wyatt has (2x-1) one-dollar bills and (4x + 2) five dollar bills. Susan has 3 x dollars more than Wyatt. Find the total amount o
2 answers:
Answer:
- Wyatt has 22x + 9 dollars
- Wyatt can buy
pens
- Susan has 901 dollars
Step-by-step explanation:
<em>Topic: Algebra</em>
Given:
<u>Wyatt</u>
<em>: 1 dollar bills; 2x - 1</em>
<em>: 5 dollar bills; 4x + 2</em>
Susan has 3x dollars more than Wyatt
- Find the total amount of money that Wyatt has in terms of x.
This is done by multiplying the dollar bill by the respective amount
Amount = (2x - 1) * 1 dollar bills + (4x + 2) * 5 dollar bills
Amount = 2x - 1 + 20x + 10 --- Collect like terms
Amount = 2x + 20x - 1 + 10
Amount = 22x + 9 dollars
Wyatt has 22x + 9 dollars
- Find the number of pens that Wyatt can buy if each pen costs 50 cents.
Given that 1 dollar = 100 cents
And each pen costs 50 cents.
First, we convert the amount Wyatt has to cent.
22x + 9 dollars = (22x + 9) * 100 cents
22x + 9 dollars = 2200x + 900 cents
If 50 cents can buy a pen,
Then 2200x + 900 cents can buy
= pens
pens
- If x = 21, find how much money Susan will have now if Wyatt gives her had the number of five dollar bills that he has.
If Wyatt has a total of 22x + 9 dollars
Susan has 3x + 22x + 9 = 25x + 9 dollars
Number of 5 dollar bills wit Wyatt = <em>5 * (4x + 2)</em>
So, Susan has a total of <em>22x + 9 + 5 (4x + 2)</em>
Total = 22x + 9 + 20x + 10
Total = 42x + 19
if x = 21
Then,
Total = 42(21) + 19
Total =882+19
Total = 901 dollars
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Answer:
Therefore the 95% confidence interval is (25,707.480 < E < 26,744.920)
Step-by-step explanation:
n = 77
mean u = 26,226.2 bushels per acre
standard deviation s = 2,322.32
let E = true mean
let A = test statistic
Find 95% Confidence Interval
so
let A = (u - E) * ( / s) be the test statistic
we want P( average_l < A < average_u ) = 95%
look for lower 2.5% and the upper 97.5% Because I think this is a 2-tail test
average_l = -1.96 which corresponds to the 2.5%
average_u = 1.96
P( -1.96 < A < 1.96) = 95%
P( -1.96 < (u - E) * ( / s) < 1.96) = 95%
Solve for the true mean E ok
E < u + 1.96* (s / )
from -1.96 < (u - E) * ( / s)
E < 26,226.2 + 1.96*( 2,322.32 / )
E < 26,226.2 + 1.96*( 2,322.32 / )
E < 26,226.2 + 518.7197348105429466
upper bound is 26,744.9197
or
u - 1.96* (s / ) < E
26,226.2 - 518.7197348105429466 < E
25,707.48026519 < E
lower bound is 25,707.48026519
Therefore the 95% confidence interval is (25,707.480 < E < 26,744.920)
Answer:
Step-by-step explanation:
Given:
Right ∆ABC
AB = 61
BC = 60
AC = 11
Required:
Value of tan A in radical form
SOLUTION:
Opposite = 60
Adjacent = 11
Answer:
a)
Highest (-3,-3)
Lowest (2,2)
b)
Farthest (-3,-3)
Closest (2,2)
Step-by-step explanation:
To solve this problem we will be using Lagrange multipliers.
a)
Let us find out first the restriction, which is the projection of the intersection on the XY-plane.
From x+y+z=12 we get z=12-x-y and replace this in the equation of the paraboloid:
completing the squares:
and we want the maximum and minimum of the paraboloid when (x,y) varies on the circumference we just found. That is, we want the maximum and minimum of
subject to the constraint
Now we have
Let be the Lagrange multiplier.
The maximum and minimum must occur at points where
that is,
we can assume (x,y)≠ (-1/2, -1/2) since that point is not in the restriction, so
Replacing in the constraint
from this we get
<em>x=-1/2 + 5/2 = 2 or x = -1/2 - 5/2 = -3 </em>
<em> </em>
and the candidates for maximum and minimum are (2,2) and (-3,-3).
Replacing these values in f, we see that
f(-3,-3) = 9+9 = 18 is the maximum and
f(2,2) = 4+4 = 8 is the minimum
b)
Since the square of the distance from any given point (x,y) on the paraboloid to (0,0) is f(x,y) itself, the maximum and minimum of the distance are reached at the points we just found.
We have then,
(-3,-3) is the farthest from the origin
(2,2) is the closest to the origin.