The curve is concave upward for t values greater than zero, according to the assertion made.
What in mathematics is a curve?Curve, An abstract phrase used to characterize the trajectory of a series of movements particle in mathematics (see continuity). Usually, an equation will create such a route. The term may also be used to describe a linear model or a collection of connected line segments. The IS curve displays combinations of borrowing costs and production levels where anticipated expenditure and income are equal. The many interest and income configurations along which is something the goods market is still in equilibrium are represented by the IS Curve.
dx/dt = e^t
dy/dt = -te^-t + e^-t
so dy/dt X dt/dx = dy/dx= -te^-t + e^-t /e^t = -t e^(-2t) + e^(-2t)
d2y/dx2 = -dt/dx e^(-2t) +2 t e^(-2t) dt/dx -2e^(-2t) dt/dx
= -e^(-3t) +2te^(-3t) -2e^(-3t)
-t e(-2t) + e(-2t) >0 for curved dy/dx >0
=> t<0 the curve is concave.
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Pls help with theseeeeeeee
Yes, you can assume both statements. In the diagram, planes W and X intersect at the line KL.
Determine whether you can assume the statement?This means that the points K, L, M, and N lie on the same plane, making them coplanar.All four points are contained within the same plane and are connected by lines, so it is clear that they all lie on the same plane.This means that statement 11 is true and statement 12 is also true.Yes, you can assume the statement in Exercises 11 and 12.The statement in Exercise 11 is true because it is shown in the diagram that Planes W and X intersect at KL.The statement in Exercise 12 is true because the points K, L, M, and N all lie on the same plane, which is Plane W.This type of reasoning is called deductive reasoning.Deductive reasoning is a logical process in which a conclusion is drawn based on the evidence that is given.In this case, the evidence is the diagram and the conclusion is the statement in the exercise.
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(9-12)x5+13-2=
explanation please
Step-by-step explanation:
(9-12)×5+13-2
=(-3)×5+13-2, (frist bracket )
=-15+13-2
=-4
Answer:
(9-12)x5+13-2= -4
Step-by-step explanation:
1. Solve the equation in parenthesis. 9-12 is -3. If you use a number line and add 9, then subtract twelve, you'll be three behind zero!
2. Then multiply -3 by five which is -15. -15+13 is -2, (since the thirteen is positive, it cancels out thirteen negative ones, and leaves us with two negative ones)
3. -2 -2=-4 (Negative two, subtracted by positive two, is negative four) subtracting a positive number, is the same as adding its opposite. Example. 8-5=3 (as we all know). And 8+-5=3. Numbers that have the same absolute value are opposites. AKA Numbers that are the same distance away from zero. -5 and 5 are both 5 spaces from zero!
Inside a square with side length 10, two congruent equilateral triangles are drawn such that they share one side and each has one vertex on a vertex of the square. What is the side length of the largest square that can be inscribed in the space inside the square and outside of the triangles
Therefore ,2.113 is the deemed appropriate of the greatest square that could be inscribed with in area between the square and the triangle.
Describe the triangle.A triangle is considered a polygon since it has four vertices or segments. It is a basic geometric form. Triangle ABC refers to a triangle the with ends A, B, and C. In Euclidean geometry, a singular plane plus square are produced when the sides are not collinear. A triangle is a polygon if it has three parts and three corners. The points where the three sides of the triangle meet are known as its corners. Three triangle angles add up to 180 degrees.
Here,
The midpoint of foot FE, G, is where we start by measuring the side length of the equilateral triangle.
Given that DE=GB and G is the midpoint, let GE equal x.
As a result, DGGB=x3 using fundamental trigonometry.
DB=2x3 follows.
We may then construct the equation 2x3=102 because DB is the orthogonal of ABCD and has length 102. Thus, the triangle's side length is
2x=(10√2)/√3.
