The amount to be paid as monthly installment for 24 equal monthly installments is given by 30,278.65 pesos.
Area bought by Vincent = 105. 7 square meters
Cost per square meters = 12,500. 00 pesos per square meter.
The total cost of the lot is the product of the area and the price per square meter,
Cost
= 105.7 sq m ×12,500.00 pesos/sq m
= 1,321,250.00 pesos
Amount paid by Vincent in cash is equals to
= 0.45 × 1,321,250.00 pesos
= 594,562.50 pesos
The remaining balance to be paid in installments is equals to,
= 1,321,250.00 pesos - 594,562.50 pesos
= 726,687.50 pesos
This balance will be paid in 24 equal monthly installments, so the monthly installment amount is equals to,
= 726,687.50 pesos / 24 months
= 30,278.65 pesos per month (rounded to the nearest cent)
Therefore, amount paid by Vincent as monthly installment is equal to 30,278.65 pesos.
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Which expression best represents the difference between triple a number and double a number
Answer: 3x-2x or (3x)-(2x)
Write an expression that best represents the difference between triple and double a number?
Step-by-step explanation: HOPE THIS HELPS!
Answer:
3x-2x
Step-by-step explanation:
I hope you this is it
one of four different prizes was randomly put into each box of a cereal. if a family decided to buy this cereal until it obtained at least one of each of the four different prizes, what is the expected number of boxes of cereal that must be purchased?
The expected number of boxes of cereal that must be purchased to obtain at least one of each of the four different prizes is 1.
Let X be the number of boxes of cereal that need to be purchased to obtain at least one of each of the four different prizes. We want to find E(X), the expected value of X.
To do this, we can use the concept of the geometric distribution. The probability of obtaining a new prize in a box of cereal is given by:
p = 4/4 = 1 (since there are four different prizes)
The probability of not obtaining a new prize in a box of cereal is
q = 1 - p = 0
Therefore, X follows a geometric distribution with parameter p = 1. The expected value of a geometric distribution with parameter p is
E(X) = 1/p
So in this case, we have
E(X) = 1/1 = 1
This means that on average, the family will need to purchase one box of cereal to obtain at least one of each of the four different prizes.
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midazolam 9 mg im now is ordered. the nurse has the following vial of midazolam. how many milliliters will the nurse administer? enter only the numeral (not the unit of measurement) in your answer.
1.8 ml (milliliters) the nurse will administer the vial of the Midazolam of ordered 9mg.
The formula of calculating this is D/H × Q = x
where x = Desired dose amount, D = ordered Dose amount, H = amount on hand and Q = quantity.
From the following questions we have.
9mg = order dose, 5mg = amount on hand and 1ml quantity.
x = 9/5 × 1
= 1.8 ml.
Midazolam is administered carefully .it is used for sedation and anesthesia before surgical procedure. Midazolam is a short acting drug under benzodiazepines which have sedation power, so use or administered carefully before surgical procedure.
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How to do a yes because yes is yes and yes in yes s how to yes and no
A little help :) Appreciated - 40 points
PLEAS HELP! PIZZA MATH PROBLEM!!!
Josh has 5 mini pizzas to share with 4 friends. Two pizzas have mushrooms, 2 have pepperoni, and 1 is plain. Jasmine only eats plain pizza. Zach won’t eat mushrooms or onions. Carly and Owen will eat pepperoni and mushrooms, but no onions. Josh will eat any
kind of pizza. If Josh cuts each mini pizza in half, how should he divide up the halves so each person gets 2 halves each? How much pizza will be left over?
Answer:
Step-by-step explanation:
4 and a half
Mr. Salinger has 8 packs of seeds. The line plot shows the weight of each pack. Mr. Salinger wants to redistribute the seeds in such a way that each pack weighs the same. What will be the weight of each pack?
Each pack should weigh 11.5 oz when the seeds are redistributed equally.
Since Mr. Salinger wants to redistribute the seeds in such a way that each pack weighs the same, he needs to find the common weight of all the packs. To do this, he can find the total weight of all the packs and divide it by the number of packs.
