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Katarina [22]
3 years ago
11

Find the value of x , if the distance between the points ( x , -1 ) and (3 , 2 ) is 5

Mathematics
1 answer:
lord [1]3 years ago
4 0
The value of X is either -1 or 7. By using distance formula.
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The answer will be c

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3 years ago
Solve the nonlinear system of equations. State the number of solutions.
WITCHER [35]

Answer:

Step-by-step explanation:

Hello,

Question 15

We can search x such that:

   x^2-4x+4=2x-5\\\\\text{*** subtract 2x-5 from both sides ***}\\ \\x^2-4x-2x+4+5=0\\ \\\text{*** simplify ***}\\ \\x^2-6x+9=0 \\ \\\text{*** we can notice a perfect square ***}\\ \\x^2 -2\cdot x \cdot 3 + 3^2=(x-3)^2=0\\\\\text{*** taking the root ***}\\\\x-3=0\\\\\large \boxed{\sf \ \ x=3 \ \ }

There is 1 solution.

Question 16

Again, we search x such that:

  x^2-8x+15=2x-6\\\\\text{*** subtract 2x-6 from both sides ***}\\\\x^2-8x-2x+15+6=0\\\\\text{*** simplify ***}\\\\x^2-10x+21=0 \\ \\\text{*** we are looking for two roots where the sum is 10 and the product is 21 = 7 x 3 ***} \\\\x^2-7x-3x+21=x(x-7)-3(x-7)=(x-3)(x-7)=0\\\\\large \boxed{\sf \ \ x= 3 \ or \ x =7 \ \ }There are two solutions.

 

Hope this helps.

Do not hesitate if you need further explanation.

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7 0
3 years ago
The annual rainfall (in inches) in a certain region is normally distributed with mean 43.2 and variance 20.8. Assume rainfall in
Wittaler [7]

Answer:

92.24% probability that out of 15 years, at most 2 have rainfall of more than 50 inches.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the binomial probability distribution.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation(which is the square root of the variance) \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

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.

In this problem, we have that:

\mu = 43.2, \sigma = \sqrt{20.8} = 4.56

Probability that a year has rainfall of more than 50 inches.

pvalue of Z when X = 50. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{50 - 43.2}{4.56}

Z = 1.49

Z = 1.49 has a pvalue of 0.9319

1 - 0.9319 = 0.0681

Find the probability that out of 15 years, at most 2 have rainfall of more than 50 inches.

This is P(X \leq 2) when n = 15, p = 0.0681. So

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)

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

P(X = 0) = C_{15,0}.(0.0681)^{0}.(0.9319)^{15} = 0.3472

P(X = 1) = C_{15,1}.(0.0681)^{1}.(0.9319)^{14} = 0.3805

P(X = 2) = C_{15,2}.(0.0681)^{2}.(0.9319)^{13} = 0.1947

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.3472 + 0.3805 + 0.1947 = 0.9224

92.24% probability that out of 15 years, at most 2 have rainfall of more than 50 inches.

8 0
3 years ago
Read 2 more answers
11. Any company plans to connect a total of 20 pF of capacitance to a 7200-V
vesna_86 [32]

Answer:

C = 80pF

Step-by-step explanation:

The total capacitance of 4 capacitors connected in series is given by:

Ct = \frac{1}{1/C1 + /C2 + 1/C3 + 1/C4}

Ct = \frac{1}{1/C + /C + 1/C + 1/C}

Ct = \frac{1}{4/C}

Ct = \frac{C}{4}=20pF

Solving for C:

C = 4*20pF

C = 80pF

3 0
3 years ago
Which orded pair is a solution of the equation 2x+4y=6x-y
Evgen [1.6K]
Y=4/5x hope that’s the right answer
7 0
2 years ago
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