1) Jay buys a house for $40,000 less than he is willing to pay. He bought a house from a seller who received $2,000 more than he was willing to sell.
4) Kevin wanted to spend $50 on a dishwasher and bought it for $45 from a manufacturer hoping to get $40.
Economic Surplus:
Economic surplus, also known in mainstream economics as general welfare or general public welfare or Marshall's surplus (after Alfred Marshall), is one of two related quantities. Pay.
Producer surplus or producer surplus is the amount a producer receives by selling at a market price higher than the lowest price they are willing to sell. This roughly equals profit margin (because producers are usually unwilling to sell at a loss and are generally uninterested in selling at a break-even price).
Total economic surplus = supplier surplus + consumer surplus
supplier surplus is the difference between the minimum price that a seller would take for his/her products and the actual selling priceconsumer surplus is the difference between the maximum price that a consumer would be willing to pay for a product and the actual priceOn scenario 1, total economic surplus = $40,000 + $2,000 = $42,000
On scenario 2, total economic surplus = $2.25 + $3 = $5.25
On scenario 3, total economic surplus = $0
On scenario 4, total economic surplus = $5 + $5 = $10
Complete Question:
Select the two situations with the highest total surplus. correct answer(s) jay buys a house for $40,000 less than he was willing to pay. he bought his home from sellers who received $2,000 more than they were willing to sell for. bonnie buys flowers for $2.25 less than she was willing to pay. she bought them from a seller would have been willing to receive $3 less from the sale. don wanted to buy a scooter for no more than $5, but was only able to find a producer who would sell for $15. kevin wanted to spend $50 on a dishwasher and bought one at $45 from a producer who was hoping to receive $40.
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a committee of 5 students is to be selected from a group of 30 students. how many different committees are possible?
There are 142,506 different committees of 5 students that can be selected from a group of 30 students.
According to given condition :The number of different committees that can be formed by selecting 5 students from a group of 30 students can be calculated using the formula for combinations, which is:
n C r = n! / r!(n - r)!
where n is the total number of items (in this case, the number of students) and r is the number of items to be selected (in this case, 5).
Substituting the values, we get:
30 C 5 = 30! / (5! * (30 - 5)!)
= (30 * 29 * 28 * 27 * 26) / (5 * 4 * 3 * 2 * 1)
= 142,506
Therefore, there are 142,506 different committees of 5 students that can be selected from a group of 30 students.
What is Probability ?Probability is a branch of mathematics that deals with the study of random events and the likelihood of their occurrence. It is a measure of the chance or likelihood of an event happening, expressed as a number between 0 and 1. A probability of 0 means the event will not occur, and a probability of 1 means the event will definitely occur.
The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This is known as the classical probability, and it assumes that all outcomes are equally likely.
There are also other types of probability, including empirical probability (based on observations and data), subjective probability (based on personal judgment and beliefs), and conditional probability (the probability of an event given that another event has occurred).
Probability has applications in many fields, including statistics, science, finance, and engineering. It is used to model and predict the occurrence of events, to make decisions under uncertainty, and to design systems and processes that can minimize risk and maximize the chances of success.
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what is curve of normal distribution
The curve of a normal distribution, also known as a Gaussian distribution, is a bell-shaped curve that is symmetric around the mean.
The shape of the curve is determined by two parameters: the mean (µ) and the standard deviation (σ) of the distribution. The curve is highest at the mean, and falls off gradually as we move away from the mean in either direction.
The standard deviation controls the width of the curve, with larger values of σ resulting in wider, flatter curves, and smaller values of σ resulting in narrower, more peaked curves.
The normal distribution is a continuous probability distribution, and it is widely used in statistics to model many natural phenomena, such as the heights of people, the weights of objects, and the scores on tests. It is also commonly used in statistical inference and hypothesis testing.
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Let f(x) = 2x^2and g(x) =x-1. Find (f • g)(x), then evaluate when x = 3.
