Both Alpha and Beta Have a dominant strategy to price low
delta and united both Have a successful pricing plan
What do the terms "alpha" and "Beta" mean pricing?
Using an approach known as alpha-beta pruning, the mini max algorithm can examine fewer nodes in its search tree.
Reason: Regardless of what the other party decides, both firms opt for low prices. Therefore, it is both companies' dominating strategy.
Both Alpha and Beta advise against raising prices.
Reason: Regardless of what the other enterprises do, both businesses have decided against raising prices. So the prevalent method is to keep costs the same.
The major strategy of both businesses is to remain the same. Therefore, both statements A and B are true.
Due to the fact that both companies always opt to remain the same, regardless of what the other player does.
Both Alpha and Beta Have a dominant strategy to price low
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Suppose that a high school marching band has 112 members. Of these 112 band members, 35 are seniors, 21 play the trumpet, and 8 are seniors who play the trumpet. What is the probability that a randomly selected band member is a senior given that he or she plays the trumpet? Give your answer as a percentage, rounded to one decimal place. What is the probability that a randomly selected band member plays the trumpet given that he or she is a senior?
Answer:
Part A: 38.1% of the members are seniors that play the trumpet
Part B: 22.9% of the members who are seniors play trumpet
Step-by-step explanation:
Part A:
8 of the 21 members play trumpet that are seniors
8/21 = .381 or %38.1 of the members
Part B:
8 of the 35 seniors in the marching band play trumpet
8/35 = .229 or %22.9 of the members
The function f(x)=9.25x + 3 represents the amount radda earns dog walking for X hours
Since the function f(x) = 9.25x + 3 represents the amount of money that Radda earns dog walking for x hours, Radda's earnings would increase by $12.25 each hour.
How to write a linear function for the total amount of money Radda earns?In Mathematics, a linear function is sometimes referred to as an expression or the slope-intercept form of a straight line and it can be used to model (represent) the total amount of money that is being earned by Radda for dog walking;
T = mx + b
Where:
T represents the total amount of money earned.m represents the rate of change (slope) per hour.x represents the number of hours or time.b represents the y-intercept or initial amount.Therefore, the required linear function that represents the total amount of money that is being earned by Radda for dog walking per hour is given by this mathematical expression;
f(x) = T = 9.25x + 3
When the number of hours Radda spend dog walking is equal to 1 (x = 1), the rate of change(slope) can be calculated as follows;
f(1) = T = 9.25(1) + 3
f(1) = T = 9.25 + 3
f(1) = T = $12.25.
In this context, we can reasonably infer and logically conclude that Radda's earnings increases each hour by $12.25.
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Complete Question:
The function f(x) = 9.25x + 3 represents the amount Radda earns dog walking for x hours. How much does Radda's earnings increase each hour?
Kim and her friends watched the server making smoothies. The table shows the number of mangos that were used for each of the different sizes of smoothies that the friends ordered
.Mich statement is correct based on the data?
The ratio of smoothie size to mangos used for Kim is 1.7, and the ratio of smoothie size to mangos used for Bri is 3: 28.
The ratio of smoothie size to mangos used for Angela is higher than the ratio of smoothie size to mangos used for Kim.
The ratio of smoothie size to mangos used for Bri is 7:1, and the ratio of smoothie size to mangos used for Angela is 4: 28.
The ratio of smoothie size to mangos used for Kim is the same as the ratio of smoothie size to mangos used for Angela.
The solution is Option D.
