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3 years ago

Distance between (-1,0) and (8,6)

Mathematics

2 answers:

Tema [17]3 years ago

7 0

Answer:

3 √ 13

Step-by-step explanation:

Vera_Pavlovna [14]3 years ago

5 0

Answer:

3√13

Step-by-step explanation:

We want to find the distance between these two points. To do so, we need to use the distance formula which states that the distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is:

d = $\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

Here, $x_1=-1,x_2=8,y_1=0$ , and $y_2=6$ . So:

d = $\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

d = $\sqrt{(-1-8)^2+(0-6)^2}=\sqrt{(-9)^2+(-6)^2} =\sqrt{81+36} =\sqrt{117} =3\sqrt{13}$

Thus, the answer is 3√13.

<em>~ an aesthetics lover</em>

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ATCs are required to undergo periodic random drug testing.

aleksandr82 [10.1K]

Answer:

The responsess to the given question can be defined as follows:

Step-by-step explanation:

$P(medication\ used) = 0.007 \\\\P( drug \not\ used ) = 1 - 0.007 = 0.993\\\\P(test\ positive | medication \ used) = 0.96 \\\\ P(test \ negative | medication \ used) = 1 - 0.96 = 0.04\\\\$

$P(Point | Non-used\ medication )=0.93\\\\ P(Point |No\ medication ) = 1 - 0.93 = 0.07$

As per the given info we draw the tree diagram which is defined in the attachment file.

$P ( test \ is\ positive ) = P( medication \ used ) \times P( Test \ positive | medication \ used ) + P( medication not \ used ) \times P( Test\ positive | medication \ not \ used )$

$= ( 0.007 \times 0.96 ) + ( 0.993\times 0.07 )\\\\= 0.0762$

$P( medication \ used | test\ positive )= \frac{\textup{P( medication used ) *P( Test positive given medication used )}}{\textup{P( medication used )}}$

$= \frac{( 0.007\times 0.96 )}{0.0762}\\\\= 0.0882$

8 0

3 years ago

According to a 2014 Gallup poll, 56% of uninsured Americans who plan to get health insurance say they will do so through a gover

Airida [17]

Answer:

a) 24.27% probability that in a random sample of 10 people exactly 6 plan to get health insurance through a government health insurance exchange

b) 0.1% probability that in a random sample of 1000 people exactly 600 plan to get health insurance through a government health insurance exchange

c) Expected value is 560, variance is 246.4

d) 99.34% probability that less than 600 people plan to get health insurance through a government health insurance exchange

Step-by-step explanation:

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

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.

The expected value of the binomial distribution is:

$E(X) = np$

The variance of the binomial distribution is:

$V(X) = np(1-p)$

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 $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

56% of uninsured Americans who plan to get health insurance say they will do so through a government health insurance exchange.

This means that $p = 0.56$

a. What is the probability that in a random sample of 10 people exactly 6 plan to get health insurance through a government health insurance exchange?

This is P(X = 6) when n = 10. So

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

$P(X = 6) = C_{10,6}.(0.56)^{6}.(0.44)^{4} = 0.2427$

24.27% probability that in a random sample of 10 people exactly 6 plan to get health insurance through a government health insurance exchange

b. What is the probability that in a random sample of 1000 people exactly 600 plan to get health insurance through a government health insurance exchange?

This is P(X = 600) when n = 1000. So

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

$P(X = 600) = C_{1000,600}.(0.56)^{600}.(0.44)^{400} = 0.001$

0.1% probability that in a random sample of 1000 people exactly 600 plan to get health insurance through a government health insurance exchange

c. What are the expected value and the variance of X?

$E(X) = np = 1000*0.56 = 560$

$V(X) = np(1-p) = 1000*0.56*0.44 = 246.4$

d. What is the probability that less than 600 people plan to get health insurance through a government health insurance exchange?

Using the approximation to the normal

$\mu = 560, \sigma = \sqrt{246.4} = 15.70$

This is the pvalue of Z when X = 600-1 = 599. Subtract by 1 because it is less, and not less or equal.

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

$Z = \frac{599 - 560}{15.70}$

$Z = 2.48$

$Z = 2.48$ has a pvalue of 0.9934

99.34% probability that less than 600 people plan to get health insurance through a government health insurance exchange

4 0

3 years ago

Dose 8 has more factors or 9

Doss [256]

Answer:

Factors for 8: 1, 2, 4, 8

Factors for 9: 1, 3, 9

So 8 has more factors

7 0

3 years ago

Explain why (–4x)0 = 1, but –4x0 = –4.

hodyreva [135]

Any number raised to power of 0 is 1.
In (-4x)^0, because of the parenthesis, the whole number is being raided to 0, which gives 1.
But in -4x^0, only x is being raised to 0, thus -4x^0 = -4(1) = -4.

5 0

3 years ago

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Vikki [24]

Answer: 156.25

Step-by-step explanation:

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3 years ago