Answer:
35/8
Step-by-step explanation:
A mixed fraction in the form [tex]a \dfrac{b}{c}[/tex] can be converted to an improper fraction using the following calculation:
[tex]a \dfrac{b}{c} = \dfrac{(a \times b) + b}{c}[/tex]
Here we have the improper fraction [tex]4 \dfrac{3}{8}[/tex]
Using the technique described
[tex]4 \dfrac{3}{8} = \dfrac{4 \times 8 + 3}{8} = \dfrac{32+ 3}{8} = \dfrac{35}{8}[/tex]
Ans: 35/8
What is the missing value in the equation shown below?
4/10+ ?/100= 7/10
A 1
B 3
C 10
D 30
Answer: D 30
Step-by-step explanation:
4/10 + 30/100
2/5 + 3/10
7/10
NB: LEFT-HAND SIDE IS EQUAL TO THE RIGHT-HAND SIDE
A triangle has an area of 144 square feet. The height is 24 feet. What is the length of the base (in feet)?
Select all the expressions that are equivalent to (12 + x)10.5.
It’s multiple choice and these are the answers
10.5(12x)
(10.5 + 12 + x)
10.5(12 + x)
126x
126 + 10.5x
22.5 + x
AA contestant on a game show has a 1 in 6 chance of winning for each try at a certain game. Which probability models can be used to simulate the contestant’s chances of winning?
Select ALL of the models that can be used to simulate this event.
A) a fair six-sided number cube
B) a fair coin
C) a spinner with 7 equal sections
D) a spinner with 6 equal sections
E) a bag of 12 black chips and 60 red chips
Answer:
Model D) a spinner with 6 equal sections can be used to simulate the contestant's chances of winning.
Step-by-step explanation:
A spinner with 6 equal sections represents the possible outcomes of the game show, where each section represents a possible win or loss. Since the contestant has a 1 in 6 chance of winning, the spinner would have one section representing a win and five sections representing a loss. Each spin of the spinner would represent one try at the game show, and the probability of winning can be determined by calculating the theoretical probability of landing on the win section.
Use the product of powers property to simplify the numeric expression. 2^2/5/2^1/10
Answer:
[tex] 2^\frac{3}{10} [/tex]
Step-by-step explanation:
[tex] \dfrac{2^\frac{2}{5}}{2^\frac{1}{10}} = [/tex]
[tex]= 2^{\frac{2}{5} - \frac{1}{10}}[/tex]
[tex]= 2^{\frac{4}{10} - \frac{1}{10}}[/tex]
[tex] = 2^\frac{3}{10} [/tex]
Solve each proportion round to the nearest tenth
Answer:
[tex]v = \frac{7}{2}[/tex]
Step-by-step explanation:
1. (Non-Isomorphic Trees) (a) Think of a by-hand method to give a list of all non-isomorphic trees on exactly (b) Use your results from (a) to give a list of all non-isomorphic trees on exactly six Be sure to explain in detail the method you came up with to acquire your five vertices. Display your results. vertices. Show you're results. lists in (a) and (b).
Method to list all non-isomorphic trees on n vertices is to add edges to a single vertex tree. Using A, B, C, D, E, we list 5 non-isomorphic trees on 6 vertices.
A by-hand method to give a list of all non-isomorphic trees on exactly n vertices is to start with a tree on n vertices and then generate all possible trees by adding edges between vertices that are not already connected.
For example, to find all non-isomorphic trees on 4 vertices, we can start with a single vertex and then add edges to form a tree with 2 vertices, then add edges to form a tree with 3 vertices, and finally add edges to form a tree with 4 vertices. We can then check each tree for isomorphism by comparing their adjacency matrices.
Using the method from (a), we can find all non-isomorphic trees on exactly six vertices by starting with a single vertex and adding edges until we have a tree on six vertices.
To ensure that we generate all possible trees, we can use the following five vertices: A, B, C, D, E. We can then generate all trees by adding edges between vertices that are not already connected, making sure to avoid creating cycles. After generating all trees, we can check for isomorphism by comparing their adjacency matrices.
The resulting list of non-isomorphic trees on six vertices, in alphabetical order, is shown. The tree 1 and tree 2 are the same. Also, trees 3, 4, and 5 are not isomorphic to each other or to trees 1 and 2.
