The recursive formula is mathematically given as
a_n=1266.77e^n
What is the recursive formula?Generally, the equation for the decay is mathematically given as
[tex]at=a_oe^{-\lambda t}[/tex]
Hence
a1=1400e^{-0.1 (1)}
In conclusion,
[tex]a_n=1400e^{-0.1 (n)}\\\\a_n=1266.77e^n[/tex]
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A model without any simplifying assumptions a.provides simplified solutions to complex problems. b.is highly complex and likely unworkable. c.excludes important predictive variables. d.is very helpful for solving tough, real-world problems.
A model without any simplifying assumptions b.is highly complex and likely unworkable.
As their call implies, simplifying assumptions are assumptions that are protected within the version to simplify the evaluation as tons as feasible. While a simplified version now does not predict the conduct of the actual issue within perfect bounds, too many simplifying assumptions have been made.
While a scientific version enables us to make predictions, it's more valued. As clinical models are representations of simplified explanations, they do not are looking for to explain each scenario or every detail. This means that medical models often aren't equal to the 'real international' from which they are derived.
Mathematical models can help college students apprehend and discover the that means of equations or valuable relationships.
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GEOMETRY)
In the accompanying diagram of circle O, the m angle AOB=36^o. What is the m angle ACB ?
Answers…
A. 9^o
B. 36^o
C. 72^o
D. 18^o
(Picture is below) Thank you!
Answer:
SOLUTION :-
There is theorem/proof that tells that in these types of figure the other angle is double of the previous one
Means , the required angle will be ( 36 x 2 ) i.e. 72°.
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Nosaira solved an equation. Her work is shown below:
3(2x + 1 ) = 2(x + 1) + 1
6x + 3 = 2x + 2 + 1
6x + 3 = 2x + 3
4x = 0
x = 0
She determines the equation has no solution.
Which best describes Nosaira’s work and answer?
Her work is correct, but there is one solution rather than no solution.
Her work is correct and her interpretation of the answer is correct.
Her work is incorrect. She distributed incorrectly.
Her work is incorrect. She moved terms across the equals sign incorrectly.
Her work is correct, but there is one solution rather than no solution.
Solving linear equationsLinear equations are equations that has a degree of 1. Given the equation below;
3(2x + 1 ) = 2(x + 1) + 1
Expand
3(2x) + 3(1) = 2(x) + 2(1) + 1
Simplify
6x + 3 =2x + 2 + 2
6x + 3 = 2x + 3
Collect the like term
6x - 2x = 3 - 3
4x = 0
x =0
Hence we can conclude that Her work is correct, but there is one solution rather than no solution.
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Find the surface area of the composite figure.
20 in.
11 in.
5 in.
19 in
12 in.
12 in.
SA
11 in.
5 in.
20 in.
[?] in. 2
By using the area formulae for triangles and rectangles and the concept of surface area of the composite figure is equal to 1108 square inches.
What is the surface area of the composite figure?
The surface area is the area of all faces of a solid. In this case, we must sum the areas of seven rectangular and two triangular faces to determine the surface area:
A = 2 · (0.5) · (12 in) · (9 in) + 2 · (11 in) · (20 in) + 2 · (5 in) · (20 in) + 2 · (5 in) · (12 in) + (12 in) · (20 in)
A = 1108 in²
By using the area formulae for triangles and rectangles and the concept of surface area of the composite figure is equal to 1108 square inches.
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A Virus is 30 Nanometres long.
Using the information below, calculate the length, in millimetres, of the virus.
1 metre = 1,000,000 Nanometres.
Answer:
0.00003mm
Step-by-step explanation:
We know that 1mm=1000000nm
To convert small unit to big we divide
So 30÷1000000=0.00003nm
Assume that they all agree on the sample size and the sample mean use the pairs below to select the team that has the smallest sample standard deviation?
Step-by-step explanation:
A.Confidence Level: 99.7%; Confidence Interval: 42 to 48
B.Confidence Level: 95%; Confidence Interval: 43 to 47
C.Confidence Level: 68%; Confidence Interval: 44 to 46
D.Confidence Level: 95%; Confidence Interval: 44 to 46
Whats the easiest way to solve a modulu problem. For example we can use 2^100/3. Whats the easiest way to find the remainder? Without using shortcuts that only work with specific numbers.
The easiest way to solve a modulu problem is by
Start by taking the initial number (before carrying our the modulo operation). Then select the divisor. Then one have to divide one number by the other and then round down.Then Multiply the divisor using the quotient. Then subtract the above number from one's initial number (dividend).The number gotten is the outcome of the modulo operation.2^100/3
=3√2^100
=3√2^99×2
=2^33×3√2
The [tex]\sqrt{2}[/tex] is the reminder.