Using the line plot, we can see that the weights of the 8 packs are:
12 oz
8 oz
10 oz
10 oz
12 oz
14 oz
10 oz
16 oz
To find the total weight of all the packs, we can add these weights together:
12 + 8 + 10 + 10 + 12 + 14 + 10 + 16 = 92 oz
So the total weight of all the packs is 92 oz.
To find the weight of each pack, we need to divide the total weight by the number of packs:
92 ÷ 8 = 11.5 oz
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From the top of an 18-meter lighthouse, the angle of depression to sight a boat is 4°. What is the distance between the boat and the base of the lighthouse, to the nearest tenth?
ASAP TIMED
Step-by-step explanation:
The side opposite to the 4 degree angle is 18 m
The side adjacent the 4 degree angle is x
tan(4) = opposite / adjacent
adjacent = opposite / (tan(4))
adjacent = 18 / tan(4)
adjacent = 257.41
student id numbers are created using the digits 0-9. how many five- digit student id numbers can be created if repeat digits are allowed? what if repeats are not allowed?
There are 100,000 possible five-digit student ID numbers that can be created if repeat digits are allowed (10^5).
However, if repeats are not allowed, there are only 9 x 9 x 9 x 9 x 9 = 590,490 possible student ID numbers that can be created (9^5).
The reason for the difference is that when repeats are allowed, you can use the same digit multiple times, for example "11111".
When repeats are not allowed, you can only use each digit once, for example "12345". The possible permutations of the digits 0-9 increase as more digits are added to the ID number, meaning that the more digits there are, the more possible combinations there are.
Therefore, when repeats are not allowed, the number of possible combinations is reduced significantly. In the case of five-digit student ID numbers, the difference is almost twofold.
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A square based pyramid has a base area of 25 square feet. If the
slant height forms a 50° angle with the base of the pyramid, find
the volume of the square pyramid to the nearest tenth of a cubic
foot.
Answer:
Step-by-step explanation:
square pyramid. Calculate the unknown defining height, slant height, surface area, side length and volume of a square pyrami
Seth is analyzing the number of students in his class and
The least likely event from given events is Option B: A randomly selected student who is freshmen owns a skateboard.
The event whose occurence is minimum is least likely event.
Suppose there are finite elementary events in sample space of considered experiment and all are equally likely.
Then, we want to find the probability of an event E.
Then, its probability is given as
P(E) = Number of favourable cases/ Number of total cases = n(E)/n(S)
where favorable cases are the elementary events who belong to E, and total cases are size of sample space.
For two events A and B, by chain rule, we have:
P(A∩B) = P(B)P(A|B) = P(A)P(A|B)
How to find the conditional probability:
Suppose that there are two events A and B. Then suppose the conditional probability are:
P(A|B) = probability of occurrence of A given B has already occurred.
P(B|A) = probability of occurrence of B given A has already occurred.
We can then use the chain rule to find them, or Bayes theorem also helps in finding these probabilities.
We are given the table of joint relative frequency:
We take events as A, A' and B and B'
Important probabilities which will be used are evaluated as:
P(A) = n(A)/n(S) = 150/1200 = 1/8
P(B) = n(B)/n(S) = 250/1200 = 5/24
P(A') = 1 - P(A) = 7/8
P(B') = 1 - P(B) = 1 - 5/24 = 19/24
P(A∩B) = n(A∩B) / n(S) = 40/1200 = 1/30
P(A'∩B') = n(A'∩B') / n(S) = 840/1200 = 7/10
P(A'∩B) = n(A'∩B) / n(S) = 210/1200 = 7/40
Evaluating probabilities of choices given, we get:
Case 1: E = A random selected student who owns skateboard is freshmen
P(E) = ?
P(E) = P(B|A) = P(A∩B) / P(A) = 1/30 ÷ 1/8 = 4/15
Case 2: E = A random selected student who is freshmen owns skateboard:
P(E) = P(A|B) = P(A∩B) / P(B) = 1/30 ÷ 5/24 = 4/25
Case 3: E = A random selected student who doesn't owns skateboard is freshmen
P(E) = P(B|A') = P(A'∩B) / P(A') = 7/40 ÷ 19/24 = 21/95
Case 4: E = A randomly selected student who doesn't owns skateboard is not freshmen
P(E) = P(B'|A') = P(A'∩B') / P(A') = 7/10 ÷ 19/24 = 84/95
So, the least probability is for second case.
