Translate the verbal expression into an algebraic expression "Four times the sum of a number and 5"?

Find x if ∠m1 = 2x + 10 and m∠2 = 3x - 6

icang [17]

Answer: 16

Step-by-step explanation:

3 0

2 years ago

Please help. :))))))

Elodia [21]

Answer:

6 because 9 is the length and you only do length times height and 54 divided by 9 is 6 therefore the height is 6

4 0

3 years ago

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The probability that a single radar station will detect an enemy plane is 0.65.

taurus [48]

Answer:

a) We need 4 stations to be 98% certain that an enemy plane flying over will be detected by at least one station.

b) If seven stations are in use, the expected number of stations that will detect an enemy plane is 4.55.

Step-by-step explanation:

For each station, there are two two possible outcomes. Either they detected the enemy plane, or they do not. This means that we can solve this problem using concepts of the binomial probability distribution.

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 combinatios 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.

In this problem, we have that:

The probability that a single radar station will detect an enemy plane is 0.65. This means that $n = 0.65$ .

(a) How many such stations are required to be 98% certain that an enemy plane flying over will be detected by at least one station?

This is the value of n for which $P(X = 0) \leq 0.02$ .

n = 1.

$P(X = 0) = C_{1,0}.(0.65)^{0}.(0.35)^{1} = 0.35$

n = 2

$P(X = 0) = C_{2,0}.(0.65)^{0}.(0.35)^{2} = 0.1225$

n = 3

$P(X = 0) = C_{3,0}.(0.65)^{0}.(0.35)^{3} = 0.0429$

n = 4

$P(X = 0) = C_{4,0}.(0.65)^{0}.(0.35)^{4} = 0.015$

We need 4 stations to be 98% certain that an enemy plane flying over will be detected by at least one station.

(b) If seven stations are in use, what is the expected number of stations that will detect an enemy plane?

The expected number of sucesses of a binomial variable is given by:

$E(x) = np$

So when $n = 7$

$E(x) = 7*(0.65) = 4.55$

If seven stations are in use, the expected number of stations that will detect an enemy plane is 4.55.

6 0

3 years ago

What is 5/8 + (-5/6)

suter [353]

Adding a negative is the same as subtracting, so here we have 5/8-5/6. Let's find our least common denominator to use as our common denominator for both fractions. That would be 24. So, we multiply 5/8 by 3/3 because to get an equivalent fraction, you multiply by a version of 1- then you multiply 5/6 by 4/4. So, you get 15/24-20/24 equals -5/24. Hope this helps!

3 0

3 years ago

Would you rather have 1 million dollars or a dollar that doubles everyday?<br> explain your answer.

Eddi Din [679]

I would rather have a dollar that doubles every day, because you can soon reach past a million dollars and it will keep growing, instead of having 1 million dollars right away, and not gaining any more.

5 0

3 years ago

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