Now, observe the diagonal AC. It is composed of the triangle's side length and the little square's diagonal multiplied by two. Let the little square's side length be y:
Let the little square's side length be y:
AC=y√2 + [(10√2)/√3]+y√2=10√2.
How to find y?
=>y√2+y√2 + (10√2√3)/3=10√2
=>y√2+y√2 + (10√6)/3=10√2
=> [3y√2+3y√2 + (10√6)] /3=10√2
=>6y√2+10√6=30√2
=>6y√2 = 30√2-10√6
=>y√2 = (30√2-10√6)/6
=>y = (30√2-10√6)/6√2
=>y = (60-20√3)/12
=>y= 5(3−√3)3 or 2.113
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The following set of ordered pairs, represents a power inverse variation. Find the value of r given that k=5. ( 1/2,20)(1,5)(2,5/4) : a. r=5 b. r=2 c. r=-5 d. r=2
The correct value of r is 2.
What is the power inverse variation?
Inverse variation is the relationship between two variables, such that if the value of one variable increases then the value of the other variable decreases.
The equation for a power inverse variation is y = kx^r,
where k is a constant, x is the independent variable, y is the dependent variable, and r is the power.
We have given the set of ordered pairs,
we can find the value of r by substituting in the known values of x and y and solving for r.
(1/2,20) => 20 = 5 * (1/2)^r => r = log(20)/log(1/2) = -2
So the answer is:
r = 2
Hence, the correct value of r is 2.
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2x^4 = 50 how do you solve this using factoring?
[tex] {2x}^{4} = 50 \\ = > {x}^{4} = \frac{50}{2} \\ = > {x}^{4} = 25 \\ = > {x}^{4} - 25 = 0 \\ = > ( {x}^{2} + 5)( {x}^{2} - 5) = 0 \\ = > {x}^{2} - 5 = 0 \\ > (x - 5)(x + 5) = 0 \\ = > x = 5 \: \: and \: \: - 5[/tex]
Answer:
5, -5
Hope it helps.
Please send your query through comment section.
Draw a model that shows 5 x 3/5 = 3
The model that shows 5 * 3/5 = 3 can be shown by sketching the boxes and shading the given parts.
What are model of multiplication?The model of multiplication is a visual representation used to show multiplication without algebraic calculation. The model includes boxes and squares to indicate the multiplication.
How to draw model of multiplication?Draw 3 boxes to represent 3 groups, and then place 8 in each box to represent 8 things in each group in order to multiply 3 by 8. There are several methods to draw this model.
We deduced from the model that the unknown value (?) may be determined by dividing the number of boxes (three, which stand for three groups) by the eight items.
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Tuxedo Rental, first day seventy-five dollars, each additional day ten dollars.
Clyde rents a tuxedo for several days. Let d represent the number of additional days Clyde uses the tuxedo. Write an algebraic expression to represent the total cost of the rental after d additional days.
The algebraic expression representing the total cost of the rental after d additional days is 75 + 10d.
What is an algebraic expression?An algebraic expression is a combination of constants, numbers, values, and variables.
Algebraic expressions are not the same as equations because they lack the equation symbol and do not lay claim to the equality of mathematical expressions.
The rental cost on the first day = $75
The rental cost per additional day = $10
The number of additional days Clyde uses the tuxedo = d
Algebraic expression to represent the situation:
75 + 10d
Thus, an algebraic expression we can use to represent the total cost that Clyde incurred for renting the tuxedo after d additional days is 75 + 10d.
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big box have 1/4 of 20
gigabytes of ram
Big boxes have 1/4 of 20 gigabytes of ram will be 5 gigabytes.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Big boxes have 1/4 of 20 gigabytes of ram.
Then the multiplication of the numbers 1/4 and 20 will be given by putting a cross sign between them. Then we have
⇒ (1/4) x 20
⇒ 20 / 4
⇒ 5 gigabytes
Big boxes have 1/4 of 20 gigabytes of ram will be 5 gigabytes.
