Answer:
There is no mode for this set of numbers.
Step-by-step explanation:
The mode is the value that appears most frequently in a data set.
54,56,60,62,64,67,76,78
In this set of numbers no value appears more than once.
This means there is no mode for this set of data.
ok this is pretty easy but I need help and thank you.
The point that satisfies this inequalities y > -(1/3)x - 2 and y > 2x + 6 is (2, 15)
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
The slope intercept form of a linear equation is:
y = mx + b
Where m is the slope (rate of change) and b is the y intercept.
Given the linear inequalities:
y > -(1/3)x - 2 (1)
y > 2x + 6 (2)
Plotting both inequalities:
The point that satisfies this graph is (2, 15)
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Simplificar -3+{4-2[6-3+4(5-7)]+3
Answer:
14
Step-by-step explanation:
Para simplificar esta expresión, debemos seguir el orden de las operaciones, también conocido como PEMDAS: paréntesis, exponentes, multiplicación y división (de izquierda a derecha), y suma y resta (de izquierda a derecha).
1. Comience por simplificar la expresión dentro de los paréntesis.
4-2[6-3+4(5-7)]
4-2[6-3+4(-2)]
4-2[6-3-8]
4-2[-5]
4+10 = 14
2. Ahora sustituya el valor simplificado dentro de los paréntesis en la expresión original:
-3+{14}+3
3. Ahora podemos sumar y restar de izquierda a derecha.
-3+14+3 = 14
Entonces, la expresión simplificada es 14.
please solve and show how!
Answer:
x = 0 and x = 16
Step-by-step explanation:
You want the solution to √(2x+4) -√x = 2.
SolutionWe eliminate the radicals by squaring until there aren't any. After the first squaring, we have to separate the radical term from the others.
[tex]\sqrt{2x+4}-\sqrt{x}=2\\\\(2x+4)-2\sqrt{(2x+4)(x)}+(x)=4\qquad\text{square both sides}\\\\3x=2\sqrt{x(2x+4)}\qquad\text{add $\sqrt{x(2x+4)}-4$}\\\\9x^2=4(2x^2+4x)\qquad\text{square both sides}\\\\x^2-16x=0\qquad\text{subtract the right side from both sides}\\\\x(x -16) = 0\qquad\text{factor}[/tex]
Zero product ruleThe solutions to this are the values of x that make the factors zero. Those values are x=0 and x=16. Trying these in the original equation, we have ...
√(2·0 +4) -√0 = 2 -0 = 2 . . . . . . x=0 is a solution
√(2·16 +4) -√16 = 6 -4 = 2 . . . . . x=16 is a solution
The two solutions to the equation are x=0 and x=16.
Answer questions but the top being the following instead of image
Investment a: $3,000 invested for six years compounded, semi annually at 6%
Investment b: $4000 invested for four years compounded quarterly at 2.7%.
Answer:
B will get more $
Step-by-step explanation:
3000 annual rate 6% so half a year is 3%, compounding semiannually for 6 years = 12 times
so 3000*(1+3%)^12 =4277.28
$4000 invested for four years compounded quarterly at 2.7%. so every quater is 2.7%/4 =0.675%, compounding quarterly for 4 years = 16 times
so 4000*(1+0.675%)^16=4454.57
please answer a, b and c please! tysm
a) The increasing line y = 2x is plotted on the graph given at the end of the answer.
b) The horizontal line y = 3 is plotted on the graph given at the end of the answer.
c) The point of intersection of the two graphs is given as follows: (1.5, 3).
How to plot the graph of the functions?The increasing line is given as follows:
y = 2x.
Hence we plot a few points of coordinate (x,y), from the numeric values of the function, and connect them through a line.
The numeric values of the function are given as follows:
x = -2: y = 2(-2) = -4.x = -1: y = 2(-1) = -2.x = 0: y = 2(0) = 0.x = 1: y = 2(1) = 2.x = 2: y = 2(2) = 4.x = 3: y = 2(3) = 6.The horizontal line is given as follows:
y = 3.
