For a normally distributed data set, approximately 68.27% of the data is within one standard deviation. i.e. approximately 0.6827 x 200 = 137 test scores is between 86 + or - 3 i.e. from 83 to 89. Hence approximately 137/2 = 68 test score is within the 86 to 89 range.
Using the Pythagorean theorem , you would find that x is 5.54.... which is closest to 6
So the answer is D
You solve this in steps.
First you find f(-1) = 3.
Then you find g(3) = 2.
g(f(-1)) = g(3) = 2
A. side AB = 38/3 units B.m∠VYX =77°
Step-by-step explanation:
A.A rhombus has its four sides equal. This means side AB=side CD
Given that AB=5x+1 and CD=2x+8 equate the two sides to find value of x as;
5x+1=2x+8
collect like terms
5x-2x=8-1
3x=7
x=7/3
side AB = 5x+1
AB= 5*7/3 +1
AB=35/3 +1
AB=35/3 +3/3 = 38/3
B.
The diagonals of a rhombus intersect to form 90°
Hence
(3n²-0.75)°=90°
3n²=90°+ 0.75°
3n² =90.75° -----dividing by 3 both sides
n² =90.75°/3 =30.25°
n²=30.25°
n=√30.25°
n=5.5°
so angle Z =90°
and angle ZVW =(9n+2)°
∠ZVW = (9*5.5 +2 )° =51.5°
In a rhombus all four sides are equal, thus side VY = YX.This means triangle VYX is an isosceles triangle.
Hence angle ∠YVZ=∠WVZ =51.5°, and because VYX is an isosceles triangle then ∠YXV =51.5° so
∠VYX= 180°-(51.5°+51.5°)
=180°-103°=77°
Learn More
Properties of a Rhombus : brainly.com/question/1305249
Keywords : Rhombus, fraction, simplest form
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Answer:
184.43in².
Step-by-step explanation:
Total surface area of the solid = volume of the cube - the volume of the cone
For the CUBE;
Volume of the cube = L³ where L is the length of one side of the cube.
Since a cone of diameter of 6in is cut into a cube, then the length of the cube will be 6in.
Volume of the cube = 6³ = 216in³
For the CONE;
Volume of the cone = 1/3 πr²h
r is the radius of the cone = diameter/2
r = 6/2 = 3in
slant height l = 4.5in
the height h of the cone will be derived using the Pythagoras theorem.
l² = h²+r²
4.5² = h²+3²
h² = 4.5²-3²
h² = 11.25
h=√11.25
h = 3.35in
Volume of the cone = 1/3 × π × 3²× 3.35
= 31.57in³
Total surface area of the solid = 216in³-31.57in³
= 184.43in²