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a food corporation declared a dividend of php 1,000,000 for its common stocks.suppose there are 60,000 shares of common stocks how much is the dividend per share?
The function cox) models the number of cookies sold each day by a bakery
during a 10-day period
between which days did the number of cookies sold by the bakery increase?
a between days 5 and 6
b. between days 3 and 4
c.between days 2 and 3
d. between days 6 and 7
The function c(x) models the number of cookies sold each day by a bakery during a 10-day period between (c) days 02 and 03 did the number of cookies sold by the bakery increase.
Cox Proportional hazards Model:
Sir David Cox observed that if the proportional hazards assumption holds (or, is assumed to hold) then it is possible to estimate the effect parameter (s), denoted β₁ below, without any consideration of the full hazard function. This approach to survival data is called application of the Cox proportional hazards model, sometimes abbreviated to Cox model or to proportional hazards model. However, Cox also noted that biological interpretation of the proportional hazards assumption can be quite tricky.
Let Xi = ([tex]X_i1[/tex] , … , [tex]X_in[/tex]) be the realized values of the covariates for subject i. The hazard function for the Cox proportional hazards model has the form:
λ (t I [tex]X_i[/tex]) = λ₀(t) exp( β₁[tex]X_i1[/tex] +...... + βₙ[tex]X_in[/tex])
= λ₀ (t) exp( [tex]X_i . \beta[/tex])
This expression gives the hazard function at time t for subject i with covariate vector (explanatory variables) Xi. Note : that between subjects, the baseline hazard is identical (has no dependency on i). The only difference between subjects' hazards comes from the baseline scaling factor exp [tex](X_i . \beta)[/tex].
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please answer my revision q xx
Answer:
k - 2n = x
Step-by-step explanation:
4^n = 2 ^ 2n
2^k/2^2n = 2^(k-2n) = 2^x
k - 2n = x
Thanks
Answer:
x = k - 2n
Step-by-step explanation:
The main exponent properties
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{m+n}[/tex] ........ (1)
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{m-n}[/tex] ........ (2)
[tex](a^{m} )^{n}[/tex] = [tex]a^{m*n}[/tex] = [tex]a^{mn}[/tex] ........ (3)
~~~~~~~~~~~~~~~~~~
[tex]\frac{2^{k} }{4^{n} }[/tex] = [tex]2^{x}[/tex]
Let apply (3) and (2) exponent properties
L.H. = [tex]\frac{2^{k} }{(2^2 )^{n} }[/tex] = [tex]\frac{2^{k} }{2^{2n} }[/tex] = [tex]2^{k-2n}[/tex]
[tex]2^{k-2n}[/tex] = [tex]2^{x}[/tex] ⇒ x = k - 2n
ANDY DALTON THREW 18 TOUCHDOWn
PASSES LAST SEASON. In 2016 He
THREW 25 TOUCHDOWN PASSES. WHAT
WAS HIS PERCENT OF CHANGE?
The percentage change in the Touchdown passes is 28 %
What is percentage ?A figure or ratio stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.
A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.
Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:
use the unitary approach.by adjusting the fraction's denominator to 100.It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied. In these situations, we employ the unitary technique.
Andy Dalton's throw is 18 touchdaown
In last saeson he threw 25 touchdown
So, the percentage change = (25-18)/25 * 100 = 28 %
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what do i do if the there is a number in a set of numbers that is much lower than the other when finding the average
Answer: Keep it in the calculation
Step-by-step explanation:
Q: Find (i) The area and (ii) The perimeter of the shaded region in each of the following figures given that all arcs are either quadrant or semicircles.
(please help me solve this and tell me how to solve it properly!)
Answer:
Step-by-step explanation:
ask if you don't understand my answer
Answer:
Shaded area = 42.1 cm^2
Shaded perimeter = 44 cm
Step-by-step explanation:
See the attached worksheet. The approach is the subtract the 4 semicircle areas from the total quare area to obtain the area of the shaded region. The perimeter is calculated by the perimeter of one complete circle. Since all four semicircles are 1/4 of the full circle, the total perimeter is equivalent to one full circle.
