Solution:
Outfit Shirt Slacks Tie
Outfit 1 Blue Black Red
Outfit 2 Blue Grey Red
Outfit 3 White Black Red
Outfit 4 White Grey Red
Outfit 5 Black Black Red
Outfit 6 Black Grey Red
We take the outfits 1, 2 , 5 and 6 as a subset of the sample space.
So these 1, 2, 5 and 6 consists either a blue shirt or a black shirt.
The subset consists of all the outfits that do not have a white shirt.
So the correct options are :
1. (Choice A)
The subset consists of all the outfits that do not have a white shirt.
2. (Choice C)
The subset consists of all the outfits that have a black shirt.
A)
The relationship between the amount of hours
spent studying and the test scores increase with time in a positive direction showing a positive correlation.
B) Y=8x+40
Y=8(3) +40
Y=24+40
Y= 64
C)
The 40 stands for the initial score the student
can get without any studying
We'll use standard labeling of right triangle ABC, C=90 degrees, legs a, b, hypotenuse c.
11.
Right triangle, cliff peak A, boat B, angle opposite cliff is B=28.9 deg. adjacent leg a=65.7 m, cliff height is leg b.
tan B = b/a
b = a tan B = 65.7 tan 28.9° = 36.3 m
12.
Similar story, boat at B, opposite b=3.5 m, rope c=12 m
sin B = b/c
B = arcsin b/c = arcsin (3.5/12) = 17.0°
13.
c=124 m, A=58°
sin A = a/c
a = c sin A = 124 sin 58 = 105.2 m
14.
That's a hypotenuse c=4-1.2 = 2.8 m to a height b=1.8m so
cos A = b/c
A = arccos b/c = arccos (1.8/2.8) = 50.0°
15.
Not a right triangle, an isosceles triangle. Half of it is a right triangle with hypotenuse one arm, c=9.8 cm and angle opposite half the base of B=62/2=31°. We're after d=2b:
sin B = b/c
b = c sin B
d = 2b = 2 c sin B = 2(9.8) sin 31 = 10.1 cm
Almost equilateral
By decomposing the figure in simpler shapes, we will see that the total area is:
a = 180 cm²
<h3>
How to find the area of the composite figure?</h3>
Remember that the area of a rectangle of width W and length L is:
A = L*W
And the area of a triangle with base B and height H is:
A = B*H/2.
Then, the upper part can be seen as a rectangle of length of 6cm and width of 6 cm, with two triangles on the sides, such that each triangle has a base of 3cm and a height of 6cm.
So the area of that part is:
A = 6cm*6cm + 2*(3cm*6cm/2) = 54cm²
Now, the bottom triangle has a base of 12 cm, and a height of:
15cm - 6cm = 9cm
Then its area is:
A' = 12cm*9cm/2 = 54cm²
This means that the total area of the figure is:
total area = 54cm² + 54cm² = 108cm²
If you want to learn more about area:
brainly.com/question/24487155
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