Let
and
be the amounts of available alloy (AA) and pure magic steel that are used, so we also have
![x + y = 2.7](https://tex.z-dn.net/?f=x%20%2B%20y%20%3D%202.7)
DA13 is supposed to contain 7% gold, 3% silver, and 90% steel, so that 2.7 kg of it is made up of
![0.07 \times 2.7 \,\mathrm{kg} = 0.189 \,\mathrm{kg} \text{ gold}](https://tex.z-dn.net/?f=0.07%20%5Ctimes%202.7%20%5C%2C%5Cmathrm%7Bkg%7D%20%3D%200.189%20%5C%2C%5Cmathrm%7Bkg%7D%20%5Ctext%7B%20gold%7D)
![0.03 \times 2.7 \,\mathrm{kg} = 0.081 \,\mathrm{kg} \text{ silver}](https://tex.z-dn.net/?f=0.03%20%5Ctimes%202.7%20%5C%2C%5Cmathrm%7Bkg%7D%20%3D%200.081%20%5C%2C%5Cmathrm%7Bkg%7D%20%5Ctext%7B%20silver%7D)
![0.90 \times 2.7 \,\mathrm{kg} = 2.43 \,\mathrm{kg} \text{ magic steel}](https://tex.z-dn.net/?f=0.90%20%5Ctimes%202.7%20%5C%2C%5Cmathrm%7Bkg%7D%20%3D%202.43%20%5C%2C%5Cmathrm%7Bkg%7D%20%5Ctext%7B%20magic%20steel%7D)
For each kg of the available alloy (AA), there is a contribution of 0.21 kg of gold, 0.09 kg of silver, and therefore 0.70 kg of steel;
kg of it will contain
kg of gold,
kg of silver, and
kg of steel. Each kg of magic steel of course contributes 1 kg of steel;
kg of it will contribute
kg of steel.
Then the dwarves need
• total gold: ![0.21x = 0.189](https://tex.z-dn.net/?f=0.21x%20%3D%200.189)
• total silver: ![0.09x = 0.081](https://tex.z-dn.net/?f=0.09x%20%3D%200.081)
• total steel: ![0.70x + y = 2.43](https://tex.z-dn.net/?f=0.70x%20%2B%20y%20%3D%202.43)
Solve for
and
. The first two equations are consistent and give
, and substituting this into the third we find
. So the dwarves must combine 0.90 kg of AA and 1.80 kg of magic steel.
Answer:
28.76 °F
Step-by-step explanation:
The temperture of sea ice frozen ocean water is about -1.8 °C .
We are to convert to a temperture in fahrenheit using the formula F=(c) (9/5)+32
°C = -1.8°C
°F=(c) (9/5)+32
= [(-1.8°C × 9/5) + 32]°F
= [-16.2/5 + 32]°F
= [-3.24 + 32]°F
= 28.76°F
<u>Given</u>:
The given geometric series is ![2 + 3 + 4.5+ 6.75 + ...](https://tex.z-dn.net/?f=2%20%2B%203%20%2B%204.5%2B%206.75%20%2B%20...)
We need to determine the value of r and a₁
<u>Value of a₁:</u>
The term a₁ denotes the first term of the geometric series.
Hence, from the given series, the first term of the series is 2.
Thus, a₁ = 2.
Therefore, the value of a₁ is 2.
<u>Value of r:</u>
The term r denotes the common ratio between the terms in the geometric series.
The value of r is given by
![r=\frac{3}{2}=1.5](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B3%7D%7B2%7D%3D1.5)
![r=\frac{4.5}{3}=1.5](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B4.5%7D%7B3%7D%3D1.5)
![r=\frac{6.75}{4.5}=1.5](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B6.75%7D%7B4.5%7D%3D1.5)
Thus, the value of r is 1.5
Answer:
14.6%
Step-by-step explanation:
Use binomial probability:
P = nCr pʳ (1−p)ⁿ⁻ʳ
where n is the number of trials,
r is the number of successes,
and p is the probability of success.
Here, n = 10, r = 4, and p = 1/4.
P = ₁₀C₄ (1/4)⁴ (1−1/4)¹⁰⁻⁴
P = 210 (1/4)⁴ (3/4)⁶
P ≈ 0.146
There is an approximate 14.6% probability that exactly 4 of the 10 adults are on a diet.
A. would be the correct choice because the x+y hast to =1.