Jackson is flying at a constant rate of 500 mph from New York, New York, to Austin, Texas, which is a distance of 1,750 miles. I
f the distance Jackson has traveled in miles is a function of time in hours he has been flying, determine an appropriate domain and range for this problem situation.
1 answer:
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Answer:
The total amount due for purchasing the new home comes to $838,014.72
Step-by-step explanation:
Provided are:
The price set for the new house is $256,000
The down payment intended is 30% of the house price
Therefore, the down payment totals = 30% of $256,000
i.e. The down payment equals to × 256000
Or, The down payment price computes to $76,800
Next, the remaining amount is financed
Thus, The financing amount is p = $256000 - $76800 = $179,200
The interest rate applied = r = 7.5%
The duration for financing = t = 20 years
Let The Amount after 20 years of financing be $A
Let the overall sum payable for the new home = $B
Using Compound Interest
Amount = Principal ×
Or, A = p ×
Or, A = $179,200 ×
Or, A = $179,200 ×
Or, A = $179,200 × 4.24785
∴ A = $761,214.72
Therefore,The Amount to be paid after 20 years of financing = A = $761,214.72
Subsequently
The final amount to be paid for the new home = Down payment total + The Amount to be paid after 20 years of financing
Or, B = $76,800 + A
Or, B = $76,800 + $761,214.72
Or, B = $838,014.72
Therefore, the overall amount due for the new home is rounded to $838,014.72 Answer
Answer:
(a) The data point that is considered an outlier is $810.
(b) The distribution regarding expenditures on textbooks among the 34 students is right skewed.
Step-by-step explanation:
The provided data regarding how much 34 college students spent on textbooks is:
S = {120, 130, 130, 140, 150, 150, 160, 170, 180, 210, 220, 230, 240, 250, 260, 280, 280, 290, 290, 290, 310, 320, 320, 370, 380, 390, 410, 440, 450, 470, 510, 530, 620, 810}
(a)
An outlier is defined as a value significantly different from the rest of the dataset, being either excessively high or low.
A widely-used approach for identifying outliers involves:
- Identifying values that fall below Q₁ - 1.5 IQR as outliers.
- Identifying values that exceed Q₃ + 1.5 IQR as outliers.
In our case,
Q₁ = first quartile
Q₃ = third quartile
IQR = Interquartile range = Q₃ - Q₁.
The first quartile value corresponds to more than 25% of the data points. It can be found by examining the median of the first half of the data.
Calculate the first quartile with the set below:
Initial half of data: {120, 130, 130, 140, 150, 150, 160, 170, 180, 210, 220, 230, 240, 250, 260, 280, 280}
This subset contains 17 values.
The median in an odd-sized dataset is the central point.
The central value here is: 180
Thus, the first quartile is Q₁ = 180.
The third quartile value corresponds to more than 75% of the data points.
We determine the third quartile from the second half of the data:
Final half of data: {290, 290, 290, 310, 320, 320, 370, 380, 390, 410, 440, 450, 470, 510, 530, 620, 810}
<pthis subset="" also="" consists="" of="" values.="">The median of an odd dataset serves as the middle value.
The central point is: 390
Hence, the third quartile is Q₃ = 390.
Calculate the interquartile range as follows:
IQR = Q₃ - Q₁
= 390 - 180
= 210
Next, we compute the value of [Q₁ - 1.5 IQR]:
And then we compute [Q₃ + 1.5 IQR]:
There are no values below [Q₁ - 1.5 IQR]. However, one value exceeds [Q₃ + 1.5 IQR].
X = 810 > [Q₃ + 1.5 IQR] = 705
Consequently, the outlier identified within the dataset is $810.
(b)
A distribution is classified as positively skewed or right-skewed when the majority of the data congregates on the lower end of the spectrum.
The stem plot indicates that most of the data values are concentrated on the left side, confirming that the distribution is indeed right skewed.
</pthis>Answer and Detailed Explanation:
→ The prime factorization of 1624 is:
= 2 × 2 × 2 × 7 × 29
→ The prime factorization of 522 is:
= 2 × 3 × 3 × 29
→ The prime factorization of 1276 is:
= 2 × 2 × 29 × 11
→
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