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2 years ago

Fine FG , given that line HF is perpendicular bisector or EG

Mathematics

1 answer:

Marta_Voda [28]2 years ago

8 0

Answer:

FG = 7

Step-by-step explanation:

We'll begin by calculating HF. This can be obtained by using the pythagoras theory as illustrated below:

EF = 7

EH = 3

HF =?

EF² = EH² + HF²

7² = 3² + HF²

49 = 9 + HF²

Collect like terms

49 – 9 = HF²

40 = HF²

Take the square root of both side

HF = √40

Finally, we shall determine FG. This can be obtained as follow:

GH = 3

HF = √40

FG =.?

FG² = GH² + HF²

FG² = 3² + (√40)²

FG² = 9 + 40

FG² = 49

Take the square root of both side

FG = √49

FG = 7

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A door delivery florist wishes to estimate the proportion of people in his city that will purchase his flowers. Suppose the true

kvv77 [185]

Answer:

99.74% probability that the sample proportion will be less than 0.1

Step-by-step explanation:

I am going to use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

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

In a set with mean $\mu$ and standard deviation $\sigma$ , 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.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 276, p = 0.06$

$\mu = E(X) = np = 276*0.06 = 16.56$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{276*0.06*0.94} = 3.9454$

What is the probability that the sample proportion will be less than 0.1

This is the pvalue of Z when X = 0.1*276 = 27.6. So

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

$Z = \frac{27.6 - 16.56}{3.9454}$

$Z = 2.8$

$Z = 2.8$ has a pvalue of 0.9974

99.74% probability that the sample proportion will be less than 0.1

5 0

3 years ago

Let x denote the lifetime of a mcchine component with an exponential distribution. The mean time for the component failure is 25

aliina [53]

Answer:

0.1353 = 13.53% probability that the lifetime exceeds the mean time by more than 1 standard deviations

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

The mean time for the component failure is 2500 hours.

This means that $m = \frac{2500}, \mu = \frac{1}{2500} = 0.0004$

What is the probability that the lifetime exceeds the mean time by more than 1 standard deviations?

The standard deviation of the exponential distribution is the same as the mean, so this is P(X > 5000).

$P(X > x) = e^{-0.0004*5000} = 0.1353$

0.1353 = 13.53% probability that the lifetime exceeds the mean time by more than 1 standard deviations

4 0

2 years ago

3. Which characteristics is correct for the function f(x) = 4x5 + 8x + 2?

MrRissso [65]

Answer:

Step-by-step explanation:

3 0

3 years ago

At the end of the Crimson Comet's soccer season, Coach Billy hosted a party for the players. He had 24 players on his team and o

stealth61 [152]

Answer:

HUH. OH 40

Step-by-step explanation:

8 0

3 years ago

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Divide 6K2 - 15k-5 by 3k

icang [17]

Answer:

Step-by-step explanation:

6k^2

------- = 2k; and:

-15k

------- = -5

-5 cannot be evenly divided by 3k, so there's a remainder instead.

6k^2 - 15k - 5

-------------------- = 2k -5 with remainder -5.

4 0

3 years ago

Read 2 more answers