(a) The statement p(2) is p(2) : 2! < 2² , and
(b) the statement p(2) is True is shown below .
In the question ,
it is given that ,
the statement is p(n) : n! < nⁿ ,
Part(a)
we have to find p(2) ,
On substituting n = 2 , in the statement
we get ,
p(2) : 2! < 2²
Part(b)
we know that 2 factorial is 2! = 2 × 1 = 2
and 2² = 2 × 2 = 4
On comparing the values of 2! and 2² , we can see that
2 < 4
which is 2! < 2² ,
Hence p(2) is True .
Therefore , p(2) is p(2) : 2! < 2² and the statement p(2) is True .
The given question is incomplete , the complete question is
Mathematical Induction can be used not only to prove equalities, but also to prove inequalities. the predicate p(n) is the statement n! < nⁿ , where n is an integer greater than 1.
(a) what is the statement p(2) ?
(b) show that p (2) is true .
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A car covers the road from city A to city B, 40 km, in 30 minutes, and the road from city B to C, 30 km, in 15 minutes. find the average speed with which the car moves all the way from A to c
Please help me please
I will give brainliest
The average speed of a car is 93.34 km/h
Average speed is the mean value of the speed of a body over a period of time. The formula for average speed is needed since the speed of a moving body is not constant and varies across a period of time.
Average speed formula is the average speed of a body is equal to the total distance covered, divided by the total time taken. The formula for average speed is given as: Total distance travelled / total speed
According to the equation,
A car covers the road from city A to city B, 40 km, in 30 minutes, and the road from city B to C, 30 km, in 15 minutes
Total distance a car covers is 40 + 30
= 70km
Total time a car takes is 30 + 15
= 45minutes = 0.75 hours
Average speed = total distance / total time
Average speed = 70 / 0.75
= 93.34 km/h
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(Answer asap pls I will give 26 pionts!!!!)One coral reef is located 17 feet below sea level. Another is located 32 feet below sea level. What is the difference in the depths of the two reefs?
49 feet
15 feet
−15 feet
−49 feet
Answer: -15
Step-by-step explanation:
do 17-32= -15
Suppoe Tyler knew there are 25 dime in the jar. Write an one quality that repreent how many quarter could be in the jar
The inequality that represents the number of quarters in the jar is [tex]y \geq 24[/tex].
What is inequality?
Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Tyler filled a little container with quarters and dimes and gave it to his school's foundation club. The club party getting the container inquired, "Do you end up realizing how much is in the container?" Tyler said, "I know it's something like $8.50, yet I don't have a clue about the specific sum."
Let x be the number of dimes and y be the number of quarters. Then the inequality is given as,
0.10x + 0.25y ≤ 8.50
The inequality that represents the relationship will be 0.10x + 0.25y ≤ 8.50.
The inequality that represents the number of quarters in the jar, can be get by solving the above inequality for y, 0.10x + 0.25y ≤ 8.50. can be written as [tex]y \geq \frac{8.5 - 2.5}{0.25}[/tex] or [tex]y \geq \frac{8.5}{0.25}[/tex] or [tex]y \geq 24[/tex] .
Hence, the inequality that represents the number of quarters in the jar is [tex]y \geq 24[/tex] .
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Chad is planning a 672–mile road trip. • Chad’s car can travel 308 miles with 11 gallons of gas. • Chad plans to drive 168 miles every 3 hours. How many hours will it take Chad to drive 672 miles, and how many gallons of gasoline will he need?
It will take Chad 12 hours to drive 672 miles and he will need 24 gallons of gasoline
How to calculate many hours will it take Chad to drive 672 miles?
