Answer:
#1 is 28
Step-by-step explanation:
Set the perimeters equal, as 6x - 2 = 8x - 12, solve for x = 5, and plug in.
Answer:
The co variance of the midterm and final exam scores is 58.76.
Step-by-step explanation:
The formula to compute the sample co variance is:

The values are computed in the table below.
Compute the co variance as follows:

Thus, the co variance of the midterm and final exam scores is 58.76.
Answer:
383 children and 361 adults
Step-by-step explanation:
Let's say there are a adults and c children. Since the total number of people was 744, we can write:
a + c = 744
We also know that children's prices are $1.75 per child and adults' prices are $2 per adult. Since the total is $1392.25, we can write:
1.75c + 2a = 1392.25
Now we have a system of linear equations:
a + c = 744
1.75c + 2a = 1392.25
Multiply the first equation by 2:
2 * (a + c = 744) ⇒ 2a + 2c = 1488
Now subtract the second equation from this one:
2a + 2c = 1488
- 2a + 1.75c = 1392.25
___________________
0a + 0.25c = 95.75
c = 383
Plug this in to find a:
a + c = 744
a + 383 = 744
a = 361
There were 383 children and 361 adults.
To solve this we are going to use the formula fro the force applied to a spring:

where

is the spring constant

is the extension
Since we know the

, we can replace that in our formula and solve for

:


where

is the acceleration

is the spring constant

is the extension

is the mass
We know for our problem that

,

, and

. So lets replace those values in our formula to find

:



We can conclude that the acceleration of the block when s=0.4m is

.
Answer:
Step-by-step explanation:
take 23 degree as reference angle
using tan rule
tan 23=opposite/adjacent
0.42=25/x
x=25/0.42
x=59.52
x=60