Question - Seth is analyzing number of students in class and high school who own skateboards. He puts the data in table shown. Given information in table, which event is least likely?
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your neighborhood fast food restaurant only sells chicken nuggets in packs of five or seven. what is the largest number of nuggets that is impossible to order?
The largest number of chicken nuggets that is impossible to order from your neighborhood fast food restaurant is eleven.
The largest number of chicken nuggets that is impossible to order from your neighborhood fast food restaurant is eleven. This is because the restaurant only sells nuggets in packs of five and seven. This means that if you wanted to order eleven nuggets, it would not be possible.
To explain this mathematically, eleven can be written as 5+5+1, 7+4, or 3+3+3+2. As none of these can be made with just five and seven packs of chicken nuggets, it is impossible to order eleven.
If the restaurant sold chicken nuggets in packs of three and seven, then it would be possible to order eleven nuggets (3+3+3+2).
In conclusion, the largest number of chicken nuggets that is impossible to order from your neighborhood fast food restaurant is eleven.
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Julian puts money into two investments on the same day. The first pays out £225 after every 4 years and the second pays out £350 after every 6 years. A) How many years must Julian wait before both of his investments pay out in the same year? b) Give one advantage of each of Julian's investments
Before both of Julian's investments make a profit in the same year, he must wait 12 years.
a) To find the year when both investments pay out in the same year, we need to find the least common multiple (LCM) of the two payout periods: 4 years and 6 years.
The prime factorization of 4 is 2², and the prime factorization of 6 is 2 x 3. The LCM of 4 and 6 is 2² x 3 = 12.
Therefore, Julian must wait 12 years before both of his investments pay out in the same year.
b) One advantage of the investment that pays out £225 after every 4 years is that it provides a steady and predictable income stream. Julian can expect to receive the same amount every 4 years, which can help him plan for future expenses.
One advantage of the investment that pays out £350 after every 6 years is that it offers a higher payout than the other investment. Julian can potentially earn more money from this investment, although it requires a longer waiting period for the payout. Overall, the two investments offer different advantages, and Julian may choose to invest in both to balance steady income with higher potential earnings.
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The Morris family is planning to carpet their entire home. The type of carpet they want is sold at two different stores. The table and graph below show the costs for different amounts of carpet sold by the two stores. Which store sells the carpet for the lesser amount, in cost per square yard? Show work or explain your answer.
By charging $11 per square yard as opposed to $12 per square yard at Shop A, Store B offers the carpet for a lower price per square yard.
What distinguishes a table from a graph?The same data that is displayed in tables is also presented in charts and graphs. Yet, compared to a table, a chart or graph provides less detail or greater imprecision.
We must divide the total cost by the quantity of carpet square yards in order to determine the price per square yard. Seeing from the table that Shop A charges $360 for 30 square yards of carpet, the following information is provided:
Shop A's price per square yard is $360.30 sq yard divided by $12 per sq yd
A similar price of $550 is charged by Store B for 50 square yards of carpet, giving us:
$550 divided by 50 square yards yields $11 per square yard at store B.
The graph also shows that, for all carpet sizes, Shop B consistently charges less per square yard than Store A.
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Mariah has an after school babysitting job, This is a record of the number of hours she worked last week on Monday 2 1//2 on Tuesday it was 3 1/2 Wednesday 2 1/4 and Thursday 3 2/3 and she gets paid 6$ per hour how much money would she make? And also this is improper fractions as well
Answer: 71 1/2$
Step-by-step explanation:
luis wants to create a graph using powerpoint to show how much weight he lost after starting an exercise plan over six months. which type of graph should he use?
Luis wants to create a graph using PowerPoint to show how much weight he lost after starting an exercise plan over six months. The type of graph that Luis should use is a line graph.
