The Bisection Method is a numerical method used to find the roots of a function within a given interval. It works by repeatedly dividing the interval in half and checking which half contains the root until the desired level of accuracy is achieved. In this case, we are using 17 iterations to extract the root of the function f(x) = x/3 + In(x) - 1 on the closed interval [1,2].
To locate the root of f(x) = x/3 + In(x) - 1 on a closed interval [1,2] using the Bisection Method with 17 iterations, we will follow the steps below:
1. Define the function f(x) = x/3 + In(x) - 1
2. Set the initial values for the interval: a = 1 and b = 2
3. Start the iteration process by finding the midpoint of the interval: c = (a+b)/2
4. Evaluate the function at the midpoint: f(c) = f((a+b)/2)
5. Determine if the root lies in the left or right half of the interval by checking the sign of f(c)
6. If f(c) is positive, then the root lies in the left half of the interval, so we set b = c and repeat the process from step 3.
7. If f(c) is negative, then the root lies in the right half of the interval, so we set a = c and repeat the process from step 3.
8. Continue the iteration process until we have completed 17 iterations.
After 17 iterations, we will have narrowed down the interval to a very small range and the midpoint of this interval will be an approximation of the root of the function.
The Bisection Method is a numerical method used to find the roots of a function within a given interval. It works by repeatedly dividing the interval in half and checking which half contains the root until the desired level of accuracy is achieved. In this case, we are using 17 iterations to extract the root of the function f(x) = x/3 + In(x) - 1 on the closed interval [1,2].
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lengths of 3 inches, 4 inches, and
5 inches. Will it fit in the corner of a
rectangular quilt? Explain.
A Yes, because it is a right triangle.
B Yes, because it is an isosceles
triangle.
No, because it is an equilateral
triangle.
No, because it is an obtuse
triangle.
Answer: A
Step-by-step explanation:
You can prove it by Pythagorean's Theorem, a² + b² = c²
3² + 4² = 5²
9 + 16 = 25
25 = 25
It has to be a right triangle.
D. Elementary Applications of the Fundamental Homomorphism Theorem In each of the following letAbe a commutative ring. Ifa∈Aandnis a positive integer, the notationnawill stand fora+a+…+a(n terms )1 Suppose2x=0for everyx∈A. Prove that(x+y)2=x2+y2for allxandyinA. Conclude that the functionh(x)=x2is a homomorphism fromAtoA. IfJ={x∈A:x2=0}andB={x2;x∈A), explain whyJis an ideal ofA,Bis a subring ofA, andA/J≅B
A/J≅B
The Fundamental Homomorphism Theorem states that for any homomorphism f from a ring A to a ring B, the kernel of f (the set of elements of A mapped to the identity of B) is an ideal of A. Applying this to the given problem, let A be a commutative ring and f:A→A be the homomorphism f(x)=x2. The kernel of f is J = {x∈A:x2=0}. Then J is an ideal of A.
To prove that (x+y)2=x2+y2 for all x,y∈A, consider (x+y)2 = (x+y)(x+y) = x2 + xy + yx + y2. Since A is commutative, xy=yx and so (x+y)2=x2+2xy+y2. Since 2xy=2yx, then (x+y)2=x2+y2, as desired.
Now, we can conclude that f is a homomorphism from A to A. In addition, B={x2;x∈A} is a subring of A, since for all x,y∈A, (x+y)2=x2+y2 and so x2+y2∈B. Moreover, since J is an ideal of A, A/J≅B.
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Feb 22, 8:31:06 AM Determine if the expression 6 is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.
The expression 6 is a polynomial. It is a constant polynomial with a degree of 0.
A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. A constant polynomial is a polynomial with no variables, and only consists of a constant term.
In the expression 6, there are no variables and it only consists of a constant term, which makes it a constant polynomial. The degree of a polynomial is the highest exponent of the variable in the polynomial. Since there are no variables in the expression 6, the degree of the polynomial is 0.
Therefore, the expression 6 is a constant polynomial with a degree of 0.
