Simplify the following expression.
1 answer:
You might be interested in
Answer:
<em>Roberto's speed in still water is 6 miles/hour and the river speed is 2 miles/hour</em>
Step-by-step explanation:
<u>Relative Speed</u>
When a body is moving at a constant speed v, the distance traveled in a time t is:
When Roberto rows downstream, his speed in still water is added to the speed of the water, making it easier to travel the required distance.
When Roberto rows upstream, his speed in still water is affected by the speed of the water, both are subtracted and the required distance is covered in more time.
Let's call
x = Roberto's rowing speed in still water
y = Speed of the river current
The speed when rowing downstream is x+y, thus the distance traveled is
Where t1=2.5 hours. Substituting values:
Rearranging, we find the downstream equation:
The speed when rowing upstream is x-y, and the distance traveled is
Where t2=5 hours. Substituting values:
Rearranging, we find the upstream equation:
Multiplying [1] by 2:
Adding this equation to [2]:
Solving:
Dividing [2] by 5:
Solving for y
Thus, Roberto's speed in still water is 6 miles/hour and the river speed is 2 miles/hour
Answer:
Step-by-step explanation:
From the given information:
The number of children that were randomly allocated to each vaccination group; n₁ = 200,000
No of polio cases X₁ = 57
Now, in the vaccine group:
the proportion of polio cases is:
= 0.000285
The number of children that were randomly allocated to the placebo group, n₂ = 200,000
No of polio cases X₂ = 142
In the placebo group
the proportion of polio cases is:
Null and alternative hypothesis is computed as follows:
H₀: There is no difference in the proportions of polio cases between both groups.
H₁: There is a difference in the proportions of polio cases between both groups.
Let assume that the level of significance ∝ = 0.05
The test statistic can be computed as:
Z = - 6.03
P-value = 2P(Z < -6.03)
From the Z - tables
P-value = 2 × 0.0000
= 0.000
We reject the H₀ provided that P-value is very less.
Therefore, we may conclude that there is a difference in the proportions of polio cases between the vaccine group and placebo group not due to chance.