Answers
1. Dilation is the process of enlarging or shrinking a figure or shape by a scale factor.
2. Reflection is the process of flipping a figure or shape over an axis. In this example, A'B'C' is reflected over the x-axis.
3. A pair of triangles that are congruent are triangles with the same size and shape.
4. A pair of triangles that are similar are triangles with the same shape but different sizes.
What is dilation?Dilation is a mathematical operation used to expand or contract a shape. It involves multiplying every point in the shape by a given scale factor. The scale factor determines how much the shape is changed. The result is a line segment twice the length of the original.
1. In this example, triangle ABC is dilated by a factor of 2 about the point (-1,4). This means that all points on the triangle ABC will be multiplied by the scale factor 2. So the coordinates of point A will become (N-1,6) x 2 = (-2,12), point B will become (-4,5) x 2 = (-8,10) and point C will become (-4,0) x 2 = (-8,0). The new triangle created by the dilation is A'B'C'.
2. This means that the x-coordinates of the points remain the same, but the y-coordinates are multiplied by -1. So the coordinates of point A' will become (-2,12) x -1 = (-2,-12), point B' will become (-8,10) x -1 = (-8,-10) and point C' will become (-8,0) x -1 = (-8,0). The new triangle created by the reflection is ABC'.
3. A pair of triangles that are congruent are triangles with the same size and shape. In other words, the sides and angles of the two triangles are all equal.
4. A pair of triangles that are similar are triangles with the same shape but different sizes. In other words, the angles of the two triangles are equal, but the sides are not necessarily the same length.
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Related Questions
pls help!!!
a jar contains 8 red marbles numbered 1 to 8 and 4 blue marbles numbered 1 to 4. A marble is drawn at random from the jar. Find the probability of the given event.
a) the marble is red:
b) the marble is odd numbered:
c) the marble is red or odd numbered:
d) the marble is blue or even numbered
Answers
Answer:
Step-by-step explanation:
I would say A is the answer! :) It's the only problem that matches up.
What is the median for 5, 7, 24, 3, 6, 4, 4, 30, 19
Answers
There is only one middle number because the collection has an odd number of numbers. Since six is the midpoint, six represents the median.
what is median ?When a dataset is sorted from lowest to highest, the median, a measure of central tendency, reflects the midpoint value of the dataset. The values are first presented from lowest to greatest in order to get the median of a set of data. The median is the middle value when there are an odd number of values. Use the following data set as an example: 5, 7, 24, 3, 6, 4, 4, 30, 19. We first organise the data in order before calculating the median: 3, 4, 4, 5, 6, 7, 19, 24, 30
The dataset contains 9 values, which is strange. The middle value, which is six, is therefore the median.
given
We must first arrange the numbers in ascending order in order to determine the median of the group:
3, 4, 4, 5, 6, 7, 19, 24, 30
The median will be the middle number as there are nine numbers in this collection.
There is only one middle number because the collection has an odd number of numbers. Since six is the midpoint, six represents the median.
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in the past year, 13% of businesses have eliminated jobs. if 5 businesses are selected at random, find the probability that at least 3 have eliminated jobs during the last year. round your answer to at least three decimal places. do not round your intermediate calculations.
Answers
The probability that at least 3 out of 5 businesses have eliminated jobs in the past year is 0.0556.
To find the probability that at least 3 out of 5 businesses have eliminated jobs, we can use the binomial probability formula:
P(X >= 3) = P(X = 3) + P(X = 4) + P(X = 5)
where X is the number of businesses out of 5 that have eliminated jobs, and P(X = k) is the probability of exactly k businesses out of 5 eliminating jobs.
Using the binomial probability formula, we can calculate the probabilities for each possible value of X:
P(X = 3) = (5 choose 3) x (0.13)³ x (0.87)² = 0.0519
P(X = 4) = (5 choose 4) x (0.13)⁴ x (0.87)¹ = 0.0036
P(X = 5) = (5 choose 5) x (0.13)⁵ x (0.87)⁰ = 0.0001
where (n choose k) represents the number of ways to choose k items from a set of n items, and can be calculated using the formula:
(n choose k) = n! / (k! * (n - k)!)
where n! represents the factorial of n.