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1. A wholesaler received a shipment of goods, which is reported to be containing at most 2% defective items. He will accept the shipment if the claim is found true and reject if the percentage of defective items is more. To verity this claim, he draws a sample of 200 items and finds that 10 items are defective. Use 5% level of significance to investigate the claim.
At a 5% level of significance, the claims that a shipment of goods contains at most 2% defective items is accepted.
To investigate the claim that the shipment contains at most 2% defective items, we can use the 5% level of significance. The claim is that the population proportion of defective items is at most 2%, or p0 ≤ 0.02. The sample size is n = 200, and the sample proportion of defective items is pobs = 10/200 = 0.05.
The test statistic is then:
z = (pobs - p0) / √(p0(1-p0) / n)
= (0.05 - 0.02) / √(0.02(1-0.02)/200)
= 1.02.
With a 5% level of significance, we can look up the critical value for a one-tailed z-test and find that it is zα/2 = 1.645. Because 1.02 < 1.645, the test statistic is not greater than the critical value, and thus we fail to reject the null hypothesis that the population proportion of defective items is at most 2%.
In conclusion, with a 5% level of significance, the claim that the shipment contains at most 2% defective items is accepted.
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Jack starts with $192. He goes to the mall with his friends and spends $7 every hour.
Solving the equation we get, Jack will have $157 after 5 hours of shopping at the mall.
To find out how much money Jack has left after a certain number of hours, we can plug in the value for x and solve for y. For example, if Jack spends 5 hours at the mall, we would plug in 5 for x:
y = -7(5) + 192
y = -35 + 192
y = 157
We can use this equation to find out how much money Jack has left after any number of hours at the mall.
Jack starts with $192. He spends $7 every hour. Jack is left with $157 at the end of 5 hours.
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Question 2 (1 point)
What is the value of the following
The value of the expression 7₂ + 3₃ is 10₅.
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is a number used before a phrase.
Given:
An expression is 7₂ + 3₃.
To find the value of the expression, first, add 7 and 3.
That means, 7 + 3 = 10.
Now add 2 and 3,
2 +3 = 5
So, the value of the expression is 10₅.
Therefore, the result is 10₅.
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Orange juice drinks were to be distributed to the schools in the District of Nueva Valencia South. 950 packs were given to La Paz Elementary School, 785 to Igdarapdap Elementary School, 1, 370 to Cabalaynan Elementary School. If there are 5, 000 packs of juice drinks, how many were distributed to different schools? How many packs were not given?
3. First Solution: ______________
4. Second Solution: ______________
By those 2 ways of solution, a total of 3,105 packs of juice drinks were distributed to different schools.
How to find out the numberFirst Solution:To find out how many packs of juice drinks were distributed to different schools, we need to add the number of packs given to each school.
950 (La Paz Elementary School) + 785 (Igdarapdap Elementary School) + 1,370 (Cabalaynan Elementary School) = 3,105 packs of juice drinks
So, a total of 3,105 packs of juice drinks were distributed to different schools.
Second Solution:To find out how many packs of juice drinks were not given, we need to subtract the number of packs distributed to different schools from the total number of packs available.
5,000 (total number of packs) - 3,105 (number of packs distributed to different schools) = 1,895 packs of juice drinks
So, a total of 1,895 packs of juice drinks were not given.
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Suppose {x1,x2,..., xn} and {y1, y2, ..., yn} are two independent samples from population N (µ1, δ^2 1) and N (µ2, δ^2 2), respectively. We wish to test H0 : µ1 = µ2 vs. HA: µ1 > µ2. Assume δ = δ2 = δ = 1. a) Find the power of the z-test to detect a difference of δ1 - δ2 = 0.1 and the sample size is 100. Use a significance level of 0.05. Hint: x -y ~ N (µ1 - µ2, 2δ^2/n). b) Suppose a research wishes to detect µ1 - µ2 = 1 with power at least 80%, how large should the sample size be? Show the key steps.
The sample size needed to detect µ1 - µ2 = 1 with power at least 80% is approximately 323.
