32^(2c)=8^(c)+7
2^10c=2^3c+21 im gonna assume 7 is in the exponent
10c=3c+21
7c=21
c=3
Answer:
Option C
Step-by-step explanation:
Point diagrams show the frequency of occurrence of a series of events after a certain number of trials. In this case, the trials were 100. During each trial it would have been possible to have proportions of {0.24, 0.25, 0.26, 0.27, 0.28 ..... 0.56}
The events with the highest probability of occurrence are those with the highest number of points in the diagram.
Note that the distribution of the points resembles a bell, with a peak (greater clustering of points) between 0.35 and 0.41.
This indicates that it is more likely that the proportion of employees who go to work in bicycles will be between 0.35 and 0.41.
Then the diagram seems to indicate that a proportion less than 0.30 or greater than 0.45 is unlikely (they have less number of points)
Based on this analysis, it can be concluded that the correct option is c)
c) It is plausible that 40% of the population rides a bike to work because the data shows that a sample proportion of 29% is unlikely.
Answer:
56/65
Step-by-step explanation:
First, we know that cos(a-b) = cos(a)cos(b) + sin(a)sin(b)
We know what sin(a) and sin(b) are, and to get cos(a), we can take the equation sin²a + cos²a = 1
Thus,
(12/13)² + cos²a = 1
1 - (12/13)² = cos²a
1- 144/169 = cos²a
cos²a = 25/169
cos(a) = 5/13
Similarly,
(3/5)² + cos²b = 1
1 - (3/5)² = cos²b
1 - 9/25 = cos²b
cos²b = 16/25
cos(b) = 4/5
Our answer is
cos(a-b) = cos(a)cos(b) + sin(a)sin(b)
cos(a-b) = (5/13)(4/5) + (12/13)(3/5)
cos(a-b) = 20/65 + 36/65
cos(a-b) = 56/65
Answer:
f(x) = -3x + 6
Step-by-step explanation:
The general linear function is;
y = mx + b
it can also be written as (x , f(x))
f(x) = mx + b
where m is the slope and b is the y-intercept
so we have the points ;
(0,6) and (4,-6)
So we have;
for f(0) to be 6, it means that the y-intercept b is 6
This is because the value of x at the y-intercept is 0
So we have this as;
f(x) = mx + 6
Now, let’s substitute the other point so as to get m
For the other point;
x = 4 and f(x) = -6
that means;
-6 = 4m + 6
4m = -6-6
4m = -12
m = -12/4
m = -3
So we have the equation as;
f(x) = -3x + 6