(f • g)(x) = f(g(x))
= f(x-1)
= 2(x-1)^2
Therefore, (f • g)(3) = 2(2)^2 = 8
Answer:
(f • g)(x) = 2(x-1)^2 and (f • g)(3) = 8.
Step-by-step explanation:
We have, to substitute g(x) into f(x) wherever we see x in f(x),to find (f • g)(x).
Which will give,
(f • g)(x) = f(g(x))
= f(x-1)
= 2(x-1)^2
We have to put x = 3 to evaluate this expression,
(f • g)(3) = 2(3-1)^2
= 2(2)^2
= 8
Therefore,
(f • g)(x) = 2(x-1)^2 and (f • g)(3) = 8.
what is the hole for this equation?
The hole for the function f(x) = √(x-2) is x < 2.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
A hole in a graph refers to a point where a function is undefined or missing.
Now,
f(x) = √(x-2)
Now,
To determine where this function is undefined, we need to consider the domain of the function, which is the set of all possible values of x that can be input into the function.
Since the square root function is defined only for non-negative numbers, The expression inside √(x-2) must be greater than or equal to zero:
i.e
x - 2 ≥ 0
Solving for x.
x ≥ 2
Therefore,
The function f(x) = √(x-2) is undefined for any value of x that is less than 2.
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The complete question.
what is the hole for this equation f(x) = √(x-2)?
Kendra earns $10 per hour babysitting and $15 per hour providing tech support. Her goal is to save at least $1,000 by the end of the month while not working more than 80 hours. Write and graph a system of inequalities that shows how many hours Kendra could work at each job to meet her goal. What is the fewest number of hours she could work and still meet her goal?
Answer: Let's use x to represent the number of hours Kendra works as a babysitter, and y to represent the number of hours Kendra works providing tech support. Then, we can write the following system of inequalities to represent Kendra's goal:
10x + 15y >= 1000 (Kendra needs to earn at least $1000)
x + y <= 80 (Kendra can't work more than 80 hours in total)
To graph these inequalities, we can start by graphing the boundary lines for each inequality. To do this, we can rewrite each inequality as an equation and graph it as a line:
10x + 15y = 1000 (the boundary for the earnings inequality)
x + y = 80 (the boundary for the total hours inequality)
We can then shade the region that satisfies both inequalities (i.e. the region that is above the earnings line and below the total hours line). This shaded region represents all the possible combinations of hours that Kendra could work to meet her goal:
|
80| .
| .
| .
| .
| .
0|___________________
0 50 80
Babysitting Hours
In the graph, the shaded region is the triangular area bounded by the x-axis, the y-axis, and the line x + y = 80. The fewest number of hours Kendra could work and still meet her goal is the point where the earnings line intersects the total hours line within the shaded region. To find this point, we can solve the system of equations:
10x + 15y = 1000
x + y = 80
One way to solve this system is to use substitution. Solving the second equation for y, we get y = 80 - x. Substituting this expression for y into the first equation, we get:
10x + 15(80 - x) = 1000
Simplifying and solving for x, we get x = 40. Substituting this value for x into the second equation, we get y = 80 - 40 = 40.
Step-by-step explanation:
TRANSPORT Mr Dlamini transport people between Butterworth and East London using a bus which has a capacity of 100 people. The transport charge starts with a minimum charge of R8 and thereafter it was increased by R2 for each kilometre. On a particular day the bus was full with passengers from Butterworth. In each and every kilometre there was a passenger getting off while no new passenger entered in the bus. Mr Dlamini was calculating total money in his hand after each passenger was getting out. The total amount he has after each stop can be written as a series as follows: S. = 8 + 10 + 12 + 14 +... Use the series to calculate the following questions 1.1 (1) Term 2 (T2) = Sum of first two terms (S2) (2) (ii) Express T2 in terms of S, and S2. (1)
From the series, it can be deduced that the sum of the first two terms will be 18.
How to calculate the series?From the information given, it was stated that the transport charge starts with a minimum charge of R8 and thereafter it was increased by R2 for each kilometre.
