The radius of the circle defined by the equation (x-x₁)² + (y-y₁)² is given by the formula √((x - x₁)² + (y - y₁)²).
You have been asked to find the radius of a circle that is defined by the equation (x-₁)² + (y-₁)². This equation represents all the points that are a certain distance away from the point (₁,₁).
To find the radius, we need to determine the distance from the center (₁,₁) to any point on the circle. Since the circle is defined by the equation (x- x₁)² + (y- y₁)², we can use the distance formula to find the radius.
The distance formula states that the distance between two points (x₁, y₁) and (x₂, y₂) is given by:
distance = √((x₂ - x₁)² + (y₂ - y₁)²)
In this case, we want to find the distance from the center (₁,₁) to a point on the circle (x,y). Using the distance formula, we can write:
radius = √((x - x₁)² + (y - y₁)²)
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The functions a ( t ) = 8.75 ⋅ ( 1 + 0.01 ) t and b ( t ) = 8.75 ⋅ e ( 0.01 t ) each model the population of a city, in thousands, t years after 2010. Describe how each model predicts that the population in the town will grow.
Using the functions, we can predict that the population in the town will grow 't' times as t is directly proportional to the function.
Define a function?A function in mathematics is a connection between two x and y values that come from different sets. These four types of correspondence are all possible. Yet not every correspondence serves a purpose.
The following are the results of a survey conducted by the National Institute of Standards and Technology (NIST) on the effectiveness of the standardised testing process. So, we state that a function can only have one input and one output. If we are given any x, the only y that can be coupled with that x is the one and only y. Two outputs cannot be connected to the same function.
Here in the given question,
The functions a(t) = 8.75 × (1+0.01) t and
b(t) = 8.75 × e × (0.01t) here are dependent on the variable t, where t is the time in years after 2010.
So, as t will increase after 2010, the value of a(t) and b(t) will increase with t.
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i need help with the question please
The equation 32 - 3x + 13 = 0 can be rewritten as 3x = 19. Therefore, x = 19/3. Because x is a real number, the solution to the equation is x = 19/3.
What is real number ?Real numbers are any number that can be expressed as a decimal number or a fraction. This includes the natural numbers (1,2,3,4, etc.), the negative numbers (-1,-2,-3, etc.), the rational numbers (fractions, such as 1/2, 3/4, etc.), and the irrational numbers (numbers that cannot be expressed as a fraction, such as pi, square root of 2, etc.). Real numbers can be manipulated with basic arithmetic operations such as addition, subtraction, multiplication, and division. Real numbers have an infinite number of decimal places, making them useful for measuring physical quantities such as time, distance, and temperature.
Expressing this answer in the form a + bi, where a and b are real numbers, gives the solution a = 19/3 and b = 0. Therefore, the answer is 19/3 + 0i = 19/3.
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A fair coin is tossed five times. Explain why the probability of getting exactly three heads is 0.3125.
The value of the probability is 0.3125 and this is proved by the calulations below
How to explain the value of the probabilityThe probability of getting exactly 3 heads in 5 coin tosses can be calculated by multiplying the probability of one specific combination of 3 heads and 2 tails by the number of possible combinations.
The probability of one specific combination, for example HHTTT, is (1/2)^5 = 1/32, because each toss has a 1/2 chance of being a head or a tail.
There are 5C3 = 10 possible combinations of 3 heads and 2 tails in 5 tosses.
For example: HHTTT, HTHTT, HTTHT, HTHHT, TTHHH, etc.
Therefore, the probability of getting exactly 3 heads is:
Probability = 10 * (1/32)
Probability = 10/32
Probability = 0.3125.
Hence, the value of the probability is 0.3125.
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Finding limits of piecewise functions!
Check the picture below.
btw, we could have used the f(4) for both subfunctions just the same.
Which expression is equivalent to
*picture shown*
√5 /x²y is equivalent expression to the given question . Then the correct option is C.
What is Expression?
A mathematical expression is a phrase with at least two variables or integers and one arithmetic operation.
According to the given information:a)Constant It has a set numerical value and is a constant.
For instance: 7,45,413,18,5.
b) Variables don't accept any predetermined values. Value is depend on Equation
Like a, p, and z
Constants, variables, or constants multiplied by variables are all acceptable terms (s). The "+" or "" symbol or both separates each term in an expression.
Instance: 5a+12b.
d) Operators: Addition (+), subtraction (-), multiplication (-), and division (-) are the four operations that are used to combine the terms in an expression.
Therfore, √5 /x²y is equivalent expression to the given question . Then the correct option is C.
