Response:
The measure of mHLK is "(204)°".
Step-by-step breakdown:
Given values include:
mJI = (3x+2)°
mHLK = (15x-36)°
and,
m∠HML = (8x-1)°
then,
What is mHLK?
Now,
Utilizing the chord-chord angle formula, we find
Inserting the known values into the equation gives us
⇒ 
By carrying out cross-multiplication, we arrive at
⇒ 
⇒ 
By subtracting "18x" from both sides, we obtain
⇒ 
⇒ 
Upon adding "2" to both sides, we end up with
⇒ 
⇒ 
⇒ 
⇒ 
By substituting the value of "x" into mHLK = (15x-36)°, we calculate
⇒ (15x-36)° = (15×16-36)°
⇒ = (240-36)°
⇒ = (204)°
Thus, mHLK = (204)°
Response:
It is inferred that the authors of the sonnets belong to a certain poet from the Elizabethan era.
Step-by-step breakdown:
The details provided in the question are as follows:
Population mean, μ = 8.9
Sample mean, 
= 10.2
Sample size, n = 6
Alpha, α = 0.05
Population standard deviation, σ = 2.5
Initially, we formulate the null hypothesis and the alternative hypothesis
To conduct this test, we utilize the One-tailed z test.
a) Equation:
By substituting in all relevant values, we determine:
Next, 
b) The p-value is computed using the z-table.
P-value = 0.1003
The p-value surpasses the alpha of 0.05
c) Because the p-value exceeds the alpha threshold, there is insufficient evidence to dismiss the null hypothesis, thereby supporting the null hypothesis.
Consequently, it is concluded that the authorship of the sonnets belongs to a particular Elizabethan poet.
The set of rental car rates making it more economical for Jamal than employing taxi services is outlined as A = {x | 0 ≤ x < 26} [where x represents dollars]. The step-by-step breakdown is as follows: Let the rental cost be $x per day. With Jamal's trip extending over 4 days, factoring in $24 for gas, and estimating taxi costs at around $128, an inequality emerges: 128 > 24 + 4x. Thus simplifying leads to 4x < 104 and consequently x < 26.
1.29(30) +2 Step-by-step explanation: Begin by calculating 1.29 multiplied by 30, which results in 38.7. Next, add 2 to this sum to arrive at 40.7. Consequently, the total expense amounts to $40.70.
They cannot possess the same number of horses; let me clarify. If you divide 21 horses among four individuals, you would perform 21/4, yielding 5.25, implying that fractional horses are unfeasible. Therefore, at least one individual must have 6 horses instead of 5. Possibly, this is what your instructor wants you to understand. For an even distribution, they could sell one horse, making it 20, so each would then have 5 horses. Alternatively, they might share the extra horse to rotate its usage.
