Answer:
3 and 4 not congruent
Step-by-step explanation:
Currently, the standard deviation is 10, because on average the cards were $10 away from the mean.
Adding another card with value $25 would decrease the standard deviation because it is closer to the mean the the current standard deviation.
Answer:
![FJ=39\ units](https://tex.z-dn.net/?f=FJ%3D39%5C%20units)
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem
△FEG is similar with △FHJ -----> by AA Similarity Theorem
so
![\frac{FE}{FH}=\frac{FG}{FJ}](https://tex.z-dn.net/?f=%5Cfrac%7BFE%7D%7BFH%7D%3D%5Cfrac%7BFG%7D%7BFJ%7D)
we have
![FE=HF+EH=26+14=40\ units](https://tex.z-dn.net/?f=FE%3DHF%2BEH%3D26%2B14%3D40%5C%20units)
![FH=HF=26\ units](https://tex.z-dn.net/?f=FH%3DHF%3D26%5C%20units)
![FG=60\ units](https://tex.z-dn.net/?f=FG%3D60%5C%20units)
substitute the given values
![\frac{40}{26}=\frac{60}{FJ}](https://tex.z-dn.net/?f=%5Cfrac%7B40%7D%7B26%7D%3D%5Cfrac%7B60%7D%7BFJ%7D)
![FJ=26(60)/40\\FJ=39\ units](https://tex.z-dn.net/?f=FJ%3D26%2860%29%2F40%5C%5CFJ%3D39%5C%20units)
Disance between (x1,y1) and (x2,y2) is
![D= \sqrt{(x2-x1)^2+(y2-y1)^2}](https://tex.z-dn.net/?f=D%3D%20%5Csqrt%7B%28x2-x1%29%5E2%2B%28y2-y1%29%5E2%7D%20)
given (-2,5) (3,-4)
![D= \sqrt{(3-(-2))^2+(-4-5)^2}](https://tex.z-dn.net/?f=D%3D%20%5Csqrt%7B%283-%28-2%29%29%5E2%2B%28-4-5%29%5E2%7D%20)
![D= \sqrt{(5)^2+(-9)^2}](https://tex.z-dn.net/?f=D%3D%20%5Csqrt%7B%285%29%5E2%2B%28-9%29%5E2%7D%20)
![D= \sqrt{25+81}](https://tex.z-dn.net/?f=D%3D%20%5Csqrt%7B25%2B81%7D%20)
D=√106
the distance is √106 units or abotu 10.2
Answer:
B. 11
Step-by-step explanation:
Set up a system of equations where a is the number of adults and c is the number of children
a + c = 87
8a + 5c = 468
Solve by substitution by rearranging the first equation, then substituting it in the second equation:
a = 87 - c
Substitute this for a in the second equation, then solve for c:
8(87 - c) + 5c = 468
696 - 8c + 5c = 468
696 - 3c = 468
-3c = -228
c = 76
Then, plug this into the first equation to solve for a:
a + c = 87
a + 76 = 87
a = 11
So, 11 adults attended the carnival.
The correct answer is B, 11