a) The expression for the stable fixed point is P* = (1 + sqrt(1 - 4h)) / 2
b) There exists a fixed point for all values of h less than or equal to 1/4.
The fixed points of the model are the values of P at which dP/dt = 0. Therefore, we need to solve the equation
P(1-P) - h = 0
Expanding the left-hand side, we get
P - P^2 - h = 0
Rearranging, we get a quadratic equation
P^2 - P + h = 0
Using the quadratic formula, the two solutions for P are
P = (1 ± sqrt(1 - 4h)) / 2
a) The larger root is the stable fixed point, as it corresponds to a minimum of the fish population growth function. Therefore, the expression for the stable fixed point is
P* = (1 + sqrt(1 - 4h)) / 2
b) For the model to have a fixed point, the quadratic equation must have real roots. This occurs when the discriminant (the expression inside the square root) is non-negative
1 - 4h ≥ 0
Solving for h, we get
h ≤ 1/4
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The given question is incomplete, the complete question is:
This problem explores some questions regarding the fishery model
dP/dt =P(1−P)−h
If you have not yet run the Jupyter notebook please do so now. Find analytical expressions for the two fixed points of the model, in terms of h
a) Give an expression for the stable fixed point. You may assume that the larger fixed point is the stable one. b) For what values of h does there exist a fixed point?
Bhujangrao invested Rs. 2,50,590 in shares of F.V. Rs. 10 when M.V. is Rs. 250. [Nov 2020]
Rate of brokerage is 0.2% and GST is 18%, then find:
a. the number of shares purchased,
b. the amount of brokerage paid, and
c. GST paid for the trading
a. The number of shares purchased can be calculated as:
Number of Shares = (Investment Amount / Face Value)
= 25,059/ 10 = 2,505.9 = 2,506 (to the nearest whole number)
b. The amount of brokerage paid can be calculated as:
Brokerage = (Investment Amount x Brokerage Rate)
= 2,50,590 x 0.002 = Rs. 501.18
c. The GST paid for the trading can be calculated as:
GST = (Brokerage Amount x GST Rate)
= 501.18 x 0.18 = Rs. 90.22
Conduct a survey with a minimum of 20 people. Complete the designed questionnaire in 1.2. Remind participants why you are doing survey and that their information will be kept confidential. Submit 20 original completed questionnaires.
Some of the tips which is used to conduct a survey are:
Determine the purpose of the survey and define the population of interest.Design the questionnaire and ensure that the questions are clear and concise.Select a sample from the population and distribute the questionnaire to the participants.Remind participants why you are conducting the survey and assure them that their responses will be kept confidential.What is the need to conduct a survey (questionnaire)?Conducting a survey is an important tool for gathering information from a large and diverse group of people. Its allows allow researchers to obtain data from a representative sample of the population, which can then be used to make informed decisions, identify trends, and measure changes over time.
Also important, its can provide insight into people's attitudes, beliefs, and behaviors, which can be valuable in developing marketing strategies, designing programs and policies, and making important decisions.
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A Triangle has a height that is half of 28 yards and an area of 56 yards^2. What is the length of the base of the trangle?
The length of the base of the triangle is 8 yards whose height is half of 28 yards.
What is triangle?A triangle is a two-dimensional geometric shape that is formed by three straight lines that connect three non-collinear points. These three lines are called the sides of the triangle, and the points where the sides meet are called the vertices of the triangle.
According to question:The following formula provides the area of a triangle:
Area = (1/2) x base x height
We are given that the height of the triangle is half of 28 yards, which is:
height = 1/2 x 28 = 14 yards
We are also given that the area of the triangle is 56 square yards. Substituting these values into the formula for the area, we get:
56 = (1/2) x base x 14
Simplifying this equation, we get:
56 = 7 x base
Dividing both sides by 7, we get:
base = 8
Therefore, the length of the base of the triangle is 8 yards.
