Slove for x : 3x + 4 = 9x + 3
2 answers:
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Answer:
The slope of a line that is perpendicular to the given line is
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
Where "m" is the slope of the line and "b" is the y-intercept.
Solve for "y" from the equation of the line :
You can observe that the slope of this line is:
By definition, the slopes of perpendicular lines are negative reciprocal, then, the slope of a line that is perpendicular to the give line, is
Method 1: In order to find out the area of an octagon with a radius of 4 feet, we have to split the whole figure into 8 equal isosceles triangles.
Therefore,
We will find out the area of one triangle and multiply the area with 8 to, figure out the area of the whole octagon there are 8 similar triangles and all of them will have the same area.
Method 2: From method 1, it would take time as there are too much of calculation, therefore we would go for the shortcut using the formula:
Area = 2√2 × r²
where r<span> is the radius of the octagon.
Substituting the values,
We get:
</span>Area = 2√2 × 4²
Area = 2√2 × 16
Area = 2× 1.41 × 16
Area = 2.828 × 16
Area = 45.25
Rounded to the nearest tenth:
Area = 45.3 ft²
Therefore,
We will find out the area of one triangle and multiply the area with 8 to, figure out the area of the whole octagon there are 8 similar triangles and all of them will have the same area.
Method 2: From method 1, it would take time as there are too much of calculation, therefore we would go for the shortcut using the formula:
Area = 2√2 × r²
where r<span> is the radius of the octagon.
Substituting the values,
We get:
</span>Area = 2√2 × 4²
Area = 2√2 × 16
Area = 2× 1.41 × 16
Area = 2.828 × 16
Area = 45.25
Rounded to the nearest tenth:
Area = 45.3 ft²
Answer:
14.63% probability that a student scores between 82 and 90
Step-by-step explanation:
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.
In this problem, we have that:
What is the probability that a student scores between 82 and 90?
This is the pvalue of Z when X = 90 subtracted by the pvalue of Z when X = 82. So
X = 90
has a pvalue of 0.9649
X = 82
has a pvalue of 0.8186
0.9649 - 0.8186 = 0.1463
14.63% probability that a student scores between 82 and 90