Please god someone help me with this, I literally do not understand. if someone coudl just please explain what I am to do, you don't have to do. please help me!
Answers
Answer:
[tex]\begin{array}{|c|c|c|c|}\cline{1-4}\vphantom{\dfrac12}\sf Bank & \sf Basic\;Fee\times 12 & \sf Bill\;Paying\;Fee\times 12 & \sf Checks\;Written-Limit\\\cline{1-4}\vphantom{\dfrac12}\sf A&\$18&\$27&20\\\cline{1-4}\vphantom{\dfrac12}\sf B&\$30&\$27&10\\\cline{1-4}\vphantom{\dfrac12}\sf C&\$18&\$21&10\\\cline{1-4}\vphantom{\dfrac12}\sf D&\$30&\$21&20\\\cline{1-4}\end{array}[/tex]
[tex]\begin{array}{|c|c|c|}\cline{1-3}\vphantom{\dfrac12}\sf Bank & \sf Column\;4\times Cost\;per\;bill\times 12 & \sf Annual\;Total\\\cline{1-3}\vphantom{\dfrac12}\sf A&\$24&\$69\\\cline{1-3}\vphantom{\dfrac12}\sf B&\$18&\$75\\\cline{1-3}\vphantom{\dfrac12}\sf C&\$24&\$63\\\cline{1-3}\vphantom{\dfrac12}\sf D&\$48&\$99\\\cline{1-3}\end{array}[/tex]
Step-by-step explanation:
Jane wants to compare the cost of online banking across 4 different banks. We are told that she writes an average of 40 checks each month.
Given monthly charges for four different banks:
[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5}\vphantom{\dfrac12}\sf Bank & \sf Basic\;Monthly\;Fee& \sf Bill\;Paying\;Monthly\;Fee & \sf Limit& \sf Cost\;per\;bill\;beyond\;limit\\\cline{1-5}\vphantom{\dfrac12}\sf A&\$1.50&\$2.25&20&\$0.10\\\cline{1-5}\vphantom{\dfrac12}\sf B&\$2.50&\$2.25&30&\$0.15\\\cline{1-5}\vphantom{\dfrac12}\sf C&\$1.50&\$1.75&30&\$0.20\\\cline{1-5}\vphantom{\dfrac12}\sf D&\$2.50&\$1.75&20&\$0.20\\\cline{1-5}\end{array}[/tex]
The "limit" is the number of checks Jane is not charged a fee to write per month. For each check Jane writes above this monthly limit, she will be charged a fee (fifth column).
To complete the first table:
The second column is the charge per year for the basic fee. So we have to multiply the given "basic monthly fee" by 12 to calculate the basic fee per year (since there are 12 months in a year).The third column is the charge per year for the bill paying fee. Again, multiply the given "bill paying monthly fee" by 12 to calculate the bill paying fee per year (since there are 12 months in a year).The fourth column is the number of checks Jane writes per month more than the given limit. So as Jane writes an average of 40 checks per month, we have to subtract the given limit from 40.[tex]\begin{array}{|c|c|c|c|}\cline{1-4}\vphantom{\dfrac12}\sf Bank&\sf Basic\;Fee\times12&\sf Bill\;Paying\;Fee\times12&\sf Checks\;Written-Limit\\\cline{1-4}\vphantom{\dfrac12}\sf A&\$1.50\times12=\$18&\$2.25\times12=\$27&40-20=20\\\cline{1-4}\vphantom{\dfrac12}\sf B&\$2.50\times12=\$30&\$2.25\times12=\$27&40-30=10\\\cline{1-4}\vphantom{\dfrac12}\sf C&\$1.50\times12=\$18&\$1.75\times12=\$21&40-30=10\\\cline{1-4}\vphantom{\dfrac12}\sf D&\$2.50\times12=\$30&\$1.75\times12=\$21&40-20=20\\\cline{1-4}\end{array}[/tex]
To complete the second table:
The second column is the charge per year for the number of checks Jane writes over each bank's "free" limit. So multiply the number from the fourth column of the first table (Checks Written - Limit) by the "Cost per bill beyond limit" from the given table of information and then multiply by 12.The third column is the annual total charged by each bank. Sum "Basic Fee x 12" and "Bill Paying Fee x 12" and "Column 4 x Cost Per Bill x 12" for each bank.[tex]\begin{array}{|c|c|c|}\cline{1-3}\vphantom{\dfrac12}\sf Bank & \sf Column\;4\times Cost\;per\;bill\times 12 & \sf Annual\;Total\\\cline{1-3}\vphantom{\dfrac12}\sf A&20\times\$0.10\times12=\$24&\$18+\$27+\$24=\$69\\\cline{1-3}\vphantom{\dfrac12}\sf B&10\times\$0.15\times12=\$18&\$30+\$27+\$18=\$75\\\cline{1-3}\vphantom{\dfrac12}\sf C&10\times\$0.20\times12=\$24&\$18+\$21+\$24=\$63\\\cline{1-3}\vphantom{\dfrac12}\sf D&20\times\$0.20\times12=\$48&\$30+\$21+\$48=\$99\\\cline{1-3}\end{array}[/tex]
Related Questions
MAA MATHEMATICAL ASSOCIATION OF AMERICA