The series is also given as S. = 8 + 10 + 12 + 14 +... Therefore, the sum of the first two terms will be:
= 8 + 10
= 18
Expressing T2 in terms of S, and S2 will be T2 = S + S2.
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Explain :Multiply: 23.2 x 0.14 ___________________
As a result, 23.2 x 0.14 equals 3.248.
What does math's multiple mean?One of the four fundamental math processes, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual adding of sets of identical size.
To multiply 23.2 and 0.14,
23.2
x 0.14
---------
32.48 (0.2 x 0.14 = 0.028, write down 8 and carry over 2)
+ 232.0 (3 x 0.14 = 0.42, add carried over 2 to get 4, write down 0 and carry over 4)
--------
3.248 (the final answer)
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a plant is 6.2cm tall
the height of the plant increases by 11% each week
find how tall the plant will be after two weeks
Answer:
7.64
Step-by-step explanation:
1 week: (100% + 11%) × 6.2
111% × 6.2 = 6.882 cm
OR
11% × 6.2 = 0.682 cm
6.2 + 0.682 = 6.882 cm
Because the plant grows 11% additional to its original height.
1 week = 6.882 cm
2 weeks = 111% × 6.882 cm
OR
11% × 6.882cm = 0.75702 cm
0.75702 cm + 6.882 = 7.63902 cm
Because an additional 11% is added to what was grown in week 1.
=7.63902 cm
= 7.64 cm (rounded to 2 decimal places)
hope this helps!
Resuelve el siguiente SUDOKU., porfa
De acuerdo con la información previa, el sudoku se completaría con los números como se muestra en la imagen anexada.
¿Cómo completar un Sudoku?Un sudoku es un juego numérico en el que tenemos 9 cuadrículas de 3 x 3 cuadros en los que tenemos que ubicar los números de 1 al 9 sin que se repitan en columnas, filas o en el mismo cuadro de 9 cuadrículas. Este juego se asocia con un buen nivel de análisis matemático. Adicionalmente, para solucionar un juego de Sudoku debemos analizar los números que ya están puestos en él como pistas para ubicar el resto de números.
De acuerdo con lo anterior, el Sudoku de la imagen muestra cómo se completó correctamente. En él ningún número se repite en filas, columnas o cuadrículas.
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There are 9 chocolate bars in a bag of Halloween candy. The bag is dropped and 5 of the chocolate bars break. You take one random chocolate bar out, eat it and take another out. What is the probability that neither of these were broken?
Answer:
Below
Step-by-step explanation:
4 out of 9 are not broken first bar not broken chance is then 4/9
now there are 8 bars left and 3 are not broken so for the second bar thee is a 3/8 chance of not being broken
4/9 * 3/8 = 12/72 = 1/6
Answer:
it's below because
Step-by-step explanation:
1/6 !!!!!!!!!!!!!!
What will be the value stored in the variable x after the execution of the following code snippet?
int a = 10;
int b = 20;
int c = 2;
int x = b / a /*c*/;
a) 1
b) 2
c) 4
d) The code has a syntax error
The value stored in the variable x after the execution of the following code snippet will be b) 2.
The right-click context menu option or a combination of hotkeys can be used to add code snippets, which are compact chunks of reusable code, to a code file. Although try-finally and if-else blocks, for example, are frequently used code blocks found in code snippets, you can also use them to add whole classes or methods.
Learn more about using the templates tool to create reusable emails. Applications and web pages use snippets. Snippets are made to be reusable and to add functionality, like connecting various parts of a program.
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Please answer Q9 parts (a),(b) and (c)
Completely confused
The area of the shaded region is 435.375 mm². The solution has been obtained by using the concept of area of figure.
What is area?
Area is the amount of space a two-dimensional figure takes up. The standard unit of area is the square, which is typically expressed as square inches, square feet, etc.
We are given an area of a square with a quarter circle outlined on it.
