Answer:
a. To find the factor by which the area decreases in 10 years, we can use the formula for exponential decay: A(t) = A0 * e^(-kt) where A0 is the initial area, k is the decay constant, and t is the time in years.
Given that A(t) = 11 -0.98^t.
so, we can say k =0.98
The area after 10 years will be:
A(10) = 11 - 0.98^10
The decrease factor is:
(A(10)/A(0)) = (11 - 0.98^10)/11
b. To find the factor by which the area decreases each month, we can first convert the annual decay rate to a monthly rate by dividing by 12, since there are 12 months in a year.
So, the monthly decay rate is 0.98/12 = 0.0816
Then we can use the formula for exponential decay again with the new decay rate:
A(t) = A0 * e^(-kt)
The area after 1 month will be:
A(1/12) = 11 - 0.0816^(1/12)
The decrease factor is :
(A(1/12)/A(0)) = (11 - 0.0816^(1/12))/11
if i helped you, can you mark my answer as best?
Here is a probability scale: 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 If I flip a coin, place a cross on the probability scale to show the probability of getting a head.
Answer:
0.5
Step-by-step explanation:
If you flip a coin, the probability of getting a head is 0.5 or 0.5 on the probability scale.
It is worth noting that when a coin is fair, the probability of getting a head or a tail is always 0.5 or 50%.
So in the probability scale you should place a cross on the point 0.5 which indicates the probability of getting a head.
the number of hours of sunlight in a particular location s(t) can be modeled by the function where t is the number of days after january 1st. (that is, t
After solving the function S(t) = 12 + 2 sin [(2π)/(365)t], the amount of sunlight becomes 12 hours for the first time is obtained as option B: t = 365/2.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The given function is -
S(t) = 12 + 2 sin [(2π)/(365)t]
Here, t is the number of days after 1st January.
S(t) is the number of hours of sunlight in a particular location.
In order to figure out when the amount of sunlight becomes 12 hours for the first time, substitute the value of S(t) = 12 and solve the function for t -
S(t) = 12 + 2 sin [(2π)/(365)t]
12 = 12 + 2 sin [(2π)/(365)t]
Simplifying the equation to get the result -
0 = 2 sin [(2π)/(365)t]
0 = sin [(2π)/(365)t]
π = (2π)/(365)t
Simplify the equation further -
365π = 2πt
t = 365π/2π
t = 365/2
Therefore, the value for t is obtained as t = 365/2.
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The number of hours of sunlight in a particular location S(t) can be modeled by the function S(t) = 12 + 2 sin [(2π)/(365)t], where t is the number of days after January 1st. (That is, t = 0 means January 1st.) After how many days will there be 12 hours of sunlight for the first time during the year?
365 over 4 days
365 over 2 days
1095 over 4 days
1095 over 2 days
find the acute angles between the curves at their points of intersection. (the angle between two curves is the angle between their tangent lines at the point of intersection. give your answers in degrees, rounding to one decimal place. enter your answers as a comma-separated list.) y
The acute angles between two curves at their points of intersection are the angles between the tangent lines of the two curves at those points. The angles should be rounded to one decimal place and given in a comma-separated list.
The acute angles between two curves at their points of intersection can be found by calculating the angles between the tangent lines of the two curves at those points. To calculate this angle you will need to calculate the gradient of the tangent lines at each point of intersection. To do this, you need to take the derivative of each curve's equation at each point of intersection. Once you have the gradients, you can then use the equation for the angle between two lines to calculate the angle between the two tangent lines. Then, the angles should be rounded to one decimal place and given in a comma-separated list.
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-7t 42t the position of an object moving along a line is given by the function . find the average velocity of the object over the following intervals.
(a) Average velocity over [1,5] is -21. (b) Average velocity over [1,4] is -14. (c) Average velocity over [1,3] is -7. (d) Average velocity over [1, 1+h] is -7t + 70 where h is any real number.
Calculating average velocity requires the calculation of the change in position divided by the change in time.
For a: The change in position is -70 and the change in time is 4. So, the average velocity is -70/4 = -17.5.
For b: The change in position is -56 and the change in time is 3. So, the average velocity is -56/3 = -18.67.
