Answer: 241
Step-by-step explanation:
This is a simple problem when using Pascal's triangle. First you look at 1 - 3, what is the difference in these 2 numbers? Its 2, then you look at 3 and 11, the difference is 8, then 11 and 35, the difference is 24. If you keep doing this you get; 2 8 24 64 142. Next you find out how these numbers are different. In the end you keep doing this until you get to the triangles point or the differences converge.
1 3 11 35 99 <u>241</u>
2 8 24 64 142
6 16 40 78
10 24 38
14 14
In the end we get 14 but there is no difference in the numbers so we cant go any farther. Hope this helps!
Answer:
Here's what I get
Step-by-step explanation:
The atomic model before Chadwick
J. J. Thomson had discovered the electron in 1897 and Rutherford discovered the proton in 1912.
So, in the 1920s, scientists thought that a helium atom (₂⁴He), for example, consisted of four protons, two electrons orbiting the nucleus, and another two electrons in the nucleus to balance the charge.
In 1932, Irène and Frédérick Joliot-Curie discovered that when α particles hit a Be target, a strange radiation was emitted that could knock protons out of paraffin. They thought it was some type of high-energy X-rays
Chadwick's experiment
Chadwick thought the radiation consisted of particles, not X-rays. He repeated the Curie's experiment and carefully measured the velocities of the scattered protons.
Using the Laws of Conservation of Energy and Momentum, he calculated that the radiation hitting the paraffin must consist of neutral particles with a mass slightly greater than that of a proton.
Chadwick had discovered the neutron.
The atomic model after Chadwick
Chemistry now made more sense. A helium atom now consisted of two electrons orbiting a nucleus containing two protons and two neutrons. There was no need to have electrons in the nucleus.
Answer:
The value of x is 13°
Step-by-step explanation:
<u>Given:</u> m || n
For a straight line = 180°
Now, by exterior angle
(7x - 1)° + (8x - 14)° = 180°
7x - 1° + 8x - 14° = 180°
15x - 15° = 180°
Now, add 15° both side we get,
15x - 15° + 15° = 180° + 15°
15x = 195°
Now, divide both side by 15
15x/15 = 195°/15
x = 13°
Thus, The value of x is 13°
<u>-TheUnknownScientist 72</u>
Here L = W, but H can be different.
The sum L+H+W must be less than or equal to 192 cm.
We can solve L + H + W = 192 for H: H = 192 - W - L. Remembering that W = L, the formula for H becomes 192 - 2W.
The formula for volume would be V = L*W*H.
This becomes V = W*W*H, or V = W^2*(192-2W)
Multiplying this out: V = w^2*192 - 2W^3
Two ways of determining W:
1) graph V = 192W^2 - 2W^3 and determine the value of W at which V is at a max with the constraint W + L + H is equal to or smaller than 192.
2) Differentiate V with respect to W and set the result equal to zero:
384W - 6W^2 = 0. Solving for W: W(384 - 6W) = 0.
W = 0 is trivial, so just solve 384 - 6W = 0 for W: 6W = 384, and W = 64.
The width is 64 cm, the length is 64 cm also, and the height is (192-2W) cm, or 64 cm.
These dimensions produce the max volume.
1. The problem indicates that 300 pounds of oranges were purchased at $0.24 per pound, so the cost is:
300x$0.24=$72
2. A percent of 21% spoilage is expected, which means that 89% of 300 pounds of oranges left, is:
300x0.89=267 pounds of oranges
3. We want to calculate the selling price per pound of 267 pounds of oranges, so let's call this value "x":
Markup %=(Markup/cost)x100
Markup=267x-72
4. The desired markup, based on selling price, is 50%. So, when we substitute the values, we obtain:
(267x-72/72)x100=50
5. Let's clear the "x":
(26700x-7200/72)=50
26700x-7200=50x72
26700x-7200=3600
26700x=3600+7200
x=10800/26700
x=$0.40
x=40 cents
What should the selling price per pound be?
The answer is: 40 cents or $0.40