webwork/math160/module1wwsp/4
Module 1 WWsp: Problem 4
Previous Problem Problem List Next Problem
(1 point) Below is an "oracle" function. An oracle function is a function presented interactively. When you type in an x value, and press the --> button and the value
f(x) appears in the right hand window. There are three lines, so you can easily calculate three different values of the function at one time.
Find the largest delta so that f(z)-f(1.382)| < 0.0008 when |x-1.382| < 8.
delta
I
Note: Your answer must be within 0.000001 of the correct answer
Answers
The delta is the difference between the values of x and f(z)-f(1.382). To find the largest delta, incrementally increase x by delta until it is less than 0.0008.
What is oracle function?A pre-defined Oracle function is a function that may be used to conduct a specific operation or computation on data contained in an Oracle database. Oracle functions are frequently used to change data from a query result or to conduct computations such calculating the average, sum, or count of a group of numbers.
The delta is the difference between the two x values. To determine the biggest delta such that f(z)-f(1.382)0.0008 when |x-1.382|8, we must first enter x=1.382 into the oracle function and note the result of f. (1.382). Then we must gradually increase x by delta, inserting the new value into the Oracle function and noting the result. Then we may compute f(x)-f(1.382) to determine if it is less than 0.0008. This method may be repeated, increasing the delta each time, until we obtain the greatest delta where f(x)-f(1.382)0.0008. The greatest delta that meets this requirement is the answer.
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There are three children, three pets, and three favorite colors. the children are: angela, lisa, and susan. the pets are: a cat, a dog, and a fish. the colors are: blue, green, and red.
Answers
6 is the number of ways described when There are 3 children, 3 pets, and 3 favorite colors. We can represent the children, pets, and colors in a list and explained below .
Children:
1. Angela
2. Lisa
3. Susan
Pets:
1.Cat
2. Dog
3. Fish
Colors:
1.Blue
2.Green
3. Red
We can use the combination rule to find the number of ways to assign a child, a pet, and a color to each other. The combination rule states that if we have n items and want to choose k items at a time, the number of ways to do this is given by the formula:
n! / (k! (n-k)!)
Where n! denotes the factorial of n, meaning the product of all positive integers less than or equal to n.
In this case, we have 3 children, 3 pets, and 3 colors, and we want to assign one of each to each other. So we can use the formula to find the number of ways to do this:
3! / (1! (3-1)!) = 3! / (1! 2!) = 3 * 2 * 1 / (1 * 2) = 3
So there are 3 ways to assign a child, a pet, and a color to each other.
We can also use the permutation rule to find the number of ways to assign a child, a pet, and a color to each other. The permutation rule states that if we have n items and want to choose k items at a time and order matters, the number of ways to do this is given by the formula:
n! / (n-k)!
In this case, we have 3 children, 3 pets, and 3 colors, and we want to assign one of each to each other. So we can use the formula to find the number of ways to do this:
3! / (3-3)! = 3! / 0! = 3 * 2 * 1 / 1 = 6
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Prove that (sinθ-cosθ)^2(sinθ+cosθ)^2 = 2
Answers
Step-by-step explanation:
(sinθ + cosθ)^2 + (sinθ − cosθ)^2
= (sin^2 θ + cos^2 θ + 2sinθ cosθ)+(sin^2 θ+cos^2 θ − 2sinθ cosθ)
= (1 + 2sinθ cosθ) + (1 − 2sinθ cosθ)
= 1 + 2sinθ cosθ + 1 − 2sinθ cosθ
= 1 + 1 = 2
Therefore, (sinθ+cosθ)^2 + (sinθ−cosθ)^2 = 2
In a bag of keys, there are 15 silver keys, 6 black keys, 8 copper keys, and 4 painted keys of various cálors. One key is drawn out
at random. What is the probability that the key that is drawn is silver or copper?
