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3 years ago

Devon has 100 dimes and quarters. If the total value of what he has is $21.40, how many of each coin type does he have?

Mathematics

2 answers:

timurjin [86]3 years ago

5 0

Answer:

4 dimes i think and 5.25 worth of quarters

Step-by-step explanation:

Alexandra [31]3 years ago

5 0

I think it’s 4 dimes with about 5.25 left

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Assuming that the equation defines x and y implicitly as differentiable functions xequals=f(t), yequals=g(t), find the slope o

Artist 52 [7]

Answer:

$\frac{-1}{18}$

Step-by-step explanation:

Given that x and y are implicitly as differentiable functions.

xequals=f(t), yequals=g(t),

$x^3+3t^2 =13,$

$2y^3-3t^2= 42$

we have to get value of x and y at t =2

$x^3+3(4) = 13\\x =1\\2y^3-12 = 42\\y^3 = 27\\y=3$

we have to find the slope of the curve at t=2

i.e. we have to find $\frac{dy}{dx}$

= $\frac{\frac{dy}{dt} }{\frac{dx}{dt} }$ at t=2

$x^3+3t^2 =13\\3x^2 \frac{dx}{dt} +6t = 0\\$ $2y^3-3t^2= 42\\6y^2 \frac{dy}{dt} -6t = 0\\$

Substitute the values of x and y and also t in these equations to get

$3(1)^2 \frac{dx}{dt} +6(2) = 0\\\frac{dx}{dt} =-4\\6(3)^2 \frac{dy}{dt} -6(2)= 0\\\frac{dy}{dt}=\frac{2}{9}$

Slope = $\frac{2/9}{-4}=\frac{-1}{18}$

5 0

3 years ago

A solid figure that has two congruent polygons as as bases and lateral faces that are rectangles

Lana71 [14]

A solid figure that has two congruent polygons as bases and lateral faces are rectangles are called rectangular prism because it has a base, and lateral faced that represents a polyhedron.

6 0

3 years ago

Given the lengths of two sides of a triangle, find the range for the length of the third side (between what two numbers should t

kobusy [5.1K]

The shortest the third side can be is the difference of the other two sides:
.. 23.6 -11.5 = 12.1
The longest the third side can be is the sum of the other two sides:
.. 23.6 +11.5 = 35.1

12.1 < third side < 35.1

8 0

3 years ago

The function f(x) = (x - 4)(x - 2) is shown.

Kay [80]

Answer:

all real numbers greater can or equal to -1

Step-by-step explanation:

Given the function: f(x) = (x - 4)(x - 2)

=> its root: x =4 and x = 2

We convert the factored form into standard form: f(x) = $x^{2} -6x + 8$

As can be seen, the parameter a in the function is positive => the graph of it open up over its domain.

and then we convert the factored form into vertex form: f(x) = $(x-3)^{2}$ - 1

<=> when x =3 we have f(x) =1 and f(x) =-1 is the lowest point of the function

=> the range of the function: all real numbers greater can or equal to -1

Hope it will find you well.

8 0

3 years ago

A room has eight switches, each of which controls a different light. Initially, exactly five of the lights are on. Three people

aivan3 [116]

Answer:

The probability that 3 lights are on after the third person exited the room is 39/128

Step-by-step explanation:

In order for 6 switches to be on at the end, we need exactly 2 people turning on a switch and the other one turning one off. There are 3 possibilities:

The first two persons turn the switch in and the last one turns it off
The first and last person turn the switch in and the middle one tunrns it off
The first person turns the switch off and the 2 remaining turn the switch in

Note that after turning off one switch one more switch will be available to be switched in and one less will be available to be switch off. The contrary happens when someone turns in a switch.

Lets calculate the probability for the first scenario. The probability for the first person to turn the switch in is 3/8, because there are 3 lights off. For the second person, there will be only 2 lights off, thus, the probability for him or her to turn the switch in is only 2/8, leaving only 1 light off and 7 on. The third person will have, as a consecuence, a probability of 7/8 to turn off one of the 7 switches. This gives us a probability of 3/8 * 2/8 * 7/8 = 21/256 for the first scenario.

For the second scenario we will have a probability of 3/8 for the first person, a probability of 6/8 for the second one (he has to turn a switch off this time), and a probability, again, of 3/8 for the third one, giving us a probability of 3/8*6/8*3/8 = 27/256 for the second scenario.

For the third scenario, the first person has to turn off the switch, and it has a probability of 5/8 of doing so. The second person will have 4 switches to turn on, so it has a probability of 4/8 = 1/2, and the third person will have one switch less, thus, a probability of 3/8 of turning a switch on. Therefore, the probability of the third scenario is 5/8*1/2*3/8 = 15/128 = 30/256

By summing all the three disjoint scenarios, the probability that six lights are on is 21/256+27/256+30/256 = 78/256 = 39/128.

8 0

3 years ago