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The Ford F-150 is the best selling truck in the United States.
The average gas tank for this vehicle is 23 gallons. On a long
highway trip, gas is used at a rate of about 3.2 gallons per hour.
The gallons of gas g in the vehicle's tank can be modeled by the
equation g(t)=23 -3.2t where t is the time (in hours).
a) Identify the domain and range of the function. Then graph
the function.
b) At the end of the trip there are 6.4 gallons left. How long
was the trip?
a) The domain and the range of the function are given as follows:
Domain: [0, 7.1875].Range: [0,23].The graph of the function is given by the image presented at the end of the answer.
b) The trip was 5.1875 hours long.
What are the domain and the range of a function?The function for this problem is defined as follows:
g(t) = 23 - 3.2t.
The domain is the set of input values that can be assumed by the function. The time cannot have negative measures, hence the lower bound of the domain is of zero, while the gas cannot be negative, hence the upper bound of the volume is given as follows:
23 - 3.2t = 0
3.2t = 23
t = 23/3.2
t = 7.1875 hours.
The range is given by the set of all output values assumed the function, which are the values of the gas, hence it is [0,23].
The graph is a linear function between points (0, 23) and (7.1875, 0).
At the end of the trip there were 6.4 gallons left, hence the length of the trip is given as follows:
23 - 3.2t = 6.4
t = (23 - 6.4)/3.2
t = 5.1875 hours.
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! 100 POINTS !
What is this question asking? What does it mean by floor plan? A step-by-step explanation would be very much appreciated.
Brainliest, ratings and thanks are promised if a helpful answer is received.
Step-by-step explanation:
So first of all u have to convert the metres into centimetres. After the conversation draw the map of both in centimetres and your map is done. The question is answered
Answer:
Determine the dimensions of the room: Measure the length and width of the room you want to draw a floor plan for using a tape measure. Record these measurements in meters.
Choose a scale: Since you want to use a scale of 1cm to 0.5m, you need to convert your measurements from meters to centimeters. For example, if your room measures 6 meters by 4 meters, you need to multiply each measurement by 100 to get 600cm by 400cm. Then, divide each measurement by 2 to get your scale measurement. In this case, your floor plan will be 300cm by 200cm.
Draw a rough sketch: Using a pencil and graph paper, draw a rough sketch of the room's shape based on the dimensions you have recorded.
Add doors and windows: Using the same scale, add doors and windows to your floor plan. Doors are typically represented by a straight line with an arc on top, while windows are represented by a straight line with a horizontal line through the middle.
Add fixtures and appliances: Add any fixtures and appliances that are permanent to the room, such as sinks, cabinets, and appliances. You can use symbols to represent these items, such as a rectangle for a refrigerator or a triangle for a sink.
Label everything: Finally, label everything on your floor plan using a legible font. This includes the dimensions of the room, the location of doors and windows, and the names of fixtures and appliances.
Step-by-step explanation:
How do you apply perimeter, area, and circumference in real world applications (One Paragraph)
Perimeter, area, and circumference are important mathematical concepts that have numerous real-world applications.
How to apply?
For example, in construction and architecture, these concepts are used to measure and design buildings, rooms, and other structures. Knowledge of perimeter is important when determining how much material is needed for a fence or wall, while understanding area is crucial for calculating how much paint or flooring material is needed for a room.
Circumference is important for designing circular objects such as wheels, pipes, and round tables. In addition to construction and design, these concepts are also used in various fields such as engineering, science, and finance.
For instance, understanding area and circumference is important in calculating the surface area and volume of 3D objects in science, while in finance, perimeter and area can be used to calculate the cost of goods or real estate. Overall, the applications of perimeter, area, and circumference are numerous and essential in many aspects of our daily lives.
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An initial deposit of $800 is put into an account that earns 5% interest, compounded annually. Each year, an additional deposit of $800 is added to the account.
Assuming no withdrawals or other deposits are made and that the interest rate is fixed, the balance of the account (rounded to the nearest dollar) after the seventh deposit is __________.
The balance of the account after the seventh deposit can be calculated using the formula below:
A = P (1 + r/n)ⁿ
where:
A = the balance of the account
P = The initial deposit of $800
r = the interest rate of 5%
n = the number of times the interest is compounded annually
n = 1
Therefore, the balance of the account after the seventh deposit is:
A = 800 (1 + 0.05/1)⁷
A = 800 (1.05)⁷
A = 800 (1.4176875)
A = 1128.54
Rounded to the nearest dollar, the balance of the account after the seventh deposit is $1128.
