Answer:

Step-by-step explanation:
Given:
KL ║ NM,
LM = 45
m∠M = 50°
KN ⊥ NM
NL ⊥ LM
To determine: KN and KL
1. Analyzing triangle NLM, we see it is a right triangle due to NL ⊥ LM. In this context,
LM = 45
m∠M = 50°
Consequently,

It is also true that
(angles LNM and M are complementary).
2. Now considering triangle NKL, it also forms a right triangle as KN ⊥ NM. Within this triangle,
(alternate interior angles)
(angles KNL and KLN are complementary).
Thus,

and

Answer:
The formula representing the penny's height as a function of time is:

After 7 seconds, the height of the penny will reach 667 feet.
Step-by-step explanation:
The penny experiences free fall.
With an initial velocity of zero and an initial height of h(0)=1,451.
Gravity acts as the acceleration, measured as g=32 ft/s^2.
The model can be initiated by analyzing speed:

Then, the height is expressed as:

The height of the penny at approximately 7 seconds can be calculated as:

After 7 seconds, the penny will stand at a height of 667 feet.
x=88. The third line serves as a transversal, meaning that 92 and x are supplementary angles.
Lacking information on the proportion, we will assume the sample proportion is 0.50
thus,
p = 0.50
The margin of error is set at 10 percentage points. This indicates that the error on either side of the population proportion is 5%, so E = 0.05
z = 1.645 (Z value for a confidence level of 90%)
The calculation for the margin of error when estimating population proportions follows:
Consequently, 271 students need to be part of the sample.