Answer:
26 blocks
Step-by-step explanation:
To determine the number of blocks Tommy walked, you will calculate the distances between each of his points (ordered pairs).
Using the distance formula i.e\(\sqrt{(c-a)^2+(d-b)^2}\)
(0,0) to (0,6) is : \(\sqrt{(0-0)^2+(6-0)^2}\) = 6 blocks
(0,6) to (7,6) is: \(\sqrt{(7-0)^2+(6-6)^2}\)= 7 blocks
(7,6) to (7,0) is: \(\sqrt{(7-7)^2+(0-6)^2}\) = 6 blocks
(7,0) to (0,0) is: \(\sqrt{(0-7)^2+(0-0)^2}\) = 7 blocks, back home
This totals 26 blocks that Tommy walked.
Write an equivalent ratio described in the situation below. The ratio of boys to girls is 5/2
Answer:
5: 2 or 10: 4
Step-by-step explanation:
as a ratio, this would be 5: 2.
Im not sure if it's asking you to also make a new ratio that fits this, but if it is you could multiply both sides by 2 to get
10 : 4
the lpga conducts a study in which they use a simple random sample of 900 golfers. they examine the data from the sample and calculate that 37% of them own golf clubs made in the usa. the 37% is the . group of answer choices confidence level population parameter sample statistic confidence interval
The correct option is "sample statistic." A sample statistic is a numerical summary of a sample. In this case, the sample statistic is the percentage of golfers in the sample who own golf clubs made in the USA, which is 37%.
The population parameter is the true value of a characteristic of the entire population, which is often unknown and estimated based on the sample data. In this case, the population parameter would be the percentage of all golfers who own golf clubs made in the USA, which we do not know based on the information given.
A confidence level is a measure of the uncertainty associated with statistical inference, such as a confidence interval. It is often expressed as a percentage, such as 95% or 99%. However, no confidence level is mentioned in the question.
A confidence interval is a range of values that is likely to contain the true value of a population parameter, based on the sample data and a specified level of confidence. Again, no confidence interval is mentioned in the question.
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Let P(t) be the population (in millions) of a certain city t years after 2015 , and suppose that P(t) satisfies the differential equation P ′(t)=0.06P(t),P(0)=3. (a) Use the differential equation to determine how fast the population is growing when it reaches 5 million people. (b) Use the differential equation to determine the population size when it is growing at a rate of 700,000 people per year. (c) Find a formula for P(t).
(a) To determine how fast the population is growing when it reaches 5 million people, we can substitute P(t) = 5 into the differential equation P'(t) = 0.06P(t). This gives us P'(t) = 0.06(5) = 0.3 million people per year. Therefore, the population is growing at a rate of 0.3 million people per year when it reaches 5 million people.
(b) To determine the population size when it is growing at a rate of 700,000 people per year, we can set P'(t) = 700,000 and solve for P(t). From the given differential equation, we have 0.06P(t) = 700,000, which implies P(t) = 700,000/0.06 = 11,666,666.67 million people. Therefore, the population size is approximately 11.67 million people when it is growing at a rate of 700,000 people per year.
(c) To find a formula for P(t), we can solve the differential equation P'(t) = 0.06P(t). This is a separable differential equation, and integrating both sides gives us ln(P(t)) = 0.06t + C, where C is the constant of integration. By exponentiating both sides, we get P(t) = e^(0.06t+C). Using the initial condition P(0) = 3, we can find the value of C. Substituting t = 0 and P(0) = 3 into the equation, we have 3 = e^C. Therefore, the formula for P(t) is P(t) = 3e^(0.06t).
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in person 1 can do a task in x hours and person 2 can do a task in y hours how many hours will it take to complete the same task together equation
the time it would take for person 1 and person 2 to complete the task together is 2xy / (x + y) hours
If person 1 can do a task in x hours and person 2 can do the same task in y hours, then the combined rate at which they can complete the task is:
rate = 1/x + 1/y
This is because each person's rate of completing the task is the reciprocal of their time to complete the task, and their combined rate is the sum of their individual rates.
