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3 years ago

Find the distance between the points (3, 8) and (-1, 9). Round the distance to the nearest hundredth. 3.87 4.12 5.74 2.24

Mathematics

2 answers:

Anastaziya [24]3 years ago

5 0

Answer:

≈ 4.12 units

Step-by-step explanation:

Calculate the distance d using the distance formula

d = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }$

with (x₁, y₁ ) = (3, 8) and (x₂, y₂ ) = (- 1, 9)

d = $\sqrt{(-1-3)^2+(9-8)^2}$

= $\sqrt{(-4)^2+1^2}$

= $\sqrt{16+1}$

= $\sqrt{17}$

≈ 4.12 ( to the nearest hundredth )

miv72 [106K]3 years ago

5 0

Answer:

The distance between given points is: 4.12 units

Step-by-step explanation:

Given points are:

(3, 8) and (-1, 9)

Here

$(x_1,y_1) = (3,8)\\(x_2,y_2) = (-1,9)$

The distance is calculated using the following formula:

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

Putting the values, we get

$d = \sqrt{(-1-3)^2+(9-8)^2}\\d = \sqrt{(-4)^2+(1)^2}\\d = \sqrt{16+1}\\d = \sqrt{17}\\d = 4.123105...$

Rounding off to nearest hundredth

d = 4.12 units

Hence,

The distance between given points is: 4.12 units

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Is 3/8 equal to 4/10?

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8ths are divided by 12.5 so 3 * 12.5 is 37.5
10ths are divided by 10 so 4 * 10 is 40

3/8 is < / = 4/10

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3 years ago

You have received an order of 100 robotic resistance spot welders which contains 5 defective welders. You randomly select 15 wel

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Answer:

$P(X = 0) = h(0,100,15,5) = \frac{C_{5,0}*C_{95,15}}{C_{100,15}} = 0.4357$

$P(X = 1) = h(1,100,15,5) = \frac{C_{5,1}*C_{95,14}}{C_{100,15}} = 0.4034$

$P(X = 2) = h(2,100,15,5) = \frac{C_{5,2}*C_{95,13}}{C_{100,15}} = 0.1377$

$P(X = 3) = h(3,100,15,5) = \frac{C_{5,3}*C_{95,12}}{C_{100,15}} = 0.0216$

$P(X = 4) = h(4,100,15,5) = \frac{C_{5,4}*C_{95,11}}{C_{100,15}} = 0.0015$

$P(X = 5) = h(5,100,15,5) = \frac{C_{5,5}*C_{95,10}}{C_{100,15}} = 0.00004$

b) 0.154% probability that there are at least 4 defective welders in the sample

Step-by-step explanation:

The welders are chosen without replacement, so the hypergeometric distribution is used.

The probability of x sucesses is given by the following formula:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

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

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

In this question:

100 welders, so $N = 100$

Sample of 15, so $n = 15$

In total, 5 defective, so $k = 5$

(a) Determine the PMF of the number of defective welders in your sample?

There are 5 defective, so this is P(X = 0) to P(X = 5). Then

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 0) = h(0,100,15,5) = \frac{C_{5,0}*C_{95,15}}{C_{100,15}} = 0.4357$

$P(X = 1) = h(1,100,15,5) = \frac{C_{5,1}*C_{95,14}}{C_{100,15}} = 0.4034$

$P(X = 2) = h(2,100,15,5) = \frac{C_{5,2}*C_{95,13}}{C_{100,15}} = 0.1377$

$P(X = 3) = h(3,100,15,5) = \frac{C_{5,3}*C_{95,12}}{C_{100,15}} = 0.0216$

$P(X = 4) = h(4,100,15,5) = \frac{C_{5,4}*C_{95,11}}{C_{100,15}} = 0.0015$

$P(X = 5) = h(5,100,15,5) = \frac{C_{5,5}*C_{95,10}}{C_{100,15}} = 0.00004$

(b) Determine the probability that there are at least 4 defective welders in the sample?

$P(X \geq 4) = P(X = 4) + P(X = 5) = 0.0015 + 0.00004 = 0.00154$

0.154% probability that there are at least 4 defective welders in the sample

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Step-by-step explanation:

1. You need to apply the following formula for calculate the slope:

$m=\frac{y_{2}-y_1}{x_{2}-x_1}$

2. Given the points, (3,-4) and (7,6), you have:

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3. Substitute these values into the formula for calculate the slope, as following:

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4. Simplify the result. Therefore, you obtain that the slope is:

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