Area of shaded region = Area of square - area of quarter circle
So, using this, we get
⇒Area of shaded region = (45 * 45) - 1/4π (45 * 45)
⇒Area of shaded region = 2025 - 506.25π
⇒Area of shaded region = 2025 - 506.25 * 3.14
⇒Area of shaded region = 2025 - 1589.625
⇒Area of shaded region = 435.375 mm²
Hence, the area of the shaded region is 435.375 mm².
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Since, there are multiple questions so, the question answered above is attached below
32/7 into a number line
Answer:
32/7 = 4 + 5/7
Step-by-step explanation:
how many acres is a lot that totals 19,602 square feet...?
The area covered by 19, 602 square feet in acres is around 0.45, according to the relation between the two.
As per the known relation between acre and square foot, the two quantities are related through the formula -
1 acre is equal to 43, 560 square feet
Therefore, formula to convert square feet to acre will be -
Amount of area in acres = area covered in square feet/unit equivalent area in square feet
So, rewriting the above mentioned relation.
43, 560 square feet is equal to 1 acre
Thus, 19, 602 square feet will be equal to acres = 19, 602/43, 560
Performing division on Right Hand Side of the equation
The amount of area in acres = 0.45 acres
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QUICKLY, PLEASE ANSWER!!!!!!!
Find the measure of angle of a, b, and c?
The measure of angle of a, b, and c are a = 90, b = 9- and c = 60 degrees
How to determine the measures of the anglesFrom the question, we have the following parameters that can be used in our computation:
The figure
The angle at the circumference in a semicircle is 90°
This means that
a = b = 90 degrees
Also, we have
Angle c and angle with a measure of 60 degrees are equal
This means that
Angle c = 60 degrees
Hence, the measure of the angles are a = 90, b = 9- and c = 60 degrees
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pls exsplain how to do this
Answer:
75.4 (rounded)
Step-by-step explanation:
V= πr² h/3
V= π x 3² x 8/3
= 75.3982236862
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how to convert ounces to tbsp
In order to convert ounces to tablespoons(tbsp), we have to multiply the number of ounces by 2.
You can use a simple conversion factor of 2 tablespoons per ounce to convert ounces to tablespoons. So, to convert a certain number of ounces to tablespoons, you just need to multiply that number by 2. For example, if you have 4 ounces of liquid, you can convert it to tablespoons by multiplying 4 by 2, which gives you 8 tablespoons. This conversion is often used in cooking and baking recipes where ingredients may be measured in different units.
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what is 20 in decimal?
The number 20 can be represented as a decimal by simply writing it as 20.0 or 20.00
The number 20 can be represented as a decimal by simply writing it as 20.00 or 20.000 This is because decimal notation is a way of writing numbers that uses a decimal point to separate the whole number part from the fractional part.
In this case, since 20 is a whole number and has no fractional part, we can represent it in decimal form by adding a decimal point and a zero or two zeros after it to indicate that there are no decimal places.
Alternatively, we can also represent 20 as a decimal by dividing it by 1, which does not change its value, and then expressing the quotient as a decimal. Since 20 divided by 1 equals 20, we can write 25 as a decimal by dividing 25 by 1 and writing the quotient as follows:
20 ÷ 1 = 20.000000... (with the decimal places repeating indefinitely)
However, in most cases, it is sufficient to represent 20 as 20.0 or 20.00, since these notations convey that the number has no fractional part.
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What is the conversion of 195 lbs to kg ?
The conversion of 195 lbs to other mass unit kilogram is equals to the 88.45051215 kg.
Kilogram (kg) and pound (lbs) are used to measure the mass of the substance/objects. In the United States and the British commonwealths, the unit used for mass is called pound. A pound is defined as aporoximatly 0.45359237 kilograms. The kilogram, or kilogramme, is the base unit of mass in the Metric system. To convert lbs to kg, multiply the particular lbs value by 0.45359237 kg. For example, to convert x lbs to kilogram, multiply the x lbs by 0.45359237 kg. So,x lbs = x × 0.45359237 kg
x lbs = 0.45359237x kg, if x = 3
Therefore, 3 lbs is approximately equal to 1.36077711 kg. It is very important skill to convert the lbs to kilograms in mass measurment. Now, we have 195 lbs. We know that one lbs
= 0.45359237 kg
Therefore, 195 lbs = 195 x 0.45359237 kg
195 lbs = 88.45051215 kg.
