Given the function f(x)= e^3x, write an expression that represents the derivative of f using the limit shown below.

Find the coordinates of the midpoint of the segment joining the given points (0,2) and (6,4)

djyliett [7]

The coordinates of the midpoint are the average of the coordinates of the given points.

So, the x coordinate of the midpoint is the average of the x coordinates of the given point:

$\dfrac{0+6}{2} = \dfrac{6}{2} = 3$

And similarly, the y coordinate of the midpoint is the average of the y coordinates of the given point:

$\dfrac{2+4}{2} = \dfrac{6}{2} = 3$

So, the midpoint is the point $(3,3)$

6 0

3 years ago

Let O and H be the circumcenter and orthocenter of triangle ABC, respectively. Let a, b, and c denote the side lengths, and let

vovikov84 [41]

Answer:

OH²=412

Step-by-step explanation:

A Circumcenter of a triangle is the point where the three perpendicular bisectors of a triangle meet.

The Orthocenter is the point where all three altitudes of the triangle intersect.

Given any triangle, the orthocenter, circumcenter and centroid are collinear on the Euler line. By Euler's Identity, the distance between the circumcenter and the orthocenter of a triangle is related to the circumradius(R) and the sides(a,b,c) of the triangle by the relation

OH²=9R²-(a²+b²+c²)

R=7, a²+b²+c²=29

OH²=9(7)²-29

OH²=412

3 0

2 years ago

Mr. Márquez had 123 eggs in a refrigerator in his restaurant. He put 32 more cartons of eggs in the refrigerator. Each carton co

jeka94

H is the best estimate

7 0

3 years ago

When doing polynomial long division, what is the first step to starting the problem?

Bond [772]

Answer:

Step 1: Make sure the polynomial is written in descending order. If any terms are missing, use a zero to fill in the missing term

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