What is a line graph?A line graph is a method of displaying data or information on a two-dimensional Cartesian plane. It is mostly used to display changes over time or trends. It is ideal for data that has a lot of numeric data or that change frequently over time.The line graph is made up of two lines, one horizontal and the other vertical, which connect the data points in a sequential order. It is best used for visual representation of data, as it provides the viewer with a simple, visual representation of the data.
The x-axis and y-axis of a line graph represent the independent and dependent variables, respectively. The x-axis is often used to represent the time or the data being analyzed, while the y-axis represents the numerical values that are being analyzed.To create a line graph using PowerPoint, you can use the Insert Chart button to add your data, then choose Line Graph as the type of chart you want to create. You can then customize the chart as you like, including changing the colors, fonts, and background.
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A certain computer can perform a maximum number of operations per second. If this computer is running at 40%
of the maximum and is performing 30 operations per second, what is the maximum number of operations the
computer can perform per second? Round your answer to the nearest whole number.
1. 70 operations per second
2. 12 operations per second
3. 1,200 operations per second
4. 75 operations per second
Answer:
Step-by-step explanation:
Let's represent the maximum number of operations per second as "x".
If the computer is running at 40% of the maximum, it is performing 0.4x operations per second.
We are given that the computer is performing 30 operations per second, so we can set up an equation:
0.4x = 30
Solving for x:
x = 75
Therefore, the maximum number of operations the computer can perform per second is 75.
So, the correct answer is 4. 75 operations per second.
if you are dealt 4 cards from a standard deck of 52 cards, what is the probability that you will get 3 black cards?
The probability of getting 3 black cards out of 4 drawn from a standard deck of 52 cards is approximately 0.253 or 25.3%.
To determine the probability of getting 3 black cards out of 4 cards drawn from a standard deck of 52 cards, we can use the hypergeometric distribution.
There are 26 black cards in the deck, and the total number of ways to choose 4 cards from 52 is given by the binomial coefficient C(52, 4). The number of ways to choose 3 black cards out of 26 is given by the binomial coefficient C(26, 3).
The number of ways to choose the fourth card from the remaining 26 non-black cards is given by the binomial coefficient C(26, 1).
Therefore, the probability of getting 3 black cards out of 4 is:
P(3 black cards) = C(26, 3) * C(26, 1) / C(52, 4)
P(3 black cards) = (2600 * 26) / 270725
P(3 black cards) ≈ 0.253
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Phillip left his house and bicycled down a trail at a rate of 12 kilometers per hour. He planned to ride his bicycle to the end of the trail, which is 28 kilometers long, and then return to his house. Christine started from Phillip’s house 20 minutes later and caught up to Phillip just as he reached the end of the trail. How fast was Christine traveling?
Answer: 14.0kph
Step-by-step explanation:
What is the slope of the line parallel to the function: * y = 50 -0.5x 50 0.5 -0.5 02
The slope of the line parallel to the function: y = 50 - 0.5x include the following: C. -0.5.
What are parallel lines?In Mathematics and Geometry, parallel lines simply refers to two (2) lines that are always the same or equal distance apart and never meet.
Generally speaking, two (2) lines are considered as parallel under the following standard conditions:
Slope, m₁ = Slope, m₂.
From the function, we have:
y = 50 - 0.5x
Slope, m = -0.5
In this context, we can reasonably infer and logically deduce that the slope of the two lines would be equal and the same:
Slope of line 1 = Slope of line 2
-0.5 = -0.5
In conclusion, we can logically deduce that the slope of the given line is equal to -0.5.
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i need this paper finished within 2 hours to stay in honors math. help? (2 attachments for 50 points)
Answers:
Q.1 B. 6.88.
Q2. Sorry Not clearly visible its blurred
Q3. The closest answer choice is C. 4.9
Q4. 2.94
Q5. Set B
Q6. C
Step-by-step explanation:
Q1.
To find the mean absolute deviation, we first need to find the mean of the data set
Data: 32, 43, 38, 28, 51
Mean = (32 + 43 + 38 + 28 + 51) / 5 = 38.4
Next, we need to find the absolute deviations of each number from the mean
|32 - 38.4| = 6.4
|43 - 38.4| = 4.6
|38 - 38.4| = 0.4
|28 - 38.4| = 10.4
|51 - 38.4| = 12.6
To find the mean absolute deviation, we need to take the average of these absolute deviations
Mean Absolute Deviation = (6.4 + 4.6 + 0.4 + 10.4 + 12.6) / 5 = 6.88
Therefore, the answer is B. 6.88.
