Lines p and q are intersecting by line r. If m<1=7x-36 and m<2=5x+12, for which value of x would p||q

nika2105 [10]

Answer:

$0.357 = (357)/(1000)$ .

Step-by-step explanation:

A number is a rational number if and only if it is equal to the ratio between two integers. In other words, a number $x$ is a rational number if and only if there are integers (whole numbers) $p$ and $q$ ( $q \ne 0$ ) such that $x = p / q$ .

Thus, the $0.357$ in this question would be a rational number as long as there are integers $p$ and $q$ ( $q \ne 0$ ) such that $p / q = 0.357$ . Simply finding the right $p\!$ and $q\1$ would be sufficient for showing that $0.357\!$ is rational.

Since $0.357$ is a terminating decimal, one possible way to find $p\!$ and $q\1$ is to repeatedly multiply $0.357\!$ by $10$ until a whole number is reached:

$10 \times 0.357 = 3.57$ .

$10^{2} \times 0.357 = 35.7$ .

$10^{3} \times 0.357 = 357$ .

Thus, $0.357 = (357) / (10^{3})$ , such that $p = 357$ and $q = 1000$ (both are integers, and $q \ne 0$ ) would ensure that $0.357 = p / q$ .

Therefore, $0.357$ is indeed a rational number.

4 0

2 years ago

A square garden plot has an area of 24 ft2.

strojnjashka [21]

The area of a square is equal to the side squared.
$s^2=A$

We can plug in 24 for A and then take the square root of each side to find s.
$s^2=24 \\ s=\sqrt{24}$

We can simplify √24.
The prime factorization of 24 is 2×2×2×3.
Since we have 2×2 inside the radical we can simplify to have 2 outside the radical.
$\sqrt{24}=\sqrt{4\times6}=\boxed{2\sqrt{6}\ ft}$

We can then use a calculator to find an approximate decimal value for 2√6.
(You could technically calculate it by hand using the Babylonian method, I don't think you're expected to do that, though)
$2\sqrt{6}\approx\boxed{4.9\ ft}$

6 0

2 years ago

<img src="https://tex.z-dn.net/?f=%5CLarge%5Cmathtt%5Ccolor%7Bred%7D%7BH%7D%5Ccolor%7Borange%7D%7BE%7D%5Ccolor%7Byellow%7D%7BL%7

Illusion [34]

Answer:

0.018

kamsahamnida

have a great day ahead

5 0

2 years ago

Read 2 more answers

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.0 inches and a standard devi

alexira [117]

Answer: 0.8490

Step-by-step explanation:

Given : The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.0 inches and a standard deviation of 0.9 inches.

i.e. $\mu=30$ and $\sigma=0.9$

Let x denotes the lengths of aluminum-coated steel sheets.

Required Formula : $z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

For n= 36 , the probability that the average length of a sheet is between 29.82 and 30.27 inches long will be :-

$P(29.82$

∴ Required probability = 0.8490

3 0

3 years ago

A spherical exercise ball has a maximum diameter of 30 inches when filled with air. The ball was completely empty at the start,

Alex73 [517]

Answer:

A) A(t) = 4500*π - 1600*t

B) A(4) = 7730 in³

C) t = 8,8 sec

Step-by-step explanation:

The volume of the sphere is:

d max = 30 r max = 15 in

V(s) = (4/3)*π*r³ V(s) = (4/3)*π* (15)³

V(s) = 4500*π

A) Amount of air needed to fill the ball A(t)

A(t) = Total max. volume of the sphere - rate of flux of air * time

A(t) = 4500*π - 1600*t in³

B) After 4 minutes

A(4) = 4500*π - 6400

A(4) = 14130 - 6400

A(4) = 7730 in³

C) A(t) = 4500*π - 1600*t

when A(t) = 0 the ball got its maximum volume then:

4500*π - 1600*t = 0

t = 14130/1600

t = 8,8 sec

8 0

2 years ago