Given the regular polygon, find the measure of each numbered angle.2
Answers
Weare given a regular figure, and asked for the measure of some indicated angles as shown below:
Notice that this is regolar figure (all sides of the same size) and also that is has 8 sides. Therefore, the central angle (360 degrees) must be divided by 8 to find the measure of angle <1:
angle <1 = 360 / 8 = 45 degrees.
Now, since the little triangles that the polygon is divided into, are all isosceles triangles (have the two sides connected to the center of the polygon, equal, then the other two angles inside each triangle must be equal (let's call them "x").
Now, for each little triangle we use the property that the addition of its internal angles must equal 180 degrees:
<1 + x + x = 180
45 + 2 x = 180
2 x = 180 - 45
2 x = 135
x = 67.5 degrees
Then <1 = 45 degrees , and <2 = 67.5 degrees.
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Answers
The volume of a sphere is given by:
V = (4/3) * (pi) * (r ^ 3)
Where,
r: sphere radio
Substituting values we have:
V = (4/3) * (3.14) * ((10/2) ^ 3)
V = 523.3333333
Rounding the nearest whole number we have:
V = 524 m ^ 3
Answer:
option 1
V = 524 m ^ 3
Question 2:
The area of a sphere is given by:
V = (4) * (pi) * (r ^ 2)
Where,
r: sphere radio
Substituting values we have:
V = (4) * (3.14) * ((15/2) ^ 2)
V = 706.5
Rounding the nearest whole number we have:
V = 706.5 yd ^ 2
Answer:
V = 706.5 yd ^ 2
option 2
2 B
3 A
4 B
5 B
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Answers
Answer: 44
Step-by-step explanation:
Answers
Answer:
Step-by-step explanation:
As the base is a square so the length is a, width is a and the height is h.
According to the question,
a + a + h = 96
h = 96 - 2a .... (1)
Volume of the box, V = length x width x height
V = a x a x h
V = a² (96 - 2a) from equation (1)
V = 96a² - 2a³
Differentiate both sides
Now put it equal to zero.
192 a - 6a² = 0
a = 32 in
h = 96 - 2 x 32
h = 32 in
Thus, the length and the width os teh base is 32 in and the height is 32 in.
Final answer:
A square-based box with the greatest volume under a restriction of the sum of length, width, and height not exceeding 96 inches must have each dimension equal to 32 inches. Therefore, its volume will be 32x32x32 = 32,768 cubic inches.
Explanation:
A square-based box with the greatest volume that can fit the airline's restrictions would have each side (length, width, height) be exactly one third of the total permitted sum, namely 32 inches each, because the volume of a square-based box (a cube in this specific case) is calculated by cubing the edge length. This is due to the nature of a cube, where all sides are equal.
So, the volume of the box would be 32in x 32in x 32in = 32,768 cubic inches. This is the maximum volume because the mathematical principle that for a given sum S of width, length & height, a cube always takes up the most volume.
Learn more about Optimization in Mathematics here:
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Answers
Answer:
x⁷ = 60
Step-by-step explanation:
Given:-
- log x⁵ + log x ¹² = 7 .
To Find:-
- The expotential equation .
Solution:-
Given logarithmic equation is ,
⇒ log x⁵ + log x ¹² = 7
⇒ log x ⁵ * ¹² = 7 [ log aⁿ + log aⁿ' = log aⁿ * ⁿ' ]
⇒log x ⁶⁰ = 7
In expotential form we can write it as ,
⇒ x⁷ = 60
Answers
Answer:
Hello! Hope you are having a good day. Your answer is F. I just did this. Good luck!
Step-by-step explanation:
Answers
Answer:
a) 0.2588
b) 0.044015
c) 0.12609
Step-by-step explanation:
Using the TI-84 PLUS calculator
The formula for calculating a z-score is is z = (x-μ)/σ,
where x is the raw score
μ is the population mean
σ is the population standard deviation.
From the question, we know that:
μ = 119 inches
standard deviation σ = 17 inches
(a) What proportion of trees are more than 130 inches tall?
x = 130 inches
z = (130-119)/17
= 0.64706
Probabilty value from Z-Table:
P(x<130) = 0.7412
P(x>130) = 1 - P(x<130) = 0.2588
(b) What proportion of trees are less than 90 inches tall?
x = 90 inches
z = (90-119)/17
=-1.70588
Probability value from Z-Table:
P(x<90) = 0.044015
(c) What is the probability that a randomly chosen tree is between 95 and 105 inches tall?
For x = 95
z = (95-119)/17
= -1.41176
Probability value from Z-Table:
P(x = 95) = 0.07901
For x = 105
z = (105 -119)/17
=-0.82353
Probability value from Z-Table:
P(x<105) = 0.2051
The probability that a randomly chosen tree is between 95 and 105 inches tall
P(x = 105) - P(x = 95)
0.2051 - 0.07901
= 0.12609