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3 years ago

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In a science class each student must choose a lab project from a list of 15, write a paper on one of 6 topics, and give a presen

tation about one of 8 subjects. How many ways can students choose to do their assignments?

1 answer:

pishuonlain [190]3 years ago

3 0

Answer:

720 ways

Step-by-step explanation:

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NEED HELP ASAP PLEASE HELP

morpeh [17]

From point A to C, which is the length of the entire line, it's 3x + 1.
AB = 2x + 4
BC = 10

This means that AB + BC = AC

All you have to do is plug in the equations.

(2x + 4) + (10) = (3x + 1)
2x + 14 = 3x + 1
2x + 13 = 3x
13 = x

Now plug in the value of x (13) into the AC equation (3x + 1).
AC = 3(13) + 1
AC = 39 + 1
AC = 40

The answer is:
a. 40

6 0

3 years ago

Read 2 more answers

The sum of the three angles of a triangle is 180°. Two angles of a triangle measure 15 and 73. Of x is the third angle, set up a

Agata [3.3K]

Answer:

The measure of the third angle is 92°

Step-by-step explanation:

We first have to make an equation that represents this equality. To do it we simply have to add the values that give us with x and this will result in 180 °

15° + 73° + x = 180°

once we have the equation what we have to do is solve x, so we will pass all the terms that are adding to x by subtracting 180

x = 180° - 73° - 15°

now that we have cleared the x we only have to perform the indicated operation and we will obtain the value of x

x = 92°

The measure of the third angle is 92°

8 0

3 years ago

Please help !<br> I need the answers for #43 and #44

Vlad [161]

43. 9 + 10 + 13 + 13 = $45

45 - 1 = 44

44 x 4 = 176

176 + 8 = 184

184/4 = 46

46 tokens per person

44. a. 22 x 5 = 110

943/110 = 8.7

you will need 9 bookcases

b. 110 x 9 = 990

990 - 943 = 47

47 - 44 = 3

There will be 3 books on the third shelf.

4 0

3 years ago

A tank contains 60 kg of salt and 1000 L of water. Pure water enters a tank at the rate 6 L/min. The solution is mixed and drain

MissTica

Answer:

(a) 60 kg; (b) 21.6 kg; (c) 0 kg/L

Step-by-step explanation:

(a) Initial amount of salt in tank

The tank initially contains 60 kg of salt.

(b) Amount of salt after 4.5 h

$\text{Let A = mass of salt after t min}\\\text{and }r_{i} = \text{rate of salt coming into tank}\\\text{and }r_{0} =\text{rate of salt going out of tank}$

(i) Set up an expression for the rate of change of salt concentration.

$\dfrac{\text{d}A}{\text{d}t} = r_{i} - r_{o}\\\\\text{The fresh water is entering with no salt, so}\\ r_{i} = 0\\r_{o} = \dfrac{\text{3 L}}{\text{1 min}} \times \dfrac {A\text{ kg}}{\text{1000 L}} =\dfrac{3A}{1000}\text{ kg/min}\\\\\dfrac{\text{d}A}{\text{d}t} = -0.003A \text{ kg/min}$

(ii) Integrate the expression

$\dfrac{\text{d}A}{\text{d}t} = -0.003A\\\\\dfrac{\text{d}A}{A} = -0.003\text{d}t\\\\\int \dfrac{\text{d}A}{A} = -\int 0.003\text{d}t\\\\\ln A = -0.003t + C$

(iii) Find the constant of integration

$\ln A = -0.003t + C\\\text{At t = 0, A = 60 kg/1000 L = 0.060 kg/L} \\\ln (0.060) = -0.003\times0 + C\\C = \ln(0.060)$

(iv) Solve for A as a function of time.

$\text{The integrated rate expression is}\\\ln A = -0.003t + \ln(0.060)\\\text{Solve for } A\\A = 0.060e^{-0.003t}$

(v) Calculate the amount of salt after 4.5 h

a. Convert hours to minutes

$\text{Time} = \text{4.5 h} \times \dfrac{\text{60 min}}{\text{1h}} = \text{270 min}$

b.Calculate the concentration

$A = 0.060e^{-0.003t} = 0.060e^{-0.003\times270} = 0.060e^{-0.81} = 0.060 \times 0.445 = \text{0.0267 kg/L}$

c. Calculate the volume

The tank has been filling at 6 L/min and draining at 3 L/min, so it is filling at a net rate of 3 L/min.

The volume added in 4.5 h is

$\text{Volume added} = \text{270 min} \times \dfrac{\text{3 L}}{\text{1 min}} = \text{810 L}$

Total volume in tank = 1000 L + 810 L = 1810 L

d. Calculate the mass of salt in the tank

$\text{Mass of salt in tank } = \text{1810 L} \times \dfrac{\text{0.0267 kg}}{\text{1 L}} = \textbf{21.6 kg}$

(c) Concentration at infinite time

$\text{As t $\longrightarrow \, -\infty,\, e^{-\infty} \longrightarrow \, 0$, so A $\longrightarrow \, 0$.}$

This makes sense, because the salt is continuously being flushed out by the fresh water coming in.

The graph below shows how the concentration of salt varies with time.

3 0

3 years ago

the ages ( in years) of the 5 employees at a particular computer store are 32,23,21,38,26 . assuming that theses ages constitute

jolli1 [7]

Step 1: Add up the ages.

32+23+21+38+26=140.

Step 2: Divide answer by the amount of used numbers (5, in this case.)

140/5=28.

Your answer is 28.

3 0

2 years ago