Answer:
slope: 3; vertex: (5, -8)
Step-by-step explanation:
Compare the given y+8=3(x−5) to the slope-vertex form y - k = m(x - h). We see that the slope, m, must be 3 and the vertex must be (h, k): (5, -8).
We have the following information:
first urn: 6 green balls and 3 red ones
total: 6 + 3 = 9
second urn: 3 green, 3 white and 3 red
total: 3 + 3 + 3 = 9
third urn: 6 green, 1 white and 2 red
total: 6 + 1 + 2 = 9
a) A green ball is more likely to be obtained, since there are more green balls than red balls, which makes the probability higher.
b) probability of drawing a green, red and white ball.
first urn:
green = 6/9 = 66.66%
red = 3/9 = 33.33%
white = 0/9 = 0%
second urn:
green = 3/9 = 33.33%
red = 3/9 = 33.33%
white = 3/9 = 33.33%
third urn:
green = 6/9 = 66.66%
red = 2/9 = 22.22%
white = 1/9 = 11.11%
c) it would be chosen where the probability of drawing green would be the highest, which means that it would be possible both in the first and in the third ballot box, the probability is equal 66.66%
d) without a green ball, the third ballot box would look like this:
5 green balls, 2 red balls and 1 white ball, with a total of 8.
The probability of drawing would be:
green = 5/8 = 62.5%
red = 2/8 = 25%
white = 1/8 = 12.5%
Your identity says ...
... sum of cubes = (sum)³ -3(product)(sum)
... = 4³ -3·1·4
... = 64 -12 = 52
_____
The two numbers are 2±√3, and the sum of their cubes is indeed 52.
You need to multiply 19.797 by 10 two times to reach 1979.7
The measure of each angles are m∠F = 46°, m∠D = 32°, m∠E = 102°.
<h3>What is angle?</h3>
An angle in plane geometry is a shape created by two rays or lines that have a common endpoint. The Latin word "angulus," which means "corner," is where the word "angle" comes from. The common endpoint of two rays is known as the vertex, and the two rays are known as sides of an angle.
The angle that lies in the plane need not be in Euclidean space. Angles are referred to as dihedral angles if they are produced by the intersection of two planes in a space other than Euclidean. The symbol "" is used to represent an angle.
We have given that Δ DEF has
m∠D = m∠F - 14
And
m∠E = 10 + 2(m∠F)
We know that that sum of all angels in a triangle is 180°, So
m∠D + m∠E + m∠F = 180°
Substituting the values we get
(m∠F - 14) + (10 + 2(m∠F)) + m∠F = 180°
m∠F - 14 + 10 + 2m∠F +m∠F
4(m∠F) - 4 = 180
4(m∠F) = 180 + 4
4(m∠F) = 184
(m∠F) = 46°
m∠D = 46° - 14
m∠D = 32°
m∠E = 10 + 2(m∠F)
m∠E = 10 + 2( 46°)
m∠E = 10 + 92°
m∠E = 102°
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