Q3.
To find the mean absolute deviation, we first need to find the mean of the data set
Data: 12.7, 22, 23.5, 24, 11, 22
Mean = (12.7 + 22 + 23.5 + 24 + 11 + 22) / 6= 18.2
Next, we need to find the absolute deviations of each number from the mean
|12.7 - 18.2| = 5.5
|22 - 18.2| = 3.8
|23.5 - 18.2| = 5.3
|24 - 18.2| = 5.8
|11 - 18.2| = 7.2
|22 - 18.2| = 3.8
To find the mean absolute deviation, we need to take the average of these absolute deviations
Mean Absolute Deviation = (5.5 + 3.8 + 5.3 + 5.8 + 7.2 + 3.8) / 6 = 5.9
Therefore, the closest answer choice is C. 4.9. However, this answer is not correct as the calculated value is 5.9.
Q4.
To find the average distance of these points from the mean of the data, we need to first find the mean of the data.
The mean of the data can be found by adding up all the values and dividing by the total number of values:
Mean = (-8 + 6.2 + 2.5 + 12 - 2 - 1.3 + 15 - 2 + 0 + 7) / 10
= 29.4 / 10
= 2.94
The average distance from the mean is found by taking the absolute value of the difference between each value and the mean, adding them up, and dividing by the total number of values:
Average Distance from Mean = (|(-8) - 2.94| + |6.2 - 2.94| + |2.5 - 2.94| + |12 - 2.94| + |-2 - 2.94| + |-1.3 - 2.94| + |15 - 2.94| + |-2 - 2.94| + |0 - 2.94| + |7 - 2.94|) / 10
= (10.94 + 3.26 + 0.44 + 9.06 + 4.94 + 4.24 + 12.06 + 4.94 + 2.94 + 4.06) / 10
= 5.688
Therefore, the average distance of these points from the mean of the data is 5.688, which is option D.
Q5.
o find out if the mean and median are equal in a set of data, we need to calculate both the mean and median and compare them.
Mean is calculated by adding up all the values and dividing by the total number of values.
Median is the middle value of the data when it is arranged in order.
Let's calculate the mean and median of both data sets:
A. (5, 3, 5, 8, 2, 5)
Mean = (5 + 3 + 5 + 8 + 2 + 5) / 6
= 4.6667
To calculate the median, we first need to arrange the data in order:
2, 3, 5, 5, 5, 8
Since the data set has an even number of values, the median is the average of the middle two values:
Median = (5 + 5) / 2
= 5
Since the mean and median of set A are not equal (4.6667 ≠ 5), set A is not the correct answer.
B. (7, 3, 5, 11, 5, 3)
Mean = (7 + 3 + 5 + 11 + 5 + 3) / 6
= 5.8333
To calculate the median, we first need to arrange the data in order:
3, 3, 5, 5, 7, 11
Since the data set has an even number of values, the median is the average of the middle two values:
Median = (5 + 5) / 2
= 5
Since the mean and median of set B are equal (5.8333 ≈ 5), set B is the correct answer.
Therefore, the set of data in which the mean and median are equal is set B: (7, 3, 5, 11, 5, 3). Answer: B.
Q6.
To answer this question, we need to first find the mean, median, and range of the data:
Data: 10, 23, 52, 18, 5, 60, 35
Mean = (10 + 23 + 52 + 18 + 5 + 60 + 35) / 7
= 28.57
Median = 23
To find the range, we need to subtract the smallest value from the largest value:
Range = 60 - 5
= 55
Now, let's evaluate each statement:
A. The mean is greater than the range.
- 28.57 > 55
- This statement is false.
B. The range is 50.
- The range is 55, not 50.
- This statement is false.
C. The median is less than the mean.
- The median is 23 and the mean is 28.57
- This statement is true.
