Normal quantile plot is a graph of points (x,y) where each x-value is from the original set of sample data, and each y-value is the corresponding Z-score that is a quantile value expected from the standard normal distribution.
What is a Normal Quantile Plot?
A normal quantile plot is a graphical tool used to determine whether a data set is normally distributed or not.
It plots sample data versus a theoretical normal distribution.
In general, the points on the plot should form a straight line if the data is normally distributed. If the data is not normally distributed, the points on the plot will not form a straight line.
A normal quantile plot can be used to evaluate the following:
Whether or not a data set is normally distributedA data set's skewnessA data set's outliersA data set's center and spread whether or not a transformation is required to make a data set normally distributed.The normal quantile plot of the residuals is the most important diagnostic tool for examining whether the assumptions of a linear regression model have been met.
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Write the HCF of x
3y
4z
2 and x
2y
3z
5, where x, y, z are
distinct prime numbers
the HCF of x, 2y, 3y, 4z, x², 3z, and 5, where x, y, z are
distinct prime numbers is 1.
To find the highest common factor (HCF) of the given numbers, we need to find the common factors of each pair of numbers and then find the highest common factor of all the resulting common factors.
First, let's find the prime factors of the given numbers:
x = a prime number (distinct from y and z)
2y = 2 × y
3y = 3 × y
4z = 2² × z
3z = 3 × z
x² = a prime number squared (distinct from y and z)
5 = a prime number
Next, we can pair up the numbers and find their common factors:
Common factors of x and 2y: 1, 2, y
Common factors of 3y and 4z: 1, 2, 3, y, z, 6
Common factors of x² and 3z: 1, 3, x, z, xz
Common factors of 5 and 2: 1
Finally, we find the highest common factor of all the resulting common factors:
The highest common factor of x, 2y, 3y, 4z, x², 3z, and 5 is 1, since it is the only factor that is common to all the pairs.
Therefore, the HCF of x, 2y, 3y, 4z, x², 3z, and 5 is 1.
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you walk 1 1.5 miles to the gym and then another 1 1/10 miles to a basketball court. How many yards did you walk in all?
You walked a total of 4576 yards to get to the basketball court.
What is unit conversion?In order to represent amounts in a more practical or acceptable unit of measurement, unit conversions are crucial for addressing mathematical issues. In this task, for instance, we were given distances in miles but had to translate them into yards to get the overall distance travelled. We wouldn't be able to compare or combine values that are stated in various units without unit conversions. When working with formulae or equations that contain physical quantities with multiple units, unit conversions are also crucial.
Given that, the distance walked is 1.5 miles and 1 1/10 miles.
Coverting into yards we have:
1.5 miles is equal to 1.5 x 1760 = 2640 yards
1 1/10 miles is equal to (1 + 1/10) x 1760 = 1936 yards
Total distance is:
2640 + 1936 = 4576 yards
Hence, you walked a total of 4576 yards to get to the basketball court.
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Find the Laplace transform Y(s) of the solution of the given initial value problem. Then invert to find y(t) . Write uc for the Heaviside function that turns on at c , not uc(t) .y'' + 16y = e^(?2t)u2y(0) = 0 y'(0) = 0Y(s) =y(t) =
The Laplace transform is a mathematical technique used to solve differential equations and analyze signals and systems in engineering, physics, and other fields. It is named after the French mathematician Pierre-Simon Laplace.
The Laplace transform of the given initial value problem is given by:
Y(s) = (2s^2 + 16) / (s^2(s^2+16))
Inverting the Laplace transform to find y(t) gives us:
y(t) = e^(-8t) * (1-cos(4t)) + 2sin(4t) + u2(t)
Where u2(t) is the Heaviside function that turns on at t = 2.
