Answer:
LCM of 3, 5, and 6 is the smallest number among all common multiples of 3, 5, and 6. The first few multiples of 3, 5, and 6 are (3, 6, 9, 12, 15 . . .), (5, 10, 15, 20, 25 . . .), and (6, 12, 18, 24, 30 . . .) respectively. There are 3 commonly used methods to find LCM of 3, 5, 6 - by division method, by prime factorization, and by listing multiples.
Step-by-step explanation:
Answer:
Parallel: y=-4x-1
Perpendicular: y=-4x+13/2
Step-by-step explanation:
For the equation y=-4x-41, the slope is -4. Writing a line related to this equation has two options:
- If the line will be parallel to it then this is the slope of the new line as well. Use the point-slope form to write the equation, then simplify and convert into the slope intercept form.
(y-7)=-4(x--2)
y-7=-4x-8
y=-4x-1
- If the line will be perpendicular to it then the slope is the negative reciprocal of the previous slope. It is 1/4.
(y-7)=1/4(x--2)
y-7=1/4x-1/2
y=-4x+13/2
Answer:
Cost of per session the average rate is $45.
Step-by-step explanation:
It is given that a gym membership with two personal training session cost $125, while gym membership with five personal training sessions cost $260.
It is required to find what is the cost per session.
Step 1 of 1
It is given that a gym membership with two personal training session cost $125, while gym membership with five personal training sessions cost $260.
To find the cost of per session calculate the average rate.
Now let $f(x)$ be the cost per session use the for the average rate of change, and the input value is the number of personal traings x.
Now substitute, $125 for 
, 260 for 
for 
and 5 for 
then,
Cost of per session the average rate is $45.
Answer:
d. The variance is 9.56 and the standard deviation is 3.09.
Step-by-step explanation:
From the above question, we are given the following data set.
3, 7, 8, 8, 8, 9, 10, 10, 13, 14
a) Mean = 3 + 7 + 8 + 8 + 8 + 9 + 10 + 10 + 13 + 14/ 10
= 90/10
= 9
b) Variance
The formula for sample Variance = (Mean - x)²/ n - 1
Mean = 9
n = 10
Sample Variance =
(3 - 9)² + (7 - 9)² + (8 - 9)² + (8 - 9)² + (8 - 9)² + (9 - 9)² + (10 - 9)² + (10 - 9)² + (13 - 9)² + (14 - 9)² / 10 - 1
= 36 + 4 + 1 + 1 + 1 + 0 + 1 + 1 + 16 + 25/9
= 86/9
= 9.555555556
≈ Approximately 9.56
Variance = 9.56
Sample Standard deviation = √Sample Variance
= √9.56
= 3.0919249667
≈ Approximately 3.09
Answer:
1. 9 < s < 17
2. 5 < MN < 19
3. AD > BD
Step-by-step explanation:
1. The triangle inequality tells you the sum of any two sides of a triangle must exceed the length of the other side. (Some versions say, "must be not less than ..." rather than "must exceed.") In practice, this means two things:
- the sum of the shortest two sides is greater than the length of the longest side
- the length of any side lies between the sum and the difference of the other two sides
Here, we can use the latter fact to write the desired inequality. The difference of the given sides is 13 -4 = 9; their sum is 13 +4 = 17. The third side must lie between 9 and 17. If that side length is designated "s", then ...
9 < s < 17
(If you don't mind a "triangle" that looks like a line segment, you can use ≤ instead of <.)
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2. Same as (1) using different numbers.
12 -7 < MN < 12 +7
5 < MN < 19
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3. Side CD is congruent to itself, and side CA is shown congruent to side CB. This means the requirements of the Hinge Theorem are met. That theorem tells you the longer side is opposite the greater angle:
AD > BD
