Answer:
x=4 1/6 y=-3 1/2
Step-by-step explanation:
RS is perpendicular to MN and PQ.
We can use the slopes of these lines to determine the answer.
Slope is given by the formula
m=.
Using the coordinates for M and N, we have:
m=.
Since PQ is parallel to MN, its slope will be as well, since parallel lines have the same slope.
Using the coordinates for points T and V in the slope formula, we have
m=.
This is not parallel to MN or PQ, since the slopes are not the same.
We can also say that it is not perpendicular to these lines; perpendicular lines have slopes that are negative reciprocals (they are opposite signs and are flipped). This is not true of TV either.
Using the coordinates for R and S in the slope formula, we have
m=. Comparing this to the slope of RS, it is flipped and the sign is opposite; they are negative reciprocals, so they are perpendicular.
Answer:
The approximate percentage of SAT scores that are less than 865 is 16%.
Step-by-step explanation:
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.
In this problem, we have that:
Mean of 1060, standard deviation of 195.
Empirical Rule to estimate the approximate percentage of SAT scores that are less than 865.
865 = 1060 - 195
So 865 is one standard deviation below the mean.
Approximately 68% of the measures are within 1 standard deviation of the mean, so approximately 100 - 68 = 32% are more than 1 standard deviation from the mean. The normal distribution is symmetric, which means that approximately 32/2 = 16% are more than 1 standard deviation below the mean and approximately 16% are more than 1 standard deviation above the mean. So
The approximate percentage of SAT scores that are less than 865 is 16%.
Answer:
105.
Step-by-step explanation:
21+21+21+21+21=105.
Answer:
6 weeks
Step-by-step explanation:
Given that :
Nikki :
Initial amount = $1100 ;
Amount spent per week = $35
Mich:
Initial amount = $520
Amount saved per week = $55
Number of weeks they'll both have the same amount :
Let number of weeks = w
For Nikki who is spending :
1100 - 35w - - - (1)
For Mich who is saving :
520 + 55w - - - (2)
Equate (1) and (2)
1100 - 35w = 520 + 55w
1100 - 520 = 55w + 35w
580 = 90w
w = 580 / 90
w = 6.444
About 6 weeks