To find the Laplace transform of y(t), we first take the Laplace transform of both sides of the differential equation:
L(y''(t)) + 16L(y(t)) = L(e^(-2t)u_2(t))
Using the property L(y''(t)) = s^2Y(s) - sy(0) - y'(0) and noting that y(0) = 0 and y'(0) = 0, we can simplify to get:
s^2Y(s) + 16Y(s) = L(e^(-2t)u_2(t))
Using the property L(e^(-at)u_c(t)) = 1/(s + a) * e^(-cs), we can substitute to get:
s^2Y(s) + 16Y(s) = 1/(s + 2)^2
Now we can solve for Y(s):
Y(s) = 1/(s^2 + 16) * 1/(s + 2)^2
To find y(t), we need to take the inverse Laplace transform of Y(s). We can use partial fraction decomposition to simplify the expression:
Y(s) = A/(s^2 + 16) + B/(s + 2) + C/(s + 2)^2
Multiplying both sides by the denominator and solving for A, B, and C, we get:
A = 1/8
B = -1/4
C = 1/8
Substituting these values, we get:
Y(s) = 1/8 * 1/(s^2 + 16) - 1/4 * 1/(s + 2) + 1/8 * 1/(s + 2)^2
Taking the inverse Laplace transform of each term, we get:
y(t) = (1/8)sin(4t) - (1/4)e^(-2t) + (1/4)te^(-2t)
Therefore, the solution to the initial value problem y'' + 16y = e^(-2t)u_2(t), y(0) = 0, y'(0) = 0 is y(t) = (1/8)sin(4t) - (1/4)e^(-2t) + (1/4)te^(-2t).
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1 0 6
0 1 1
0 0 0
Find the solution(s) to the system, if it exists. State the solution as a point (be sure to use parentheses), use parameter(s) s and t if needed. If the system is inconsistent, then state no solution.
The system has infinitely many solutions, which can be written as (x, y, z) = (1 - 60s, -10 + 600s, s) where s is a parameter.
To solve the system of equations:
1x + 0y + 60z = 1
1x + 10y + 0z = 0
0x + 0y + 0z = 0
The third equation is an identity, implying that it does not give us any new information. The first two equations can be used to solve for x, y, and z:
From the first equation, we get x = 1 - 60z
From the second equation, we get y = 0 - 10x = -10(1 - 60z) = -10 + 600z
Therefore, the solution to the system can be written as a point in terms of z as:
(x, y, z) = (1 - 60z, -10 + 600z, z)
Since z can take on any value, there are infinitely many solutions to the system, which can be parameterized as:
(x, y, z) = (1 - 60s, -10 + 600s, s) where s is a parameter.
he system has infinitely many solutions, which can be written as (x, y, z) = (1 - 60s, -10 + 600s, s) where s is a parameter.
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a parachutist rate during a free fall reaches 132 feet per second. what is this rate in meters per second? at this rate, how many meters will the parachutist fall during 10 seconds of free fall. in your computations, assume that 1 meter is equal to 3.3 feet. (do not round your answer)
Parachutist's rate during free fall is 40 meters per second and will fall approximately 490 meters during 10 seconds of free fall.
How to convert feet to meters?First, we need to convert 132 feet per second to meters per second. We know that 1 meter is equal to 3.3 feet, so we can use the following conversion factor:
[tex]$\frac{3meter}{3.3 feet}[/tex]
To convert feet per second to meters per second, we can multiply by the conversion factor:
[tex]132 (\frac{1}{3.3} ) = 40 meters/second[/tex]
Therefore, the parachutist's rate during free fall is 40 meters per second.
Next, we can use the following formula to find the distance the parachutist falls during 10 seconds of free fall:
distance =[tex]\frac{1}{2}[/tex] * acceleration * time²
where acceleration due to gravity is approximately 9.8 meters/second^2.
Substituting the given values, we get:
distance = [tex]\frac{1}{2}[/tex] * 9.8 meters/second² * (10 seconds)²
distance = 490 meters
Therefore, the parachutist will fall approximately 490 meters during 10 seconds of free fall.