For c: The change in position is -35 and the change in time is 2. So, the average velocity is -35/2 = -17.5.
For d: The change in position is -7t and the change in time is h. So, the average velocity is -7t/h = -7t + 70.
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A complete question: The position of an object moving along a line is given by the function s(t) = -7t^2 +70t. Find the average velocity of the object over the following intervals.
(a) [1,5]
(b) [1,4]
(c) [1,3]
(d) [1, 1+h] where h > 0 is any real number
song of myself is written by?
Answer:
“Song of myself ” is written by Walt Whitman in 1855
hope it helps<3Answer:
The Song of Myself is written by Walt Whitman in 1855
Step-by-step explanation:
Use the four intervals shown. I. (0, 2) II. (0, 2]III. [0, 2) IV. [0, 2]Based on the extreme value theorem, on which interval must the function f(x) = xhave both a maximum and minimum value?O IO IIO IIIO IV
Each interval (a, a), [a, a), and (a, a] represents the empty set, whereas [a, a] denotes the singleton set {a}
What do you meant by interval?
The empty set is represented by the intervals (a, a), [a, a), and (a, a, while the singleton set an is denoted by [a, a]. All four notations are often taken to denote the empty set when a > b. Both notations may be used in conjunction with other mathematical parentheses and brackets.For instance, in analytic geometry, linear algebra, and set theory, the notation (a, b) is frequently used to represent an ordered pair, the coordinates of a point or vector, or (sometimes) a complex number.Bourbaki created the notation]a, b[to signify the open interval for this reason. For ordered pairings, the notation [a, b] is also occasionally used, particularly in computer science.a ) [0, 2]
The empty set is represented by the intervals (a, a), [a, a), and (a, a, while the singleton set an is denoted by [a, a].
b ) iv
If a function f(x) is continuous on a closed interval [ a, b], then f(x) has both a maximum and minimum value on [ a, b].
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The center of the equilateral triangle below is at the origin. Which of the following rotational symmetries apply to the equilateral triangle? Rotation Applies to the figure?
Rotational symmetry of 120 about the origin
Yes/No
Rotational symmetry of 180 about the origin
Yes/No
Yes. An equilateral triangle has rotational symmetry of 120 and 180 degrees about the origin.
What is triangle?A triangle is a three-sided polygon, with three angles and three sides. It is one of the most basic and fundamental shapes in geometry, and is used in many different areas of math and science. Triangles are also often used in architecture, art, and other areas of design. Triangles come in many different forms, such as equilateral, isosceles, and scalene, and can be classified by their angles, sides, or both.
This means that the triangle can be rotated by 120 degrees or 180 degrees around the origin and still maintain its shape.
Yes, rotational symmetry of 120 about the origin applies to the equilateral triangle. This means that the triangle can be rotated by 120 degrees about the origin and the resulting shape will be exactly the same as the original triangle.
No, rotational symmetry of 180 about the origin does not apply to the equilateral triangle. This is because an equilateral triangle has rotational symmetry of 60 degrees about the origin, not 180 degrees.
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Lana has 4 bags with the same amount of marbles in them, totaling 14 marbles. Markus has 4 bags with the same amount of marbles in them, totaling 20 marbles. How many more marbles does Markus have in each bag?
Answer:
Lana: 4 / 14 = 3.5
Markus: 4 / 20 = 5
I'm not completely sure how they can have the same amount of marbles for both of them but... Markus does have 2.5 more than Lana in each bag.
Hope this helps <3
Step-by-step explanation:
Let's call the number of marbles in each bag "x". We can set up two equations based on the given information:
4x = 14 (for Lana)
4x = 20 (for Markus)
Solving for x in each equation, we get:
x = 14/4 = 3.5 (for Lana)
x = 20/4 = 5 (for Markus)
So Markus has 5 marbles in each bag, which is 1.5 more marbles per bag than Lana.
use the following for the first two problems. Listed are 32 ages for Academy Award winning best actors in order from smallest to largest. (Round your answers to the nearest whole number.)