The ratio of smoothie size to mangoes used for Kim is the same as the ratio of smoothie size to mangoes used for Angela
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
Given data ,
Let the equation be represented as A
Now , the value of A is
The number of mangoes used by Bri = 1 mango
The amount of smoothie size of Bri = 7 oz
The number of mangoes used by Kim = 3 mangoes
The amount of smoothie size of Kim = 21 oz
The number of mangoes used by Angela = 4 mangoes
The amount of smoothie size of Angela = 28 oz
Now , the proportion is given by
The ratio of smoothie size to mangoes used by Kim = amount of smoothie size of Kim / number of mangoes used by Kim
Substituting the values in the equation , we get
The ratio of smoothie size to mangoes used by Kim = 21 / 3
The ratio of smoothie size to mangoes used by Kim = 7 : 1
Now , the proportion is
The ratio of smoothie size to mangoes used by Angela = amount of smoothie size of Angela / number of mangoes used by Angela
Substituting the values in the equation , we get
The ratio of smoothie size to mangoes used by Angela = 28 / 4
The ratio of smoothie size to mangoes used by Angela = 7 : 1
So , The ratio of smoothie size to mangoes used by Kim = The ratio of smoothie size to mangoes used by Angela = 7 : 1
Hence , ratio of smoothie size to mangoes used by Kim is equal to ratio of smoothie size to mangoes used by Angela
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Answer:
d
Step-by-step explanation:
i took the test and its right :)
please help meeeeeeee
Answer: B & A
Step-by-step explanation: I think?
You intend to estimate a population mean with a confidence interval. You believe the population to have a normal distribution. Your sample size is 7.
While it is an uncommon confidence level, find the critical value that corresponds to a confidence level of 95.9%.
(Report answer accurate to three decimal places with appropriate rounding.)
ta/2 = ±
The critical value that corresponds to a confidence interval of 95.9% is 1.99.
The distribution of the sample mean will be roughly normally distributed, according to the Central Limit Theorem, if we have an unknown population with a mean and standard deviation and adequately small random samples (n < 30) are chosen from the population with replacement.
Then, the mean of the sample means is given by,
μ(x) = μ
And the standard deviation of the sample means is given by,
σ = σ / [tex]\sqrt{n}[/tex]
In this case the sample selected is of size, n = 7.
As the sample size n = 7 < 30, the sampling distribution of sample mean will be approximately normal.
So, a z-interval will be used to estimate the population mean.
The confidence level is, 95.9%.
The value of α is:
∝ = 1 - confidence level
∝ = 1 - 0.959
∝ = 0.041
The critical value is:
[tex]z_{\frac{∝ }{2} }[/tex] = [tex]z_{\frac{0.041}{2} }[/tex]
[tex]z_{\frac{∝ }{2} }[/tex] = [tex]z_{0.0205}[/tex]
[tex]z_{\frac{∝ }{2} }[/tex] = -1.99
[tex]z_{1-∝/2}[/tex] = 1.99
Use a z-table.
Therefore,
The critical value that corresponds to a confidence interval of 95.9% is 1.99.
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-y + 7y -54 = 0 what is the linear equation for y
The linear equation for y is y=9.
What is linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) component are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
-y+7 y-54=0
Add similar elements: -y+7 y=6 y
6 y-54=0
Move 54 to the right side
6 y=54
Divide both sides by 6
[tex]\frac{6 y}{6}=\frac{54}{6}[/tex]
Simplify
y=9
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g ranking/unranking algorithms to generate a uniform random binary string of length n with exactly k ones.
The solution is written in Python
binary = ""decimal = 13quotient = int (decimal / 2) remainder = decimal % 2binary = str(remainder) + binarywhile(quotient >0):decimal = int(decimal / 2)quotient = int(decimal / 2) remainder = decimal % 2binary = str(remainder) + binaryprint(binary)The given problem can be solved by using the rand() function that generates a random number over the range [0, RAND_MAX] and with the help of the value returned by this function, any number in any range [L, R] can be generated as (rand() % (R – L + 1)) + L. Follow the steps below to solve the problem:
Initialize an empty string, say S.
Iterate over the range [0, N – 1] and perform the following steps:
Store a random number in the range [0, 1] using rand() function.
Append the randomly generated 0 or 1 to the end of the string S.
After completing the above steps, print the string S as the resulting binary string.
This binary is to hold the binary string.
Next, we declare variable decimal, quotient and remainder (Line 2-4). We assign a test value 13 to decimal variable and then get the first quotient by dividing decimal with 2 (Line 3). Then we get the remainder by using modulus operator, % (Line 4). The first remainder will be the first digit joined with the binary string (Line 5).
