Answer:
The price per kilogram of salami amounts to = $9.1
Step-by-step explanation:
Given:
Hailey spent $13 on 
kg of sliced salami.
We need to determine the cost per kg of the salami.
Solution:
We will use the unitary method to find the cost for one kilogram of salami.
If kg of salami costs $13
Then the cost for 1 kg of salami in dollars = 
When dividing mixed numbers, we convert them to fractions.
⇒ 
⇒ 
To divide fractions, we take the reciprocal of the divisor and multiply.
⇒ 
⇒ 
⇒ 
⇒ 
Hence, the cost per kilogram of salami is = $9.1
Response:
The goat population will reach 1000 in a time span of 12.4 years
Detailed explanation:
After t years, the population of goats is described by
where 
indicates the initial count of goats and b is the growth rate per capita.
Based on the problem,
- b = 0.5
- N = 1000
The attached graph illustrates the region. The centroid's coordinates are (5/3, 1). The centroid's coordinates are determined by averaging the coordinates of the area; Oₓ = (Aₓ+Bₓ+Cₓ)/3 = (0+1+4)/3 = 5/3 and O(y) = (A(y) + B(y) + C(y)) = (0+3+0)/3=3/3=1.
Response:
MAD value comes out to be 3.
Detailed Breakdown:
The given sales forecasts for the last four months are 5, 6, 11, and 12 units.
To calculate the Mean Absolute Deviation (MAD) for these forecasts:
The average of the forecasts across four months is 
.
Thus, the total of absolute differences between the forecast values and the average is = |5 - 8.5| + |6 - 8.5| + |11 - 8.5| + |12 - 8.5| = 3.5 + 2.5 + 2.5 + 3.5 = 12.
Hence, the MAD value will be = 
(Final Answer)
The P-value to evaluate the claim that the mean length of pencils produced in this factory equals 18.0 cm is 0.00736. Step-by-step explanation: In this case, a quality control specialist extracted a random sample of 45 pencils from the assembly line, which exhibited a mean length of 17.9 cm. With a known population standard deviation of 0.25 cm, we denote by the population mean length for pencils produced in the factory. Thus, Null Hypothesis: = 18.0 cm (indicating that the population mean length equals 18.0 cm). Alternate Hypothesis: ≠ 18.0 cm (suggesting different from 18.0 cm). We apply the one-sample z-test since the population standard deviation is known. The test statistic yields: T.S. ~ N(0,1), with the sample mean length 17.9 cm and population standard deviation 0.25 cm for a sample size of 45. Hence, the calculated test statistic is -2.68. The corresponding P-value is derived from P(Z < -2.68) = 1 - P(Z > 2.68), equating to 1- 0.99632 = 0.00368. For a two-tailed test, the resulting P-value computes to 2 * 0.00368 = 0.00736.
