Answer:
12° and 168°
Step-by-step explanation:
If x is the angle, and y is the supplementary angle, then:
x + y = 180
x = y − 156
Solve the system of equations using substitution:
y − 156 + y = 180
2y = 336
y = 168
Plug back into either equation to find x:
x = 12
Answer:
thats quadrant 2
Step-by-step explanation:
The surface area of the triangular prism is of 140 cm².
<h3>What is the surface area of a prism?</h3>
It is the sum of the areas of all faces of a prism. In this problem, the prism has these following faces:
- One rectangle of dimensions 8 cm and 6 + 4 + 5 = 15 cm.
- Two right triangles with sides 4 cm and 5 cm.
For a rectangle, the area is given by the multiplication of the dimensions, hence:
Ar = 8 x 15 = 120 cm²
For each right triangle, the area is given by half the multiplication of the sides, hence:
At = 2 x 0.5 x 4 x 5 = 20 cm².
Then the surface area of the prism is:
S = 120 cm² + 20 cm² = 140 cm².
More can be learned about surface area at brainly.com/question/28123954
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Experimental probability = 1/5
Theoretical probability = 1/4
note: 1/5 = 0.2 and 1/4 = 0.25
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How I got those values:
We have 12 hearts out of 60 cards total in our simulation or experiment. So 12/60 = (12*1)/(12*5) = 1/5 is the experimental probability. In the simulation, 1 in 5 cards were a heart.
Theoretically it should be 1 in 4, or 1/4, since we have 13 hearts out of 52 total leading to 13/52 = (13*1)/(13*4) = 1/4. This makes sense because there are four suits and each suit is equally likely.
The experimental probability and theoretical probability values are not likely to line up perfectly. However they should be fairly close assuming that you're working with a fair standard deck. The more simulations you perform, the closer the experimental probability is likely to approach the theoretical one.
For example, let's say you flip a coin 20 times and get 8 heads. We see that 8/20 = 0.40 is close to 0.50 which is the theoretical probability of getting heads. If you flip that same coin 100 times and get 46 heads, then 46/100 = 0.46 is the experimental probability which is close to 0.50, and that probability is likely to get closer if you flipped it say 1000 times or 10000 times.
In short, the experimental probability is what you observe when you do the experiment (or simulation). So it's actually pulling the cards out and writing down your results. Contrast with a theoretical probability is where you guess beforehand what the result might be based on assumptions. One such assumption being each card is equally likely.
78,000 rounded to the nearest ten thousand is 80,000.
