Write the equation of the line with the give information: Through (5,3) m=2

Step-by-step to reduce the radical of the square root Of 160

notka56 [123]

Answer:

$4\sqrt{10}$

Step-by-step explanation:

$\sqrt{160}$

$\sqrt{16 * 10}$

$4\sqrt{10}$

because 16 is a perfect square root and it splits into 4 * 4 while 10 isnt a perfect square root so it stays inside.

8 0

2 years ago

Read 2 more answers

Which applies the power of a power rule to simplify the expression (8 Superscript 12 Baseline) cubed?

rodikova [14]

Answer: (8^{12})^3=8^{12\times 3}=8^{36}

Step-by-step explanation:

Given : the expression (8^{12})^3

We have to simplify the given expression and choose the correct from the given options.

Consider the expression (8^{12})^3

Using property of exponents,

\left(a^b\right)^c=a^{b\times c}

We have,

(8^{12})^3=8^{12\times 3}=8^{36}

7 1

4 years ago

Read 2 more answers

A ball of mass 0.4 kg flies through the air at low speed, so that air resistance is negligible. What is the net force acting on

arsen [322]

Answer:

-3.92 N

Step-by-step explanation:

We are given that

Mass of ball=0.4 kg

Acceleration due to gravity= $-9.8m/s^2$

Because the ball flies against to gravity

We have to find the net force acting on the ball while it is in motion.

We know that when there is no air resistance then the net force acts on the ball is equal to weight of ball.

Net force,F =mg

Substitute the values then we get

$F=0.4(-9.8)$

$F=-3.92N$

Hence, the net force acting on the ball while it is on motion=-3.92 N

6 0

3 years ago

A company makes rubber rafts. 12% of them develop cracks within the first month of operation. 27 new rafts are randomly sampled

rewona [7]

The probability that the number of tested rafts that develop cracks is no more than 3 is .00006.

The true proportion, p for the population is given to 0.12.

Thus, the mean, μ, for the sample = np = 27*0.12 = 3.24.

The sample size, n, given to us is 27.

Thus, the standard deviation, s, for the sample can be calculated using the formula, s = √{p(1 - p)}/n.

s = √{0.12(1 - 0.12)}/27 = √0.003911 = 0.0625389.

We are asked to calculate the probability that the number of tested rafts that develop cracks is no more than 3, that is, we need to calculate P(X ≤3).

P(X ≤ 3)

= P(Z ≤ {(3 - 3.24)/0.0625389) {Using the formula z = (x - μ)/s}

= P(Z ≤ -3.8376114706)

= .00006 {From table}.

Thus, the probability that the number of tested rafts that develop cracks is no more than 3 is .00006.

Learn more about sampling distributions at

brainly.com/question/15507495

#SPJ4

8 0

1 year ago

Of the entering class at a college, % attended public high school, % attended private high school, and % were home schoole

Veronika [31]

Answer:

(a) The probability that the student made the Dean's list is 0.1655.

(b) The probability that the student came from a private high school, given that the student made the Dean's list is 0.2411.

(c) The probability that the student was not home schooled, given that the student did not make the Dean's list is 0.9185.

Step-by-step explanation:

The complete question is:

Of the entering class at a college, 71% attended public high school, 21% attended private high school, and 8% were home schooled. Of those who attended public high school, 16% made the Dean's list, 19% of those who attended private high school made the Dean's list, and 15% of those who were home schooled made the Dean's list.

a) Find the probability that the student made the Dean's list.

b) Find the probability that the student came from a private high school, given that the student made the Dean's list.

c) Find the probability that the student was not home schooled, given that the student did not make the Dean's list.

Solution:

Denote the events as follows:

A = a student attended public high school

B = a student attended private high school

C = a student was home schooled

D = a student made the Dean's list

The provided information is as follows:

P (A) = 0.71

P (B) = 0.21

P (C) = 0.08

P (D|A) = 0.16

P (D|B) = 0.19

P (D|C) = 0.15

(a)

The law of total probability states that:

$P(X)=\sum\limits_{i} P(X|Y_{i})\cdot P(Y_{i})$

Compute the probability that the student made the Dean's list as follows:

$P(D)=P(D|A)P(A)+P(D|B)P(B)+P(D|C)P(C)$

$=(0.16\times 0.71)+(0.19\times 0.21)+(0.15\times 0.08)\\=0.1136+0.0399+0.012\\=0.1655$

Thus, the probability that the student made the Dean's list is 0.1655.

(b)

Compute the probability that the student came from a private high school, given that the student made the Dean's list as follows:

$P(B|D)=\frac{P(D|B)P(B)}{P(D)}$

$=\frac{0.21\times 0.19}{0.1655}\\\\=0.2410876\\\\\approx 0.2411$

Thus, the probability that the student came from a private high school, given that the student made the Dean's list is 0.2411.

(c)

Compute the probability that the student was not home schooled, given that the student did not make the Dean's list as follows:

$P(C^{c}|D^{c})=1-P(C|D^{c})$

$=1-\frac{P(D^{c}|C)P(C)}{P(D^{c})}\\\\=1-\frac{(1-P(D|C))\times P(C)}{1-P(D)}\\\\=1-\frac{(1-0.15)\times 0.08}{(1-0.1655)}\\\\=1-0.0815\\\\=0.9185$

Thus, the probability that the student was not home schooled, given that the student did not make the Dean's list is 0.9185.

3 0

3 years ago