Step-by-step explanation:
Use the Pythagorean theorem: a^2 + b^2 = c^2. In this case, sides a and b are each 7sqrt(3), and c is the diagonal of the square.
a^2 + b^2 = c^2
(7sqrt3)^2 + (7sqrt3)^2 = c^2
294 = c^2
c = sqrt(294) = 7sqrt(6)
Find the general solution of the system of equations Ax=b whose augmented matrix is given below and write it in parametric form. [b] Show the augmented matrix precisely after the first column has been "swept" to have only a "1" in the first row and 0 below- but no other operations have been performed. [c] Show the reduced echelon form [A b]= [ -3, 1, -1, 2, -9, -26, -20] [ 15, -5, 5, -10, 45, 130, [ -30, 10, -8, -62, 12, 32, -178] [ 9, -3, 3, -6, 27, 78, 60] 100] [d] Find 2 linearly independent solutions of the homogeneous system Ax=0 [e] Find a 3rd linearly independent solution of Ax=0 or give a valid reason why you could not find one. [f] Show that v=[ 1] is NOT in the span of the columns of A? [-5] i.e., give a valid proof or reason [10] [-4] [g] Do the first 4 columns of A span State a reason. [h] Give a linearly dependency relation for the first 5 columns of A R"?
[1, 0, 0, 0] [1] + [0, 1, 0, 0] the span of the columns of A and the general solution of the system of equations Ax = [ 9, -3, 3, -6, 27, 78, 60].
What do you mean by equation?An equation is a mathematical statement that shows the equality of two expressions. It is represented by an equal sign (=) and is used to solve for unknown values or to describe relationships between variables. Equations can be simple or complex, involving basic arithmetic operations or advanced mathematical concepts like trigonometry and calculus. They can also involve constants, variables, functions, and symbols.
An equation can be used to solve for a single unknown value, for example, the equation 2x + 3 = 7 can be solved for x by subtracting 3 from both sides, giving us 2x = 4 and then dividing both sides by 2, giving us x = 2. In this example, x = 2 is the solution to the equation.
[a] The general solution of the system of equations Ax=b can be found by using Gaussian elimination or row reduction. The augmented matrix [A b] is:
[-3, 1, -1, 2, -9, -26, -20]
[15, -5, 5, -10, 45, 130, 100]
[-30, 10, -8, -62, 12, 32, -178]
[ 9, -3, 3, -6, 27, 78, 60]
[b] The first step in row reduction is to get a 1 in the first row and 0s below it in the first column. We can do this by dividing the first row by -3 and subtracting multiples of it from the other rows:
[1, -1/3, 1/3, 2/3, 3, 26/3, 20/3]
[0, 20/3, 4/3, 8/3, 12, 104/3, 140/3]
[0, -40/3, 20/3, 4, -24, 68/3, 140/3]
[0, 3, -3, 0, 9, -78/3, 180/3]
Next, we can use row operations to get 0s in the second column below the first row:
[1, -1/3, 1/3, 2/3, 3, 26/3, 20/3]
[0, 1, 2/5, 4/5, 6, 42/5, 70/5]
[0, 0, 2/5, 2, -18, 26/5, 110/5]
[0, 0, 0, 0, 3, -78/5, 180/5]
Continuing with this process, we get the reduced echelon form of the augmented matrix:
[1, 0, 0, 0, 3, -26/5, 20/5]
[0, 1, 0, 0, 6, 42/5, 70/5]
[0, 0, 1, 0, -18, 26/5, 110/5]
[0, 0, 0, 1, 3, -78/5, 180/5]
[c] The reduced echelon form of [A b] is:
[1, 0, 0, 0, 3, -26/5, 20/5]
[0, 1, 0, 0, 6, 42/5, 70/5]
[0, 0, 1, 0, -18, 26/5, 110/5]
[0, 0, 0, 1, 3, -78/5, 180/5]
[d] The homogeneous system Ax=0 has the general solution:
x1 = t
x2 = 6t
x3 = -18t
x4 = 3t
where t is an arbitrary constant. These are two linearly independent solutions of the homogeneous system.
