The value of x for the given equation (x + 50)/2 = 13x is 2.
According to the given question.
We have an equation (x + 50)/2 = 13x, which represents when two tutoring services with different rate plans charge the same fees for a session of x hours.
So, we have to solve the given equation (x + 50)/2 = 13x for x.
Therefore,
x + 50 = 2(13x)
⇒ x + 50 = 26x
⇒ 26x - x = 50
⇒ 25x = 50
⇒ x = 50/25
⇒ x = 2
Hence, the value of x for the given equation (x + 50)/2 = 13x is 2.
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Based on the information given, it should be noted that the probability that the mean value is less will be 0.9863.
<h3>
Solving the probability.</h3>
From the complete information, the mean of the distribution is $403,000 and the standard deviation is $278,000 and the number of houses is 40.
Therefore, the probability that the mean value of the 40 houses is less than 500000 will be:
= P [Z < (500000 - 403000)/43955.66)
= P(Z < 2.2067)
Looking at the z value, this will be 0.9863.
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Answer:
0.456
0.324
Explanation:
The null and alternative hypothesis :
H0 : p = 0.40; HA :p < 0.40
Test statistic :
(Ph - P) / sqrt[(p*(1-p))/n]
Ph = X / n
X = 34 ; n = sample size = 80
Ph = 34 / 80 = 0.425
(0.425 - 0.4) / sqrt[(0.4(0.6)) / 80]
0.025 / sqrt(0.003)
0.025 / 0.0547722
Test statistic = 0.4564359
Test statistic = 0.456
Using the P-value from Zscore calculator :
Significance level of 95% ; one tailed
Z statistic value = 0.456
P value = 0.324195
= 0.324 ( 3 decimal places)
The net force on the bookcase in the direction of its motion is
∑ F = 65 N - F[friction] = (41 kg) (0.12 m/s²)
so that friction has a magnitude of
F[friction] = 65 N - (41 kg) (0.12 m/s²) = 60.08 N
The net force on the bookcase perpendicular to the surface is
∑ F = F[normal] - (41 kg) g = 0
so that
F[normal] = (41 kg) g = 401.8 N
If µ is the coefficient of kinetic friction, then
F[friction] = µ F[normal]
so that
µ = F[friction] / F[normal] = (60.08 N) / (401.8 N) ≈ 0.15
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