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Lori is moving and must rent a truck. There is an initial charge of $60 for the rental plus an additional fee per mile driven. Would a linear, quadratic or exponential function be the best type of equation to model this function? Exponential Quadratic Linear
Answer:
A linear function would be the best type of equation to model this situation. The total cost of renting the truck increases linearly with the number of miles driven. The initial charge of $60 can be considered as the y-intercept of the linear function, and the additional fee per mile driven can be considered as the slope of the line. Therefore, the equation that models this situation can be written in the form y = mx + b, where y is the total cost of renting the truck, x is the number of miles driven, m is the additional fee per mile driven (the slope of the line), and b is the initial charge of $60 (the y-intercept).
Answer:
A linear function would be the best type of equation to model this function.
Step-by-step explanation:
The total cost of renting the truck is composed of two parts:
Initial charge of $60.Additional fee per mile driven.The initial charge of $60 is the fixed charge, and the additional fee is the variable charge that is proportional to the number of miles driven.
Let "x" be the number of miles driven and "y" be the total cost of the rental (in dollars), then the linear equation is:
y = mx + 60
where "m" is the additional fee (in dollars) per mile driven.
Therefore, a linear function, in the form y = mx + b, where m represents the slope or rate of change, and b represents the initial fixed charge, is the most appropriate function to model this situation.
1.
What is the average rate of change between
the points (3,9) and (5, 15)?
Therefore, the average rate of change between the points (3,9) and (5,15) is 3.
What is coordinates?Coordinates are a set of values that locate the position of a point in space. In mathematics, coordinates are used to represent the position of points on a plane or in space, using a set of numerical values that correspond to the distance along each axis from an origin point. In two-dimensional Cartesian coordinate systems, for example, a point is represented by two numbers (x, y) that indicate its position relative to the x and y axes. In three-dimensional Cartesian coordinate systems, a point is represented by three numbers (x, y, z) that indicate its position relative to the x, y, and z axes.
Here,
The average rate of change between the points (3,9) and (5,15) is the slope of the line passing through those two points. We can use the slope formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) = (3,9) and (x2, y2) = (5,15).
slope = (15 - 9) / (5 - 3)
= 6 / 2
= 3
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Find x, if √x +2y^2 = 15 and √4x - 4y^2=6
Answer:
x = 52.2
Step-by-step explanation:
Add 4x - 4y^2 = 36 and x + 2y^2 = 225
x + 2y^2 + 4x - 4y^2 = 225 + 36
5x = 261
x = 261/5=52.2
if cot0=3/4 and the terminal point determined by 0 is in quadrant 3, then
If cotθ = 3/4 then cosθ = -3/5 is the right option according to the rules of trigonometry.
What is Trigonometry?Trigonometry is a branch of mathematics that deals with the study of relationships between the sides and angles of triangles. It is primarily concerned with the study of the six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent, and their applications in various fields such as engineering, physics, and navigation.
What are angles of triangle?A triangle is a three-sided polygon, and its angles are the angles formed by the intersection of its sides. The sum of the angles in a triangle is always 180 degrees.
First, we know that cot(0) = adjacent / opposite = 3/4.
In quadrant 3, the adjacent side is negative and the opposite side is positive, so we can draw a right triangle in quadrant 3 with adjacent side -3 and opposite side 4.
The hypotenuse can be found using the Pythagorean theorem.
h² = adjacent²+ opposite²
h² = (-3)^2 + 4^2
h²= 9 + 16
h² = 25
h = 5
So we have a right triangle in quadrant 3 with adjacent side -3, opposite side 4, and hypotenuse 5.
Using the definitions of the trigonometric functions, we can find the values of the other functions:
sin(0) = opposite / hypotenuse = 4/5
cos(0) = adjacent / hypotenuse = -3/5
tan(0) = opposite / adjacent = -4/3
csc(0) = hypotenuse / opposite = 5/4
sec(0) = hypotenuse / adjacent = -5/3
cot(0) = adjacent / opposite = 3/4 (given)
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michael scott picks up the donut and coffee order for hos office. yesterday he bought 6 donuts and 8 cups of coffee for $21. today he bought 10 donuts and 5 cups of coffee for $16.25. what is the cost of each item?
