Answer:
1/6
The probability of rolling a specific number twice in a row is indeed 1/36, because you have a 1/6 chance of getting that number on each of two rolls (1/6 x 1/6). The probability of rolling any number twice in a row is 1/6, because there are six ways to roll a specific number twice in a row (6 x 1/36).
Answer:
Step-by-step explanation:
Horizontal translations = f(x ± h)
Reflection over the x-axis = - f(x)
For the function 
, translating the parabola 8 units to the right means the horizontal shift of the graph, adding (- 8) to the <em>h</em> input. This is represented by: 
.
Next, flipping the graph over the x-axis represent a reflection. Since we currently have a negative coefficient for the value of <em>a</em>, then the opposite of a negative coefficient is a positive coefficient.
Therefore, the rightward horizontal translation of 8 units, and the reflection of the graph over the x-axis is represented by:
For your reference, the three images below shows the transformations on the graph. The first image is the original function (in red parabola). The second image represents the reflection over the x-axis (green parabola). The third image shows the horizontal shift, 8 units to the right (blue parabola). If you take note of the varying values in vertices, (<em>h, k </em>) for the three graphs, you'll see that the original vertex was (4, 5) and the new vertices for the transformations are (4, -5) for the <u>reflection</u> and (12, -5) for the <u>shift</u>.
I must assume that you meant t=1 (not t=?1). If t=1, here's what we'd do:
1. Find the x and y values corresponding to t=1. They are:
x=(1)^7+1=2 and y=(1)^8+1=2. (Please note: write t^8 instead of t8, and write t^7 instead of t7.)
2. The slope of the tangent line to the graph is
dy/dt 8t^7+1
dy/dx = ---------- = ---------------- with 1 substituted for t
dx/dt 7t^6
Thus, dy/dx (at t=1) = 9/7
3. Now we have both a point (2,2) on the graph and the slope of the tangent line to the curve at that point: 9/7
4. The tangent line to the curve at (2,2) is found by using the point-slope formula:
y-y1 = m(x-x1)
which comes out to y-2 = 9/7(x-2), or 7y-14 = 9(x-2). You could, if you wished, simplify this result further (e. g., by solving for y in terms of x).
Answer: If interest is not given, it would be 25,000+ interest as your answer
Step-by-step explanation:
