Solve this inequality 2(4x-3)≥-3(3x)+5x?
2 answers:
Answer:
x ≥0.5
Step-by-step explanation:
Given : 2(4x-3)≥-3(3x)+5x.
To find : solve this inequality.
Solution : We have given that
2(4x-3)≥-3(3x)+5x.
Distributes 2 over (4x-3) and -3 over 3x.
8x - 6 ≥ -9x + 5x .
8x - 6 ≥ -4x .
On adding both side by 4x
8x + 4x - 6 ≥ 0 .
12 x - 6 ≥ 0
On adding both sides by 6.
12 x ≥ 6.
On dividing both sides by 12.
x ≥ .
x ≥ .
x ≥0.5.
Therefore, x ≥0.5
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Answer:
a) 0.0304 = 3.04% probability a randomly chosen apple exceeds 100 g in weight.
b) The weight that 80% of the apples exceed is of 78.28g.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Weights of apples are normally distributed with a mean of 85 grams and a standard deviation of 8 grams.
This means that
a. Find the probability a randomly chosen apple exceeds 100 g in weight.
This is 1 subtracted by the p-value of Z when X = 100. So
has a p-value of 0.9697
1 - 0.9696 = 0.0304
0.0304 = 3.04% probability a randomly chosen apple exceeds 100 g in weight.
b. What weight do 80% of the apples exceed?
This is the 100 - 80 = 20th percentile, which is X when Z has a p-value of 0.2, so X when Z = -0.84.
The weight that 80% of the apples exceed is of 78.28g.
Answer:
Check the explanation
Step-by-step explanation:
Here we have to first of all carry out dependent sample t test. consequently wore goggles first was selected at random for the reason that the reaction time in an emergency taken with goggles would be greater than the amount of reaction time in an emergency taken with not so weakened vision. So that we will get the positive differences d = impaired - normal
b)
To find 95% confidence interval first we need to find sample mean and sample sd for difference d = impaired minus normal.
We can find it using excel that is in the first attached image below,
Therefore sample mean = 0.98
Sample sd = 0.3788
To find 95% Confidence interval we can use TI-84 calculator,
Press STAT ----> Scroll to TESTS ---- > Scroll down to 8: T Interval and hit enter.
Kindly check the attached image below.
Therefore we are 95% confident that mean difference in braking time with impaired vision and normal vision is between ( 0.6888 , 1.2712)
Conclusion : As both values in the interval are greater than 0 , mean difference impaired minus normal is not equal to 0
There is significant evidence that there is a difference in braking time with impaired vision and normal vision at 95% confidence level .
