The two positive numbers that satisfy the given requirements, the product of which is 768 and the sum of the first plus three times the second is a minimum are 16, 48.
What is a product?A product is a result of multiplying two or more numbers or values together. It's a fundamental mathematical operation that is used in a variety of applications.
For example, if you have two integers, say 3 and 4, you can multiply them to get 12. The product of these two numbers is 12.
What is a sum?When two or more numbers are added together, the resulting value is referred to as the sum. It is one of the most basic mathematical concepts, and it is frequently used in a variety of applications.
For example, if you add 1 and 2 together, the sum is 3.
How to find two positive numbers that satisfy the given requirements?
Let's assume that the two positive numbers are x and y.
Therefore, we know the following: x * y = 768
The sum of the first plus three times the second is a minimum: x + 3y = minimum
We need to find two positive numbers that satisfy both of the above equations.
Solve for y by substituting y= 256/x into x+3y = minimum: x + 3(256/x) = minimum
Differentiate the above equation with respect to x and equate it to 0 to find the minimum value:
1-768/x² = 0x² = 768x = ±sqrt(768)
Since we need positive solutions: x = sqrt(768) = 16
Substitute x = 16 into y = 256/x to obtain:y = 256/16 = 16
Therefore, the two positive numbers that satisfy the given requirements, the product of which is 768 and the sum of the first plus three times the second is a minimum are 16, 48.
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answer quick please am i correct
Answer:
6/11 = 0.54
Step-by-step explanation:
Answer: Yes you are correct
Step-by-step explanation:
Q1 NEED HELP PLEASE HELP
Answer:
the maximum height is 2 meters
Find the value of 2 - 3x when x = 7
2 - 3x is a(n)__________.
Therefore, when the equation x = 72 - 3x, the value of 2 - 3x is -52.
What is equation?An equation is a mathematical statement that shows the equality of two expressions. It typically contains one or more variables, which are symbols that can represent any number or value. The expressions on both sides of the equal sign are called the left-hand side (LHS) and the right-hand side (RHS) of the equation. Equations are used to describe relationships between quantities or to solve problems. They can be represented in various forms, including linear equations, quadratic equations, exponential equations, and trigonometric equations. Equations can be solved by performing operations on both sides of the equation to isolate the variable or variables.
Here,
When we are given that x = 72 - 3x, we can solve for x by first adding 3x to both sides of the equation:
x + 3x = 72
Combining like terms, we get:
4x = 72
Dividing both sides by 4, we get:
x = 18
Now that we know x = 18, we can substitute this value into the expression 2 - 3x:
2 - 3x = 2 - 3(18)
2 - 3x = 2 - 54
2 - 3x = -52
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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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write down the name of shape W
A hexagon with two lines
hope helped you please make me brainalist and keep smiling dude
I hope you are form India
In Drosophila, the allele for normal-length wings is dominant over the allele for vestigial wings. In a population of 1,000 individuals, 360 show the recessive phenotype. How many individuals would you expect to be homozygous dominant and heterozygous for this trait?1:2:1 :1:2:1 is the expected genotypic ratio in the progeny derived from a cross involving two heterozygotes of the same gene. The first "1" represents the proportion of dominant homozygotes, the second class, or class "2", the heterozygotes, and the second "1" the recessive homozygotes. This also means that the phenotypic ratio should be 3 dominant phenotype:1 recessive phenotype. From the phenotypic class "3", 2/3 are represented by the heterozygotes, while the remaining 1/3 by the dominant homozygotes.
The number of individuals who are homozygous dominant (VV) is 160 individuals, and the number of individuals who are heterozygous (Vv) is 320 individuals.
The population of Drosophila has 1000 individuals, 360 of which display the recessive phenotype. Homozygous dominant and heterozygous for this trait in Drosophila would be expected to be found in how many individuals?
