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motikmotik
3 years ago
15

Barney and Betty break into a parking meter with $3.90 in dimes and quarters in it (legal disclaimer: don't do this) and agree t

hat Barney will get all the dimes, and Betty will get all the quarters. (Barley isn't terribly bright) Barney ends up with four more coins than Betty. How much money did each get(
Mathematics
1 answer:
Crank3 years ago
7 0

Answer:

Barney got 14 dimes and Betty got 10 quarters.

Step-by-step explanation:

Since there are only dimes and quarters in the parking meter, the total money must be equal to:

0.1*dimes + 0.25*quarters = 3.9

Since Barney got all the dimes and he has four more coins than Betty, then the number of dimes is:

dimes = quarters + 4

Applying the second expression on the first, we have:

0.1*(quarters + 4) + 0.25*quarters = 3.9\\0.1*quarters + 0.4 + 0.25*quarters = 3.9\\0.35*quarters = 3.9 - 0.4\\0.35*quarters = 3.5\\quarters = \frac{3.5}{0.35} = 10

dimes = quarters + 4 = 10 + 4 = 14

Barney got 14 dimes and Betty got 10 quarters.

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Answer:

4) Alternate  Interior angles 5) Parallel lines property.

Step-by-step explanation:

The question is asking us to Complete the statements to prove that line AB ⩭ to line CD and line BC ⩭ to line AD.

In statement 4 .∠CAB is congruent to ∠ACD as AB is parallel to CD  and ∠BCA  is congruent to∠CAD as AD is parallel to BC  and these are Alternate interior angles to the parallel lines .

In statement 5.m∠CAB =∠ACD and ∠BCA = ∠CAD as by property of parallel lines Alternate interior angles are equal.

6 0
3 years ago
Read 2 more answers
Make U the subject of the formula <br> D = ut + kt2
natali 33 [55]

Remark

I'm going to interpret this equation as

D = ut + kt²  The only difference is the 2.

Solution

Subtract kt² from both sides.

D - kt² = ut   Now divide by u on both sides.

\dfrac{D - kt^2}{t} = \dfrac{ut}{t}

The t's cancel out. on the right.  You are left with u on the right.

\dfrac{D - kt^2}{t} =\text{u}


6 0
3 years ago
A rectangular pyramid has a volume of 1,296 mc014-1.jpg, a height of 24 in., and a base length of 6 in. What is the width of its
stiks02 [169]
V=L X W X H

1,296=6 x w x 24
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3 0
3 years ago
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You have just opened a new nightclub, Russ' Techno Pitstop, but are unsure of how high to set the cover charge (entrance fee). O
Neko [114]

Answer:

a)q(p)=-15p+ +300

b)R(p)=-15p²+300p

c)C(p)=-30p+1600

d.1)P(p)=-15p²+330p-1600

d.2)p=$11

Step-by-step explanation:

(a).Before getting started, we are going to consider  the cartesian plane, where x-axis corresponds to the cover charge and y-axis corresponds to number of guests per night . There, we will locate the following coordinates according to the previous information:

(9,165)  (10,150).

Remember that  the slope-intercept form of the  linear equation is y=mx+b where m is the slope and b  is te intercept.

The slope can be calculated  by the next formula:

m=\frac{y2-y1}{x2-x1}

In this case we will assign  (9,165) as the first coordinate and (10,150) as the second one. The order does not matter. At the end we get the same value for m.

Therefore:

m=\frac{150-165}{10-9} = -15

Now, we have the slope and two poitns. According to this, and taking into account that  point-slope form of the equation of a line is y-y1=m(x-x1),   find a linear demand equation.

Any of two coordintates can be selected. In this case we will select the second one.

y-150=-15(x-10)   equation 1

Solve equation 1 for y

y=-15x+150+150

y=-15x+300

Above we had defined x as cover charge (p) and y as number of guests (q). Thus, rewrite equation 1.

q(p)=-15p+ +300.  

it equation shows the number of guests per night as a function of the cover charge,

(b). The nightly revenue can be calculated multplying the price of the cover charge by  the number of guests. So, we just have to multiply the equation 1 by p.

p*q(p)=p*(-15p +300)

R(p)=-15p²+300p   equation 2

(c) To get the cost function of the nightclub  we just have to multiply the cost of the two non-alcoholic drinks   by the number of the guests ( equation 1) and add to it  nightly overheads.

C(p)=2*(-15p+300)+1000

C(p)= -30p+600+1000

C(p)=-30p+1600  equation 3

(d) In order to find the profit in terms of the cover charge we will  subtract nightly costs ( equation 3) from nightly revenue (equation 2)

P(p)=R(p)-C(p)

P(p)=-15p²+300p - (-30p+1600)

P(p)=-15p²+300p+30p-1600

P(p)=-15p²+330p-1600

To determine that  the entrance fee we should charge for a maximum profit we are going to use the first derivative test (y'(x)=0) in order to find an extremum point.

Compute the first derivative of P(p)

P'(p)=-30p+330=0

30p=330

p=330/30

p= $11

The entrance fee that we should charge for a maximum profit is p=$11 per guest.

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3 years ago
The cost of a home is finaced with a $120,000 30-year fixed rate mortage at 4.5%
almond37 [142]

Answer:

$162,000

Step-by-step explanation:

4.5 of 120,000 is 5400

multiply 5400 by 30 and you get your answer.

7 0
2 years ago
Read 2 more answers
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