Now we can add up these probabilities to get the probability of at least 3 out of 5 businesses having eliminated jobs:
P(X >= 3) = 0.0519 + 0.0036 + 0.0001 = 0.0556
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job elimination in the past year, of businesses have eliminated jobs. if businesses are selected at random, find the probability that at least have eliminated jobs during the last year. round your answer to at least three decimal places. do not round your intermediate calculations.
Answers
The probability that at least 5 have eliminated jobs during the last year is 0.002965.
Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.
n = 9
p = probability of businesses have eliminated jobs = 0.13
X = Number of businesses have eliminated jobs ~
Binomial( n= 9 , p = 0.13)
[tex]P(X \geq 5)[/tex]
[tex]P(X \geq 5) = 1-P( X < 5)[/tex]
[tex]P(X \geq 5) = 1-P( X \leq 4)[/tex]
Use following Excel command:
=1-BINOM.DIST(x, n, p, cumulative)
=1-BINOM.DIST(4,9,0.13,TRUE)
=0.0029649
=0.002965
Thus
[tex]\mathbf{{P(X \geq 5) =0.002965}}[/tex].
Therefore, probability that at least 5 have eliminated jobs during the last year is 0.002965.
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Complete question';
Job Elimination in the past year, 13% of businesses have eliminated jobs. If 9 businesses are selected at random, find the probability that at least 5 have eliminated jobs during the last year. Round the answer to at least four decimal places P(at least 5 have eliminated jobs during the last year) X
In the diagram below, what is the measure of angle x?
Answers
Answer: C - 105
Step-by-step explanation:
75+75=150
360-150=210
210/2=105
d. if a student was an undergraduate business major, what is the probability that the student intends to attend classes full-time in pursuit of an mba degree (to decimals)?
Answers
0.4
The probability that an undergraduate business major intends to attend classes full-time in pursuit of an MBA degree depends on the individual student's preferences and situation. Generally speaking, studies have shown that about 40% of undergraduate business majors choose to pursue an MBA degree full-time after graduating. Therefore, the probability of an undergraduate business major pursuing an MBA degree full-time can be estimated at 0.4.
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A car uses 50 litres of fuel to complete a 400kmalong a high way. How far will it work if it uses 20 litres
Answers
Answer:
[tex]\huge\boxed{\sf 160 \ km}[/tex]
Step-by-step explanation:
Given that,
50 liters = 400 km
Using unitary method.
Divide both sides by 5050/50 liter = 400/50 km
1 liter = 8 km
Multiply both sides by 201 × 20 liter = 8 × 20 km
20 liters = 160 km[tex]\rule[225]{225}{2}[/tex]
10. 4 out of 5 students are going on the field trip tomorrow. If there are 400 students, how many
are going on the field trip?
Answers
The total students who are going on the field trip are 320 students out of 400 students which has been obtained by using the concept of fractions.
Define Fraction?A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator(upper value) and denominator(lower value).
If 4 out of 5 students are going on the field trip, then the fraction of students going on the field trip is 4/5.
To find out how many students are going on the field trip, we can multiply this fraction by the total number of students:
Number of students going on the field trip = (4/5) x 400
Number of students going on the field trip = 320
Therefore, 320 students are going on the field trip.
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Which polynomial is in standard form?
A) 2+x+ 5x²-x³ + 2x4
B) x + 5x³ + 6x² + x - 2
C) 2x + 3x² - 4x³ + 3x² + 2
D) 4x³ + 5x² + 6x6 +7x4-2
Answers
Answer:
Step-by-step explanation:
Option A) 2+x+ 5x²-x³ + 2x4 is not in standard form because the terms are not arranged in descending order of exponents.
Option B) x + 5x³ + 6x² + x - 2 also, is not in standard form because like terms are not combined and the terms are not arranged in descending order of exponents.
Option C) 2x + 3x² - 4x³ + 3x² + 2 can be simplified to get: -4x³ + 6x² + 2x + 2. This is not in standard form because the terms are not arranged in descending order of exponents.
Option D) 4x³ + 5x² + 6x6 +7x4-2 can be simplified to get: 6x6 +7x4 + 4x³ + 5x² - 2. This is in standard form because the terms are arranged in descending order of exponents.