[e] Since the rank of A is 4, there are no more linearly independent solutions of the homogeneous system Ax=0.
[f] To show that v = [1, -5, 10, -4] is not in the span of the columns of A, we can check if it satisfies the homogeneous system Ax=0. Plugging in the values, we have:
[1, 0, 0, 0] [1] + [0, 1, 0, 0]
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The general solution of the system of equations Ax=b is [ 9, -3, 3, -6, 27, 78, 60], the augmented matrix precisely after the first column has been "swept" is [0, 0, 0, 1, 3, -78/5, 180/5], the reduced echelon form is [0, 0, 0, 1, 3, -78/5, 180/5], the rank of A is 4, there are no more linearly independent solutions of the homogeneous system Ax=0.
What do you mean by equation?An equation is a mathematical statement that shows the equality of two expressions. It is represented by an equal sign (=) and is used to solve for unknown values or to describe relationships between variables. Equations can be simple or complex, involving basic arithmetic operations or advanced mathematical concepts like trigonometry and calculus. They can also involve constants, variables, functions, and symbols.
An equation can be used to solve for a single unknown value, for example, the equation 2x + 3 = 7 can be solved for x by subtracting 3 from both sides, giving us 2x = 4 and then dividing both sides by 2, giving us x = 2. In this example, x = 2 is the solution to the equation.
[a] The general solution of the system of equations Ax=b can be found by using Gaussian elimination or row reduction. The augmented matrix [A b] is:
[-3, 1, -1, 2, -9, -26, -20]
[15, -5, 5, -10, 45, 130, 100]
[-30, 10, -8, -62, 12, 32, -178]
[ 9, -3, 3, -6, 27, 78, 60]
[b] The first step in row reduction is to get a 1 in the first row and 0s below it in the first column. We can do this by dividing the first row by -3 and subtracting multiples of it from the other rows:
[1, -1/3, 1/3, 2/3, 3, 26/3, 20/3]
[0, 20/3, 4/3, 8/3, 12, 104/3, 140/3]
[0, -40/3, 20/3, 4, -24, 68/3, 140/3]
[0, 3, -3, 0, 9, -78/3, 180/3]
Next, we can use row operations to get 0s in the second column below the first row:
[1, -1/3, 1/3, 2/3, 3, 26/3, 20/3]
[0, 1, 2/5, 4/5, 6, 42/5, 70/5]
[0, 0, 2/5, 2, -18, 26/5, 110/5]
[0, 0, 0, 0, 3, -78/5, 180/5]
Continuing with this process, we get the reduced echelon form of the augmented matrix:
[1, 0, 0, 0, 3, -26/5, 20/5]
[0, 1, 0, 0, 6, 42/5, 70/5]
[0, 0, 1, 0, -18, 26/5, 110/5]
[0, 0, 0, 1, 3, -78/5, 180/5]
[c] The reduced echelon form of [A b] is:
[1, 0, 0, 0, 3, -26/5, 20/5]
[0, 1, 0, 0, 6, 42/5, 70/5]
[0, 0, 1, 0, -18, 26/5, 110/5]
[0, 0, 0, 1, 3, -78/5, 180/5]
[d] The homogeneous system Ax=0 has the general solution:
x1 = t
x2 = 6t
x3 = -18t
x4 = 3t
where t is an arbitrary constant. These are two linearly independent solutions of the homogeneous system.
[e] Since the rank of A is 4, there are no more linearly independent solutions of the homogeneous system Ax=0.
[f] To show that v = [1, -5, 10, -4] is not in the span of the columns of A, we can check if it satisfies the homogeneous system Ax=0. Plugging in the values, we have:
[1, 0, 0, 0] [1] + [0, 1, 0, 0]
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help me please and thank you!!!
hope this helps :)
Model a desert community where 19% of the area is desert and the rest is houses.
squares represent the area of the community that is desert.