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It is well documented that a typical washing machine can last anywhere between 5 to 20 years. Let the life of a washing machine be represented by a lognormal variable, Y = eX where X is normally distributed. In addition, let the mean and standard deviation of the life of a washing machine be 14 years and 2 years, respectively. [You may find it useful to reference the z table.] a. Compute the mean and the standard deviation of X. (Round your intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.) b. What proportion of the washing machines will last for more than 15 years? (Round your intermediate calculations to at least 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.) c. What proportion of the washing machines will last for less than 10 years? (Round your intermediate calculations to at least 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.) d. Compute the 90th percentile of the life of the washing machines. (Round your intermediate calculations to at least 4 decimal places, "z" value to 3 decimal places, and final answer to the nearest whole number.)
a. The mean of X is 1.7549 and the standard deviation is 0.3536.
b. To calculate the proportion of washing machines that will last for more than 15 years, we need to use the standard normal distribution table. The z-score for 15 years is (15-14)/0.3536 = 2.822. Using the table, we find that the proportion of washing machines that will last for more than 15 years is 0.9968.
c. To calculate the proportion of washing machines that will last for less than 10 years, we need to use the standard normal distribution table. The z-score for 10 years is (10-14)/0.3536 = -2.822. Using the table, we find that the proportion of washing machines that will last for less than 10 years is 0.0032.
d. To calculate the 90th percentile of the life of the washing machines, we need to use the standard normal distribution table. The z-score for the 90th percentile is 1.28. Using the table, we find that the 90th percentile is 17 years.
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Let n be a positive integer. If a == (3^{2n}+4)^-1 mod(9), what is the remainder when a is divided by 9?
Let n be a positive integer. We can use the properties of modular arithmetic to calculate this remainder. Let's start with a = (32n + 4)-1 mod 9. We can rewrite this as a = 9 - (32n + 4)-1 because 9 = 0 mod 9.
We can use Fermat's Little Theorem to calculate (32n + 4)-1. This theorem states that (32n + 4)-1 mod 9 = (32n + 4)8 mod 9.
Using the identity (a + b)n mod m = ((a mod m) + (b mod m))n mod m, we can simplify the equation to (32n mod 9 + 4 mod 9)8 mod 9.
32n mod 9 = 0, so (32n mod 9 + 4 mod 9)8 mod 9 = 48 mod 9 = 1.
Finally, a = 9 - 1 = 8 mod 9, so the remainder when a is divided by 9 is 8.
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which part of this graph shows a non-linear relationship
Answer:
A.
Step-by-step explanation:
The _________ method is equivalent to a lottery system in which all the available names are placed in a container, the container is shaken, and the names of the "winners" or participants are then drawn out in an unbiased manner.- Non probability sampling- Systematic sampling- Simple random sampling - Stratified sampling
The Simple random sampling method is equivalent to a lottery system in which all the available names are placed in a container, the container is shaken, and the names of the "winners" or participants are then drawn out in an unbiased manner.
What is Simple random sampling?
The Simple random sampling is a sampling technique in which every member of the population has an equal chance of being chosen as a sample. The samples are chosen randomly, without any specific criterion. In this method, the selection of individuals for the sample is done without any specific pattern. This means that each member of the population is equally likely to be selected as a sample.In Simple random sampling, each member of the population is assigned a number, and the samples are selected using a random number generator or drawing names out of a hat. The selected samples are then analyzed to make predictions about the entire population.For example, if a researcher wanted to know the average age of students in a school, they might use Simple random sampling to choose a sample of 50 students. The researcher would assign each student a number and then use a random number generator to select the samples.There are some advantages and disadvantages of Simple random sampling, which are listed below:Advantages of Simple random sampling It is easy to understand and conduct the process.Each member of the population has an equal chance of being selected as a sample.It ensures that the sample is representative of the entire population.Disadvantages of Simple random sampling It can be time-consuming to select the samples.There may be a chance of human error when selecting samples.The sample size may not be large enough to draw meaningful conclusions.
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Weight: 20kg Order: 10 mg q6 hours Therapeutic range : 2-3 mg/kg/day. What is daily dose? Is it safe? Is it therapeutic?
The daily dose is 40mg, this dose per kilogram per day is within the therapeutic range of 2-3mg/kg/day, which means that the medication is within the safe and effective range for this patient's weight.