To find the time it would take for both persons to complete the task working together, we can use the formula:
time = 1 / rate
Substituting the expression for the rate above, we get:
time = 1 / (1/x + 1/y)
Simplifying this expression, we can use the formula for the harmonic mean of two numbers:
time = 2xy / (x + y)
Therefore, the time it would take for person 1 and person 2 to complete the task together is 2xy / (x + y) hours
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Use completing the square to determine which of the following gives the solutions to 3x2 - 24x + 40 = 28.
A 2+413
O B. 4+2√3
o C. 37312
D. 6+2/5
Answer:
\(x=4+2\sqrt{3}\)
\(x=4-2\sqrt{3}\)
Step-by-step explanation:
Completing the square
when \(ax^2+bx+c=0\)
Given equation:
\(3x^2-24x+40=28\)
Subtract 40 from both sides:
\(\implies 3x^2-24x=-12\)
Divide both sides by 3:
\(\implies x^2-8x=-4\)
Add the square of half the coefficient of \(x\) to both sides:
\((\frac{b}{2})^2=(\frac{-8}{2})^2=16\)
\(\implies x^2-8x+16=-4+16\)
Factor the left side and simplify the right side:
\(\implies (x-4)^2=12\)
Square root both sides:
\(\implies x-4=\pm\sqrt{12}\)
Add 4 to both sides and simplify the radical:
\(\implies x=4\pm\sqrt{4 \cdot 3}\)
\(\implies x=4\pm\sqrt{4}\sqrt{3}\)
\(\implies x=4\pm2\sqrt{3}\)
Can someone help me with the questions in the picture?
Answer:
25) B obtuse scalene
26) A acute isosceles
27) A acute isosceles
28) D obtuse isosceles
29) D right scalene
30) C obtuse isosceles
31) C obtuse scalene
32) C acute scalene
Step-by-step explanation:
A scalene triangle has sides of no equal measures (no side has the same length as another). An isosceles triangle has two sides of the same length. An equilateral triangle has three sides that all have the same lengths.
An acute triangle has all three angles that each measure less than 90°. An obtuse triangle has one angle that measures greater than 90°. A right angle has one angle that measures exactly 90°.
Hope this helps :)
A password consists of 3 digits (0 - 9) followed by two letters (a-z or A-Z; note: 26 letters in the alphabet). i) How many different passwords are possible if repetition of digits and letters is allowed and passwords are not case sensitive (so 123AB is the same as 123aB)? ii) How many different passwords are possible if repetition of digits and letters is not allowed and the passwords are case-sensitive? (s0 123AB is different from 123aB)? b) A 4-student committee is to be randomly selected from a pool of 5 Biology Majors, 10 Math Majors and 5 Music Majors. 1) What is the probability that all 4 randomly selected students were Math Majors? (State your answer as a reduced fraction OR a decimal rounded to 3 places) ii) Suppose now that the 4 student committee needs to have exactly two math majors. How many different pairs of math majors could be chosen.
a. i. There are 27,040,000 different passwords are possible if repetition of digits and letters is allowed and passwords are not case sensitive (so 123AB is the same as 123aB)
ii. There will be 99,532,800 different passwords are possible if repetition of digits and letters is not allowed and the passwords are case-sensitive
b. i. The probability that all 4 randomly selected students were math majors is 0.520
ii. There are 4,725 different pairs of math majors that could be chosen for the committee.
a. i) There are 10 choices for each of the first 3 digits, and 26 choices for each of the last 2 letters. Since the password is not case sensitive, we can choose either uppercase or lowercase letters, so there are 26 + 26 = 52 choices in total for each letter. Therefore, the total number of different passwords is:
10 x 10 x 10 x 52 x 52 = 27,040,000
ii) There are 10 choices for the first digit, 9 choices for the second digit (since we can't repeat the first digit), 8 choices for the third digit (since we can't repeat the first two digits), and 52 choices for the first letter. For the second letter, there are 51 choices left (since we can't repeat the first letter), but we need to distinguish between uppercase and lowercase letters, so there are 52 x 51 = 2,652 choices for the two letters in total. Therefore, the total number of different passwords is:
10 x 9 x 8 x 52 x 2,652 = 99,532,800
b) i) The total number of ways to select a 4-student committee from 20 students is:
20 choose 4 = 4,845
The number of ways to select a committee consisting of 4 math majors is:
10 choose 4 = 2,520
Therefore, the probability that all 4 randomly selected students were math majors is:
2,520 / 4,845 = 0.520
ii) The number of ways to select a 4-student committee with exactly two math majors is:
(10 choose 2) x (10 choose 2) x (15 choose 0) = 4,725
(We choose 2 math majors from 10, and 2 non-math majors from 15, since there are 5 biology majors and 5 music majors to choose from.)