The area of the community that is houses is represented by
squares
19 squares represent the area of the community that is desert
The area of the community that is houses is represented by 81 squares
What is a percentage?Percentage is defined as the number that represents a ratio of a total that is divided by 100 equal parts. It is represented by the symbol %.
To solve this exercise, the percentage formula and the procedure to be applied is as follows:
As we can see in the picture the the desert has 10 square each side so the area will be:
A = 10*10
A = 100 squares
As the 19% of the area is only desert we have:
Desert = A*19%
Desert = 100*0.19
Desert = 19 squares
Now, the rest of area is the community that has houses, it is represented by:
A(houses) = A - desert
A(houses) = 100 squares - 19 squares
A(houses) = 81 squares
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This figure is made up of two rectangular prisms. What is the volume of the figure? Enter your answer in the box. ft³ Three-dimensional figure that could be formed by placing a smaller rectangular prism on top of a larger rectangular prism such that the widths of the prisms are the same. The larger bottom prism has a length of 19 feet, a width of 12 feet, and a height of 6 feet. The smaller top prism has a length of 10 feet and a height of 3 feet.
The required volume of the given figure made up of two rectangular prisms is 1728 cubic feet.
What is the volume of a rectangular prism?The volume of the rectangular prism is the product of the base area and the height.
The volume of the larger rectangular prism is 19 feet x 12 feet x 6 feet = 1368 cubic feet.
The volume of the smaller rectangular prism is 10 feet x 12 feet x 3 feet = 360 cubic feet.
Overall volume of rectangular prisms = 1368 cubic feet + 360 cubic feet
Overall volume of rectangular prisms = 1728 cubic feet
Therefore, the volume of the figure made up of two rectangular prisms is 1728 cubic feet.
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The triangles below are similar. Find the value of the variable.
The measure of the variable z is 44.
What is Similarity of Triangles?Two triangles are said to be comparable if their two sides are in the same ratio as the two sides of another triangle and their two sides' angles inscribed in both triangles are equal.
Given:
As, the Triangles are similar.
and, we know that similar triangles have their ratio of the corresponding sides equal.
Then, z/ 45 = 44/ 45
45z = 44 x 45
z = 44
Hence, the measure of z is 44.
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A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.
A spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.
Which statement about probability is true?
The probability of landing on orange is greater than the probability of landing on purple.
The probability of landing on yellow is less than the probability of landing on blue.
The probability of landing on orange is equal to the probability of landing on yellow.
The probability of landing on purple is equal to the probability of landing on blue.
The answer is a.) The probability of landing on orange is greater than the probability of landing on purple.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
A spinner with repeated colors numbered from 1 to 8 is shown.
Sections 1 and 8 are purple.
Sections 2 and 3 are yellow.
Sections 4, 5, and 6 are blue.
Section 7 is orange.
A spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.
so, we get,
true statement about probability is,
The probability of landing on orange is greater than the probability of landing on purple.
because, there are more spaces for blue than any other section.
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Simplify the expression by combining like
terms:
b+3b²+ b-b²
Enter the number that goes in the green box.
[?]b² + [ ]b
Enter
We can simplify the expression to get:
2*(b + b²)
How to simplify the expression?Here we want to simplify the following expression:
b + 3b² + b - b²
We can reorder that expression in the following way.
b + b + 3b² - b²
And now group like terms, we will get:
b + b + 3b² - b²
2b + (3 - 1)* b²
2b + 2b²
Now we can take 2 as a common factor to get:
2*(b + b²)
That is the expresion simplfied.
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For the function shown below, the definite integral integral_0^10 f(x) dx is closest to which of the following? a.-8 b.4 c.-4 d.0 e.8
The provided function's definite integral from 0 to 10 is closest to 4.