A. 7/11
B. 8/33
C. 5/11
D. 23/33
Answers
Answer:
C
Step-by-step explanation:
Answer:
23/33
Step-by-step explanation:
The copper keys and the silver keys in total is 23 and the amount of keys in total is 33.
PLEASE HELP FAST WILL MARK BRAINLYISNT
You are a plumber who needs to replace a broken pipe that is 12.5 feet long. You have 2 pipes, A and B, that are 3.75 meters and 4.25 meters long, respectively. A pipe longer than the broken pipe can be cut to fit. Which pipe can be used to complete the task, and why?
either, because the broken pipe is 2.51 meters long either, because the broken pipe is 2.67 meters long
pipe B, because the broken pipe is 3.81 meters long
pipe B, because the broken pipe is 4.20 meters long
neither, because the broken pipe is 4.80 meters long
Answers
Answer: either, because the broken pipe is 2.51 meters long either, because the broken pipe is 2.67 meters long
Step-by-step explanation:
Y=2x + 9; 6x -3y = 0 / 4x -2y = 3; 2x -4y -3 cual de la siguientes parejas de rectas no son paralelas?
Answers
Yes, 6x -3y = 0 and 2x -4y -3 are parallel. This is because they both have the same slope, -3/2. The slope of a line can be calculated from its equation, by dividing the coefficient of the x term by the coefficient of the y term.
How to solve the problem?Two lines are parallel if they have the same slope. The slope of a line is represented by the letter "m" in the equation y = mx + b.
In this case, Y=2x + 9 has a slope of 2 and 4x -2y = 3 has a slope of -1/2, these slopes are different, which means that these two lines are not parallel.
On the other hand, 6x -3y = 0 and 2x -4y -3 are parallel because they have the same slope, -3/2. The slope of a line is the amount of change in the y coordinate for each unit of change in the x coordinate.
Yes, 6x -3y = 0 and 2x -4y -3 are parallel. This is because they both have the same slope, -3/2. The slope of a line can be calculated from its equation, by dividing the coefficient of the x term by the coefficient of the y term.
In the case of 6x -3y = 0, the slope is -3/6 = -1/2. In the case of 2x -4y -3, the slope is -4/2 = -2. Since both lines have the same slope, they are parallel. This means that they never intersect and have the same direction.
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What is the resultant vector of ? A+B?
Answers
The resultant vector of A+B is C (5,3) with the length of √34.
Resultant vector is the sum of 2 or more vectors. In this case, we give the name of the resultant vector as C.
Please refer to the attached picture below.
Vector C is the resultant vector of A+B and we will use the tail-to-head appraoch.
From the given graph, we know that:
vector A = (2 - 0) = (2)
(4 - 0) (4)
Vector B = (5 - 2) = (3)
(3 - 4) (-1)
Vector C = Vector A + Vector B
Vector C = (2 + 3)
(4 + (-1))
Vector C = (5,3)
The length of Vector C can be calculated using the phytagoras theorem:
Length of vector C = √(5² + 3²)
Length of vector C = √(25 + 9)
Length of vector C = √34
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Three views of a soild are shown. Find the number of the faces, edges, and veritices of the soild.
Answers
Faces 6
Edges 12
Vertices 8
In a group of 30 pupils, 13 play the flute only. 1 plays the piano only. 4 play both instruments. A student is chosen at random. What is the probability the student plays neither instrument?
Answers
A student who is chosen at random has a 2/5 chance of playing neither instrument.
What is probability?Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Given, a group of 30 pupils, 13 play the flute only. 1 plays the piano only. 4 play both instruments
From the general formula of probability:
Probability = desired outcome / total outcomes
Total outcomes = 30
In our case desired outcome = is chosen student plays neither instrument
desired outcome = 30 - 13 -1 -4
desired outcome = 12
thus,
Probability = 12/30
probability = 2/5
Therefore, the probability of a randomly selected student playing neither instrument is 2/5.
