We cannot calculate the confidence interval without the sample size. However, for the second question, the sample size needed would be 49.
The formula we use is

To find the z-score:
Convert 98% to a decimal: 0.98
Subtract from 1: 1-0.98 = 0.02
Divide by 2: 0.02/2 = 0.01
Subtract from 1: 1-0.01 = 0.99
Using a z-table (http://www.z-table.com) we see that this value is closest to a z-score of 2.33.
Using the z-score, our standard deviation (9) and our margin of error (3), we have:
The length of OM is 4/3 the length of OJ, and the length of ON is 4/3 the length of OK. Thus, two pairs of sides from the triangles are proportional to each other.
Also, angle O from one of the triangles is equal to angle O of the other triangle because they are the same angle.
Thus, the two triangles are similar by SAS (side-angle-side) similarity theorem. This theorem is quite similar to the SAS congruence theorem.
To make a similarity statement, we just have to match corresponding parts when naming the triangle.
Similarity statement: ΔOJK~ΔOMN
<h3>
Answer: Max height = 455.6 feet</h3>
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Explanation:
The general equation
y = ax^2 + bx + c
has the vertex (h,k) such that
h = -b/(2a)
In this case, a = -16 and b = 147. This means,
h = -b/(2a)
h = -147/(2*(-16))
h = 4.59375
The x coordinate of the vertex is x = 4.59375
Plug this into the original equation to find the y coordinate of the vertex.
y = -16x^2+147x+118
y = -16(4.59375)^2+147(4.59375)+118
y = 455.640625
The vertex is located at (h,k) = (4.59375, 455.640625)
The max height of the rocket occurs at the vertex point. Therefore, the max height is y = 455.640625 feet which rounds to y = 455.6 feet
Answer:
t=10
Step-by-step explanation:
3t + 15 = 45
3t = 30
t = 10
Answer:
length = 49 m
width = 46 m
Step-by-step explanation:
Length= w+3
width = w
Perimeter = 2L +2W
190=2(w+3) +2w
190=2w+6+2w (combine like terms now
190=4w+6
184=4w
w=46
PLUG IN
Length
46+3 = 49