Hence, 195 lbs is equal to 88.45051215 kg.
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please finish these 4 I need help pls
the line plot shows the cost of 5 books.A teacher buys all 5 books.She pays with a $100 bill. How much change should she get?
Answer:
Look at the screenshot
Step-by-step explanation:
A ballet school wants to buy new slippers for students in a class. They collected the sizes and displayed them in a line plot.
A horizontal number line starting at 3.5 with tick marks every 0.5 units up to 8. The following values are labeled: the value of 4 has two dots, the value of 4.5 has one dot, the value of 5 has one dot, the value of 6 has 2 dots, the value of 6.5 has one dot, the value of 7 has one dot, and the value of 7.5 has one dot. The image is titled Ballet Shoe Sizes.
What is the range, and what does it mean in terms of this data set?
The range is 4.5 and it means that the ballet shoe sizes in this class vary by 4.5, with the largest size being 8 and the smallest size being 3.5.
What is range?The difference between the highest and lowest values for a given data collection is the range in statistics.
In statistics, we must put the given values, set of data, or set of observations in ascending order in order to determine the range. It indicates that you should start by writing the observations from lowest to highest value. The formula must now be used to determine the range of observations.
The range is the difference between the largest and smallest values in a data set.
For the given data, the largest value is 8 and the smallest value is 3.5.
Thus,
range = 8 - 3.5 = 4.5.
Hence, the range is 4.5 and it means that the ballet shoe sizes in this class vary by 4.5, with the largest size being 8 and the smallest size being 3.5.
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Answer:
Step-by-step explanation:The range is 4.5 and it means that the ballet shoe sizes in this class vary by 4.5, with the largest size being 8 and the smallest size being 3.5.
Please Help Me!! Will Mark Brainliest!! It's Due Tonight!! 20 Points!! :)
Jeff has a sack full of marbles. Each time he picks one out, he puts it back into the sack before drawing another. In his sack there are 5 red marbles, 6 yellow marbles, and 8 blue marbles. Find the following probabilities.
c. If two marbles are drawn, what's the chance they are both the same color?
d. If two marbles are drawn, what's the chance they are NOT the same color?
Therefore , the solution of the given problem of probability comes out to be P(not same color) = 236/361.
What precisely does the probability method suggest?Calculating the likelihood that a statement is true or that an event will take place is the focus of probability theory, a branch of mathematics. Any number range between 0 and 1, where 1 is frequently used to describe certainty and 0 is commonly used to denote possibility, can be used to represent chance. A probability diagram shows the likelihood that a particular event will occur.
Here,
There are three cases to consider:
Case 1: both marbles are red
Case 2: both marbles are yellow
Case 3: both marbles are blue
The probability of drawing two red marbles can be found by multiplying the probability of drawing a red marble on the first draw (5/19) by the probability of drawing a red marble on the second draw (5/19):
P(red and red) = (5/19) * (5/19) = 25/361
Similarly, the probability of drawing two yellow marbles is:
P(yellow and yellow) = (6/19) * (6/19) = 36/361
And the probability of drawing two blue marbles is:
P(blue and blue) = (8/19) * (8/19) = 64/361
So, the probability of drawing two marbles that are the same color is:
P(same color) = P(red and red) + P(yellow and yellow) + P(blue and blue)
P(same color) = (25/361) + (36/361) + (64/361)
P(same color) = 125/361
d. If two marbles are drawn, what's the chance they are NOT the same color?