Josh graphs a system of equations to determine the roots of the polynomial equation x Superscript 5 Baseline
The statement 2 is true i.e. He is not correct because the greatest exponent of the system is five so there must be five solutions, three of which must be root multiplicities or complex.
Understanding the fundamental theorem of algebra, the number of roots of a polynomial equation must be equal to the degree of the equation. While been given any polynomial in factored form, we must expand the parentheses to find the highest-degree term.
For the equation provided, simplified form could be x⁵ + 2x² = 0, and as looking at this polynomial and graphing it, it is evident that the total roots or solutions is equal to the highest exponent of the term x which is 5. Hence, Josh makes an incorrect statement.
The multiplicity of a root is the number of occurrences of the said root in the entire complete factorization of the polynomial, as by the means of the fundamental theorem of algebra. The root multiplicities are thus the repeated roots as involved in the full factorization process of a single equation of a polynomial.
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The correct question is:
Josh graphs a system of equations to determine the roots of the polynomial equation x⁵ = -2x² . From the graph, he determines that there are two solutions to the equation. Which statement is true?
He is correct because the least exponent of the system is two so there must be two solutions.He is not correct because the greatest exponent of the system is five so there must be five solutions, three of which must be multiplicities or complex.He is correct because the graph shows two intersection points.He is not correct because the difference of the exponents is three, so there must be three solutions, one of which is a multiplicity.M109) solve
cos²x + 2 cosx + 1 = 0
Answer:
Step-by-step explanation:
[tex] \: \: \: \: \: \: \: \: \: \huge \color{green}{ \fbox \colorbox{black}{ \fbox{ \green {Answer} \: }}}[/tex]
[tex] \longrightarrow \sf \color{teal}{ \cos {}^{2} (x) + 2 \cos(x) + 1} = 0[/tex]
[tex] \longrightarrow \sf \color{teal}{ \cos {}^{2} (x) + \cos(x) + \cos(x) + 1} = 0[/tex]
[tex] \longrightarrow \sf \color{teal}{ \cos {}^{} (x) ( \cos(x) + 1)+ 1(\cos(x) + 1} )= 0[/tex]
[tex] \longrightarrow \sf \color{teal}{ ( \cos(x) + 1)(\cos(x) + 1} )= 0[/tex]
[tex] \longrightarrow \sf \color{teal}{ ( (\cos(x) + 1} {}^{} ) {}^{2} = 0[/tex]
[tex] \longrightarrow \sf \color{teal}{ ( (\cos(x) + 1} {}^{} ) {}^{} = 0[/tex]
[tex] \longrightarrow \sf \color{teal}{ \cos(x) {}^{} }= - 1[/tex]
[tex]\longrightarrow \sf \color{teal}{ x{}^{} }= \cos {}^{ - 1}( - 1)[/tex]
[tex]\longrightarrow \sf \color{teal}{ x = (2n + 1) \pi \: \: \: \: rad}[/tex]
where, [tex]{ n \in \{whole \:\; number\}} [/tex]
Principle value -
[tex] \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = \cos {}^{ - 1} ( - 1) [/tex]
[tex] \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = (2n + 1) \pi \: \: \: \: rad \: [/tex]
put n = 0
[tex] \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = (2(0) + 1) \pi \: \: \: \: rad \: [/tex]
[tex] \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = (0 + 1) \pi \: \: \: \: rad \: [/tex]
[tex] \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = \pi \: \: \: \: rad \: = 180 \degree[/tex]
GEOMETRY/ TRIG
Anything helps! Thank you
This is an example of a triangle with two missing sides.
