This statement is incorrect.
In f(3x), the input 'x' is multiplied by 3 prior to being substituted into the function.
Conversely, with 3f(x), the result (output) is multiplied by 3 after you have calculated the output from the input value.
The two lines are perpendicular since y = -6 represents a horizontal line characterized by a slope of 0, while x = 6 depicts a vertical line with an undefined slope.
Let x represent the number of caps
cost per cap = $6
cost for x caps = 6x
shipping charge = $25
overall budget = $1000
We can set up the following inequality:
Because the total amount cannot exceed 1000, we have
25 + 6x ≤ 1000
6x ≤ 975
x ≤ 162.5
rounding,
x ≤ 163
This means she can purchase a maximum of 163 caps.
Response:
Maureen's null hypothesis is, H₀: p₁ ≥ p₂.
Detailed explanation:
Maureen McIlvoy, as the owner and CEO of a mail-order business specializing in windsurfing gear, is scrutinizing the order fulfillment processes in her warehouses. Her objective is to achieve a 100% shipment rate of orders within 24 hours. Upon examining her warehouse operations, she discovers that both the East coast and West coast warehouses have not met this goal, although the East Coast warehouse has consistently outperformed its counterpart.
To verify this finding, Maureen’s team randomly sampled 200 orders from the West Coast warehouse (population 1) and 400 from the East Coast warehouse (population 2).
Of the sampled 200 orders from the West Coast warehouse, 190 were delivered within the specified time. In contrast, 372 out of 400 orders from the East Coast warehouse were processed within 24 hours.
The hypotheses can be formulated as followed:
H₀: The proportion of timely shipments from the East Coast does not exceed that from the West Coast warehouse, thus, p₁ ≥ p₂.
Hₐ: The proportion of timely shipments from the East Coast warehouse is indeed greater than that from the West Coast warehouse, stated as p₁ < p₂.
Thus, Maureen's null hypothesis becomes, H₀: p₁ ≥ p₂.
<span>It is likely that Chad will qualify, as his annual earnings are below California's median yearly income.
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