In an arithmetic sequence
a₁, a₂, a₃,...,
the n-th term is
where d = the common difference
Given that a₅ = 12.4,
a₁ + 4d = 12.4 (1)
With a₉ = 22.4,
a₁ + 8d = 22.4 (2)
Subtracting (1) from (2) yields:
a₁ + 8d - (a₁ + 4d) = 22.4 - 12.4
4d = 10
Thus, d = 2.5
From (1),
a₁ = 12.4 - 4*2.5 = 2.4
Consequently,
a₃₁ = 2.4 + 30*2.5 = 77.4
Answer: a₃₁ = 77.4
Revenue = price * quantity of backpacks
quantity of backpacks = -2p + 50
For p = 9: -2(9) + 50 = -18 + 50 = 32
thus, revenue = 9 * 32 = 288
For p = 12: -2(12) + 50 = -24 + 50 = 26
therefore, revenue = 12 * 26 = 312
For p = 12.50: -2(12.50) + 50 = -25 + 50 = 25
thus, revenue = 12.50 * 25 = 312.50 MAXIMIZES REVENUE
For p = 15: -2(15) + 50 = -30 + 50 = 20
so, revenue = 15 * 20 = 300
The likelihood of observing a sample mean that is less than 18 hours is 0.0082. \nTo evaluate this probability, we calculate the z-score for a sample mean of 18. Accordingly, the probability of getting a sample mean below 18 hours becomes P(z<z(18)). \nThe z-score is calculated as follows: \nz(18) = [(X - M) / s] where: \n- X is the sample mean (18 hours) \n- M is the average hours dentists devote weekly to fillings (20 hours) \n- s is the standard deviation (10 hours) \n- N is the sample size (144) \nSubstituting the numbers leads to: \nz(18) = [(18 - 20) / (10/sqrt(144))]. Using the z-table, we find that P(z<z(18)) is 0.0082.
Answer:
The recorded temperature is -0.675ºC.
Detailed explanation:
To tackle problems involving normally distributed samples, the z-score formula can be utilized.
In a distribution with mean 
and standard deviation 
, the z-score for a specific measure X is calculated as follows:
The Z-score indicates how many standard deviations a given measure deviates from the mean. Once the Z-score is determined, we refer to the z-score table to obtain the corresponding p-value. This p-value represents the likelihood that the measure's value is less than X, thereby indicating the percentile of X. By taking 1 minus the p-value, we find the probability that the measure's value exceeds X.
For this scenario, we know that:
Assuming the thermometer readings follow a normal distribution with a mean of 0◦ and a standard deviation of 1.00◦C, this leads us to 
We need to determine P25, which is the 25th percentile.
This represents the value of X corresponding to Z with a p-value of 0.25, thus we utilize 
, applicable between 
and 
.
The recorded temperature is -0.675ºC.
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)°