TrigonometryTo find the missing sides of a triangle, you can use the trigonometric ratios of sine, cosine, and tangent. All of these are based on the reference angle, which is the angle between the two known sides.For example, if the reference angle is 30°, then the trigonometric ratios are: sine of 30° is 1/2, cosine of 30° is √3/2, and tangent of 30° is √3/3.To find the missing sides of a triangle, you can use the Law of Sines and Law of Cosines. The Law of Sines states that the ratio of the lengths of the sides of a triangle to the sines of their opposite angles is the same for all three sides. The Law of Cosines states that the sum of the squares of the two sides of a triangle is equal to the square of the third side minus twice the product of the two sides multiplied by the cosine of the angle between them.Using these two laws, you can solve for the missing sides of the triangle. For example, if you know the length of two sides and the angle between them, you can use the Law of Cosines to find the length of the third side. Then, you can use the Law of Sines to find the angles of the other two sides. This method of finding the missing sides of a triangle is called trigonometry.To learn more about trigonometry refer to:
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if In = 5 x"" (1+x)0.5 dx ,n= 0,1,2.... where the integral is for x e [0,1]. By first finding a bound on the integrand, which of these is an upper bound on In? Pick ONE option O 1/(n+1) O 1/2(n+1) O 1/(n+1) + 1/(n+2) O N^N
On solving the provided question we cans ay that the upper bound for the integral is 1/(n+1).
what is integral?In mathematics, integrals translate integers into functions that express concepts like displacement, area, and volume that result from the combination of little facts. Integral discovery is a process that is referred to as integration. Integrals are mathematical constructs that, in calculus, have the same meaning as areas or generalized versions of areas. The main goal of calculus is to work with derivatives and integrals. Primitives and inverse derivatives are other terms for integral. Integration is essentially utilized to determine the area of 2D space and determine the volume of 3D objects. As a result, calculating an integral of a function with respect to x entails calculating the area between the curve and the x-axis.
The maximum value of the integrand on the interval [0, 1] is:
f(x) = 5x(1 + x)^(0.5)
At x = 1, f(x) = 5(1 + 1)^(0.5) = 5√2.
Therefore, an upper bound for the integral is:
In ≤ 5√2∫x^n dx
Using integration by parts, we obtain:
In ≤ 5√2[x^(n + 1)/(n + 1)]_0^1
= 5√2/ (n + 1)
Therefore, the upper bound for the integral is 1/(n+1).
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In ΔCDE, the measure of ∠E=90°, DC = 97, CE = 72, and ED = 65. What ratio represents the sine of ∠C?
The ratio that represents the sine of angle C is 65/97
Determining the ratio of the sine of an angleFrom the given information, we are to determine the ratio that represents the sine of angle C
From SOH CAH TOA, we know that
sin(angle) = Opposite / Hypotenuse
Given triangle CDE with C as reference angle,
DE = Opposite
CD = Hypotenuse
Then,
We can write that
sin(C) = DE/CD
From the given information
DE = 65
CD = 97
Thus,
sin(C) = 65/97
Hence, the ratio is 65/97
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same has 4 times as many nickels as dimes. he had 0.90 in all. how many coins of each type does he have>
The number of dimes are 2 and number of nickels are 8 according to the sum and number of coins.
Let the number of dimes be x. The number of nickels will be 4x. Also, as per the known fact, the value of dimes is 0.1 and value of nickels is 0.05. Keeping the values in formula -
0.05x + 0.1×4x = 0.90
0.05x + 0.4x = 0.90
Performing addition on Left Hand Side of the equation
0.45x = 0.9
Rewriting the equation
x = 0.9/0.45
Performing division on Right Hand Side of the equation
x = 2
Number of dimes = 2
Number of nickels = 4×2
Performing multiplication
Number of nickels = 8
Thus, there 2 dimes and 8 nickles.