D. The median is greater than the range.
- 23 > 55
- This statement is false.
Therefore, the statement that is true is C. The median is less than the mean.
How can I solve this? ASAP
Answer:
544 in²
Step-by-step explanation:
Find the area of the rectangle, then the triangle, then add them together to get the total SA.
Rectangle = l x w = 10 x 14 = 140 in²
SA of the 2 rectangular sides = 140 x 2 = 280 in²
Triangle = 1/2bh = 1/2(12)(8) = 48²
SA of the 2 triangular ends = 2 x 48 = 96 in²
Rectangular base = 14 x 12 = 168 in²
Total SA = 280 + 96 + 168 = 544 in²
The ordered pairs (−4, 7) and (2, −2) are points on a graph of a linear equation. Which other points are also on the same line?
Select ALL that apply.
(−2, −6)
(−2, −5)
(4, −6)
(4, −5)
(0, −5)
(0, 1)
We can find the equation of the line passing through the given two points (-4, 7) and (2, -2) using the slope-intercept form of a linear equation:
slope (m) = (change in y) / (change in x) = [tex](-2 - 7) / (2 - (-4)) = -9/6 = -3/2[/tex]
Using point-slope form with the first given point (-4, 7), we get:
[tex]y - 7 = (-3/2)(x - (-4))\\y - 7 = (-3/2)x - 6\\y = (-3/2)x + 1[/tex]
Now we can plug in the x-coordinates of the other points given and check if they satisfy the equation.
[tex](−2, −6):\\y = (-3/2)x + 1\\-6 = (-3/2)(-2) + 1\\-6 = 3 + 1\\-6 ≠ 4 (not on the line)[/tex]
[tex](−2, −5):\\y = (-3/2)x + 1\\-5 = (-3/2)(-2) + 1\\-5 = 3 + 1\\-5 ≠ 4 (not on the line)(4, −6):\\y = (-3/2)x + 1\\-6 = (-3/2)(4) + 1\\-6 = -6 + 1\\-6 ≠ -5 (not on the line)(4, −5):\\y = (-3/2)x + 1\\-5 = (-3/2)(4) + 1\\-5 = -6 + 1\\-5 = -5 (on the line)[/tex]
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the university of montana ski team has eight entrants in a men's downhill ski event. the coach would like the first, second, and third places to go to the team members. in how many ways can the eight team entrants achieve first, second, and third places?
There are 336 ways for the 8 team entrants to achieve the desired outcome of first, second, and third place positions.
The problem involves selecting 3 individuals out of 8 to fill the 1st, 2nd, and 3rd place positions. Since the order in which the individuals are selected matters, we need to use the permutation formula to determine the total number of ways to achieve the desired outcome.
The formula for permutation is:
P(n,r) = n! / (n-r)!
Where n is the total number of individuals, and r is the number of positions to be filled.
In this case, we need to select 3 individuals out of 8 to fill the 1st, 2nd, and 3rd place positions. Using the permutation formula, we get:
P(8,3) = 8! / (8-3)!
= 8! / 5!
= (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (5 x 4 x 3 x 2 x 1)
= 8 x 7 x 6
= 336
In other words, the coach has 336 possible ways to select three team members for the podium, assuming all team members have an equal chance of winning.
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What is the answer to this? Pls help
(9x10^4)+(7x10)
Answer:
(9x10^4)+(7x10) = 90,000 + 70 = 90,070
PLEASE HELP ME SOMEONE its due tomorrow.
The analysis of the data to obtain the best fit line equations that model the data, indicates;
5. a. Quadratic
b. y = -0.1179·x² + 2.1124·x + 4.215
c. Please find the completed chart showing the predicted values and the in the residuals in the following section.
6. a. A linear model may not be appropriate for the data in the residual plot
b. 4
c. 5
4. a. The exponential model of the function is; y = 100·e^(-0.124·t)
b. The weight after 8 weeks is about 37.1 grams
c. The sample will be 4 grams in about 26 weeks
5. a. The equation is; y = 22.703·x + 2.5733
b. The predicted y-value at x = 10 is; y = 229.60
c. The first time is about x ≈ 3.54
What is the best fit line?The best fit line is a line that is drawn through a set of data points in such a way that it minimizes the sum of squared errors of the data.