The weight of the patient is 20kg, and the prescribed dosage is 10mg every 6 hours. To calculate the daily dose, we need to multiply the prescribed dosage by the number of doses per day. Since the medication is prescribed every 6 hours, this means that the patient will take it 4 times a day.
=> (10mg x 4 doses) = 40 mg
The therapeutic range is the range of doses at which the medication is most effective and safe. In this case, the therapeutic range is 2-3mg/kg/day. To determine if the daily dose is within the therapeutic range, we need to divide the daily dose (40mg) by the patient's weight (20kg) to get the dose per kilogram per day, which is 2mg/kg/day.
However, it's important to note that the therapeutic range is a general guideline and may vary depending on the patient's individual circumstances and medical history.
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how to calculate the product of two random variable that follows normal distribution with mean 0 and variance 1
The product of two random variables that follows the normal distribution with mean 0 and variance 1 is expected 0.
To compute the product of two random variables that are normal distributed with a mean of 0 and a variance of 1, the following procedure can be employed:
Since the mean of the normal distribution is 0 and the variance is 1, we can assume that the standard deviation is also 1.Thus, we can write the probability density function of the normal distribution as:
f(x) = (1/√2π) * e^(-x^2/2)
Using the definition of expected value, we can write the expected value of a random variable X as:E[X] = ∫x * f(x) dx, where the integral is taken over the entire range of X.
Similarly, we can write the expected value of a random variable Y as:E[Y] = ∫y * f(y) dy, where the integral is taken over the entire range of Y.
Since the two random variables are independent, the expected value of their product is the product of their expected values. Thus, we can write:E[XY] = E[X] * E[Y]
Substituting the probability density function of the normal distribution into the expected value formula, we can write:E[X] = ∫x * f(x) dx = ∫x * (1/√2π) * e^(-x^2/2) dx = 0
E[Y] = ∫y * f(y) dy = ∫y * (1/√2π) * e^(-y^2/2) dy = 0
Thus, the expected value of the product of two random variables that follow a normal distribution with mean 0 and variance 1 is:E[XY] = E[X] * E[Y]
= 0 * 0 ⇒ 0
Therefore, the product of two random variables that follow a normal distribution with mean 0 and variance 1 has an expected value of 0.
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8. A department store
buys 300 shirts for
a total cost of $7,200 and sells them for
$30 each. Find the percent markup.
The percent markup is 25%.
What is percent markup?Markup percentage is calculated by dividing the gross profit of a unit (its sales price minus it's cost to make or purchase for resale) by the cost of that unit.
Given that, A department store buys 300 shirts for a total cost of $7,200 and sells them for $30 each.
Cost of one shirt [tex]= 7200 \div 300 = \$24[/tex]
And they sold at $30 each,
Percent markup [tex]= 30-24 \div 24 \times 100[/tex]
[tex]= 25\%[/tex]
Hence, the percent markup is 25%.
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calculate the expected value, the variance, and the standard deviation of the given random variable x. (round all answers to two decimal places.) x is the number of red marbles that suzan has in her hand after she selects three marbles from a bag containing three red marbles and two green ones. expected value variance standard deviation
The expected value of x is 1.80, the variance is 0.72, and the standard deviation is 0.85.
Calculate the expected value, variance, and standard deviation of the random variable x as follows. Round all answers to two decimal places, and keep in mind that x is the number of red marbles that Suzan has in her hand after selecting three marbles from a bag containing three red marbles and two green ones.
Expected Value: Since there are 3 red marbles and 2 green marbles in the bag, the probability of drawing a red marble is: P(R) = 3/5The probability of drawing a green marble is P(G) = 2/5Therefore, the expected value of the random variable X is: E(X) = μ = np = 3/5 * 3 = 1.80
Variance can be calculated using the following formula: Var(X) = npq, where p is the probability of success and q is the probability of failure of the event. In this scenario, the probability of drawing a red marble is P(R) = 3/5, and the probability of drawing a green marble is P(G) = 2/5.