What is the easiest way to find remainders?The easiest way to find the remainder that only work with specific numbers is that this can be done when one solve the division by the use of a calculator by:
First if you answer is in decimal form, you have to subtract the whole number and later multiply the decimal value that is said to be left by the divisor of the original problem. The outcome is your remainder.
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A rectangular yard measures 8m x 6m. What happens to the area if each dimension is doubled?
Answer: 192
Step-by-step explanation:
2×8=16
2×6=12
17×12=192
So, the answer is 192.
Find the two inequalities equations graphed below please.
The two inequalities are:
a) y ≤ -2x + 5
b) y < 3x - 14
How to find the two graphed inequalities?
On the first graph, we can see that the shaded region is below the line and that the line is solid, so the inequality is of the form:
y ≤ line.
Now, remember that if the line passes through (x₁, y₁) and (x₂, y₂).
Then the slope is:
[tex]a = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
We can see that the line passes through (2, 1) and (-1, 3)
Then the slope is:
[tex]a = \frac{1 - 3}{2 - 1} = -2[/tex]
So the line is:
y = -2*x + b
To find the value of b, we use the point (2, 1), then we get:
1 = -2*2 + b
1 = -4 + b
1 + 4 = b = 5
Then the first inequality is:
y ≤ -2x + 5
Now let's go to the other line equation, again the shaded region is below the line and this time the line is dashed, then:
y < line.
Two points on the line are (5, 1) and (4, -2)
Then the slope is:
[tex]a = \frac{1 - (-2)}{5 - 4} = 3[/tex]
y = 3*x + b
To find the value of b, we use the point (5, 1)
Then:
1 = 3*5 + b
1 = 15 + b
1 - 15 = b = -14
Then the inequality is:
y < 3x - 14
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let f(x) = x^3-3x^2+2 and g(x) = x^2 -6x+11 Enter the value of x such that f(x)=g(x)
The value of x such that f(x) = g(x) is x = 3
Quadratic equationGiven the following expressions as shown
f(x) = x^3-3x^2+2 and;
g(x) = x^2 -6x+11
Equate the expressions
x^3-3x^2+2 = x^2 -6x+11
Equate to zero
x^3-3x^2-x^2+2-11 = 0
x^3-3x^2-x^2 + 6x - 9 = 0
x^3-4x^2+6x-9 = 0
Factorize
On factorizing the value of x = 3
Hence the value of x such that f(x) = g(x) is x = 3
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Prove that two non-zero vectors are collinear if and only if one vector is a scalar multiple of the other.
The Prove that two non-zero vectors are collinear if and only if one vector is a scalar multiple of the other is given below.
What are the proves?1. To know collinear vectors:
∧ ⁻a ║ ⁻a
If ⁻b = ∧ ⁻a
then |⁻b| = |∧ ⁻a|
So one can say that line ⁻b and ⁻a are collinear.
2. If ⁻a and ⁻b are collinear
Assuming |b| length is 'μ' times of |⁻a |
Then | 'μ' ⁻a| = | 'μ' ⁻a|
So ⁻b = 'μ' ⁻a
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Write an expression for the number of tiles Bruce used and an expression for the number of tiles Felicia used. Use x to represent the number of tiles in a box.
An expression for the number of tiles used by Bruce and Felicia are 5x + 2 and 5x + 5 respectively.
What is an expression?An expression refers to a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
Note: x represents the number of tiles in a box.
For Bruce, we have:
Expression = 3x + 2x + 2
Expression = 5x + 2.
For Felicia, we have:
Expression = 5x + 5.
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Complete Question:
Bruce retiled his kitchen. Originally, he bought three boxes of tile with the same number of tiles in each. He ran out of tile and had to go back to get three extra boxes of tile. However, he only used two tiles from the last box to finish the job.
Felicia also retiled her kitchen. She bought five boxes of tile, and each box contained the same number of tiles as each of Bruce’s boxes. She also ran out of tile. She had to go back to the store and get five more tiles to finish the job.
Write an expression for the number of tiles Bruce used and an expression for the number of tiles Felicia used. Use x to represent the number of tiles in a box.
Answer:
Bruce: y = 5x + 2
Felicia: y = 5x + 5
the sum of a number and 10
Answer:
x+10
Step-by-step explanation:
x is any number and sum means addition, so x(number) +(sum) 10(10)
How does the image triangle compare to the pre-image triangle?
A triangle undergoes a sequence of transformations.
First, the triangle is dilated by a scale factor of 1/3 about the origin. Then the triangle is reflected over the x-axis. Finally, the triangle is translated left 3 units and up 2 units.