18; 18; 21; 22; 25; 26; 27; 29; 30; 31; 31; 33; 36; 37; 37; 41; 42; 47; 52; 55; 57; 58; 62; 64; 67; 69; 71; 72; 73; 74; 76; 77
(a) Find the percentile of 37. 14/32= .4375
44 th percentile
(b) Find the percentile of 71 27/32=.8437?
I get the 1st one but can't seem to get the 2nd, i come up with 27/32 but the computer doesn't agree can anyone help?
Similarly, 27 out of the 32 ages are equal to or less than 71, so the percentile of 71 is 27/32, which is equal to 84.375%. This means that 84.375% of the Academy. Award winning best actors are 71 years old or younger.
The percentile of a number is the percentage of numbers that are equal to or less than that number. In this case, 27 out of the 32 ages are equal to or less than 71, so the percentile of 71 is 27/32, which is equal to 84.375%. This means that 84.375% of the Academy Award winning best actors are 71 years old or younger.
The percentile of a number is the percentage of numbers that are equal to or less than that number. For example, among the 32 Academy Award winning best actors, 37 is the 14th smallest number, so the percentile of 37 is 14/32, which is equal to 43.75%. This means that 43.75% of the Academy Award winning best actors are 37 years old or younger. Similarly, 27 out of the 32 ages are equal to or less than 71, so the percentile of 71 is 27/32, which is equal to 84.375%. This means that 84.375% of the Academy Award winning best actors are 71 years old or younger.
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A hypothetical university has two departments, A and B. There are 2,000 male applicants, of whom half apply to each department. There are 1,100 female applicants: 100 apply to department A and 1,000 apply to department B. Department A admits 60% of the men who apply and 60% of the women. Department B admits 30% of the men who apply and 30% of the women. "For each department, the percentage of men admitted equals the percentage of women admitted,; this must be so for both departments together." True or False
The statement regarding the percentages of men and women admitted is true.
How to obtain the percentages?A percentage is obtained similarly to a proportion, with the division of the number of desired outcomes by the number of total outcomes, and then multiplied by 100%.
The number of applicants for each department is given as follows:
Department A: 1000 male and 100 female.Department B: 1000 male and 1000 female.The percentages of admitted people for each department is 50% men and 50% women, meaning that the statement in this problem is true.
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Based on the table, do the data support the use of a normal model to approximate population characteristics?
A. Yes, because the sum of the relative frequencies is 1.00.
B. Yes, because the distribution of relative frequencies is very close to the empirical rule for normal models.
с. No, because the values are negative and normal models are used for positive values.
D. No, because the distribution of relative frequencies is very far from the empirical rule for normal models.
E. No, because the sample size and the population parameters are not known.
Yes, because the distribution of relative frequencies is very close to the empirical rule for normal models.
Interval Relative Frequency
−0.34≤x<−0.31 0.02
−0.31≤x<−0.28 0.15
−0.28≤x<−0.25 0.33
−0.25≤x<−0.22 0.36
−0.22≤x<−0.19 0.11
−0.19≤x<−0.16 0.03
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
According to the question,
The values that are one standard deviation away are:
0.33 + 0.36 = 0.69
As per the empirical rule, the value will be: 0.68
Consequently, with two standard deviations, the quantities have always been 0.95, and according to the empirical rule. So the empirical rule followed by the data.
Therefore the correct option is (B).
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The complete question includes :
The mean and standard deviation of the sample data collected on continuous variable x, x are −0.25 and 0.03, respectively. The following table shows the relative frequencies of the data in the given intervals.
Select the number that round to 387.4 when rounded to the nearest tenth.
A. 387.461
B. 387.344
C. 387.309
D. 387.352
E. 387.779
Answer:
D
Step-by-step explanation:
When rounding, the number 5 is rounded up. So the number 387.352 will be rounded up 387.4. Other options are not suitable. Correct answer is "D"
If you think my answer is the best, please mark it as the Brainliest.
Thank you! :))
PLS HELP FOR REAL!!! WHAT IS THE ANSWER FOR THE 2nd ONE!! I NEED AN EXPLANATION AND ANSWER FOR IT! HUGE POINTS IF ANSWER!