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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Find the missing side in each triangle using any method.
AC has a length of ____ units. DE has a length of ____ units.
ƒ and g, ƒ(2) = −3 and g( − 3) = 10. Find g(f(2)) .
Answer:
To find g(f(2)), we first need to find f(2) and then use that result as the input for g.
We are given that f(2) = -3, so we substitute that value into g(x) to get:
g(f(2)) = g(-3)
We are also given that g(-3) = 10, so we substitute that value in:
g(f(2)) = g(-3) = 10
Therefore, g(f(2)) = 10.
The number of people who took I-45 to Houston in one day was 31,426. The number of people who took the bus was one and a half times the number of people who took the highway. How many more people took the bus?
Answer:
Bus vs Highway: Houston
Let's start by finding out how many people took the bus.
If the number of people who took the highway is x, then the number of people who took the bus is 1.5x (since it's one and a half times the number of people who took the highway).
We know that the total number of people who traveled to Houston is 31,426, so we can write an equation:
x + 1.5x = 31,426
Simplifying the equation:
2.5x = 31,426
Dividing both sides by 2.5:
x = 12,570.4
Since we can't have a fraction of a person, we can round this down to 12,570.
Now we can find the number of people who took the bus:
1.5x = 1.5(12,570) = 18,855
To find out how many more people took the bus, we can subtract the number of people who took the highway from the number of people who took the bus:
18,855 - 12,570 = 6,285
Therefore, 6,285 more people took the bus.
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The photographer picks up the camera and puts it in a different place
in the field. She points the camera at the tree and takes a photo of it.
Then she turns the camera clockwise to take a photo of the pond.
She turns the camera again to take a photo of the spider's web,
and turns it clockwise a third time to take a photo of the bird's nest.
Finally, she turns the camera clockwise again to point it back towards
the tree. She notices that each of the four times she turns the camera,
it turns through the same angle.
Where has the photographer put the camera in the field?
How many degrees does it turn between each pair of animal homes?
As a result, there is a 90° angle separating each couple of animal residences.
what is angle ?A geometric shape known as an angle is created by two rays that meet at a spot in the middle known as the vertex. The rays are typically depicted as a line section with an arrow pointing in the direction of the ray's extension on one end. When a complete circle is divided into 360 equal parts, each component being one degree, an angle is created that is measured in terms of degrees. The angle created when the radius of a circular equals the length of its arc is measured in radians.
given
A circle that includes the tree, pond, spider web, and bird's nest has been drawn by the photographer, with the camera in its middle. This is due to the fact that each time she rotates the camera anticlockwise, she is actually rotating it around the middle of this circle.
Call the angle between each set of animal residences "x" for simplicity. We can infer the following because the shooter always rotates the camera through the same angle:
Angle from pond to spider's web turned equals x Angle from tree to pond turned equals x
Angle from bird's nest to branch turned equals x
Since the photographer has made a full rotation, the total of these angles must be 360 degrees. Therefore:
x + x + x + x = 360
4x = 360
x = 90
As a result, there is a 90° angle separating each couple of animal residences.
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Decrease R450 in the ratio 9:8
The value of R500 decrease to ratio 9:8 is x = 400.
What is cross multiplication?By using the cross multiplication approach, the denominator of the first term is multiplied by the numerator of the second term, and vice versa. Using the mathematical rule of three, we may determine the answer based on proportions. The best illustration is cross multiplication, where we may write in a percentage to determine the values of unknown variables.
Given that, decrease R450 in the ratio 9:8.
Let 9 = 450
Then 8 will have the value = x.
That is,
9 = 450
8 = x
Using cross multiplication we have:
9x = 450(8)
x = 50(8)
x = 400
Hence, the value of R500 decrease to ratio 9:8 is x = 400.
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Given that x is a positive integer less than 100, how many solutions does the congruence x+13=55 (mod 34) have?
The congruence x + 13 ≡ 55 (mod 34) simplifies to x ≡ 12 (mod 34). There are three solutions for x less than 100 that satisfy this congruence.
The given congruence is x + 13 ≡ 55 (mod 34). Simplifying this, we get x ≡ 12 (mod 34).
We need to find the number of solutions for x that are less than 100 and satisfy this congruence.
The general solution for the congruence x ≡ 12 (mod 34) is x = 12 + 34k, where k is an integer.
The solutions that are less than 100 are obtained when k = 0, 1, or 2.
Thus, the number of solutions is 3.