The cost of each item would be = $1.5 each of cup of coffee and donuts.
How to calculate the cost of each item bought by Michael?For yesterday, the number of donut he ordered = 6
The number of cup of coffee he ordered = 8cup
Total cost = $21
The total number of items he ordered = 6+8 = 14
The cost for donuts alone,
= 6/14× 21/1
= 126/14
= $9
The cost of each donut = 9/6 = $1.5
The cost of cup of coffee ;
= 8/14× 21/1
= 168/14
= 12
for each cup of coffee;
= 12/8
=$1.5
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In the year 1985, a house was valued at $108,000. By the year 2005, the value had appreciated to $148,000. What was the annual growth rate percentage between 1985 and 2005? Assume that the value continued
to grow by the same percentage. What was the value of the house in the year 2010?
Answer:
To find the annual growth rate percentage, we can use the formula:
annual growth rate = [(final value / initial value)^(1/number of years)] - 1
where "final value" is the value in the ending year, "initial value" is the value in the starting year, and "number of years" is the total number of years between the starting and ending years.
Using the given values, we have:
annual growth rate = [(148,000 / 108,000)^(1/20)] - 1
= 0.0226 or 2.26%
So the house appreciated at an annual growth rate of 2.26%.
To find the value of the house in 2010, we can use the same growth rate to project the value from 2005 to 2010:
value in 2010 = 148,000 * (1 + 0.0226)^5
= $175,465.11 (rounded to the nearest cent)
Therefore, the value of the house in the year 2010 was $175,465.11.
Joann had a vegetable stand where she sold tomatoes. She sold 15 tomatoes the first day. The second day she sold half of what was left. On the third day she sold 12 and sold half of what was left on the fourth day. On the fifth day there were 4 tomatoes left to be sold. How many tomatoes did she have to begin with?
On the fifth day there were 4 tοmatοes left tο be sοld. Jοann had 71 tοmatοes tο begin with.
What is prοbability?Prοbability is a measure οf the likelihοοd οr chance οf an event οccurring. It is a number between 0 and 1, where 0 indicates that the event is impοssible, and 1 indicates that the event is certain tο οccur.
Let's wοrk backwards frοm the last day and figure οut hοw many tοmatοes Jοann had οn the fοurth day.
On the fifth day, there were 4 tοmatοes left tο be sοld, which means she sοld half οf what was left οn the fοurth day. Sο she must have started with 8 tοmatοes οn the fοurth day (since half οf 8 is 4).
On the fοurth day, she sοld half οf what was left, which means she had 16 tοmatοes befοre she sοld any.
On the third day, she sοld 12 tοmatοes, which means she had 28 tοmatοes befοre she sοld any.
On the secοnd day, she sοld half οf what was left, which means she had 56 tοmatοes befοre she sοld any.
Finally, οn the first day, she sοld 15 tοmatοes.
Therefοre, Jοann had 71 tοmatοes tο begin with.
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jerome haw 1,040 songs downloaded on his spotify account and 30% of the songs are country songs. How many of the songs are not country
Using your favorite statistics software package, you generate a scatter plot which displays a linear form. You find a regression equation and the standard deviation for both variables. The standard deviation for x is 1.67, and the standard deviation for y is 3.76. The regression equation is reported as
y = 3.3 + 1.13x
What fraction of the variation in y can be explained by the variation in the values of x? (Enter your answer as a decimal between 0 and 1.)
A fraction of the variation in y that can be explained by the variation in the values of x is equal to 0.25189186354.
What is a regression equation?In Mathematics, the standard form of the equation of a regression line is represented or modeled by the following mathematical expression;
y = bx + c
Where:
b represent the gradient, slope, or rate of change.x and y represent the data points.c represents the y-intercept, vertical intercept, or initial value.How to determine the fraction of the variation?In Mathematics and Statistics, the value of slope can be calculated by using the following mathematical expression;
[tex]b=r(\frac{S_y}{S_x})[/tex]
where:
r is correlation coefficient.Sy represent the sample standard deviation of the y-values.Sx represent the sample standard deviation of the x-values.By rearranging, we have:
[tex]r=b(\frac{S_x}{S_y})[/tex]
r = 1.13(1.67/3.76)
r = 0.50188829787
By taking the square of both sides, we have:
r² = 0.25189186354.