We need to repeat the process from Line 3-5 to get the following binary digits. Therefore create a while loop (Line 7) and set a condition that if quotient is bigger than 0 we keep dividing decimal by 2 and calculate the quotient and remainder and use the remainder as a binary digit and join it with binary string from the front (Line 9-11).
At last, we print the binary to terminal (Line 13).
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A random sample of 75 students at the University of Minnesota spend an average of $614 per month in rent
with a standard deviation of $219. The distribution is moderately skewed to the high end. Which of the
following statements are true?
i. 95% of students at the university spend $564 to $664 on rent.
ii. We are 95% confident that the average rent for students at the university is between $564 and $664.
iii. Because we cannot examine other characteristics of the students in the random sample, it is not
advisable to construct a confidence interval.
Oi only
O ii only
O iii only
Oi and ii
Oi, ii, and iii
Check Answer
The correct option is b) ii only
From the given data we can construct confidence interval. So, the statement that we are 95% confident that the average rent for students at the university is between $ 564 and $664 is true.
What is meant by distribution?
The methodical effort to account for how the owners of the labor, capital, and land inputs divide the country's income. Rent, wages, and profit margins have historically been the focus of economists' research into how these expenses and margins are set.
What are the 3 types of distribution?
The Three Types of Distribution
Intensive Distribution: As many outlets as possible. The goal of intensive distribution is to penetrate as much of the market as possible.Selective Distribution: Select outlets in specific locations. ...Exclusive Distribution: Limited outlets.What are the 5 factors of distribution?
Market, Product, Company, Channel, and Environment Related Factors are 5 Important Factors Affecting Distribution Channel Selection. The distribution of goods can be done through a variety of routes.
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The angle formed between one side and another, always less than 180 degrees.
Answer:obtuse angle
Step-by-step explanation:
An obtuse angle is an angle of greater than 90° and less than 180°. It is bigger than an acute angle. It is smaller than a straight angle, which measures 180°. Angles are measured with a protractor obtuse angle is specifically present in hexagon and pentagon and others.
Marco has $16.72. He spends $9.21 on a movie ticket. How much money does Marco have left?
Responses
A $7.68$7.68
B $7.51$7.51
C $7.48$7.48
D $7.61
Answer:
7.51
Step-by-step explanation:
16.72 - 9.21
8.1.2 Exam: Semester 1 Exam Question 36 of 40 Solve 3-212. A. X≥-18 Correct! B. X. The answer is in the picture.
The solution to the given inequality is x ≤ -18 which is the correct answer that would be an option (D).
The inequality is given in the question as:
3 -x/2 ≥ 12
To solve this inequality, we need to isolate the variable x. To do this, we can start by subtracting 12 from both sides of the inequality:
3 - x/2 ≥ 12
3 - x/2 - 12 ≤ 0
Next, we can simplify the left side of the inequality by combining like terms:
-x/2 - 9 ≤ 0
Finally, we can solve for x by adding 9 to both sides and multiplying both sides by -2:
x ≤ -18
Thus, the solution to the inequality is x ≤ -18.
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2. Which of the following ordered pairs is a solution to the system of linear inequalities given below?
{2x³
(2y ≥-4x + 4
(x-2> 2y
I.(-2, 1)
II.(0, -2)
III.(4,-2)
IV. (1, 2)
The solutions to the given Inequalities are Option II. (0, -2) and Option IV. (1, 2).
What are inequalities:In mathematics, inequalities describe the connection between two non-equal numbers. Equal does not imply inequality.
Various types of inequalities are used to compare the values and determine whether they are smaller than or greater than.
It indicates that the phrase on the left should be either larger or smaller than that of the expression on the right, or vice versa.
