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romanna [79]
3 years ago
5

Use the counting principle to determine the number of elements in the sample space. The possible ways to complete a multiple-cho

ice test consisting of 16 questions, with each question having four possible answers (a, b, c, or d).
Mathematics
1 answer:
nadezda [96]3 years ago
3 0

Answer:

The correct answer is 4294967296 possible ways to complete such a test.

Step-by-step explanation:

Step 1

The first step is to define the fundamental principle of counting. The fundamental principle of counting states that if a process can be carried out in n steps, where there are n_1  ways to complete the first step, n_2 ways to complete the second step, n_3, and n_k ways to complete the k^{th} step, this process can be carried out in  n_1\times n_2\times n_3\times ...\times n_k ways.

Step 2

We use the fundamental principle of counting with n=4 for a total of k=16 steps.  This test can be carried out in 4^{16}=4294967296 ways. This comes from multiplying 4 by itself 16 times.

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X =x=x, equals <br> ^\circ <br> ∘<br> degrees
Andrej [43]

Step-by-step explanation:

x = 145°

we don't even need the upper parallel line with the 35° angle.

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3 0
2 years ago
Which property justifies the procedure used to eliminate fractions and decimals from equations?
igor_vitrenko [27]
By multiplying both sides of an equation by a number, you can eliminate all decimals and fractions, so the answer is C.
4 0
3 years ago
1) Q: A: If 5 + x = 12, and you add -5 to the left side of equation, what should you add to right side of equation
san4es73 [151]

You can "add" like you say or you could just call it subtracting. If you subtract 5 from 5 you still get zero.  Then on the right side, you would do the same. You would subtract 5 from 12 getting x, which is 7.

If you added you would still get the same answers but it is easier to say just subtract. Anything you do to the left, do to the right.

Hope this helps :)

3 0
3 years ago
Read 2 more answers
A metal beam was brought from the outside cold into a machine shop where the temperature was held at 65degreesF. After 5 ​min, t
ivolga24 [154]

Answer:

The beam initial temperature is 5 °F.

Step-by-step explanation:

If T(t) is the temperature of the beam after t minutes, then we know, by Newton’s Law of Cooling, that

T(t)=T_a+(T_0-T_a)e^{-kt}

where T_a is the ambient temperature, T_0 is the initial temperature, t is the time and k is a constant yet to be determined.

The goal is to determine the initial temperature of the beam, which is to say T_0

We know that the ambient temperature is T_a=65, so

T(t)=65+(T_0-65)e^{-kt}

We also know that when t=5 \:min the temperature is T(5)=35 and when t=10 \:min the temperature is T(10)=50 which gives:

T(5)=65+(T_0-65)e^{k5}\\35=65+(T_0-65)e^{-k5}

T(10)=65+(T_0-65)e^{k10}\\50=65+(T_0-65)e^{-k10}

Rearranging,

35=65+(T_0-65)e^{-k5}\\35-65=(T_0-65)e^{-k5}\\-30=(T_0-65)e^{-k5}

50=65+(T_0-65)e^{-k10}\\50-65=(T_0-65)e^{-k10}\\-15=(T_0-65)e^{-k10}

If we divide these two equations we get

\frac{-30}{-15}=\frac{(T_0-65)e^{-k5}}{(T_0-65)e^{-k10}}

\frac{-30}{-15}=\frac{e^{-k5}}{e^{-k10}}\\2=e^{5k}\\\ln \left(2\right)=\ln \left(e^{5k}\right)\\\ln \left(2\right)=5k\ln \left(e\right)\\\ln \left(2\right)=5k\\k=\frac{\ln \left(2\right)}{5}

Now, that we know the value of k we can use it to find the initial temperature of the beam,

35=65+(T_0-65)e^{-(\frac{\ln \left(2\right)}{5})5}\\\\65+\left(T_0-65\right)e^{-\left(\frac{\ln \left(2\right)}{5}\right)\cdot \:5}=35\\\\65+\frac{T_0-65}{e^{\ln \left(2\right)}}=35\\\\\frac{T_0-65}{e^{\ln \left(2\right)}}=-30\\\\\frac{\left(T_0-65\right)e^{\ln \left(2\right)}}{e^{\ln \left(2\right)}}=\left(-30\right)e^{\ln \left(2\right)}\\\\T_0=5

so the beam started out at 5 °F.

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3 years ago
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koban [17]
So 20% of $1,080 is 216.

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