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HELP!! i want the answer
Answers
The tangent line to the given circle passing through the point B is given by the image presented at the end of the answer.
What is a tangent line?A tangent line to a circle is a line that only touches the circumference of the circle, not crossing.
If the line crosses the circle, then the line is called a secant line, which crosses the circumference of the circle twice.
Then the tangent line, only touching the circumference of the circle, is given by the image presented at the end of the answer.
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In a bowling class, the students are organized into teams. The number of students in the class is used to calculate how many teams will be formed.
s = the number of students in the class
t = the number of teams to be formed
Which of the variables is independent and which is dependent?
Answers
The attached file, data_red_banjo_pints_sold.xlsx, lists the daily sales of IPA beer, in pints, for the first three years of operations of Red Banjo Brewing Company. Construct a histogram with lower bin limit of O and bin width 50 for the variable IPA beer (pints). Which of the following best describes the sales data? symmetric negatively skewed positively skewed flat A C 1 Day 2 3 4 3 4 8 9 8 6 7 8 9 10 11 12 13 14 15 B IPA (pints) 1 158 2 169 162 4 154 5 154 6 275 7 277 8 154 9 161 10 166 11 159 12 168 13 262 14 283 15 154 16 164 17 165 18 156 19 164 20 258 21 260 22 155 23 155 24 159 25 164 26 165 27 255 28 268 29 152 30 162 CO 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Red Banjo Pints Produced А B C D 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 163 154 267 272 158 162 162 166 138 260 267 160 148 152 164 168 267 267 152 164 150 160 170 248 275 160 162 153 157 79 80 81 82 83 84 85 86 87 85 86 88 87 89 90 91 88 89 90 157 273 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 273 270 162 164 164 150 168 258 263 158 166 165 154 169 250 270 160 164 157 157 168 265 285 150 150 162 155 160 262 260 160
Answers
The data can be analyzed to determine the distribution of the data.
In order to construct a histogram for the daily sales of IPA beer, in pints, for the first three years of operations of Red Banjo Brewing Company, the lower bin limit is set to 0 and the bin width is set to 50. The data can be analyzed to determine the distribution of the data. To calculate the distribution, the data points are counted and the number of occurrences of each data point is divided by the total number of data points.
Using this formula, the data can be analyzed to determine if the data is symmetric, negatively skewed, positively skewed, or flat. The formula used is:
(Number of Occurrences / Total Number of Data Points) * 100
In the case of the Red Banjo Brewing Company data, the data is found to be positively skewed. This means that there are more data points in the higher range than in the lower range. This suggests that the brewery has seen a steady increase in the sale of IPA beer over the past three years.
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Find the values of x and y in each parallelogram
Answers
In parallelogram of 17th problem the x is 12 and y is 14 and in 18th problem value of x is 8 and y is 29.
What is Polygon?polygon, in geometry, any closed curve consisting of a set of line segments (sides) connected such that no two segments cross
A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length
4x-9=3x+3
4x-3x=9+3
x=12
2y-3=2x+1
2y-3=24+1
2y=28
Divide both sides by 2
y=14
The opposite angles of a parallelogram are of equal measure.
7x+8=8x
x=8
and y+87=4y
87=3y
Divide both sides by 3
29=y
Hence, in parallelogram of 17th problem the x is 12 and y is 14 and in 18th problem value of x is 8 and y is 29.
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A population proportion is 0.30. A random sample of size 150 will be taken and the sample proportion will be used to estimate
the population proportion. Use the z-table.
Round your answers to four decimal places.
a. What is the probability that the sample proportion will be within ±0.03 of the population proportion?
b. What is the probability that the sample proportion will be within ±0.08 of the population proportion?
