Answer:
36.65 ft (2 dp)
Step-by-step explanation:
- Angles around a point sum to 360°
- 1 hour = 60 minutes
Therefore, the minute hand of a clock travels 360° in 60 minutes
Number of degrees the minute hand will travel in 25 minutes:

To find how far the tip of the minute hand travels in 25 minutes, use the Arc Length formula:


Given:
- r = length of minute hand = 14 ft
= 150°

Answer:
0.0025 = 0.25% probability that both are defective
Step-by-step explanation:
For each item, there are only two possible outcomes. Either they are defective, or they are not. Items are independent of each other. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which
is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.
5 percent of these are defective.
This means that 
If two items are randomly selected as they come off the production line, what is the probability that both are defective
This is P(X = 2) when n = 2. So


0.0025 = 0.25% probability that both are defective
1.
the x value of the vertex in form
ax^2+bx+c=y
is
-b/2a
so
-2x^2+8x-18
x value of vertex is
-8/(2*-2)=-8/-4=2
plug it in to get y value
-2(2)^2+8(2)-18
-2(4)+16-18
-8-2
-10
vertex is at (2,-10)
or you could complete the square to get into y=a(x-h)^2+k, where the vertex is (h,k)
so as follows
y=(-2x^2+8x)-18
y=-2(x^2-4x)-18
y=-2(x^2-4x+4-4)-18
y=-2((x-2)^2-4)-18
y=-2(x-2)^2+8-18
y=-2(x-2)^2-10
vertex is (2,-10)
5.
vertex is the time where the speed is the highest
at about t=10, the speed is at its max
Answer:
C.I. = (2.297, 11.703)
Step-by-step explanation:
The t-statistic for difference of mean is given by,

Here,
= 84
= 7
s₁ = 4
n₁ = 12
s₂ = 6
n₂ = 18
Substituting all value in formula,
We get, t = -3.541 at 28 degree of freedom.
Using this formula, we get, t = 1.5342
Therefore, based on the data provided, the 99% confidence interval for the difference between the population means
is: 2.297 <
< 11.703
which indicates that we are 99% confident that the true difference between population means is contained by the interval (2.297, 11.703)
Answer:
(12)(3)(-2)
Step-by-step explanation: