Answer:
Step-by-step explanation:
For the null hypothesis,
H0 : p = 0.63
For the alternative hypothesis,
Ha : p < 0.63
This is a left tailed test
Considering the population proportion, probability of success, p = 0.63
q = probability of failure = 1 - p
q = 1 - 0.63 = 0.37
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 478
n = number of samples = 800
P = 478/800 = 0.6
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.6 - 0.63)/√(0.63 × 0.37)/800 = - 1.76
From the normal distribution table, the area below the test z score in the left tail 0.039
Thus
p = 0.039
Answer:
- DNE
- 3
- 0
- 0
- 1
Step-by-step explanation:
1. The limit of f+g is the sum of the limits: lim(f)+lim(g). Unfortunately, the limit of g from the left (2) is different from the limit of g from the right (1) at x=1. Hence, the limit of g does not exist, so the limit of f at that point (2) is irrelevant.
2. lim(f+g) = lim(f)+lim(g) = 1 + 2 = 3. Both functions are defined and continuous at x=2, so their values can be read from the graphs.
3. lim(f·g) = lim(f)·lim(g) = 0·(3/2) = 0. Both functions are defined and continuous at x=0, so their values can be read from the graphs. We doubt that g(0) = 3/2 exactly, but it doesn't matter since f(0) = 0.
4. lim(f/g) = lim(f)/lim(g) = 0/(3/2) = 0. See the explanation for 3, immediately above.
5. f(-1) = -2, which is the limit aproaching either from the left or right. √(3-2) = 1. The function f is defined and continuous at x=-1, so its value can be read from the graph.
Given that KL/KM = KP/KN = PL/MN = k, m∠K = m∠K, m∠L = m∠M and m∠P = m∠N, then by SAS theorem we conclude that ΔLKP ∼ ΔMKN.
<h3>How to define the similarity between the two triangles</h3>
By Euclidean geometry we know that two triangles are similar when the two triangles have the <em>same</em> angles in the <em>same</em> order. Thus, the sides between the two triangles have the <em>same</em> proportionality, then:
KL/KM = KP/KN = PL/MN
Given that KL/KM = KP/KN = PL/MN = k, m∠K = m∠K, m∠L = m∠M and m∠P = m∠N, then by SAS theorem we conclude that ΔLKP ∼ ΔMKN.
To learn more on similar triangles: brainly.com/question/25882965
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If you would like to know the least possible pair of integers, you can find this using the following steps:
integer ... n
the sum of two consecutive integers ... n + (n+1) = n + n + 1 = 2 * n + 1
is at least 36 ... >= 36
n + (n+1) >= 36
2 * n + 1 >= 36
2 * n >= 36 - 1
2 * n >= 35 /2
n >= 35/2
n >= 17.5
n = 18: 18 + (18+1) = 18 + 19 = 37 >= 36
The correct result would be C. 18 and 19.