The vertices are typically denoted by letters, such as A, B, and C. The three angles formed by the sides are also part of the triangle.
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PLEASE HELP ME YOU WILL BE MARKED BRAINLIEST!!!1
The experimental probability of winning the contest based on the data of all 3 games is 0.432.
What is experimental probability ?
Experimental probability is a measure of the likelihood of an event occurring based on the results of an experiment or observation. It is determined by dividing the number of times the event occurred by the total number of trials or observations. The more trials or observations conducted, the more accurate the experimental probability will be. Experimental probability is often used in situations where the probability of an event cannot be determined theoretically or where the theoretical probability is difficult to calculate. It is also commonly used in scientific experiments, market research, and other fields where the results of an experiment or observation can be used to make predictions or inform decisions.
Finding the experimental probability of winning the contest :
In this case, the event is winning the contest by choosing a marble from a bag, and the trials are the three games played by Hal.
Total number of players in all three games = 123 + 155 + 172 = 450
Total number of winners in all three games = 52 + 63 + 65 = 180
Experimental probability of winning the contest = Number of winners / Total number of players = 180/450 = 0.432
Therefore, the experimental probability of winning the contest based on the data of all 3 games is 0.432.
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I will mark you brainiest!
A concave polygon can never be classified as a regular polygon.
A) True
B) False
Answer:
False.
Step-by-step explanation:
A concave polygon can never be a regular polygon as it can never be equiangular. Each side of a regular polygon must be the same length, and all interior angles must also be equal.
A parent donated 36 fruit cups and 24 bananas to fifth grade. The teacher wanted to make field trip snack bags with the donated food and wondered about the ways snacks could be packed. To be fair the teacher wants to make sure that all bags are exactly the same.
A) What is the greatest number of snack bags that the teacher can make, if each bag is identical? How do you know ?
B) What other numbers of snack bags could she make? How do you know?
2) Another parent also donated 24 bananas, so there are 48 bananas total. Now what is the greatest number of snack bags can that can be made?
3) The teacher realized that she miscounted and had only 30 fruit cups. How many snack bags can she make with 48 bananas and fruit cups?
4) What do the different numbers of snack bags that can be made have to do with the number of fruit cups and number of bananas?
PLEASE HELP ASAP! This composite figure is created by placing a sector of a circle on a triangle. What is the area of this composite figure? Use 3.14 for n. Round to the nearest hundredth. Show your work.
Answer: 24
Step-by-step explanation:
To find the area of the composite figure, we need to find the area of the sector and the area of the triangle and then add them together.
Area of sector = (θ/360) * π * r^2, where θ is the angle of the sector in degrees, r is the radius of the circle.
The angle of the sector can be found by subtracting the angle of the triangle from 360 degrees. The radius of the circle can be found by dividing the length of the arc by the angle of the sector.
Length of the arc = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 4 = 4.19
Radius of the circle = 4.19/60 = 0.07
Angle of sector = 360 - 60 = 300 degrees
Area of sector = (300/360) * 3.14 * 0.07^2 = 0.0041
The area of the triangle can be found using the formula:
Area of triangle = (1/2) * base * height = (1/2) * 8 * 6 = 24
Therefore, the total area of the composite figure is:
0.0041 + 24 = 24.0041
Rounding to the nearest hundredth, the area of the composite figure is approximately 24.00.
Increase £16470.45 by 3.5%
Give your answer rounded to 2 DP
Step-by-step explanation:
"increase" means to take the original 100% and put an additional 3.5% of these 100% on top of it.
so, we have to calculate
100% + 3.5% of £16470.45
100% of £16470.45 = £16470.45 × 100/100
3.5% of £16470.45 = £16470.45 × 3.5/100
the sum is therefore
£16470.45 × (100/100 + 3.5/100) =
= £16470.45 × (1 + 0.035) = £16470.45 × 1.035 =
= £17,046.91575 ≈ £17,046.92
when comparing the distribution of the population of individual scores to the distribution of means, the distribution of means will always have
The population distribution of scores has a similar average as the distribution of means.
