Response:
Step-by-step breakdown:
When you sketch that diagram (great description, by the way!), what you essentially have is a right triangle with a base of 32 and a hypotenuse of 45. The right angle resides at one of the base's ends, and x represents the vertex angle. We must find this vertex angle first to determine the angle of depression from the second bird to the watcher. The side measuring 32 is opposite to angle x, with 45 being the hypotenuse; hence, the trigonometric relation we need is sine:
and
sin(x) =.711111111
Go to your calculator, press the 2nd key followed by the sin key, and your display will show:
then, enter in your decimal.711111111 and hit equals. You should arrive at an angle of 45.325. That angle is x. However, that's not the angle of depression. The angle of depression is the complementary angle to x.
Angle of depression = 90 - angle x and
Angle of depression = 90 - 45.325, resulting in
Angle of depression = 44.67 or 44.7 degrees.
75,88,90,96,98,100
minimum = 75
Q1 = 88.....this indicates the start of the box
Q2 (the median) = (90 + 96) / 2 = 186/2 = 93....this signifies the line within the box
Q3 = 98....this indicates the end of the box
maximum = 100
88_93______98
75_______| | |___100
|___|_______|
To derive the function that characterizes the bee population:
1) Initially, there are 9,000 bees in the first year.
2) In the second year, a reduction of 5% occurs => 9,000 - 0.05 * 9,000 = 9,000 * (1 - 0.05) = 9,000 * 0.95
3) Each subsequent year sees a 5% decline => 9,000 * (0.95)^(number of years)
4) Let x represent years and f(x) signify the bee count, then: f(x) = 9,000 (0.95)^x.
Evaluation of the claims:
<span>1) The function f(x) = 9,000(1.05)x applies to the scenario.
FALSE: WE ESTABLISHED IT AS f(x) = 9,000 (0.95)^x
2) The function f(x) = 9,000(0.95)x applies to the scenario.
TRUE: THIS IS THE RESULT OF OUR PRIOR ANALYSIS.
3) After 2 years, the farmer projects approximately 8,120 bees will be left.
Calculating:
f(2) = 9,000 * (0.95)^2 = 9,000 * 0.9025 = 8,122
Thus, this statement is TRUE
4) After 4 years, the farmer can predict there will be roughly 1,800 bees left.
f(4) = 9,000 * (0.95)^4 = 9,000 * 0.81450625 = 7,330
This statement is therefore FALSE
5) The domain values contextual to this situation are restricted to whole numbers.
FALSE: DOMAIN VALUES INCLUDE ALL NON-NEGATIVE REAL NUMBERS. FOR INSTANCE, THE FUNCTION IS VALID AT X = 5.5
6) The range values pertinent to this situation are restricted to whole numbers.
TRUE: FRACTIONS OF BEES CANNOT EXIST.
</span>
Answer:
The artist begins to profit when n > 8.18
That means the quantity of necklaces must exceed 8.18.
Step-by-step explanation:
Given
let n represent the number of necklaces
booth fee= $135
The expense for materials per necklace = $4.5n
the overall selling price for all necklaces = $12n
total costs= booth fee + material costs = $135 + 4.5n
profit = selling price - total costs
12n > 135 + 4.50n
By solving for n, we find
12n=135 + 4.50n
12n + 4.5n = 135
16.5n = 135
n = 135/16.5
n = 8.18
Hence, the artist achieves profits when n > 8.18.