The power of a test is the probability of correctly rejecting the null hypothesis when the alternative hypothesis is true. In this case, we wish to find the power of the z-test to detect a difference of δ1 - δ2 = 0.1 when the sample size is 100 and the significance level is 0.05.
a) First, we need to find the critical value for the z-test at a significance level of 0.05. This can be found using a z-table or a calculator. The critical value is 1.645.
Next, we need to find the standardized difference between the two means, which is (δ1 - δ2)/√(2δ^2/n) = (0.1)/√(2(1)^2/100) = 0.1/√(0.02) = 0.7071.
Finally, we can find the power of the test by subtracting the standardized difference from the critical value and finding the corresponding probability from a z-table or calculator. The power is 1 - P(Z < 1.645 - 0.7071) = 1 - P(Z < 0.9379) = 1 - 0.8264 = 0.1736.
Therefore, the power of the z-test to detect a difference of δ1 - δ2 = 0.1 with a sample size of 100 and a significance level of 0.05 is 0.1736.
b) To find the sample size needed to detect µ1 - µ2 = 1 with power at least 80%, we can use the formula for power:
Power = 1 - P(Z < (critical value - standardized difference))
We can rearrange this formula to solve for the sample size:
Standardized difference = (critical value - Z value corresponding to power)/√(2δ^2/n)
n = (2δ^2(critical value - Z value corresponding to power)^2)/(standardized difference)^2
Plugging in the values for critical value (1.645), Z value corresponding to power (0.8416), and standardized difference (1), we get:
n = (2(1)^2(1.645 - 0.8416)^2)/(1)^2 = 322.69
Therefore, the sample size needed to detect µ1 - µ2 = 1 with power at least 80% is approximately 323.
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Lee wants to make at least $400 profit from selling t-shirts. The initial start up costs for making t-shirts is $125. Write an inequality that represents the amount of sales, s, that Lee must have to reach the goal. Please answer!!
Answer:4
Step-by-step explanation:
Simplify, leaving as little as possible inside absolute value signs. |(5t^(3))/(-25t)|
Simplified expression of (5t^(3))/(-25t)| is (1/5)( [tex]t^{2}[/tex] ).
To simplify the expression |(5[tex]t^{(3))}[/tex]/(-25t)|, we need to follow these steps:
1. Start by simplifying the fraction inside the absolute value signs.
2. The 5 in the numerator and the 25 in the denominator can be reduced to 1/5.
3. The t in the denominator can be reduced with one of the t's in the numerator, leaving us with [tex]t^{2}[/tex] in the numerator. This gives us |(1/5)( [tex]t^{2}[/tex]))|.
5. The absolute value signs mean that we need to take the positive value of whatever is inside.
6. Since both 1/5 and [tex]t^{2}[/tex] are positive, we can remove the absolute value signs.
This leaves us with (1/5)( [tex]t^{2}[/tex])) as our simplified expression.
So the final answer is (1/5)( [tex]t^{2}[/tex] ).
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Starting at the origin, a bug jumps randomly along a number line. Each second it jumps either one unit to the right or one unit to the left, either move being equally likely. This is called a one-dimensional random walk. What is the probability that,
after eight jumps, the bug has returned to the point of departure?
b. After eight jumps, the bug will be within three units of the point of departure?
After eight leaps, there is a 0.3828 percent chance that the bug will still be within three units of where it started.
a. To return to the origin after eight jumps, the bug must take an equal number of left and right jumps. Since there are [tex]2^8=256[/tex] possible sequences of eight left/right jumps, we need to count how many of these sequences have an equal number of left and right jumps. To do this, we can use the binomial coefficient:
[tex]C(8,4) = 8! / (4! * 4!) = 70[/tex]
This counts the number of ways to choose 4 out of 8 jumps to be leftward, with the other 4 jumps being rightward. Therefore, the probability of returning to the origin after eight jumps is:
[tex]P(return to origin) = 70 / 256 = 0.2734[/tex]
b. To be within three units of the origin after eight jumps, the bug must take at most three more rightward than leftward jumps or three more leftward than rightward jumps. We can compute the probabilities of each of these cases separately and add them up. Let's first consider the case where there are three more rightward jumps than leftward jumps. To count the number of such sequences, we can choose three out of the eight jumps to be leftward, with the other five jumps being rightward. Therefore, the probability of this case is:
P(3 more rightward) = C(8,3) / 256 = 0.1094
Similarly, the probability of having three more leftward jumps than rightward jumps is also 0.1094. To count the number of sequences where there are two more rightward jumps than leftward jumps, we can choose two out of the eight jumps to be leftward, with the other six jumps being rightward. There are also C(8,2) sequences with two more leftward jumps than rightward jumps. Therefore, the probability of being within three units of the origin after eight jumps is:
[tex]P(within 3 units) = 2 * 0.1094 + 2 * C(8,2) / 256 = 0.3828[/tex]
Therefore, the probability that the bug is within three units of the point of departure after eight jumps is 0.3828.