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Evaluate the expression.
|-2| – |-1|
Answer:
1
Step-by-step explanation:
We must solve the absolute values first
An absolute value is the numbers distance from zero
So a simplified version of your problem would be
2-1
So your answer is 1
The absolute value of a number is its distance from 0, so |-2| is 2 and |-1| is 1. Substituting these back in, the expression 2 - 1 equals 1.
Explanation:To evaluate the expression |-2| – |-1|, you first need to understand what the absolute value symbol does. The absolute value of a number is its distance from 0 on the number line, regardless of direction. So, both |-2| and |-1| become positive numbers, as distance is always positive.
Therefore, |-2| equals 2 and |-1| equals 1. If we substitute these values back into the original expression, 2 - 1, the result is 1.
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Solve the equation
(down)
5+50
2/3/4/5/6
The value of x in the equation that is given as 2/3x + 4/5x = 6 will be 4.
How to calculate the equationBased on the information given, one should note that an equation has to do with the statement in a question which depicts the variables given. In this case, one should note in an equation, one will need to consider two or more components are to be able to illustrate the scenario.
In this case, it is important to note that an equation simply depicts the mathematical statement which can be made up of two expressions which are simply connected by an equal sign.
The equation is explained thus:
2/3x + 4/5x = 6
10/15x + 12/15x = 6
22/15x = 6
1.467x = 6
x = 6 / 1.467
x = 4
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Solve the equation
2/3x + 4/5x = 6
HELP ASAP WILL GIVE BRAINLYEST AND 100 POINTS
IF YOU DON"T TRY TO ANSWER THE QUESTION RIGHT I WILL REPORT YOU
Label the Standard Form, the Scientific Notation Form, the Coefficient, the Exponent, and the Base.
Answer:
45,000 is standard form.
4.5 is the coefficient.
4 of 10⁴ is the exponent.
7.6 × 10⁻⁴ is scientific notation.
10 of 10⁻⁴ is the base.
Step-by-step explanation:
Scientific notation is a way of writing very large or very small numbers in a compact and convenient form. It consists of two parts:
The coefficient: a number between 1 and 10.The exponent: an integer that indicates how many times 10 is multiplied by the coefficient.The base of scientific notation is always 10, which means that the number is written in terms of powers of 10.
For example, the number 4,000,000 can be written in scientific notation as 4 x 10⁶. In this case, the coefficient is 4, and the exponent is 6.
The standard form of a number is simply the usual way of writing it, without using scientific notation. For example, the standard form of 4 x 10⁶ is just 4,000,000.
Therefore, for the given problem:
45,000 is standard form.4.5 is the coefficient.4 of 10⁴ is the exponent.7.6 × 10⁻⁴ is scientific notation.10 of 10⁻⁴ is the base.calculate 20 1/3 -7 1/2
Answer: 77/6 or 12 5/6
Step-by-step explanation:
To solve this subtraction problem, we need to first convert the mixed numbers to improper fractions.
20 1/3 can be written as:
20 + 1/3 = 60/3 + 1/3 = 61/3
7 1/2 can be written as:
7 + 1/2 = 14/2 + 1/2 = 15/2
So, the problem becomes:
61/3 - 15/2
To subtract two fractions, we need to have a common denominator. The smallest number that both 3 and 2 divide into is 6. So we will convert both fractions to have a denominator of 6.
61/3 = (61/3) * (2/2) = 122/6
15/2 = (15/2) * (3/3) = 45/6
Now we can subtract the two fractions:
122/6 - 45/6 = 77/6
So, the final answer is:
20 1/3 - 7 1/2 = 77/6 or 12 5/6 (as a mixed number)
If 50% of a number is 170 and 80% of the same number is 272, find 30% of that number.
Answer:
30% of the number is 102.
The average cost of a lost laptop using information from various industries is $49,246. This average includes laptop replacement, data breach cost, lost productivity cost, and other legal and forensic costs. A separate study of 30 cases from the health care industry produced a mean of $67,873. Given these figures, is there sufficient evidence to support the claim that health care laptop replacement costs are higher in general? Use a .01 level of significance and a standard deviation of = $25,000. Perform your hypothesis testing using a one tail “P-value probability” concept.
Answer:
The claim that healthcare laptop replacement costs are higher than in other industries.
HELP ME ASAPPP!!! Ill mark you brasinlisest
Step-by-step explanation:
Theoretical probabilities can be calculated using the concept of probability. Each student has a 0.5 chance of selecting either List A or List B. Therefore, the probability of getting 27 heads and 33 tails can be calculated as:
P(27 heads and 33 tails) = (60 choose 27) * (0.5)^27 * (0.5)^33 where (60 choose 27) is the number of ways to select 27 students out of 60.