Therefore, there are 4,725 different pairs of math majors that could be chosen for the committee.
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Numbers 100 to 125 are written on separate slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking in to it. What is the probability of getting a) A number 108? B) a number less than 107 c) A number greater than 120?
Step-by-step explanation:
The numbers are given as;
100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125
What is the probability of getting;
a) A number 108?
Probability = Number of favorable outcomes / Total number of outcomes
Number of favourable outcome = 1
Total number of outcomes = 26
Probability = 1 / 26
B) a number less than 107
Probability = Number of favorable outcomes / Total number of outcomes
Number of favourable outcome = 100, 101, 102, 103, 104, 105, 106 = 7
Total number of outcomes = 26
Probability = 7 / 26
c) A number greater than 120
Probability = Number of favorable outcomes / Total number of outcomes
Number of favourable outcome = 121, 122, 123, 124, 125 = 5
Total number of outcomes = 26
Probability = 5 / 26
slove for n:(3 over 5 to the power of 2 ×25=3 n
Answer:
n = 2
Step-by-step explanation:
Given equation:
\(\left(\dfrac35\right)^2 \times 25=3^n\)
\(\textsf{Apply exponent rule }\left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c} :\)
\(\implies \left(\dfrac{3^2}{5^2}\right) \times 25=3^n\)
\(\textsf{Apply}\: \left(\dfrac{a}{b}\right) \times c=\dfrac{ac}{b} :\)
\(\implies \dfrac{3^2\cdot 25}{5^2}=3^n\)
\(\textsf{Apply}\:5^2=5 \times 5=25:\)
\(\implies \dfrac{3^2\cdot 25}{25}=3^n\)
Cancel the common factor 25:
\(\implies 3^2=3^n\)
\(\textsf{If}\:a^{f(x)}=a^{g(x)},\:\textsf{then}\:f(x)=g(x) :\)
\(\implies 2=n\)
Answer:
n = 2
Step-by-step explanation:
Hello!
Step 1: Expand the fractionWe can use the exponent rule to square 3/5.
(\(\frac35\))² = \(\frac{3^2}{5^2}\)\(\frac{9}{25}\)Step 2: SimplifyNow, we can multiply
\(\frac{9}{25} * 25 = 3^n\)\(9 = 3^n\)Now, we need to find how many times 3 is multiplied to get 9 ,and that would be 2
Dakota went on a bike ride of 60 miles. He realized that if he had gone 12 mph faster, he would have arrived 16 hours sooner. How fast did he actually ride
Dakota rode his bike for 60 km. He understood that he could have been there 16 hours earlier if he had traveled 12 mph quicker. Dakota's actual speed during the bike ride was approximately 41.8 mph.
Let's assume that Dakota's actual speed during the bike ride was x miles per hour.
Using the distance formula:
distance = speed x time
We can calculate the time it took Dakota to complete the ride at his actual speed as:
60 = x * t
where t is the time in hours.
Now, according to the problem, if he had gone 12 mph faster, he would have arrived 16 hours sooner. This means that he would have covered the same distance in less time.
So we can set up another equation:
60 = (x + 12) * (t - 16)
Simplifying this equation:
60 = xt - 16x + 12t - 192
76 = xt - 16x + 12t
Substituting the value of t from the first equation, we get:
76 = 60 - 16x + 12(60/x)
Simplifying this equation:
\(16x^2 - 720x + 7200 = 0\)
Dividing both sides by 16:
\(x^2 - 45x + 450 = 0\)
Solving this quadratic equation using the quadratic formula:
\($x = \frac{45 \pm \sqrt{45^2 - 41450}}{2}$\)
\($x = 22.5 \pm 7.5\sqrt{5}$\)
We can reject the negative root because it doesn't make sense in the context of the problem.