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The permutation ([1,2,3,4,5,6],[6,5,4,3,1,2]) can be written as a product of disjoint cycles as (A) ([1,6,2,5])([3,4]) (B) ([1,2,3,4])([5,6]) (C) ([1,3,4,5])([2,6]) (D) ([1,2,5,6])([3,4])
The permutation ([1,2,3,4,5,6],[6,5,4,3,1,2]) can be written as a product of disjoint cycles as (A) ([1,6,2,5])([3,4]).
To find the product of disjoint cycles, we can start by looking at the first element in the first cycle, which is 1. We see that 1 maps to 6 in the given permutation, so we write ([1,6. Next, we see that 6 maps to 2, so we write ([1,6,2. Finally, 2 maps to 5, so we write ([1,6,2,5. Since 5 maps back to 1, we can close the cycle and write ([1,6,2,5]).
Next, we look at the remaining elements, which are 3 and 4. We see that 3 maps to 4 and 4 maps back to 3, so we write ([3,4]).
Therefore, the permutation ([1,2,3,4,5,6],[6,5,4,3,1,2]) can be written as a product of disjoint cycles as ([1,6,2,5])([3,4]). The correct answer is (A) ([1,6,2,5])([3,4]).
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In art class students are mixing black and white paint to make gray paint. Riley mixes 4 cups of black paint and 3 cups of white paint. Christian mixes 7 cups of black paint and 4 cups of white paint. Use Riley and Christian percent of white paint to determine whose gray paint will be lighter.( Riley percent of white paint to the nearest whole number) (Christian percent of white paint to the nearest whole number). I been stuck on this for 20 mins!!!!! help
After taking out percentages we know that Riley has used more percentage of white paint which is 42.85% and her grey paint would be lighter.
What is the percentage?A % is a quantity or ratio that, in mathematics, represents a portion of one hundred.
A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.
The symbol "%" is frequently written after the number to indicate percentages.
So, the percentages would be:
Riley:
4 black and 3 white
Total = 7
Percentage of white paint:
3/7 * 100 = 42.85%
Christian:
7 black and 4 white
Total = 11
Percentage of white paint:
4/11 * 100 = 36.36%
We know that: 42.85% > 36.36%
Therefore, after taking out percentages we know that Riley has used more percentage of white paint which is 42.85% and her grey paint would be more lighter.
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water sprinkler sends water out in a circular pattern. What is the area formed by the water pattern if it can spray out 24 feet in any direction? Use 3.14 for π.
1808.64 is the area formed by the water pattern if it can spray out 24 feet in any direction.
What is an area of a circle?The circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve. The distance between the circle's points and its center is fixed. r2 is the area that a circle with radius r encloses. Here, the Greek letter stands for the constant proportion of a circle's circumference to its diameter,
Here, we have
Given: water sprinkler sends water out in a circular pattern. It can spray out 24 feet in any direction.
Since the water is being sent out in a circular pattern, the maximum distance at which the water is reaching out will be equal to the radius of the circle as the sprinkler is at the center of the circle.
The area of a circle is given as:
Area = πr²
Radius = 24 feet
Area = 3.14(24)²
Area = 1808.64
Hence, 1808.64 is the area formed by the water pattern if it can spray out 24 feet in any direction.
