In the exponential decrease function, the rate of decline is approximately 17.7%
Exponential FunctionAn exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828. An exponential curve grows, or decay depends on the exponential function. Any quantity that grows or decays by a fixed per cent at regular intervals should possess either exponential growth or exponential decay.
In this problem, we can write an exponential function as
58000 = 1763000(1 + x)⁻²¹
Solving for x
x = 0.1765
Converting this into percentage;
x = 0.1765 * 100 = 17.7%
The rate is 17.7%
Learn more on exponential function here;
https://brainly.com/question/2456547
#SPJ1
If P(t) is the size of a population at time t, which of the following differential equations describes linear growth in the size of the population?dPdt=200Answer A: d cap p over d t is equal to 200AdPdt=200tAnswer B: d cap p over d t is equal to 200 tBdPdt=100t2Answer C: d cap p over d t is equal to 100 t squaredCdPdt=200PAnswer D: d cap p over d t is equal to 200 cap pDdPdt=100P2
If P(t) is the size of a population at time t , the differential equation describes linear growth in the size of the population is [tex]\frac{dP}{dt}=200[/tex]
The differential equation is is an equation that contains one or more functions with its derivatives. The derivatives of the function define the rate of change of a function at a point.
dy/dx = f(x)
Here “x” is an independent variable and “y” is a dependent variable
According to the question,
Size of population at t time = P(t)
Also given ,The differential equations have a linear growth in the size of the population.
So, The degree of the variable must be one. And the equation of the population will be quadratic.
Therefore , dP/dt = 200 tells us the rate change of population with respect to time.
A derivative of linear function is constant .
Hence , option B is correct.
To know more about Differential equation here
https://brainly.com/question/2273154
#SPJ4
What is a prime number Class 8?.
Natural numbers known as prime numbers can only be divided by one (1) and by the number itself.
In the given question we have to explain about the prime number.
Natural numbers known as prime numbers can only be divided by one (1) and by the number itself. In other terms, prime numbers are positive integers greater than one that only have the number itself and the number's first digit as factors. 2, 3, 5, 7, 11, 13, and other prime numbers are only a few examples.
To learn more about prime number link is here
brainly.com/question/9315685
#SPJ4
What are the 5 congruence theorems?.
The five rules of congruence theorem are described below.
Statement of congruence.The sign for congruence is ≅ and we compose △ABC≅△DEF. ∠A relates to ∠D, ∠B compares to ∠E, and ∠C relates to ∠F. Side Stomach muscle relates to DE,BC compares to EF, and AC relates to DF.
Five rules of congruence theorem:Side-Side-Side(SSS):Corresponding sides of two triangles are equal, then triangles are congruent.
Side-Angle-Sid(SAS):Corresponding two sides and one angle are equal, then triangles are congruent.
Angle-Side- Angle(ASA):One side and two angles are equal, then triangles are congruent.
Angle-Angle-Side(AAS):Corresponding conductive two angles and one side are equal, then triangles are congruent.
Right angle- Hypotenuse-Side(RHS): assuming the hypotenuse and side of one right-calculated triangle are equivalent to the hypotenuse and the comparing side of another right-calculated triangle, the two triangles are consistent.
To know about congruence visit:
brainly.com/question/7888063
#SPJ4
A painter leans a 10 ft ladder against a building. The base of the ladder is 7 ft from the building. To the nearest foot, how high on the building does the ladder reach?.
The nearest foot, on the building does the ladder reach is 7.1 ft
Because of Pythagorean Theorem.
Since the ladder is leaning against a building it makes 10ft the hypotenuse, (c).
Additionally, they give you one of the bases = 7ft, (a)
So in order to find the other base you must plug in what you already know.
= [tex]10^{2} = 7^{2} + b^{2}[/tex]
Which equals to 100= 49 + [tex]b^{2}[/tex]
Then you have to subtract 49 on both sides ending up with
[tex]b^{2}[/tex] = 51.
Then you have to square root on both sides and we will get [tex]\sqrt{51}[/tex].
Which is around 7.1 ft.