Answers
The advantage of a larger sample size is that the estimate covers more ground and is more reliable.Answer:a) 0.6180 b) 0.7817 c) 0.9484 d) 0.994
What is the population proportion?z = (x - xbar)/σ
Standard deviation = σ = √variance = √[(p)(1-p)/n]
p = population proportion = 0.3
n = sample size
Sample proportion = (x - xbar) = ± 0.04
z = (sample proportion)/(standard deviation)
a) sample proportion = ± 0.04
n = 100
Standard deviation = √[(0.3)(1 - 0.3)/100] = 0.0458
z = ± 0.04/0.0458 = ± 0.873
Using normal probability distribution tables
P(|x- xbar| < 0.04) = P(-0.873 < z < 0.873) = P(z < 0.873) - P(z < -0.873) = 0.809 - 0.191 = 0.6180
b) sample proportion = ± 0.04
n = 200
Standard deviation = √[(0.3)(1 - 0.3)/200] = 0.0324
z = ± 0.04/0.0324 = ± 1.23
Using normal probability distribution tables
P(|x- xbar| < 0.04) = P(-1.23 < z < 1.23) = P(z < 1.23) - P(z < -1.23) = 0.891 - 0.1093 = 0.7817
c) sample proportion = ± 0.04
n = 500
Standard deviation = √[(0.3)(1 - 0.3)/500] = 0.0205
z = ± 0.04/0.0205 = ± 1.95
Using normal probability distribution tables
P(|x- xbar| < 0.04) = P(-1.95 < z < 1.95) = P(z < 1.95) - P(z < -1.95) = 0.974 - 0.0256 = 0.9484
d) sample proportion = ± 0.04
n = 1000
Standard deviation = √[(0.3)(1 - 0.3)/1000] = 0.0145
z = ± 0.04/0.0145 = ± 2.76
Using normal population proportion tables
P(|x- xbar| < 0.04) = P(-2.76 < z < 2.76) = P(z < 2.76) - P(z < -2.76) = 0.997 - 0.0029 = 0.9941
e) the advantage of a larger sample size is that the estimate covers more ground and is more reliable.
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The graph shows the relationship between time and the number of soda bottles a machine can make. Use the points (5,100) and (7,140) to find the number of soda bottles the machine can make each minute.
Answers
Based on the graph which shows the relationship between time and the number of soda bottles a machine can make, this machine can make 20 soda bottles each minute.
How to calculate the number of soda bottles?In Geometry, the rate of change of any straight line simply refers to the slope and it can be calculated by using this mathematical equation (expression);
Rate of change (slope), m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Rate of change (slope), m = (y₂ - y₁)/(x₂ - x₁)
From the information provided in the graph above, we can logically deduce the following data points located on the line:
Points on the x-coordinate = (5, 7).Points on the y-coordinate = (100, 140).Substituting the given data points into the rate of change formula, we have the following;
Rate of change (slope), m = (y₂ - y₁)/(x₂ - x₁)
Rate of change (slope), m = (140 - 100)/(7 - 5)
Rate of change (slope), m = 40/2
Rate of change (slope), m = 20.
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NEED HELP ASAP!!! DUE TOMORROW
Answers
Answer:M<R corresponds to M<T, meaning M<R is 4x+1.
Step-by-step explanation:
Find the domain and range y = 3 * (2) ^ x
Answers
The domain of y = 3 * (2) ^ x is set of all real numbers i.e. (-∞,∞) and the range is (0,∞).
What is domain and range of a function?
The domain is the set or a collection of all the possible values that can go in the function.
The range is collection of all the output values of a function.
Domain
For the given function, the domain is the set of all real numbers because there is no value for 'x' where the function is not defined.
Thus, the domain is (-∞,∞).
Range
For the given function, the values for y range from 0 to infinity.
Therefore, the range is (0,∞).
Hence, the domain of y = 3 * (2) ^ x is (-∞,∞) and the range is (0,∞).
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What does 4 x -1 equal
Answers
Answer -4
Step-by-step explanation:
In our class, there are 11 female and 14 male students. Among 11 female students, 5 get grade A. Among 14 male students, 4 get grade A.
Let A= `pick a student randomly, the grade of this student is A', and M=` pick a student randomly, this student is a male’.
Then, the conditional probability P(A|M) is:
Answers
The conditional probability that the selected student is male and got grade A is 2/7.
Define the term conditional probability?The possibility of an outcome or an event happening contingent on the incidence of a prior event or outcome is known as conditional probability. The likelihood of an event happening given the another has already happened.P(A|M) stands for the probability of such a considering that M has happened.
Then, formula for the conditional probability is-
P(A|M) = P(A∩M) / P(M)
P(A∩M) = Probability that the student is male M and got grade A = 4/25.