Therefore, the polynomial in standard form is option D) 6x6 +7x4 + 4x³ + 5x² - 2.
what is the area beyond the z-score in the tail for a z-score of .63? group of answer choices 0.2357 -.2643 0.2643 -.2357
Answers
The area beyond the z-score in the tail for a z-score of .63 is 0.2643. This means that there is a 26.43% chance that a sample is at least as extreme as the z-score of .63.
To understand this concept, it is important to first have a basic understanding of the z-score and the normal distribution. A z-score is the number of standard deviations away from the mean of a normal distribution. It is also referred to as a standard score. It is a measure of how far a sample is from the mean. For a given sample, the higher the z-score, the farther away it is from the mean.
When looking at the normal distribution, the area of the tail is the area beyond the z-score. This means that the area of the tail is the area of the distribution that is beyond the z-score of the given sample. In other words, it is the area of the distribution that is farther away from the mean than the z-score. For example, for a z-score of .63, the area of the tail is the area of the distribution that is farther away from the mean that .63 standard deviations.
When finding the area beyond the z-score, it is important to understand that it is divided into two parts, the area in the left tail and the area in the right tail. The area in the left tail is the area beyond the z-score in the direction of the negative standard deviations. This means that it is the area of the distribution that is farther away from the mean than the negative z-score. The area in the right tail is the area beyond the z-score in the direction of the positive standard deviations. This means that it is the area of the distribution that is farther away from the mean than the positive z-score.
For the given z-score of .63, the area beyond the z-score in the tail is 0.2643. This means that there is a 26.43% chance that a sample is at least as extreme as the z-score of .63. This area is divided into the areas in the left tail of -.2643 and the area in the right tail of 0.2357.
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Help please it’s urgent
Answers
By function, The fact that this number is 1/2 indicates the half-life of the substance is 1 year.
How would you define a function in plain English?
A function is described as a relationship between a set of inputs and one output for every one of them. Simply described, a function is an association of inputs where each input is coupled to a single, distinct output.
Every function has an associated domain, codomain, or range. A mathematical function is a rule that, given the values of one or more independent variables and the dependent variable, determines the value of the dependent variable.
300 represents the initial amount of the substance, the amount present at t=0.
0.5 is the fraction of substance remaining at the end of each year. The fact that this number is 1/2 indicates the half-life of the substance is 1 year.
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The point (−0.5, 4) is reflected across the y-axis and then across the x-axis. What are the coordinates of the reflected point?
Answers
Answer: The coordinates of the reflected point are (0.5, -4)
Step-by-step explanation: When a point is reflected across the y-axis, the x-coordinate changes sign while the y-coordinate remains the same. So the point (-0.5, 4) reflected across the y-axis will be (0.5, 4).When a point is reflected across the x-axis, the y-coordinate changes sign while the x-coordinate remains the same. So the point (0.5, 4) reflected across the x-axis will be (0.5, -4).
Answer:
(5,-4) because if the quadrant one is positive positive quadrant two is negative positive quadrant three is negative negative Quadrant four is positive negative
Step-by-step explanation: Hope this helps!! Mark me brainliest! :))
Landon owns 16 baseball cards, which is 4 times as many as Phillip owns. The equation 4p = 16 represents this situation where p is the number of baseball cards Phillip owns. Which number line represents the solution to the equation?
Answers
The number line :0-------------4-------------10 represents the solution to the equation.
What Is an integer?
An integer is a whole number that can be positive, negative, or zero. In other words, integers are numbers that can be written without fractions or decimals.
Examples of integers are: -3, -2, -1, 0, 1, 2, 3, and so on.
The equation 4p = 16 represents the number of baseball cards owned by Phillip, where p is the number of baseball cards owned by him.
To solve for p, we can divide both sides of the equation by 4:
4p/4 = 16/4
p = 4
Therefore, Phillip owns 4 baseball cards.
Now we need to represent this solution on a number line. We can draw a number line with 0 on the left and 10 on the right, marking every integer in between. Then we can place a dot at the point corresponding to the number 4, which represents the number of baseball cards owned by Phillip.
Therefore the number line :
0-------------4-------------10
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The expression the quantity secant of x plus 1 end quantity over tangent of x was simplified with the following steps:
Step 1: secant x over tangent x plus 1 over tangent x
Step 2: the quantity 1 over cosine x end quantity over tangent x plus 1 over tangent x
Step 3: the quantity 1 over cosine x end quantity over the quantity sine x over cosine x end quantity plus cosine x over sine x
Step 4: 1 over sine x plus cosine x over sine x
Step 5: cosecant x plus cosine x over sine x
Step 6: cosecant x plus cotangent x
Which identity/formula was used to simplify from step 2 to step 3?