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Workers are preparing an athletic field by mixing soil and sand
in the correct ratio. The table shows the volume of sand to mix
with different volumes of soil. Which statement is correct?
A For 1,425 m³ of soil, the workers should use 375 m³ of sand.
B The ratio of the volume of soil to the volume of sand is 1:4.
C A graph of the relationship includes the point (900, 225).
D The equation y = 4x models the relationship.
Option B: The ratio of the volume of soil to the volume of sand is 1:4.
Looking at the table, we can see that for every 100 m³ increase in soil, the sand volume increases by 25 m³. This gives us a ratio of 4:1, which means that the volume of sand is one-fourth of the volume of soil. Therefore, option B is correct.
Option D: The equation y = 4x models the relationship.
We can see that the volume of sand is always one-fourth of the volume of soil. Therefore, we can write y = (1/4)x or y = 0.25x. This equation is the same as y = 4x. Therefore, option D is also correct.
So, the correct statements are B and D.
What is a graph?In mathematics, a graph is a visual representation of data or a mathematical function. It consists of a set of points or vertices connected by lines or curves called edges or arcs, which represent the relationships between the points. Graphs can be used to show trends, patterns, and relationships in data, and they are commonly used in fields such as statistics, economics, and computer science. Some common types of graphs include line graphs, bar graphs, pie charts, scatterplots, and network graphs.
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The table mentioned in the question has been attached below.
HELP ME ASAP PLEASE!!!!!!!!!
Answer:
See step by step.
Step-by-step explanation:
lets define the events:
A: cuban festival C: tropical Garden
B: street art show D: african festival
a) theoretically the probability is
[tex]P(A)=P(B)=P(C)=P(D)= \frac{1}{4} = 0.25 \\[/tex]
This is 25% (for each one, equally)
b) The experimental probability is given by:
[tex]P(A)= \frac{32}{150} =0.2133[/tex]
[tex]P(B)= \frac{38}{150} =0.2533[/tex]
[tex]P(C)= \frac{35}{150} =0.2333[/tex]
[tex]P(D)= \frac{45}{150} =0.3000[/tex]
c) The theoretically probabilities are all equally, the experimental probabilities are close to 25% each one, but differ lightly each one, since is an experiment and the result is random.
I will mark you brainiest!
Given parallelogram STUV, what is the length of TV?
TW = y2
WV = 2y − 1
A) 2
B) 8
C) 4
The required value of TV is 2 units.
What is parallelogram?
A parallelogram is a straightforward quadrilateral with two sets of parallel edges in Euclidean geometry. A parallelogram's confronting or opposing sides are of equal length, and its opposing angles are of equal size.
According to question:
We have given that;
TW = y²
WV = 2y − 1
We know that in parallelogram
TW = WV
y² = 2y − 1
y² - 2y + 1 = 0
y² - y - y + 1 =0
y(y - 1)-1(y - 1) = 0
(y - 1)(y - 1) = 0
(y - 1)² = 0
y - 1 = 0
y = 1
So;
TV = TW + WV
TV = y² + 2y − 1
TV = 1² + 2(1) - 1
TV = 1 + 2 - 1
TV = 2 units
Thus, required value of TV is 2 units.
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Zinnia wrote the following proof to show that the diagonals of rectangle ABCD are congruent:
Zinnia's proof:
Statement 1: Rectangle ABCD is given
Statement 2: segment AD ≅ segment BC because opposite sides of a rectangle are congruent
Statement 3: segment DC ≅ segment DC by the reflexive property of congruence
Statement 4: Angles ADC and BCD are both right angles by definition of a rectangle
Statement 5: Angles ADC and BCD are congruent because all right angles are congruent
Statement 6:
Statement 7: segment AC ≅ segment BD by CPCTC
Which statement below completes Zinnia's proof? (1 point)
Triangles ADC and BCD are congruent (by ASA postulate)
Triangles ADC and BCD are congruent (by SAS postulate)
Triangles ADC and CBA are congruent (by ASA postulate)
Triangles ADC and CBA are congruent (by SAS postulate)
ADC & BCD are congruent triangles (by SAS postulate). Since triangle ADC & BCD are congruent according to the SAS postulate, we may utilize CPCTC to determine that section AC is equal to segment BD.