Here we have
2y ≥ -4x + 4 --- (1)
x - 2 > 2y ---- (2)
Substitute each given point and find for which both equations will be satisfied
For Option I. (-2, 1)
(1) => 2(1) ≥ -4(-2) + 4
=> 2 ≥ - 4 [ Which is true ]
(2) => -2 - 2 > 2(1)
=> - 4 > 2 [ which is not true ]
For Option II. (0, -2)
(1) => 2(-2) ≥ -4(0) + 4
=> -4 ≥ 4 [ Which is true ]
(2) => 0 - 2 > 2(-2)
=> - 2 > - 4 [ which is true ]
For option III. (4,-2)
(1) => 2(-2) ≥ -4(4) + 4
=> - 4 ≥ - 12 [ Which is true ]
(2) => 4 - 2 > 2(1)
=> 2 > 2 [ which is not true ]
For option IV. (1, 2)
(1) => 2(2) ≥ -4(1) + 4
=> 4 ≥ 0 [ Which is true ]
(2) => 1 - 2 > 2(2)
=> - 1 > 4 [ which is true ]
From above calculations
The solutions to the given Inequalities are Option II. (0, -2) and Option IV. (1, 2).
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(Score for Question 1: of 3 points)
1. Represent each situation with an inequality.
(a) The sum of a number and 12 is at most -8.
(b) A number increased by -8 is greater than 12.
(c) -8 less than a number is no more than 12.
Answer:
Inequality for each part be
a) x + 12 ≤ -8
b) x - 8 > 12
c) x + 8 < 12
What do you mean by inequality?
In mathematics, an inequality is a relationship in which two numbers or other mathematical expressions compare unequal. Most commonly used to compare two numbers on the number line based on size.
The notation a < b means that a is less than b.
The notation a > b means that a is greater than b.
Let the number be x
According to the question:
a) The sum of a number and 12 is at most -8.
inequality become:
x + 12 ≤ -8
b) A number increased by -8 is greater than 12
inequality become:
x + (-8) > 12
⇒ x - 8 > 12
c) -8 less than a number is no more than 12
x - (-8) < 12
⇒ x + 8 < 12
Therefore, inequality for each part be
a) x + 12 ≤ -8
b) x - 8 > 12
c) x + 8 < 12
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How long is 10 percent of a 24 hour day
Answer:
Step-by-step explanation:
2.4 hours, aint no way this is college math
Answer:2.4 hours
Step-by-step explanation:
Dan has a jar full of quarters and dimes. He has 21 more dimes than he has quarters. Overall, Dan has 67 coins. How many of each coin does Dan have?
The number of dimes and quarters that Dan has will be 44 and 23, respectively.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Dan has a container loaded with quarters and dimes. He has 21 additional dimes than he has quarters. Generally, Dan has 67 coins.
Let 'x' be the number of dimes and 'y' be the number of quarters. Then the equations are given as,
x = y + 21 ...1
x + y = 67 ...2
From equations 1 and 2, then we have
y + 21 + y = 67
2y = 46
y = 23
Then the value of the variable 'x' is calculated as,
x = 23 + 21
x = 44
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at high temperatures, the partition function for rotational energy of a molecule of nitrogen is , where is the energy as in eq. 6.29.
True, at high temperatures, the partition function for rotational energy of a molecule of nitrogen is k T ϵ, where ϵ is the energy [tex]z_{rot}=\sum_{j=0}^{\infty}(2j+1)e^{-j(j+1)\epsilon/kT}[/tex].
As we know the rotational energy levels of a diatomic molecule are given by,
[tex]E_{rot}[/tex] (J) = BJ(J+1)
Where, B is the rotational constant.
From explicit summation, expression for rotational partition function ([tex]z_{rot}[/tex]), Equation 18.6.518.6.5, we can do an explicit summation
[tex]z_{rot}=\sum_{j=0}^{\infty}(2j+1)e^{-j(j+1)\epsilon/kT}[/tex]
When the rotational energy levels are lying very close to one another, we can integrate just as above, and we gets the equation you just provided.
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The right question is:
At high temperatures, the partition function for rotational energy of a molecule of nitrogen is k T ϵ, where ϵ is the energy in Eq. 6.29.