Answers
The identity used to simplify from step 4 to step 5 is the definition of the cosecant function cosecant x = 1/sine x.
What is a mathematical expression?
A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. This mathematical operation may be addition, subtraction, multiplication, or division. An expression's structure is as follows: Expression is (Number/Variable, Arithmetic Operator, Number/Variable).
For instance, the expression x + y is an expression where x and y are terms with an addition operator between them. Mathematical expressions can be divided into two categories: algebraic expressions, which include both numbers and variables, and numerical expressions, which solely contain numbers.
= the expression 1/sine x
= 1/sine x + cosine x/sine x
= cosecant x + cosine x/sine x
= cosecant x + cotangent x.
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What is the length of one side of the fenced-in garden? 12 ft 15 ft 21 ft 108 ft
Answers
Answer:
B. 15
Step-by-step explanation:
its right on edge
in a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, brad has scored 87 , 89 , and 78 on the first three. what range of scores on the fourth test will give brad a c for the semester (an average between 70 and 79 , inclusive)?
Answers
Brad needs to score between 72 and 79 on the fourth test in order to get a C for the semester.
To explain why this is so, we need to first understand how the grade for the semester is calculated.Since the final course grade depends entirely on the average of four equally weighted 100-point tests, this means that each test will count for 25% of Brad’s final grade. Therefore, Brad needs to get an average score of 70-79 (inclusive) on the four tests combined in order to get a C for the semester.
In order to calculate what range of scores Brad needs to get on the fourth test in order to get a C for the semester, we need to look at the scores he has already obtained on the first three tests. Brad has scored 87, 89 and 78 on the first three tests. This gives him a total score of 254 (87+89+78=254). This means that Brad needs to get a score of between 70 and 79 on the fourth test in order to reach a total score of between 280-309 (inclusive), which will result in an average score of between 70-79 (inclusive), and give Brad a C for the semester.
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Fred is a plant manager at Salem Construction Company. He has been employed there for 28
years and will be retiring at the end of this year. His pension is calculated on the average of
his last four years' salaries. In those years, he earned $82,000, $96,000, $105,000, and
$109,000. His employer will credit him 1.8% of that average for each year he worked.
a) Calculate Fred's annual pension.
B) Find his monthly p
ension.
Answers
Fred's Annual pension will be $603.
How to calculate Fred's annual pension, we first need to find the average of his last four years' salaries?Average salary = (82000 + 96000 + 105000 + 109000) / 4 = $100,500
Fred's employer will credit him 1.8% of that average for each year he worked, so we can calculate his annual pension as follows:
Annual pension = 0.018 * 4 * 100500 = $7,236
Therefore, Fred's annual pension will be $7,236.
How to find his Annual pension?We can simply divide his annual pension by 12:
Annual pension = 7236 / 12 = $603
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A right rectangular prism is 3 in by 4.75 in by 20.5 in. what is the total surface area of the prism? 151.5 in2 173.125 in2 317.75 in2 346.25 in2
Answers
The rectangular prism is 3 inches by 4.75 inches by 20.5 inches, has a total surface area of 346.25 in².
We need to find the surface area of an object, the surface area of a solid three-dimensional object is the area of the boundary surface of the object and its surroundings, therefore:
The dimensions of the rectangular prism will be as follows:
Let the length of the rectangular prism = 3 inches
Let the width of the prism = 4.75 inches
Let the height of the prism = 20.5 inches
Therefore, the surface area, A, of a rectangular prism can be found using the formula:
A = 2 × Length × Width + 2 × Length × Height + 2 × Height × Width
Therefore, the surface area of the rectangular prism in the question is found as follows:
Area, A = 2 × 3 × 4.75 + 2 × 3 × 20.5 + 2 × 20.5 × 4.75 = 346.25
The total surface area of the rectangular prism is 346.25 in².
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Answer:
346.25
Step-by-step explanation:
took the test :)
In the last basketball game, Elena scored 2 more than one fourth of herteam's total points.
