Answer:
84
Step-by-step explanation:
I don't really know how to explain it but I'll try my best
Visualize line AB extending past point A (like it does at point B)
You'll see that 180 ( line AB ) minus 129 is 51
Angle 51 is vertical to the other angle inside the triangle that is unnamed.
Now you have 2 angles.
180-45-51=84
Answer:
180 degrees
Step-by-step explanation:
Answer:
a) 30 inches × 30 inches × 30 inches
b) 27,000 inches³
c) 14,130 inches³
d) 12,870 inches³
Step-by-step explanation:
Edge of the cube = diameter = 30 inches
Volume of cube = s³
30³ = 27000 inches³
Radius = 30/2 = 15
Volume of sphere:
(4/3) × 3.15 × 15³
14130 inches³
Difference:
27000 - 14130
12870 inches³
The standard deviation is 9.27. The typical heart rate for the data set varies from the mean by an average of 9.27 beats per minute.
<h3>How to determine the standard deviation of the data set?</h3>
The dataset is given as:
Heart Rate Frequency
60 1
65 3
70 4
75 12
80 8
85 15
90 9
95 5
100 3
Calculate the mean using
Mean = Sum/Count
So, we have
Mean = (60 * 1 + 65 * 3 + 70 * 4 + 75 * 12 + 80 * 8 + 85 * 15 + 90 * 9 + 95 * 5 + 100 * 3)/(1 + 3 + 4 + 12 + 8 + 15 + 9 + 5 + 3)
Evaluate
Mean = 82.25
The standard deviation is

So, we have:
SD = √[1 * (60 - 82.25)^2 + 3 * (65 - 82.25)^2 + 4 * (70 - 82.25)^2 + 12 * (75 - 82.25)^2 + 8 * (80 - 82.25)^2 + 15 * (85 - 82.25)^2 + 9 * (90 - 82.25)^2 + 5 * (95 - 82.25)^2 + 3 * (100 - 82.25)^2)]/[(1 + 3 + 4 + 12 + 8 + 15 + 9 + 5 + 3 - 1)]
This gives
SD = √85.9533898305
Evaluate
SD = 9.27
Hence. the standard deviation is 9.27. The typical heart rate for the data set varies from the mean by an average of 9.27 beats per minute.
Read more about standard deviation at:
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Answer:
B
Step-by-step explanation:
First label the equations.
6x +3y= 18 -----(1)
y= -2x +5 -----(2)
subst. (2) into (1):
6x +3(-2x +5)= 18
6x +3(-2x) +3(5)= 18 (expand)
6x -6x +15= 18
15= 18 (simplify)
(reject)
There is no solution.
<u>Further explanation</u><u>:</u>
If I rewrite the first equation into the form of y=mx+c, I would get
6x +3y=18
3y= 18 -6x (bring y term to one side)
y= 6- 2x (÷3 throughout)
y= -2x +6
Notice that the gradients of both lines are equal ( -2). This implies that they are parallel to each other and will never meet. Hence there are no solutions.