Answer:
19
Step-by-step explanation:
<u>Step 1: Solve</u>
13 - (-6)
13 + 6
<em>19</em>
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Answer: 19
Hey so yeah this can be a challenging problem, Vol (V) is much easier to solve than surface area (SA), but I'll show you how it's done, my friend.
First of all, V (prism) = area of base (B) × h
We know that the height (h) of this prism is given, which we'll need later on: h = 5 ft, and area of base (B) is given as 60 ft2
So V = 60 ft2 × 5 ft = 300 ft3
So now for the hard part... how to calculate the SA of this prism
IF YOU DON'T NEED SA FOR THIS TYPE OF PROBLEM, DO NOT PROCEED!!!
[VERY DETAILED]
means solving the dimensions (sides) of that pesky polygon base (B) or lid.
The most important things about polygons are:
1) is it regular (same angle ° and side length)??
2) How many sides or angles??
This has to be regular, because they give you no other info so it has to be, in order to solve. And then it has 5 sides and angles = regular pentagon. ("penta" means 5).
Now there are 360° in any circle, so:
take the central angles of where the sides meet at the center forming triangles (see drawing above), each of those (5) central <'s = 360/5 = 72°
Now the apex of each of these triangles = 72°
but with our 5 triangles, we need to find the height of each triangle -- which is the midpoint of the side (base (b) of triangle), and h is perpendicular to this b. By bisecting that apex angle of 72, it forms 2 equal right triangles of
72/2 = 36°. So each right triangle has 36, 90, and?? 180-36-90 = 90-36 = 54°
let's call the base (b) = 1 side of pentagon
= side (s)
Therefore (see 2nd image drawn above) tangent (tan) of € = opposite/adjacent, or
tan (54) = h÷1/2b --> h = [tan (54)]×(1/2)b
1/2b = h/[tan (54)] = h/1.38
Also the area of each of the larger 5 triangles A(t) = 1/2b×h, and that area A(t) × 5 = area of whole pentagon base A(B)
So now after all that... our A(B) given at beginning = 60ft2. let's put it all together:
1/2b = h/[tan (54)] = h/1.38
A(t) = 1/2b×h, and A(B) = 5×A(t)
which means that A(B) = 5×(1/2b×h)
AND since the other calculation shows that 1/2b = h/1.38, plug that value into the A(B) formula...
.
.
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now that we have height (h) of each triangle, we can go back to our tan equation for the triangle: tan (54) = 1.38 = h/(1/2b)
--> 1/2×b = h/1.38 --> base (b) = 2h/1.38
b = 2(4.06 ft)/1.38 = 8.12 ft/1.38 = 5.90 ft, for which b us also the width of each rectangular side panel (w)
length (l) of these sides was given as height of the whole prism = 5 ft
NOW FINALLY... THE FINAL SURFACE AREA OF THE PRISM (SA) = (2×A(B)) + (5×rectangular side)
SA = (2×60 ft2) + (5×(l×w)) = 120 ft2 + 5×5ft×5.9ft
SA = 120 ft2 + 147.62 ft2 = 267.62 ft2
Answer:
1, 2, 6
Step-by-step explanation:
The z score shows by how many standard deviations the raw score is above or below the mean. The z score is given by:
Given that mean (μ) = 130 texts, standard deviation (σ) = 20 texts
1) For x < 90:
From the normal distribution table, P(x < 90) = P(z < -2) = 0.0228 = 2.28%
Option 1 is correct
2) For x > 130:
From the normal distribution table, P(x > 130) = P(z > 0) = 1 - P(z < 0) = 1 - 0.5 = 50%
Option 2 is correct
3) For x > 190:
From the normal distribution table, P(x > 3) = P(z > 3) = 1 - P(z < 3) = 1 - 0.9987 = 0.0013 = 0.13%
Option 3 is incorrect
4) For x < 130:
For x > 100:
From the normal table, P(100 < x < 130) = P(-1.5 < z < 0) = P(z < 0) - P(z < 1.5) = 0.5 - 0.0668 = 0.9332 = 93.32%
Option 4 is incorrect
5) For x = 130:
Option 5 is incorrect
6) For x = 130:
Since 1.5 is between 1 and 2, option 6 is correct
Answer:
-2 < x < 35
Step-by-step explanation:
We have that the larger side has a larger opposite angle and the smaller sides and a smaller opposite angle.
The opposite angle of the 14 unit side is 37 °.
The opposite angle of the 13-unit side is (x + 2) °.
Since 13 <14, it would be:
x + 2 <37
we subtract 2 on both sides
x <35
The value of x must be less than 35.
Now, to form a triangle, the angle must be greater than 0.
x + 2> 0
we subtract 2 on both sides
x> -2
The value of x must be greater than - 2.
Therefore the answer would be:
-2 <x <35
Answer:a
a
b
The margin of error will increase
c
The margin of error will decreases
d
The 99% confidence interval is
Step-by-step explanation:
From the question we are told that
The sample size
The sample mean is
The standard deviation is
Given that the confidence level is 95% then the level of significance is mathematically represented as
Next we obtain the critical value of from the normal distribution table
So
The margin of error is mathematically represented as
=>
=>
The 95% confidence interval is
=>
=>
When the confidence level increases the also increases which increases the margin of error hence the confidence level becomes wider
Generally the sample size mathematically varies with margin of error as follows
So if the sample size increases the margin of error decrease
The sample proportion is mathematically represented as
Given that the confidence level is 0.99 the level of significance is
The critical value of from the normal distribution table is
Generally the margin of error is mathematically represented as
=>
=>
The 99% confidence interval is