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Answer:
1808.64 is the area formed by the water pattern if it can spray out 24 feet in any direction.
step by step explanationWhat is an area of a circle?
The circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve. The distance between the circle's points and its center is fixed. r2 is the area that a circle with radius r encloses. Here, the Greek letter stands for the constant proportion of a circle's circumference to its diameter,
Here, we have
Given: water sprinkler sends water out in a circular pattern. It can spray out 24 feet in any direction.
Since the water is being sent out in a circular pattern, the maximum distance at which the water is reaching out will be equal to the radius of the circle as the sprinkler is at the center of the circle.
The area of a circle is given as:
Area = πr²
Radius = 24 feet
Area = 3.14(24)²
Area = 1808.64
Hence, 1808.64 is the area formed by the water pattern if it can spray out 24 feet in any direction.
1. Which of the following are the possible
lengths to complete a triangle with
side lengths of 14 in. and 8 in.?
A greater than 6 in., less than 20 in.
B greater than 6 in., less than 22 in.
Ogreater than 4 in., less than 20 in.
D greater than 4 in., less than 22 in
Answer: A
Step-by-step explanation:
To form a triangle, the two smaller lengths must be bigger than the largest side(Hopotonuse or sum, cant spell)
8 + 7 = 15
15>14
The possible lengths to complete a triangle with side lengths of 14 in. and 8 in. are 6 < x < 22.
What is Triangle Inequality?The triangle inequality theorem states that for any given triangle, the total of the two sides is always greater than the sum of the three sides. The Triangle is a polygon with three line segments as its boundaries. That is the tiniest polygon imaginable.
We have side lengths of 14 in. and 8 in.
Using Triangle inequality we know that the sum of two is greater than the third side.
Also, the range for third side is
14 + 8 = 22 inch
14 - 8 = 6 inch
So, the third side lies between as 6 < x < 22.
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Estrella is the manager of a candy store. She is in charge of buying
candy for the store to sell. She buys candy from a wholesaler for $6 per
pound. The wholesaler also charges a fee of $250 for each bulk
purchase. Estrella then sells the candy for $10 per pound. Calculate the
cost to buy 75 pounds of candy from the wholesaler.
$725
$675
$650
$700
Cost of 75 pound of candy = 75×6 = $450
Additional fee for each bulk = $250
Total = $700
Therefore, $700 is the correct answer.
Use line direction to:
A. eliminate the imaginary cross contour lines of fabric.
B. hide the underlying form of the fabric.
C. show the undulating forms of fabric.
Answer:
C.
Step-by-step explanation:
C. show the undulating forms of fabric.
given the hyperbolic spiral r=1/theta at t=pi, find the slope of
the curve
A. -pi
B. pi
C. 2pi
D. -2pi
The slope of the curve at a particular point on the hyperbolic spiral, we need to take the derivative of the equation with respect to θ and evaluate it at the given value of θ. Slope of the curve found to be = 2pi. The correct answer is option C
The equation of the hyperbolic spiral is given by: r = 1/θ To express this equation in terms of x and y, we use the polar-to-rectangular coordinate transformation: x = r cos(θ) y = r sin(θ)
Substituting the equation for r, we get: x = (cos(θ))/θ y = (sin(θ))/θ Taking the derivative of y with respect to x using the chain rule, we get:
[tex](dy/dx) = (dy/dθ)/(dx/dθ) (dy/dx) = [(cos(θ)/θ^2) + (sin(θ)/θ)] / [(-sin(θ)/θ^2) + (cos(θ)/θ)] At t = π, θ = π/2.[/tex]
Therefore, the slope of the hyperbolic spiral at t = π is: (dy/dx) = 2/π The correct option to this value is C. 2pi
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what is an equilvalent expression to 15x + 10
Answer:
5 (3x+2)
Step-by-step explanation:
Hope this helps! :)
Francine goes to the grocery store and spends $31.79. She pays The cashier with a $50 bill. What will her change be?