Hence the answer is the nearest foot, on the building does the ladder reach is 7.1 ft
To learn more about Pythagorean Theorem click here https://brainly.com/question/16176867
#SPJ4
A function f is defined for all real numbers and has the following three properties: f(1)=5 \quad f(3)=21 \quad f(a+b)-f(a)=k a b+2 b^{2}f(1)=5f(3)=21f(a+b)−f(a)=kab+2b 2 for all real numbers a and b where k is a fixed real number independent of a and b. (a) Use a=1 and b=2 to find k. (b) Find f^{\prime}(3)f ′(3) (c) Find f^{\prime}(x)f (x) for all real x.
The solutions of given function;
(a) k = -12
(b) f'(3) = 0
(c) f'(x) = 0
Given info,
A function f is defined for all real numbers and has the following three properties:
[tex]f(1)=5 \quad f(3)=21 \quad f(a+b)-f(a)=k a b+2 b^{2}f(1)\\[/tex]
for all real numbers a and b where k is a fixed real number independent of a and b.
To find,
(a) Use a = 1 and b = 2 to find k.
[tex]f(a+b)-f(a)=k a b+2 b^{2}f(1)[/tex]
f(1 + 2) - f(1) = k(1 * 2) + 2 * 2² * f(1)
f(3) - f(1) = 2k + f(1) * 8
21 - 5 = 2k + 8 * 5
16 = 2k + 40
-2k = 24
k = -12
(b) Find f'(3).
f(3) = 21
f'(3) = d/dx(21) = 0
(c) Find f'(x) for all real x.
f'(x) = 0
To learn more about function click here:
brainly.com/question/5975436
#SPJ4
the environmental protection agency is concerned with the problem of setting criteria for the amounts of certain toxic chemicals to be allowed in freshwater lakes and rivers. a common measure of toxicity for any pollutant is the concentration of the pollutant that will kill half of the test species in a given amount of time (usually 96 hours for fish species). this measure is called lc50 (lethal concentration killing 50% of the test species). in many studies, the values contained in the natural logarithm of lc50 measurements are normally distributed, and, hence, the analysis is based on ln(lc50) data. studies of the effects of copper on a certain species of fish (say, species a) show the variance of ln(lc50) measurements to be around 0.6 with concentration measurements in milligrams per liter. suppose that the effects of copper on a second species of fish (say, species b) show the variance of ln(lc50) measurements to be 0.2. if the population means of ln(lc50) for the two species are equal, find the probability that, with random samples of seven measurements from each species, the sample mean for species a exceeds the sample mean for species b by at least 1 unit. (round your answer to four decimal places.)
The probability that, with random samples of seven measurements the sample mean for species a and b by at least 1 unit is 0.9999
1) Using by the central limiting theorem:
We know the formula for the z-score for the normal distribution is given by:
z = (x - μ) /( ρ√n)
Follows normal distribution with mean 0 and the variance of 1.
Where
x is the sample mean,
μ is the population mean,
ρ denotes population standard deviation
n = sample size
The required probability is
P(z < 0.5/[0.4/√ 10])
= P(z < 3.95)
P = 0.9999
Therefore the probability that, with random samples of seven measurements the sample mean for species a and b by at least 1 unit is 0.9999 .
Normal distributions are crucial to statistics because they are commonly used in the natural and social sciences to describe real-valued random variables with uncertain distributions. They are important in part because of the central limit theorem.
To learn more about probability visit:
https://brainly.com/question/28087511
#SPJ4
at the ccny holiday party, you are told there are soft drinks in the cooler. the cooler contains 18 regular soft drinks and 12 diet soft drinks. suppose you quickly grab 3 soft drinks for you and your friends without looking. what is the probability you grab 2 diet soft drinks?
The Total Proability will be 297 / 1015
What is Probability?
Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
Solution:
Total Number of Regular Soft Drinks = 18
Total Number of Diet Soft Drinks = 12
Total Drinks = 18 + 12 = 30
Probability of selecting Diet Soft Drink in the first two attempt = 12/30 * 11/29 * 18/28 = 2376 / 24360
Probability of selecting Diet Soft Drink in the first and last attempt = 12/30 * 18/29 * 11/28 = 2376 / 24360
Probability of selecting Diet Soft Drink in the second and last attempt = 18/30 * 12/29 * 11/28 = 2376 / 24360
Total Probability = 3 * 2376 / 24360
Total Probability = 2376 / 8120
Total Probability = 297 / 1015
To learn more about Probability from the given link
https://brainly.com/question/25870256
#SPJ4
If Lisa is x years old now, how old will she be in 10 years. (Represent the answers in terms of x) this question makes zero sense to me
If the is lets say 5 years old, in 2 years, she will be 5 + 2 = 7 years old, and in 10 years 5 + 10 = 15 years old
so age in the future is the present age + how many years from now she will be
in this example the present age is 5 years old , if you replace that 5 with an x, the age in 10 years will be x + 10
What do you call a triangle that has less than 90 angle?.
Answer:
A triangle in which each angle is less than 90 degrees is called an acute angled triangle.
Step-by-step explanation:
Two curves are orthogonal if their tangent lines are perpendicular at each point of intersection. Are the given families of curves orthogonal trajectories of each other? That is, is every curve in one family orthogonal to every curve in the other family? x^2 + y^2 = ax
x^2 + y^2 = by
Yes, the given curves are orthogonal.
What is orthogonal trajectory?In mathematics, an orthogonal trajectory is a curve, which intersects any curve of a given pencil of (planar) curves orthogonally.
Given equation is,
x²+y²=ax
Differentiating,
2x+2yy'=a
y' = (a-2x)/2y = m1
Again,
x²+y²=by
Differentiating,
2x+2yy'=by'
y' = -2x/(2y-b) = m2
For both curves are orthogonal, we have
m1*m2 = -1
(a-2x)/2y*-2x/(2y-b) = -1
-2ax+4x² = -4y²+2yb
4(x²+y²) = 2ax+2yb
Since, ax = (x²+y²)
by = (x²+y²)
Then,
4(x²+y²) = 2(x²+y²) +2(x²+y²)
4(x²+y²) = 4(x²+y²) (true)
Hence, the above response is appropriate.
Learn more about orthogonal here:
brainly.com/question/20308962
#SPJ1
Alicia has a collision deductible of $500 and a bodily injury liability coverage limit of $50,000. She hits another driver and injures them severely. The case goes to trial and there is a verdict to compensate the injured person for $40,000. How much does alicia have to pay? how much does her insurance pay?.
Alicia have to pay $10,000 and her insurance will pay $10,500.
What is limit of coverage in insurance?
This limit is the most the insurer will pay for sums as damages because of bodily injury or property damage included within the products-completes operations hazard during the policy period.
Given that Alicia has a collision deduction of $500 and a bodily injury coverage limit of $50,000.
And there is a verdict to compensate the injured person for $40,000
Therefore Alicia have to pay
$50,000-$40,000 = $10,000
And her insurance will pay
$10,000 + $500 = $10,500
Hence Alicia have to pay $10,000 and her insurance will pay $10,500.
To know more about insurance here
https://brainly.com/question/27796059
#SPJ4
There is a line through the origin that divides the region bounded by the parabola and the x-axis into two regions with equal area. What is the slope of that line?.