Answer:
76ft^3
Step-by-step explanation:
Volume of a cube is Length x Width x Height, basically: 4 x 4 x 4 which is 64 ft^3. Add that to the small box gives you 64 + 12 or just 76 ft^3
4x-y=3 6y=4+2x solve by substitution
Using the substitution method the equation 4x - y = 3 and 6y = 4 + 2x is solved to be
x = 1y = 1How to solve the equation using substitution methodIn this method, the equation 4x - y = 3 will first be written in terms of y
4x - y = 3
y = 4x - 3
substituting y = 4x - 3 into 6y = 4 + 2x
6y = 4 + 2x
6(4x - 3) = 4 + 2x
24x - 18 = 4 + 2x
collecting like terms
24x - 2x = 18 + 4
22x = 22
x = 1
substituting x = 1 into y = 4x - 3
y = 4x - 3
y = 4(1) - 3
y = 4 - 3
y = 1
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ASAPPPPPPPPPPPPPP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: 5 11/12 not sure
Which of the following statements is/are true? I. If f'(x) exists and is nonzero for all x, then f(1) is not equal f(0). II.If f is differentiable for all x and f(-1) = f (1), then there is a number c, such that |c| < 1 and f'(c) = 0. III. If f'(c) = ), then f has a local maximum or minimum at x = c.
The evaluation of the values of the derivative of the function f, using Lagrange's theorem indicates that the true statements is the following option;
I and III anlyWhat does the Lagrange's Theorem highlights?Lagrange Theorem states that there is a point, c between points a and b of an arc such the slope at c is the same as the average slope of the arc between points a and b.
The evaluation of the statements in the question are as follows;
I. If f'(x) exists and is nonzero for all x, then f(1) is not equal to f(0)
If f'(x) exists and the value is non zero, then the slope is not infinite, and the sign of the slope of the function f(x) never changes, such that the as the input (x) value increases the output value decreases, when the slope is negative, or increases when the slope of f(x) is positive, therefore;
The value of f(1) is either larger than or lesser than the value of f(0), which proves that f(1) is not equal to f(0).
The first statement, I, is therefore, trueII. If f is differentiable for all x and f(-1) = f(1), then there is a number c, such that |c| < 1 and f'(c) = 0
The condition if f is differentiable for all x, then according to Lagrange's, mean value theorem, we get;
When f(|c| < 1) < f(1)
f'(c) < (f(1) - f(-1))/(1 - (-1)) = (f(1) - f(-1))/(2)
f'(c) < (f(1) - f(-1))/(1 - (-1)) = (f(1) - f(-1))/(2) = 0
f'(c) < 0
Similarly, when f(|c| < 1) > f(1), then, f'(c) < 0
Therefore, f'(c) ≠ 0
The statement II is not trueIII. If f'(c) = 0, then f has a local maximum or minimum at x = c.
The slope of the function f at point x = c is f'(c)
A local maximum or minimum is a point after which the slope of the graph changes sign, and the point at which the slope is zero as the change in the output variable is zero
Therefore, if f'(c) = 0, the graph has a local maximum or minimum at the point f = c
The true statements from the specified options, and based on the possible options in the question, obtained from a similar question posted online are;
I and III onlyThe possible question options are;
I and II only
I and III only
I only
II only
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what are tangible items sold by retailers called
Answer:
A tangible asset is an asset that has physical substance. Examples include inventory, a building, rolling stock, manufacturing equipment or machinery, and office furniture. There are two types of tangible assets: inventory and fixed assets.
Step-by-step explanation:
suppose you are eating slices of pizza and after consuming the first slice you receive 14 utils of total utility, after the second you receive 22 utils of total utility, and after the third 25 utils of total utility. then group of answer choices the law of diminishing marginal utility is not applicable because your total utility is increasing instead of diminishing. your total utility is 61 utils. your total utility is 25 utils, and the marginal utility of the first slice is 8 utils (22 - 14). your total utility is 25 utils, and the marginal utility of the third slice is 3 utils.
The correct answer choice is the last one, your total utility is 61 utils, and the marginal utility of the first slice is 8 utils (22 - 14).
What is marginal utility?