Using a calculator, we can compute the above probability as approximately 0.109. This means that if we were to repeat this experiment many times, we would expect to get 27 heads and 33 tails about 10.9% of the time.
Comparing this theoretical probability to the experimental results, we see that the observed proportion of heads (27/60 = 0.45) is lower than the expected proportion of heads (0.5) and the observed proportion of tails (33/60 = 0.55) is higher than the expected proportion of tails (0.5).
However, it is important to note that due to the random nature of the experiment, we would not expect the exact theoretical probabilities to match the experimental results exactly. In other words, there is always some amount of variation expected in the results. Nonetheless, the experimental results are consistent with the theoretical probabilities, and we can conclude that there is no significant deviation from what we would expect by chance.
1. The population of California was 10,586,223 in 1950 and 23,668,562 in 1980. Assume the population grows exponentially. a) Find an exponential function that models the population, P, in terms of t, the years after 1950. b) Use your model, to predict the population of California in 2020.
An exponential function can model California's population growth from 1950 to 1980. The predicted population in 2020 is around 43.3 million (43,301,300), assuming exponential growth.
To find an exponential function that models the population, we can use the formula:
P(t) = P0 * e^(rt)
where P0 is the initial population, r is the growth rate, and t is the time in years. We can use the information given to find P0, r, and then plug in t = 0 to find the exponential function.
P0 = 10,586,223 (initial population in 1950)
P(30) = 23,668,562 (population in 1980, 30 years later)
t = 30
P(0) = P0 * e^(0*r) = P0 (population in 1950)
So we have:
23,668,562 = 10,586,223 * e^(30r)
Dividing both sides by 10,586,223:
e^(30r) = 2.234
Taking the natural logarithm of both sides:
30r = ln(2.234)
r = ln(2.234)/30
Now we can use this value of r to find the exponential function:
P(t) = 10,586,223 * e^(t*ln(2.234)/30)
To predict the population in 2020, we can plug in t = 70 (since 2020 is 70 years after 1950) into the function we just found:
P(70) = 10,586,223 * e^(70*ln(2.234)/30) ≈ 43,301,300
Therefore, the predicted population of California in 2020 is approximately 43,301,300.
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Marcos had $60 in his savings account in January. He continued to add money to his account and by June, the value of the savings account had increased by 50%. How much money is in Marcos's account in June?
Answer: 90$
Step-by-step explanation: 50% of 60 is 30 so 60+30=90
Fred and George share some money. If Fred gets 3/11 of the money,in what ratio did they share it?
Answer:
Step-by-step explanation:
If they had $11: Fred gets $3, George gets $8.
So the ratio is: 3:8
PLS HELP FAST 20 POINTS + BRAINLIEST
Answer:
£22
Step-by-step explanation:
50% of 88=88/100 ×50=44
44÷2=25%=22
75% of £88 is deducted, so that 88-66=£22
Don't forget my BrainliestURGENT WILL MARK BRAINLIEST
The graph shown here is the graph of which of the following rational functions?
Answer:
The correct answer is B.
[tex]f(x) = \frac{1}{(x - 1)(x + 1)} [/tex]
The vertical asymptotes are at x = -1 and at x = 1.
she earned $480 in one week. If she worked 40 hours, how much did she earn per hour?
Answer:
12 dollars
Step-by-step explanation:
480 / 40 = 12
12 dollars
Carli is getting new carpet for her rectangular bedroom. Her room is 14 feet long and
10 feet wide.
If the carpet costs $2.50 per square foot, how much will it cost to carpet her room?
Therefore, it will cost $350 to carpet Carli's rectangular bedroom with carpet that costs $2.50 per square foot.
What is area?Area is a measure of the size of a two-dimensional surface or region. It is usually expressed in square units, such as square meters (m²) or square feet (ft²). To calculate the area of a shape, you need to multiply its length by its width or use an appropriate formula for the specific shape. The concept of area is important in many fields, including mathematics, geometry, physics, engineering, architecture, and more. It is used to quantify the space occupied by objects or regions, to determine the amount of material needed to cover a surface, or to calculate the amount of paint or wallpaper required to decorate a room, among other applications.
Given by the question.
The area of Carli's rectangular bedroom can be calculated by multiplying its length by its width:
Area = Length × Width
Area = 14 ft × 10 ft
Area = 140 sq ft
The cost of carpeting her room can be found by multiplying the area of the room by the cost per square foot of carpet:
Cost = Area × Cost per square foot
Cost = 140 sq ft × $2.50/sq ft
Cost = $350
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