The slope of that line through the origin that divides the region bounded is 1.0315
y = 5x - 3x2
5x - 3x2 = 0
x(5 - 3x) = 0
x = 0 , x = 5/3
Area under y = 5x - 3x2 is A = [0 to 5/3] 5x - 3x2 dx
A = [0 to 5/3] 5x2/2 - 3x3/3
A = [0 to 5/3] 5x2/2 - x3
A = 5(5/3)2/2 - (5/3)3 = 125/54
line passing through origin is in the form of y = mx
==> mx = 5x - 3x2
==> 3x2 + mx - 5x = 0
==> 3x2 + x(m -5) = 0
==> x(3x + (m -5)) = 0
==> x = 0 , x = (5 -m)/3
Area under y = 5x - 3x2 and y = mx is (125/54)/2 = 125/108
==> ?[0 to (5 -m)/3] 5x - 3x2 -mx dx = 125/108
==> ?[0 to (5 -m)/3] (5 - m)x - 3x2 dx = 125/108
==> [0 to (5 -m)/3] (5 - m)x2/2 - x3 = 125/108
==> (5 - m)[(5 -m)/3]2/2 - ((5 -m)/3)3 = 125/108
==> (5 -m)3/18 - (5 -m)3/27 = 125/108
==> (5 -m)3/54 = 125/108
==> (5 -m)3 = 125/2
==> (5 -m) = 3.9685
==> m = 5 - 3.9685
==> m = 1.0315
Hence slope of line = 1.0315
To learn more about slope
https://brainly.com/question/3605446
#SPJ4
The complete question is given below
There is a line through the origin that divides the region bounded by the parabola y=5x−3x^2 and the x-axis into two regions with equal area. What is the slope of that line?
employees of a firm receive annual reviews. in a certain department, 5 employees received excellent ratings, 14 received good ratings, and 1 received a marginal rating. if 3 employees in this department are randomly selected to complete a form for an internal study of the firm, find the probability that the following occurs. (enter your probabilities as fractions.)
The probability of all 3 selected were rated excellent is 1/114 and the probability of one from each category was selected, is 7/114.
In the given question,
In a certain department, 5 employees received excellent ratings, 14 received good ratings, and 1 received a marginal rating.
So total number of employees = 5+14+1 = 20
If 3 employees in this department are randomly selected to complete a form for an internal study of the firm, then we have to find the probability that the following occurs.
The following occurs given below:
(a) We have to find the probability of all 3 selected were rated excellent.
5 employees who got excellent rating. So the selection of 3 employees from 5 employees who got excellent rating is:
selection of 3 employees from 5 employees = [tex]^5C_{3}[/tex]
Using, [tex]^nC_{r}=\frac{n!}{r!(n-r)!}[/tex]
selection of 3 employees from 5 employees = [tex]\frac{5!}{3!(5-3)!}[/tex]
selection of 3 employees from 5 employees = [tex]\frac{5!}{3!2!}[/tex]
selection of 3 employees from 5 employees = [tex]\frac{5\times4\times3!}{3!\times2\times1}[/tex]
selection of 3 employees from 5 employees = 5×2
selection of 3 employees from 5 employees = 10
Selection of 3 employees from 20 employees= [tex]^{20}C_{3}[/tex] = 1140
Probability of 3 employees who got excellent rating
P(E) = 10/1140
P(E) = 1/114
(b) We have to find the probability of one from each category was selected.
One candidate selected from excellent category = [tex]^5C_{1}[/tex] = 5
One candidate selected from marginal category = [tex]^1C_{1}[/tex] = 1
One candidate selected from good category = [tex]^{14}C_{1}[/tex] = 14
Selection of 3 employees from 20 employees= [tex]^{20}C_{3}[/tex] = 1140
The probabilty of one from each category = (5*1*14)/1140
The probabilty of one from each category = 70/1140
The probabilty of one from each category = 7/117
To learn more about probability link is here
brainly.com/question/29584794
#SPJ4
For what value of the variable doe the following expreion make ene: quare root of (-5x)^3
take any negative value of x suppose x= -1,-2 ....etc then it makes sence and it is valid cube
What are types of expressions?
There are three kinds of expressions: An arithmetic expression evaluates to a single arithmetic value. A character expression evaluates to a single value of type character. A logical or relational expression evaluates to a single logical value.
learn more about of expression here
https://brainly.com/question/29461191
#SPJ4
you start driving west for 3 miles, turn right, and drive north for another 13 miles. at the end of driving, what is your straight line distance from your starting point?
Answer:
[tex]\sqrt{178}[/tex] or 13.3 rounded to the nearest tenth
Step-by-step explanation:
Determine which of the following relations is a function.
The relation between the given function is X cannot repeat itself.
What is the function?A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of a varying quantity depends on another quantity.
We have given that the functions table.
We need to determine which relation is a function.
The relation between the function, that is;
X cannot repeat itself
Hence, the option C is correct.