Therefore, Var(X) = npq Var(X) = (3/5)*(2/5)*3Var(X) = 1.80 * 0.4Var(X) = 0.72Standard Deviation: The square root of the variance is equal to the standard deviation. Hence, the formula for standard deviation is: S.D. = √Var(X)S.D. = √0.72S.D. = 0.85
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What is the next number in the sequence 3, 4, 7, 12, 19
Answer:28
Step-by-step explanation:
Answer: 28
Explanation: Look for a pattern or reason for the following number in the sequence. In this case 3+1=4, 4+3=7, 7+5=12, 12+7=19, so the probable answer is to add the following odd number to the last one in the line to get the next. (19+9=28)
One little cat can eat a bag of treats in 15 minutes while another cat can eat the same bag of treats in 10 minutes. What part of the bag can they eat together in the given time? 1 minute. 2 minute, and 3 min
Answer:
1 minute = 1/6
2 minutes = 1/3
3 minutes =1/2
Step-by-step explanation:
one can eat a bag in 15 minutes so in 1 minute this cat can eat 1/15 of a bag
the other cat can eat a bag in 10 minutes so in 1 minute the cat can eat 1/10 of the bag
to find how much they can eat in 1 minute, add 1/10 and 1/15 which gives you 1/6. to find 2 and 3 minutes just multiply by 1/6 by 2 or 3
Help me solve it I need to show my work please help
Step-by-step explanation:
5x - 30 = 3x
2x = 30
x = 15
that's the answer
[Pre-calculus honors, grade 11] The light from a lighthouse can be seen from an 18-mile radius. A boat is anchored so that it can just see the light from the lighthouse. A second boat is located 25 miles from the lighthouse and is headed straight toward it, making a 44° angle with the lighthouse and the first boat. Find the distance between the two boats when the second boat enters the radius of the lighthouse light.
Using trigonometry, the distance between the two vessels when the second boat enters the lighthouse's radius is 13.46 miles.
Trigonometry: What Is It?The relationships between angles and length ratios are investigated in the branch of mathematics known as trigonometry. The use of geometry in astronomical study led to the establishment of the field during the Hellenistic era in the third century BC.
The distance between the two boats when the second boat enters the radius of the lighthouse light is 13.46 miles using trigonometry.
Triangle - what is it?A triangle is a polygon with three edges and three vertices. It belongs to the basic geometric shapes. A triangle with the vertices A, B, and C is represented by the Δ ABC.
Any three points that are not collinear create a singular triangle and a singular plane in Euclidean geometry. (i.e. a two-dimensional Euclidean space). In other words, every triangle is a part of a plane, and that triangle is a part of only one plane. In the Euclidean plane, all triangles are contained within a single plane, but in higher-dimensional Euclidean spaces, this is no longer the case. This page covers triangles in Euclidean geometry, especially the Euclidean plane, unless otherwise specified.
In this question,
The side of the isosceles triangle is given by,
l=2a sin(θ/2)
where a= 18 miles
θ= 44°
l= 2*18*sin 22°
= 36*0.374
= 13.46 miles
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Suppose that the insurance companies did do a survey. They randomly surveyed 400 drivers and found that 320 claimed they always buckle up. We are interested in the population proportion of drivers who claim they always buckle up.a.i. x = __________ii. n = __________iii. p′ = __________b. Define the random variables X and P′, in words.c. Which distribution should you use for this problem? Explain your choice.d. Construct a 95% confidence interval for the population proportion who claim they always buckle up.i. State the confidence interval.ii. Sketch the graph.iii. Calculate the error bound.e. If this survey were done by telephone, list three difficulties the companies might have in obtaining random results.
We are interested in the population proportion of drivers who claim they always buckle upa.i. x = 320 ii. n = 400 iii. p′ = 0.8
b. The random variable X represents the number of drivers out of the sample of 400 who claim they always buckle up, while P′ represents the sample proportion of drivers who claim they always buckle up.
c. The distribution to use for this problem is the normal distribution because the sample size is large enough (n=400) and the population proportion is not known.
d. i. The 95% confidence interval for the population proportion who claim they always buckle up is (0.7709, 0.8291).
ii. The graph is a normal distribution curve with mean p′ = 0.8 and standard deviation σ = sqrt[p′(1-p′)/n].
iii. The error bound is 0.0291.
e. Three difficulties the insurance companies might have in obtaining random results from a telephone survey are:
Selection bias: The survey might not be truly random if the telephone numbers selected are not representative of the population of interest.
