Which number is located between 1.2 and 1.4 on the number line
2 answers:
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Answer:
Length of package can be = 22 inches
Step-by-step explanation:
Given:
For a package to qualify for a certain postage rate, the sum of its length and girth cannot exceed 85 inches
To find length of package when girth of package is = 63 inches
Solution:
Let length of package be = inches
Let girth length of package be = inches
Sum of length and girth of package = inches
To qualify for a certain postage rate the sum of length and girth should not exceed 85 inches.
Thus, the inequality representing the situation can be given as:
We are given girth of package is = 63 inches
So, inequality to find length would be:
Subtracting both sides by 63.
inches
So, length should not exceed 22 inches in order to qualify.
Thus, the maximum length of package to qualify for the postal rate must be = 22 inches
Answer:
There is an 8.38% probability that the anchor will be fired.
Step-by-step explanation:
For each resident, there is only two possible outcomes. Either they can name the news anchor on the evening news at their station, or they cannot.
This means that the binomial probability distribution will be used in our solution.
However, we are working with samples that are considerably big. So i am going to aaproximate this binomial distribution to the normal.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that .
In this problem, we have that:
400 city residents are going to be asked. So .
Suppose that in fact 12% of city residents could name the anchor if asked. This means that .
So,
.
They plan to fire the news anchor if fewer than 10% of the residents in the sample can do so.
What is the approximate probability that the anchor will be fired?
10% of the residents is 0.10*400 = 40 residents.
Fewer than 10% is 39 residents. So the probability that the anchor will be fired is the pvalue of Z when .
So:
has a pvalue of 0.0838. This means that there is an 8.38% probability that the anchor will be fired.
Answer:
The actual number of calories that Mya burned when she
trained for 30 minutes is 240.
Step-by-step explanation:
We have an exponential function that is the best fit for the number of calories Mya burns, in function of time (minutes).
The function is:
Where y: calories burned, and x: training time.
Whenever we use regression models, we have a real value and a predicted value. The difference between them, the measure we want to minimize when we adjust with this typo of models, is called residual.
In the table is shown as one of the columns.
For example, for x=10 minutes, we have a real value of 30 and a predicted value of 78.36, so the residual becomes e=30-78.36=-48.36.
For x=30 minutes, we have only the residual, that has a value of 5.53. That means that the predicted value, which we can calculate, is 5.53 below the real value.
The predicted value for x=30 is:
Using the equation for the residual e, we can calcualte the actual number of calories that Mya burned in 30 minutes: