Answer:
<u>Option b. (x = 3, y = 20, z = -14)</u>
Step-by-step explanation:
Given:
2x + 2y + 3z = 4
5x + 3y + 5z = 5
3x + 4y + 6z = 5
Solve using Cramer’s rule
∴ ![\left[\begin{array}{ccc}2&2&3\\5&3&5\\3&4&6\end{array}\right] =\left[\begin{array}{ccc}4\\5\\5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%262%263%5C%5C5%263%265%5C%5C3%264%266%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C5%5C%5C5%5Cend%7Barray%7D%5Cright%5D)
∴A = ![\left[\begin{array}{ccc}2&2&3\\5&3&5\\3&4&6\end{array}\right] = -1](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%262%263%5C%5C5%263%265%5C%5C3%264%266%5Cend%7Barray%7D%5Cright%5D%20%3D%20-1)
Ax = ![\left[\begin{array}{ccc}4&2&3\\5&3&5\\5&4&6\end{array}\right] = -3](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%262%263%5C%5C5%263%265%5C%5C5%264%266%5Cend%7Barray%7D%5Cright%5D%20%3D%20-3)
Ay = ![\left[\begin{array}{ccc}2&4&3\\5&5&5\\3&5&6\end{array}\right] =-20\\](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%264%263%5C%5C5%265%265%5C%5C3%265%266%5Cend%7Barray%7D%5Cright%5D%20%3D-20%5C%5C)
Az = ![\left[\begin{array}{ccc}2&2&4\\5&3&5\\3&4&5\end{array}\right] = 14](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%262%264%5C%5C5%263%265%5C%5C3%264%265%5Cend%7Barray%7D%5Cright%5D%20%3D%2014)
∴ x = Ax/A = -3/-1 = 3
y = Ay/A = -20/-1 = 20
z = Az/A = 14/-1 = -14
<u>So, the answer is option b. (x = 3, y = 20, z = -14)</u>
Answer:
2c + 8
Step-by-step explanation:
Apply the Distributive Property of Multiplication:
(c + 4)(2) = (2)(c + 4) = 2c + 8
Answer:
$0.10/oz
Step-by-step explanation:
Unit rate simply means the amount per 1 unit of something.
In this case, we want to find the amount of money for 1 oz of something.
So, we divide 1.99 by 30 and divide 30 by 30 to get:
(1.99 / 30) / (30 / 30) = $0.0663 / 1 oz
Rounded to the nearest tenth, 0.0663 is about 0.1.
Thus, the answer is $0.10/oz.
For the<span> geometric sequence, it has two forms of formula
</span>
<span>We are interested in the recursive formula now
</span>
<span>
{-80, 20, -5, ...}
The common ratio is (20/-80)=(-5/20)=-1/4=-0.25
So our r</span><span>ecursive formula would be
</span>
I hope that
helps!
Answer:
68%
Step-by-step explanation:
The Standard Deviation Rule = Empirical rule formula states that:
68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ.
95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.
99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.
From the question,
Step 1
We have to find the number of Standard deviation from the mean. This is represented as x in the formula
μ = Mean = 61
σ = Standard Deviation = 8
For x = 53
μ - xσ
53 = 61 - 8x
8x = 61 - 53
8x = 8
x = 8/8
x = 1
For x = 69
μ + xσ
69 = 61 + 8x
8x = 69 - 61
8x = 8
x = 8/8
x = 1
This falls within 1 standard deviation of the mean where: 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ.
Therefore, according to the Standard Deviation Rule, the approximate percentage of daily phone calls numbering between 53 and 69 is 68%