P(M) = Probability that the student is male M = 14/25.
Then,
P(A|M) = 4/25 / 14/25
P(A|M) = 4/14 = 2/7
Thus, the conditional probability that the selected student is male and got grade A is 2/7.
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Alewuya invests $1,000 at 13% simple interest for 6 years. How much is in the account at the end of the 6 year period?
Answer: $
Answers
The amount of money with the simple interest is A = $ 1,780
What is Simple Interest?Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.
Simple Interest = ( Principal Amount x Rate x Time Period ) / 100
Given data ,
Let the simple interest be represented as I
Now , the amount with simple interest A = P + I
Now , the principal P = $ 1,000
The interest rate R = 13 %
The number of years T = 6 years
And , Simple Interest I = ( Principal Amount x Rate x Time Period ) / 100
Substituting the values in the equation , we get
Simple Interest I = ( 1000 x 13 x 6 ) / 100
On simplifying the equation , we get
Simple Interest I = $ 780
Now , the amount after 6 years = $ 1,000 + $ 780
The amount after 6 years = $ 1,780
Hence , the simple interest is $ 780
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a rectangle has a perimeter of 38. find the length and the width of the rectangle if the length is 5 less than twice the width. hint: the equation for the perimeter of a rectangle is:
Answers
The length and width of the given rectangle are 11 units and 8 units.
Let the length and breadth of rectangle be l and b.
The perimeter of a rectangle is given by the formula:
P=2( l + b )
It is given that Perimeter of the rectangle is 38.
2( l + b ) = 38
( l + b ) = 19
l = 19 - b
Also, length is 5 less than twice the width.
l = 2b - 5
⇒19 - b = 2b - 5
⇒3b = 24
⇒b = 8
Now, The length can be calculated as:
⇒l = 19 - b
⇒l = 19 - 8
⇒l = 11
Therefore, The length and Width of the rectangle are 11 and 8 respectively
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A rectangular garden has a walkway around it. The area of the garden is 2(5.5x +3.5). The combined area of the garden and the walkway is 3.5(8x + 6). Find the area of the walkway around the garden as the sum of two terms.
Answers
The area of the walkway around the garden is 17x+14.
What is area?Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.
Given that, the area of the garden is 2(5.5x +3.5). The combined area of the garden and the walkway is 3.5(8x + 6).
Area of a walkway = The combined area of the garden and the walkway - The area of the garden
= 3.5(8x+6)-2(5.5x +3.5)
= 28x+21-11x-7
= 17x+14
Therefore, the area of the walkway around the garden is 17x+14.
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shawn knows that his student loan interest is calculated at a rate of 0.34% per month what is his apr andapy
Answers
The APR (Annual Percentage Rate) is 4.08% while the APY (Annual Percentage Yield) is 4.16%.
What is the difference between APY and APR?The annual percentage yield (APY) is the normal annual percentage rate (APR) based on a compounding period of one year.
The annual percentage rate (APR) represents the cost of borrowing expressed as a percentage.
Thus, while APY considers compound interest, APR does not.
MPR = 0.34%
APR = 4.08% (0.34 x 12)
The formula for computing the APR is as follows:
APY = (1 + APR/N)^N - 1
Where APR is the normal interest rate, N is the number of compounding period in a year.
= (1 + 0.0408/12)^12 - 1
= (1 + 0.0034)^12 - 1
= (1.0034)^12 = 1
= 1.0416 - 1
= 0.0416
= 4.16%
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3. Consider a large slice of air over a city to be a box 125 km x 125 km (L x W) that reaches up to an altitude of 1.5 km. Clean air is blowing into the box along one of its sides with a speed of 4 m/s. Suppose an air pollutant with a reaction rate of k = 0.23/hr is emitted into the box at a total mass loading rate of 10 kg/s. a. Find the steady state concentration if the air in the box is assumed to be perfectly mixed. b. If the wind speed suddenly drops to 1 m/s, estimate the concentration of this pollutant 3-hr later.
