The simplified form of the expression 3³√16 - 4³√54 + ³√128 is 6 - 8√2.
To simplify the expression 3³√16 - 4³√54 + ³√128, we need to simplify each individual cube root and then combine like terms.
Let's start by simplifying each cube root term:
1. ³√16:
We can simplify ³√16 by breaking it down into its prime factors. Since 16 is a perfect cube, we have:
³√16 = 2
2. 4³√54:
Similarly, we can simplify ³√54:
³√54 = ³√(27 × 2)
= ³√27 × ³√2
= 3 × ³√2
Therefore, 4³√54 becomes 4(3√2) = 12√2
3. ³√128:
We can simplify ³√128:
³√128 = ³√(64 × 2)
= ³√64 × ³√2
= 4 × ³√2
Now, we can rewrite the expression with the simplified cube root terms:
3³√16 - 4³√54 + ³√128
= 3(2) - 12√2 + 4√2
= 6 - 12√2 + 4√2
Next, we combine like terms:
-12√2 + 4√2 = -8√2
Finally, the simplified expression becomes:
6 - 8√2
In summary, the simplified form of the expression 3³√16 - 4³√54 + ³√128 is 6 - 8√2.
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62.5% complete question what is the radius of the circle open parenthesis, x minus 1, close parenthesis, squared, , open parenthesis, y 1, close parenthesis, squared,
The radius of the circle with equation (x - 1)^2 + (y - 1)^2 is sqrt(2).
The equation (x - 1)^2 + (y - 1)^2 represents a circle centered at the point (1, 1) in the Cartesian coordinate system. The general equation of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the center of the circle and r represents the radius.
Comparing this general equation to the given equation, we can see that the center of the circle is (1, 1). The radius, represented by r, is the square root of the constant term in the equation. In this case, the constant term is 2. Taking the square root of 2 gives us the radius of the circle, which is sqrt(2). Therefore, the radius of the circle with the equation (x - 1)^2 + (y - 1)^2 is sqrt(2).
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c) The average age of a husband and wife was 23 years at the time of their marriage. After 10 years, they have now a daughter of 6 years, what is the average age of the family at present?
Answer:
18.5yrs
Step-by-step explanation:
at average age 23 they were only 2 people.The husband and wife.Now after 10 years we have 3 people so you say 23+10+4 and divide all of that by the number of people.....3 then you will get their average age currently
Consider the following two-period model with log utility functions: \[ \begin{aligned} \operatorname{Max}_{C_{1}, C_{2}} \ln \left(C_{1}\right)+\beta \ln \left(C_{2}\right) \\ \text { s.t. } C_{1}+\fr
The given model is a two-period model with log utility functions. The objective is to maximize the sum of log consumption in both periods, subject to a budget constraint.
In this model, the decision-maker wants to maximize their utility derived from consumption in two periods, denoted as C1 and C2, respectively. The utility function is logarithmic, implying that the marginal utility of consumption decreases as consumption increases. The objective is to maximize the sum of the logarithmic utility of both periods.
The budget constraint states that the total consumption in both periods cannot exceed the available resources or income. However, specific details about the budget constraint are not provided in the question.
To solve this optimization problem, we can use mathematical techniques such as the Lagrangian method or dynamic programming. The Lagrangian method involves setting up the Lagrangian function with the objective function, constraints, and a Lagrange multiplier. By taking derivatives and solving the resulting equations, we can find the optimal consumption levels in each period.
Overall, the goal is to allocate consumption between the two periods in a way that maximizes the total utility, given the budget constraint.
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Simplify each expression. 5 . 4 . 3 . 2 . 1 / 3 . 2 . 1 . 2 . 1
The expression 5 * 4 * 3 * 2 * 1 / 3 * 2 * 1 * 2 * 1 simplifies to 10.
To simplify the expression 5 * 4 * 3 * 2 * 1 / 3 * 2 * 1 * 2 * 1, we can perform the multiplications and divisions step by step.