[tex]z_{rot}=\sum_{j=0}^{\infty}(2j+1)e^{-j(j+1)\epsilon/kT}[/tex]
A True
B False
1,458, 486, 162, 54, … patterns
1,458, 486, 162, 54,
Every succeeding number is getting divided by 3.
What is patterns ?
A recurring arrangement of numbers, shapes, colors, and other elements is known as a pattern. The Pattern may be connected to any kind of occasion or thing. When a group of numbers are arranged in a certain way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series.
Pattern of even numbers: 2, 4, 6, 8, 10, 1, 14, 16, 18...
Pattern of odd numbers: 3, 5, 7, 9, 11, 13, 15, 17, 19.
Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, and 21. so on.
The patterns among our 1,458, 486, 162, and 54 data must be found.
1458/3 = 486
486/3 = 162
162/3 = 54
54/3 = 18
18/3 = 6
6/3 = 2
so the patterns is Every succeeding number is getting divided by 3.
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Cone W has a radius of 6 cm and a height of 5 cm. Square pyramid X has the same base area and height as cone W.
Paul and Manuel disagree on the reason why the volumes of cone W and square pyramid X are related. Examine their arguments. Which statement explains whose argument is correct and why?
Manuel's argument is correct on why the volume of cone W and square pyramid are related . Paul used the incorrect base area to find the volume of square pyramid X. Then the correct option is C.
Define cone and square pyramid
A thick or empty device with an approximately round or elliptical base that tapers to a notch is known as a cone.
on the other hand ,
A three-dimensional geometric shape having a square base and four triangular faces/sides that meet at a single point (called vertex) is called a square pyramid.
CalculationCone W has a radius of 6 cm and a height of 5 cm.
The base area of the cone will be
A = πr²
A = π (6)²
A = 113.04 square cm
Then the volume of the cone will be
V = (1/3) x base area x height
V = (1/3) x 113.04 x 5
V = 188.4 cubic cm
Square pyramid X has the same base area and height as cone W.
Then the volume of the square pyramid will be
V = (1/3) x base area x height
V = (1/3) x 113.04 x 5
V = 188.4 cubic cm.
Manuel's argument is correct on why the volume of cone W and square pyramid are related . Paul used the incorrect base area to find the volume of square pyramid X. Then the correct option is C.
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In APQR, m/P = (x + 13)°, m/Q = (10x + 13)°, and
m/R = (2x − 2)°. Find m/Q.
Answer:
[tex]133^{\circ}[/tex]
Step-by-step explanation:
Angles in a triangle add to [tex]180^{\circ}[/tex].
[tex]x+13+10x+13+2x-2=180 \\ \\ 13x+24=180 \\ \\ 13x=156 \\ \\ x=12 \\ \\ m\angle Q=10(12)+13=133^{\circ}[/tex]
Find the value of the expression. x(x–y)–y(y^2–x) for x=4 and y=2
If h= 12 and g = 4, which of the following has a value of 3?
g+1
h-g
H/g
h÷3
Answer:
h/g is 3
Step-by-step explanation:
h=12 and g=4 12/4 is 3 so its h/g
Answer:
H/g
Step-by-step explanation:
12/4 = 3
Does the given matrix, A, have an inverse? If it does, what is A^-1?
The inverse of the matrix A is (b) [tex]A^{-1} = \left[\begin{array}{cc}7&25\\-2&-7\end{array}\right][/tex]
How to determine the inverse of the matrix?From the question, we have the following parameters that can be used in our computation:
[tex]A = \left[\begin{array}{cc}-7&-25\\2&7\end{array}\right][/tex]
To calculate the inverse of the matrix, we start by calculating the determinant of the matrix
This is calculated as follows
|A| = -7 * 7 + 25 * 2
Evaluate the products in the above equation
So, we have the following representation
|A| = -49 + 50
Evaluate the sum in the above equation
So, we have the following representation
|A| = 1
The inverse is then calculated as
[tex]A^{-1} = \frac{1}{|A|} * \left[\begin{array}{cc}7&25\\-2&-7\end{array}\right][/tex]
Substitute the known values in the above equation, so, we have the following representation
[tex]A^{-1} = \frac{1}{1} * \left[\begin{array}{cc}7&25\\-2&-7\end{array}\right][/tex]
Evaluate the quotient
[tex]A^{-1} = 1 * \left[\begin{array}{cc}7&25\\-2&-7\end{array}\right][/tex]
This gives
[tex]A^{-1} = \left[\begin{array}{cc}7&25\\-2&-7\end{array}\right][/tex]
Hence, the inverse is (b)
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What is the quotient of
102 and 5?