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Which property is illustrated?
x=y so 4x=4y
A) Associative property of multiplication
B) Distributive property of equality
C) Symmetric property of equality
D) Multiplication property of equality
E) Commutative property of multiplication
Answer: Commutative Property of multiplication
Step-by-step explanation:
The property illustrated in the given statement "x=y so 4x=4y" is: Multiplication property of equality. Correct option is D.
The Multiplication Property of Equality states that if you have an equation, and you multiply both sides of the equation by the same non-zero number, the resulting equation remains true.
In the given statement "x=y," it means that x and y are equal. Now, if you multiply both sides of this equation by the non-zero number 4, you get:
4x = 4y
The relationship between x and y hasn't changed because you're multiplying both sides of the equation by the same number (4). This is a direct application of the Multiplication Property of Equality. It maintains the equality between the quantities involved.
So, the statement "x=y so 4x=4y" illustrates the Multiplication Property of Equality because it shows that if two quantities are equal (x=y), then multiplying both sides by the same non-zero number (4) preserves that equality (4x=4y).
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what is the coefficient in the expression? 7x+56
Answer:
7
Step-by-step explanation:
Coefficient is the number that comes before x
That's why 7 is the answer
Using the .01 level of significance means that, in the long run, 1) a Type I error occurs 1 time in 100. O2) a Type I error occurs 1 time in 20. 3) a Type II error occurs 1 time in 20. 4) a Type II error occurs 1 time in 100.
Using the .01 level of significance means that, in the long run, a Type I error occurs 1 time in 100. This means that if we perform a statistical test 100 times, and we set the level of significance at .01, then we can expect to observe one false positive result due to chance alone. So, the correct option is 1).
A Type I error occurs when we reject a true null hypothesis, or when we conclude that there is a significant difference or relationship between two variables when in fact there is not.
By setting the level of significance at .01, we are minimizing the risk of making a Type I error while increasing the risk of making a Type II error, which occurs when we fail to reject a false null hypothesis. So, the correct answer is 1).
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what is the process of displaying large quantities of data in a meaningful way called?
The process of displaying the large quantities of data in a meaningful way is called Data Visualization .
The Data Visulalization involves presenting data in a graphical or pictorial format to help people understand and analyze the data more easily.
The goal of data visualization is to make complex data sets more accessible, understandable, and actionable by presenting them in a clear and visually appealing way.
The Common types of data visualization include bar charts, line graphs, scatter plots, heat maps, and infographics, among others.
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Please help me with question
Answer:
Yes, you are right.
Step-by-step explanation:
RS = 20
UT = 20
UT also = x + 10
x = 20 - 10
x = 10
So, yes, you are right.
Hope that helps!
3. A florist sells large floral arrangements for $50 each. Small floral arrangements sell for $15 each. Jenna is buying 2 large floral arrangements and x small floral arrangements. Let y represent the total cost Jenna must pay in dollars.
(a) Write an equation in slope-intercept form to model this description.
(b) What is Jenna’s total cost given she purchases 4 small floral arrangements? Show your work.
Answer:
a y=(15)x+100
b y =(15) (4) +100 y =160
Step-by-step explanation:
y = mx + b
large arrangment cost $50
$50 x 2 = 100
b=100
x = the number of small arrangments that jenna is buying .in this case 4 so
x= 4
m is the cost of one small arranment so
m=15
y represents the total cost jenna pust may in dollars so you would do
15 x 4 =60 50x2=100 100 +60 = 160
giving y = 160
Is the product of 12 and 3/4 more or less than 12? Explain your answer in complete sentences.
PLEASE HELP
Answer:
en español por favor por qué no se inglés
Here is a diagram of a person standing next to a lorry.
The diagram shows two centimetre rulers.
The person and the lorry are drawn to the same scale.
The lorry is approximately 9 m in length.
Using the scale diagram, estimate the height of the person in metres.
In light of our responses to the presented questions, using equations, we can deduce that the person's estimated height is 0.0225 meters, or 2.25 centimeters.
What is equation?A mathematical equation is a sentence that suggests that other equations are equivalent. The two sides of an equation are separated by the algebraic symbol (F).