In a sample distribution of means, the distribution will roughly resemble a normal distribution, the sampling distribution's mean will be equal to the population's mean, and the sampling distribution's standard deviation is based on the Central Limit Theorem.
The central limit theorem (CLT) of probability theory states that the distribution of a sample variable tends towards a normal distribution (i.e., a "bell curve") as the sample size increases, under the premise that all samples are of equal size and regardless of the population's actual distribution shape.
In other terms, the central limit theorem (CLT) is a statistical presumption that the mean of all sampled variables from the same population will be substantially equal to the mean of the entire population, given a large enough sample size from a population with little volatility. These samples likewise resemble a normal distribution in accordance with the law of large numbers, with their variances nearly matching the variance of the population as the sample size rises.
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the actual question is :
When comparing the size of the standard error of the mean with the size of the standard deviation of the underlying distribution of individual scores:
a. the standard error of the mean is always larger
b. the standard error of the mean is always smaller
c. the standard error of the mean is sometimes larger and sometimes smaller, depending on the sample size
d. none of these
When a researcher wants to report the average cost of college tuition from the 1950s until present time, he or she enlists _______ statistics.a) Inferentialb) Descriptivec) Correlationald) Predictive
Descriptive statistics are used to summarize and describe data, making them useful for providing a clear understanding of a dataset's important features.
When a researcher wants to report the average cost of college tuition from the 1950s until present time, descriptive statistics are the appropriate method to use. Descriptive statistics are used to summarize and describe data, making them useful for providing a clear understanding of a dataset's important features. By using descriptive statistics, the researcher can calculate measures of central tendency, such as the mean, median, and mode, to determine the typical or average cost of college tuition over time. Additionally, measures of variability, such as the range and standard deviation, can be calculated to understand the spread of the data. Descriptive statistics are commonly used in many fields, including business, economics, psychology, and education, and can provide valuable insights into trends, patterns, and distributions within a dataset.
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Use implicit differentiation to find an equation of the tangent line to the curve sin(x+y)=8x−8y at the point (π,π)
The equation of the tangent line to the curve sin( x y) = 8x- 8y on the factor( π, π) is y = (7/9) x-( 2π/ 9).
To discover the equation of the tangent line to the curve sin( x y) = 8x- 8y on the point( π, π), we want to apply implicit differentiation to discover the pitch of the tangent line at that point.
We begin through differencing both sides of the equation with reference to xcos( x y)( 1 dy/ dx) = eight- 8dy/ dx
After, we can simplify the expression by isolating the terms beholding dy/ dx on one aspect
cos( x y) cos( x y) dy/ dx = 8- 8dy/ dx
8 cos( x y)) dy/ dx = 8- cos( x y)
dy/ dx = ( 8- cos( x y))( 8 cos( x y))
Now we're suitable to discover the pitch of the tangent line at the factor( π, π) by plugging in x = π and y = π into the expression we simply derived
dy/ dx = ( 8- cos( 2π))( 8 cos( 2π))
dy/ dx = ( 8- 1)/( 8 1)
dy/ dx = 7/ nine
Thus, the pitch of the tangent line to the curve sin( x y) = 8x- 8y at the factor( π, π) is7/9.
To find the equation of the tangent line, we can use the point- slope form of the equation
y- y1 = m( x- x1)
In which m is the pitch we simply set up, and( x1, y1) is the point( π, π). Plugging in the values, we get
y- π = ( 7/ nine)( x- π)
Simplifying, we get
y = ( 7/ nine) x-( 2π/ nine)
Thus, the equation of the tangent line to the curve sin( x y) = 8x- 8y on the factor( π, π) is y = (7/9) x-( 2π/ 9).
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Zaheer had a set of marbles, he used 2/3 to make a design and he had 14 left. How many did he used to make the design?