The area of each zone that the function, the x-axis, and the two vertical lines at x = 0 and x = 10 bounds is added to form the definite integral of the function. The definite integral that results from adding up each of these areas is the one that is closest to 4. The area of the region above the x-axis is larger than the area of the region below the x-axis, which explains this. The area of the region above the x-axis is higher than the area below the x-axis because the function is rising across the interval. The overall area is closer to 4 since the area of the region below the x-axis is negative. As a result, 4 is the closest value for the definite integral of the 0–10 function.
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The graph of y = tan x is concave up on which of the following intervals?A. (0,π/2)B. (-π/2,0)C. (-π/4, π/4) D. (0,π)E.(-π,0)
The graph of y = tan x is concave up on the interval (0,π/2).
The graph of y = tan x is concave up on the interval (0,π/2). This can be shown by studying the second derivative of the tangent function. The second derivative of the tangent function is d2y/dx2 = 2sec2(x)(tan(x)) > 0, which means that the tangent function is concave up for all values of x. This implies that the graph of y = tan x is concave up on the interval (0,π/2). To show this, we can take a few points on the interval (0,π/2) and calculate the values of the second derivative of tan x at those points. For example, for x = π/4, the second derivative of tan x is 2sec2(π/4)(tan(π/4)) = 2(1.1547)(1.7321) = 4.9289 which is positive. This shows that the graph of y = tan x is concave up on the interval (0,π/2).
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13.
Sara says that 2 - 5d = 5d - 2.
Junior says that 2 - 5d = -5d + 2.
Who is correct? Why?
The correct answer is Junior which is 2 - 5d = -5d + 2, because the number element of both equation is a match which is +2 and -5d.
This is mathematical equation. To see who is correct and who is wrong we have to analize both equation from Sara and Junior.
First we analize Sara equation.
First Equation : 2 - 5d contains 2 number element which is +2 and -5d
Second Equation : 5d - 2 contains 2 number element which is 5d and -2
We see that the number element from first and second equation from Sara is not match. So Sara is wrong.
Last we analize Junior equation
First Equation : 2 - 5d contains 2 number element which is +2 and -5d
Second Equation : -5d + 2 contains 2 number element which is -5d and +2
We see that the number element from first and secong equation from Junior is a match. So Junior is right.
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a women made a deposit of $218. if her deposit consisted of 62 bills, some of them one-dollar bills and the rest being five-dollar bills, how many one-dollar bills did she deposit?
F = quantity of five dollar bills
S = quantity of single dollar bills
so she deposited 62 bills, that means that whatever F and S are, we know that F + S = 62.
we also know that all those amount to $218, so the fives are really 5*F or 5F from those $218, and the singles are just 1*S of the same $218, so we can also say that 5F + S = 218.
[tex]F+S=62\implies F=62-S \\\\\\ 5F+S=218\implies \stackrel{\textit{substituting from above}}{5(62-S) +S=218}\implies 310-5S+S=218 \\\\\\ 310-4S=218\implies 310=4S+218\implies 92=4S\implies \cfrac{92}{4}=S\implies 23=S[/tex]
A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.
Number of Hours Total Number of Students
0 1
1 8
2 2
3 5
4 9
5 7
6 3
Determine the probability that a student studied for exactly 1 hour. Round to the nearest hundredth.
0.03
0.23
0.30
0.77
The probability that a student studied for 5 hours is 0.23.
What is the probability?Probability refers to the likelihood or chance that an expected success is observed over many possible observations, outcomes, or events.
Probability can be expressed as a percentage, decimal, or fraction.
here, we have,
In this situation, the probability that a student studied for 5 hours is the quotient of the division of the number of students who studied for 5 hours and the total number of students who studied.
Number of hours Total number
of students
0 1
1 3
2 2
3 5
4 9
5 7
6 3
Total 30
Probability a student studied 5 hours = 0.23 (7/30)
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The equation 9t = 27.99 models a constant rate situation.
What is 1t?
The value of t from the given equation is 3.11.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is 9t=27.99
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Now, t=27.99/9
t=3.11
Therefore, the value of t is 3.11.
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13 less than b In algebraic expression
13 less than b as an algebraic expression would be [tex]b - 13[/tex].
