Answer:
1 Superscript 13 and 1 Superscript 15
Step-by-step explanation:
The process of exponentiation can be mathematically written as:
a^b
where a is called the base, and b is called the exponent.
Basically it means that we have to multiply the base with itself as many times as the value of the exponent.
For example 2^4 is 2•2•2•2
Having this in mind, 1^13 and 1^15 have equivalent values, because no matter how many times we multiply 1 with itself it will always be equal to 1.
Answer:
a) P(μ-k*σ≤ Y ≤ μ+k*σ ) ≥ 0.90
a= μ-3.16*σ , b= μ+3.16*σ
b) P(Y≥ μ+3*σ ) ≥ 0.90
b= μ+3*σ
Step-by-step explanation:
from Chebyshev's inequality for Y
P(| Y - μ|≤ k*σ ) ≥ 1-1/k²
where
Y = the number of fish that need be caught to obtain at least one of each type
μ = expected value of Y
σ = standard deviation of Y
P(| Y - μ|≤ k*σ ) = probability that Y is within k standard deviations from the mean
k= parameter
thus for
P(| Y - μ|≤ k*σ ) ≥ 1-1/k²
P{a≤Y≤b} ≥ 0.90 → 1-1/k² = 0.90 → k = 3.16
then
P(μ-k*σ≤ Y ≤ μ+k*σ ) ≥ 0.90
using one-sided Chebyshev inequality (Cantelli's inequality)
P(Y- μ≥ λ) ≥ 1- σ²/(σ²+λ²)
P{Y≥b} ≥ 0.90 → 1- σ²/(σ²+λ²)= 1- 1/(1+(λ/σ)²)=0.90 → 3= λ/σ → λ= 3*σ
then for
P(Y≥ μ+3*σ ) ≥ 0.90
Answer:
7.5 seconds.
Step-by-step explanation:
Substitute the distace 220m in the given equation:
d = 19t + t^2
200 = 19t + t^2
t^2 + 19t - 200 = 0
t = [-19 +/- sqrt(19^2 - 4*1*-200)] / 2
t = -19 +/- sqrt(1161) / 2
t = ( -19 +/- 34.07) / 2
t = 7.535 seconds
Answer:
Here we have given two catogaries as degree holder and non degree holder.
So here we have to test the hypothesis that,
H0 : p1 = p2 Vs H1 : p1 not= p2
where p1 is population proportion of degree holder.
p2 is population proportion of non degree holder.
Assume alpha = level of significance = 5% = 0.05
The test is two tailed.
Here test statistic follows standard normal distribution.
The test statistic is,
Z = (p1^ - p2^) / SE
where SE = sqrt[(p^*q^)/n1 + (p^*q^)/n2]
p1^ = x1/n1
p2^ = x2/n2
p^ = (x1+x2) / (n1+n2)
This we can done in TI_83 calculator.
steps :
STAT --> TESTS --> 6:2-PropZTest --> ENTER --> Input all the values --> select alternative "not= P2" --> ENTER --> Calculate --> ENTER
Test statistic Z = 1.60
P-value = 0.1090
P-value > alpha
Fail to reject H0 or accept H0 at 5% level of significance.
Conclusion : There is not sufficient evidence to say that the percent of correct answers is significantly different between degree holders and non-degree holders.
<h3>Answer: 32%</h3>
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Explanation:
There are 10 cards total. Of which, 8 are not blue. You can think of it as "there are 2 blue, so 10-2 = 8 are not blue", or you can count out the non-blue cards. The first option is faster in my opinion.
The probability of not getting blue is 8/10 = 0.80
After picking a first card and then putting it back, we will still have 10 cards. There are 4 pink cards out of this total, so 4/10 = 0.40 is the probability of getting a pink card.
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Multiply the two values we found earlier
0.80 * 0.40 = 0.32 = 32/100 = 32%
