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2 years ago

A) Find the distance of line segment PR. Round answer to the nearest tenth. B) Find the distance around the park (perimeter).

Mathematics

1 answer:

juin [17]2 years ago

7 0

Answer:

A. $PR = 80.6 yd$

B. Perimeter = 190.6 yd

Step-by-step explanation:

A. Distance between P(10, 50) and R(80, 10):

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

$PR = \sqrt{(80 - 10)^2 + (10 - 50)^2}$

$PR = \sqrt{(70)^2 + (-40)^2}$

$PR = \sqrt{4,900 + 1,600}$

$PR = \sqrt{6,500}$

$PR = 80.6 yd$ (nearest tenth)

B. Distance around the park = Perimeter = PR + PQ + QR

PR = 80.6 yd

PQ = |50 - 10| = 40 yd

QR = |80 - 10| = 70 yd

Perimeter = 80.6 + 40 + 70

Perimeter = 190.6 yd

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Write equation parallel to x=5 through the point (_6,6)

uranmaximum [27]

Answer:

$\boldsymbol x\boldsymbol=\boldsymbol - \bold6$

Step-by-step explanation:

Graph of x=5 is vertical straight line parallel to y-axis and perpendicular to x-axis. The points on graph have the x-coordinate as 5 and y-coordinate varies.

Similarly, line parallel to x=5 or y-axis passing through point (-6,6), in that all the points have same x-coordinate as -6. So the equation of line will be x=-6

For simplicity of visualization graph of both the equation x=5 and x=-6 are attached.

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2 years ago

USA Today reported that about 20% of all people in the United States are illiterate. Suppose you take eight people at random off

Law Incorporation [45]

Answer:

a) Figure and code attached

b) $E(X)=\mu = np = 8*0.2= 1.6$

$Var(X) =\sigma^2= np(1-p) = 8*0.2*(1-0.2) = 1.28$

$Sd(X)=\sigma= \sqrt{1.28}= 1.131$

c) $P(X\geq 7) =0.97$

And we can calculate this with the complement rule.

$P(X \geq 7) = 1-P(X$

So then we have:

$P(X \leq 6) = 0.03$

And we are interested on the valueof n who satisfy this expression.

And for this we can verify this with the following code:

"=BINOM.DIST(6,E54,0.2,TRUE)"

And as we can see on the second figure attached the value who satisfy the condition would be n = 60.

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:

$X \sim Binom(n=8, p=0.2)$

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 can use the following R code to generate the histogram for this case:

> x <- seq(0,8,by = 1)

> y <- dbinom(x,8,0.2)

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

And as we can see we got the result on the figure attached. And the distribution seems to be skewed to the right.

Part b

For this case the expected value is given by:

$E(X)=\mu = np = 8*0.2= 1.6$

The variance is given by:

$Var(X) =\sigma^2= np(1-p) = 8*0.2*(1-0.2) = 1.28$

And the standard deviation would be:

$Sd(X)=\sigma= \sqrt{1.28}= 1.131$

Part c

For this case we have the following inequality:

$P(X\geq 7) =0.97$

And we can calculate this with the complement rule.

$P(X \geq 7) = 1-P(X$

So then we have:

$P(X \leq 6) = 0.03$

And we are interested on the valueof n who satisfy this expression.

And for this we can verify this with the following code:

"=BINOM.DIST(6,E54,0.2,TRUE)"

And as we can see on the second figure attached the value who satisfy the condition would be n = 60.

5 0

3 years ago

PLZ HELP!<br>dont just answer something random for points:)tysm

sergiy2304 [10]

Answer:

$4(x^{2} -4)^{2} -76$

Step-by-step explanation:

Take out 4:

4(x^2-8x)-12

=4(x^2-8x+16-16)-12

=4(x^2-8x+16)-64-12

=4(x^2-4)^2 - 76

= $4(x^{2} -4)^{2} -76$

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2 years ago

If f(x) = x2 – 2x, find:<br> f(-3) = [?]

maksim [4K]

9514 1404 393

Answer:

Step-by-step explanation:

Put the value where the variable is and do the arithmetic.

f(-3) = (-3)² -2(-3) = 9 +6

f(-3) = 15

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2 years ago

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Write the standard equation of the circle with the given center and passes through the given point. Center (7,-2); Point= (1,-6)

vodomira [7]

Answer:

(x - 7)² + (y + 2)² = (2√13)²

Step-by-step explanation:

We already know that the center is at (7, -2), but must find the radius. The radius is the distance between the points (7, -2) and (1, -6):

r = √ [6² + 4²] ) = √(36 + 16) = √52 = √4√13 = 2√13.

Then the desired equation is (x - 7)² + (y + 2)² = (2√13)²

6 0

2 years ago