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The true statements about the diagram given are:
3. m∠JKL = 45°
4. m∠MKQ + m∠PKQ = m∠PKM
5. PK is an angle bisector
<h3>What is an Angle Bisector?</h3>An angle bisector is a segment that divides a given angle into two parts that are congruent to each other.
The missing part of the question is in the image attached below.
In the image given, PK bisects the straight angle JKM since angles JKP and MKP both equal 90 degrees (right angle).
Therefore, m∠JKL = m∠PKL = 45°
m∠MKQ + m∠PKQ = m∠PKM based on the angle addition theorem.
Therefore, the true statements are:
3. m∠JKL = 45°
4. m∠MKQ + m∠PKQ = m∠PKM
5. PK is an angle bisector
(see image attached below)
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1) 3.8x + 5.2x - 6.7 = 11.3
9x = 11.3 + 6.7
9x = 18
x = 18/9
x = 2
2) 7.8y - 4.9 - 5.4y = 2.3
2.4y = 7.2
y = 7.2/2.4
y = 3
3)
Multiply by 3 by both sides:
Simplify:
2x = 18
x = 18/2
x = 9
4)
Do lowest common denominator:
Simplify by 5 by both sides:
9x = 11.3 + 6.7
9x = 18
x = 18/9
x = 2
2) 7.8y - 4.9 - 5.4y = 2.3
2.4y = 7.2
y = 7.2/2.4
y = 3
3)
Multiply by 3 by both sides:
Simplify:
2x = 18
x = 18/2
x = 9
4)
Do lowest common denominator:
Simplify by 5 by both sides:
We have
Mean, μ = 25 minutes
Standard Deviation, σ = 6.1
X = 30 minutes
The probability we are looking for is shown in the first diagram; it's the area on the right of X=30
We need to standardized the value X=30 using the formula
rounded to two dp
The z-table is shown on the second diagram only gives the probability when P(Z<z), so to work out the probability when P(Z>z), we do 1-P(Z<z)
P(Z>0.82) = 1 - P(Z<z) = 1 - 0.7939 = 0.2061
Mean, μ = 25 minutes
Standard Deviation, σ = 6.1
X = 30 minutes
The probability we are looking for is shown in the first diagram; it's the area on the right of X=30
We need to standardized the value X=30 using the formula
The z-table is shown on the second diagram only gives the probability when P(Z<z), so to work out the probability when P(Z>z), we do 1-P(Z<z)
P(Z>0.82) = 1 - P(Z<z) = 1 - 0.7939 = 0.2061