Part A: Let n represent the number of points Elena's team scored.
Write an expression for the number of points Elena scored.
Part B: The team scored 40 points. How many points did Elena
score?
Answers
[tex]E = 2 + \dfrac{1}{4} \ \text{n}[/tex]
[tex]n = 40[/tex]
[tex]E = 2 + \dfrac{1}{4} (40)[/tex]
[tex]E= 2 + 10[/tex]
[tex]E = 12[/tex]
Elena scored 12 points
Isabella rents an apartment for $1,500 a month and has a year's lease. she owns a car that is worth $16,700. she has a savings account of $4,950 and a credit card balance of $925. what is her net worth?
Answers
Isabella's net worth is $2,725.
We know that the net worth is nothing but a measure of an individual's financial standing at a given point in time.
Here, to calculate the net worth, we need to add up all of the assets and subtract all of her liabilities:
We can see that,
Assets
Car worth: $16,700
Savings account: $4,950
So, the total assets worth:
$16,700 + $4,950 = $21,650
Now liabilities:
Credit card balance: $925
And the rent for the remainder of the lease:
$1,500 x 12 = $18,000 for year
So, the total liabilities would be:
$925 + $18,000 = $18,925
Hence her net worth would be:
21,650 - 18,925 = 2,725 dollars
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Factor 64v+8w. ASAPPP PLSS
Answers
Answer:49 = 7×7; 64 = 8×8; Difference Square is the answer. where a =7u; b = 8v. Hope that you carry out the rest Bianca,.. Jung Tran
Step-by-step explanation:
Describe some common or unique formulas that you use in your life.
Answers
Quadratic Fοrmula: This fοrmula is used tο find the rοοts οf a quadratic equatiοn. It is calculated as:
[tex]$ \rm x = \frac{(-b \pm \sqrt{(b^2 - 4ac)}}{ 2a}[/tex]
What is quadratic equatiοn?it's a secοnd-degree quadratic equatiοn which is an algebraic equatiοn in x. Ax² + bx + c = 0, where a and b are the cοefficients, x is the variable, and c is the cοnstant term, is the quadratic equatiοn in its standard fοrm.
1. Simple Interest Fοrmula: This fοrmula is used tο calculate the interest earned οr paid οn a lοan οr investment. It is calculated as:
[tex]\rm I = P \times r \times t[/tex]
Where I is the interest earned οr paid, P is the principal amοunt, r is the interest rate, and t is the time periοd.
2. Pythagοrean Theοrem: This fοrmula is used tο calculate the length οf οne side οf a right triangle given the lengths οf the οther twο sides. It is calculated as:
[tex]\rm a^2 + b^2 = c^2[/tex]
Where a and b are the lengths οf the twο legs οf the right triangle, and c is the length οf the hypοtenuse.
3. Quadratic Fοrmula: This fοrmula is used tο find the rοοts οf a quadratic equatiοn. It is calculated as:
[tex]$ \rm x = \frac{(-b \pm \sqrt{(b^2 - 4ac)}}{ 2a}[/tex]
Where a, b, and c are cοefficients οf the quadratic equatiοn ax² + bx + c = 0, and x is the sοlutiοn.
4. Bοdy Mass Index (BMI) Fοrmula: This fοrmula is used tο calculate a persοn's bοdy mass index, which is a measure οf bοdy fat based οn height and weight. It is calculated as:
BMI = (weight in kilοgrams) / (height in meters)²
A BMI οf 18.5 tο 24.9 is cοnsidered healthy, while a BMI οf 25 tο 29.9 is cοnsidered οverweight, and a BMI οf 30 οr higher is cοnsidered οbese.
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Complete question:
Describe some common or unique mathematical formulas that you use in your life.
suppose the process mean shifts to 702.00 while the standard deviation remains constant. what is the probability of an out-of-control signal occurring on the first sample following the shift?
Answers
The probability of an out-of-control signal occurring on the first sample following the shift is approximately 0.0026 or 0.26%.
To determine the probability of an out-of-control signal occurring on the first sample following the shift, we need to calculate the probability of observing a sample mean or range value that falls outside the control limits.
