Answer:
a) 0.8333
b) 0.75
c) 0.8181 or 0.9090
Step-by-step explanation:
a)
The probability the visitor selects an authentic painting is
10/12 = 0.8333
b)
Since the opinion of the expert does not depend on your choice, the events are <em>independent</em>, so the probability that the expert says is authentic and it really is, is
0.8333*0.9 = 0.75
c)
If the expert decides the painting is a copy and it is not, then there are 11 paintings of which 9 are authentic, so the probability the visitor selects a new original painting is
9/11= 0.8181
If the expert decides the painting is a copy and it is, then there are 11 paintings of which 10 are authentic, so the probability the visitor selects a new original painting is
10/11= 0.9090
In this question, we would be multiplying.
In this case, you would multiply 20000 by 1.9, since 1.9 is the decimal form of 190%.
Solve:
20000 · 1.9 = 38,000
Answer:
38,000
Since the height of an equilateral triangle in terms of its side s is s√3/2, the height of the triangle is 6√3/2 = 3√3 and so the area is (1/2)(6)(3√3) = 9√3.
<span>If we draw a horizontal line a height of h from the base of the triangle, the region is split into two regions: the lower region consisting of a trapezoid of height h and the upper region consisting of a triangle of height 3√3 - h. </span>
<span>Since the upper triangle and the triangle itself are similar triangles, the base and height are proportional. If we let x denote the base of the length of the upper triangle, we have: </span>
<span>(S. of small triangle)/(S. of big triangle) = (Ht. of small triangle)/(Ht. of big triangle) </span>
<span>==> x/6 = (3√3 - h)/(3√3) </span>
<span>==> x = (6√3 - 2h)/√3 </span>
<span>Thus, the area of the upper triangle is: </span>
<span>A = (1/2)[(6√3 - 2h)/√3](3√3 - h) = [(6√3 - 2h)(3√3 - h)]/(2√3). </span>
<span>(Made a dumb mistake about the height here for some reason) </span>
<span>Since we require that the area of this triangle is to be half of the total area (9√3/2), we need to solve: </span>
<span>[(6√3 - 2h)(3√3 - h)]/(2√3) = 9√3/2 </span>
<span>==> (6√3 - 2h)(3√3 - h) = 27 </span>
<span>==> 54 - 6h√3 - 6h√3 + 2h^2 = 27 </span>
<span>==> 2h^2 - 12h√3 + 27 = 0. </span>
<span>Solving with the Quadratic Formula gives: </span>
<span>h = (6√3 + 3√6)/2 ≈ 8.87 units and h = (6√3 - 3√6)/2 ≈ 1.52 units. </span>
<span>Since h = (6√3 + 3√6)/2 would place the line outside of the triangle, we pick h = (6√3 - 3√6)/2. </span>
<span>Therefore, the line should be ==> (6√3 - 3√6)/2 units from the base. </span>
<span>I hope this helps! ^^ Brainliest Please?</span><span>
</span>
Answer:
y=1
x=-5
Step-by-step explanation:
3x+y=-14
4x+4y=-16
y=-3x-14
4x+4y=-16
y=-3x-14
4(-3x-14)+4x=-16
y=-3x-14
-8x-56=-16
y=-3x-14
-8x=40
y=-3x-14
x=-5
y=1
x=-5
Answer:
area =4*13*12=624
Therefore the area is 626 units square
