The diagram represents the polynomial 4x2 + 23x – 72. A 2-column table with 2 rows. The labels for both the columns and the rows
2 answers:
Answer:
Option D.
Step-by-step explanation:
The given polynomial is
We need to find the factored form of given polynomial.
Splitting the middle term, then given polynomial can be rewritten as
Taking out the common factors from each parenthesis.
Taking out the common factors.
The factored form of given polynomial is (4x-9)(x+8).
Therefore, the correct option is D.
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Let x be the amount of cement and y be the amount of sand. If <span>the ratio of cement to sand for mortar is 1:3, then 
and y=3x.
</span>
So, if <span>Sandy puts in x=7 shovels of cement, then she puts
shovels of sand.
</span><span>
</span><span>Answer: 21 shovels of sand.
</span>
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So, if <span>Sandy puts in x=7 shovels of cement, then she puts
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</span><span>Answer: 21 shovels of sand.
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Answer:
a) 33% probability that a single student randomly chosen from all those taking the test scores 21 or higher.
b) 0.39% probability that the mean score for 76 students randomly selected from all who took the test nationally is 20.4 or higher
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:
Problems of normally distributed samples are 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.
Central limit theorem:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, the sample means with size n of at least 30 can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
a) What is the probability that a single student randomly chosen from all those taking the test scores 21 or higher?
This is 1 subtracted by the pvalue of Z when X = 21. So
has a pvalue of 0.67
1 - 0.67 = 0.33
33% probability that a single student randomly chosen from all those taking the test scores 21 or higher.
b) The average score of the 76 students at Northside High who took the test was x =20.4. What is the probability that the mean score for 76 students randomly selected from all who took the test nationally is 20.4 or higher?
Now we have
This probability is 1 subtracted by the pvalue of Z when X = 20.4. So
By the Central Limit Theorem
has a pvalue of 0.9961
1 - 0.9961 = 0.0039
0.39% probability that the mean score for 76 students randomly selected from all who took the test nationally is 20.4 or higher