Can someone solve this for me
1 answer:
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Answer:
The possible locations are;
(3, 4), (3, 12), (7, 4), and (7, 12)
Please find attached the plot of the points created with Microsoft Excel
Step-by-step explanation:
The given parameters of the plot of Oliver's backyard are;
The area of the right triangular plant bed Oliver wants to design, A = 8 yd²
The length of a/each unit of the plot = 1 yard
The location of one of the vertex of the right triangular area = (3, 8)
The location of the other vertex of the right triangular area = (7, 8)
We note that the area of a triangle, A = 1/2 × Base length, B × Height, h
Let the distance between the two plotted point represent the base length, 'B', therefore;
B = 7 - 3 = 4 (We subtract only the x-values (7 and 3) given that the y-values (8 and 8) are the same;
Therefore, the base length, B = 4 yards
A = 1/2 × B × h
∴ A = 8 yd.² = 1/2 × 4 yd. × h
h = 8 yd.²/ 2 yd. = 4 yd.
The height of the right triangle, h = 4 yd.
Therefore the possible locations of the last vertex the right triangle on the coordinate plane, given that the first two points are parallel with the x-axis, are points 4 units above or the y-axis value of the plotted points with the x-value of the last vertex being either 3, or 7 as follows;
(3, 8 ± 4) or (7, 8 ± 4) which give points, (3, 4), (3, 12), (7, 4), and (7, 12).
Given, in the spinner 8 equal sectors, numbered 1 to 8.
So total numbers = 8.
Let, the probability of spinning a 3 is P(Three) and spinning an 8 is P(Eight).
Now we know that, probability of an event E is
P(E) = (number of outcomes in the event)/ (total number of possible outcomes).
So here number of outcomes for spinning a 3 is 1 and we have got total outcomes = 8.
So P(Three) =
Similarly, P(Eight) =
Probability of spinning a 3 or an 8 = P(Three) + P(Eight)
=
As the denominator is same we can add the numerator.
=
=
Now we have to simplify the fraction by dividing the numerator and denominator by a common factor of them.
The common factor of 2 and 8 is 2. So by dividing them we will get,
=
We have got the required answer.
The probability of spinning a 3 or an 8 is