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3 years ago

15

Melissa has been given a list of 3 bands and asked to place a vote. Her vote must have the names of her favorite and second favo

rite bands from the list. How many different votes are possible?

1 answer:

Minchanka [31]3 years ago

7 0

3
Brand 1 and 3
Brand 1 and 2
Brand 2 and 3

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A cup of coffee contains about 100 mg of caffeine. Caffeine is metabolized and leaves the body at a continuous rate of about 12%

Mamont248 [21]

Answer:

a. $A = C_{0}(1-x)^t\\x: percentage\ of \ caffeine\ metabolized\\$

b. $\frac{dA}{dt}= -11.25 \frac{mg}{h}$

Step-by-step explanation:

First, we need tot find a general expression for the amount of caffeine remaining in the body after certain time. As the problem states that every hour x percent of caffeine leaves the body, we must substract that percentage from the initial quantity of caffeine, by each hour passing. That expression would be:

$A= C_{0}(1-x)^t\\t: time \ in \ hours\\x: percentage \ of \ caffeine\ metabolized\\$

Then, to find the amount of caffeine metabolized per hour, we need to differentiate the previous equation. Following the differentiation rules we get:

$\frac{dA}{dt} =C_{0}(1-x)^t \ln (1-x)\\\frac{dA}{dt} =100*0.88\ln(0.88)\\\frac{dA}{dt} =-11.25 \frac{mg}{h}$

The rate is negative as it represents the amount of caffeine leaving the body at certain time.

3 0

3 years ago

#12 with explanation please

4vir4ik [10]

Answer:

30.01 units

Step-by-step explanation:

<u>Given vertices WXYZ:</u>

W(-4,5), X(2,4), Y(3, -4), Z(-1, -6)

Perimeter is the sum of the side length.

<u>Use distance formula to find each side:</u>

WX = $\sqrt{(2+4)^2+(4-5)^2} =\sqrt{37}$ ≈ 6.08
XY = $\sqrt{(3-2)^2+(-4-4)^2} =\sqrt{65}$ ≈ 8.06
YZ = $\sqrt{(-1-3)^2+(-6+4)^2} =\sqrt{20}$ ≈ 4.47
WZ = $\sqrt{(-1+4)^2+(-6-5)^2} =\sqrt{130}$ $\sqrt{(-1+4)^2+(-6-5)^2}=\sqrt{130}$ ≈ 11.40

<u>Find perimeter:</u>

P = 6.08 + 8.06 + 4.47 + 11.40 = 30.01 units

7 0

2 years ago

There are 50 tickets in a raffle bag, and 10 of the tickets belong to Gary. A ticket is chosen at random, and the ticket owner's

Helga [31]

The probability of it happening once is 1/5, since 10/50 simplifies to 1/5. Because the ticket goes back in the bag, the probability stays constant at 1/5.

For it to happen twice, you multiply the probability of it happening once, twice.

1/5 • 1/5 = 1/25 probability of it being Gary's name twice in a row.

8 0

3 years ago

A 13- ounce package of pistachios costs $5.99. What is the unit rate?

statuscvo [17]

The unit rate is 2.17

5 0

2 years ago

(IF CORRECT WILL MARK BRAINLIEST!)Which of the following equations has exactly one real solution?

telo118 [61]

A
explanation:
2x+10=-6-30
8x+40=0
x=-5

5 0

2 years ago