Given:
A figure of a right triangle.
To find:
The missing side by using the trigonometric ratios.
Solution:
In a right angle triangle,
In triangle ABC,
Multiply both sides by 270.
Therefore, the missing side length is b=231.4 inches.
Answers: A) $44,944
B) $50,499.0784
Math: Using the percentage calculator linked below 6% of $40,000 is $2,400. Since you're getting your second raise after your first and since it is a 6% raise from what you're getting paid at that time we add pay raise 1 to your starting pay before calculating the 6% for pay raise 2. $40,000+$2,400=$42,400. 6% of $42,400 is $2,544. $42,400+$2,544=$44,944, Since that is two pay raises that would be your earnings at the end of year two (answer A).
We continue calculating 6% then adding that onto the total before calculating it for the next year for problem B.
6% of $44,944 is $2,696.64. $44,944+$2,696.64=$47,640.64.
6% of $47,640.64 is $2,858.4384. $47,640.64+$2,858.4384=$50,499.0784. That's answer B.
Hopefully you can figure out C on your own! I feel a little bad for giving a partial answer but I think you can do this!
Percentage calculator used-https://percentagecalculator.net/
Note: can't handle commas, remove all commas before entering data in.
The angle measures of triangle ABC is ∠A=90°, ∠B= 60°, ∠C = 30°. Thus, the correct option is B.
<h3>What is a triangle?</h3>
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
As it is known that the angles of the triangle are 30°, 60°, and 90°. Therefore, the largest angle is 90° which will be the opposite of the largest side of the triangle, therefore, the measure of ∠A=90°.
Also, the shortest angle of the triangle is 30°, which will lie at the opposite of the smallest side of the triangle, therefore, the measurement of the ∠C=30°.
Now, the angle left is ∠B therefore, the measure of ∠B=60°.
Hence, the angle measures of triangle ABC is ∠A=90°, ∠B= 60°, ∠C = 30°. Thus, the correct option is B.
Learn more about Triangle:
brainly.com/question/2773823
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The valid conclusions for the manager based on the considered test is given by: Option
<h3>When do we perform one sample z-test?</h3>
One sample z-test is performed if the sample size is large enough (n > 30) and we want to know if the sample comes from the specific population.
For this case, we're specified that:
- Population mean =
= $150 - Population standard deviation =
= $30.20 - Sample mean =
= $160 - Sample size = n = 40 > 30
- Level of significance =
= 2.5% = 0.025 - We want to determine if the average customer spends more in his store than the national average.
Forming hypotheses:
- Null Hypothesis: Nullifies what we're trying to determine. Assumes that the average customer doesn't spend more in the store than the national average. Symbolically, we get:
- Alternate hypothesis: Assumes that customer spends more in his store than the national average. Symbolically
where 
is the hypothesized population mean of the money his customer spends in his store.
The z-test statistic we get is:
The test is single tailed, (right tailed).
The critical value of z at level of significance 0.025 is 1.96
Since we've got 2.904 > 1.96, so we reject the null hypothesis.
(as for right tailed test, we reject null hypothesis if the test statistic is > critical value).
Thus, we accept the alternate hypothesis that customer spends more in his store than the national average.
Learn more about one-sample z-test here:
brainly.com/question/21477856
