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3 years ago

What is the smallest degree of rotation that will map a regular 18 gon on to itself

Mathematics

1 answer:

natali 33 [55]3 years ago

5 0

Answer:

20°

Step-by-step explanation:

Rotating the figure through an angle equal to the central angle of one "sector" will do the required mapping. That is 360°/18 = 20°.

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How do you think you could simplify f(x) + g(x) if f(x) = 3x + 2 and g(x) = 4x?

NARA [144]

Step-by-step explanation:

f(x) = 3x + 2

g(x) = 4x

= f(x) + g(x)

= 3x + 2 + 4x

= (3 + 4)x + 2

= 7x + 2

(f+g)(x) = 7x + 2

7 0

2 years ago

Given that f(x) = x2 – 3x - 10 and g(x) = x – 5, find (f - g)(x) and express

Roman55 [17]

Answer:

$(f-g)(x)= x^2-4x-5$

Step-by-step explanation:

We have the two functions:

$f(x)=x^2-3x-10\text{ and } g(x)=x-5$

And we want to find (f-g)(x).

(f-g)(x) is equivalent to f(x)-g(x).

Therefore:

$\begin{aligned} (f-g)(x)&=f(x)-g(x)\\ &=(x^2-3x-10)-(x-5)\end{aligned}$

Simplify:

$\begin{aligned} &=x^2-3x-10-x+5 \\ &=(x^2)+(-3x-x)+(-10+5) \\ &=x^2-4x-5\end{aligned}$

Therefore:

$(f-g)(x)= x^2-4x-5$

8 0

2 years ago

Read 2 more answers

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

A group of students are planning a mural at a wall the rectangular wall has dimensions of (6x+7) by (8x+5) and they are planning

zvonat [6]

Answer: $46x^2+73x+15$