Answer:
JK = 12.6
Step-by-step explanation:
Similarity says ratio of any cooresponding sides are equal to the ratio of any other cooresponding sides. SO
25.2/66 = JK/33
33(25.2/66) = JK
12.6 = JK
Answer:
Expected Value = -$0.41
Step-by-step explanation:
Expected Value = [$6,200*(1/17000) + $940*(3/17000) + $98*(8/17000) + $25*(10/17000)] - 1
Expected Value = [0.59]-1
Expected Value = -$0.41
Area = (base * height) / 2
60 = (12 * h) / 2
120 = 12h
h=10 yards
Answer:
The sample size required is 102.
Step-by-step explanation:
The (1 - <em>α</em>)% confidence interval for population mean <em>μ</em> is:
The margin of error for this interval is:
Given:
<em>σ</em> = 9.2
(1 - <em>α</em>)% = 90%
MOE = 1.5
The critical value of <em>z</em> for 90% confidence level is:
*Use a <em>z</em>-table.
Compute the value of <em>n</em> as follows:
![n=[\frac{z_{\alpha/2}\times \sigma}{MOE}]^{2}](https://tex.z-dn.net/?f=n%3D%5B%5Cfrac%7Bz_%7B%5Calpha%2F2%7D%5Ctimes%20%5Csigma%7D%7BMOE%7D%5D%5E%7B2%7D)
![=[\frac{1.645\times 9.2}{1.5}]^{2}\\=101.795\\\approx102](https://tex.z-dn.net/?f=%3D%5B%5Cfrac%7B1.645%5Ctimes%209.2%7D%7B1.5%7D%5D%5E%7B2%7D%5C%5C%3D101.795%5C%5C%5Capprox102)
Thus, the sample size required is 102.
Part (i)
I'll use H in place of T to represent the heat of the object. That way there isn't a clash of variables lowercase t vs uppercase T.
The equation we're working with is updated to:
H(t) = 22 + a*2^(bt)
Plugging in t = 0 as the initial time value should lead to the temperature being H = 86 degrees Celsius.
So,
H(t) = 22 + a*2^(bt)
86 = 22 + a*2^(b*0)
86 = 22 + a*2^0
86 = 22 + a*1
86 = 22 + a
a+22 = 86
a = 86-22
a = 64
<h3>Answer: 64</h3>
=====================================================
Part (ii)
We'll use the value of 'a' we found earlier. Plus we'll use the fact that H = 28 when t = 0.5 (since 30 min = 30/60 = 0.5 hr).
H(t) = 22 + a*2^(bt)
28 = 22 + 64*2^(b*0.5)
28-22 = 64*2^(0.5b)
64*2^(0.5b) = 6
2^6*2^(0.5b) = 6
2^(6+0.5b) = 6
log( 2^(6+0.5b) ) = log(6)
(6+0.5b)*log(2) = log(6)
6+0.5b = log(6)/log(2)
6+0.5b = 2.5849625
0.5b = 2.5849625-6
0.5b = -3.4150375
b = -3.4150375/(0.5)
b = -6.830075
<h3>Answer: Approximately -6.830075</h3>
