Perimeter P=2L+2W
P=24
L=w+4
P=2(w+4)+2w
24=2w+8+2w
24=8+4w
16=4w
w=4
L=8
Answer:
(a) x = 260.52
(b) x = 249.24
(c) x = 265.22
(d) x = 297.65
Step-by-step explanation:
Here,
Mean = 
= 300
Standard deviation = 
= 47
(a)
Using standard normal table,
P(Z > z) = 80%
1 - P(Z < z) = 0.8
P(Z < z) = 1 - 0.8
P(Z < -0.52) = 0.2
z = -0.84
Using z-score formula,
x = z × σ + μ
x = -0.84 × 47 + 300 = 260.52
(b) Using standard normal table,
P(Z < z) = 14%
P(Z < -1.08) = 0.1
4
z = -1.08
Using z-score formula,
x = z × σ + μ
x = -1.08 × 47 + 300 = 249.24
(c)
Using standard normal table,
P(Z < z) = 23%
P(Z < -0.74) = 0.243
z = -0.714
Using z-score formula,
x = z × σ + μ
x = -0.74 × 47 + 300 = 265.22
(d) Using standard normal table,
P(Z > z) = 52%
1 - P(Z < z) = 0.52
P(Z < z) = 1 - 0.52
P(Z < -0.25) = 0.4
8
z = -0.05
Using z-score formula,
x = z × σ + μ
x = -0.05 × 47 + 300 = 297.65
You can use SAS since you know one pair of sides are congruent and AC splits them so those must make those sides equal. And since those sides, DC and BC, are congruent, the angles must be as well. You can use numbers to prove the angles of D and B or just use that when 2 sides and an angle are congruent, the 3rd side must be congruent.
The surface area of the cylinder is 18.84 square feet
<h3>How to determine the surface area?</h3>
The given parameters are
Height, h = 2 ft
Diameter, d = 2 ft
The radius (r) is half of the diameter (d)
This is calculated as:
Radius = Diameter/2
So, we have:
r = d/2
Substitute 2 for d
r = 2/2
Evaluate the quotient i.e. divide 2 by 1
r = 1
The surface area is then calculated using the following formula
A = 2πr² + 2πrh
Substitute the given values in the above equation
So, we have:
A = 2 * 3.14 * 1^2 + 2 * 3.14 * 1 * 2
Evaluate the exponents
A = 2 * 3.14 * 1 + 2 * 3.14 * 1 * 2
Evaluate the products
A = 6.28 + 12.56
Evaluate the sum
A = 18.84
Hence, the surface area of the cylinder with the given height and radius is 18.84 square feet
Read more about surface area at:
brainly.com/question/2835293
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So,
Let x represent the first angle and y represent the second angle.
x + y = 90
x = y + 26
Substitute
y + 26 + y = 90
Collect Like Terms
2y + 26 = 90
Subtract 26 from both sides
2y = 64
Divide both sides by 2
y = 32
Substitute
x = 32 + 26
x = 58
Check
58 + 32 = 90
90 = 90 This checks.
58 = 32 + 26
58 = 58 This also checks.
The measure of one angle is 58° and the measure of the other angle is 32°.
