The graph is the one that correctly represents the linear piece-wise function is the first graph.
<h3>How to solve for the graph</h3>
First we have a linear function as
Mx + b
mc= slope, this is the rate of change, how y changes as x changes by 1.
b = y-intercept, y value as x = 0
y = 5 + x
x ≤ 10
at 10 we have 5 + 10 = 15
at 2 dollars
y = 15 + 2(x - 10)
at 14
y = 15 + 2(14 - 10)
15 + 2*4
= 23
Hence we can conclude that the first graph here is the correct one.
Read more on graphs here:
brainly.com/question/22295833
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Answer:
B. They are similar but not congruent
Step-by-step explanation:
Similar means when two figures have the same shape, so it doesn't matter if its smaller or bigger
Congruent means two figures with the same proportions
Try this option:
1. rule: P(E)+P(not E)=1.
2. according to the rule above
P(not E)=1-P(E)=1-0.3=0.7;
P(E)=1-P(not E)=(100-65)%=35%.
Answer:
(a) 5 mayflies
(b) 15 mayflies
(c) 84 flying flies
Step-by-step explanation:
Represent Mayflies with M and the total flying insects with F
The ratio can be represented as:
![M : F = 5 : 14](https://tex.z-dn.net/?f=M%20%3A%20F%20%3D%205%20%3A%2014)
Solving (a):
![F = 14](https://tex.z-dn.net/?f=F%20%3D%2014)
Find M
Substitute 14 for F in ![M : F = 5 : 14](https://tex.z-dn.net/?f=M%20%3A%20F%20%3D%205%20%3A%2014)
![M : 14 = 5 : 14](https://tex.z-dn.net/?f=M%20%3A%2014%20%3D%205%20%3A%2014)
Convert to fraction
![\frac{M}{14} = \frac{5}{14}](https://tex.z-dn.net/?f=%5Cfrac%7BM%7D%7B14%7D%20%3D%20%5Cfrac%7B5%7D%7B14%7D)
Multiply through by 14
![14 * \frac{M}{14} = \frac{5}{14} * 14](https://tex.z-dn.net/?f=14%20%2A%20%5Cfrac%7BM%7D%7B14%7D%20%3D%20%5Cfrac%7B5%7D%7B14%7D%20%2A%2014)
![M = 5](https://tex.z-dn.net/?f=M%20%3D%205)
Solving (b):
![F = 42](https://tex.z-dn.net/?f=F%20%3D%2042)
Find M
Substitute 42 for F in ![M : F = 5 : 14](https://tex.z-dn.net/?f=M%20%3A%20F%20%3D%205%20%3A%2014)
![M : 42 = 5 : 14](https://tex.z-dn.net/?f=M%20%3A%2042%20%3D%205%20%3A%2014)
Convert to fraction
![\frac{M}{42} = \frac{5}{14}](https://tex.z-dn.net/?f=%5Cfrac%7BM%7D%7B42%7D%20%3D%20%5Cfrac%7B5%7D%7B14%7D)
Multiply through by 42
![42 * \frac{M}{42} = \frac{5}{14} * 42](https://tex.z-dn.net/?f=42%20%2A%20%5Cfrac%7BM%7D%7B42%7D%20%3D%20%5Cfrac%7B5%7D%7B14%7D%20%2A%2042)
![M = \frac{5}{14} * 42](https://tex.z-dn.net/?f=M%20%3D%20%5Cfrac%7B5%7D%7B14%7D%20%2A%2042)
![M=5*3](https://tex.z-dn.net/?f=M%3D5%2A3)
![M= 15](https://tex.z-dn.net/?f=M%3D%2015)
Solving (c):
![M = 30](https://tex.z-dn.net/?f=M%20%3D%2030)
Find F
Substitute 30 for M in ![M : F = 5 : 14](https://tex.z-dn.net/?f=M%20%3A%20F%20%3D%205%20%3A%2014)
![30 : F = 5 : 14](https://tex.z-dn.net/?f=30%20%3A%20F%20%3D%205%20%3A%2014)
Convert to fraction
![\frac{F}{30} = \frac{14}{5}](https://tex.z-dn.net/?f=%5Cfrac%7BF%7D%7B30%7D%20%3D%20%5Cfrac%7B14%7D%7B5%7D)
Multiply through by 30
![30 * \frac{F}{30} = \frac{14}{5} * 30](https://tex.z-dn.net/?f=30%20%2A%20%5Cfrac%7BF%7D%7B30%7D%20%3D%20%5Cfrac%7B14%7D%7B5%7D%20%2A%2030)
![F = \frac{14}{5} * 30](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7B14%7D%7B5%7D%20%2A%2030)
![F = 14*6](https://tex.z-dn.net/?f=F%20%3D%2014%2A6)
![F = 84](https://tex.z-dn.net/?f=F%20%3D%2084)