In Drosophila, the dominant allele for normal-length wings is denoted as 'V' and the recessive allele for vestigial wings is denoted as 'v.'To determine the number of individuals who are homozygous dominant or heterozygous for this trait, we'll first determine the number of individuals who are homozygous recessive:
Homozygous recessive individuals in the population = number of individuals displaying the recessive phenotype = 360
This indicate that there are 360 individuals with the genotype vv (homozygous recessive), which will be used to determine the remaining genotypes via the Punnett square. To get the number of individuals who are heterozygous (Vv), we first need to identify the number of individuals with the dominant V allele (VV and Vv). The sum of these two genotypes equals the total number of individuals minus the homozygous recessive individuals, as follows:
Total number of individuals - homozygous recessive individuals = (VV + Vv) individuals+ (vv) individuals = 1000 individuals
Hence, VV + Vv = 1000 - 360 = 640 individuals.Now that we know VV + Vv = 640, we can use the expected genotypic ratio of 1:2:1 to calculate the number of homozygous dominant (VV) and heterozygous (Vv) individuals.1:2:1 represents the expected genotypic ratio in the progeny derived from a cross involving two heterozygotes of the same gene. The first "1" represents the proportion of dominant homozygotes, the second class, or class "2", the heterozygotes, and the second "1" the recessive homozygotes.
Therefore, homozygous dominant (VV) and heterozygous (Vv) individuals in the population would be expected in the following ratio:VV:Vv:vv = 1:2:1. Therefore, the number of individuals who are homozygous dominant (VV) is 1/4 of the total individuals (VV + Vv + vv):
Number of individuals who are homozygous dominant (VV) = 1/4 (VV + Vv + vv)= 1/4 (640) = 160 individuals
And the number of individuals who are heterozygous (Vv) is 2/4 of the total individuals (VV + Vv + vv):
Number of individuals who are heterozygous (Vv) = 2/4 (VV + Vv + vv)= 2/4 (640) = 320 individuals
Therefore, the number of individuals who are homozygous dominant (VV) is 160 individuals, and the number of individuals who are heterozygous (Vv) is 320 individuals.
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A graph of an equation in two variables or a function is a representation of an infinite number of solutions to the equation or function.
A system of equations may not have an exact solution that meets the conditions of a real-world solution.
Using graphing technology is a very efficient way to find solutions to equations and systems of equations.
The intersection point of two graphed functions is the solution for a system of equations. It is the point that makes both equations true.
When two different functions f(x) and g(x) are graphed, the x-coordinate of the point of intersection is the solution to the equation formed from f(x) = g(x)
Systems of equations may be a combination of linear and non-linear functions.
A table of values very rarely shows every possible solution to a system of equations. Finding the approximate solution that is between two values on the table can be a good answer in many situations.
Answer:
All of the statements are true.
The first statement is true because a graph represents all the possible solutions to an equation or function.
The second statement is true because a system of equations may have no solution, one solution, or infinitely many solutions, depending on the equations.
The third statement is true because graphing technology allows us to see the visual representation of the functions and their intersection points, which are the solutions to the system of equations.
The fourth statement is true because the solution to a system of equations is the point where both equations intersect and are true.
The fifth statement is also true because finding the x-coordinate of the point of intersection is equivalent to finding the solution to f(x) = g(x).
The sixth statement is true because systems of equations can involve any combination of linear, quadratic, exponential, or other functions.
The seventh statement is true because a table of values can only show a limited number of solutions, but finding the approximate solution between two values on the table can still be useful in many practical situations.
We can see that:
1. True: A graph of an equation in two variables or a function represents an infinite number of solutions because each point on the graph corresponds to a solution of the equation or function.
2. True: A system of equations may not have an exact solution that meets the conditions of a real-world solution. It is possible for a system to have no solution or infinite solutions.
3. False: Using graphing technology is a very efficient way to find solutions to equations and systems of equations.
What is graph?In mathematics, a graph is a visual representation or diagram that displays the relationship between different elements or variables.
4. True: The intersection point of two graphed functions represents the solution for a system of equations. The coordinates of the intersection point satisfy both equations simultaneously.
5. True: When two different functions f(x) and g(x) are graphed, the x-coordinate of the point of intersection represents a solution to the equation formed from f(x) = g(x). However, it's important to note that there could be multiple points of intersection, so the x-coordinate of the intersection is not necessarily the only solution.