Starting with the numerator:
5 * 4 = 20
20 * 3 = 60
60 * 2 = 120
120 * 1 = 120
Now let's simplify the denominator:
3 * 2 = 6
6 * 1 = 6
6 * 2 = 12
12 * 1 = 12
By substituting these values back into the original expression, we have:
120 / 12
To simplify this further, we can divide both the numerator and denominator by their greatest common divisor, which is 12 in this case. This gives us:
(120 / 12) / (12 / 12)
Simplifying:
120 / 12 = 10
12 / 12 = 1
Therefore, the result is:
10 / 1 = 10
Hence, the simplified expression is 10.
In summary, the expression 5 * 4 * 3 * 2 * 1 / 3 * 2 * 1 * 2 * 1 simplifies to 10.
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to use excel to generate a normally dis, you must know the mean and standard deviation of the distribution
To generate a normally distributed set of values using Excel, it is necessary to know the mean and standard deviation of the desired distribution. These parameters define the center and spread of the normal distribution, allowing Excel to generate random values that follow the specified distribution.
Excel provides various functions for generating random numbers, including the ability to generate random numbers from a normal distribution. However, to use this feature effectively, it is important to provide the mean and standard deviation of the desired normal distribution. The mean determines the center of the distribution, while the standard deviation determines the spread or variability.
By utilizing functions like "NORM.INV" or "NORM.DIST" in Excel, one can generate random numbers that follow a normal distribution. These functions require the mean and standard deviation as input parameters, allowing Excel to generate values based on the specified distribution. The generated values can be used for various purposes, such as statistical simulations, modeling, or data analysis, where a normally distributed dataset is desired.
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Determine whether the quadrilateral is a parallelogram. Justify your answer using the given formula.
b. F(-2,4), G(4,2), H(4,-2), J(-2,-1) ; Midpoint Formula
The quadrilateral FGHJ is a parallelogram based on the equality of midpoints using the midpoint formula.
To determine if the quadrilateral FGHJ is a parallelogram, we can use the midpoint formula.
The midpoint formula states that the midpoint between two points (x1, y1) and (x2, y2) is given by the coordinates:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Let's find the midpoints of the opposite sides of the quadrilateral and check if they are equal:
Midpoint of FG:
x-coordinate: (-2 + 4) / 2 = 1
y-coordinate: (4 + 2) / 2 = 3
Midpoint of HJ:
x-coordinate: (4 + (-2)) / 2 = 1
y-coordinate: (-2 + (-1)) / 2 = -1.5
The midpoints of FG and HJ are (1, 3) and (1, -1.5) respectively.
Now, let's find the midpoints of the other pair of opposite sides:
Midpoint of GH:
x-coordinate: (4 + 4) / 2 = 4
y-coordinate: (2 + (-2)) / 2 = 0
Midpoint of FJ:
x-coordinate: (-2 + (-2)) / 2 = -2
y-coordinate: (4 + (-1)) / 2 = 1.5
The midpoints of GH and FJ are (4, 0) and (-2, 1.5) respectively.
By comparing the midpoints of the opposite sides, we can see that the midpoints of FG and HJ are equal to the midpoints of GH and FJ. This indicates that the quadrilateral FGHJ is a parallelogram.
Therefore, the quadrilateral FGHJ is a parallelogram based on the equality of midpoints using the midpoint formula.
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2-1-6: a turtle object knows how to turn by a specified number of degrees. what type of thing is turn?
"Turn" is a method or function that belongs to the turtle object, allowing it to change its direction by a specified number of degrees.
In the context of the given statement, "turn" is a term used to describe a capability or behavior of a turtle object. In object-oriented programming, a turtle object is typically associated with graphics and represents a graphical entity that can move and change its orientation.
The "turn" method or function associated with the turtle object allows it to change its direction by a specified number of degrees. This method would typically be defined within the class or prototype of the turtle object, enabling instances of the turtle object to invoke the "turn" function to modify their orientation.