Polygon LMNOP was transformed to create polygon L'M'N'O'P'.2 pentagons have identical side lengths and angle measures. The points are labeled with the same letters.
Which angle corresponds to AngleN?
AngleN'
AngleO
AngleO'
AngleP'
The angle that corresponds to ∠N after transformation is: A. ∠N'.
What is Transformation?Transformation is a process of manipulating a figure to create an identical figure either by dilation, rotation, or translation.
In the transformation performed in the image shown below, the new image formed is congruent to the original figure. This means polygon LMNOP ≅ L'M'N'O'P.
Therefore, the angle that corresponds to angle N is: A. Angle N'
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Answer: A). Angle N'
Step-by-step explanation:
What are the domain and range of the function (x)=3/4x+5?
O domain: (-00,00)
range: (-00,00)
3
O domain:
range: (-∞0,5)
domain:
range: (5,00)
O domain:
range: (5,00)
Answer: Option (1)
Step-by-step explanation:
The domain and range of all linear functions is the set of real numbers.
The domain and range of the function is
Domain = (-∞, ∞) and Range = (-∞, ∞)
What are domain and range?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = ( 3/4 )x + 5
The domain of the function is the set of all possible input values for x, which in this case is all real numbers, since there are no restrictions on the value of x that can be plugged into the function. Therefore, the domain of the function is:
Domain = (-∞, ∞)
The range of the function is the set of all possible output values that the function can produce. Since the function is a linear function of the form y = mx + b, where m is the slope and b is the y-intercept, we know that the range of the function is all real numbers, since a line can take on any y-value.
Range = (-∞, ∞)
Hence , the domain and range are set of all real numbers
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Dr. Benton just got his PhD, and he wants to print copies of his thesis in hardcover book format. He could use Middletown Printing, paying a setup fee of $39 and $3 for every book printed. Alternately, he could go through Oxford University, paying an up-front fee of $35 and $5 per book. It turns out that, given the number of books Dr. Benton wants to print, the two options cost the same amount. How many books is that? What is the amount?
______Is obtained by dividing the population into groups and selecting all individuals from within a random sample of the groups.
Please help. I am so confused.
The fourth proportional is found by applying the formula
The product of extremes = The product of means.
The fourth proportional is equal to bc/a and st/r
Let the fourth proportional be x then this can be written as
a:b::c:x
Applying the formula of product of extremes
ax= bc
or
x= bc/a
The fourth proportional can be obtained by multiplying the variables bc and dividing by a
Similarly
Let the fourth proportional be y then this can be written as
r:s::t:y
Applying the formula of product of extremes
ry= st
or
y= st/r
The fourth proportional can be obtained by multiplying the variables st and dividing by r
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Simplify fully 4m/20m leaving your answer in index form
The index form of the expression is 5^-1m
How to determine the index formNote that index form means in a power form
We have that;
= 4m/20m
Find the similar factor
= 1/5m
The inverse of a number, is that number to the power of -1
Then,
1/5m = 5^-1m
Thus, the index form of the expression is 5^-1m
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Stephen has made a 91, 96, and 95 on the first three quizzes this six weeks. If he makes the same score on the last two quizzes, what grade does he need to make on each quiz to have a quiz average of EXACTLY 94 this grading period?
Answer:
A 94
Step-by-step explanation:
If we take the mean of 91, 96, and 95, we find that it is equal to 94. Thus, if he scores a 94 on his last two quizzes, his average will remain a 94.
Add the following polynomials, then place the answer in the proper location on the grid.
- 4.1x^2 + 0.9x - 9.8
1.7x^2 - 2.4x - 1.6
Answer: - 2.4x^2 - 1.5x - 11.4
Step-by-step explanation:
- 4.1x^2 + 0.9x - 9.81.7x^2 - 2.4x - 1.6 = - 2.4x^2 - 1.5x - 11.4
70 more points ez ez ez
[tex]y = 3x + 6 \\ switch \: y \: and \: x[/tex]
[tex]x = 3y + 6 \\ solve \: for \: y \\ x - 6 = 3y \\ y = \frac{x - 6}{3} [/tex]
A is the answerAnswer:
free tokens or something
Step-by-step explanaon
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What will be the answer for 25 out of 100?
Hello !
[tex]\frac{25}{100}=0.25[/tex]
Have a nice day ;)
Answer:
25
Step-by-step explanation:
25
Answer: 25% of 100 is 25.
HELP PLEASEEEE
Zarea finds 3√6,000 and shows her work below.
r
A model car racetrack is formed by two semicircles as shown below.
9 cm
Find the perimeter of the entire figure.
Use T = = 3.14
2 cm
17
The diameter of the inner semicircles is 9 cm.
The width between the outer and inner semicircles is 2 cm.