6. True: Systems of equations may indeed be a combination of linear and non-linear functions. The equations in a system can involve various types of functions, including linear, quadratic, exponential, logarithmic, etc.
7. True: A table of values may not show every possible solution to a system of equations. It provides a limited set of data points, and there may be solutions that fall between the values in the table. However, finding an approximate solution that lies between two values in the table can be a reasonable approach in many situations.
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The complete question is seen below:
True or False:
A graph of an equation in two variables or a function is a representation of an infinite number of solutions to the equation or function.
A system of equations may not have an exact solution that meets the conditions of a real-world solution.
Using graphing technology is a very efficient way to find solutions to equations and systems of equations.
The intersection point of two graphed functions is the solution for a system of equations. It is the point that makes both equations true.
When two different functions f(x) and g(x) are graphed, the x-coordinate of the point of intersection is the solution to the equation formed from f(x) = g(x)
Systems of equations may be a combination of linear and non-linear functions.
A table of values very rarely shows every possible solution to a system of equations. Finding the approximate solution that is between two values on the table can be a good answer in many situations.
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
Find the mean and variance of each of the random variables described below; each of parts a-o refers to a different random variable. c. P(X--5) = 1/4, P(X = 0) = 1 /2, P(X = 5) 1 /4. d. P(X =-5) = .01 , P(X 0) = .98, P(X = 5) = .01 e. P(X-_50) = .0001, P(X = 0) .9998, P(X = 50) = .0001. g. P(X =0)=1/2, P(X = 2) = 1/2. h, P(X = .01) = .01, P(X = 1.01) = .99.
c. The mean of the random variable X is calculated as:
mean(X) = (-5)(1/4) + (0)(1/2) + (5)(1/4) = 0
The variance of X is calculated as:
var(X) = (-5 - 0)^2(1/4) + (0 - 0)^2(1/2) + (5 - 0)^2(1/4) = 25/2
d. The mean of the random variable X is calculated as:
mean(X) = (-5)(.01) + (0)(.98) + (5)(.01) = 0
The variance of X is calculated as:
var(X) = (-5 - 0)^2(.01) + (0 - 0)^2(.98) + (5 - 0)^2(.01) = 50.25
e. The mean of the random variable X is calculated as:
mean(X) = (-50)(.0001) + (0)(.9998) + (50)(.0001) = 0
The variance of X is calculated as:
var(X) = (-50 - 0)^2(.0001) + (0 - 0)^2(.9998) + (50 - 0)^2(.0001) = 500
g. The mean of the random variable X is calculated as:
mean(X) = (0)(1/2) + (2)(1/2) = 1
The variance of X is calculated as:
var(X) = (0 - 1)^2(1/2) + (2 - 1)^2(1/2) = 1
h. The mean of the random variable X is calculated as:
mean(X) = (.01)(.01) + (1.01)(.99) = 1
The variance of X is calculated as:
var(X) = (.01 - 1)^2(.01) + (1.01 - 1)^2(.99) = .098
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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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I need help soon pls
The volume of the solid is 2160ft^3
Define the volume of cuboid?Volume of Cuboid is the multiplication of length breath and height.
We know that, Volume of Cuboid = l×b×h
put the given values from figure,
= 12×10×15
=1800ft^3
Volume of top = Area of triangle × length
= 1/2 × 4× 12× 15
=360ft^3
Total volume= 1800 + 360
= 2160ft^3
Therefore, the volume of the solid is 2160ft^3
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Cuboid: According to the question the volume of the solid is [tex]2160ft^3[/tex].
What is cuboid?A cuboid is a three-dimensional geometric shape which is composed of six rectangular faces. It has 12 edges and 8 vertices. It is also referred to as a rectangular prism. The three dimensions of a cuboid are its length, width, and height. The cuboid is a versatile shape that can be used in many different ways and can be seen in everyday objects such as boxes, desks, and bookshelves. It is also a common shape for mathematically-based problems such as calculating the volume of a cuboid.
