Given the following system of equations:
1 answer:
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Answer:
Equal to 3
The drawing will help
Hey. Let me help you on this one.
In order for us to solve this problem easier, let's break it apart. We can also graph the triangle so we get visual of this problem.
I drew a quick graph for you to easier understand this question. As you can see, Charlie is standing below the tree 45 feet from it, and we need to find the unknown angle measure.
Let's form a SOHCAHTOA function which you have probably already learned in your Geometry course.
First of all let's identify our sides. The side opposite of the right triangle is a Hypotenuse, and the side that's 45 feet is adjacent, since it's adjacent to the unknown angle.
We know that we need to use
(Cosine) with negative power to it in order to solve this question, since we are looking for the unknown angle measure.
Let's form the function which, Hypotenuse, and Adjacent side.
Now, let's solve the left part of this function
Awesome. You will need to use your calculator for this part. Find the value of 0.45 when negative Cosine is used on it.
Awesome. Let's round this number to the closest tenth
is the rounded value we have discussed below.
Answer: 63.3 degrees is the unknown measure of the angle
In order for us to solve this problem easier, let's break it apart. We can also graph the triangle so we get visual of this problem.
I drew a quick graph for you to easier understand this question. As you can see, Charlie is standing below the tree 45 feet from it, and we need to find the unknown angle measure.
Let's form a SOHCAHTOA function which you have probably already learned in your Geometry course.
First of all let's identify our sides. The side opposite of the right triangle is a Hypotenuse, and the side that's 45 feet is adjacent, since it's adjacent to the unknown angle.
We know that we need to use
Let's form the function which
Now, let's solve the left part of this function
Awesome. You will need to use your calculator for this part. Find the value of 0.45 when negative Cosine is used on it.
Awesome. Let's round this number to the closest tenth
Answer: 63.3 degrees is the unknown measure of the angle
Answer:
a. 0.0582 = 5.82% probability that the heart rate is less than 25 beats per minute.
b. 0.1762 = 17.62% probability that the heart rate is greater than 60 beats per minute.
c. 0.7656 = 76.56% probability that the heart rate is between 25 and 60 beats per minute
Step-by-step explanation:
Empirical Rule:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean:
(95% of data) range from 19 to 75 beats per minute.
This means that between 19 and 75, by the Empirical Rule, there are 4 standard deviations. So
a. What is the probability that the heart rate is less than 25 beats per minute?
This is the p-value of Z when X = 25. So
has a p-value of 0.0582.
0.0582 = 5.82% probability that the heart rate is less than 25 beats per minute.
b. What is the probability that the heart rate is greater than 60 beats per minute?
This is 1 subtracted by the p-value of Z when X = 60. So
has a p-value of 0.8238.
1 - 0.8238 = 0.1762
0.1762 = 17.62% probability that the heart rate is greater than 60 beats per minute.
c. What is the probability that the heart rate is between 25 and 60 beats per minute?
This is the p-value of Z when X = 60 subtracted by the p-value of Z when X = 25. From the previous two items, we have these two p-values. So
0.8238 - 0.0582 = 0.7656
0.7656 = 76.56% probability that the heart rate is between 25 and 60 beats per minute