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4 years ago

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This table contains data on the number of people visiting a historical landmark over a period of one week. Using technology, fin

d the equation of the regression line for the following data. Round values to the nearest tenth if necessary. Day (x) Number of visitors (y) 1 120 2 124 3 130 4 131 5 135 6 132 7 135 A. B. C. D.

1 answer:

dybincka [34]4 years ago

8 0

I wish i knew i am really sorry

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If m<5 is 50 degrees then what is the measure of angle 7?

geniusboy [140]

Answer:

is it just 2 angles on straight line? if so, angle 7 is 130

Step-by-step explanation:

any 2 angles on one straight line must equal 180

180-50=130

7 0

3 years ago

A company is in the business of finding addresses of long-lost friends. The company claims to have a 70% success rate. Suppose t

Galina-37 [17]

Answer:

a) Figure attached

b) $E(X) =\mu= np = 9*0.7=6.3$

$Sd(X) =\sigma= \sqrt{np(1-p)}= \sqrt{9*0.7*(1-0.7)}=1.375$

c) For the case n= 6

$P(X \leq 2) = 0.9891$

For the case n= 5

$P(X \leq 2) = 0.9692$

So then we need at least n=5 or n=6 to satisfy the condition required.

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=9, p=0.7)$

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

For this case we can use the following R code:

> x <- seq(0,9,by = 1)

> y <- dbinom(x,9,0.7)

> plot(x,y,main="Histogram",type = "h")

And we can see on the figure attached the solution.

We see that the higher probabilities are from 4 to 9

Part b

The expected value is given by:

$E(X) =\mu= np = 9*0.7=6.3$

The variance is given by:

$Var (X) =\sigma^2= np(1-p) = 9*0.7*(1-0.7)= 1.89$

And the standard deviation is:

$Sd(X) =\sigma= \sqrt{np(1-p)}= \sqrt{9*0.7*(1-0.7)}=1.375$

Part c

First we can find the probability that at least two addresses will be found in the list of 9 that we have like this:

$P(X \geq 2)$

We can use the complement rule and we have:

$P(X \geq 2) = 1-P(X$

We find the indicidual probabilities:

$P(X=0)=(9C0)(0.7)^0 (1-0.7)^{9-0}=0.00001968$

$P(X=1)=(9C1)(0.7)^1 (1-0.7)^{9-1}=0.000413$

$P(X \geq 2) = 1-[0.00001968+0.000413]=0.9996$

If we use the case of n=8 and we find $P(X\leq 2)$ , we got:

$P(X \leq 2) = 0.9987$

For the case n= 7

$P(X \leq 2) = 0.9962$

For the case n= 6

$P(X \leq 2) = 0.9891$

For the case n= 5

$P(X \leq 2) = 0.9692$

So then we need at least n=5 or n=6 to satisfy the condition required.

5 0

3 years ago

24 quarts of oil at $1.79 per quart

WITCHER [35]

Answer:

It would be $42.96.

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

A piece of paper is to display ~128~ 128 space, 128, space square inches of text. If there are to be one-inch margins on both si

Grace [21]

Answer:

The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Step-by-step explanation:

We have that:

$Area = 128$

Let the dimension of the paper be x and y;

Such that:

$Length = x$

$Width = y$

So:

$Area = x * y$

Substitute 128 for Area

$128 = x * y$

Make x the subject

$x = \frac{128}{y}$

When 1 inch margin is at top and bottom

The length becomes:

$Length = x + 1 + 1$

$Length = x + 2$

When 2 inch margin is at both sides

The width becomes:

$Width = y + 2 + 2$

$Width = y + 4$

The New Area (A) is then calculated as:

$A = (x + 2) * (y + 4)$

Substitute $\frac{128}{y}$ for x

$A = (\frac{128}{y} + 2) * (y + 4)$

Open Brackets

$A = 128 + \frac{512}{y} + 2y + 8$

Collect Like Terms

$A = \frac{512}{y} + 2y + 8+128$

$A = \frac{512}{y} + 2y + 136$

$A= 512y^{-1} + 2y + 136$

To calculate the smallest possible value of y, we have to apply calculus.

Different A with respect to y

$A' = -512y^{-2} + 2$

Set

$A' = 0$

This gives:

$0 = -512y^{-2} + 2$

Collect Like Terms

$512y^{-2} = 2$

Multiply through by $y^2$

$y^2 * 512y^{-2} = 2 * y^2$

$512 = 2y^2$

Divide through by 2

$256=y^2$

Take square roots of both sides

$\sqrt{256=y^2$

$16=y$

$y = 16$

Recall that:

$x = \frac{128}{y}$

$x = \frac{128}{16}$

$x = 8$

Recall that the new dimensions are:

$Length = x + 2$

$Width = y + 4$

So:

$Length = 8 + 2$

$Length = 10$

$Width = 16 + 4$

$Width = 20$

To double-check;

Differentiate A'

$A' = -512y^{-2} + 2$

$A" = -2 * -512y^{-3}$

$A" = 1024y^{-3}$

$A" = \frac{1024}{y^3}$

The above value is:

$A" = \frac{1024}{y^3} > 0$

This means that the calculated values are at minimum.

<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>

3 0

3 years ago

Greatest common factor 48x^5,39x^6

lora16 [44]

4,853,096 is the number

6 0

4 years ago