To learn more about the function visit:
brainly.com/question/4025726
#SPJ1
Marshall is writing an equivalent equation to solve for x. what should be his next step? 5 x 4 y = 8. 5 x 4 y minus 4 y = 8 minus 4 y. 5 x = 8 minus 4 y. add 5x to both sides of the equation. subtract 5x from both sides of the equation. multiply both sides of the equation by 5. divide both sides of the equation by 5.
The next step of marshall should be divide both sides of the equation by 5.
Given:
Marshall is writing an equivalent equation to solve for x. what should be his next step.
5 + 4 y = 8.
5+4y-4y = 8-4y
5x = 8 - 4y
To solve for x:
The correct step is:
divide by 5 on both sides
5x/5 = 8-4y / 5
x = 8/5 - 4y/5
x = 1/5(8-4y).
Therefore The next step of marshall should be divide both sides of the equation by 5.
Learn more about the equation here:
https://brainly.com/question/10413253
#SPJ4
R Markdown is a file format for making dynamic documents with R. What are the benefits of creating this kind of document? Select all that apply.
Multiple Choice Question. Please Choose The Correct Options A
Perform calculations for analysis more efficiently
B
Generate a report with executable code chunks
C
Save, organize, and document code
D
Create a record of your cleaning process
An writing format called R Markdown (. Rmd) makes it simple to create dynamic documents, presentations, and reports with R.
It mixes R code chunks that are embedded and run so that their result can be included in the final document with the basic grammar of R markdown, a simple plain text format. The following are some benefits of utilizing R markdown: explicitly connects your data, R code, and output to produce a workflow that is completely reproducible. You can include ALL of the R code that was used to explore, summarize, and analyze your data in a single, simple-to-read document.
Learn more about R markdown here
https://brainly.com/question/29555402
#SPJ4
The density curve for a continuous random variable x has which of the following properties
a. the probability of any event is the area under the density curve and above the values of X that make up the event
b. the total are under the density curve for X must be exactly 1
c. the probability of any event of the form x= constant is 0
d. all of the above
Out of the choices provided, the density curve for a continuous and a random variable ''x'' has all the properties, which have been listed above. Therefore, the option D holds true.
A density curve can be referred to or considered as the smooth curve, which is used for the purpose of representation of shape of a variable's distribution, which is easily identified through the properties that it contains. A density curve can be used for the purpose of graphical representation, such as a histogram.
Learn more about a density curve here:
https://brainly.com/question/13534411
#SPJ4
Are whole numbers are closed under addition True or false?.
True, whole numbers are closed under addition because Any two whole numbers added together result in a whole number. is a whole number as well.
Define whole numbers.The term "whole numbers" refers to numbers devoid of fractions, which are made up of positive integers and zero. It is denoted by the letter "W," and its corresponding set of numbers are "0," "1, 2, 3,,","5,,"6,,"7,","8,"..." The whole numbers are 0 through 9, then 1, 2, 3, 4, 5, and so on. The set of numbers without fractions, decimals, and negative numbers is known as the "whole number." It consists entirely of positive numbers, even zero.
Given,
Whole numbers are closed under addition
Any two whole numbers added together result in a whole number. is a whole number as well. Therefore, the whole numbers cannot be added.
To learn more about whole numbers, visit:
https://brainly.com/question/19161857
#SPJ4
What do all agile framework have in common TCS?.
The agile frameworks that have in common are:
Self-organized teams can better adapt to business requirements with a lightweight strategy.
All agile frameworks use iterative and incremental development and have a set, defined iteration duration. They also all take a lightweight approach that enables self-organized teams to better adapt to business needs. It's a term for methods used in software development.
What is the Agile cycle?
The systematic succession of phases that a product goes through as it develops from start to finish is known as the agile software development life cycle. Concept, conception, iteration, release, maintenance, and retirement are its six phases.
The systematic succession of phases that a product goes through as it develops from start to finish is known as the agile software development life cycle. Concept, conception, iteration, release, maintenance, and retirement are its six phases.