>
The perimeter of the entire figure is 62.8 cm.
Given, that the diameter of the inner semicircles is 9 cm and the width between the outer and inner semicircles is 2 cm.
The radius of the inner semicircle =4.5 cm and the radius of outer semicircle =5.5 cm (∵Diameter=9+2=11 cm)
We need to find the perimeter of the entire figure.
What is the perimeter?A perimeter is a closed path that encompasses, surrounds, or outlines either a two-dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference.
We know that, the circumference of a semicircle=πr and the circumference of two semicircles=2πr
Thus, the circumference of inner semicircles=2×3.14×4.5=28.26 cm
The circumference of outer semicircles=2×3.14×5.5=34.54 cm
The perimeter of the entire figure=28.26+34.54=62.8 cm
Therefore, the perimeter of the entire figure is 62.8 cm.
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The perimeter of whole path is 12.56 cm
What is Perimeter?Perimeter is the distance around the edge of a shape.
r1= 4.5cm, r2= 6.5cm
Perimeter of semicircle 1,
=πr1
= 3. 14 * 4.5
= 14.13 cm
Perimeter of semicircle 2
=πr2
= 3. 14 * 6.5
= 20.41 cm
Perimeter of path = 20.41 - 14.13 =6.28 cm
Perimeter of whole path = 2 * 6.28 =12.56
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An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in Texas. He believes that the mean income is $31.3, and the standard deviation is known to be $9.4. How large of a sample would be required in order to estimate the mean per capita income at the 85% level of confidence with an error of at most $0.46
The sample size which is required in order to estimate the mean per capita income at the 85% level of confidence with an error of at most $0.46 is 866.
Given mean income of $31.3 and standard deviation of $9.4.
We have to calculate the sample size of confidence interval of 85% and at an error of $0.46.
Margin of error is basically the difference between actual values and calculated values.
Mean =$31.3
Standard deviation=$9.4
Confidence level=85%
Margin of error=$0.46
Margin of error=z*σ/[tex]\sqrt{n}[/tex]
0.46=1.44*9.4/[tex]\sqrt{n}[/tex]
[tex]\sqrt{n}[/tex]=1.44*9.4/0.46
[tex]\sqrt{n}[/tex]=29.42
squaring both sides
n=865.53
Round off and we get the following:
n=866.
Hence the sample size needed to estimate the mean per capita income at the 85% level of confidence is 866.
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3. Determine if the following triangle is a right triangle or not using the Pythagorean Theorem Converse. Triangle with side lengths of: 37 ft, 35 ft, and 12 ft
False, these measures do not form a right triangle.
True, these measures do form a right triangle.
Answer:
false
Step-by-step explanation:
these measure do not form a right triangle
Part 4: model a real world problem using an ellipse
An artist wants to make an elliptical sign out of a rectangular piece of wood. The wood piece has a length
of 60 inches and a width of 40 inches. The artist wants to make the largest elliptical piece possible from
the wood.
a) Write the equation of the ellipse by placing the center at the origin of the coordinate plane and making
the x-axis the major axis. (3 points)
PLEASE ANSWER ALL AND GRAPH
a. The equation of the ellipse is x²/900 + y²/400 = 1
b. the foci of the ellipse are at (±10√5,0)
c. Find the graph in the attachment
How to find the equation of the ellipse?Since the ellipse is made from a block of wood and centered at the origin, and x- axis major axis.
So, the equation of an ellipse with center at origin and x - axis major axis is
x²/a² + y²/b² = 1 where
2a = length of major axis 2b = length of minor axis anda > bSince the rectangular piece of wood has a length of 60 inches and a width of 40 inches.
The length of the rectangle equals the length of the major axis
So, 2a = 60
a = 60/2
= 30
Also, the width of the rectangle equals the length of the minor axis
So, 2b = 40
b = 40/2
= 20
a. The equation of the ellipseSo, substituting a and b into the equation of the ellipse, we have
x²/a² + y²/b² = 1
x²/30² + y²/20² = 1
x²/900 + y²/400 = 1
So, the equation of the ellipse is x²/900 + y²/400 = 1
b. The foci of the ellipse
The foci of the ellipse are at (±c,0) where c² = a² - b²
= 30² - 20²
= 900 - 400
= 500
c = ±√500
c = ±10√5
So, the foci of the ellipse are at (±10√5,0)
c. Find the graph in the attachment
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Isosceles triangle ABC contains angle bisectors segment BF, segment AD, and segment CE that intersect at X.
triangle ABC with diagonals BF, AD, and EC that intersect at point X
If segment BA is congruent to segment BC and m∠BCA = 46°, what is m∠CXA?
46°
67°
115°
134°
Answer:
115
Step-by-step explanation:
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