Marginal utility refers to the additional satisfaction or benefit that a consumer derives from consuming one more unit of a good or service. It is the change in total utility resulting from a change in the quantity consumed. It is a way to measure the additional benefit a consumer receives from consuming one more unit of a good or service.
your total utility is 61 utils, and the marginal utility of the first slice is 8 utils (22 - 14). The law of diminishing marginal utility states that as the consumption of a good or service increases, the additional satisfaction or utility from consuming one more unit of the good or service will decline. In this example, as you consume more slices of pizza, the marginal utility of each slice decreases (8 utils for the first slice, 3 utils for the third slice). This is consistent with the law of diminishing marginal utility. Therefore, choice A is incorrect.
Hence, The correct answer choice is the last one, your total utility is 61 utils, and the marginal utility of the first slice is 8 utils (22 - 14).
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the length of a rectangular platform is 2 feet longer than three times its width. The area of the platform is 56 square feet. Write a polynomial that represents the area of the platform
Answer
The area of the platform :
56 = (3x+2) × x
Explanation (+ solving for x)
Let the width of Rectangular Platform is x feet.
Then,
Length of Rectangular Platform is (3x+2) feet
Area of Rectangular Platform = Length × width
[tex]56=(3x+2) × x \\ 56 = 3x² + 2x \\ 3x² +2x-56= 0 \\ x = \frac{ -2±\sqrt{ {2}^{2} - 4 \times 3 \times ( - 56)} }{2 \times 3} \\ = \frac{-2± \sqrt{4 + 672} }{6} \\ = \frac{ - 2±26}{6} \\ = - \frac{28}{6} or \: 4 [/tex]
Since x can't be negative,
Value of x is 4 feet.
So, width of Platform= 4
feet Length of Platform = 14 feet
either show that b cannot be expressed as a linear combination, or find weights that express it as such
b = (2,-1,6) is a linear combination of a1 = (1,-2,0), a2 = (0,1,2) and a3 = (5,-6,8) with weights (1,3,1) respectively.
To determine if b is a linear combination of a1, a2, and a3, we can set up a system of equations using the coefficients of the linear combination and the variables a1, a2, and a3. The equation for a linear combination of the form b = k1a1 + k2a2 + k3a3, where k1, k2 and k3 are the coefficients, can be written as:
b = k1 × (1,-2,0) + k2 × (0,1,2) + k3 × (5,-6,8)
So,
x = k1 + 5k3
y = -2k1 + k2 - 6k3
z = 2k2 + 8k3
We know the values of x,y,z from b = (2,-1,6)
So, we can set up the following system of equations:
x = k1 + 5k3 = 2
y = -2k1 + k2 - 6k3 = -1
z = 2k2 + 8k3 = 6
We can solve the system of equations using methods such as substitution or elimination to find the values of k1, k2, and k3.
k1 = 1, k2 = 3, k3 = 1
Therefore, we can express b as a linear combination of a1, a2, and a3 with the weights k1, k2, and k3 which are (1, 3, 1) respectively.
b = 1a1 + 3a2 + 1 × a3
This means that b is a linear combination of a1, a2, and a3 with weights (1, 3, 1) respectively.
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The question is -
Determine if b is a linear combination of a1, a2, and a3.
a1=(1,-2,0)
a2=(0,1,2)
a3=(5,-6,8)
b=(2,-1,6)
On January 1st, the temperature in St Petersburg was -7°C and the temperature in Rome was 15°C. The temperature in Reigate was exactly halfway between St Petersburg and Rome. What was the temperature in Reigate?
To find the temperature in Reigate, which is halfway between St. Petersburg and Rome, we need to find the average of the two temperatures.
Average = (Temperature1 + Temperature2) / 2
Average = (-7 + 15) / 2 = 8 / 2 = 4
So, the temperature in Reigate was 4°C.
Answer:
4°C
Step-by-step explanation:
Try drawing it on a number line and counting 11 from -7° C and 11 from 15°C you'll end up with 4°C as the middle
A garden hose can fill a swimming pool in 7 days, and a larger hose can fill the pool in 4 days. How long will it take to fill the pool if both hoses are used?