Answer: 42
Step-by-step explanation:
1. 1/3=14
2. 14x3=42
x P(x)
0 0.1
1 0.05
2 0.1
3 0.75
Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places
Answer: To find the standard deviation of a probability distribution, we need to first calculate the mean or expected value of the distribution, which is given by:
E(X) = Σ [xi * P(xi)]
where xi is the ith outcome and P(xi) is its probability.
So, for the given distribution:
E(X) = (0 * 0.1) + (1 * 0.05) + (2 * 0.1) + (3 * 0.75) = 2.4
Next, we need to calculate the variance of the distribution, which is given by:
Var(X) = Σ [(xi - E(X))^2 * P(xi)]
So, for the given distribution:
Var(X) = (0 - 2.4)^2 * 0.1 + (1 - 2.4)^2 * 0.05 + (2 - 2.4)^2 * 0.1 + (3 - 2.4)^2 * 0.75 = 0.69
Finally, the standard deviation of the distribution is the square root of the variance:
SD(X) = sqrt(Var(X)) = sqrt(0.69) ≈ 0.83
Therefore, the standard deviation of this probability distribution is approximately 0.83, rounded to 2 decimal places.
Step-by-step explanation:
Parts A-D. What is the value of the sample mean as a percent? What is its interpretation? Compute the sample variance and sample standard deviation as a percent as measures of rotelle for the quarterly return for this stock.
The sample mean is 2.1, the sample variance is 212.5% and the standard deviation is 14.57%
What is the sample mean?a. The sample mean can be computed as the average of the quarterly percent total returns:
[tex](11.2 - 20.5 + 13.2 + 12.6 + 9.5 - 5.8 - 17.7 + 14.3) / 8 = 2.1[/tex]
So the sample mean is 2.1%, which can be interpreted as the average quarterly percent total return for the stock over the sample period.
b. The sample variance can be computed using the formula:
[tex]s^2 = sum((x - mean)^2) / (n - 1)[/tex]
where x is each quarterly percent total return, mean is the sample mean, and n is the sample size. Plugging in the values, we get:
[tex]s^2 = (11.2 - 2.1)^2 + (-20.5 - 2.1)^2 + (13.2 - 2.1)^2 + (12.6 - 2.1)^2 + (9.5 - 2.1)^2 + (-5.8 - 2.1)^2 + (-17.7 - 2.1)^2 + (14.3 - 2.1)^2 / (8 - 1) = 212.15[/tex]
So the sample variance is 212.15%. The sample standard deviation can be computed as the square root of the sample variance:
[tex]s = \sqrt(s^2) = \sqrt(212.15) = 14.57[/tex]
So the sample standard deviation is 14.57%.
c. To construct a 95% confidence interval for the population variance, we can use the chi-square distribution with degrees of freedom n - 1 = 7. The upper and lower bounds of the confidence interval can be found using the chi-square distribution table or calculator, as follows:
upper bound = (n - 1) * s^2 / chi-square(0.025, n - 1) = 306.05
lower bound = (n - 1) * s^2 / chi-square(0.975, n - 1) = 91.91
So the 95% confidence interval for the population variance is (91.91, 306.05).
d. To construct a 95% confidence interval for the standard deviation (as percent), we can use the formula:
lower bound = s * √((n - 1) / chi-square(0.975, n - 1))
upper bound = s * √((n - 1) / chi-square(0.025, n - 1))
Plugging in the values, we get:
lower bound = 6.4685%
upper bound = 20.1422%
So the 95% confidence interval for the standard deviation (as percent) is (6.4685%, 20.1422%).
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Colin buys gas for her car at $4 a gallon. Write an equation using two variables to show the relationship between the number of gallons of gas, g, and the total amount of amount she spends, s.
Answer:
s = 4g ..........................................................
Prove that the diagonals of rectangle are equal vectorically in easy way
Answer: Imagine a rectangle with its centre (point of intersection of diagonals) situated at the origin of the XY plane and it's each of the sides being aligned with the co-ordinate axis.