Nonresponse bias: People may choose not to participate in the survey or may not be reached, which could bias the results.
Social desirability bias: Respondents may give socially desirable answers rather than their true opinions, which could also bias the results.
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Helppppp will give brainlyest
Answer: 4
Step-by-step explanation:
4. shift the boundary line up 1
Consider a square whose side-length is one unit. Select any five points from inside this square. Prove that at least two of these points are within squareroot 2/2 units of each other.
The given square with a side length of one unit is known to contain five points. One must prove that at least two of these points are within square root 2/2 units of each other.
According to the Pigeonhole principle, "if n items are put into m containers, with n > m, then at least one container must contain more than one item."In this context, the square is the container, and the points inside it are the objects. If more than four points are picked, the theorem is true, and two points are nearer to each other than the square root of 2/2 units.
Let's place four points on the square's four corners. The distance between any two of these points is the square root of two units since the square's side length is 1.
Let's add another point to the mix. That point is either inside the square or outside it. Without loss of generality, let us assume that the point is inside the square. It must then be within the perimeter outlined by joining the square's corners to the point that was not a corner already.
The perimeter of the square described above is a square with a side length of square root 2 units.
Since we have five points in the square, at least two of them must be in the same smaller square, due to the pigeonhole principle. Without loss of generality, let's assume that two of the points are in the upper-left square. As a result, any points within this square are within the square root 2 units of any of the other four points. Hence, at least two points of the five selected are within the square root of 2/2 units of each other.
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Find the volume and surface area of soda if the radius is 6cm and the height is 11cm
The soda can has an estimated volume of 1,026.72 cubic centimeters and an estimated surface area of 452.39 square centimeters.
To find the volume and surface area of a soda can with radius 6 cm and height 11 cm, we can use the formulas:
Volume of cylinder = πr²h
Surface area of cylinder = 2πrh + 2πr²
Substituting the given values, we get:
Volume = π × 6² × 11
Volume = 1,026.72 cubic centimeters (rounded to two decimal places)
Surface area = 2π × 6 × 11 + 2π × 6²
Surface area = 452.39 square centimeters (rounded to two decimal places)
Therefore, the volume of the soda can is approximately 1,026.72 cubic centimeters, and the surface area is approximately 452.39 square centimeters.
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the number of minutes needed to complete a job, m, varies inversely with the number of workers, w. three workers can complete a job in 30 minutes. how many minutes would it take 6 workers to complete the job?
The number of minutes needed to complete a job, m, varies inversely with the number of workers, w.
Three workers can complete a job in 30 minutes.
To find, out how many minutes would it take 6 workers to complete the job.
The formula used for inverse variation is, m1w1 = m2w2
Where, m1 = 30,
w1 = 3,
m2 = ?
and w2 = 6
Substitute the given values in the above formula, 30 × 3 = m2 × 6
Simplify the above expression,90 = 6m2
Divide both sides by 6,90 / 6 = m2m2 = 15
Hence, it will take 15 minutes for 6 workers to complete the job.
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The coordinates of the endpoints of PQ are P( – 12,7) and Q( – 4, – 9). Point R is on PQ and divides it such that PR:QR is 3:5
The coordinates of R are (-8,-1). To find the coordinates of R, we first need to find the length of PQ.
Using the distance formula, we have:
d(P,Q) = √((x2-x1)² + (y2-y1)²)
= √((-4-(-12))² + (-9-7)²)
= √(8² + (-16)²)
= √(320)
= 8 √(5)
Since PR:QR is 3:5, we can set up the following equation:
d(P,R)/d(R,Q) = 3/5
Let the coordinates of R be (x,y). We can use the midpoint formula to find the coordinates of the midpoint of PQ, which is also the coordinates of the point that divides PQ into two parts in the ratio of 3:5.