The project management approach a team decides on will have a small impact on the Agile life cycle. For instance, Scrum teams work in sprints, which are brief timeframes akin to iterations. They also have responsibilities that are precisely defined, like Scrum master. Kanban teams, on the other hand, operate more continuously and don't have set roles. Another illustration is Extreme Programming, where teams frequently work in shorter iterations and give engineering practices more attention.
Hence,
The agile frameworks that have in common are:
Self-organized teams can better adapt to business requirements with a lightweight strategy. All agile frameworks use iterative and incremental development and have a set, defined iteration duration. They also all take a lightweight approach that enables self-organized teams to better adapt to business needs. It's a term for methods used in software development.
To learn more about the Agile cycle, visit:
brainly.com/question/29036637
#SPJ4
the angle of depression is measured from the top of a 43 ft tower to a reference point on the ground. its value is found to be 63 degrees. how far is the base of the tower from the point on the ground
The required distance between point on the ground and foot of the tower.
What is the angle of depression?On the off potential for success that an individual has and peers down at an item, the angle of depression is the point between the level view and the item. Geometry can be utilized to take care of issues that utilization a point of rise or sorrow.
According to given data in the question:Height of the tower = 43 ft
And angle of depression = 63 degree
we know that
tan(theta) = P/B
P is height of tower, B distance between tower and point on the ground.
tan(63)= 43/B
B = 43/tan(63)
B = 43/1.96 = 21.93 = 22 ft approx.
To know more about application of trigonometry visit:
brainly.com/question/11687813
#SPJ4
In which case is it possible to draw a triangle?.
The case in which the triangle can be drawn are
the triangle is most effective viable while the sum of aspects is exactly extra than the 0.33 side.
This hassle is primarily based totally at the triangle inequality assets which states that if the sum of lengths of any aspects of a triangle is extra than the 0.33 side, then it's miles viable to attract a triangle. The indoors angles rule states that the 3 angles of a triangle need to identical 180°. As you may see below, the 3 perspective measurements of obtuse triangle ABC upload to 180°.
Even, if there may be a single pair now no longer enjoyable the circumstance, the triangle will now no longer be viable.The sum of the lengths of aspects needs to be extra than the 0.33 side. If the given lengths fulfill this circumstance then most effective it's miles viable to assemble a triangle.
Read more about traingle:
https://brainly.com/question/17335144
#SPJ4
assume that adults have iq scores that are normally distributed with a mean of and a standard deviation . find the probability that a randomly selected adult has an iq less than .
the probability that a randomly selected when the IQ is lower than 136 is 0.9641
Given that
The mean is 100
The standard deviation is 20
We need to find out the probability when the IQ is lower than 136
So,
z value equivalent to 136 = (136 - 100) ÷ 20 = 1.8
Now
p (z < 1.8) = 0.9641
hence, the probability when the IQ is lower than 136 is 0.9641
learn more about of mean here
https://brainly.com/question/23548526
#SPJ4
Sunil took an education loan for his mba today. He borrowed 404040 lakh from the bank at a rate of interest of 30\%30%30, percent per annum. The interest is compounded annually. How much money will sunil owe to the bank after two years?.
Using Compund interest formula, we can say that total Rs. 67 lakh and sixty thousand is owned by Sunil to the bank after 2 years .
Compound Interest Formulas :
You can also use the principal and interest rate to find compound interest. H. Total interest on principal and accrued interest not repaid within the repayment period. The compound interest formula is:
A = P( 1 + r/100)ᵗ
where A --> amount to pay by person after t years
P --> amount borrowed by person
r ---> rate of interest annually
t-----> time period
We have given that,
The amount borrowed by Sunil for education loan(P) = Rs. 40 lakh
Rate of interest (r) = 30% per annum
Interest is compunded annually.
time period (t) = 2 years
we have to calculate the amount to pay by Sunil after two years .
putting all known values in above formula,
A = 40,00000 ( 1+ 30/100)²
=> A = 40,00000(13/10)²
=> A = 40,00000×13×13/100
=> A = 40,000×169
=> A = 67,60,000
Hence, the amount that Sunil own to bank after two year is 67 lakh sixty thousand.