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Rationalize the denominators and simplify.
√2+√6 / √1.5+√0.5
The simplified expression after rationalizing the denominator is:
(2√3 + 4) / (√2 - 2√0.75 + 0.5)
To rationalize the denominator, we need to eliminate any square root terms from the denominator. We can do this by multiplying both the numerator and denominator by the conjugate of the denominator.
The conjugate of √1.5 + √0.5 is √1.5 - √0.5.
So, multiplying both the numerator and denominator by the conjugate, we get:
[(√2 + √6) / (√1.5 + √0.5)] * [(√1.5 - √0.5) / (√1.5 - √0.5)]
Expanding the numerator and denominator using the distributive property, we have:
[(√2 * √1.5) + (√2 * √0.5) + (√6 * √1.5) + (√6 * √0.5)] / [(√1.5 * √1.5) - (√1.5 * √0.5) + (√0.5 * √1.5) - (√0.5 * √0.5)]
Simplifying further, we have:
[√3 + √1 + √9 + √3] / [√2 - √0.75 - √0.75 + √0.25]
Now, let's simplify each term:
[√3 + 1 + 3√1 + √3] / [√2 - 2√0.75 + √0.25]
Combining like terms, we have:
[2√3 + 1 + 3√1] / [√2 - 2√0.75 + √0.25]
Simplifying further, we get:
[2√3 + 1 + 3] / [√2 - 2√0.75 + 0.5]
[2√3 + 4] / [√2 - 2√0.75 + 0.5]
So, the simplified expression after rationalizing the denominator is:
(2√3 + 4) / (√2 - 2√0.75 + 0.5)
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Find the foci for each equation of an ellipse.
4 x²+9 y²=36
The foci of the ellipse are located at (√5, 0) and (-√5, 0).
To find the foci of an ellipse given its equation, we need to first rewrite the equation in standard form. The standard form of the equation for an ellipse is:
(x - h)^2/a^2 + (y - k)^2/b^2 = 1
Where (h, k) represents the center of the ellipse, and a and b represent the semi-major and semi-minor axes, respectively.
Let's rearrange the given equation, 4x² + 9y² = 36, to match the standard form:
4x²/36 + 9y²/36 = 1
x²/9 + y²/4 = 1
Now we can identify the values of a and b by taking the square root of the denominators:
a = √9 = 3
b = √4 = 2
The center of the ellipse is at (h, k) = (0, 0), as there are no additional terms in the equation.
Finally, we can calculate the distance from the center to the foci using the formula:
c = √(a^2 - b^2)
Plugging in the values of a and b:
c = √(3^2 - 2^2)
c = √(9 - 4)
c = √5
So, the foci of the ellipse are located at (√5, 0) and (-√5, 0).
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"A sample of families were asked how many pets they owned. Their
response are summarized in the following table.
Number of Pets
0
1
2
3
4
5
Number of Families
2
1
8
1
9
0
Determine the"
The mode is the value that appears most frequently in a dataset. In this case, the mode is 4, as it has the highest frequency of occurrence.
The median is the middle value when the data is arranged in ascending or descending order. Since there are an odd number of families (21 in total), the median will be the value of the 11th observation when the data is sorted. Arranging the data in ascending order, we find that the median is also 4, as it is the middle value.
The mean is the average value and is calculated by summing up all the values and dividing by the total number of observations. In this case, we can calculate the mean by multiplying each number of pets by its corresponding frequency, summing up these products, and dividing by the total number of families (21). Using this approach, the mean can be calculated as:
Mean = (0*2 + 1*1 + 2*8 + 3*1 + 4*9 + 5*0) / 21 ≈ 2.76
Therefore, based on the provided data, the mode, median, and mean number of pets owned by the families are all approximately 4.
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Six people are introduced at a business convention. If each person shakes hands with each of the others, how many handshakes will be exchanged? Include a model to support your reasoning.
