Answer:
The first listed equation is the correct equation to solve
The correct answer is: t = 5 seconds
Step-by-step explanation:
Let me mention first that there is an error in the statement that the gravitational pull of the Earth is 16 ft/s^2. It is in fact 32 ft/s^2, and the actual equation uses half of the acceleration multiplied by the square of the variable time, so it gives as final expression :

and we want to find the value/s for "t" that make this equation equal zero (when it reaches the ground and the object just touches the ground. This makes the equation we want to solve:

which solving for "t" becomes:

So we adopt the positive answer (positive time) since the negative value has no physical meaning for this problem.
That is: t = 5 seconds
The perimeter is the total of adding all of the sides together. A rectangle has 2 lengths and 2 widths. The equation would be:
P = 2l + 2w or P = l + l + w + w
Since you know the perimeter, you can plug it into the equation
53 = 2l + 2w
You can divide the 2 on both sides
26.5 = l + w
l = w + 2.3 because the length is 2.3 meters longer/more than the width. You can substitute (w + 2.3) for "l" in the equation. So instead of:
26.5 = l + w
It will be:
26.5 = (w + 2.3) + w
26.5 = w + 2.3 + w
Subtract 2.3 on both sides
24.3 = w + w
24.3 = 2w
Divide 2 on both sides
12.1 = w
The width is 12.1 meters
She needs 1/6 almonds , 1/3 walnuts and 1/2 of raisins as a fraction of total trail mix.
So she spends $2.5 on almonds. $5 on walnuts and $10 on raisins (total $15)
so that is 2.5/12 = 0.208 pounds almonds
5 / 10.5 = 0.476 pound walnuts
10/4 = 2.5 pounds raisins
so total wieght of the trail mix is 3.19 pounds
Answer:
(53.812 ; 58.188) ; 156
Step-by-step explanation:
Given that :
Sample size (n) = 51
Mean (m) = 56
Standard deviation (σ) = 9.5
α = 90%
Using the relation :
Confidence interval = mean ± Error
Error = Zcritical * (standard deviation / sqrt (n))
Zcritical at 90% = 1.645
Error = 1.645 * (9.5 / sqrt(51))
Error = 1.645 * 1.3302660
Error = 2.1882877
Hence,
Confidence interval :
Lower boundary = 56 - 2.1882877 = 53.8117123
Upper boundary = 56 + 2.1882877 = 58.1882877
Confidence interval = (53.812 ; 58.188)
2.)
Margin of Error (ME) = 1.25
α = 90%
Sample size = ((Zcritical * σ) / ME)^2
Zcritical at 90% = 1.645
Sample size = ((1.645 * 9.5) / 1.25)^2
Sample size = (15.6275 / 1.25)^2
Sample size = 12.502^2 = 156.3000
Sample size = 156