We know that, Volume of Cuboid = l×b×h
put the given values from figure,
= 12×10×15
=[tex]1800ft^3[/tex]
Volume of top = Area of triangle × length
= 1/2 × 4× 12× 15
=[tex]360ft^3[/tex]
Total volume= 1800 + 360
= [tex]2160ft^3[/tex]
Therefore, the volume of the solid is [tex]2160ft^3[/tex]
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PLEASE HELPP!! i’ve been struggling with this problem for the past 30 min.. lessons about polynomials.
Answer:
39.77 -> 39 or 40, depending on rounding
Step-by-step explanation:
Since 2002-1992 is 10. T would equal 10. At that point, it would be a gesture of plugging in 10 whereever you see a "t" and solve for both
Decrease R450 in the ratio 9:8
Step-by-step explanation:
9+8=17
for ratio 9: 9/17 * 450=R238.24
for ratio 8: 8/17* 450= R211.17
g company xyz know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 17 years and a standard deviation of 1.7 years. find the probability that a randomly selected quartz time piece will have a replacement time less than 13.3 years?
The probability that a randomly selected quartz timepiece will have a replacement time less than 13.3 years is approximately 0.015 with a mean of 17 years and a standard deviation of 1.7 years.
What is Probability?To find the probability that a randomly selected quartz timepiece will have a replacement time of less than 13.3 years, we need to use the standard normal distribution formula which is as follows:
[tex]Z =\frac{X -μ }{σ}[/tex]
Where Z is the standard score
X is the variable value
μ is the mean
σ is the standard deviation
Given that the mean (μ) of the replacement times for the quartz timepieces is 17 years, the standard deviation (σ) is 1.7 years, and the variable value (X) we are looking for is 13.3 years.
Substitute the values into the standard normal distribution formula to get:
[tex]Z = \frac{13.3-17}{1.7} = -2.17[/tex]
Looking at the standard normal distribution table, we can find the probability of the standard score Z = -2.17 to be 0.015.
Therefore, the probability that a randomly selected quartz timepiece will have a replacement time less than 13.3 years is approximately 0.015.
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Point C is 3/4 of the way from point A(-4,-2) to point B(8, 6). What are the coordinates of C?
The coordinates of point C are: C = (2 + (3/2) * √(13), 2 + (3/2) *√ ((13))
How to find coordinates of point?
To find the coordinates of point C, we can use the midpoint formula, which gives the coordinates of the midpoint of a line segment. We know that point C is 3/4 of the way from point A to point B, so it is closer to B than to A. Therefore, we can find the coordinates of C by finding the midpoint of the line segment AB and then moving 3/4 of the distance from the midpoint to B.
The midpoint of AB can be found by averaging the x-coordinates and the y-coordinates of A and B, respectively:
Midpoint M = ((-4 + 8)/2 , (-2 + 6)/2) = (2, 2)
Now, we need to find the distance from M to B and move 3/4 of that distance in the direction of B. We can use the distance formula to find the distance between two points:
distance MB = √((8 - 2)² + (6 - 2)²) = √(36 + 16) = √(52)
So, the distance from M to C is 3/4 of √(52), which is:
distance MC = (3/4) * √(52) = (3/4) * 2 * √(13) = (3/2) * √(13)
To move in the direction of B, we need to add the x-component and y-component of the distance MC to the x-coordinate and y-coordinate of M, respectively:
x-coordinate of C = 2 + (3/2) * √(13)
y-coordinate of C = 2 + (3/2) * √(13)
Therefore, the coordinates of point C are:
C = (2 + (3/2) * √(13), 2 + (3/2) * √(13))
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120% is 30 of what number
120 is 30 percent of 400
Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. Assume that the groups consist of 17 couples. Complete parts (a) through (c) below.
a. Find the mean and the standard deviation for the numbers of girls in groups of 17 births.
The value of the mean is μ=_____ (Type an integer or a decimal. Do not round.)
The value of the standard deviation is σ=____(Round to one decimal place as needed.)
b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high.
Values of ___ girls or fewer are significantly low. (Round to one decimal place as needed.)
Values of ___ girls or greater are significantly high. (Round to one decimal place as needed.)
c. Is the result of 15 girls a result that is significantly high? What does it suggest about the effectiveness of the method?
The result ____ is not. is. significantly high, because 15 girls is greater than. less than. equal to _______ __ girls. A result of 15 girls would suggest that the method _______ is effective. is not effect.