Answer:
[tex]2 \frac{6}{11}\; \rm days\;[/tex]
2 days 13 hours 5 minutes 27 seconds
Step-by-step explanation:
First hose:
If the first hose can fill the pool in 7 days, then it can fill 1/7 of the pool in 1 day.Second hose:
If the second hose can fill the pool in 4 days, then it can fill 1/4 of the pool in 1 day.When both hoses are being used to fill the pool, their rates are additive:
[tex]\implies \dfrac{1}{7}+\dfrac{1}{4}=\dfrac{4}{28}+\dfrac{7}{28}=\dfrac{11}{28}[/tex]
Therefore, both hoses can fill 11/28 of the pool in 1 day.
To calculate how long it will take to fill the pool, divide 1 day by the combined rate:
[tex]\implies 1 \div \dfrac{11}{28}=1 \times \dfrac{28}{11}= \dfrac{28}{11}=2 \frac{6}{11}\; \rm days\;[/tex]
Therefore it takes 2 ⁶/₁₁ days to fill the pool if both hoses are used.
To find the time it takes in days, hours, minutes and seconds:
6/11 days as hours is:Therefore, it takes:
2 days 13 hours 5 minutes 27 seconds to fill the pool if both hoses are used (to the nearest second).Find the product of the binomial factors using the appropriate special product (difference of two squares, square of a binomial sum, or square of a binomial difference).
(x−5)2
The product of the binomial factors is x² - 10x + 25.
What is Binomials?Binomials are kind of polynomials which consist of only two terms.
The given binomial factor is x - 5
We have to find the product of this binomial with itself, (x - 5)².
We have to use the special product of square of a binomial difference, which is defined as,
(a - b)² = a² - 2ab + b²
The given product of the binomial factors is (x - 5)².
(x - 5)² = x² - (2 × x × 5) + 5²
= x² - 10x + 25
Hence the product of the binomial factors is x² - 10x + 25.
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Consider a linear model for the progression of a contagious virus through a population, described by: Si+1=S; - ali, li+1=1; +al; - B1, Ri+1 = R; + 1;In this model S; describes the number of people that have never been infected, I; describes the number of people who are currently infected, and R; describes the number for people that have recovered from infection, with i representing time counted in days. a is a parameter that describes the infectivity of the virus, and B is a parameter that describes how long it takes to recover from an infection. (a) Write a matrix expression Tit1 = A7; for this model, with a = 0.10 and B = 0.05
The matrix expression for this model is given by
T=
[ 1-a, a, 0; 0, 1-B, B; 0, 0, 1]
When a = 0.10 and B = 0.05, the matrix expression becomes:
T=
[ 0.90, 0.10, 0; 0, 0.95, 0.05; 0, 0, 1]
This matrix expression describes the transition probabilities of the virus over time. Specifically, it describes the probability of a person who has never been infected (S) becoming infected (I) in the next day (a = 0.10), the probability of a person who is infected (I) in the current day in the next day (B = 0.05), and the probability of a person who has recovered (R) staying recovered in the next day (1). Thus, this matrix expression models the progression of a contagious virus through a population over time.
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A farmer has a rectangular field with dimensions 200m (north) by 150m (east). A sheep is put on a 20 meter leash whose end is tied to a pole. (Hint: Draw the situation!) (a) Assume the south west corner of the field is the origin of a coordinate system. The pole is placed at 40 meters east and 20 meters north from this origin. Will the sheep be able to eat grass from the neighbor's field? If so, where? (b) Same situation as in (a). But the pole is now put 180m north and 160m east. Will the sheep be able to eat grass from the neighbor's field? If so, where?
a) The sheep will not be able to eat grass from the neighbor's field. The leash is 20 meters long and is tied to a pole at the point (40, 20) in the field. The farthest point the sheep can reach is a point on the circle with radius 20 centered at (40,20), which is completely contained within the rectangular field.
b) The sheep will be able to eat grass from the neighbor's field. The leash is 20 meters long and is tied to a pole at the point (180,160) in the field. The farthest point the sheep can reach is a point on the circle with radius 20 centered at (180,160), which extends beyond the east and north boundaries of the rectangular field. Specifically, the sheep can reach the area on the northeast corner of the field.
