Solve the given quadratic equation. x^2=112
2 answers:
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Firts, Let 
be the repeated decimal that we are trying to convert , so 
equation (1)
Next, lets find how many digits are repeating:
It is pretty cleat that 90 is repeating, and 90 has two digits. So we are going to multiply our equation by 100 to move the decimal point two places:
(2)
Subtract equation (1) from equation (2):
Solve for
We can conclude that 10.9090909091... expressed as a rational number, i<span>n the form pq where p and q are positive integers with no common factors, is </span>
.
Next, lets find how many digits are repeating:
It is pretty cleat that 90 is repeating, and 90 has two digits. So we are going to multiply our equation by 100 to move the decimal point two places:
Subtract equation (1) from equation (2):
Solve for
We can conclude that 10.9090909091... expressed as a rational number, i<span>n the form pq where p and q are positive integers with no common factors, is </span>
Answer:
1) B. The differences are normally distributed or the sample size is large
C. The sample size mus be large
E. The sampling method results in an independent sample
2) The null hypothesis H₀: =
The alternative hypothesis Hₐ: <
Test statistic, t = -0.00693
p- value = 0.498
Do not reject Upper H₀ because, the P-value is greater than the level of significance. There is sufficient evidence to conclude that sons are the same height as their fathers at 0.10 level of significance
Step-by-step explanation:
1) B. The differences are normally distributed or the sample size is large
C. The sample size mus be large
E. The sampling method results in an independent sample
2) The null hypothesis H₀: =
The alternative hypothesis Hₐ: <
The test statistic for t test is;
The mean
Height of Father, h₁, Height of Son h₂
72.4, 77.5
70.6, 74.1
73.1, 75.6
69.9, 71.7
69.4, 70.5
69.4, 69.9
68.1, 68.2
68.9, 68.2
70.5, 69.3
69.4, 67.7
69.5, 67
67.2, 63.7
70.4, 65.5
= 69.6
s₁ = 1.58
= 69.9
s₂ = 3.97
n₁ = 13
n₂ = 13
(We reversed the values in the square root of the denominator therefore, the sign reversal)
t = -0.00693
p- value = 0.498 by graphing calculator function
P-value > α Therefore, we do not reject the null hypothesis
Do not reject Upper H₀ because, the P-value is greater than the level of significance. There is sufficient evidence to conclude that sons are the same height as their fathers at 0.10 lvel of significance