01 19:33:00 (Show Source):

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(C) and (D) have the same slope of two.
Answer: (A)

Volume/44562: What is the measurement of the height if the radius of the cylinder is 2 centimeters?
1 solutions

Answer 29459 by Nate(3500) on 2006-07-01 19:32:12 (Show Source):

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Not enough information is given. What is the volume, or what is the area?

Distributive-associative-commutative-properties/44565: Can someone help me with this problem?
I need to WRITE 30,672 in expanded form.
Thanks,
sher
1 solutions

Answer 29458 by Nate(3500) on 2006-07-01 19:31:18 (Show Source):

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30,672
2 * 15,336
2 * 2 * 7668
2 * 2 * 2 * 3834
2 * 2 * 2 * 2 * 1917
2 * 2 * 2 * 2 * 3 * 639
2 * 2 * 2 * 2 * 3 * 3 * 213
Answer: 2 * 2 * 2 * 2 * 3 * 3 * 3 * 71
2^4 * 3^3 * 71

Miscellaneous_Word_Problems/44428: One day, the temperature at 8:00 A.M. was 41°F, and by 1:00 P.M. the temperature was 61°F. What was the hourly rate of temperature change?
A) 6°F/h B) 3°F/h C) 4°F/h D) 5°F/h

1 solutions

Answer 29443 by Nate(3500) on 2006-07-01 16:49:16 (Show Source):

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Already Did This One
(C)

Graphs/44444:

thank u
1 solutions

Answer 29442 by Nate(3500) on 2006-07-01 16:47:03 (Show Source):

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Slope: 3
Y-Intercept: (0,1)
Equation: y = 3x + 1
(C)

Equations/44446: Given f(x) = 5x2 – 3x + 1, find f(–2).

Im getting -13
Am I correct?

1 solutions

Answer 29441 by Nate(3500) on 2006-07-01 16:45:27 (Show Source):

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Given f(x) = 5x2 – 3x + 1, find f(–2).
f(x) = 5x^2 – 3x + 1
f(-2) = 5(-2)^2 – 3(-2) + 1
f(-2) = 5(4) + 6 + 1
f(-2) = 27

Equations/44461: Find the y-intercept.
–x + 3y = 15
A) (5, 0) B) (0, –15) C) (0, 5) D) (–15, 0)

1 solutions

Answer 29440 by Nate(3500) on 2006-07-01 16:42:42 (Show Source):

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Find the y-intercept.
–x + 3y = 15
0 + 3y = 15
y = 5
y-intercept: (0,5)
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F3%29x+%2B+5+%29+

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F3%29x+%2B+5+%29+

Exponents/44464: Find the slope and y-intercept.
x = –8
A) Slope: undefined; y-intercept: (0, –8) C) Slope: undefined; y-intercept: none
B) Slope: 0; y-intercept: none D) Slope: 0; y-intercept: (0, –8)

1 solutions

Answer 29439 by Nate(3500) on 2006-07-01 16:41:08 (Show Source):

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Just Did This One
Answer: (C)

Geometry_Word_Problems/44466: Find the slope and y-intercept.
x = –8
A) Slope: undefined; y-intercept: (0, –8) C) Slope: undefined; y-intercept: none
B) Slope: 0; y-intercept: none D) Slope: 0; y-intercept: (0, –8)

1 solutions

Answer 29438 by Nate(3500) on 2006-07-01 16:40:23 (Show Source):

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Just Did This One
Answer: (C)

Geometry_Word_Problems/44465: Find the slope and y-intercept.
x = –8
A) Slope: undefined; y-intercept: (0, –8) C) Slope: undefined; y-intercept: none
B) Slope: 0; y-intercept: none D) Slope: 0; y-intercept: (0, –8)

1 solutions

Answer 29437 by Nate(3500) on 2006-07-01 16:39:29 (Show Source):

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x = –8
This is vertical line, so the slope is undefined. Also, the line never touches the y-axis, so there is no y-intercept.
(C)

Graphs/44547: solve graphically
a+1=b
b=5-2a
1 solutions

Answer 29436 by Nate(3500) on 2006-07-01 16:36:49 (Show Source):

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'a' determines x-values
'b' determines y-values
We Have:
a + 1 = b
and
b = 5 - 2a
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x+%2B+1%2C+-2x+%2B+5%29+

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x+%2B+1%2C+-2x+%2B+5%29+

Answer: (4/3,7/3)

Graphs/44548: solve graphically
y=-x-1
4x-3y=24
1 solutions

Answer 29435 by Nate(3500) on 2006-07-01 16:32:15 (Show Source):

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y = - x - 1
and
4x - 3y = 24
-3y = -4x + 24
y = (4/3)x - 8
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x+-+1%2C+4x%2F3+-+8+%29+

Answer: (3,-4)

Numeric_Fractions/44540: Can someone help me with this problem?
I nned to add and write the answer in simplest form:
3/11 + 9/11 + 1/11

is it (A) 2 1/11
(B) 13/33
(C) 2 7/13
(D) 1 2/11
Thank you,
Sher
1 solutions

Answer 29434 by Nate(3500) on 2006-07-01 16:29:20 (Show Source):

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3/11 + 9/11 + 1/11
(3 + 9 + 1)/11
(13/11)
1 (2/11)
(D)

Equations/44546: elimination method
3(a-b)=15
4a=b+1
1 solutions

Answer 29433 by Nate(3500) on 2006-07-01 16:27:17 (Show Source):

