Answer:
H(t) = 15 -6sin(2.5π(t -0.5))
Step-by-step explanation:
For midline M, amplitude A, period T and time t0 at which the function is decreasing from the midline, the function can be written as ...
H(t) = M -Asin(2π/T(t -t0))
Using the given values of M=15, A=6, T=0.8 and t0 = 0.5, the equation is ...
H(t) = 15 -6sin(2.5π(t -0.5))
Answer:
- 23
Step-by-step explanation:
We could do this the long way and expand the whole product or note that the
terms arise from the product of the a³ and a terms and the product of the a² and a² terms, that is
4a³ × 3a = 12
+ 5a² × - 7a² = - 35
Summing gives
12
- 35
= - 23
with coefficient - 23
Answer: The average number of hours she danced per day is 1.9 hours (rounded to the nearest tenth)
Step-by-step explanation: We start by calculating how many hours she danced all together which can be derived as follows;
Summation = 3 +2 +2 + 1 + 1.5 + 2 = 11.5
The number of days she danced which is the observed data is 6 days (she did not dance at all on Wednesday).
The average (or mean) hours she danced each day can be calculated as
Average = ∑x ÷ x
Where ∑x is the summation of all data and x is number of observed data
Average = (3+2+2+1+1.5+2) ÷ 6
Average = 11.5 ÷ 6
Average = 1.9166
Approximately, average hours danced is 1.9 hours (to the nearest tenth)
<u>Part 1) which angle is congruent to Angle 1?</u>
we know that
When two lines are crossed by another line (which is called the Transversal), the angles in matching corners are called <u>corresponding angles</u>
m∠5=m∠1 ----------> by corresponding angles postulate
therefore
<u>the answer Part 1) is </u>
Angle 
Part 2) Which can be used to directly prove that Angle 1 =~ Angle 8?
we know that
<u>Alternate exterior angles</u> are defined as two exterior angles on opposite sides of a transversal which lie on different parallel lines.
in this problem
m∠1=m∠8 -------> by alternate exterior angles theorem
therefore
<u>the answer part 2) is the option </u>
Alternate Exterior Angles Theorem
<u>Part 3) If m Angle 5 = 42 degrees, what is m Angle 4?</u>
we know that
<u> Alternate interior angles</u> are two interior angles which lie on different parallel lines and on opposite sides of a transversal
m∠4=m∠5 --------> by alternate interior angles theorem
so
m∠4=
therefore
<u>the answer Part 3) is</u>

The total number of possible classifications for the students of this college is found by multiplying 4 (which is the classification for the year level:freshman, sophomore, juniou, senior) and 2 (which is the number of sexes: female and male). So 4 x 2 = 8. There are eight possible classifications, which are:
(Male, Freshman)
(Male, Sophomore)
(Male, Junior)
(Male, Senior)
(Female, Freshman)
(Female, Sophomore)
(Female, Junior)
(Female,Senior)