The suggest that the method is effective.
Assuming different groups of couples use a particular method of gender selection and each couple gives birth to one baby, the probability of a girl is 0.5, and the groups consist of 17 couples, then:
a. The mean is μ= 8.5, and the standard deviation is σ= 3.5.
b. The values separating results that are significantly low or significantly high are 8.5 girls or fewer are significantly low, and 11.5 girls or greater are significantly high.
c. The result of 15 girls is significantly high, because 15 girls is greater than 11.5 girls. This would suggest that the method is effective.
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the customers of rhythm time, an online music service, download 278,579 songs this year. that number is 30% lower than last year. how many songs did they downloaded last year?
The customers of Rhythm Time, an online music service, downloaded 397,970 songs last year.
How many songs did they download?Rhythm Time, an online music service, had 278,579 songs downloaded this year by its customers. That figure is 30% less than last year. Last year
We can begin by assuming that the total number of songs downloaded last year was x. According to the problem statement, 278,579 songs were downloaded this year, which is 30% less than last year. We can write it as an equation:x - 0.30x = 278,579 Simplifying, we get:0.70x = 278,579 Dividing both sides by 0.70, we get:x = 397,970Therefore, last year, Rhythm Time's customers downloaded 397,970 songs.
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Why is the probability that a continuous random variable is equal to a single number zero? (i.e. Why is P(X=a)=0 for any number a) [1 sentence]
What is meant by the 95% confidence interval of the mean? [1-2 sentences]
What two quantities do we need to fully describe a normal distribution? [1 sentence]
In determining the sample size for a confidence interval, is the size of the population relevant? [3 sentences]
List the steps in Hypothesis Testing. [4-5 bullets]
The probability that a continuous random variable is equal to a single number zero because the area under a continuous probability density function (pdf) between any two points, even two extremely close points, is never equal to zero.
In other words, since the continuous random variable is infinite and continuous, the probability that it is equal to a single value is almost zero.
Steps in Hypothesis Testing:State the null and alternative hypotheses.Calculate the test statistic.
Determine the critical value or p-value.Calculate the p-value, if necessary.Make a decision and interpret the results.
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Please need help in math
I inserted in an image below to help you with the rule.
The 1st point is (6,1) . This becomes (1,-6).
The 2nd point is (-5,-6). This becomes (-6, 5)
The volume of a solid hemisphere of radius 2 cm
Answer:
The volume of a solid hemisphere with radius r is given by the formula:
V = (2/3)πr^3
In this case, the radius of the hemisphere is 2 cm. Substituting this value into the formula, we get:
V = (2/3)π(2 cm)^3
V = (2/3)π(8 cm^3)
V = (16/3)π cm^3
Therefore, the volume of the solid hemisphere is (16/3)π cubic centimeters.
Answer:
(16/3)π cm³ ≈ 16.76 cm³ (nearest hundredth)
Step-by-step explanation:
The volume of a solid hemisphere is given by the formula:
[tex]\boxed{V = \dfrac{2}{3}\pi r^3}[/tex]
where r is the radius of the hemisphere.
Substitute the given radius, r = 2 cm, into the formula, and solve for V:
[tex]\begin{aligned}\implies V &= \dfrac{2}{3}\pi(2)^3\\\\&= \dfrac{2}{3}\pi \cdot 8\\\\&= \dfrac{16}{3}\pi\; \sf cm^3\end{aligned}[/tex]
Therefore, the volume of the solid hemisphere of radius 2 cm is (16/3)π cm³ or approximately 16.76 cm³ (nearest hundredth).
It is given that quadrilateral abcd is a kite. we know that ad ≅ cd by the definition of . by the kite diagonal theorem, ac is to bd this means that angles aed and ced are right angles. we also see that ed ≅ ed by the property. therefore, we have that δaed ≅ δced by .
By the congruence postulate, we have shown that the quadrilateral is ΔAED ≅ ΔCED.
Let's start by showing that AD = CD. Since AB = AD and BC = CD, we can rewrite AB + BC as AD + CD. This means that AD = AB + BC - CD. But we know that AB = AD, so we can substitute AD for AB to get AD + BC = 2AD + CD. Simplifying this equation, we get AD = CD.
