Answer:
16 lessons
Step-by-step explanation:
12 divided by .75 = 16
Answer:
Because -3-/8 itself is an irrational number. No matter the operation it wil always be irrational
Step-by-step explanation:
Answer:
a) There are 9 outcomes.
b) **i have attached the tree diagram**
c) 1/9
d) 1/9
Step-by-step explanation:
Both events (choosing a shirt and choosing pants) are not mutually exclusive (disjoint). Meaning that both events can occur at the same time.
a) For a sequence of two events in which the first event can occur <em>m</em> ways and the second event can occur <em>n</em> ways, the events together can occur a total of <em>m</em> • <em>n</em> ways. So for this problem, you would do 3 • 3 which equals 9.
b) **tree diagram is attached**
c) Because there are two different events occurring (choosing a shirt and choosing pants) you need to multiply using the Multiplication Rule for Independent Events : P(A and B) = P(A) * P(B)
The probability of event A occurring (choosing a red shirt) is 1/3 and the probability of event B occurring (choosing brown pants) is also 1/3.
1/3 * 1/3 = 1/9
d) You would do the same thing here as part c.
The probability of event A occurring (choosing a blue shirt) is 1/3 and the probability of event B occurring (choosing blue pants) is again 1/3.
1/3 * 1/3 = 1/9
I hope this was helpful!! :)
One way to write a ratio is 5:8 or 5 to 8 and <u>5</u>
8
1. 60,30,90 right triangle. y will be hypotenuse/2, x will be
hypotenuse*sqrt(3)/2. So x = 16*sqrt(3)/2 = 8*sqrt(3), approximately 13.85640646
y = 16/2 = 8
2. 45,45,90 right triangle (2 legs are equal length and you have a right angle).
X and Y will be the same length and that will be hypotenuse * sqrt(2)/2. So
x = y = 8*sqrt(2) * sqrt(2)/2 = 8*2/2 = 8
3. Just a right triangle with both legs of known length. Use the Pythagorean theorem
x = sqrt(12^2 + 5^2) = sqrt(144 + 25) = sqrt(169) = 13
4. Another right triangle with 1 leg and the hypotenuse known. Pythagorean theorem again.
y = sqrt(1000^2 - 600^2) = sqrt(1000000 - 360000) = sqrt(640000) = 800 5. A 45,45,90 right triangle. One leg known. The other leg will have the same length as the known leg and the hypotenuse can be discovered with the Pythagorean theorem. x = 6. y = sqrt(6^2 + 6^2) = sqrt(36+36) = sqrt(72) = sqrt(2 * 36) = 6*sqrt(2), approximately 8.485281374
6. Another 45,45,90 triangle with the hypotenuse known. Both unknown legs will have the same length. And Pythagorean theorem will be helpful.
x = y.
12^2 = x^2 + y^2
12^2 = x^2 + x^2
12^2 = 2x^2
144 = 2x^2
72 = x^2
sqrt(72) = x
6*sqrt(2) = x
x is approximately 8.485281374
7. A 30,60,90 right triangle with the short leg known. The hypotenuse will be twice the length of the short leg and the remaining leg can be determined using the Pythagorean theorem.
y = 11*2 = 22.
x = sqrt(22^2 - 11^2) = sqrt(484 - 121) = sqrt(363) = sqrt(121 * 3) = 11*sqrt(3). Approximately 19.05255888
8. A 30,60,90 right triangle with long leg known. Can either have fact that in that triangle, the legs have the ratio of 1:sqrt(3):2, or you can use the Pythagorean theorem. In this case, I'll use the 1:2 ratio between the unknown leg and the hypotenuse along with the Pythagorean theorem.
x = 2y
y^2 = x^2 - (22.5*sqrt(3))^2
y^2 = (2y)^2 - (22.5*sqrt(3))^2
y^2 = 4y^2 - 1518.75
-3y^2 = - 1518.75
y^2 = 506.25 = 2025/4
y = sqrt(2025/4) = sqrt(2025)/sqrt(4) = 45/2
Therefore:
y = 22.5
x = 2*y = 2*22.5 = 45
9. Just a generic right triangle with 2 known legs. Use the Pythagorean theorem.
x = sqrt(16^2 + 30^2) = sqrt(256 + 900) = sqrt(1156) = 34
10. Another right triangle, another use of the Pythagorean theorem.
x = sqrt(50^2 - 14^2) = sqrt(2500 - 196) = sqrt(2304) = 48