All are triangles 3/4 of a five?In arithmetic progression, the triangles 3: 4: 5 are the only ones with edges. Pythagorean triple-based triangles are Herodian, which means they have integer areas and sides.
Are the numbers 3 4 5 a right triangle?The easiest approach I've found to know for sure if an aspect is 90 degrees is to use the 3:4:5 triangle. According to this rule, a triangle is said to be a right triangle if one of its sides is 3 and the other is 4.
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Chaz is a college student. He has a checking account balance of -$52.00. His roommate Will's
checking account balance is -$59.25. Chaz thinks that Will owes more to the bank than Chaz
does. Is Chaz correct? Explain your answer.
Answer: No, Chaz is not correct. Although their balances are both negative, we cannot compare them simply based on their numeric values. The magnitude of the balance does not indicate who owes more to the bank, as it depends on various factors such as account activity, fees, and interest rates. We would need to know more information about their accounts, such as the interest rates and any fees, in order to determine who owes more to the bank.
Excluding the bank fees Chaz would technically be correct.
No, Chaz is not correct.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
No, Chaz is not correct.
Although both Chaz and Will have negative checking account balances, we cannot determine who owes more to the bank based solely on the balance amount.
The balance amount only indicates how much money they owe to the bank, but it does not give any information about the amount they initially deposited or any other financial transactions they may have made.
To determine who owes more to the bank, we would need to know the initial deposit amount, the transaction history, and any fees or interest charges that have been applied to the accounts.
Without this additional information, we cannot accurately compare the two balances or determine who owes more to the bank.
Thus,
No, Chaz is not correct.
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What is the solution of
O x≤-3 or 2
Ox<-3 or 2
O-3≤x≤2
or x > 7
O-3 7
x²+x-6
<0?
X-7 50₂
Answer:
[-3, 7].
Step-by-step explanation:
do i need to explain all that?
Answer:
The inequality can be rewritten as x-7 ≤ 50, which we can solve by adding 7 to both sides to get x ≤ 57.
Step-by-step explanation:
It seems like there are multiple questions combined in this one prompt. I will break them down and provide solutions for each one.
Solution for O x≤-3 or 2 Ox<-3 or 2 O-3≤x≤2 or x > 7:
To find the solution for this inequality, we need to solve each part separately and then combine the solutions using the union (OR) operation.
a) x ≤ -3: This part is already solved for x. The solution is x ≤ -3.
b) 2x < -3: We divide both sides by 2 to isolate x and get x < -3/2.
c) 2 ≤ x ≤ -3: This is not possible as there is no number that is both greater than or equal to 2 and less than or equal to -3.
d) x > 7: This part is already solved for x. The solution is x > 7.
The solution to the entire inequality is the union of these solutions: x ≤ -3 OR x < -3/2 OR x > 7.
Solution for x²+x-6 < 0
To solve this quadratic inequality, we can factor it as (x-2)(x+3) < 0 and use the sign chart method.
We create a sign chart for the expression (x-2)(x+3) and test the sign of the expression in each interval
-3 2
---|-------|---
- +
(x-2) - 0 + +
(x+3) - - - 0 +
-------------
- + - 0 +
The sign chart tells us that the expression is negative when x is between -3 and 2. Therefore, the solution to the inequality is -3 < x < 2.
Solution for x-7 ≤ 50₂
It seems like the expression "50₂" is intended to represent the number 50 in base 2 (binary). To convert this number to base 10 (decimal), we can write 50₂ as
50₂ = 12^5 + 12^4 + 02^3 + 02^2 + 12^1 + 02^0 = 32 + 16 + 2 = 50
Therefore, the inequality can be rewritten as x-7 ≤ 50, which we can solve by adding 7 to both sides to get x ≤ 57.
Question 12 (2 points)
Among the seniors at a small high school of 150 total students, 80 take Math, 41
take Spanish, and 54 take Physics. 10 seniors take Math and Spanish. 19 take Math
and Physics. 12 take Physics and Spanish. 7 take all three.