This is because 13 less than a number is the same as that number being subtracted by 13. Let me know if you have any questions, thanks!
Explain what each point on the least-squares regression line represents.
Choose the correct answer below.
A.Each point on the least-squares regression line represents the y-value of the data set at that corresponding value of x.
B.Each point on the least-squares regression line represents the y-values that would be considered ideal at that corresponding value of x.
C.Each point on the least-squares regression line represents the predicted y-value at the corresponding value of x.
D.Each point on the least-squares regression line represents one of the points in the data set.
The correct statement is "Each point on the least-squares regression line represents the predicted y-value at the corresponding value of x". Thus, Option C is correct.
A least-squares regression line is a mathematical model that is used to predict the value of a dependent variable (y) based on the value of an independent variable (x). The regression line is created by fitting a line to the data set that minimizes the differences between the actual y-values and the predicted y-values (the line).
Each point on the regression line represents the predicted y-value for a given value of x. In other words, if we know the value of x, we can use the regression line to predict the value of y that is most likely to occur based on the data set. The least-squares regression line is a useful tool for understanding the relationship between two variables and making predictions about future values.
A is incorrect because it states that each point on the least-squares regression line represents the actual y-value of the data set at that corresponding value of x, which is not necessarily the case. The regression line is a model that predicts y-values based on the relationship between x and y, but it is not necessarily equal to the actual y-values in the data set.
B is incorrect because it states that each point on the least-squares regression line represents the ideal y-values at that corresponding value of x, which is not a characteristic of a regression line. A regression line represents a predicted y-value based on the data set and the relationship between x and y, but it does not necessarily represent ideal values.
D is incorrect because it states that each point on the least-squares regression line represents one of the points in the data set, which is not necessarily the case. A regression line represents a predicted y-value based on the data set and the relationship between x and y, and it may not necessarily match the actual data points in the data set.
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determine f(x) and f(x) for the following function. then give the horizontal asymptotes of f, if any.
The function f(x) = (x + 1)^2 / (x - 2)(x + 2), with f(x) = 1.
The function f(x) is given as f(x) = (x^2 + 2x + 1) / (x^2 - 4). To determine f(x) and f(x), we must first factor the numerator and denominator. We can factor the numerator as (x + 1)^2, and the denominator as (x - 2)(x + 2). Thus, f(x) = (x + 1)^2 / (x - 2)(x + 2).
To determine the horizontal asymptotes, we must divide the leading terms of the numerator and denominator. The leading terms are x^2 for the numerator and x^2 for the denominator, so the horizontal asymptotes are y = 1.
Therefore, we can conclude that the function f(x) = (x + 1)^2 / (x - 2)(x + 2), with f(x) = 1.
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How to convert 4.5 kilograms to pounds?
4.5 kilos to pounds equal 9.9208. We convert one kilogram (kg) to 2.2 pounds (lb), which is a rough conversion.
How are pounds and kilos converted?One kilogram (kg) equals 2.2 pounds (lb), which is the approximate conversion we use. We multiply by 2.2 to change a kilogram into a pound. By dividing by 2.2, we may convert a pound to a kilogram.For the usual equation, multiply the amount of pounds by 2.2046. For instance, you can convert 50 pounds to kilograms by multiplying 50 by 2.2046, which is 22.67985 kg. 200 pounds are equivalent to 90.71940 kilograms when 200 is divided by 2.2046. In the fields of math and engineering, converting between kilograms and pounds frequently arises; fortunately, it is a simple process.Simply multiply the amount in kilograms by the conversion factor, 2.204622622, to convert 4.5 kilograms to pounds.
Therefore, 4.5 kilos in pounds = 9.920801798319491 pounds when multiplied by 2.204622622.
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Wilson Middle School has 1,500 students. Marshall Middle School has 340 fewer
students. Let m represent the number of students at Marshall Middle School
Let m represent the number of students at Marshall Middle School.