Meaning that a single horizontal line through y = 3 is traced, for which we are going to use the same domain as the increasing line.
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A jailer carries a large key ring. The key ring has a diameter of 4 inches. What is the key ring's radius?
Answer:
2 inches
Step-by-step explanation:
The radius is simply the distance from the edge if you were at the center, which is equal to half the diameter. So given the diameter is 4 inches, we divide that by two, [tex]\frac{4\text{ inches}}{2}=2\text{ inches}[/tex] and that's our radius!
a popular theater has had 399,867,231 visitors since it opened. Which number, written in scientific notation, is the best approximation of the number of visitors
Answer:
4 x [tex]10^{8}[/tex]
Step-by-step explanation:
Round the number to
400,000,000
4 x [tex]10^{8}[/tex]
We moved the decimal 8 places.
Answer:
4 x 10^8 (four times ten to the power of eight) is the best approximation of the number 399,867,231 written in scientific notation.
Step-by-step explanation:
Can someone help me with this word problem? The answer is supposed to be 3 in. but I don't know how to get there.
The border should be 6 inches wide.
What is area?The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.
Given that, A picture is to be put on a poster board that is 18 in. by 22 in. there is to be an even amount of poster board around the picture, the area of the picture is 192 in.²
Let the marginal space left is x in
Therefore,
(18-x)(22-x) = 192
396 -18x - 22x + x² = 192
x² - 40x + 204 = 0
Factorizing the expression, we get,
x = 34 or x = 6
(Note :- Neglecting 34 because 34 is grater than the dimensions given)
Therefore, the marginal space is 6 inches.
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D The point-slope form of the equation of a straight line is y + 3 = −2/7 (x − 5) . What is the general form of the equation?
Answer:
Step-by-step explanation:
The general form of the equation for the line described by the point-slope form y + 3 = −2/7 (x − 5) is y = -2/7x + 19/7.
One serving of trail mix has 69 grams of carbohydrates, which is 22% of the recommended daily amount. What is the total recommended daily amount of carbohydrates in grams? (Round your answer to one decimal place.)
Answer:
We can use the equation:
amount of a given nutrient / % of recommended daily amount = recommended daily amount
Here, we know that 69 grams of carbohydrates is 22% of the recommended daily amount, so we can plug in the given values and solve for the recommended daily amount:
69 / 0.22 = Recommended Daily Amount
Recommended Daily Amount = 69 / 0.22 = 313.64 grams (rounded to one decimal place)
So, the total recommended daily amount of carbohydrates in grams is 313.6 grams.
The gate code at your apartment complex is three numerical digits followed by the "#" sign. If each code
contains non-repeating digits, how many possible gate codes does your apartment complex have?
There are 720 possible gate codes your apartment complex have.
What is algebra?The subject matter of the math discipline of algebra is symbols and the arithmetic operations performed on them. Variable describes these symbols because they don't have any fixed values. We frequently notice values that are in constant flux in our day-to-day problems.
To represent these shifting values, however, is always necessary. These values are frequently represented in algebra with symbols like x, y, z, p, or q; these symbols are referred to as variables.
The gate code at your apartment complex is three numerical digits followed by # sign.
There are 10 digits (0 to 9).
Compute the number of possible gate codes if each code contains non-repeating digits as follows.
The first 3 place in the code must be filled by three non-repeating digits.
So, there are 10 possibilities for the first digit, 9 possibilities for the second digit and 8 possibilities for the third digit.
Hence, the three non-repeating digits can occur in 10×9×8 ways.
The three non-repeating digits are followed by "#" sign. The sign # can occur in only one way.
Combine the above results and obtain the number of possible gate codes as,
10×9×8×1=720
Thus, there are 720 possible gate codes.
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For how many years would $1,000 need to be invested at a 1% annual Interest rate to have an invest-
ment with a Future Value of $2,000?
Answer:
To find out how many years it would take to double an initial investment with a 1% annual interest rate, you can use the rule of 72. The rule of 72 states that you can divide 72 by the annual interest rate to find out how many years it would take to double an investment.