There are three cases to consider:
Case 1: one marble is red and one marble is yellow
Case 2: one marble is red and one marble is blue
Case 3: one marble is yellow and one marble is blue
The probability of drawing one red marble and one yellow marble can be found by multiplying the probability of drawing a red marble on the first draw (5/19) by the probability of drawing a yellow marble on the second draw (6/19), and then multiplying by 2 (since the order of the marbles doesn't matter):
P(red and yellow) = 2 * (5/19) * (6/19) = 60/361
Similarly, the probability of drawing one red marble and one blue marble is:
P(red and blue) = 2 * (5/19) * (8/19) = 80/361
And the probability of drawing one yellow marble and one blue marble is:
P(yellow and blue) = 2 * (6/19) * (8/19) = 96/361
So, the probability of drawing two marbles that are not the same color is:
P(not same color) = P(red and yellow) + P(red and blue) + P(yellow and blue)
P(not same color) = (60/361) + (80/361) + (96/361)
P(not same color) = 236/361
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Which function is positive for the entire interval [–3, –2]? On a coordinate plane, a curved line with a minimum value of (0, negative 3) crosses the x-axis at (negative 3, 0) and (3, 0), and crosses the y-axis at (0, negative 3). On a coordinate plane, a curved line with a minimum value of (2, negative 3) crosses the x-axis at (negative 1, 0) and (5, 0), and crosses the y-axis at (0, negative 1. 5). On a coordinate plane, a curved line with a minimum value of (2, 4) and a maximum value of (0. 5, 6), crosses the x-axis at (negative 1. 5, 0) and crosses the y-axis at (0, 5). On a coordinate plane, a curved line with a minimum value of (negative 1. 75, negative 3. 9) and a maximum value of (0, 2), crosses the x-axis at (negative 2. 2, 0), (negative 0. 75, 0), and (0. 75, 0), and crosses the y-axis at (0, 2)
The function that is positive for the entire interval [-3, -2] is:
The function has a minimum value of (0, -3) and crosses the x-axis at (-3, 0) and (3, 0). This means that the function is positive for the entire interval [-3, -2] because it is above the x-axis for this interval.
To further explain, a function is positive when its value is above the x-axis on a coordinate plane. In this case, the first function has a minimum value of (0, -3) which means that it is below the x-axis at this point. However, it crosses the x-axis at (-3, 0) and (3, 0), meaning that it is above the x-axis for the entire interval between these two points, including the interval [-3, -2].
The other functions are not positive for the entire interval [-3, -2] because they either have minimum values that are below the x-axis within this interval, or they cross the x-axis within this interval, meaning that they are not positive for the entire interval.
In conclusion, the function that is positive for the entire interval [-3, -2] is the first one because it is above the x-axis for this entire interval.
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what does the percentage of completion method calculate?
The percentage of completion method is a widely used accounting method to recognize revenue and expenses over the life of a long-term project or contract.
It is primarily used in construction, real estate, and other industries that undertake large projects that span over extended periods. The method estimates the percentage of work completed, and then assigns that percentage of revenue and expenses to that period.
Under the percentage of completion method, revenue and expenses are recognized proportionally to the progress of the project, and the calculation is based on the cost incurred to date relative to the total estimated cost of the project.
This method is advantageous because it allows for more accurate financial statements that reflect the actual progress and costs of the project.
Overall, the percentage of completion method provides a more accurate representation of the financial position of long-term projects and contracts, and is therefore an essential tool for companies in industries that undertake such projects.
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What is the conversion of 85 c to f ?
85 degrees Celsius is equal to 185 degrees Fahrenheit.
To convert Celsius (C) to Fahrenheit (F), you can use the formula:
F = (C × 9/5) + 32
where C is the temperature in Celsius and
F is the temperature in Fahrenheit.
Using this formula,
we can convert 85 degrees Celsius to Fahrenheit as follows:
F = (85 × 9/5) + 32
F = 153 + 32
F = 185
The average body temperature is widely regarded to be between 36.5 °C (97.7 °F) and 37.5 °C (99.5 °F).
Fever is defined as an increase in body temperature of one degree Celsius or more over the average of 37.0 degrees Celsius (98.6 degrees Fahrenheit).