The leftover after dividing 102 by 5 is the quotient, which is:
Quotient 20
Remainder 2
102 5: Quotient and Remainder
The quotient and remainder method is one way to determine the quotient and remainder of a division. The dividend (102) and the divisor are already known to us (5). Now, we need to determine the residual and the quotient:
The Quotient and Remainder procedure is as follows:
20 quotient, 5 | 102 dividend, -10 2, and a reminder
As can be seen:
The remainder is 2, while the quotient is 20.
Sometimes, the remaining part is referred to as the "modulo," or simply "mod." This notation is used to say that:
102 mod 5 = 2
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Help with this plsssss !!!
Answer:
58
Step-by-step explanation:
There are 5 lines between 50 and 60
60 - 50 = 10
10 / 5 = 2
This means that each increment is 2.
We see the end of the box plot is above the fourth increment above 50.
4 x 2 = 8
50 + 8 = 58
Kevin has an annual salary of $41,732, and he earned $33.52 interest from his savings account. He also paid $1050 in student loan interest and contributed $3900 to an IRA retirement account. Calculate Kevin’s adjusted gross income.
Kevin's adjusted gross income is $36, 815. 52
What is adjusted gross income?Adjusted gross income is simply described as gross income minus certain adjustments from the income.
These adjustments includes;
Educator expensesStudent loan interestAlimony paymentsContributions to an account, etcIt is calculated as;
Adjusted gross income = sum total of income - expenses
Now, let's substitute the values into the formula, we have;
Adjusted gross income = $(41,732 + 33.52) - $(1050 + 3900)
Add the values
Adjusted gross income = $(41, 765. 52 - 4950)
Subtract the values
Adjusted gross income = $36, 815. 52
Hence, the value is $36, 815. 52
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A triangle has vertices D (-2,-4), E (4, -2) and F (1, 7). What is the length of FD?
6.325
9.487
11.402
2/3
-3
7.892
-3/4
The length of FD with given coordinates F (1, 7) and D (-2,-4) will be 11.402 thus option (C) is correct.
How to find the distance between two points?Let's consider we have two points (x₁, y₁) and (x₂, y₂) the distance between these two points is given by the formula;
[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]
As per the given points,
F (1, 7) and D (-2,-4)
The distance between above both points will be as,
[tex]d = \sqrt {\left( {1 + 2 } \right)^2 + \left( {7 + 4 } \right)^2 }[/tex]
d = √(9 + 121)
d = √130 = 11.102
Hence "With the provided coordinates F (1, 7) and D (-2, -4), the length of FD will be 11.402".
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a 9 foot ladder is leaning against a wall. if the top of the ladder is sliding down the wall at a rate of
The rate at which the top of ladder slide down is 8.48 ft/s. The negative sign implies that the height is reducing with time which is true because it is sliding down.
The well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, [tex]a^{2}+b^{2} =c^{2}[/tex]
Given that,
Length of the ladder is, [tex]l=9ft[/tex]
Let the top of ladder be at height of 'h' and the bottom of the ladder be at a distance of 'b' from the wall.
Now, from triangle ABC,
[tex]AB^{2} +BC^{2} =AC^{2}[/tex]
[tex]h^{2} +b^{2} =l^{2}[/tex]
[tex]h^{2} +b^{2}[/tex] = [tex]9^{2}[/tex]
[tex]h^{2} +b^{2}[/tex] = 81 (Equation-1)
Differentiating the above equation with respect to time, 't'.