In this case, you would divide 72 by 1 to get 72 years. Therefore, it would take 72 years for an investment of $1,000 at a 1% annual interest rate to have a future value of $2,000.
in an exam 11 student got the following marks. find the median and no of students above and below the median 60,64,95,99,65,70,72,80,85,90,75
The precise middle value of a data set when it is ordered is called the median.Consequently, 7 is the needed median for the specified data set.
What is the median?The precise middle value of a data set when it is ordered is called the median.Separating the lowest 50% of data from the top 50% of values is a measure of central tendency.If you have an odd or even number of data points, the processes for calculating the median will be different.
The exact middle value in an ordered data set is known as the median.It is a metric of central tendency that separates the bottom and top half of the data.
Sort the provided data set into the following order: 1, 4, 5, 7, 8, 9, 15, and 16.
Eight terms total, all even.
The data set's median is equal to the nth term, the eighth term, and the fourth term. = 7
Consequently, 7 is the needed median for the specified data set.
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Alton shoveled snow on 5/6 of his driveway before lunch. Then he shoveled 2/7 of it after lunch. How much more of his driveway did Alton shovel before lunch than after lunch?
The required difference is equal to 25x/42
What is a fraction in math?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
Given here: Alton shoveled snow on 5/6 of his driveway before lunch. Then he shoveled 2/7 of it after lunch.
Let the total snow quantity be x then we have
Before lunch as = 5/6×x
=5x/6
After lunch = 5x/6 × 2/7
=5x/21
∴ Difference = 5x/6 - 5x/21
=35x-10x / 42
= 25x/42
Hence, The required difference is equal to 25x/42
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if the radius of the circle below is 9m find the approximate area of the shaded region
The approximate area of the shaded region of the circle is 191 metres squared.
How to find the area of a region in a circle?The radius of the circle below is given as 9 metres. The approximate area of the shaded region of the circle can be found as follows:
area of the shaded region = area of the circle - area of the sector uncoloured
Therefore,
area of the circle = πr²
where
r = radiusTherefore,
area of the circle = π × 9²
area of the circle = 81π m²
Hence,
area of the sector uncoloured = ∅ / 360 × πr²
where
∅ = central angler = radiusTherefore,
area of the sector uncoloured = 90 / 360 × π × 9²
area of the sector uncoloured = 1 / 4 × π × 81
area of the sector uncoloured = 81 / 4 π
Hence,
area of the shaded region = 81π - 20.25π
area of the shaded region = 60.75π
area of the shaded region = 190.755
area of the shaded region = 191 m²
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Assuming that there are 95 million workers in the labor force in 2030 and 55 million retirees drawing Social Security, how many workers will be paying in per retiree at that time? Round to 2 decimal places.
However, the recent 2022 Social Security Trustees report finds that in 2034, retirees will start receiving a reduced benefit if Congress doesn't fix funding issues for the social program. In other words, Social Security will exist after 2034, but retirees will only receive 77% of their full benefit starting then.
What is Social Security?Social Security has provided financial protection for our nation's people for over 80 years. Chances are, you either receive Social Security benefits or know someone who does. With retirement, disability, and survivors benefits, Social Security is one of the most successful anti-poverty programs in our nation's history.We are passionate about supporting our customers by delivering financial support, providing superior customer service, and ensuring the safety and security of your information — helping you secure today and tomorrow.Social Security is committed to helping maintain the basic well-being and protection of the people we serve. We pay benefits to about 64 million people including retirees, children, widows, and widowers. From birth, to marriage, and into retirement, we are there to provide support throughout life's journey.To learn more about Social Security refer to:
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QUESTION: AOB is a right isosceles triangle of vertex O. [OH] is the altitude relative to [AB]. P is the symmetric of H with respect to (OA).
Prove that OHAP is a square.
×i have did half of the question i still the other half, how to proof HA=PA so i xan prove it as a rhombus then to a square.PLEASE HELP I NEEEED ITT NOWWW!