Can someone please help me with these and a tip on how to solve em step by step please
Applying the definition of complementary angles, the measures are:
7. m<DBE = 64°; m<CBE = 26°
8. m<WVZ = 84°; m<XVW = 96°
9. m<RTS = 63°; m<PTQ = 27°
10. m<EFG = 139°
m<IFH = 49°
What are Complementary Angles?Complementary angles are two angles whose sum is equal to 90 degrees. In other words, when two angles are placed side by side, forming a right angle, they are said to be complementary.
7. Angles DBE and CBE are complementary angles, therefore:
17x + 13 + 32 - 2x = 90
15x + 45 = 90
15x = 90 - 45
15x = 45
x = 3
m<DBE = 17x + 13 = 17(3) + 13 = 64°
m<CBE = 32 - 2x = 32 - 2(3) = 26°
8. 5x + 29 = 9x - 15 [vertical angles are equal]
5x - 9x = -29 - 15
-4x = -44
x = 11
m<WVZ = 9x - 15 = 9(11) - 15 = 84°
m<XVW = 180 - 84 = 96° [linear pair]
9. 8x - 17 = 5x + 13 [vertical angles]
8x - 5x = 17 + 13
3x = 30
x = 10
m<RTS = 5x + 13 = 5(10) + 13 = 63°
m<PTQ = 180 - 90 - 63 = 27°
10. (2x + 3) + (6x + 25) = 180 [linear pair]
8x + 28 = 180
8x = 180 - 28
8x = 152
x = 19
m<EFG = 6x + 25 = 6(19) + 25 = 139°
m<IFH = 90 - (2x + 3) = 90 - (2(19) + 3)
m<IFH = 49°
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5. In A LMN, LM = 12, LN = 10. and angle L = 52° What is the length, to the nearest tenth of a unit, of MN?
7.4 units
15.6 units
9.8 units
14.4 units
The length of MN, to the nearest tenth of a unit is equal to: C. 14.4 units.
What is the law of cosine?In order to determine the missing side length of a geometric figure with the adjacent and hypotenuse side lengths given, you should apply the law of cosine:
C² = A² + B² - 2(A)(B)cosθ
Where:
A, B, and C is the length of side of a given triangle.
By substituting the given side lengths and angle into the law of cosine formula, we have the following;
MN² = LM² + LN² - 2(LM)(LN)cosθ
MN² = 12² + 10² - 2(12)(10)cos(52)
MN² = 144 + 100 - 147.76
MN = √96.24
MN = 9.8 units.
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The height of a plant over time is shown in the table below. Using a logarithmic model, what is the best estimate for the age of the plant when it is 19 inches tall?
Moreover, we should evaluate the model's goodness of fit and take into expressions account additional elements that can influence plant development.
what is expression ?Mathematical operations include doubling, dividing, adding, and subtracting. A phrase is constructed as follows: Expression, monetary value, and mathematical operation Numbers, parameters, and functions make up a mathematical expression. It is possible to use words and terms in contrast. Every mathematical statement including variables, numbers, and a mathematical operation between them is called an expression, sometimes referred to as an algebraic expression. For example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.
In the formula, h is the height, t is the time, and a and b are the parameters that need to be approximated.
The information in the table may be used to estimate the values of a and b. The equation is first transformed to yield:
[tex]log(b*t) = log(h/a)[/tex]
[tex]19 = 19.24 * log(53.89*t)[/tex]
t = 0.186 months, or approximately 5.58 days, or log(53.89*t) = 1 53.89*t = 10
Hence, 5.58 days is the best guess for the age of the plant at 19 inches tall. Seeing that this is a very little period of time, it is probable that the model will not be correct for values of t this low. Moreover, we should evaluate the model's goodness of fit and take into account additional elements that can influence plant development.
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Determine algebraically whether the function is even, odd or neither: g(x) = x/x^2+3
The function [tex]g(x) = \frac{x}{x^2+3}[/tex] is neither even nor odd.
To determine if a function is even, we can use the following test:
f(x) = f(-x)
If this is true, then the function is even.
For the given function, [tex]g(x) = \frac{x}{x^2+3}[/tex], let's plug in -x for x and see if the function is equal to itself:
[tex]g(-x) = \frac{-x}{(-x)^2+3} = \frac{-x}{x^2+3}[/tex]
As we can see, g(x) does not equal g(-x), so the function is not even.