Students at a virtual school are allowed to sign up for one math class each year. The numbers of students signing up for various math classes for the next school year are given in the following table:
Grade Geometry Algebra I Pre-Calculus AP Statistics Total
A student calculated the joint relative trequency of 10th grade students in geometry as being 71.4%. What did the student actually calculate and what is the correct answer?
A) The student calculated the conditional relative frequency for students who are in 10th grade, given that they are enrolled in Geometry. The correct value of the joint relative frequency of 10th grade students in geometry is 20.7%.
B) The student calculated the conditional relative frequenc for students who are in 10th grade, given that they are enrolled in Geometry. The correct value of the joint relative frequency of 10th grade students in geometry is 29%.
C) The student calculated the marginal relative frequency for 10th grade students in geometry. The correct value of the joint relative trequency of 10th grade students in geometry is 20.7%.
D) The student calculated the marginal relative frequency for 10th grade students in geometry. The correct value of the joint relative frequency of 10th grade students in geometry is 29%
Option C) The student calculated the marginal relative frequency for 10th grade students in geometry. The correct value of the joint relative frequency of 10th grade students in geometry is 20.7%.
How to calculate a relative frequency?Relative frequency is a measure of the proportion or percentage of times an event occurs in a given sample. It is calculated by dividing the frequency of an event by the total number of events in the sample. The formula for relative frequency is given as follows:
Relative frequency = Frequency of an event / Total number of events in the sample
For the joint relative frequency of 10th grade students in geometry, the parameters are given as follows:
Frequency of 10th grade students in geometry: 20.7%.Total number of events in the sample: 100% of students.Hence the joint relative frequency is obtained as follows:
20.7/100 x 100%= 20.7%.
Hence option C is correct.
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The Millers have hired an interior designer to decorate their family room. They want to have a 29" by 29" oil painting framed and incorporated in the design plan. If the designer chooses molding that is 4" wide and is priced at $3.65 per inch, how much will the molding cost (before tax)?
Answer: I really don't know i'm just trying to get a quest done sorry
2(x-6)²
could you please explain this to me, thanks!
Answer:
expand the square
2(x-6) (x-6)
2(x(x-6)-6(x-6)
2(x²-6x-6(x-6)
2(x²-6x-6x+36)
2(x²-12x+36)
2x²-24x+72
Step-by-step explanation:
hope this helps
Suppose Set A contains 98 elements and Set B contains 93 elements. If Sets A and B have 35 elements in common, what is the total number of elements in either Set A or Set B.
The total number of elements in either Set A or Set B is 156.
How are sets and subsets different from one another?A set is a collection of unique items, but a subset is a set that contains only components that belong to another set, termed the superset. In other words, set A is a subset of set B if all of its items are also found in set B.
Given that, Set A contains 98 elements and Set B contains 93 elements.
Total number of elements in either Set A or Set B = number of elements in Set A + number of elements in Set B - number of common elements
Total number of elements in either Set A or Set B = 98 + 93 - 35
Total number of elements in either Set A or Set B = 156
Hence, the total number of elements in either Set A or Set B is 156.
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Change the following equation of a line into slope-intercept form.
y + 4 = 2x
Answer:
Step-by-step explanation:
[tex]y=2x-4[/tex] (slope-intercept form is [tex]y=mx+b[/tex] where m=gradient
and b is where line intercepts y-axis)
Se depositan $ 8.000 en un banco que reconoce una tasa de interés del 36% anual, capitalizable mensualmente. ¿Cuál será el monto acumulado en cuatro años?
Answer:
Se depositan $ 8.000 en un banco que reconoce una tasa de interés del 36% anual, capitalizable mensualmente. ¿Cuál será el monto acumulado en cuatro años?