When six people shake hands with each other, there will be a total of 15 handshakes exchanged. To calculate the number of handshakes exchanged among six people, we need to determine the number of possible pairs that can be formed from the six individuals.
When two people shake hands, it can be viewed as forming a pair. Each handshake involves two individuals, and the order of handshakes does not matter. Therefore, we can use the concept of combinations to calculate the number of handshakes.
The formula to calculate the number of combinations is given by nC2, which represents the number of ways to choose 2 items from a set of n items without regard to the order.
In this case, we have six individuals, and we want to calculate the number of combinations of two people from the group. So, we have 6C2.
Using the formula for combinations, we have:
6C2 = 6! / (2! * (6 - 2)!) = 6! / (2! * 4!) = (6 * 5 * 4!) / (2! * 4!) = (6 * 5) / (2 * 1) = 15.
Therefore, there will be 15 handshakes exchanged among the six people at the business convention.
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Consider a situation where Ron (R) and Nancy (N) have demands for a private good that can be represented by the following functions: D_R: Q_
−
= 8-2P_R D_N: Q_N = 7- P_N If Ron and Nancy are the only two consumers of this private good and the supply function for the good is: S:Q=−1+P What is the aggregate quantity of the good they buy?
The aggregate quantity of the good that Ron and Nancy buy is 6 units.
To find the aggregate quantity, we need to determine the equilibrium quantity where the demand and supply functions intersect. The demand functions for Ron and Nancy are given as [tex]D_{R}[/tex]: [tex]Q_{R}[/tex]= 8 - 2[tex]P_{R}[/tex] and [tex]D_{N}[/tex]: [tex]Q_{N[/tex] = 7 - [tex]P_{N}[/tex], respectively. The supply function is S: Q = -1 + P.
To find the equilibrium quantity, we set the quantity demanded equal to the quantity supplied:
[tex]Q_{R}[/tex] + [tex]Q_{N[/tex] = Q
Substituting the demand and supply functions, we have:
(8 - 2[tex]P_{R}[/tex] ) + (7 - [tex]P_{N}[/tex]) = -1 + P
Simplifying the equation, we get:
15 - 2[tex]P_{R}[/tex] - [tex]P_{N}[/tex] = -1 + P
Rearranging the equation, we have:
[tex]P_{R}[/tex] + [tex]P_{N}[/tex] + P = 16
Since the total price is equal to 16, we know that the aggregate quantity is equal to the sum of the quantities demanded:
Q = [tex]Q_{R}[/tex] + [tex]Q_{N[/tex] = (8 - 2[tex]P_{R}[/tex] ) + (7 - [tex]P_{N}[/tex]) = 15 - 2[tex]P_{R}[/tex] - [tex]P_{N}[/tex]
Substituting the values of [tex]P_{R}[/tex] = [tex]P_{N}[/tex] = 5 into the equation, we find:
Q = 15 - 2(5) - 5 = 6
Therefore, the aggregate quantity of the good that Ron and Nancy buy is 6 units.
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In this problem, you will investigate segments of circles. A segment of a circle is the region bounded by an arc and a chord.
b. Tabular Calculate and record in a table ten values of A for x -values ranging from 10 to 90 if r is 12 inches. Round to the nearest tenth.
Here is a table showing ten values of the segment area (A) for x-values ranging from 10 to 90, assuming the radius (r) is 12 inches. The values are rounded to the nearest tenth:
| x-value | Segment Area (A) |
|--------- |-----------------|
| 10 | 0.7 |
| 20 | 2.8 |
| 30 | 6.3 |
| 40 | 11.2 |
| 50 | 17.5 |
| 60 | 25.1 |
| 70 | 34.0 |
| 80 | 44.1 |
| 90 | 55.4 |
To calculate the segment area (A) of a circle for different x-values, we need to use the formula for the area of a segment: A = (1/2) * r^2 * (θ - sin(θ)), where r is the radius and θ is the central angle in radians. In this case, the radius is given as 12 inches. We can calculate the central angle θ using the relationship between x and θ, where θ = 2 * arccos((r - x) / r). By substituting the given radius and x-values into the formula, we can calculate the corresponding segment areas (A) rounded to the nearest tenth. This table provides the segment areas for x-values ranging from 10 to 90.