Next, we can show that AE = CE. Since AC is a diagonal of the kite, we know that AC bisects angle BAD and angle BCD. This means that angle BAC = angle DAC and angle BDC = angle CDC. Since AD = CD, we know that triangle ACD is isosceles, so angle ACD = angle CAD.
Using these angle equalities, we can conclude that angle CAE = angle CDE. Since AC ⊥ BD, we know that angle CAD = angle CDE, so we can conclude that triangle ACE is isosceles, which means that AE = CE.
Finally, we need to show that angle AED = angle CED. Since AD = CD and AE = CE, we know that triangles AED and CED have two pairs of congruent sides. Additionally, we know that AC is a common side of the triangles.
Since AC is perpendicular to BD, we know that angle ACD and angle BDC are complementary angles.
This means that angle ACD = 90 - angle BDC and angle CAD = 90 - angle BAC. Using these angle equalities, we can conclude that angle AED = angle CED.
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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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During the day, 25 trains pulled into the subway station. Of those trains, 14 were full.
Find the experimental probability that the next train that pulls into the station is full
The experimental likelihood that probability the incoming train will be fully occupied is 0.56, or 56%.
What is the simplest method for resolving probability?It's simple to calculate the likelihood of a simple event occurring by adding the probabilities together. Your overall odds to win something, for instance, are 10% + 25% = 35% if your chances of winning $10 or $20, respectively, are 10% and 25%, respectively.
In this instance, 14 of the 25 arriving trains were completely full.
The following train's likelihood of being full is determined by the proportion of full trains to all other trains.
14/25 are in favor of the upcoming train being fully loaded.
The likelihood that the following train will have every seat taken is 0.56, or 56%.
Which four rules of probability are there?It either happens or it doesn't, according to the four significant rules of probability. The chance of an event occurring when the probability of it not occurring is put together is always 1. The same principles apply to empirical probability.
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A 2014 Ford F150 was purchased new for $35,000. If the truck's current value in 2021
is $26,796.88 what is the annual rate of depreciation? (round answer to the nearest
tenth of a percent)
According to the solving the annual rate of depreciation is approximately 4.77%.
What does "annual rate" refer to?Annual percentage rate (APR) is the word used to define the annual interest that is generated by a payment that is due to investors or assessed to borrowers. The annual percentage rate, or APR, is a gauge of how much it actually costs to borrow cash over the duration of a loan or the income from an investment.
According to the given information:V = V0 * e[tex]^(^-^r^t^)[/tex]
where:
V0 is the initial value of the asset (in this case, $35,000)
V is the current value of the asset (in this case, $26,796.88)
r is the annual rate of depreciation (what we want to find)
t is the time elapsed (in years)
We know that the time elapsed is 2021 - 2014 = 7 years.
26,796.88 = 35,000 * e[tex]^(^-^7^r^)[/tex]
Dividing both sides by 35,000, we get:
0.766195 = e[tex]^(^-^7^r^)[/tex]
ln(0.766195) = -7r
Solving for "r", we get:
r = -ln(0.766195) / 7
r ≈ 0.0477
the annual rate of depreciation is approximately 4.77%.
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a parachutist rate during a free fall reaches 132 feet per second. what is this rate in meters per second? at this rate, how many meters will the parachutist fall during 10 seconds of free fall. in your computations, assume that 1 meter is equal to 3.3 feet. (do not round your answer)
Parachutist's rate during free fall is 40 meters per second and will fall approximately 490 meters during 10 seconds of free fall.
How to convert feet to meters?First, we need to convert 132 feet per second to meters per second. We know that 1 meter is equal to 3.3 feet, so we can use the following conversion factor:
[tex]$\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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Question
Find the value of y
for the given value of x
.
y=x+5;x=3
Answer: y is equal to 8
Step-by-step explanation:
by substituting the x for its vale of three we can add the two values to get 8 or y=8
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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HELP PLS ILL GIVE U POINTS
Answer:
i think 16 im not sure
Step-by-step explanation:
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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