Step-by-step explanation:
Para resolver este problema, podemos utilizar la fórmula del interés compuesto:
A = P*(1 + r/n)^(n*t)
Donde:
A: el monto acumulado después de t años
P: el capital inicial
r: la tasa de interés anual
n: el número de veces que se capitaliza el interés por año
t: el tiempo en años
En este caso, tenemos:
P = $8.000
r = 36% = 0.36
n = 12 (ya que la tasa de interés se capitaliza mensualmente)
t = 4 años
Sustituyendo estos valores en la fórmula, obtenemos:
A = $8.000*(1 + 0.36/12)^(124)
A = $8.000(1 + 0.03)^48
A = $8.000*(1.03)^48
A = $16.751,83
Por lo tanto, el monto acumulado en cuatro años será de $16.751,83.
A weight is attached to a spring that is oscillating up and down. It takes 2 seconds for the spring to complete one cycle, and the distance from the highest to the lowest point is 5 in. What equation models the position of the weight at time t seconds?
The equation that models the position of the weight at time t seconds is y(t) = 2.5 sin (πt) + 2.5
The equation that models the position of the weight at time t seconds is
y(t) = 2.5 sin (πt) + 2.5
The position of the weight at time t seconds can be modeled by a sinusoidal function of the form
y(t) = A sin (ωt + φ) + C
where
A is the amplitude of the oscillation (half the distance between the highest and lowest points), which is 2.5 in.
ω is the angular frequency of the oscillation, which is 2π divided by the period (the time for one complete cycle), which is 2 seconds. So, ω = 2π/2 = π radians/second.
φ is the phase angle, which depends on the initial position of the weight. We can assume that the weight starts at the highest point (the crest), so φ = 0.
C is the vertical shift, which is the midpoint of the oscillation (half the distance between the highest and lowest points added to the starting point). So, C = 2.5 + 0 = 2.5 in.
Putting it all together, we get
y(t) = 2.5 sin (πt) + 2.5
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Find the value of X using the picture below.
Answer:
x = 7
Step-by-step explanation:
The two angles are equal so the opposite sides are equal.
5x-2 =33
Add two to each side.
5x-2+2 = 33+2
5x=35
Divide by 5
5x/5 =35/5
x = 7
What was your recommended intake of carbohydrates (grams), and how far were you from it? Show the mathActual Intake Recommended Intake Percentage159.00 115-166 100%
The actual intake of carbohydrates is 138% as compare to recommended intake.
Recommended intake of carbohydrates or any other nutrient are,
Based on the information provided,
Consumed 159 grams of carbohydrates,
Recommended intake is between 115 and 166 grams.
Calculate the percentage of actual intake compared to the recommended intake, use the following formula,
Percentage = (Actual Intake / Recommended Intake) x 100%
Substituting the values in the formula we have,
⇒Percentage = (159 / 115) x 100%
⇒Percentage ≈ 138.3%
Therefore, the actual intake of carbohydrates is about 138% of the recommended intake, indicating that consumption of more carbohydrates than recommended.
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I don’t understand please help me with this
Answer:
Greg bought a pack of X jumbo stickers during the back - to - school sale at Crafty's craft store. He ( uses 4 ( -4 ), ( you didn't give options ). There were 8 stickers left in the pack.
Hope this helps!
Step-by-step explanation:
Find dz/dt in two ways: by using the Chain Rule, and by first substituting the expressions for x and y to write z as a function of t. Do your answers agree?z= x^2y+xy^2, x = 3t y = t^2
The derivative of the function z= x^2y+xy^2, x = 3t y = t^2 using the chain rule is given by dz/dt = 36t^3 + 15t^4.