Answers
a. Steady state concentration = 10/0.23 = 43.48 kg/m^3
b. Concentration 3 hrs later = 10/0.23 * e^(-3*0.23/1) = 34.99 kg/m^3
a. The steady state concentration of the air pollutant can be found by the equation C = M/k, where C is the concentration, M is the mass loading rate, and k is the reaction rate. In this case, C = 10 kg/s/0.23/hr = 43.48 kg/m^3. b. To calculate the concentration of the pollutant 3 hours later, we can use the equation C = M/k * e^(-kt), where t is the time in hours. In this case, C = 10/0.23 * e^(-3*0.23/1) = 34.99 kg/m^3. This equation takes into account the decrease in wind speed and the decrease in reaction rate due to the decrease in concentration.
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Consider the linear system
x+y-y z=2
x+2y+ z=3
x+y+(k^2-5)z= k
where k is an arbitrary constant. For which value(s) of k does this system have a unique solution? For which value(s) of k does the system have infinitely many solutions? For which value(s) of k is the system inconsistent?
Answers
The system is inconsistent for k=0.
The system has a unique solution when k=1 and k=-3. To see this, we plug in these values of k into the system and solve the resulting three equations in three unknowns. For k=1, we have x=2, y=1, and z=0. For k=-3, we have x=3, y=2, and z=0.
The system has infinitely many solutions when k=5. In this case, we have x+y-5z=2, x+2y+z=3, and x+y+25z=5, which yields the solution x=2, y=1, and z=0/5. Since any non-zero value of z will also satisfy the system, the system has infinitely many solutions.
The system is inconsistent when k=0. In this case, we have x+y=2, x+2y+z=3, and x+y-z=0, which has no solution. Therefore, the system is inconsistent for k=0.
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You buy a milkshake from a shoppe that only has chocolate, vanilla, and strawberry flavors. Find the probability that your milkshake consists of more than 3
flavors.
Answers
Step-by-step explanation:
soln on
n(s)=6
n(p)=3
therefore
probability =6/3
Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wherever appropriate. (Round your answers to four decimal places.)(a) P(0≤Z≤2.54)(b) P(0≤Z≤2)(c) P(−2.40≤Z≤0)(d) P(−2.40≤Z≤2.40)(e) P(Z≤1.36)(f) P(−1.25≤Z)(g) P(−1.40≤Z≤2.00)(h) P(1.36≤Z≤2.50)(i) P(1.40≤Z)(j) P(|Z|≤2.50)
Answers
(a) P(0≤Z≤2.54) represents the area under the standard normal curve between 0 and 2.54 on the x-axis. This can be found by using a standard normal table or calculator to find the area between 0 and 2.54, which is approximately 0.4966.
(b) P(0≤Z≤2) represents the area under the standard normal curve between 0 and 2 on the x-axis. This can be found by using a standard normal table or calculator to find the area between 0 and 2, which is approximately 0.4772.
(c) P(−2.40≤Z≤0) represents the area under the standard normal curve between −2.40 and 0 on the x-axis. This can be found by using a standard normal table or calculator to find the area between −2.40 and 0, which is approximately 0.3821.
(d) P(−2.40≤Z≤2.40) represents the area under the standard normal curve between −2.40 and 2.40 on the x-axis. This can be found by using a standard normal table or calculator to find the area between −2.40 and 2.40, which is approximately 0.7621.
(e) P(Z≤1.36) represents the area under the standard normal curve to the left of 1.36 on the x-axis. This can be found by using a standard normal table or calculator to find the area to the left of 1.36, which is approximately 0.9155.
(f) P(−1.25≤Z) represents the area under the standard normal curve to the right of −1.25 on the x-axis. This can be found by using a standard normal table or calculator to find the area to the right of −1.25, which is approximately 0.1151.
(g) P(−1.40≤Z≤2.00) represents the area under the standard normal curve between −1.40 and 2.00 on the x-axis. This can be found by using a standard normal table or calculator to find the area between −1.40 and 2.00, which is approximately 0.7170.
(h) P(1.36≤Z≤2.50) represents the area under the standard normal curve between 1.36 and 2.50 on the x-axis. This can be found by using a standard normal table or calculator to find the area between 1.36 and 2.50, which is approximately 0.0951.
(i) P(1.40≤Z) represents the area under the standard normal curve to the right of 1.40 on the x-axis. This can be found by using a standard normal table or calculator to find the area to the right of 1.40, which is approximately 0.0821.
(j) P(|Z|≤2.50) represents the area under the standard normal curve between −2.50 and 2.50 on the x-axis. This can be found by using a standard normal table or calculator to find the area between −2.50 and 2.50, which is approximately 0.5199.
