Question:
Solution:
Let the following equation:
![\sqrt[]{12-x}=\text{ x}](https://tex.z-dn.net/?f=%5Csqrt%5B%5D%7B12-x%7D%3D%5Ctext%7B%20x%7D)
this is equivalent to:
![(\sqrt[]{12-x})^2=x^2](https://tex.z-dn.net/?f=%28%5Csqrt%5B%5D%7B12-x%7D%29%5E2%3Dx%5E2)
this is equivalent to:

this is equivalent to:

thus, we can conclude that
x= 3.
Answer:
see explanation
Step-by-step explanation:
Use the points to find a and b, that is
(2, 18)
18 = a
→ (1)
(4, 162)
162 = a
→ (2)
divide (2) by (1)
=
= 9
b² = 9 ⇒ b = 3
substitute b = 3 into (1)
18 = 9a ⇒ a = 2
y = 2
← exponential equation
Answer:
y = 30.96
Step-by-step explanation:
take 23 degree as reference angle
using tan rule
tan 23 = opposite / adjacent
0.42 = 13/y
y = 13/0.42
y = 30.96
Answer:
Step-by-step explanation:
Answer:
- Using conditional probabilities it can be shown that the results are influenced by the gender.
Explanation:
To prove that the results are influenced by <em>gender</em> you can calculate both the probability of preferring hot dogs and the conditional probability of preferring a hot dog given that is a female.
If the two results are different the probability of preferring hot dog is dependent on whether the person is a female or a male.
The probability of preferring hot dogs given that is a female is stated by the problem: 34.2%.
The probability of preferring hot dogs by the whole sample is:
- Number of males that prefer hot dogs: 184 (stated by the problem)
- Number of females that prefer hot dogs:
100% - 34.2% = 65.8%
65.8% of 635 = 0.658 × 635 = 417.83 ≈ 418
- Samples size: 542 males + 635 females = 1177
- Probability of preferring hot dogs =
number of students that preffer hot dogs / number of students =
(184 + 418) / 1177 = 602 / 1177 = 0.5115 ≈ 51.2%
Thus, the probability of preferring hot dogs given that the student is a female (34.2%) is different from the probability of preferring hot dog for the whole sample, making the results dependent of the gender.