Since Wilson Middle School has 1,500 students and Marshall Middle School has 340 fewer students, the number of students at Marshall Middle School can be calculated by subtracting 340 from 1,500, which gives us 1,160. Therefore, m = 1,160.
Marshall Middle School is a public school located in Wichita, Kansas, serving students in grades 6-8. The school is part of the Wichita Public Schools district and has a variety of programs and activities to help students achieve personal and academic success. Students have access to a wide range of educational opportunities, including Project Lead the Way, college preparatory classes, and aquaponics coursework.
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Shelley has a piece of yellow ribbon that is 7.7 inches long and a piece of purple ribbon that is 6.99 inches long. How much longer is the yellow ribbon?
HELPPpp
Answer:
0.71
Step-by-step explanation:
To find how much longer the 1st one is, subtract: 7.7-6.99=0.71
The heights of the bars of a histogram correspond to _______ values.
the quadrilateral EFGH has vertices E (-3,2) F(3,2), G(3,-2), and H(-3,-2) which statement is correct
The statement that is correct on Quadrilateral EFGH is B. Quadrilateral EFGH is a rectangle.
What kind of shape is Quadrilateral EFGH ?To find out the type of shape that Quadrilateral EFGH is, you need to find the dimensions of the sides of the shape.
This can be found by the formula :
d=√(( x2 – x1 ) ² + ( y2 – y1 ) ² )
Using the formula, Side EF is 6 units
Side FG = 4 units
Side GH = 6 units
Side EH = 4 units
Two sides are therefore the same which means that this is a rectangle.
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Options for this question include:
A. Quadrilateral EFGH is a square.
B. Quadnlateral EFGH is a rectangle.
C. Quadrilateral EFGH is a rhombus
D. Quadriateral EFGH is a trapezium.
A mass of 6.005 g of carbon contains
The 6.005 g of carbon contains 0.5000 moles of C. option C
What is the mole?The mole is a unit of measurement in chemistry used to quantify the amount of a substance. One mole of a substance contains Avogadro's number of entities of that substance. Avogadro's number is defined as 6.022 x 10^23 entities per mole and is a fundamental constant in chemistry.
The mole is used to convert the amount of a substance in mass or volume to the number of entities (such as atoms, molecules, or ions) of that substance. The mole is useful in chemical reactions, where it provides a convenient way to express the amounts of reactants and products involved in a reaction.
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Find the indicated measure.
Answer:
∠ C = 40° , x = y = 118
Step-by-step explanation:
10
BC is the diameter of the circle then ∠ A = 90° , angle in a semicircle.
the sum of the 3 angles in Δ ABC = 180° , then
∠ A + ∠ B + ∠ C = 180°
90° + 50° + ∠ C = 180°
140° + ∠ C = 180° ( subtract 140° from both sides )
∠ C = 40°
11
ABCD is a cyclic quadrilateral
• the opposite angles are supplementary, sum to 180°
x + 62 = 180 ( subtract 62 from both sides )
x = 118
similarly
y + 62 = 180
y = 118
thus x = y = 118
Divide 16 by v. Then, subtract 7
Answer:
Step-by-step explanation:
The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Please help
The function f(t)=8000(0. 15)^{24t}f(t)=8000(0. 15)
24t
represents the change in a quantity over t days. What does the constant 0. 15 reveal about the rate of change of the quantity?
The function is decreasing exponentially at a rate of 85% every hour.
What does the constant 0. 15 reveal about the rate of change of the quantity?Here, 0.15 is the change the factor and since 0.15 is less than 1. Therefore , the it represents negative rate of change in the quantity that is decreasing.
Now, put t = 1/24 days
f(t) = 8000
= 8000 (0.15)
= 1200
Now, put t = 2/24 days
f(t) = 8000
= 8000
= 180
So, change in 1 hour = 1200 - 180
= 1020
Rate of change of decrease = 1020 x 100 / 1200
= 85%
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How many more unit tiles need to be added to the expression x2+4x+3 in order to form a perfect square trinomial? 1 2 3 4.