So,
We can write,
[tex]\frac{d}{dt} (h^{2}+b^{2} )[/tex] = [tex]\frac{d}{dt}[/tex] (81)
[tex]\frac{d}{dt} (h^{2}+b^{2} )[/tex] = 0
[tex]2h\frac{dh}{dt} +2b\frac{db}{dt}[/tex] = 0
[tex]h\frac{dh}{dt} +b\frac{db}{dt}[/tex] = 0 (Equation-2)
In the above equation the term [tex]\frac{dh}{dt}[/tex] is the rate at which top of ladder slides down and [tex]\frac{db}{dt}[/tex] is the rate at which bottom of ladder slides away.
Let us assume,
h = 3 ft and db/dt = 3 ft/s
We can substitute values in equation-1,
[tex]3^{2} +b^{2}[/tex] = 81
9 + [tex]b^{2}[/tex] = 81
[tex]b^{2}[/tex] = 81-9
[tex]b^{2}[/tex] = 72
b = [tex]\sqrt{72}[/tex]
b = 8.48 ft
Now, plug in all the given values in equation (2) and solve for [tex]\frac{dh}{dt}[/tex]
3*[tex]\frac{dh}{dt}[/tex] + 8.48 * 3 = 0
3*[tex]\frac{dh}{dt}[/tex] + 25.44 = 0
3*[tex]\frac{dh}{dt}[/tex] = - 25.44
[tex]\frac{dh}{dt}[/tex] = -25.44/3
[tex]\frac{dh}{dt}[/tex] = - 8.48 ft/s
Therefore,
The rate at which the top of ladder slide down is 8.48 ft/s. The negative sign implies that the height is reducing with time which is true because it is sliding down.
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The function below has at least one rational zero. Use this fact to find all zeros of the function. f(x)=7x^4 +27x^3 -40x^2 +x +5
The rational zeros of the function can be found using the Rational Zero Theorem. The possible rational zeros of the function are ±1, ±5, ±1/7, ±5/7.
Zeros:
x=-5, -1/7, 0, 1, 5
The Rational Zero Theorem states that if a polynomial function of degree n has integer coefficients, then the possible rational zeros of the function will be of the form ±p/q, where q is a factor of the leading coefficient and p is a factor of the constant term.
In this case, the degree of the polynomial is 4, which means that the leading coefficient is 7 and the constant term is 5. Thus, the possible rational zeros of the function will be of the form ±p/q, where p is a factor of 5 and q is a factor of 7. The factors of 5 are ±1 and ±5, and the factors of 7 are ±1 and ±7. This means that the possible rational zeros of the function are ±1, ±5, ±1/7, and ±5/7.
To find the zeros of the function, we can use the rational zeros we found and plug them into the original equation. We can then solve for the zeros and find that the zeros of the function are x=-5, -1/7, 0, 1, 5.
x=-5: 7(-5)^4 +27(-5)^3 -40(-5)^2 +(-5) +5= 0
x=-1/7: 7(-1/7)^4 +27(-1/7)^3 -40(-1/7)^2 +(-1/7) +5= 0
x=0: 7(0)^4 +27(0)^3 -40(0)^2 +(0) +5= 0
x=1: 7(1)^4 +27(1)^3 -40(1)^2 +(1) +5= 0
x=5: 7(5)^4 +27(5)^3 -40(5)^2 +(5) +5= 0
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what number is 16 2/3% more than 240
280 is the number which is 16 2/3% more than 240
What is the percentage?
It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
We would receive 16 times 3 plus 2 if we converted 16 2/3 to an improper fraction. Then, we would divide this number by 3, getting 50/3, which is equal to 50/3 divided by 100, or 1/6.
(1/6) th of 240 = 240/6 = 40
40 more than 240 = 280
So, 280 is the number which is 16 2/3% more than 240
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4. Solve the equation 10x = 10,563. Be sure
to provide the solution both exactly and
approximately.