Answer:
Step-by-step explanation:
To prove that OHAP is a square, we need to show that all four sides are congruent and all four angles are right angles.
Since AOB is a right isosceles triangle, we know that angle OAB and angle OBA are both congruent to 90 degrees, which means that they are both right angles. Since [OH] is the altitude relative to [AB], it bisects angle OAB, which means that angle AOH and angle HOA are both congruent to 45 degrees. Since P is the symmetric of H with respect to OA, we know that OA is congruent to OP, and we also know that OH is congruent to OP. Therefore, all four sides of OHAP are congruent, which means that OHAP is a square.
In the late afternoon, Tessa is standing next to an old maple tree in her backyard. Tessa's shadow is 2' 3" long, and the maple tree's shadow is 18' long. Tessa is 5' 8" tall.
How tall is the maple tree?
15ft
Step-by-step explanation:
bc I said so..............
are the two triangles below similar? If so, write a similarity statement in state which similarity criteria can be used to prove it?
A. Similarity Statement
1. ABC DEF
2. ABC FDE
3. ABC EFD
4. The triangles are not similar
B. Criteria
1. AA
2. SAS
3. SSS
4. Not applicable, the triangles are not similar
The triangles are similar as follows:
ABC ~ DEF
The criteria is AA(angle angle)
How to find similar triangles?Similar triangles are the triangles that have corresponding sides as a ratio of each other and corresponding angles congruent to each other.
Therefore, the corresponding angles of the triangles are suppose to be congruent and the corresponding sides in proportion for it to be similar.
Hence, If two triangles have two of their angles equal, the triangles are similar by AA(angle angle).
Therefore, the triangles are similar by AA.
Triangle ABC is similar to triangle DEF.
The criteria for the similarity is AA.
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ES = ___ units
Round your answer to the nearest tenth.
ES = 10.63 units
How to find the length of the line ?The length of the line segment connecting any two points represents the distance between them. There is just one line that connects the two places. Therefore, by measuring the length of the line segment that connects the two sites, the distance between them may be determined.
When given a straight line on a graph, you can find the length of this line by using the Distance Between Two Points Formula. This formula uses the vertices of the beginning and ending points of a straight line to find the length of the line, which is the distance between the two points.
The Distance Between Two Points Formula is:
= √(( x₂ – x₁ )² + ( y₂ – y₁) ²)
The vertices of the line ES are E ( -3, -4 ) and S ( 4, 4 ).
The distance is:
= √(( 4 – (-3) )² + ( 4 ( - 4 )) ²)
= 10. 63 units
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One aircraft has a capacity of 64 more seats than a second
aircraft. A third aircraft has 152 seats less than twice the seating
capacity of the second aircraft. If their total number of seats is
1900, find the number of seats for each aircraft.
Using the provided conditions and values, This is solved with the concept of word problem, The answer is first, second and third aircrafts have 576,512 and 864 seats.
What is word problem?A word problem in mathematics is a problem that is written in natural language (i.e., words) rather than in mathematical notation. It presents a real-world scenario that requires the use of mathematical concepts and skills to solve. Word problems often involve finding unknown quantities based on given information, and they can be challenging because they require students to understand the problem and translate it into mathematical equations or formulas. They are often used in primary and secondary education to help students apply their math skills to real-world situations and develop critical thinking skills.
What do you mean by mathematical expression?A mathematical expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that represents a mathematical statement or equation. Mathematical expressions can be evaluated to find a numerical value. They can also be simplified by applying the order of operations (PEMDAS) to combine like terms or to remove unnecessary parentheses. Additionally, mathematical expressions can also be used to represent the relationship between different variables.
Let x be the number of seats on the second aircraft. Then, the first aircraft has x+64 seats and the third aircraft has 2x-152 seats.
We know that the total number of seats for all three aircraft is 1900, so we can set up the following equation:
x + (x+64) + (2x-152) = 1900
Solving this equation gives us x = 512, which means the second aircraft has 512 seats. We can then use this information to find the number of seats for the other two aircraft:
First aircraft: 512 + 64 = 576 seats
Third aircraft: 2(512) - 152 = 864 seats.
