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3 years ago

How to to determine if two polygons have the same side and shape

1 answer:

3 0

Recall that two shapes are congruent if they have the same shape and size. When two shapes have the same shape but different sizes, we call the shapes similar. You can also think of similar objects or shapes as scaled versions of each other.

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According to a survey, 65% of murders committed last year were cleared by arrest or exceptional means. Fifty murders committed

monitta

Answer:

a) $P(X=41)=(50C41)(0.65)^{41} (1-0.65)^{50-41}=0.00421$

b) $P(X=36)=(50C36)(0.65)^{36} (1-0.65)^{50-36}=0.0714$

$P(X=37)=(50C37)(0.65)^{37} (1-0.65)^{50-37}=0.0502$

$P(X=38)=(50C38)(0.65)^{38} (1-0.65)^{50-38}=0.0319$

And adding these values we got:

$P(36 \leq X \leq 38)= 0.1535$

c) We can find the expected value given by:

$E(X) = np =50*0.65 = 32.5$

And the standard deviation would be:

$\sigma = \sqrt{np(1-p)} \sqrt{50*0.65*(1-0.65)}= 3.373$

We can use the approximation to the normal distribution and we have at leat 95% of the data within 2 deviations from the mean. And the lower limit for this case would be:

$\mu -2\sigma = 32.5- 2*3.373 = 25.75$

And then we can consider a value of 18 as unusual lower for this case.

Step-by-step explanation:

Let X the random variable of interest "number cleared by arrest or exceptional", on this case we can model this variable with this distribution:

$X \sim Binom(n=50, p=0.65)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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

Part a

We want this probability:

$P(X=41)=(50C41)(0.65)^{41} (1-0.65)^{50-41}=0.00421$

Part b

We want this probability:

$P(36 \leq X \leq 38)$

We can find the individual probabilities:

$P(X=36)=(50C36)(0.65)^{36} (1-0.65)^{50-36}=0.0714$

$P(X=37)=(50C37)(0.65)^{37} (1-0.65)^{50-37}=0.0502$

$P(X=38)=(50C38)(0.65)^{38} (1-0.65)^{50-38}=0.0319$

And adding these values we got:

$P(36 \leq X \leq 38)= 0.1535$

Part c

We can find the expected value given by:

$E(X) = np =50*0.65 = 32.5$

And the standard deviation would be:

$\sigma = \sqrt{np(1-p)} \sqrt{50*0.65*(1-0.65)}= 3.373$

We can use the approximation to the normal distribution and we have at leat 95% of the data within 2 deviations from the mean. And the lower limit for this case would be:

$\mu -2\sigma = 32.5- 2*3.373 = 25.75$

And then we can consider a value of 18 as unusual lower for this case.

6 0

3 years ago

Millie has a bank account balance of $1200. Each week, her balance changes by

Hatshy [7]

Answer:

at least 8

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

Write an equation in slope intercept form of the line passing through (5,-4) and is perpendicular to a line whose equation is -2

Sergeu [11.5K]

Rearrange the given equation in slope intercept form
$y = \frac{3x - 1}{ - 2} \\ y = - \frac{3}{2} x + \frac{1}{2}$
slope of the required line is
$- \frac{1}{ - \frac{3}{2} } = \frac{2}{3}$
equation is given by
$y - y1 = m(x - x1) \\ y - - 4 = \frac{2}{3} (x - 5) \\ y + 4 = \frac{2x}{3} - \frac{10}{3} \\ y = \frac{2x}{3} - \frac{10}{3} - 4 \\ y = \frac{2}{3} x - \frac{22}{3}$

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3 years ago

Mr. Adams has 14 boys and 8 girls in his mathematics class. If he chooses

scZoUnD [109]

Answer:

it is more likely that both of the students will be boys because there are 14 boys and 8 girls. 14 is greater than 8. So, both of the students that are chosen will be boys,

5 0

3 years ago

Greastest common factor of 24 and 18

Vilka [71]

Answer: 6

Step-by-step explanation:

the biggest number that can go into both 24 and 18 evenly is 6. 24/6 is four, and 18/6 is three

4 0

3 years ago

Read 2 more answers