The unit tiles that needs to be added to the equation x²+4x+3 will be 1. The correct answer is A.
A square number, also known as a perfect square, is an integer that is the square of another integer. It results from dividing two integers by two.
When converting an expression to a perfect square trinomial
x²+4x+3
We must rearrange the statement in order to transform it into the perfect square.
x²+(2x+2x)+3
Extend the formula (x+2)²
(x+2)² = x² + 2(2x) + 2(2) (2)
(x+2)² = x² + 4 + 4x
(x+2)² = x² + 4x + 4
Add the constant terms together, then subtract them.
Difference is 4 minus 3.
Difference = 1
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Find the slope of the tangent line to the given polar curve at the point specified by the value of theta.
r = 6 cos(theta),
theta = ????/3
*its not negative square root of 3
The slope of the line would be theta = cos⁻¹ (r/6)
The Slope is what?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
By taking the derivative of the polar equation with respect to theta and evaluating it at the provided value of theta, one can determine the slope of the tangent line to the polar curve at the indicated position.
The rise divided by the run formula is used to calculate the percent of slope, which is calculated by multiplying the result by 100 and dividing the elevation change by the horizontal distance travelled.
d(r)/d(theta) = -6 sin(theta)
So, for theta = ????/3, the slope of the tangent line is:
-6 sin(????/3)
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What is the greatest three-digit number that is a multiple of three and eight?
"984" will be the biggest three-digit number that is a multiple of three and eight.
What is the number line?A horizontal line with evenly spaced numerical increments is called a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.
To find the greatest three-digit number that is a multiple of three and eight.
Multiple of 3 and 8 will have to be the multiple of 24.
Since the maximum three-digit number is 999.
We will divide 999 by 24 and the remainder:
Remainder = 15
Thus,
The Greatest three-digit number will be = 999-15
The greatest three-digit number will be = 984
therefore, the Greatest three-digit number that is a multiple of three and eight will be "984".
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Identify the reflection rule on a coordinate plane that verifies that triangle a(-2,3), b(-3,-2), c(-10,0) and triangle a'(2,3), b'(3,-2), c'(10,0) are congruent when reflected over the y-axis.
The triangles are not congruent. Three edges and three vertices make up a triangle, which is a polygon. It is among the fundamental shapes in geometry. Triangle ABC refers to a triangle with the vertices A, B, and C.
What is meant by congruent?In geometry, two figures or objects are congruent if they have the same shape and size, or if one is the mirror image of the other. If two shapes are similar in size and shape, they are said to be congruent. Additionally, if two shapes are congruent, then their mirror images are same.comparable to or in accord with something so that the two things can coexist or be joined without conflict: There is no conflict because our objectives are compatible. Congruent means "absolutely equal" in terms of size and shape. The forms hold their equality no matter how they are rotated, flipped, or turned.To learn more about congruent refer to:
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A student randomly draws a card from a standard deck of 52 cards. He records the type of card drawn and places it back in the deck. This is repeated 20 times. The table below shows the frequency of each outcome.
Outcome Frequency
Heart 7
Spade 3
Club 6
Diamond 4
Determine the experimental probability of drawing a spade.
0.15
0.25
0.35
0.50
The experimental probability of drawing a spade is 0.15.
What is probability?The probability that an event will occur is equal to the ratio of positive outcomes to all outcomes, according to the probability formula. The proportion of positive outcomes to overall outcomes, or P(E), determines the likelihood that an event will occur.
Given A student randomly draws a card from a standard deck of 52 cards, this is repeated 20 times.
total outcome = 20
The table below shows the frequency of each outcome.
Outcome Frequency
Heart 7
Spade 3
Club 6
Diamond 4
to find the probability of drawing a spade,
a favorable outcome for spade = 3
probability = favorable outcome/total outcome
P(spade) = 3/20
P(spade) = 0.15
Hence option A is correct.
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Answer:
Step-by-step explanation: .15 because there are 20 in total, and there are 3 spade.
3/20=.15
Hope this helps!