5. The best fit model can be obtained by plotting a scatter plot of the graph, which indicates that the best fit line resembles the shape of a parabola.
Therefore;
a. The best fit equation is; Quadratic
b. The best fit equation, obtained using technology is; y = -0.1179·x² + 2.1124·x + 4.215
The square of the correlation coefficient is; R² = 0.9584
The chart can be filled with the best fit equation as follows;
[tex]\begin{tabular}{ | c | c | c | c | c | }\cline{1-4}Distance (foot) & Height (foot) & Predicted Value &Residual \\ \cline{1-4}0 & 4 & 4.215 & -0.215 \\\cline{1-4}2 & 8.4 & 8.16588 & 0.23412 \\\cline{1-4}6 & 12.1 & 13.23804 & -1.13804 \\\cline{1-4}9 & 14.2 & 14.56626 & -0.36626\\\cline{1-4}12 & 13.2 & 13.77228 & -0.57228 \\\cline{1-4}13 & 10.5 & 13.03602 & -2.53602 \\\cline{1-4}15 & 9.8 & 10.8561 & -1.0561 \\\cline{1-4}\end{tabular}[/tex]
The predicted value are obtained by plugging in the x-value into the best fit equation and the residuals is the difference between the actual value and the predicted value.
6. a. A residual plot can be used to as assessment with regards to meeting the assumptions of a linear regression model.
A residual plot that is randomly scattered about zero indicates that a linear model is appropriate for the data.
The data points in the residual plot are not expressed as being randomly scattered around zero.
The pattern that exists in the residual plot indicates that the values are positive for x-values that are either low or high, and the middle x-values have a negative residuals. Therefr;
The pattern indicates that a linear regression model may not be appropriate for the datab. The number of positive residuals = 4
c. The number of negative residuals = 5
4. The general form of the exponential model of a function, y = A × e^(-k·t) can be used to find the function for the data as follows;
A = The initial amount = The value at 0 = 100
y = The amount of radioactive material at a given time t
e = Euler's number = 2.71828
The datapoints in the table indicates;
88.3 = 100 × e^(-k × 1)
k = -㏑(0.883) ≈ 0.124
The exponential model is therefore; y = 100 × e^(-0.124·t)
b. The weight of the sample after 8 weeks can be obtained by plugging in t = 8 in the exponential function for the weight of the radioactive substance as follows;
y = 100 × e^(-0.124 × 8) ≈ 37.1
The weight of the sample after 8 weeks is about 37.1 grams
c. When the sample is 4 grams we get;
y = 4
4 = 100 × e^(-0.124 × t)
e^(-0.124 × t) = 4/100 = 1/25
-0.124 × t = ln(1/25) = -ln(25)
t = ln(25)/0.124 ≈ 26
t ≈ 26 weeks
Therefore; The weight will be 4 grams after approximately 26 weeks
5. A linear regression can be performed using MS Excel to obtain the equation that models the data as follows;
y = 22.703·x + 2.5733
The square of the regression coefficient is; R² = 0.9995
a. The most appropriate equation to model the data in the table is; y = 22.703·x + 2.5733
b. The y-value when x = 10 can be predicted by plugging in x = 10 into the model equation for the data as follows;
y = 22.703 * 10 + 2.5733 ≈ 229.60
Therefore;
The predicted y-value when x is 10 is 229.60 (rounded to the nearest tenth)c. The first time the y-value is 83, can be found by setting y = 83 in the equation and solve for x as follows;
83 = 22.703·x + 2.5733
22.703·x = (83 - 2.5733)
x = (83 - 2.5733)/22.703 ≈ 3.54
Therefore, the first time the y-value is 83 is when x is approximately 3.54
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how do you do this? I need helppppp
The constant of proportionality of the graph is k = 3/2.
How to get the constant of proportionality?A general proportional relation between two variables y and x can be written as:
y = k*x
Were k is the constant of proportionality.