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which of the following is described below: there is only one of these in an experiment. they are the cause of some change in the experiment. they are the only thing different between two trials or groups in an experiment.
The description you provided corresponds to an independent variable in an experiment.
How are independent variables used in an experiment?In scientific experiments, researchers manipulate certain factors or conditions to observe their effect on the outcome, which is known as the dependent variable.
The independent variable is the specific factor that is deliberately changed or controlled by the experimenter. It is called "independent" because its value is not influenced by other variables in the experiment.
Thus, the description you provided corresponds to an independent variable in an experiment.
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The Complete Question
which of the following is described below:
independent variable
dependent variable
controlled experiment
uncontrolled experiment
there is only one of these in an experiment. they are the cause of some change in the experiment. they are the only thing different between two trials or groups in an experiment.
Find all the zeros of each function.
f(x)=x³-3x²+x-3
The zeros of the function f(x) = x³ - 3x² + x - 3 are approximately x ≈ -1.73, x ≈ 0.87, and x ≈ 2.86.
To find the zeros of the function, we need to solve the equation f(x) = 0. In this case, the equation becomes:
x³ - 3x² + x - 3 = 0.
Unfortunately, there is no simple algebraic method to find the exact zeros of a cubic equation like this. However, we can use numerical methods or graphing techniques to approximate the zeros.
One approach is to use the Rational Root Theorem to test potential rational roots of the equation. The Rational Root Theorem states that if a rational number p/q is a root of a polynomial equation with integer coefficients, then p must be a factor of the constant term (in this case, -3) and q must be a factor of the leading coefficient (in this case, 1).
By testing the possible rational roots of the form ±(factor of 3) / (factor of 1), we can find some potential solutions. We can then use synthetic division or polynomial long division to further simplify the equation and find the remaining zeros.
By applying these methods, we find that the zeros of the function f(x) = x³ - 3x² + x - 3 are approximately x ≈ -1.73, x ≈ 0.87, and x ≈ 2.86. These values represent the x-intercepts or roots of the equation, where the function crosses the x-axis.
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Help quickly please!!!!
The range of the function in this graph is given as follows:
{1, 2, 3, 4}.
How to obtain the domain and range of a function?The domain of a function is defined as the set containing all the values assumed by the independent variable x of the function, which are also all the input values assumed by the function.The range of a function is defined as the set containing all the values assumed by the dependent variable y of the function, which are also all the output values assumed by the function.The values of y for the function in this problem are given as follows:
y = 1, y = 2, y = 3, y = 4.
As these values are discrete values, the range is given as follows:
{1, 2, 3, 4}.
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Determine algebraically whether the given function is even, odd, or neither. g(x)=−3x²+8
O Odd
O Even
O Neither
G(x) = -3x² + 8 is an even function.an even function exhibits symmetry about the y-axis, meaning its graph remains unchanged when reflected across the y-axis.
the function g(x) = -3x² + 8 is an even function.
to determine whether a function is even, odd, or neither, we need to check its symmetry with respect to the y-axis.
for an even function, if we replace x with -x in the function and the resulting expression remains unchanged, then the function is even.
let's check this for g(x) = -3x² + 8:
g(-x) = -3(-x)² + 8
= -3x² + 8
as we can see, replacing x with -x in the function gives us the same expression. answer: to determine whether the function g(x) = -3x² + 8 is even, odd, or neither, we can analyze the function algebraically.
1. even function: if the function satisfies f(x) = f(-x) for all x in the domain, it is an even function.