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Identify the kind of sample that is described. A sports columnist contacts a random sample of 3 owners, a random sample of 6 players, and a random sample of 20 fans to ask their opinion about the potential basketball lockout. the sample is a (Choose one) A) convenience B) voluntary response C) simple random D) stratified E) cluster F) systematic
A cluster sample is a type of sampling technique wherein clusters of subjects that are similar in certain characteristics are selected for the study. In this case, the sample includes 3 owners, 6 players, and 20 fans, all of whom have something in common - an interest in basketball. Therefore, the sample described is a cluster sample.
A cluster sample is a type of sampling technique wherein clusters of subjects that are similar in certain characteristics are selected for the study. In this case, the sample includes 3 owners, 6 players, and 20 fans, all of whom have something in common - an interest in basketball. Therefore, the sample described is a cluster sample. This type of sample is helpful when the researcher is interested in specifically examining a certain group of people and their opinions. A cluster sample is relatively easy to implement and can be used to quickly obtain a large amount of data in a short period of time. It also eliminates the need to identify and select individuals from a population. By using a cluster sample, the sports columnist was able to quickly get feedback from a variety of individuals who may have different opinions on the potential basketball lockout.
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Solve the following system of equations. Express your answer as an ordered pair in the format (a,b), with no spaces between the numbers or symbols. 3x+4y=17 4x - 3y= -18
The solution of the system of equation in ordered pair is,
⇒ (- 0.84, 4.88)
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The system of equation is,
⇒ 3x + 4y = 17 .. (i)
⇒ 4x - 3y = - 18 ... (ii)
Now, We can solve the equations as;
Multiply by 4 in equation (i) and subtract from (ii) × 3, we get;
⇒ 12x + 16y - 12x + 9y = 68 - (- 54)
⇒ 25y = 68 + 54
⇒ 25y = 122
⇒ y = 4.88
And, From (i);
⇒ 3x + 4y = 17
⇒ 3x + 4×4.88 = 17
⇒ 3x + 19.52 = 17
⇒ 3x = 17 - 19.52
⇒ 3x = - 2.52
⇒ x = - 0.84
Thus, The solution is,
⇒ (- 0.84, 4.88)
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Among all positive numbers a, b whose sum is 8 , find those for which the product of the two numbers and their difference is largest.
The value of 1st number is 4 + 4/√3 and value of 2nd number is 4 - 4/√3
let the 2 number be a,b
given a+b=8 -- (i)
let the difference of the number is x
so let a-b =x
a-b = x ---(ii)
adding equation (i) and equation (ii) we get
2a = 8 +x
=> a = (8+x)/2
so a = 4+x/2
subtract (ii) from (i) we get:
2b = 8-x
=> b = (8-x)/2
so b = 4-x/2
now the product of both number and their difference is given as a*b*x
=> (4+x/2)*(4-x/2) *x
=> (16 - x²/4)*x
=> 16x - x³/4
let the above value be A
so A = 16x - x³/4
in order to find maximum value of A we have to made dA/dx = 0
=> d(16x - x³/4)dx
=> 16 - 3x²/4
so 16 - 3x²/4 =0
=> 3x²/4 = 16
=> 3x² = 64
=> x² = 64/3
so x = 8/√3
now we got value of x
so a = 4+ x/2
=> 4 + 8/2√3
=> 4 + 4/√3
so value of a = 4 + 4/√3
value of b = 4 - 4/√3
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Someone is having a wedding, and they need champagne bottles. The bottles are 25.4 oz, the glasses are 6 oz a person, and there are going to be 80 guests. How many champagne bottles are going to be needed to serve all the guests?
help me with this if u can thank you!! god bless you
The value of the equation is A = 11,025
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = 105²
On simplifying the equation , we get
A = ( 100 + 5 )²
The equation is of the form ( a + b )² = a² + 2ab + b²
On further simplification , we get
A = ( 100 )² + 2 ( 100 ) ( 5 ) + ( 5 )²
A = 10000 + 1000 + 25
A = 11,025
Hence , the equation is A = ( 100 + 5 )² = 11,025
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