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in a stem-and-leaf display, . a. a single digit is used to define each stem, and one or more digits are used to define each leaf b. one or more digits are used to define each stem, and a single digit is used to define each leaf c. a single digit is used to define each stem, and a single digit is used to define each leaf d. one or more digits are used to define each stem, and one or more digits are used to define each leaf
in a stem-and-leaf display: b. one or more digits are used to define each stem, and a single digit is used to define each leaf
What is stem-and-leaf plot?A stem and leaf plot, often known as a stem plot, is a method for categorizing discrete or continuous data. Data are organized as they are gathered using a stem and leaf plot. A stem and leaf plot resembles a bar graph in appearance. As each integer throughout the database is divided into a stem and a leaf, thus the name fits.
The last digit of each data point serves as the "leaf" in a stem and leaf plot, which divides the data into numerical points (the leading digit or digits).
Thus, in this case, correct option is:b
in a stem-and-leaf display: b. one or more digits are used to define each stem, and a single digit is used to define each leaf
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What is the difference between a class boundary and a class limit? (Select all that apply.)
A. Class limits specify the span of data values that fall within a class.
B. Class boundaries are values halfway between the upper-class limit of one class and the lower class limit of the next.
C. Class boundaries specify the span of data values that fall within a class.
D. Class boundaries are not possible data values.
E. Class limits are not possible data values.
F. Class limits are possible data values.
G. Class limits are values halfway between the upper-class boundary of one class and the lower-class boundary of the next.
H. Class boundaries are possible data values.
Class limits indicate the largest and smallest data values that can be included in the class. Class limits are referred to actual data values. On the other hand, class boundaries give values that remove gaps between the classes in the frequency distribution. Class boundaries are considered to be one decimal place more accurate in comparison to the data. Options A, B, D, and F correctly describe differences between a class boundary and a class limit.
Following are the potential differences between a class boundary and a class limit.
Class limits define the span of data values that fall within a class.Class boundaries are referred to the values halfway between the upper-class limit of one class and the lower-class limit of the next.Class boundaries are not possible data values.Class limits are possible data values.You can learn more about class boundary and a class limit at
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z is a standard normal random variable. the p(z ≥ 2.11) equals
The area of the tail is 1 minus the area to the left of 2.11. So, you can look up the area to the left of 2.11 in the z-table, which is 0.9823, and subtract it from 1 to get the area of the tail, which is 0.0177.
The p(z ≥ 2.11) is 0.0177.
To calculate the p(z ≥ 2.11), you can use a z-table to look up the z-score. This z-score falls in the area of the tail of the distribution, which means it is the area to the right of 2.11.
The area of the tail is 1 minus the area to the left of 2.11. So, you can look up the area to the left of 2.11 in the z-table, which is 0.9823, and subtract it from 1 to get the area of the tail, which is 0.0177.
The p(z ≥ 2.11) is 0.0177.
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When 6 is added to a number, the result is 50. Which equation would help you find your solution?
Answer:
Step-by-step explanation:
the answer is 44
if the heights of 99.7 of american men are between 5 and 7 what is the estimate of the standard deveiation of the height of american men
The value of 99.7% is the closest to the percentage of these heights that is within 3 standard deviations of the mean.
What is the empirical rule?
If your distribution follows a normal distribution, the standard deviation and mean can tell you where the majority of the data are.
It is given that the heights of a large population of ostriches are normally distributed. The percentage of these heights is within 3 standard deviations of the mean.
As we know from the empirical rule:
It is the rule of 68-95-99.7.
From the data given in the question: The height of a large population of ostriches is normally distributed.
X ~ (u, б²)
Normal distribution.
P{u - 3б < X < u + 3б}
From the distribution table:
P{u - 3б < X < u + 3б} = 99.7%
Thus, the value of 99.7% is the closest to the percentage of these heights that is within 3 standard deviations of the mean.
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How does the us tax policy encourage long-term investments?
a. by making long-term investments tax exempt
b. by making treasury bonds tax exempt
c. by making it illegal to earn short-term gains
d. by providing a lower tax rate for long-term gains
The US tax policy encourage long-term investments by providing a lower tax rate for long-term gains.
Therefore the answer is d. by providing a lower tax rate for long-term gains.