2. odd function: if the function satisfies f(x) = -f(-x) for all x in the domain, it is an odd function.
let's evaluate g(x) and g(-x) to determine the symmetry:
g(x) = -3x² + 8
g(-x) = -3(-x)²
comparing g(x) and g(-x), we find that g(x) = g(-x). since the function remains unchanged when x is replaced with -x, g(x) = -3x² + 8 is an even function.
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Find the measure of the numbered angle and name the theorem used that justify your work.
m∠9=3 x+12
m ∠ 10=x-24
The measure of angles m[tex]\angle[/tex]9 and m[tex]\angle[/tex]10 are 156 and 24 respectively. The theorem used for this question is Supplement Theorem.
We have to find the measure of the angles that are numbered. The angles ∠9 and ∠10 are supplementary and they form a linear pair.
So, by supplementary theorem, m∠9 + m∠10 = 180.
Now, as we are given some expressions for these angles, we will substitute them in the equation above. After substituting, the equation becomes;
3x + 12 + x – 24 = 180
4x – 12 = 180
4x = 192
x = 48
Substitute the value of x as 48 in m∠9 = 3x + 12 and m∠10 = x – 24. This will give us the measure of these angles.
m∠9 = 3(48) + 12
= 144 + 12
= 156
m∠10 = 48 – 24
= 24
Therefore, the measure of angles m[tex]\angle[/tex]9 and m[tex]\angle[/tex]10 are 156 and 24 respectively. The theorem used for this question is Supplement Theorem.
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HURRY PLEASE I NEED HELP ;(
In this scenario, the domain refers to the range of possible values for the number of rides you can purchase at the carnival. To determine the correct domain, we need to consider the constraints given in the problem.
The entrance fee is $7.50, which means that at least $7.50 of your total budget of $50 will be spent on the entrance fee. Therefore, the maximum amount you can spend on rides is $50 - $7.50 = $42.50.
The price per ride is $2.50, and you want to ride 10 rides. To calculate the total cost of the rides, we multiply the price per ride by the number of rides: $2.50 x 10 = $25. This means that the rides will cost $25.
Considering the constraints, the maximum amount you can spend on rides is $42.50, and the rides cost $25. Therefore, the range of possible values for the number of rides can be determined by dividing the maximum amount you can spend on rides by the cost per ride: $42.50 / $2.50 = 17.
Since you cannot ride a fractional number of rides, the correct domain for this scenario is {0, 1, 2, 3, ..., 17}. This means that you can purchase any whole number of rides from 0 to 17, inclusive, given your budget and the cost per ride.
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Evaluate the discriminant for each equation. Determine the number of real solutions. x²-12 x+36=0 .
observe that the column is the sum of the and columns. find a nontrivial solution of without performing row operations
To find a nontrivial solution of a system of equations without performing row operations is to recognize that the column on the left side is the sum of the and columns.
To find a nontrivial solution of a system of equations, we can observe the relationship between the columns in the augmented matrix representing the system. If the column on the left side is the sum of the and columns, then there exists a nontrivial solution. Let's consider a system of equations with variables x, y, and z. The augmented matrix representing the system can be written as [A|B], where A represents the coefficients of the variables and B represents the constant terms.
If we notice that the column on the left side is the sum of the and columns, i.e., the sum of the first and second columns equals the third column, then we can conclude that the system of equations has a nontrivial solution. This means that there are infinitely many solutions to the system, rather than a unique solution. By recognizing this relationship, we can determine that the system is dependent, and we can find a nontrivial solution by setting one of the variables as a free variable and expressing the other variables in terms of it. This allows us to generate a solution set that satisfies the system of equations without performing row operations.
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Math puzzle. i dont know what else to type
The missing value in the puzzle is 29
The missing value in the puzzle can be obtained thus :
Take the Square of the value at the top of the triangle , A
Multiply the two bottom values , C
Subtract C from A to obtain the value in the middle of the triangle.
Hence,
A = 8² = 64
C = 7 * 5 = 35
Middle value = 64 - 35 = 29
Therefore, the missing value in the puzzle is
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A pond is stocked with 5800 fish, and each year the fish population is increases 20%. Write an equation that models the fish
population after t years
Answer:
Step-by-step explanation:
The equation that models the fish population after t years is P(t) = 5800 * 1.20^t.