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3(a - b) = 15
3a - 3b = 15
+
4a = b + 1
4a - b = 1
-12a + 3b = -3
=
-9a = 12
a = -4/3
so:
4a = b + 1
4(-4/3) = b + 1
(-16/3) = b + 1
(-19/3) = b
Check:
'a' are x-values
'b' are y-values
Answer: (-1 1/3, -6 1/3)
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x+-+5%2C+4x+-+1+%29+

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x+-+5%2C+4x+-+1+%29+

Equations/44463: Given f(x) = 5x2 – 3x + 1, find f(–2).
A) 15 B) 27 C) –13 D) –25

1 solutions

Answer 29432 by Nate(3500) on 2006-07-01 16:19:30 (Show Source):

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Given f(x) = 5x^2 – 3x + 1, find f(–2).
f(-2) = 5(-2)^2 – 3(-2) + 1
f(-2) = 5(4) + 6 + 1
f(-2) = 20 + 6 + 1
f(-2) = 27
(B)

Equations/44448:

1 solutions

Answer 29431 by Nate(3500) on 2006-07-01 16:17:48 (Show Source):

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Perpendicular to Slope: -3
Which is: 1/3
Use point-slope form:
y+-+y1+=+m%28x+-+x1%29

(C)

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-3x+%2B+1%2C+x%2F3+%2B+5+%29+

Polynomials-and-rational-expressions/44533: This question is from textbook
If f(x)=x(x+3)(x-1), use interval notation to give all values of x where f(x)>0.
Thanks for your time.
1 solutions

Answer 29429 by Nate(3500) on 2006-07-01 16:13:35 (Show Source):

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f(x) = x(x+3)(x-1)
Look at this ---->
0 < x(x + 3)(x - 1)
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E3+%2B+2x%5E2+-+3x+%29+

Answer: (-3,0) and (1,+infinity)

percentage/44542: Can someone help me with this problem?
I need to write 0.06 as a percent.
Thanks,
Sher
1 solutions

Answer 29428 by Nate(3500) on 2006-07-01 16:04:06 (Show Source):

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100% is 1.0
60% is 0.6
1% is 0.01
Move the decimal two units to the left.
0.01 is 1%
0.6 is 60%
1.0 is 100%
Move the decimal two units to the right.
So:
0.06 is 6%

Travel_Word_Problems/44544: A car leaves a town at 40 miles per hour. Two hours later a second car leaves the town traveling the same route and overtakes the first car in 5 hours and 20 minutes. how fast was the second car traveling?
1 solutions

Answer 29427 by Nate(3500) on 2006-07-01 16:02:01 (Show Source):

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Since the first car was given a two-hour head start, it traveled 2(40 mi/h) = 80 miles ....
First Car's Rate: 40t + 80
Second Car's Rate: xt
The different of the two car's traveled distance is equal to zero:
40t + 80 - xt = 0
40(16/3) + 80 - (16/3)x = 0
-(16/3)x = -240/3 - 640/3
-(16/3)x = -880/3
x = (880/3)(3/16) = 55
The second car was traveling 55 miles per hour.
Check:
First Car: y = 40x + 80
Second Car: y = 55x
Where 'y' is the distance and 'x' is the time:
-y + 40x = -80
+
y - 55x = 0
-15x = -80
x = 16/3
5 hours and 20 minutes

Miscellaneous_Word_Problems/44468: One day, the temperature at 8:00 A.M. was 41°F, and by 1:00 P.M. the temperature was 61°F. What was the hourly rate of temperature change?
A) 6°F/h B) 3°F/h C) 4°F/h D) 5°F/h

1 solutions

Answer 29369 by Nate(3500) on 2006-06-30 21:42:09 (Show Source):

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(change of temp)/(change of time)
(61 - 41)/(13 - 8)
(20)/(5)
4°F
(C)

Graphs/44487: I am working a lesson involving inequalities and am a little stuck. I must graph the problems and describe them.
-6 < x + 3 < 6
Thanks
1 solutions

Answer 29368 by Nate(3500) on 2006-06-30 21:38:03 (Show Source):

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-6 < x + 3 < 6
-6 - 3 < x + 3 - 3 < 6 - 3
-9 < x < 3
<---(-9)======(3)--->

Equations/44364: substitution method
m-2n=16
4m+n=1
1 solutions

Answer 29295 by Nate(3500) on 2006-06-29 20:19:23 (Show Source):

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m+-+2n+=+16

Plug:

<------------------------------------>
y-axis: 'm' values
x-axis: 'n' values

Equations/44351: Solve each problem. Use your choice of methods.

x + y = -4
4x + y = -13
y + 3z = -10
1 solutions

Answer 29294 by Nate(3500) on 2006-06-29 20:10:08 (Show Source):

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x + y = -4
Means:
y = -x - 4
Plug:
4x + y = -13
4x - x - 4 = -13
3x = -9
x = -3
Plug:
x + y = -4
-3 + y = -4
y = -1
Plug:
y + 3z = -10
-1 + 3z = -10
3z = -9
z = -3
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x+-+4%2C+-4x+-+13++%29+

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x+-+4%2C+-4x+-+13++%29+

Number-Line/44357: Can someone help me with this problem?
I need to write the following number in expanded form:
684
Thank you,
Ashley
1 solutions

Answer 29293 by Nate(3500) on 2006-06-29 20:05:24 (Show Source):

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684
3 * 228 = 684
3 * 3 * 76 = 684
3 * 3 * 2 * 38 = 684
3 * 3 * 2 * 2 * 19 = 684

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Recent problems solved by 'Nate'