Answer:
11.4
Step-by-step explanation:
Answer:
m∠RPQ = 8°
Step-by-step explanation:
m∠QRS = 4x - 15
m∠RPQ = x + 1
m∠PQR = x - 2
m∠QRS is exterior angle and m∠RPQ and m∠PQr are opposite interior angles to m∠QRS
m∠QRS = m∠RPQ + m∠PQR {Exterior angle property of triangle}
4x - 15 = x +1 + x - 2
4x - 15 = x + x + 1-2 {Combine like terms}
4x - 15 = 2x - 1 {Subtract 2x from both sides}
4x - 2x - 15 = - 1
2x - 15 = - 1 {Add 15 to both sides}
2x = -1 + 15
2x = 14 {Divide both sides by 2}
x = 14/2
x = 7
m∠RPQ = x + 1 = 7 + 1 = 8°
Answer: 3 acute angles
and 2 acute angles, 1 obtuse angle
and 2 acute angles, 1 right angle
Step-by-step explanation:
the key is just to imagine it
also you have to know that right angle is 90° acute is less than 90° and obtuse is more than 90°
Answer:
The proportion of children that have an index of at least 110 is 0.0478.
Step-by-step explanation:
The given distribution has a mean of 90 and a standard deviation of 12.
Therefore mean, 
= 90 and standard deviation, 
= 12.
It is given to find the proportion of children having an index of at least 110.
We can take the variable to be analysed to be x = 110.
Therefore we have to find p(x < 110), which is left tailed.
Using the formula for z which is p( Z < 
) we get p(Z < 
= 1.67).
So we have to find p(Z ≥ 1.67) = 1 - p(Z < 1.67)
Using the Z - table we can calculate p(Z < 1.67) = 0.9522.
Therefore p(Z ≥ 1.67) = 1 - 0.9522 = 0.0478
Therefore the proportion of children that have an index of at least 110 is 0.0478
Answer:
a) 3x-5=16
b) 30cm
Step-by-step explanation:
a) 5(x-1)=2(x+8)
5x-5=2x+16
5x-2x-5=16
3x-5=16
b) solving the equation gives x=7
put x=7 into first line, 5(7-1)=30cm
to check we can place it into second one as well
2(7+8)=30cm