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its math's question pleases help me to solve
The domain of the composite function f(g(x)) is equal to (x - 2)/(4 + 4x).
What is composite functionA function is composite when the co- domain of the first mapping is the domain of the second mapping
We shall evaluate the domain of the function f(g(x)) as follows:
f(g(x)) = 1 ÷ 12/[(x - 2) + 4]
f(g(x)) = 1 ÷ [12 + 4(x - 2)]/(x - 2) {simplify the denominator to a single fraction}
f(g(x)) = 1 ÷ (12 + 4x - 8)/(x - 2) {open bracket for 4(x - 2)}
f(g(x)) = 1 ÷ (4 + 4x)/(x - 2) {simply like terms}
f(g(x)) = 1 × (x - 2)/(4 + 4x) {changing division to multiplication}
f(g(x)) = (x - 2)/(4 + 4x)
Therefore, the result (x - 2)/(4 + 4x) is the domain of the composite function f(g(x)).
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Hi please help me with this project I really need help I!!!!
6. The measure of angle BEC is 48°
7. The measure of angle 1 is 41°
8. The value of x is 12
The measure of angle UST is 36°
6. The angles AEB and BEC form a straight line whose angle measure is 180°.
So that,
∠AEB + ∠BEC = 180°
132° + ∠BEC = 180°
∠BEC = 180° - 132°
∠BEC = 48°
7. The angles 1 and 5 form a right angle whose measure is 90°.
So that,
∠5 + ∠1 = 90°
49° + ∠1 = 90°
∠1 = 90° - 49°
∠1 = 41°
8. The angles RSU and UST form a right angle whose measure is 90°.
∠RSU + ∠UST = 90°
(5x - 6)° + (2x + 12)° = 90°
(7x + 6)° = 90°
7x° = (90 - 6)°
7x° = 84°
x = 12
∠UST = (2x + 12)°
∠UST = (2(12) + 12)°
∠UST = (24 + 12)°
∠UST = 36°
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Find the unit rate of the price per apple.
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below.
[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{0}}} \implies \cfrac{4 }{ 5 }\implies \cfrac{\$ 4}{5~apples}\implies \cfrac{0.8}{1}~\cfrac{\$}{apples}~\hfill \textit{80 cents per apple}[/tex]
Which of the following is equivalent to cosine of 2 times x over the quantity cosine of x end quantity question mark
cos x − (sin x)(tan x)
2 times sine of x minus the quantity 2 over cotangent of x end quantity
2cos x − sec x
I only
I and II
I and III
I, II, and III
The trigonometric identities equivalent to cos(2·x)/cos(x) are;
cos(x) - (sin(x))/(tan (x))
2·cos(x) - sec(x)
What are trigonometric identities?Trigonometric identities are equations of trigonometric functions that are correct for the values of the input and output variables in the equations.
The trigonometric identity for cos(2·x) is specified as follows;
cos(2·x) = cos²x - sin²x
Therefore;
cos(2·x)/(cos(x)) = (cos²x - sin²x)/(cos(x))
(cos²x)/(cos(x)) = cos(x)
sin²(x)/(cos(x) = sin(x) × sin(x)/(cos(x)) = sin(x)·tan(x)
(cos²x - sin²x)/(cos(x)) = (cos²x)/(cos(x)) - sin²(x)/(cos(x)
(cos²x)/(cos(x)) - sin²(x)/(cos(x) = cos(x) - sin(x)·tan(x)
cos(2·x)/(cos(x)) = cos(x) - sin(x)·tan(x)cos(2·x) = 2·cos²x - 1
Therefore; cos(2·x)/cos(x) = (2·cos²x - 1)/cos(x)
(2·cos²x - 1)/cos(x) = 2·cos(x) - 1/cos(x)
2·cos(x) - 1/cos(x) = 2·cos(x) - sec(x)
cos(2·x)/cos(x) = 2·cos(x) - sec(x)cos(2·x) = 1 - 2·sin²x
cos(2·x)/cos(x) = (1 - 2·sin²x)/cos(x)
(1 - 2·sin²x)/cos(x) = sec(x) - 2·sin(x)
The expressions equivalent to cos(2·x)/cos(x) are therefore;
cos x - (sin x)·(tan x) and 2·cos x - sec x, which are I and III
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A doctor is administrating medicine to a patient and needs to adjust the dosage based on the patients weight. The number of teaspoons of medicine t that a person of a certain weight w, in pounds, should take is approximated by the equation t=3+0.05w. Which of the following is the appropriate dosage of medicine, in ounces, for the doctor to administer to a 180 lb person?