Expressions are equals to,
z= x^2y+xy^2
x = 3t
y = t^2
Using the chain rule calculate dz/dt,
which states that if z is a function of x and y,
And x and y are both functions of t, then,
dz/dt = (dz/dx)(dx/dt) + (dz/dy)(dy/dt)
Using these expressions, calculate the value of dz/dt using the chain rule,
z= x^2y+xy^2
This implies,
dz/dx = 2xy + y^2
dz/dy = x^2 + 2xy
x = 3t
⇒ dx/dt = 3
y = t^2
⇒ dy/dt = 2t
Substituting these values into the chain rule formula, we get,
dz/dt = (2xy + y^2)(3) + (x^2 + 2xy)(2t)
= [2(3t)(t^2 ) + (t^2)^2 ]3 + [(3t)^2 + 2(3t)(t^2)](2t )
= [ 6t^3 + t^4 ]3 + [ 9t^2 + 6t^3 ]2t
= 18t^3 + 3t^4 + 18t^3 + 12t^4
= 36t^3 + 15t^4
Substituting the given expressions for x and y into z, we get,
z = (3t)^2(t^2) + (3t)(t^2)^2
= 9t^4 + 3t^5
here also,
dz/dt = 36t^3 + 15t^4
Therefore, the value of the function using the chain rule dz/dt is equals to 36t^3 + 15t^4.
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01106115 Ex-1 Find the height of a tree if the angle of elevation Of its top Changes from 25 to 50° as the Observer advanced 15 meters toward
it's base
Answer:
about 11.5 m
Step-by-step explanation:
You want the height of a tree when the angles of elevation to its top are 25° and 50° from points 15 m apart.
TangentThe tangent relation between angles and sides in a right triangle is ...
Tan = Opposite/Adjacent
In the attached diagram, this means ...
tan(25°) = TX/AX
tan(50°) = TX/BX
SolutionThe difference between AX and BX is known, so we can rearrange this to ...
AX -BX = 15 = TX/tan(25°) -TX/tan(50°)
15·tan(25°)·tan(50°) = TX(tan(50°) -tan(25°) . . . multiply by tan(25°)tan(50°)
TX = 15·tan(25°)·tan(50°)/(tan(50°)-tan(25°) ≈ 11.5 . . . . meters
The height of the tree is about 11.5 meters.
__
Additional comment
The value of the height can be computed by finding each tangent only once if we use ...
TX = 15/(1/tan(25°) -1/tan(50°))
You recognize 1/tan(x) = cot(x) = tan(90°-x), so this is ...
TX = 15/(tan(65°) -tan(40°))
In the New York State Numbers Lottery, you pay $1 and pick a number from 000 to 999. If your number comes up, you win $750, which is a profit of $749. If you lose, you lose $1. Your probability of winning is 0.001.
The expected value of playing this game is -$0.251. This means that, on average, you can expect to lose 25.1 cents every time you play this game.
What is outcome?The term "outcome" generally refers to the result or effect of an action, process, or event. It refers to what happens as a consequence of a particular decision, activity, or circumstance.
According to question:To calculate the expected value, we multiply the possible outcomes by their probabilities and then sum them up.
Let's start with the possible outcomes:
If you win, you make a profit of $749, so the outcome is $749.
If you lose, you lose $1, so the outcome is -$1.
The probabilities are:
Probability of winning is 0.001.
Now we can calculate the expected value:
Expected value = (0.001 * $749) + (0.999 * -$1)
Expected value = $0.748 - $0.999
Expected value = -$0.251
Therefore, the expected value of playing this game is -$0.251. This means that, on average, you can expect to lose 25.1 cents every time you play this game.
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Evaluate the logarithmic expression without using a calculator. Answer exactly. log 2 ( 1/16 ) + 4 =
[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{we'll use this one} }{log_a a^x = x}\qquad \qquad a^{log_a (x)}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{1}{16} \right)+4\implies \log_2\left( \cfrac{1}{2^4} \right)+4\implies \log_2(2^{-4})+4\implies -4+4\implies \text{\LARGE 0}[/tex]
[tex]\rule{34em}{0.25pt}\\\\ \textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b\qquad\qquad \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{1}{16} \right)=y\implies 2^y=\cfrac{1}{16}\implies 2^y=2^{-4}\implies y=-4[/tex]