The answer is x = 4, y = -1 or (4, -1).
We are given :
- <u>2x + 7y = 1</u>
- <u>3x + 4y = 8</u>
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Multiply the 1st equation with 3 and 2nd equation with 2.
<u>3. 3(2x + 7y) = 3(1) ⇒ 6x + 21y = 3</u>
<u>4. 2(3x + 4y) = 2(8) ⇒ 6x + 8y = 16</u>
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Now, subtract : Equation 3 - Equation 4.
- 6x + 21y - 6x - 8y = 3 - 16
- 13y = -13
- y = -1
Substitute in the 1st equation.
- 3x + 4(-1) = 8
- 3x - 4 = 8
- 3x = 12
- x = 4
Answer:
a) 0.6517; b) 0.9115; c) No
Step-by-step explanation:
For part a, we will use the formula for a z score of an individual:
Using a z table, we see that the area under the curve to the left of this value is 0.3483. However, we want the probability greater than this, which is the area to the right of this value under the curve; this means we subtract from 1:
1-0.3483 = 0.6517
For part b, we will use the formula for a z score of the mean of a sample:
Using a z table, we see that the area under the curve to the left of this value is 0.0885. This means the area under the curve to the right of this value is
1-0.0885 = 0.9115
For part c,
The fact that the probability that any 12 men on the elevator will have a mean weight greater than 167, putting their total weight above 2004 pounds, is 91% means the elevator does not have the appropriate limit. There is a high chance the maximum will be exceeded.
It's B, and being mental won' help when having a calculator next to you) It's B for sure!!!
Answer:
16 ft
Step-by-step explanation:
Based on the situation above, it forms into a right triangle. Therefore we can apply the Pythagorean Theorem. We will use the formula below:
c = √( a² + b²)
In the problem above, the ladder acts as the hypotenuse denoted by c. It has a length of 20 ft. While the base denoted by b is 12 ft. Therefore, we need to solve for a. We will derive the formula above.
c² = a² + b²
a² = c² - b²
a = √( c² - b² )
a = √( 20² - 12² )
a = 16
The unit is in ft.
Correct me if I'm wrong. I hope it helps.
The percentage increase in the student's height is 10.52%.
Here we are given that a student's height increases from 1.52m to 1.68m.
Thus, the absolute increase in the student's height will be-
1.68 - 1.52 = 0.16 meters.
Now, we need to find the percentage increase in the student's height.
The formula for calculating percentage increase is given by-
Percentage increase = change in value/ initial value * 100
Here, the change in value is 0.16 meters and the initial value is 1.52 meters.
Thus, percentage increase in height = 0.16 / 1.52 *100
= 1600/ 152
= 400/ 38
= 200/ 19
= 10.52%
Thus, the increase in the student's height is 10.52%.
Learn more about percentage change here-
https://brainly.in/question/19592355
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