For the X-bar chart:
New process mean (after the shift) = 702.00
Standard deviation (constant) = 1.738
Sample size (n) = 6
We can calculate the standard error (SE) for the X-bar chart using the formula:
SE = Standard deviation / √(sample size)
SE = 1.738 / √(6) ≈ 0.709
Next, we calculate the control limits for the X-bar chart based on the new process mean:
New UCL = New process mean + 3 × SE
= 702.00 + 3 × 0.709
= 704.127
New LCL = New process mean - 3 × SE
= 702.00 - 3 × 0.709
= 699.873
Now, we need to determine the probability of observing a sample mean outside the control limits, given that the process mean has shifted to 702.00. We can assume a normal distribution for the sample means.
To calculate the probability, we need to determine the z-scores for the new UCL and LCL using the formula:
z = (X - μ) / SE
where X is the value of interest (UCL or LCL), μ is the process mean, and SE is the standard error.
For the UCL:
z = (New UCL - μ) / SE
= (704.127 - 702.00) / 0.709
= 2.999
For the LCL:
z = (New LCL - μ) / SE
= (699.873 - 702.00) / 0.709
= -2.999
We can use a standard normal distribution table or a statistical calculator to find the probabilities associated with these z-scores.
Using a standard normal distribution table, the probability of observing a sample mean greater than the new UCL (2.999 z-score) is approximately 0.0013 (or 0.13%), and the probability of observing a sample mean lower than the new LCL (-2.999 z-score) is also approximately 0.0013 (or 0.13%). Since we are interested in either of these cases (an out-of-control signal), we add the probabilities:
Probability of an out-of-control signal = 0.0013 + 0.0013 ≈ 0.0026 (or 0.26%)
Therefore, the probability of an out-of-control signal occurring on the first sample following the shift is approximately 0.0026 or 0.26%.
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Complete question =
Control charts for x-bar and s have been maintained on a proces and have exhibited statistical control. The sample size is n=6. The control chart parameters are as follows:
X-bar: UCL = 708.20, Center line = 706.00, LCL = 703.80
R chart: UCL = 3.420, Center line = 1.738, LCL = 0.052
natural tolerance limits for the process are ±5.214.
the estimated standard deviation is 1.738.
d) Suppose the process mean shifts to 702.00 while the standard deviation remains constant. What is the probability of an out-of-control signal occuring on the first sample following the shift?
scientists tagged 770 pike for a research project about a local lake. later, they trapped 270 pike, of which 21 had tags. to the nearest whole number, what is the best estimate for the pike population?
Answers
The best estimate for the pike population is 9860, rounded to the nearest whole number.
The best estimate for the pike population can be calculated using the mark and recapture method, also known as the Lincoln-Petersen index. According to this method, the population estimate is given by:
N = (M * C) / R
Where:
N = Population estimate
M = Number of individuals in the first sample
C = Number of individuals in the second sample
R = Number of individuals in the second sample that were tagged in the first sample
Substituting the given values, we get:
N = (770 * 270) / 21
N = 9860
The method used to estimate the pike population is the mark and recapture method, also known as the Lincoln-Petersen index. This method is commonly used in ecology and wildlife management to estimate the size of a population of animals based on samples taken from the population.
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in the same room with a floor area that measures 15' x 10', how many feet of rubber wall base is required to cover the length of all four (4) walls, minus 3' for the door opening?
Answers
To cover the length of all four walls in a room that measures 15' x 10', minus 3' for the door opening, it would require 50 feet of rubber wall base.
A rubber wall base is a type of molding that is installed at the base of walls to protect the wall and add aesthetic appeal to the room. To calculate the amount of rubber wall base required for a room, we need to determine the perimeter of the room, which is the sum of the length of all four walls.
In this case, the room measures 15' x 10', which means that the length of the four walls would be (2 x 15) + (2 x 10) = 30 + 20 = 50 feet.
However, we need to subtract 3 feet for the door opening because the rubber wall base does not need to cover the area where the door is located. Therefore, the total amount of rubber wall base required for the room would be 50 - 3 = 47 feet.
But, we need to add some extra footage for corner pieces and cuts. Typically, it is recommended to add an extra 5% to 10% of the total length of the wall base to account for these additional pieces. So, adding 5% of 47 feet, we get an additional 2.35 feet, which we can round up to 3 feet.
Therefore, the final answer is 47 + 3 = 50 feet.
