Plss help me!!!!!!!!!!
1 answer:
Answer: 12 outcomes total
Check out the diagram below
Edit: I added the tree diagram as well
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Explanation:
I prefer to make a two way table for problems like this. Such diagrams make it fairly clear why multiplication is used when it comes to probability and counting problems.
Check out the diagram below.
The table has 6 rows and 2 columns.
The 6 rows represents the outcomes 1 through 6 on the number cube.
The 2 columns represent the outcome of heads (H) vs tails (T)
Inside the 6*2 = 12 inner cells, we'll have each outcome.
For example, the upper left corner has H1 to mean "flipped heads and got a 1 on the number cube". The next cell over is T1 to mean "tails on the coin, 1 on the number cube". The rest of the table is filled out in this manner.
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Answer:
6 in
Step-by-step explanation:
Let x = the side length of the original square.
They removed 3 in from each side of the original square, so the side lengths of the remaining square are x - 3 in.
The area of the smaller square is (x - 3)².
The area of the original square is x²
I assume the area of the smaller square is ¼ that of the original square. Then
1. Solve for x
2. Calculate the side length of the smaller square
(a) x = 2
Side length = x - 3 = 2 - 3 = -1 in.
IMPOSSIBLE. You can't have a negative side length.
(b) x = 6
Side length of smaller square = 6 - 3 = 3 in.
Side length of original square = x = 6 in
Check:
OK.
Cot θ = -24/7 and cos θ < 0
"cos θ < 0" means cosine is negative
Remember osmething like "ALL students Take Calculus"?
all is positive in quadrant 1
sine/cosecant is positive only in quadrant 2
tangent/cotangent is positive only in quadrant 3
cosine/secant is positive only in quadrant 4
since cot(angent) is the reciprocal of tangent, tangent must also be negative.
tangent is negative in quadrants II and IV
cosine is negative in quadrants II and III
therefore, θ must lie in quadrant II.
remember the tan θ = y / x. it is the y-coordinate divided by the x-coodinate. the y-coordinate would be the height of this 90 degree triangle that forms. the x-coordinate would be the bottom leg of the 90 degree triangle
then cot θ = x / y. therefore, cot θ = -24 / 7 means x = -24 and y = 7. we draw a triangle with these dimensions.
csc θ = r / y = hypotenuse over opposite (when you view the reference angle labeled as the one to base the hypotenuse/oppoiste on) because it is the reciprocal of sine
the hypotenuse can be found w/ pythagorean theorem
hypotenuse = √[(-24)² + 7²] = 25
therefore,
cot θ = 25/7
"cos θ < 0" means cosine is negative
Remember osmething like "ALL students Take Calculus"?
all is positive in quadrant 1
sine/cosecant is positive only in quadrant 2
tangent/cotangent is positive only in quadrant 3
cosine/secant is positive only in quadrant 4
since cot(angent) is the reciprocal of tangent, tangent must also be negative.
tangent is negative in quadrants II and IV
cosine is negative in quadrants II and III
therefore, θ must lie in quadrant II.
remember the tan θ = y / x. it is the y-coordinate divided by the x-coodinate. the y-coordinate would be the height of this 90 degree triangle that forms. the x-coordinate would be the bottom leg of the 90 degree triangle
then cot θ = x / y. therefore, cot θ = -24 / 7 means x = -24 and y = 7. we draw a triangle with these dimensions.
csc θ = r / y = hypotenuse over opposite (when you view the reference angle labeled as the one to base the hypotenuse/oppoiste on) because it is the reciprocal of sine
the hypotenuse can be found w/ pythagorean theorem
hypotenuse = √[(-24)² + 7²] = 25
therefore,
cot θ = 25/7