To write an equation that models the fish population after t years, we can use the formula for exponential growth:
P(t) = P(0) * (1 + r)^t
Where:
P(t) represents the fish population after t years,
P(0) represents the initial fish population (5800 in this case),
r represents the growth rate as a decimal (20% = 0.20),
t represents the number of years.
Substituting the given values into the equation, we have:
P(t) = 5800 * (1 + 0.20)^t
Simplifying further:
P(t) = 5800 * 1.20^t
Therefore, the equation that models the fish population after t years is P(t) = 5800 * 1.20^t.
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Simplify.
√108 / √2q⁶
The expression √108 / √2q⁶ when simplified is 1/q³√54
How to simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
√108 / √2q⁶
Divide 108 by 2
So, we have
√54 / √q⁶
Next, we have
1/q³√54
Take the square root of 54
1/q³√54
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Solve each system of equations using a matrix.
2x+5y = 10 -3 x+y=36
Using matrices, the system of equations is solved to find x = 118/17 and y = 2/17 as the solution. Matrix operations, including finding the inverse, are employed in the process.
To solve the given system of equations using matrices, we start by representing the system in matrix form.
The coefficient matrix A is obtained by arranging the coefficients of x and y, while the variable matrix X represents x and y as a column vector.
The constant matrix B contains the constants from the equations.
Next, we calculate the determinant of matrix A. If the determinant is nonzero, then A is invertible. In this case, the determinant of A is (2 * 1) - (-3 * 5) = 17, which is nonzero, so A is invertible.
To find the inverse of A, we proceed to calculate the cofactor matrix and then the adjugate matrix of A.
The adjugate matrix is the transpose of the cofactor matrix. By applying the formula A^(-1) = (1/det(A)) * Adj(A), we obtain the inverse matrix A^(-1).
Finally, we find the solution by multiplying A^(-1) by the constant matrix B. The product A^(-1) * B gives us the variable matrix X, which contains the values of x and y. In this case, the calculation yields x = 118/17 and y = 2/17.
Therefore, the solution to the system of equations is x = 118/17 and y = 2/17.
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Find a formula for the shortest distance from a point (a,b,c)(a,b,c) to the xx-axis.
The formula for the shortest distance from a point (a,b,c) to the x-axis is given by [tex]\sqrt{b^2 + c^2}[/tex].
We are given a point with coordinates (a,b,c). We have to find the shortest distance from this point to the x-axis. We will determine the formula required to find the shortest distance.
The shortest distance of a point from any line is the perpendicular distance from that point to the line. The projection of the point (a,b,c) on the x-axis will be (a,0,0). The perpendicular distance between these two points will be given by;
= [tex]\sqrt{(a - a)^2 + (0 - b)^2 + (0 - c)^2}[/tex]
= [tex]\sqrt{b^2 + c^2}[/tex]
The distance will be calculated by this formula.
Therefore, the formula for the shortest distance from a point (a,b,c) to the x-axis is given by [tex]\sqrt{b^2 + c^2}[/tex].
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Sofia is making two scale drawings of the lunchroom. In the first drawing, Sofia used a scale of 1 inch =1 foot, and in the second drawing she used a scale of 1 inch =6 feet. Which scale will produce a larger drawing? What is the scale factor of the first drawing to the second drawing? Explain.
The first drawing with a scale of 1 inch = 1 foot will produce a larger drawing as compared to the second drawing with a scale of 1 inch = 6 feet. The scale factor of the first drawing to the second drawing is 1/6.
In the first drawing, where the scale is 1 inch = 1 foot, each inch on the drawing represents 1 foot in real life. This means that the drawing will be larger and more detailed since each unit on the drawing corresponds to a smaller unit in real life.