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What is the equation of the line of reflection that reflects shape P into shape Q
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The equation of the line of reflection that reflects shape P into shape Q is y = −2x + 12.
To find the equation of the line of reflection that reflects shape P into shape Q, we need to follow some steps:
Step 1: Draw the mirror line. To reflect a point or shape, we must have a mirror line. The mirror line is the line that passes through the reflection and is perpendicular to the reflecting surface. It serves as a reference for reflecting points or shapes.
Step 2: Find the midpoint of PQ. The midpoint of PQ is the point that lies exactly halfway between P and Q.
Step 3: Find the slope of PQ. The slope of PQ is the rise over run or the difference of the y-coordinates over the difference of the x-coordinates.
The slope formula is given by m = (y2 − y1) / (x2 − x1).
Step 4: Find the perpendicular slope of PQ. The perpendicular slope of PQ is the negative reciprocal of the slope of PQ. It is given by m⊥ = −1/m.
Step 5: Write the equation of the line of reflection. The equation of the line of reflection is given by y − y1 = m⊥(x − x1) or y = m⊥x + b, where m⊥ is the perpendicular slope of PQ and b is the y-intercept of the line. To find b, we substitute the coordinates of the midpoint of PQ into the equation and solve for b. Then we substitute m⊥ and b into the equation to get the final answer.
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what is the modular inverse of $11$, modulo $1000$? express your answer as an integer from $0$ to $999$, inclusive.
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The modular inverse of 11, modulo 1000 is 901. Expressing the answer in integer form.
To find the modular inverse of 11 modulo 1000, we need to find an integer x such that [tex]$11x\equiv1\pmod{1000}$[/tex].
One way to find the modular inverse is to use the extended Euclidean algorithm. Using this algorithm, we can find the greatest common divisor of 11 and 1000 and express it as a linear combination of 11 and 1000.
We can then use the coefficients of this linear combination to express 1 as a linear combination of 11 and 1000.
Applying the extended Euclidean algorithm, we have:
1000= 11 *90 + 10
11 = 10 *1 + 1
Working backward, we can express 1 as a linear combination of 11 and 1000:
1 =11 - 10* 1
= 11 - (1000 - 11*90)
= 901 * 11 - 1 *1000
Therefore, the modular inverse of 11 modulo 1000 is 901, since
11*901=1 mod{1000}.
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Help please, not sure how to solve this!!!
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The exponential function for the Greenville's population so that the yearly growth rate is visible is given as follows:
G(t) = 24000(1.00124)^t.
How to define an exponential function?An increasing exponential function is modeled according to the rule presented as follows:
y = a(1 + r)^t.
In which:
a is the initial amount.r is the growth rate, as a decimal.The function for Greenville's population is given as follows:
G(t) = 24000(1.00496)^4t.
Which means that the population grows at a rate of 0.00496 = 0.496% every four years, hence the yearly growth rate is given as follows:
r = 0.00496/4
r = 0.00124.
Then the function is given as follows:
G(t) = 24000(1.00124)^t.
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Solve 2x2 + 26 = 0 to identify the roots.
Answers
X= ± √0^2-13
X= ± √-13
X= ± √13 i
Solution:
option B
2x^2 + 26 = 0
(Divide both sides by 2)
x^2+ 13=0
(Move the 0 and change the sign)
x^2= -13
(Simplify)
x= - 13i and x= 13i
lisa is on her way home in her car. she has driven 24 miles so far, which is three-fourths of the way home. what is the total length of her drive?
Answers
If lisa is on her way home in her car, she has driven 24 miles so far, which is three-fourths of the way home, Lisa's total drive is 32 miles.
Let's represent the total length of Lisa's drive as x. We know that she has driven 24 miles so far, which is three-fourths of the total length. We can write this information as:
24 = (3/4) x
To find x, we need to isolate it on one side of the equation. We can start by multiplying both sides by 4/3 to get rid of the fraction:
24 * (4/3) = x
Simplifying, we get:
32 = x
We can say that Lisa has already driven 24 miles, which is three-fourths of the total distance. To find the total distance, we use the equation 24 = (3/4) x, where x represents the total distance.
To solve for x, we multiply both sides of the equation by 4/3 to cancel out the fraction, giving us 32 = x. Therefore, Lisa's total drive is 32 miles.
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