In the United States, the tax code provides a lower tax rate for long-term capital gains, which are gains on investments held for more than one year, as a way to encourage long-term investments. This means that when an investor sells an asset that they have held for more than one year, they will pay a lower tax rate on the gain than they would if they had held the asset for less than one year. This provides an incentive for investors to hold on to their investments for a longer period of time, rather than engaging in short-term buying and selling.
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The volume of a cylinder is 90 cm³. If the radius is 3 cm, what is the height of the cylinder? OA. 10 cm OB. 30 cm C. 15 cm D. 5 cm 3 cm
Answer:
3 cm
Step-by-step explanation:
Volume of a cylinderThe formula of a cylinder is given by:
[tex]\pi r^{2} h[/tex]
where r is the radius and h is the height of the cylinder.
SolutionGiven information from the question:
Volume of cylinder = [tex]90cm^{3}[/tex]
Radius of cylinder = 3cm
We can derive an equation to find the height:
[tex]90=\pi 3^{2} h\\9\pi h=90\\h = \frac{90}{9\pi } \\h = 3.18cm[/tex]
Given the height is 3.18cm, we will choose the closest answer which is 3 cm.
Name the property of real numbers illustrated by the equation.
-2(x+4)=2x-8
A. Associative property of multiplication
B. Commutative property of addition
C. Distributive property
D. Associative property of addition
The property of real numbers illustrated by the equation -2(x+4)=-2x-8 is option C: Distributive property.
What is Distributive property?
The distributive law of multiplication and addition and subtraction is another name for the distributive property. By its very name, the procedure implies that something will be divided or distributed.
The given equation is -2(x+4)=-2x-8.
According to the distributive property, an expression of the form A (B + C) can be resolved as A (B + C) = AB + AC.
In the equation it can be clearly seen that the form is distributive form as -
A = -2
B = x
C = 4
Therefore, the equation uses distributive property.
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Solve the triangle. Round each angle to the nearest degree and round each side to the nearest hundredth. Do not use rounded answers In Your calculations to find missing measures
Rounded answers In Your calculations to find missing measures is given below.
Given: a = 8.72, b = 11.1, c = 11.7
Using the Law of Cosines, we can calculate angle A:
A = arccos((b2 + c2 - a2)/2bc)
A = arccos((11.12 + 11.72 - 8.722)/(2*11.1*11.7))
A = arccos(2.61/265.57)
A = arccos(0.00984)
A = 89.8°
Using the Law of Sines, we can calculate angle B:
Using the Law of Cosines, we can calculate side c:
c2 = a2 + b2 - 2abcos(C)
c2 = 8.722 + 11.12
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olve the differential equation by variation of parameters. Y" + y = sin?(x) y(x) =
The provided statement indicates that the differential equation's solution will be y = c₁ + c₂ e⁻ˣ - 1/2 cos x
With examples, define differential equation:Equations with General Differential. Consider the differential equation y′=3x2, which has a derivative and is an illustration of a differential equation. The variable x and y are related because y is an unidentified function of x. The component of y is also on the equation's left-hand side.
The analytical solution is, given that.
⇒ y'' + y = sin x
Now,
The system of equations as follows:
The difference between these two is,
⇒ y'' + y = sin x
Find its auxiliary equation as;
⇒ m² + m = 0
⇒ m (m + 1) = 0
⇒ m = 0 or m = - 1
Therefore, the auxiliary equation is c1 e0 + c2 ex.
= c₁ + c₂ e⁻ˣ
And, Particular integral = 1/(D² + D) (sin x)
= 1/2D (sin x)
= 1/2 (- cos x)
= - 1/2 cos x
Consequently, the differential equation's solution will be;
⇒ y = A.E + P.I
⇒ y = c1 + c2 e x - cos x / 2
As a result, the differential equation's solution is;
⇒ y = c1 + c2 e x - cos x / 2
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The complete question is-
Solve the differential equation by variation of parameters.
y'' + y = sin x
