Answer:
Step-by-step explanation:
Since population std deviation is not known, we use t critical value for testing of hypothesis.
a) 90% conf level when n =28
df = 27, t critical = 1.706
b) 95% 28
df =27 and t critical = 2.052
c) 90% and 15
df =14 and t critical = 1.761
d) 95% and n =15
df =14: t critical = 2.145
After solving for both variables, you find that each bus can hold 59 students and each van can hold 18 students.
Step-by-step explanation:
You can find the amount of students each vehicle can carry by representing the two scenarios in equations.
You are trying to find how many students will fit in each bus or van, so the two variables used will be "b" to represent how many students can fit in a bus and "v" to represent how many students can fit in a van.
High school A used 1 van and 6 buses, so there will be 1"v" and 6"b" for 372 students.
High school B used 4 vans and 12 buses, so there will be 4"v" and 12"b" for 780 students.
Now, represent these in equations:
We can use substitution to solve this system:
can be rewritten as 
after subtracting 6b from both sides. You can then substitute this new value of "v" into the other equation to solve for "b":
After solving for b, you can then substitute the new value of b into the other equation to find the value of v:
After solving for both variables, you find that each bus can hold 59 students and each van can hold 18 students.
Answer:
29.4 cm
Step-by-step explanation:
The length of the space diagonal can be found to be the root of the squares of the three orthogonal edge lengths. For a cube, those edge lengths are all the same, so the diagonal length is ...
d = √(17^2 + 17^2 +17^2) = 17√3 ≈ 29.4 . . . . cm
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Consider a rectangular prism with edge lengths a, b, c. Then the face diagonal of the face perpendicular to edge "a" has length ...
(face diagonal)^2 = (b^2 +c^2)
and the space diagonal has length ...
(space diagonal)^2 = a^2 + (face diagonal)^2 = a^2 +b^2 +c^2
So, the length of the space diagonal is ...
space diagonal = √(a^2 +b^2 +c^2)
when the prism is a cube, these are all the same (a=b=c). This is the formula we used above.
Answer:
a) 1/64
b) 1/4096
Step-by-step explanation:
As you can tell from the example, the exponent of 1/2 is the number of heads in a row.
a) p(6 heads in a row) = (1/2)^6 = 1/(2^6) = 1/64
b) p(12 heads in a row) = (1/2)^12 = 1/(2^12) = 1/4096
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<em>Additional comment</em>
The probability of a head is 1/2 because we generally are concerned with a "fair coin." That is defined as a coin in which each of the 2 possible outcomes has the same probability, 1/2. Similarly, a "fair number cube" has 6 faces, and the probability of each is defined to be the same as any other, 1/6. Loaded dice and unfair coins do sometimes show up in probability problems.
The angle of STV would be 140 degrees.
