Darwin’s age is 6 years greater than twice fiona’s age. if darwin is 50 years old, how many years old is fiona?

Mary is a scientist. Using a microscope, she looks at a salt crystal and discovers it is shaped like a cube. Each square face ha

Annette [7]

<h2>Explanation:</h2>

A cube is a prism whose sides all have the same length. You can think of a cube like the three dimensional version of a square. In this problem, we know that Mary is using a microscope in order to look at a salt crystal and discovers it is shaped like a cube. Each square face has side length:

$s=0.1mm$

This diagram is shown in the first figure below. A crystal's square face is one of the six faces of the cube. So in order to draw it we need to know how many units we'll have in each side. Since we know that 1 unit on the grid represents 0.01mm, then:

$No. \ units=\frac{0.1mm}{0,01mm}=10$

So we will have 10 units that measure 0.01mm in each side. This is shown in the second figure below.

5 0

2 years ago

Derive an equation d = acos(bt) for the displacement d (in feet) in relation to sea level of a piece of cloth tied to a water wh

Alisiya [41]

Answer:

hjjhbvbyj

Step-by-step explanation:

a=10

b=pi/12

d=10cos(pi/12t)

t=6

d=5

4 0

2 years ago

A stone is dropped into a barrel of water and sinks to the bottom. The ball is completely covered by water. By how much does the

Rom4ik [11]

Answer:

Answer: 5/12 or approx. 0.42

Step-by-step explanation:

The ball will displace as much water as its volume.

Meaning, the volume of the ball and the volume of the increase in water in the barrel will be equal.

Volume of a sphere:

$V_s=\frac{4}{3} \pi r^3$

The radius is half the diameter. The diameter of the sphere is 10, thus:

$r = d/2 = 10/2 = 5$

5^3 = 5*5*5 = 25*5 = 125

$V_s=\frac{4}{3} \pi * 5^3=\frac{4}{3} \pi * 125$

The volume of a cylinder, which will be the shape of the increase in water, is the following:

$V_c=\pi r^2 h$

We know the radius r, as we know the diameter.

$r=d/2=40/2=20$

$V_c=\pi r^2 h=\pi h * 20^2 = \pi h * 400$

We are looking for the height of the cylinder, h, as that will be the height of the water rise.

Since we know these 2 volumes are the same, we'll set them equal to each other and solve the equation:

$V_s = V_c$

$\frac{4}{3} * 125 * \pi = 400 * h * \pi$

We can get rid of pi by dividing both sides by pi:

$\frac{4}{3} * 125 = 400 * h$

And now divide both sides by 400:

$\frac{4}{3} * \frac{125}{400}= h$

Just reversing it and putting h to the left:

$h = \frac{4}{3} * \frac{125}{400} = \frac{4 * 125}{3 * 400}$

I see that I can divide both the numerator and the denominator by 4:

$h =\frac{125}{3 * 100}= \frac{125}{300}$

I'll now divide both the numerator and the denominator by 25 to simplify the expression:

$h=\frac{125}{300} =\frac{125 / 25}{300 / 25} = \frac{5}{12}$

Answer: The water rises by 5/12 (five twelfths).

If I want an approximate decimal answer, I can simply run this expression in a calculator:

$\frac{5}{12}$ ≈ $0.416666667$ ≈ $0.42$

7 0

1 year ago

The probability density function of the time to failure of an electronic component in a copier (in hours) is f(x) = (e^-x/1076)/

kozerog [31]

Answer:

(a) 0.06154

(b) 0.2389

(c) 0.6052

(d) 2478

Step-by-step explanation:

probability density function of the time to failure of an electronic component in a copier (in hours) is

P(x) = 1/1076e^−x/1076

λ = 1/1076

A) A component lasts more than 3000 hours before failure:

P(x>3000) = 1 − e^−3000/1076

= 0.06154

B) A component fails in the interval from 1000 to 2000 hours:

P(1000>x>2000) =1 − e^−2000/1076 − 1 +e^−1000/1076 = e^−1000/1076 − e^−2000/1076 = 0.3948 − 0.1559

= 0.2389

C) A component fails before 1000 hours:

P(x<1000) = 0.6052

D) The number of hours at which 10% of all components have failed:

e^−x/1076 = 0.1

= −x/1076

= ln(0.1)

x =(2.3026)×(1076)

x = 2478

4 0

1 year ago

Matthew goes hiking every 12 days and swimming every 6 days. He did both

AlexFokin [52]

The next 18 days because your trying to see how many days it is until he does BOTH

3 0

2 years ago