What is 6/10 as a decimal

Determine the root of the equation

larisa [96]

Answer:

0.97087

Step-by-step explanation:

Given the function:

$f(x) = e^{2x} - x - 6$

Its first derivative is:

$f'(x) = 2e^{2x} - 1$

Using Newton's method:

$x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$

and starting with the point:

$x_1 = 0.95$

we get:

$f(x_1) = e^{2(0.95)} - 0.95 - 6 = -0.26410$

$f'(x_1) = 2e^{2(0.95)} - 1 = 12.37178$

$x_2 = x_1 - \frac{f(x_1)}{f'(x_1} = 0.95 - \frac{-0.26410}{12.37178} = 0.97134$

$f(x_2) = e^{2(0.97134)}- 0.97134 - 6 = 0.00608$

$f'(x_2) = 2e^{2(0.97134)} - 1 = 12.95485$

$x_3 = 0.97134 - \frac{0.00608}{12.95485} = 0.97087$

$f(x_3) = e^{2(0.97087)} - 0.97087 - 6 = -2.6240413 \cdot 10^{-7}$

6 0

4 years ago

The principal P is borrowed at a simple interest rate r for a period of time t. Find the simple interest owed for the use of the

-BARSIC- [3]

Answer:

$7

Step-by-step explanation:

Simple interest formula:

I = Prt

6 months = 6 * 30 days = 180 days

1 year = 360 days

t = (180 days)/(360 days) = 0.5

I = $7000 * 0.002 * 0.5

I = $7

8 0

3 years ago

Read 2 more answers

Suppose 1% of people in a large population are over 6 feet 3 inches tall. Approximately what is the chance that from a group of

stepladder [879]

Answer:

14.19% probability that from a group of 200 people picked at random from this population, at least four people will be over 6 feet 3 inches tall

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they are over 6 feet 3 inches tall, or they are not. The probability of a person being over this height is independent of any other person. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

1% of people in a large population are over 6 feet 3 inches tall.

This means that $p = 0.01$

200 people

This means that $n = 200$

At least four people will be over 6 feet 3 inches tall

Either there is less than four people over this height, or there is more than 4 people. The sum of the probabilities of these events is decimal 1. So

$P(X < 4) + P(X \geq 4) = 1$

We want $P(X \geq 4)$ . So

$P(X \geq 4) = 1 - P(X < 4)$

In which

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{200,0}.(0.01)^{0}.(0.99)^{200} = 0.1340$

$P(X = 1) = C_{200,1}.(0.01)^{1}.(0.99)^{199} = 0.2707$

$P(X = 2) = C_{200,2}.(0.01)^{2}.(0.99)^{198} = 0.272$

$P(X = 3) = C_{200,3}.(0.01)^{3}.(0.99)^{197} = 0.1814$

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.1340 + 0.2707 + 0.272 + 0.1814 = 0.8581$

$P(X \geq 4) = 1 - P(X < 4) = 1 - 0.8581 = 0.1419$

14.19% probability that from a group of 200 people picked at random from this population, at least four people will be over 6 feet 3 inches tall

6 0

4 years ago

If 12 people at a party shake Hands once and only once with everyone else how many handshakes occur

egoroff_w [7]

serian 144 apretones de manos en total

4 0

3 years ago

Point Q lies on the circle and has an x-coordinate of 4.

spin [16.1K]

Answer:

2 square root 5

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The equation of the circle is equal to

$(x-h)^2+(y-k)^2=r^2$

where

(h,k) is the center and r is the radius of the circle

In this problem we have

center at (0,0) and radius equal 6 units

so

$x^2+y^2=6^2\\x^2+y^2=36$

Remember that

If a point lie on the circle, then the point must satisfy the equation of the circle

Substitute the x-coordinate of point Q in the equation of the circle and solve for the y-coordinate of point Q

For x=4

$4^2+y^2=36\\y^2=36-16\\y^2=20$

$y=\pm\sqrt{20}$

simplify

$y=\pm2\sqrt{5}$

The point Q lie on the first Quadrant (see the picture)

The y-coordinate is positive

therefore

The y-coordinate of point Q is $2\sqrt{5}$

4 0

3 years ago

Read 2 more answers