To determine if a function is odd, we can use the following test:
f(x) = -f(-x)
If this is true, then the function is odd.
For the given function, let's plug in -x for x and see if the function is equal to the negative of itself:
[tex]g(x) = \frac{-x}{(-x)^2+3} = \frac{-x}{x^2+3}\\\\ -g(-x) = \frac{x}{-x^2+3}[/tex]
As we can see, g(x) does not equal -g(-x), so the function is not odd.
After the algebraic analysis, we can conclude that the function g(x) is neither, i.e., it is neither even nor odd.
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3
The drama club at Hawthorne Middle School is selling tickets to their spring musical. Student tickets
cost $10 and adult tickets cost $15. Last week, they sold 120 tickets for the Sunday matinee show. If those
ticket sales totaled to $1,400, how many adult tickets were sold? How many student tickets were sold?
40 adult tickets were sold and 80 student tickets were sold.
What is an equation?
An equation is a mathematical statement that asserts that two expressions are equal. It typically consists of variables, constants, and mathematical operations.
Let's use algebra to solve this problem.
Let's call the number of student tickets sold "s" and the number of adult tickets sold "a".
From the problem, we know two things:
The total number of tickets sold was 120:
s + a = 120
The total amount of money made from ticket sales was $1,400:
10s + 15a = 1400
Now we have two equations with two variables, so we can solve for "a" and "s".
Let's start by solving for "s" in the first equation:
s + a = 120
s = 120 - a
Now we can substitute this expression for "s" into the second equation:
10s + 15a = 1400
10(120 - a) + 15a = 1400
1200 - 10a + 15a = 1400
5a = 200
a = 40
So 40 adult tickets were sold.
Now we can substitute this value of "a" into the first equation to find "s":
s + a = 120
s + 40 = 120
s = 80
So 80 student tickets were sold.
Therefore, 40 adult tickets were sold and 80 student tickets were sold.
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−3(0.75x−2y)+6(0.5x−2y) ?
Adriana’s family went to the state fair on a Tuesday night special event. The admission cost for the whole family was $42 and parking was $15. During the special event, all the ride tickets cost $2 each. If the total amount of money they had to spend for the evening was $120, how many tickets could Adriana’s family buy?
The unknown quantity, inequality, and the answer in a complete sentence.
Let B be an invertible matrix such that B^(-1) (see photo)
Find the solution of the equation Bx = (see photo)
Bx = 1
2
3
B^-1 = -1 0 1
2 2 0
1 0 1
The solution of the equation Bx = 1 2 3 is x = 2 6 4.
To find the solution of the equation Bx =
1
2
3
, we can multiply both sides of the equation by the inverse of B, B^-1. This will give us:
B^-1 Bx = B^-1
1
2
3
Since the product of a matrix and its inverse is the identity matrix, I, we can simplify the left side of the equation to:
Ix = B^-1
1
2
3
And since the product of the identity matrix and any vector is just the vector itself, we can simplify further to:
x = B^-1
1
2
3
Now, we can plug in the given values for B^-1 and the right side of the equation to find the solution for x:
x =
-1 0 1
2 2 0
1 0 1
*
1
2
3
Multiplying the matrices gives us:
x =
(-1)(1) + (0)(2) + (1)(3)
(2)(1) + (2)(2) + (0)(3)
(1)(1) + (0)(2) + (1)(3)
Simplifying further gives us:
x =
2
6
4
So, the solution of the equation Bx = 1 2 3 is x = 2 6 4
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All help is appreciated this is due RLLY SOON HAHAH :D
DUE TODAY HELP!!!!!!!!!!!!
What is the radius of the circle?
The radius of the circle is 13 units
How to determine the radius of the circleFrom the question, we have the following parameters that can be used in our computation:
The circle
Where we have
Center = (0, 0)
Point - (-5, 12)
The radius of the circle is the distance between the point and the center
So, we have
Radius = √[(0 + 5)² + (0 - 12)²]
Evaluate
Radius = 13
Hence, the radius is 13 units
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