Midpoint of PQ = ((-12-4)/2, (7-9)/2) = (-8,-1)
Using the distance formula again, we can find the distance between P and R:
d(P,R) = (3/8) d(P,Q)
= (3/8) (8 √(5))
= 3 √(5)
Now we can use the ratio PR:QR = 3:5 to find the distance between R and Q:
d(R,Q) = (5/3) d(P,R)
= (5/3) (3 √(5))
= 5 √(5)
Finally, we can use the midpoint formula to find the coordinates of R:
x = (-12 + (3/8) (8))/2 = -8
y = (7 + (-1))/2 = 3
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Complete Question:
The coordinates of the endpoints of bar (PQ) are P(-12,7) and Q(-4,-9). Point R is on bar (PQ) and divides it such that PR:QR is 3:5. What are the coordinates of R ?
If Jacob spent 45$ on dinner and wanted to top the waitress 15%, which of the following would be a good estimate for the tip?
Answer: 6.75
Step-by-step explanation:
45 x 0.15= 6.75
The tires on Mavis’ car will have to be replaced when they each have 160 000 km of wear on them. If new tires cost $140.00 each, what is the total cost of the wear on Mavis’ tires for a year in which she drives 25 000 km?
Answer:
If the tires on Mavis’ car have to be replaced when they each have 160 000 km of wear, then the total distance Mavis can drive on a set of tires is:
4 tires * 160,000 km = 640,000 km
If Mavis drives 25,000 km in a year, she will need to replace her tires after:
640,000 km ÷ 25,000 km/year = 25.6 years
Since Mavis will need to replace her tires once every 25.6 years, the cost of the wear on her tires for a single year is:
$140.00/tire * 4 tires = $560.00
So the total cost of the wear on Mavis’ tires for a year in which she drives 25,000 km is $560.00.
Step-by-step explanation:
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find the area and circumference of the circle below.round your answers to the nearest hundredth
Answer:
Step-by-step explanation:
The area of given circle is 28.27 sq.m. The circumference of given circle is 18.85 m (rounded to the nearest hundredth).
Give a short note on Circumference?The circumference of a circle is the distance around the edge or boundary of the circle. It is also the perimeter of the circle. The circumference is calculated using the formula:
C = 2πr
where "C" is the circumference, "π" is a mathematical constant approximately equal to 3.14159, and "r" is the radius of the circle.
The circumference of a circle is proportional to its diameter, which is the distance across the circle passing through its center. Specifically, the circumference is equal to the diameter multiplied by π, or:
C = πd
where "d" is the diameter of the circle.
Given that the diameter of the circle is 6m.
We know that the radius (r) of the circle is half of the diameter (d), so:
r = d/2 = 6/2 = 3m
The area (A) of the circle is given by the formula:
A = πr²
Substituting the value of r, we get:
A = π(3)² = 9π ≈ 28.27 sq.m (rounded to the nearest hundredth)
The circumference (C) of the circle is given by the formula:
C = 2πr
Substituting the value of r, we get:
C = 2π(3) = 6π ≈ 18.85 m (rounded to the nearest hundredth)
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The complete question is:
evaluate the diagram below, and find the measures of the missing angles
Answer:
A=100
B= 80
C=80
D=100
E=80
F=80
G=100
Step-by-step explanation:
Michaela holds her state high school record for the 500-meter freestyle swimming event. She can swim the event in 4 minutes and 50 seconds. At this same rate, how far will she swim in 10 minutes?
Answer: To solve the problem, we need to use the given time to find Michaela's swimming rate in meters per second, and then use that rate to calculate the distance she will swim in 10 minutes.
1 minute = 60 seconds
4 minutes and 50 seconds = 4 x 60 + 50 = 290 seconds
So, Michaela's rate is:
distance / time = x / 290 seconds
where x is the distance she can swim in 290 seconds.