Given that: Chad is planning a 672–mile road trip
Chad’s car can travel 308 miles with 11 gallons of gas. We can use this information to calculate the miles 1 gallon can cover. Thus:
Number of miles per gallon = 308/11 = 28 miles per gallon
Also, Chad plans to drive 168 miles every 3 hours. We can use this information to calculate Chad's speed. Thus:
Speed = 168/3 = 56 miles per hour
To determine how many hours it will take Chad to drive 672 miles:
Speed = distance/time
=> time = distance/speed
Speed = 56 miles per hour and distance = 672 miles
time = 672/56 = 12 hours
Number of gallons = distance / Number of miles per gallon
Number of gallons = 672/28 = 24 gallons
Therefore, it will take Chad 12 hours to drive 672 miles and he will need 24 gallons of gasoline
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What are the 3 ways to prove two triangles are similar?.
The 3 ways to prove two triangles are similar are AA, SSS and SAS Similarity Postulate.
In the given question we have to explain the 3 ways to prove two triangles are similar.
Similar triangles are described as having the same shape but varying sizes. Examples of related objects include squares with any side length and all equilateral triangles. Alternatively put, if two triangles are similar, their corresponding sides will be proportionately equal and their corresponding angles will be congruent.
The 3 ways to prove two triangles are similar are:
Angle-Angle(AA) Similarity PostulateSide-Side-Side(SSS) Similarity PostulateSide-Angle-Side(SAS) Triangle Similarity PostulateTo learn more about Similarty Theorem link is here
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Given m||n, find the value of x.
Answer:
16
Step-by-step explanation:
You have to know which theorem applies. This theorem only works because we know line m and line n are parallel.
Alternate Exterior Angles theorem says 111 degrees and 7x-1 are congruent.
This means we can set them equal to each other:
7x - 1 = 111
Solve for x:
7x = 112
112 / 7 = x
x = 16
Solve negative one sixth times the quantity 3 minus 15 times the quantity one third squared end quantity end quantity.
Negative one-sixth times the quantity 3 minus 15 times the quantity one-third squared end quantity is C. negative two ninths.
Fractions: A fraction can represent any number of equal parts or a portion of a whole. A fraction is a word used in everyday English to indicate the number of parts of a given size, such as one-half, eight-fifths, or three-quarters.
we will compute the expression,
The expression will be, based on the information provided:
= 1/6 ×( 3 - 15 ) × (1/3)²
= -1/6 × -12 × 1/9
= -2 × 1/9
= -2/9
thus, we can conclude that a negative two-ninth is the correct answer to the expression.
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How do you tell if a graph is an exponential function?.
An exponential function is a mathematical function in which the output of the function increases (or decreases) at a rate that is proportional to the current value of the output.
Exponential functions have an “asymptote”, which is a line that the graph approaches but never crosses. This asymptote is often a horizontal line, and it can be used to identify exponential functions.
To determine if a graph is an exponential function, look for a curve that rises or falls steeply and then levels off. The curve should be smooth and symmetrical, and the points should lie along a straight line when plotted on a logarithmic scale. The equation for the graph should also have an exponential form, such as y=ab^x. If these characteristics are present, then the graph is an exponential function.
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What is the equation of the line that passes through (1, 2) and is parallel to the line whose equation is 4x y - 1 = 0? 4x - y - 6 = 0 4x y 6 = 0 4x y - 6 = 0
The equation of the line that passes through (1, 2) and is parallel to the line whose equation is 4x + y - 1 = 0 is 4x+y-6=0.
What is meant by slope-intercept form?The line's equation is expressed in slope-intercept form: y = mx + b, where m represents the slope and b represents the y-intercept.
The slope intercept form is used to calculate the y-intercept and slope of a straight line.
We know that the equation of the line is, y= mx +b
4x+y-1=0 is the same as y= -4x+1
For this equation, b=1, but for a line with slope -4 passing through the point (1,2), the y-intercept changes.
y= -4x+b
The above line is passing through the point (1, 2)
2=-4(1)+b
Now, we have to solve for b value we get b=6.
The equation that we get is,
y= -4x+6 or 4x+y-6=0.
The equation of the line that passes through (1, 2) and is parallel to the line whose equation is 4x + y - 1 = 0 is 4x+y-6=0.
