A triangle has side lengths of (2.4k-7.4) centimeters, (6.3k-2.2) centimeters and (6.8m+2.4) centimeters. which expression repre
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Answer:
(a) The probability that only one goblet is a second among six randomly selected goblets is 0.3888.
(b) The probability that at least two goblet is a second among six randomly selected goblets is 0.1776.
(c) The probability that at most five must be selected to find four that are not seconds is 0.9453.
Step-by-step explanation:
Let <em>X</em> = number of seconds in the batch.
The probability of the random variable <em>X</em> is, <em>p</em> = 0.31.
The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> and <em>p</em>.
The probability mass function of <em>X</em> is:
(a)
Compute the probability that only one goblet is a second among six randomly selected goblets as follows:
Thus, the probability that only one goblet is a second among six randomly selected goblets is 0.3888.
(b)
Compute the probability that at least two goblet is a second among six randomly selected goblets as follows:
P (X ≥ 2) = 1 - P (X < 2)
Thus, the probability that at least two goblet is a second among six randomly selected goblets is 0.1776.
(c)
If goblets are examined one by one then to find four that are not seconds we need to select either 4 goblets that are not seconds or 5 goblets including only 1 second.
P (4 not seconds) = P (X = 0; n = 4) + P (X = 1; n = 5)
Thus, the probability that at most five must be selected to find four that are not seconds is 0.9453.
A rigid transformation preserves the dimensions of the image
The option that gives the sequence of transformation that takes ΔB to ΔB is the option B.
<u>(B) Reflection across y-axis and a translation 2 units down </u>
Reason:
Question: The sequence of transformation that takes ΔA to image ΔB
<em>From a similar question, we have, ;</em>
<em>The vertices of triangle ΔA are; (-8, 9), (-9, 4), (-3, 4)</em>
<em>The vertices of triangle ΔB are; (8, 7), (3, 2), (9, 2)</em>
<em>The options are; </em>
<em>(A) Reflection over the x-axis and 2 units translation down</em>
<em>(B) Reflection over the y-axis and 2 units translation down</em>
<em>(C) 90° rotation after a translation of 2 units down</em>
<em>(D) 90° rotation after a translation of 12units right</em>
Solution;
The length of the base of ΔA = -3 - (-9) = 6
The length of the base of ΔB = 9 - 3 = 6
Therefore, the length s of triangle A and triangle B are equal
The orientation of the base of ΔA and ΔB are both horizontal
The location of the the side that traverses four cells are both furthest from the y-axis, or the vertical
Therefore, ΔB is a reflection of ΔA across the y-axis
We also have;
The base of ΔB is 2 units lower than the base ΔA
Therefore, the correct option is option B, reflection across y-axis and a translation 2 units down
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Answer:
The product is the difference of squares is
Step-by-step explanation:
Explanation
- The given expression is (x y-9)(x y+9).
- We have to multiply the given expression.
- Square the first term xy. Square the last term 9 .
Answer:
The correct option is 1. The area of cross section area is 48 mm².
Step-by-step explanation:
From the find it is noticed that the cross section is a rectangle with length 4 mm and width is 12 mm.
The area of a rectangle is the product of its dimensions.
Where, l is length of the rectangle and w is width of the rectangle.
The area of cross section is
Therefore the area of cross section area is 48 mm². Option 1 is correct.
