Answer:
B) Independent; the 1st marble selection will not affect the 2nd marble selection.
Step-by-step explanation:
When finding the probability of events in mathematics, we have both independent and dependent events.
Independent events are events that occur when the results of selection of the first events does not affect the results or outcomes of the second events.
Dependent events are the opposite of Independent events. They are events that occur when the results or outcomes obtained from the second events is affected by the results or outcomes from the selection of the first events.
From the question, we can see that the first event is she picked one marble from the bag. The second event is she replaced the marble before picking another marble. By doing this, the total number of possible outcomes for the probabilities of both events remains the same and they are unaffected.
Therefore, we can say that the two events are Independent because the 1st marble selection will not affect the 2nd marble selection.
The circumference of the top of the cake is 
in.
It sounds like the baker is trying to line the circumference with cherriesto fit as many as possible along the border, like in the picture I've attached below.
This comes down to dividing the cake's circumference by the diameter of each cherry:
or about 39 cherries, making the answer D.
Answer:
0
Step-by-step explanation:
since 2 isnt up to 5, it cannot equate to 1
Answer:
c = 3√5 ≈ 6.708
Step-by-step explanation:
Use the Pythagorean Theorem because this is a right triangle.
a^2 + b^2 = c^2
3^2 + 6^2 = c^2
9 + 36 = c^2
45 = c^2
√45 = c
<u>c = 3√5 ≈ 6.708</u>
Answer:
Step-by-step explanation:
f(x) is quadratic function and g(x) is linear (since AP in the right column).
<u>Find the equation of the function f(x), use the points on the graph:</u>
- c = 5 as the y-intercept is (0, 5)
- a(-1)² + b(-1) + 5 = 0 ⇒ a + 5 = b
- a(5²) + b(5) + 5 = 0 ⇒ 25a + 5b + 5 = 0 ⇒ 25a + 5a + 25 + 5= 0 ⇒ a = -1 ⇒ b= 4
<u>The function is:</u>
Find the equation of g(x)
<u>Find the slope of g(x):</u>
- m = (1 - 7)/(-1 + 4) = -2
<u>Use (-4, 7) to find its equation:</u>
- y - 7 = -2(x + 4)
- y = -2x + 7 - 8
- y = -2x - 1
<h3>See the required comparison below</h3>
<u>The y-intercepts:</u>
- f(x) ⇒ 5,
- g(x) ⇒ -1
- -5 < - 1
<u>Values at x = 3:</u>
- f(3) = -3² + 4(3) + 5 = 8
- g(3) = -2(3) - 1 = - 7
- 8 > 7
<u>Average rate of change in the interval [2,5]:</u>
- f(x) ⇒ (0 - 9)/(5 - 2) = -3
- g(x) ⇒ (-11 + 5)/ (5 - 2) = -2
- -3 < -2
<u>Max of function in the interval [-5, 5];</u>
- f(x) ⇒ 9, vertex of the function
- g(x) ⇒ g(-5) = -2(-5) - 1 = 9, taken the least point of x as it is a decreasing function
- 9 = 9