For example, the statement "\(2x+3=9\)" states that the value "9" in the total is indicated by the combination "\(2x + 3\)". The goal of equation solving is to determine the value or values of the fact(s) that will allow an equation to be true.
Equations can be simple or complicated, linear or nonlinear, and they can involve one or more variables. For example, in the equation "\(2x^2+2x-3-0,\) *the variable x is raised to the power of 2 for the solution. Lines are frequently used in geometry, algebra, and equations.
We may determine the person's height in meters using the scale diagram. Assume the individual's height is "h" metres.
As a result, the ratio of the length of the lorry to the height of the person in the diagram is:
\(900cm : 4.5cm\)
When we simplify this ratio, we get:
\(20 : 01\)
As a result, the individual's height in metres is:
\((4.5cm) \times (1metre/100cm) \times (1/200)=0.0225m\)
As a result, the person's estimated height is 0.0225 metres or 2.25 Centimetres.
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2.11.2 Project task: the parallax problem
The parallax problem is a phenomenon that arises when measuring the distance to a celestial object by observing its apparent shift in position relative to background objects due to the motion of the observer.
The parallax effect is based on the principle of triangulation. By observing an object from two different positions, such as opposite sides of Earth's orbit around the Sun, astronomers can measure the change in its apparent position. The greater the shift observed, the closer the object is to Earth.
However, the parallax problem introduces challenges in accurate measurement. Firstly, the shift in position is extremely small, especially for objects that are very far away. The angular shift can be as small as a fraction of an arcsecond, requiring precise instruments and careful measurements.
Secondly, atmospheric conditions, instrumental limitations, and other factors can introduce errors in the measurements. These errors need to be accounted for and minimized to obtain accurate distance calculations.
To overcome these challenges, astronomers employ advanced techniques and technologies. High-precision telescopes, adaptive optics, and sophisticated data analysis methods are used to improve measurement accuracy. Statistical analysis and error propagation techniques help estimate uncertainties associated with parallax measurements.
Despite the difficulties, the parallax method has been instrumental in determining the distances to many stars and has contributed to our understanding of the scale and structure of the universe. It provides a fundamental tool in astronomy and has paved the way for further investigations into the cosmos.
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compute the remainder when the product of all positive integers less than and relatively prime to 2019 is divided by 2019.
The remainder when the product of all positive integers less than and relatively prime to 2019 is divided by 2019 is 0.
To compute the remainder when the product of all positive integers less than and relatively prime to 2019 is divided by 2019, we need to find the Euler's totient function value for 2019.
The Euler's totient function, denoted as , gives the count of positive integers less than n that are relatively prime to n.
In this case, we have n = 2019. To find φ(2019), we can factorize 2019 into its prime factors: 2019 = 3 * 673.
The Euler's totient function φ(n) is calculated as \(\phi(n) = n * (1 - 1/p_1) * (1 - 1/p_2) * ... * (1 - 1/p_a)\) , where p₁, p₂, ..., pₙ are the distinct prime factors of n.
For 2019, we have:
\(\phi(2019) = 2019 * (1 - 1/3) * (1 - 1/673)\\= 2019 * (2/3) * (672/673)\\= 2019 * 2 * 672 / (3 * 673)\\= 8064\)
Now, we need to find the remainder when the product of all positive integers less than and relatively prime to 2019 is divided by 2019.
Let's denote this product as P. We can write P ≡ X (mod 2019), where X is the remainder we want to find.
Since the numbers less than 2019 that are relatively prime to it form a complete set of residues modulo 2019, we know that \(\phi(2019) \equiv P|2019|\).
Substituting the value of \(\phi(2019) = 8064\), we have:
\(8064 \equiv X |2019|\)
To find the remainder X, we can divide 8064 by 2019 and take the remainder:
X = 8064 % 2019
X = 0
Therefore, the remainder when the product of all positive integers less than and relatively prime to 2019 is divided by 2019 is 0.
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estimate the value(s) of c that satisfy the conclusion of the mean value theorem on the interval [2, 6]. (enter your answers as a comma-separated list. round your answers to one decimal places. if an answer does not exist, enter dne.)
