Two sides of a triangle measure

Use differentials to approximate the value of the expression. Compare your answer with that of a calculator. (Round your answers

Vesna [10]

Answer:

726.572699

Step-by-step explanation:

According to differentials

(x+Δx)³ = x³ + 3x²Δx + 3x(Δx)² + (Δx)³ (Using binomial expansion)

Using this formula to solve (8.99)³, this can also be written as;

(8.99)³ = (9-0.01)³ where

x = 9

Δx = -0.01

Substitute this vales into the differential expression above

(9+(-0.01))³ = 9³ + 3(9)²(-0.01) + 3(9)(-0.01)² + (-0.01)³

(9+(-0.01))³ = 729 + (243)(-0.01) + 27(0.0001) + (-0.000001)

(9+(-0.01))³ = 729-2.43+0.0027-0.000001

(9+(-0.01))³ = 726.572699

Hence 8.99³ = 726.572699 (Using differential)

Using calculator;

8.99³ = 726.572699

4 0

3 years ago

In a recent survey of 25 voters, 17 favor a new city regulation and 8 oppose it. What is the probability that in a random sample

Rasek [7]

Answer:

$P(X=2)=(6C2)(0.68)^2 (1-0.68)^{6-2}=0.0727$

Step-by-step explanation:

1) 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".

2) Solution to the problem

The probability in favor of the regulation based on the recent survey is:

$p = \frac{17}{25}=0.68$

Let X the random variable of interest "Number of favor respondents about the regulation", on this case we now that:

$X \sim Binom(n=6, p=0.68)$

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:

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

And we want to find this probability:

$P(X=2)=(6C2)(0.68)^2 (1-0.68)^{6-2}=0.0727$

If we use X= "Number of respondednts opposed to the regulation we got the same answer", but on this case p = 1-0.68=0.32, and we want this probability:

$P(X=4)=(6C4)(0.32)^4 (1-0.32)^{6-4}=0.0727$

6 0

3 years ago

Which values of m and b will create a system of equations with no solution? Check all that apply.

Law Incorporation [45]

Answer:

y = -2x + 1

Step-by-step explanation:

Then any equation of the form y = -2x + b, b≠1 will create a system with no solution. Hence the values of m and b are m = -2, b ≠ 1.

hope i helped

8 0

4 years ago

Read 2 more answers

The roof of the Terminal Tower is 709 feet above ground. A window washer dropped a bucket from the edge of the roof. How many se

Masja [62]

Answer:

6.64 seconds

Step-by-step explanation:

Given that:

Distance between roof of the terminal and ground = 709 feet

A bucket was dropped from the roof.

To find:

The time taken by the bucket to hit the ground?

Solution:

Distance traveled, $s$ = 709 feet

Initial velocity of the bucket, $u$ = 0 feet/sec (because initially it was at rest)

Acceleration of the bucket will be equal to acceleration due to gravity i.e.

$g$ or 32.1741 $ft/sec^{2}$

Let the time taken is $t$ seconds.

Formula for distance is given as:

$s = ut+\dfrac{1}{2}at^2$

Putting all the values:

$709 = 0 (t) + \dfrac{1}{2}(32.1741) t^2\\\Rightarrow 1418 = 32.1741 t^2\\\Rightarrow t^2 = 44.07\\\Rightarrow t \approx \bold{6.64\ sec}$

6 0

3 years ago

Molly has 190 dollars in her bank account and spend 10 dollars every trip write an equation for molly

leonid [27]

10xt=190
T represents the amount of trips and 10 represents the amount of money she spends each trip. Since she has $190 already it will be on the other side of the equation after the equal sign

3 0

3 years ago