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please help and explain how to solve this
A cone with height h and radius r has volume V = 1/3πr^2h. If a certain cone with a height of 9 inches has volume V = 3πx^2 + 42πx + 147π, what is the cone’s radius r in terms of x?
The cone’s radius r in terms of x is x + 7
How to determine tthe cone’s radius r in terms of x?From the question, we have the following parameters that can be used in our computation:
Volume, V = 3πx^2 + 42πx + 147π
Height, h = 9
The volume of a cone is
V = 1/3πr^2h
Substitute the known values in the above equation, so, we have the following representation
1/3πr^2 * 9 = 3πx^2 + 42πx + 147π
So, we have
3πr^2 = 3πx^2 + 42πx + 147π
Divide by 3π
r^2 = x^2 + 14x + 49
So, we have
r = √(x² + 14x + 49)
Evaluate
r = x + 7
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Describe all solutions of Ax = 0 in parametric vector form, where A is a row equivalent to the given matrix.[1−3−85012−4][1−3−85012−4]
The parametric vector form of the matrix is AX = < t 0 3/5t> where t is any real number.
Matrices are an important mathematical tool that can be used to represent and solve a wide array of problems.
In this problem, we are given a matrix A, which is row equivalent to the given matrix [1 -3 -8 5 0 12 -4] and asked to describe all solutions of Ax = 0 in parametric vector form.
To answer this question, we first need to use row operations to transform the given matrix into row-echelon form. After applying row operations, the matrix becomes [1 0 -5/3 0 2/3 0 1].
We can now use this matrix and the equation Ax = 0 to identify the solutions in parametric vector form.
The first column of the matrix has a coefficient of 1, indicating that x₁ is free and can take on any real value.
The second column has a coefficient of 0, indicating that x₂ = 0.
The third column has a coefficient of -5/3, indicating that x₃ = 3/5t, where t is a real number.
Then the resulting vector form is written as,
=> AX = < t 0 3/5t> where t is any real number.
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what is arc length calculus formula?
Arc length formula is L = ∫a^b √[1 + (dy/dx)^2] dx . The arc length of a curve is the length of the curve between two points, and it can be calculated using the arc length formula in calculus.
The arc length formula can be used to find the length of a curve in terms of the function that describes the curve.
The arc length formula is given by:
L = ∫a^b √[1 + (dy/dx)^2] dx
where L is the arc length of the curve, a and b are the endpoints of the curve, dy/dx is the derivative of the function that describes the curve with respect to x, and ∫ represents the integral of the function over the interval from a to b.
To use the formula, we first find the derivative of the function that describes the curve, dy/dx. Then we plug this expression into the arc length formula and integrate the expression over the interval from a to b to find the arc length of the curve.
The arc length formula is useful in many applications, such as physics, engineering, and geometry, and it allows us to find the length of a curve even when it is not a straight line.
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QUESTION 1 In observational studies, the variable of interest A. cannot be numerical.B. must be numerical. C. is controlled. D is not controlled.
In observational studies, the variable of interest is not controlled.
The correct answer is D.
Observational studies are a type of research design used to investigate the relationship between variables. In an observational study, the researcher observes and records data without manipulating any variables. The variable of interest is the one that the researcher wants to investigate and understand its relationship with other variables.
Numerical variables are those that can be measured and expressed as numbers. Examples of numerical variables include age, weight, height, temperature, and income. These variables are important in observational studies because they can be analyzed quantitatively and compared to other variables of interest.
In contrast, categorical variables are not numerical, and they cannot be measured or expressed as numbers. Examples of categorical variables include gender, race, occupation, and marital status. These variables are not appropriate as the variable of interest in observational studies because they cannot be analyzed quantitatively.
In observational studies, the variable of interest is not controlled, meaning the researcher does not manipulate or control it. Instead, the researcher observes and records data on the variable and its relationship with other variables. This is in contrast to experimental studies, where the researcher manipulates one or more variables to observe their effect on another variable. Therefore the answer is D) is not controlled.
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