Answer: The appropriate dosage of medicine for a 180 Ib person is 12 ounces.
Step-by-step explanation:
From the word problem, we know that:
t = number of teaspoons of medicinew = the weight of the personequation: t= 3 + 0.05wThe person weighs 180 lbSince we are given w (the amount the person weighs is 180 Ib), we can plug the value into the equation to solve for t.
t= 3 + 0.05 (180)
t = 3 + 9
t = 12
So the appropriate dosage of medicine for a 180 Ib person is 12 ounces.
Use elimination to solve
2x+y=-3
-6x-3y=-2
Answer: There is no solution for these equations.
Explanation: This equation system is not solvable. Because we cannot eliminate x or y while holding one of them in the equation.
A car dealership pays a wholesale price of $14,000 to purchase a vehicle. They sell the car for $16,100.
Answer:
15%
Step-by-step explanation:
markup = 16100 - 14000 = 2100
percent markup = 2100/14000 × 199% = 15%
Answer: The percent markup is 15%.
7) Yesterday, Cindy re-posted a meme on social media and tagged 3 of her friends. Today, each
of her 3 friends re-posts the meme and tags 3 of their friends. This pattern of re-posting and
tagging 3 friends continues for several days. How many people have re-posted the meme
after 8 days? (Hint: If this is geometric, you should write a formula to help answer the
question)
The people that have posted the meme after 8 days using the exponential equation y=t^3 will be 512.
What are Exponential Equations?
An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable. For example, 3^x = 81, 5^x - 3 = 625, 62^y - 7 = 121, etc are some examples of exponential equations. We may come across the use of exponential equations when we are solving the problems of algebra, compound interest, exponential growth, exponential decay, etc.
Now,
To find number of people who have re-posted
we need to make a exponential equation
Here, As cindy tags meme to 3 people in starting and they also tag 3 people in subsequent days, then equation will be y=t^3 where t=no of days.
No of people after 8 days,
y=8^3
y=512 (no of people after 8 days)
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This is an example of geometric growth, So after 8 days 6561 people will have re-posted the meme.
What is geometric growth and explanation of above answer? Geometric growth is a type of exponential growth where a quantity increases at a fixed rate multiplied by itself over time. It is represented by a geometric sequence, where each term is the previous term multiplied by a constant factor. It is commonly used to model population growth, compound interest, and viral spread of information.where each day the number of people who have re-posted the meme is multiplied by 3. The formula to calculate the total number of people who have re-posted the meme after 8 days is 3^8 = 6561 peopleTo learn more about geometric growth refer:
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How would yo do this problem? Could it be done a ti-84 calculator?
Answer:
71
Step-by-step explanation:
the circle standard form is
(x - h)² + (y - k)² = r²
r being the radius, (h, k) being the coordinates of the center.
fully multiplied that is
x² - 2hx + h² + y² - 2ky + k² = r²
we have here
4x² + 12x + 4y² - 40y - B = 0
our first step is to bring this back to an excision in x² and y². so, we divide everything by 4.
x² + 3x + y² - 10y - B/4 = 0
by comparing this to the general equation we see
3 = -2h
h = -3/2 = -1.5
-10 = - 2k
k = 5
-B/4 = h² + k² - r² = 9/4 + 25 - (3×sqrt(5))² =
= 9/4 + 25 - 9×5 = 9/4 + 25 - 45 = 9/4 - 20
-B = 9 - 80 = -71
B = 71
