A building casts a shadow 25 m long. At the same time, the shadow cast by a 44-cm tall pole is 59 cm long. Find the height of th
1 answer:
In order to solve this, we will use proportions. The first step involves converting centimeters to meters by applying dimensional analysis:
Once everything is expressed in meters, we can set up the proportions accordingly. Our proportion becomes
First, we perform cross-multiplication:
Then, by dividing both sides by 0.59, we arrive at x = 18.6 m, or D.
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Given:
A quadratic function has a line of symmetry positioned at x = –3.5 with one root located at –9.
To find:
The second root.
Solution:
It is understood that the line of symmetry splits the quadratic function's graph into two identical halves. Hence, both roots are equidistant from this line.
This implies that the line of symmetry passes through the midpoint of the two roots.
Let the other root be denoted as x.
Multiply both sides by 2.
Add 9 to both sides.
Consequently, the other zero of the quadratic function is concluded to be 2.
Answer:
a.[144;158]$
b. The parameter being estimated is the average weekly food expenses of American families.
Step-by-step explanation:
Hello!
The variable studied here represents "Weekly food expenses incurred by an American family"($)
From a sample of n=1014 American families, the sample mean is x[bar]=$151
It is indicated that for the 95% confidence interval, the margin of error is ±$7
a.
The estimated confidence interval for the population mean is formed as "estimator ± margin of error." In a Standard Normal distribution, the confidence interval formula is:
[x[bar]±*(δ/√n)]
For the provided sample, we have:
[151±7]
The lower limit equates to 144$
The upper limit amounts to 158$
b.
The parameter being contemplated is the average weekly food expenses of American families.
The confidence level for this interval reflects the likelihood that if 100 such intervals were constructed, approximately 95 would encompass the true value of the population mean we aim to estimate.
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The maximum value of P is determined to be 33. 
). The solutions to both sets of constraints lie beneath the lines. Solve the equations 5x + y = 16 and 2x + 3y = 22 simultaneously to find their intersection point at (2, 6).
Step-by-step explanation: Start by graphing the constraints represented by the lines
5x + y = 16, which has intercepts at (16, 0) and (0, 16), and
2x + 3y = 22, with intercepts at (11, 0) and (0,The vertices of the feasible region are determined to be (0, 0), (0, 16), (2, 6), and (11, 0). Evaluate the objective function at each vertex.
At (0, 0), P = 0. At (0, 16), P = 32. At (2, 6), P = 18. Finally, at (11, 0), P = 33. Thus, the maximum P value occurs when x = 11 and y = 0.