To learn more about Compund nterest , refer:
https://brainly.com/question/12325365
#SPJ4
What is a function give 4 examples?.
Answer:
a function is like f(X)=2x+6 where X can be anything , you just substitute in the number u have been given
Step-by-step explanation:
other examples could include
f(X)=X+1
or they can start with
g(X)=3x+7
h(X)=4-3x
and there are inverse functions witch can be found be rearranging the function
example if substituteing a function
if
f(X)= 2x+1
f(3)=2(3)+1
f(3)=6+1=7
Hope this helps
a six-sided die is rolled three times. the probability of observing a 1 three times in a row is . a. .037 b. .004629 c. .3 d. .16
The correct option b. 0.004629 for the probability of observing a 1 three times in a row.
Explain the meaning of the term probability?Mathematics' branch of probability studies the likelihood of a random event occurring. In mathematics, probability is used to determine how likely an event is to occur. Only the numbers 0 and 1 can be used to express probability, which can also be expressed as a percentage.Probability of an event = (Number of favorable events) / (total number of event).
P(B) = (Event B) / (total number of event).
The number of times the dice are rolled has no bearing on the outcome of the roll.
The likelihood of receiving 1 is 1/6.
The likelihood of obtaining 1 three times in a row is equal to the likelihood of getting 1 the first time, the second time, and the third time.
Receiving 1 three times in succession has a probability;
= 1/6 x 1/6 x 1/6
= 1/216.
As a result, there is a 0.463% chance that you'll get 1 three times in a row.
To know more about the probability, here
https://brainly.com/question/13604758
#SPJ4
what is the relationship between the determinant of a square matrix and the determinant of the matrix multiplied by a sclar
The relationship between the determinant of a square matrix and the determinant of the matrix multiplied by a scalar is, the determinant of the matrix multiplied by a scalar is [tex]k^{n}[/tex] times the determinant of a square matrix, det(kA) = [tex]k^{n} D[/tex]
Let A be a square matrix,
And the det(A) = D, equation (1)
If we multiply the square matrix with a scalar k, then the matrix becomes, kA, and its determinant is given as,
det(kA) = [tex]k^{n} D[/tex] , equation (2)
where k is the scalar,
n is the order of the square matrix and
Dis the determinant of the square matrix A.
Thus, the relationship between the determinant of a square matrix and the determinant of the matrix multiplied by a scalar is, the determinant of the matrix multiplied by a scalar is [tex]k^{n}[/tex] times the determinant of a square matrix.
To read more about matrix, visit : https://brainly.com/question/28180105
#SPJ4
Kristen is investigating the opinions of students at her high school on the new school hours proposed by the school board. Which of the following is her population of interest?
All students at her high school
The population of interest in Kristen's investigation is the students at her high school.
What is meant by population of interest?The specific group of people or items that a researcher is researching in a given study is known as the population of interest. This group may be categorized according to factors like age, gender, employment, geography, or a particular health condition. The target audience for the study is the population of interest, and this demographic is generally the one to which the study's findings are applied. Identifying the population of interest is a crucial phase in the research process because it allows the researcher to focus on a specific group and develop meaningful findings that are applicable to that group.
To know more about population of interest, visit:
https://brainly.com/question/28568627
#SPJ4
simplify a^4b^3/cd x c^2/a^4b^5
The solution for the given expression is a⁴b³/cd × c²/a⁴b⁵ = c/b²d.
What are the rules of exponents?Some of the rules of exponents are as follows,
The product of two exponents having the same power is equal to the power of their base multiplied.
The product of two exponents having the same base is equal to the sum of the powers of different exponents to the same base.
The given algebraic expression is as below,
a⁴b³/cd × c²/a⁴b⁵
It can be simplified by using the rules of exponent as follows,
a⁴b³/cd × c²/a⁴b⁵
= a⁴b³ c²/(cd × a⁴b⁵)
= b³ c²/b⁵cd
= c²/b²cd
= c/b²d
Hence, the given expression can be simplified as c/b²d.
To know more about exponents click on,
https://brainly.com/question/5497425
#SPJ1
