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astraxan [27]
3 years ago
7

Expand and simplify the equation 5(m+2)+9(n+4)

Mathematics
1 answer:
ale4655 [162]3 years ago
7 0

Answer: 5.4

Step-by-step explanation:3 (m-2)-5=8-2 (m-4)

Simplifying

3(m + -2) + -5 = 8 + -2(m + -4)

Reorder the terms:

3(-2 + m) + -5 = 8 + -2(m + -4)

(-2 * 3 + m * 3) + -5 = 8 + -2(m + -4)

(-6 + 3m) + -5 = 8 + -2(m + -4)

Reorder the terms:

-6 + -5 + 3m = 8 + -2(m + -4)

Combine like terms: -6 + -5 = -11

-11 + 3m = 8 + -2(m + -4)

Reorder the terms:

-11 + 3m = 8 + -2(-4 + m)

-11 + 3m = 8 + (-4 * -2 + m * -2)

-11 + 3m = 8 + (8 + -2m)

Combine like terms: 8 + 8 = 16

-11 + 3m = 16 + -2m

Solving

-11 + 3m = 16 + -2m

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add '2m' to each side of the equation.

-11 + 3m + 2m = 16 + -2m + 2m

Combine like terms: 3m + 2m = 5m

-11 + 5m = 16 + -2m + 2m

Combine like terms: -2m + 2m = 0

-11 + 5m = 16 + 0

-11 + 5m = 16

Add '11' to each side of the equation.

-11 + 11 + 5m = 16 + 11

Combine like terms: -11 + 11 = 0

0 + 5m = 16 + 11

5m = 16 + 11

Combine like terms: 16 + 11 = 27

5m = 27

Divide each side by '5'.

m = 5.4

Simplifying

m = 5.4

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I really need help please answer
belka [17]

Answer: Choice B) between 6:48 AM and 5:12 PM

=========================================================

Explanation:

I've seen this problem before, and the first part states that if the temperature is above 25 degrees C, then the air conditioner turns on to start cooling the castle.

We want to find values of t that satisfy f(t) > 25

This is the same as trying to solve f(t) - 25 > 0

So we have,

f(t) = 24 - 5\cos\left(\frac{\pi}{12}t\right)\\\\   f(t)-25 = 24 - 5\cos\left(\frac{\pi}{12}t\right)-25\\\\   f(t)-25 = -1 - 5\cos\left(\frac{\pi}{12}t\right)\\\\   f(t)-25 > 0\\\\ -1 - 5\cos\left(\frac{\pi}{12}t\right) > 0\\\\

To solve this inequality, we can graph using Desmos as I've done so below. See the attached image.

Note how I used x in place of t. This is because the graphing calculator graphs (x,y) coordinates.

Furthermore, note how I marked the two points (6.769, 0) and (17.231, 0)

Between these two points is when the curve is above the x axis, when f(t) > 25 is true. This is when the temperature is above 25 degrees C, and when the air conditioner is working.

When t = 6.769, this means that roughly 6.769 hours have passed since midnight which means we're somewhere between 6 am and 7 am. The only value that works from the answer choices is 6:48 AM.

Note how 0.769*60 = 46.14 is fairly close to 48. This error is likely due to how things are rounded.

Then focusing on the point  (17.231, 0) means that t = 17.231. So 17.231 hours have elapsed since midnight and we're now at roughly 1700 hours

1700 hours in military time = 17-12 = 5 pm

The time value t = 17.231 is between 5 pm and 6 pm. The only thing that works is 5:12 pm.

We can then note how 0.231*60 = 13.86 which is also probably due to rounding error (it's fairly close to 12 though).

--------------------------

In short, we found the function for f(t)-25 and graphed it as shown below. The two points (6.769, 0) and (17.231, 0) help us see when the AC is turned on, which is roughly between 6:48 AM and 5:12 PM. This seems like a reasonable time for the AC to be operational. Something like between 5:12 PM and 6:48 AM seems like a bad idea because the AC would be working mostly at night, instead of during the day.

Anything beyond t = 24 represents the next day, which is when the cycle starts all over again. So we only need to focus on the window from t = 0 to t = 24. Specifically, the portion of the f(t)-25 curve that is above the x axis.

8 0
3 years ago
What is the equation of a line that is parallel to the line y = 2x + 7 and passes through the point (–2, 4)? A. y = −12x + 3 B.
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Answer:

the answer to this question is x=21

Step-by-step explanation:

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A center for medical services reported that there were 295,000 appeals for hospitalization and other services. For this group, 4
pshichka [43]

Answer:

a) 0.0025 = 0.25% probability that none of the appeals will be successful.

b) 0.0207 = 2.07% probability that exactly one of the appeals will be successful.

c) 0.9768 = 97.68% probability that at least two of the appeals will be successful

Step-by-step explanation:

For each appeal, there are only two possible outcomes. Either it is succesful, or it is not. The probability of an appeal being succesful is independent of other appeals, so we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

45% of first-round appeals were successful.

This means that p = 0.45

Suppose 10 first-round appeals have just been received by a Medicare appeals office.

This means that n = 10

(a) Compute the probability that none of the appeals will be successful.

This is P(X = 0).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{10,0}.(0.45)^{0}.(0.55)^{10} = 0.0025

0.0025 = 0.25% probability that none of the appeals will be successful.

(b) Compute the probability that exactly one of the appeals will be successful.

This is P(X = 1).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 1) = C_{10,1}.(0.45)^{1}.(0.55)^{9} = 0.0207

0.0207 = 2.07% probability that exactly one of the appeals will be successful.

(c) What is the probability that at least two of the appeals will be successful

This is P(X \geq 2)

Either less than two appeals are succesful, or at least two are. The sum of the probabilities of these events is decimal 1. So

P(X < 2) + P(X \geq 2) = 1

P(X < 2) = P(X = 0) + P(X = 1) = 0.0025 + 0.0207 = 0.0232

P(X \geq 2) = 1 - P(X < 2) = 1 - 0.0232 = 0.9768

0.9768 = 97.68% probability that at least two of the appeals will be successful

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