The scores of eighth-grade students in a math test are normally distributed with a mean of 57.5 and a standard deviation of 6.5.
2 answers:
As given, the scores of eighth-grade students in a math test are normally distributed with a mean of 57.5 and a standard deviation of 6.5.
This means that around 68% of the distributed data lies within the ranges of -6.5 to +6.5 of the given standard deviation.
This implies to:
and
So, the range of scores lies between (51,64)
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Answer:
a). x = 11
b). m∠DMC = 39°
c). m∠MAD = 66°
d). m∠ADM = 36°
e). m∠ADC = 18°
Step-by-step explanation:
a). In the figure attached,
m∠AMC = 3x + 6
and m∠DMC = 6x - 49
Since "in-center" of a triangle is a points where the bisectors of internal angles meet.
Therefore, MC is the angle bisector of angle AMD.
and m∠AMC ≅ m∠DMC
3x + 6 = 8x - 49
8x - 3x = 49 + 6
5x = 55
x = 11
b). m∠DMC = 8x - 49
= (8 × 11) - 49
= 88 - 49
= 39°
c). m∠MAD = 2(m∠DAC)
= 2(30)°
= 60°
d). Since, m∠AMD + m∠ADM + m∠MAD = 180°
2(39)° + m∠ADM + 66° = 180°
78° + m∠ADM + 66° = 180°
m∠ADM = 180° - 144°
= 36°
e). m∠ADC =
=
= 18°
Answer:
The area of the pyramid is 360 unit²
Step-by-step explanation:
Given
Base Edge, a = 10
Height, h = 12
Required
Determine the surface area
The surface area of a regular pyramid is calculated as thus;
Substitute values for a and h
Evaluate all squares
Take positive square root of 169
<em>Hence, the area of the pyramid is 360 unit²</em>