In all cases, a standard normal table or calculator is used to find the area under the standard normal curve. The area represents the probability of the given event.
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Factor the trinomial by grouping. -
8x²2² +14x+3.
a. Find two numbers whose product is 8.3=24 and whose sum is 14.
b. Write 14x using the factors from part (a).
c. Factor by grouping.
Answers
a. The two numbers whose product is 24 and whose sum is 14 are 6 and 4
b. 14x = 6x + 8x
c. 8x²2² + 6x + 8x + 3
=8x²2² + (6x + 8x) + 3
=8x²2² + 14x + 3
The trinomial 8x²2² + 14x + 3 can be factored by grouping as (8x²2² + 14x) + 3
The area of a triangle can be calculated using various formulas. For example, Heron’s formula is used to calculate the triangle’s area, when we know the length of all three sides. Trigonometric functions are also used to find the area of a triangle when we know two sides and the angle formed between them. However, the basic formula that is used to find the area of a triangle is:
Answers
The basic formula that is used to find out the area of a triangle is:
Area = (1/2) * base * height.
where "base" is one of the sides of the triangle, and "height" is the perpendicular distance from the vertex opposite the base to the line formed by the base. This formula is based on the fact that the area of a triangle is equal to half of the product of its base and its height. The height is also known as the altitude, and it is the distance from the vertex opposite the base to the line formed by the base. It is important to note that the height must be perpendicular to the base. This formula is valid for any type of triangle, whether it is right-angled or not, and it works well when the base and the height are known. This formula can be used in any triangle, and can be applied to any side as base, not only the bottom side. Another important formula is Heron's formula which is used to find the area of a triangle when the lengths of all three sides are known. Heron's formula is given by:
Area = √(s(s-a)(s-b)(s-c))
where s is said as semi-perimeter of the triangle, and a, b and c are the lengths of the three sides of a given triangle.
Finally, trigonometric functions like sine, cosine, and tangent can also be used to find the area of a triangle when we know two sides and the angle formed between them. The formula used is:
Area = (1/2) * a * b * sin(C)
where let us assume a and b are the lengths of two sides of the given triangle and C is the angle which is between them.
In conclusion, there are different formulas for calculating the area of a triangle, the most common one is the base times height formula, but depending on the information you have, you can also use Heron's formula or trigonometric functions.
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decide whether enough information is given to prove that the triangles are congruent. if so, state the theorem you can use. $\triangle abc,\ \triangle dbc$
Answers
11. The ΔACD is not equal and congruent to ΔBCD.
12. The ΔXYZ is equal and congruent to ΔPQZ.
13. The ΔMNL is not equal and congruent to ΔRSL.
What is congruency?
Congruent refers to something that is "absolutely equal" in terms of size and shape. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, and stack them on top of one another.
It is known that -
If two triangles are congruent, when they meet one of the following criteria -
a) All three pairs of corresponding sides should be equal.
b) Two pairs of corresponding sides and the corresponding angles between them should be equal.
c) Two pairs of corresponding angles and the corresponding sides between them should be equal.
11. In the first diagram, it is given that line segments -
AD = BD
CD = CD (common in both the triangles)
It is given that angles -
∠A ≅ ∠B
This proves that AD ≅ BD and CD = CD.
If ΔACD is congruent with ΔBCD then ∠ADC ≅ ∠BDC.
But not enough information is given about ∠ADC and ∠BDC.
Therefore, ΔACD is not congruent with ΔBCD.
12. In the second diagram, it is given that -
Z is the midpoint of line segment XQ and YP.
This means that line segments -
XZ = ZQ
YZ = ZP
It is also given that ∠XZY = ∠PZQ as they form a pair of vertically opposite angles which are equal.
So, the criteria two pairs of corresponding sides and the corresponding angles between them should be equal is fulfilled.
Therefore, ΔXYZ is congruent with ΔPQZ.
13. In the third diagram, it is given that line segments-
MN ≅ LR
LN ≅ LS
It is given that angles -
∠LMN ≅ ∠LRS
If the line segments MN ≅ LR and LN ≅ LS, then ∠MNL ≅ ∠NLS
But not enough information is given about ∠MNL and ∠NLS being equal.
Therefore, ΔMNL is not congruent with ΔRSL.
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