To find the value of k, we need to identify a point of the form (x, y) on the given graph, and then replace the values in the equation above, for example, we can use the point (4, 6), replacing that we will get:
6 = k*4
6/4 = k
3/2 = k
That is the constant of proportionality.
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AP Statistics Hypothesis Testing
The average amount of rainfall in the Amazon Rainforest for a year is recorded to be normally distributed with a
mean of 200 cm. Twelve regions in the Amazon Rainforest are randomly sampled. The total yearly rainfalls, in
centimeters, for these regions were reported as follows:
188 232 210 198 202. 193. 219. 202, 252, 156, 184, 222
Do this data provide sufficient evidence that the annual rainfall in the Amazon rainforest is different than 200 cm?
Therefore, based on this collection of data during a significance level of 0.05, there is insufficient proof to draw the conclusion that the average annual precipitation in the Amazonian rain forest is less than 200 cm.
What kind of hypothesis would you use?Hypothesis The amount of pleasure increases with daily solar exposure. The presumed reason in this case and the factor that is independent is sun exposure. The expected impact, or dependent variable, is the degree of happiness.
To determine if the data provide sufficient that the annual rainfall in the Amazon rainforest is different than 200 cm, we can perform a hypothesis test with the following hypotheses:
Null hypothesis: The true mean annual rainfall in the Amazon rainforest is equal to 200 cm.
Alternative hypothesis: The true mean annual rainfall in the Amazon rainforest is different than 200 cm.
We can use a two-sided t-test with a significance level of 0.05 to test this hypothesis.
We must first determine the population mean and standard variation.
x = (188 + 232 + 210 + 198 + 202 + 193 + 219 + 202 + 252 + 156 + 184 + 222)/12 = 202.17 cm
Sample standard deviation, s = 26.770 cm
Next, we can calculate the t-statistic:
t = (x - μ) / (s / sqrt(n)) = (202.17 - 200) / (26.770 / sqrt(12)) = 0.491
Using a t-distribution table with 11 degrees of freedom (n-1), at a significance level of 0.05, we find the critical values to be ±2.201. Since the calculated t-statistic of 0.491 is within the range of -2.201 to 2.201, we fail to reject the null hypothesis.
Therefore, there is not sufficient evidence to conclude that the annual rainfall in the Amazon rainforest is different than 200 cm based on this sample data at a significance level of 0.05.
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Activity 2 Synthesis
1. Precious says you can estimate the area of a circle by calculating 32. What do you think
each part of her expression means?
2. Do you agree with Precious? Use your earlier work to help support your thinking.
In a hospital, the number of nurses is proportional to the number of patients. Different
departments follow different rules for these proportions. The table shows the rules for a
surgical department. The graph shows the rules for a newborn department.
Which department allows more patients per nurse? Explain.
The newborn department allows more patients per nurse than the surgical department.
What is number?Number is a mathematical object used to count, measure, and label. In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers. Numbers can be represented in a variety of ways, including words, symbols, or images. Additionally, numbers are used in many different areas, including science, engineering, finance, economics, and computing.
The newborn department allows more patients per nurse than the surgical department. This is because the newborn department follows a lower nurse-to-patient ratio. The graph for the newborn department shows that for every two nurses, there are three patients, while the table for the surgical department shows that for every one nurse, there are two patients. This means that the newborn department has a ratio of 1:1.5 nurses to patients, while the surgical department has a ratio of 1:2 nurses to patients. This means that the newborn department allows more patients per nurse than the surgical department.
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The newborn department allows more patients per nurse than the surgical department.
What is number?Number is a mathematical object used to count, measure, and label. In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers. Numbers can be represented in a variety of ways, including words, symbols, or images. Additionally, numbers are used in many different areas, including science, engineering, finance, economics, and computing.
The newborn department allows more patients per nurse than the surgical department. This is because the newborn department follows a lower nurse-to-patient ratio. The graph for the newborn department shows that for every two nurses, there are three patients, while the table for the surgical department shows that for every one nurse, there are two patients. This means that the newborn department has a ratio of 1:1.5 nurses to patients, while the surgical department has a ratio of 1:2 nurses to patients. This means that the newborn department allows more patients per nurse than the surgical department.
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complete questions as follows-