How many seniors were taking none of these courses?
Note: Consider making a Venn Diagram to solve this problem.
0
5
9
22
150 - 141 = 9 seniors are not enrolled in any classes.
What is statistics, and how can it be used?The area of mathematics known as statistics is used to gather, analyse, and interpret data. To predict the future, determine the likelihood that a specific event will occur, or learn more about a survey, statistics can be employed.
The Venn diagram reveals the amount of seniors enrolling in at least one of the courses as follows:
80 + 41 + 54 - 10 - 19 - 12 + 7
= 141
Therefore, 150 - 141 = 9 seniors are not enrolled in any classes.
= 9
So, there are 9 seniors taking none of the courses. Answer: 9.
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5) A research study gives a 95% confidence interval for the proportion of subjects helped by a new anti- inflammatory drug is (0.56, 0.65). (a) Interpret this interval in the context of the problem. dolo hoone (b) What is the TRUE meaning of "95%" confidence interval as stated in the problem?
(a) This 95% confidence interval indicates that there is a 95% chance that between 56% and 65% of subjects will be helped by the new anti-inflammatory drug.
(b) There is a 95% confidence level that the percentage of participants who benefit from a new anti-inflammatory medication falls between (0.56, 0.65).
(a) According to this 95% confidence interval, there is a 95% likelihood that the new anti-inflammatory medication will be beneficial to between 56% and 65% of participants.
(b) There is a 95% confidence interval for the percentage of subjects who were benefitted by a new anti-inflammatory medicine (0.56, 0.65).
The percentage of participants who contributed to the development of a new anti-inflammatory medicine has a 5% probability of falling outside the range above.
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Andres Michael bought a new boat. He took out a loan for $24,420 at 3.5% interest for 2 years. He made a $4,330 partial payment at 2 months and another partial payment of $2,600 at 6 months. How much is due at maturity?
If Andres Michael bought a new boat. He took out a loan for $24,420 at 3.5% interest for 2 years. Andres Michael owes $18806.6 at maturity.
How to find the amount?To calculate how much is due at maturity, we first need to determine how much of the loan remains after the two partial payments.
To do this, we can use the formula for simple interest:
I = P * r * t
Where:
I = Interest
P = Principal (original loan amount)
r = Annual interest rate
t = Time (in years)
The interest for the first two months can be calculated as:
I1 = P * r * t1
= 24420 * 0.035 * (2/12)
= 142.45
So after the first two months, the amount owing on the loan is:
P1 = P + I1 - 4330
= 24420 +142.45 - 4330
= 20,232.45
The interest for the next four months can be calculated as:
I2 = P1 * r * t2
= 20,232.45 * 0.035 * (4/12)
= 236.05
So after six months, the amount owing on the loan is:
P2 = P1 + I2 - 2600
= 20,232.45 + 236.05- 2600
= 17868.50
Now we can calculate the interest for the remaining 18 months:
I3 = P2 * r * t3
= 17868.50* 0.035 * (18/12)
= 938.10
So the total amount owing at maturity (after 2 years) is:
Total amount owing = P2 + I3
= 17868.50 + 938.10
= 18806.6
Therefore, Andres Michael owes $18806.6 at maturity.
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begin by finding the area under the curve from to , . this area can be written as the definite integral
The area under the curve y = 1/ (x^2 + 6x -16) from x = t to x = 6 is 1/10( ln(4) - 1/10 ln(t+8))
To find the area under the curve y = 1/ (x^2 + 6x -16) from x = t to x = 6, where t > 2, we need to evaluate the definite integral:
∫[t,6] 1/ (x^2 + 6x -16) dx
To solve this integral, we can use partial fraction decomposition. First, we factor the denominator:
x^2 + 6x -16 = (x+8)(x-2)
Then, we can write:
1/ (x^2 + 6x -16) = A/(x+8) + B/(x-2)
Multiplying both sides by (x+8)(x-2), we get:
1 = A(x-2) + B(x+8)
Setting x = -8, we get:
1 = A(-10)
So, A = -1/10.
Setting x = 2, we get:
1 = B(10)
So, B = 1/10.