The mean value theorem states that if a function f(x) is continuous on the interval [a, b] and differentiable on (a, b), then there exists a value c in (a, b) such that:
f'(c) = (f(b) - f(a))/(b - a)
In this case, the interval is [2, 6]. So, we need to find the value(s) of c that satisfy:
f'(c) = (f(6) - f(2))/(6 - 2)
We can make an estimate based on the graph of the function.
If the graph of f(x) is a straight line between (2, f(2)) and (6, f(6)), then the derivative is constant over the interval [2, 6]. In this case, we can use the formula:
f'(c) = (f(6) - f(2))/(6 - 2) = (y2 - y1)/(x2 - x1)
where (x1, y1) = (2, f(2)) and (x2, y2) = (6, f(6)).
Solving for c, we get:
c = (x1 + x2)/2 = (2 + 6)/2 = 4
This is the only value of c that satisfies the conclusion of the mean value theorem in this case.
If the graph of f(x) is not a straight line, then we cannot make a simple estimate for c based on the graph alone.
To estimate the value(s) of c that satisfy the conclusion of the Mean Value Theorem (MVT) on the interval [2, 6], you need to follow these steps:
1. Identify the function, f(x), that you're working with.
2. Ensure the function is continuous on the interval [2, 6] and differentiable on the open interval (2, 6). This is required for MVT to be applicable.
3. Calculate the average rate of change (mean value) of the function over the interval [2, 6] by using the formula (f(6) - f(2)) / (6 - 2).
4. Take the derivative of the function, f'(x).
5. Set f'(x) equal to the mean value calculated in step 3 and solve for the value(s) of x, which will give you the value(s) of c that satisfy the MVT.
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Mr. Ramsey just finished bathing his kids, and now he is draining the tub. The tub contains 32 gallons of water and is draining at a rate of 3 gallons per minute. After 7 minutes, how many gallons are left in the tub?
Answer:
y=-3x + 32
Hope this
The triangles are similar. Find the value of the variable.
When factoring an expression, how can you tell if you used the GCF as the factor? Explain.
Answer:
LARGEST FACTOR
Step-by-step explanation:
The greatest common factor or GCF is the largest factor that all terms have in common. Step 2: Factor out (or divide out) the greatest common factor from each term. Step 1: Determine the greatest common factor of the given terms. The greatest common factor or GCF is the largest factor that all terms have in common.
If A is invertible, then A∼I (A is row equivalent to the identity matrix). Therefore, A has n pivots, one in each column, which means that the columns of A are linearly independent.
The given statement is correct. If a matrix A is invertible, then it means that it has a unique inverse.
What is the identity matrix?
The identity matrix is a square matrix with 1's on the main diagonal and 0's everywhere else. It is denoted as I. The identity matrix has the property that for any square matrix A, the product of A and I is equal to A itself, so I serve as a sort of "do-nothing" matrix.
Yes, this is correct. If a matrix A is invertible, then it means that it has a unique inverse. This implies that the columns of A are linearly independent, as they form a basis for the space. A row equivalent matrix to the identity matrix (A∼I) will have one pivot in each column, indicating that the columns are linearly independent.
Hence, the given statement is correct. If a matrix A is invertible, then it means that it has a unique inverse.
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y = x² – 5x + 21
y=6x -9
Answer:
Step-by-step explanation:
The chosen topic is not meant for use with this type of problem. Try the examples below.
How to change a fraction into a percentage
Answer:
divide the numerator by the denominator
Step-by-step explanation:
2 = 2/3 = 0.666666667
3
Which of the following is the equation for the line perpendicular to the line y= -x + 20 that passes through the point (-4, 2)?
A. Y = x + 6
B. Y = -x - 2
C. Y = -x + 6
D. Y = x - 2
Answer:
Step-by-step explanation:
A 10= 4 plus 6
2\sqrt((25)/(64))-(3)/(8)
Answer:
ookStep-by-step explanation:
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donvc
Evaluate the series 1 + 2 + 4 + 8 to S10.
The series to 10 term is
1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512
What is recurrent relation?An equation that represents a sequence based on a rule is called a recurrence relation.
Finding the following term, which is dependent upon the prior phrase, is made easier (previous term). We can readily predict the following term in a series if we know the preceding term.
The term is predicted by multiplying the preceding term by 2
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