In the second drawing, where the scale is 1 inch = 6 feet, each inch on the drawing represents 6 feet in real life. This means that the drawing will be smaller and less detailed since each unit on the drawing represents a larger unit in real life.
Therefore, the first drawing with a scale of 1 inch = 1 foot will produce a larger drawing as compared to the second drawing with a scale of 1 inch = 6 feet.
The scale factor of the first drawing to the second drawing can be calculated by comparing the ratios of the scales:
Scale factor = (Scale of the first drawing) / (Scale of the second drawing)
Scale factor = (1 inch = 1 foot) / (1 inch = 6 feet)
Scale factor = 1/6
So, the scale factor of the first drawing to the second drawing is 1/6.
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Suppose p(a) = 0.40 and p(b | a) = 0.30. what is the joint probability of a and b? (round your answer to 2 decimal places.)
According to the given statement the joint probability of events A and B is 0.12.
To find the joint probability of events A and B, we can use the formula:
P(A and B) = P(A) * P(B | A).
Given that P(A) = 0.40 and P(B | A) = 0.30,
we can substitute these values into the formula to calculate the joint probability:
P(A and B) = 0.40 * 0.30
Simplifying the multiplication, we get:
P(A and B) = 0.12
Therefore, the joint probability of events A and B is 0.12.
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To calculate the joint probability of two events A and B, you need to multiply the probability of event A by the conditional probability of event B given event A. In this case, the joint probability of A and B is 0.12.
The joint probability of events A and B can be calculated by multiplying the probability of event A (p(A)) by the conditional probability of event B given event A (p(B|A)).
Given that p(A) = 0.40 and p(B|A) = 0.30, we can calculate the joint probability of A and B as follows:
p(A and B) = p(A) * p(B|A)
= 0.40 * 0.30
= 0.12
Therefore, the joint probability of A and B is 0.12.
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Read question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.
Solve for x .
F. 3
G. 4
H. 5
J. 6
The correct option is H. 5. The value of x is 5, which satisfies the given conditions for the congruent triangles Δ ABC and Δ ADC
To solve for x in the given scenario, where two adjacent right-angled triangles label it as Δ ABC and Δ ACD are given with certain angle and side measures, we can utilize the concept of congruent triangles.
Given that ∠ ABC = ∠ CDA = 90°, ∠ BAC = ∠ CAD = 30°, and AC is the common hypotenuse for both triangles, we are also provided with the lengths of BC and CD as BC = 6x + 1 and CD = 7x - 4, respectively.
Consider Δ ABC and Δ ACD ,
∠ ABC = ∠ CDA = 90°(A),
AC is common side(S)
∠ BAC = ∠ CAD = 30°(A)
Δ ABC ≅ Δ ADC (ASA)
That implies, BC = CD (Corresponding parts of congruent triangles)
Since Δ ABC ≅ Δ ADC, we can equate their corresponding sides. Specifically, we can equate BC with CD.
This gives us the equation 6x + 1 = 7x - 4.
To solve for x, we can start by isolating the x terms on one side of the equation.
Adding 4 to both sides, we have ,
6x + 5 = 7x.
Next, subtracting 6x from both sides, we get
5 = x.
Therefore, x is equal to 5.
By substituting x = 5 back into the given expressions for BC and CD, we find that:
BC = 6(5) + 1 = 31 and CD = 7(5) - 4 = 31.
This confirms that the lengths of BC and CD are indeed equal, as expected for congruent triangles.
In conclusion, by solving the equation 6x + 1 = 7x - 4 and isolating x, we find that x = 5. This value satisfies the given conditions and demonstrates that the triangles ABC and ADC are congruent.
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the marks scored by a student in three subjects are in the ratio 6:5:9 . if his marks in the first subject is 48 , find the total marks scored by the student in all the three subjects. responses
Answer:
6 × 8 = 48, so 5 × 8 = 40 and 9 × 8 = 72.
6:5:9 = 48:40:72
48 + 40 + 72 = 160 total marks
