If you assign variables to the problem, it can make things a lot simpler. Lets say chairs are x and tables are y. Therefore you have:
2x+6y=40
5x+3y=25
Now you can isolate the variable of one equation and put it into another (it doesn't matter which. I'm going to manipulate the top equation to plug into the bottom one).
2x=40-6y
x=20-3y
Now I plug into bottom equatioin:
5(20-3y) + 3y=25
100-15y+3y=25
100-12y=25
-12y=-75
y=$6.25
Now you can plug in y in either equation to get x.
2x+6(6.25)=40
37.5+2x=40
2x=2.5
x=1.25
So it costs $6.25 for each table and $1.25 for each chair. If you think about it, it would make sense for the table to cost more for the chair.
Answer:
The bulbs should be replaced each 1436.9 hours.
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:
How often should the bulbs be replaced so that no more than 1% burn out between replacement periods?
This is the first percentile of hours. So it is X when Z has a pvalue of 0.01.
So it is X when Z = -2.33.
The bulbs should be replaced each 1436.9 hours.
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Answer:
Option D is right,.
Step-by-step explanation:
-a+4b+2c=-8 ... i
3a+b-4c=9 ... ii
b=-1 ... iii
Substitute the value of b, in i and ii
-a-4+2c =-8 or -a+2c = -4
and 3a-1-4c = 9 or 3a -4c =8
Now we have two equations in two variables
-a+2c =-4 and 3a-4c =8
a = 2c+4: substitute this in the other equatin.
3(2c+4)-4c =8 Or 2c +12 =8
2c =-4 or c = -2
Substitute in -a+2c =12
-a-2 = -4
a = -2+4 =2
a=2, b=-1 and c =-1 is the solution.
Wassup
Steps:
1. Draw a line connecting the point to the center of the rectangle
2. Then construct a perpendicular bisector to the line drawn in step 1
3. Place the compass on the midpoint of the line, adjust its length to reach the end point, and draw an arc across the circle
4. Where the arc crosses the circle will be the tangent points. So connect the endpoint to the tangent point
Hope the picture helps you too