Simplifying the equation:
x = distance = (time x distance) / time = (290 seconds x distance) / 290 seconds = distance
We know that Michaela can swim 500 meters in 290 seconds:
500 meters / 290 seconds = 1.724 meters per second
Therefore, in 10 minutes (600 seconds), she will swim:
distance = rate x time = 1.724 meters/second x 600 seconds = 1034.4 meters
So, Michaela will swim 1034.4 meters in 10 minutes.
Step-by-step explanation:
Of first-time college students who matriculate to a certain university, the odds in favor of having graduated in the top 25 percent of their high school class are 2.06 to 1. Of transfer students who matriculate to the same university, 0.666666666666667 proportion graduated in the top 25 percent of their high school class.
(a) For first-time college students, what is the proportion who graduated in the top 25 percent of their high school class (rounded to three decimal places)?
(b) For transfer students, what is the ratio in favor of having graduated in the top 25 percent of their high school class?
Odds and Probability:
Odds in favor of an event is expressed as a ratio:
O
(
f
)
=
favorable cases
:
unfavourable cases
Similarly odds against are expressed as:
O
(
a
)
=
unfavorable cases
:
favourable cases
.
Odds and probability are closely related, as the probability in favor of an even is computed as:
P
=
favorable cases
favorable cases+unfavorable cases
The answers to the questions (a) the proportion who graduated in the top 25 percent of their high school class will be 0.672 and (b) the ratio in favor of having graduated in the top 25 percent of their high school class is 2:3.
(a) For first-time college students, the proportion who graduated in the top 25 percent of their high school class (rounded to three decimal places) is 0.672.
(b) For transfer students, the ratio in favor of having graduated in the top 25 percent of their high school class is 0.67:1. It is said that 0.666666666666667 proportion graduated in the top 25 percent of their high school class. This can be simplified as follows:0.666666666666667=20/30=10/15=2/3. Therefore, the ratio in favor of having graduated in the top 25 percent of their high school class is 2:3.
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I need help asap I just need atleast one of these explained and I can do the rest
The factοred fοrm οf a pοlynοmial is
1. 30b³- 54b² = 6b²(5b−9)
2. 3y⁵ - 48y³ = 3y³(y −4)(y + 4)
3. x³ + 8 = (x + 2) (x² – 2x + 2²)
4. y³ - 64 = (y - 4) (y² – 4y + 4²)
5. 8c³ + 343(2c + 7)(4c² − 14c + 49)
What dοes a pοlynοmial functiοn in factοred fοrm lοοk like?The factοred fοrm οf a pοlynοmial is represented as a³ + b³ = (a + b) (a² – ab + b²). All equatiοns are cοmpοsed οf pοlynοmials. Earlier we've οnly shοwn yοu hοw tο sοlve equatiοns cοntaining pοlynοmials οf the first degree, but it is οf cοurse pοssible tο sοlve equatiοns οf a higher degree.
One way tο sοlve a pοlynοmial equatiοn is tο use the zerο-prοduct prοperty. If yοu remember frοm earlier chapters the prοperty οf zerο tells us that the prοduct οf any real number and zerο is zerο.
We will use the formula
a³ + b³ = (a + b) (a² – ab + b²)
And
a³ - b³ = (a - b) (a² – ab + b²)
1. [tex]30b^3-\ 54b^2[/tex]
⇒ 6b²(5b−9)
2. 3y⁵ - 48y³
⇒ 3y³( y² - 16y)
⇒ 3y³( y² - 4 + 4 - 16y)
⇒ 3y³(y −4)(y + 4)
3. x³ + 8
⇒ x³ + 2³
Using a³ + b³ = (a + b) (a² – ab + b²)
⇒ x³ + 2³
⇒ (x + 2) (x² – 2x + 2²)
4. y³ - 64
⇒ y³ - 4³
Using a³ - b³ = (a - b) (a² – ab + b²)
⇒ y³ - 4³
⇒ (y - 4) (y² – 4y + 4²)
5. 8c³ + 343
Using a³ + b³ = (a + b) (a² – ab + b²)
2c + 7
(2c + 7)(4c² − 14c + 49)
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