So,
The probability of drawing a yellow marble is
.
Since he replaces the marble after it is drawn out, the probability of drawing another yellow is the same:
.
The probability of drawing a red marble is
.
In order to get the probability of drawing 2 yellow marbles and 1 red marble, given that each marble is replaced after it is drawn out, we must multiply the fractions together.
Because the order of the marbles doesn't matter, we will multiply the probability by 3.
Answer:
The first one is c the second is b
Answer:
The bottom left one
Step-by-step explanation:
They are the only graph that has one output for each x value
The ratio of the sides EF/LM after the transformation is 1/8
<h3>
Transformation</h3>
Transformation is the movement of a point from its initial location to a new location. Types of transformation are <em>rotation, translation, reflection and dilation.</em>
Dilation is the increase or decrease in size of a figure by a factor while translation is the movement of a point up, down, left or right.
Given the tansformation:
- (x,y) → (8x, 8y) → (x - 4, y - 4).
- This means a dilation of CDEF by 8 and translated 4 units down and 4 units left.
Hence:
LM = 8 * EF
EF/LM = 1/8
The ratio of the sides EF/LM after the transformation is 1/8
Find out more on transformation at: brainly.com/question/1548871
Answer:
a. 235°
b. 146.03 km
c. 105 km
d. 193 km
Step-by-step explanation:
a. The bearing of E from A is given as 55°. The bearing in the opposite direction, from E to A, is this angle with 180° added:
bearing of A from E = 55° +180° = 235°
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b. The internal angle at E is the difference between the external angle at C and the internal angle at A:
∠E = 134° -55° = 79°
The law of sines tells you ...
CE/sin(∠A) = CA/sin(∠E)
CE = CA(sin(∠A)/sin(∠E)) = (175 km)·sin(55°)/sin(79°) ≈ 146.03 km
CE ≈ 146 km
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c. The internal angle at C is the supplement of the external angle, so is ...
∠C = 180° -134° = 46°
The distance PE is opposite that angle, and CE is the hypotenuse of the right triangle CPE. The sine trig relation is helpful here:
Sin = Opposite/Hypotenuse
sin(46°) = PE/CE
PE = CE·sin(46°) = 146.03 km·sin(46°) ≈ 105.05 km
PE ≈ 105 km
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d. DE can be found from the law of cosines:
DE² = DC² +CE² -2·DC·CE·cos(134°)
DE² = 60² +146.03² -2(60)(146.03)cos(134°) ≈ 37099.43
DE = √37099.43 ≈ 192.6 . . . km
DE is about 193 km