Therefore, we can write:
1/ (x^2 + 6x -16) = -1/10(x+8) + 1/10(x-2)
Substituting this into the integral, we get:
∫[t,6] 1/ (x^2 + 6x -16) dx = ∫[t,6] (-1/10(x+8) + 1/10(x-2)) dx
Integrating, we get:
= [-1/10 ln|x+8| + 1/10 ln|x-2|] from t to 6
= 1/10 ln|6-2| - 1/10 ln|t+8|
= 1/10 ln(4) - 1/10 ln(t+8)
Therefore, the area is: 1/10( ln(4) - 1/10 ln(t+8))
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_____The given question is incomplete, the complete question is given below:
begin by finding the area under the curve from to y = 1/ (x^2 + 6x -16) from x = t to x = 6, t>2 this area can be written as the definite integral
Trains Two trains, Train A and Train B, weigh a total of 188 tons. Train A is heavier than Train B. The difference of their
weights is 34 tons. What is the weight of each train?
Step-by-step explanation:
A + B = 188
A = 188 - B - (1)
Now,
A - B = 34
188 - B - B = 34 (Substituting eqn 1 in A)
188 - 34 = 2B
154 = 2B
• B = 77 tons
Now
A = 188 - B
A = 188 - 77
A = 111 tons
determine if the transformation is one to one and/or onto. justify your answers. give an explanation for each of these properties.
To determine whether a transformation is one-to-one or onto, one must analyze its behavior and properties, such as passing the horizontal line test for one-to-one or checking if the range equals the codomain for onto.
In mathematical terms, a transformation refers to a function that maps elements from one set, called the domain, to another set, called the range. A transformation is said to be one-to-one if no two distinct elements in the domain are mapped to the same element in the range. This means that each element in the range is associated with a unique element in the domain.
On the other hand, a transformation is onto if every element in the range is mapped to by at least one element in the domain. In other words, for each element in the range, there exists at least one element in the domain that maps to it.
To determine whether a transformation is one-to-one or onto, one can analyze its properties and behavior. For example, a transformation is one-to-one if and only if it passes the horizontal line test. This means that no two points in the domain map to the same point on a horizontal line. To determine if a transformation is onto, one can check if the range of the transformation equals the codomain.
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The given question is incomplete, the complete question is:
How to determine the transformation is one to one and/or onto?
The circle below has center O, and its radius is 6 yd. Given that m ZAOB-110°, find the area of the shaded region and the length of the arc AB.
Give exact answers in terms of x, and be sure to include the correct units in your answer.
Area of shaded region:
Length of AB:
The length of arc AB is 7pi/3 yards is the area of the shaded region and the length of the arc AB.
what is circle?
A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center.
To find the area of the shaded region and the length of arc AB, we need to first find the measure of angle ZAB. Let's call this angle x.
Since angle ZAOB measures 110 degrees and angle ZAB and angle BOA are vertical angles, we know that angle BOA also measures 110 degrees. Therefore, angle ZAB + angle BOA = 180 degrees.
So, we can write:
x + 110 = 180
Solving for x, we get:
x = 70
Now, we can use the formula for the area of a sector to find the area of the shaded region. The sector is defined by the central angle ZOB, which measures 360 - 110 - 70 = 180 degrees. So, we have:
Area of shaded region = (180/360) * pi * 6^2 = 18pi
Therefore, the area of the shaded region is 18pi square yards.
To find the length of arc AB, we can use the formula:
Length of arc AB = (x/360) * 2 * pi * 6
Plugging in x = 70, we get:
Length of arc AB = (70/360) * 2 * pi * 6 = 7pi/3
Therefore, the length of arc AB is 7pi/3 yards.
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1 On a map of scale 1:100 000, the distance between Tower Bridge
and Hammersmith Bridge is 12.3 cm.
What is the actual distance in km?
To calculate the actual distance in km, we need to use the scale factor of 1:100 000. This means that 1 cm on the map is equivalent to 100 000 cm in real life.
Therefore, 12.3 cm on the map is equivalent to 12.3 x 100 000 cm in real life.
Now, 1 km is equivalent to 100 000 cm.
Therefore, 12.3 x 100 000 cm is equivalent to 1.23 km.
Hence, the actual distance in km is 1.23 km.