By applying the law of sines and some algebraic handling, the length of the side LJ is approximately equal to 3.517 units. (Right choice: D)
<h3>What is the missing side of the triangle according to the law of sines?</h3>
The law of sines presents a relationship between sides and <em>opposite</em> angles, which is described below:
9/sin 89° = LJ/sin 23° (1)
LJ = 9 × sin 23°/sin 89°
LJ ≈ 3.517
By applying the law of sines and some algebraic handling, the length of the side LJ is approximately equal to 3.517 units. (Right choice: D)
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The sum of 31/4+42/4= 18.25
<u>Step-by-step explanation</u>:
- The denominators are same.
- Then add the numerators and keep the denominators same.
The sum of (31/4) + (42/4) = (31+42)/4
⇒ 73/4
⇒ 18.25
Answer:
95% two-sided confidence interval on the true mean breaking strength is (94.8cm, 99.2cm)
Step-by-step explanation:
Our sample size is 11.
The first step to solve this problem is finding our degrees of freedom, that is, the sample size subtracted by 1. So
.
Then, we need to subtract one by the confidence level 
and divide by 2. So:
Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 10 and 0.025 in the two-sided t-distribution table, we have 
Now, we find the standard deviation of the sample. This is the division of the standard deviation by the square root of the sample size. So
Now, we multiply T and s
![M = Ts = 1.812*1.2060 = 2.19/tex]For the lower end of the interval, we subtract the sample mean by M. So the lower end of the interval here is[tex]L = 97 - 2.19 = 94.81 = 94.8](https://tex.z-dn.net/?f=M%20%3D%20Ts%20%3D%201.812%2A1.2060%20%3D%202.19%2Ftex%5D%3C%2Fp%3E%3Cp%3E%3Cstrong%3EFor%20the%20lower%20end%20of%20the%20interval%2C%20we%20subtract%20the%20sample%20mean%20by%20M.%3C%2Fstrong%3E%20So%20the%20lower%20end%20of%20the%20interval%20here%20is%3C%2Fp%3E%3Cp%3E%5Btex%5DL%20%3D%2097%20-%202.19%20%3D%2094.81%20%3D%2094.8)
cm
For the upper end of the interval, we add the sample mean and M. So the upper end of the interval here is
cm
So
95% two-sided confidence interval on the true mean breaking strength is (94.8cm, 99.2cm).
Answer:
Horizontal shift of 4 units to the left.
Vertical translation of 8 units downward.
Step-by-step explanation:
Given the quadratic function, y = (x + 4)² - 8, which represents the horizontal and vertical translations of the parent graph, y = x²:
The vertex form of the quadratic function is y = a(x - h)² + k
Where:
The vertex is (h , k), which is either the <u>minimum</u> (upward facing graph) or <u>maximum</u> (downward-facing graph).
The axis of symmetry occurs at <em>x = h</em>.
<em>a</em> = determines whether the graph opens up or down, and makes the graph wider or narrower.
<em>h</em> = determines how far left or right the parent function is translated.
<em>k</em> = determines how far up or down the parent function is translated.
Going back to your quadratic function,
y = (x + 4)² - 8
- The vertex occrs at (-4, -8)
- a is assumed to have a value of 1.
- Given the value of <em>h</em> = -4, then it means that the graph shifted horizontally by <u>4 units to the left</u>.
- Since k = -8, then it implies that the graph translated vertically at <u>8 units downward</u>.
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Sienna was dividing 12.76 by 0.001.Let's find out which one is correct based on the given choices. Let's perform division
=> 12.76 / 0.001 = 12 760
Thus, the correct answer is B. It will be less than 13,000.