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Select all of the true tatement. Repone
π i the area of a circle of radiu 1. Π i the area of a circle of radiu 1. Π i the area of a circle of diameter 1. Π i the area of a circle of diameter 1. Π i the circumference of a circle of radiu 1
The true Statements are : π is the area of the circle of radius 1 and π is the circumference of diameter 1.
What is Area of a Circle ?
The area of a circle is pi times the radius squared (A = π r²)
Putting r =1 ,we get
A = π×(1)² = π
What is Circumference of a Circle ?
To calculate the circumference of a circle, multiply the diameter of the circle with π (pi).
C = π×D
putting D =1 , we get
C = π
Hence, π is the area of the circle of radius 1 and π is the circumference of diameter 1.
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NEED AN ANSWER NOW!
A coach asked her athletes if they enjoy running. Fifty-five percent of the team do not like to run. Of those, 70% enjoy cycling, while 80% of those who enjoy running also enjoy cycling. The tree diagram shows how the athletes are divided into subgroups.
The tree diagram shows athletes branching off into two categories, enjoys running and does not enjoy running. Enjoys running branches off into two sub-categories, enjoys cycling and does not enjoy cycling. Does not enjoy running branches off into two subcategories, enjoys cycling and does not enjoy cycling.
What is the total percentage of the athletes who enjoy cycling?
9%
25.5%
55%
74.5%
The total percentage of athletes who enjoy cycling is given by:
74.5%.
How to obtain a percentage?A percentage is the division of an amount by a total amount, which is then multiplied by 100%.
In this problem, the percentages are already given for the entire population.
The percentage of athletes who enjoy cycling is divided into two nodes, as follows:
Enjoy running.Do not enjoy running.The percentages associated from each node are given on the text as follows:
45% enjoy running, an of those, 80% enjoy cycling.55% do not enjoy running, and of those, 70% also enjoy cycling.Hence the proportion of athletes who enjoy cycling is given as follows:
0.45 x 0.80 + 0.55 x 0.70 = 0.745.
Then the percentage is of:
0.745 x 100% = 74.5%.
Which means that the last option is correct.
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Sat mathematics scores are normally distributed with a mean of 517 and a standard deviation of 118. a university plans to recruit whose scores are in the top 11 % . what is the minimum score required for recruitment? round your answer to the nearest whole if necessary.
The minimum score required for recruitment is 669
The normal distribution is expressed as
z = (x - µ)/σ
Where
x = SAT Mathematics scores.
µ = mean score
σ = standard deviation
From the question, we have
µ = 518
σ = 113
The probability value for the top 9% would be (1 - 9/100) = (1 - 0.09) = 0.91
the z score corresponding to the probability value is 1.34
1.34 = (x - 518)/113
1.34 × 113 = x - 518
151.42 = x - 518
x = 151.42 + 518
x = 669 to the nearest whole number.
Probability:
Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.
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Annie was given two pieces of information and must write the equation of a line. She knows the line crosses the y-axis at the point (0,6) and has a slope of 7. What is the equation of the line?.
The equation of the line is y = 7x + 6 when the line crooses the y-axis at the point (0,6) and has a slope of 7
The line crosses the y-axis at the point (0,6)
The slope of the line is 7
The equation of a line in slope point form is
y - y' = m(x - x')
Where m stands for the slope of the line and x' y' are the coordinates of the point through which the line passes.
So, the point x',y' is 0, 6 and the slope m is 7
y - y' = m(x - x')
y - 6 = 7 (x - 0)
y - 6 = 7x
y = 7x + 6
Therefore, the equation of the line which crosses the y-axis at the point (0,6) and has a slope of 7 is y = 7x + 6
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in the marital instability over the life course project, men were asked to indicate the cause of their divorce. what was the most common response from the men (with 19% of men reporting this cause)?
In the Marital Instability Over the Life Course project, when men were asked to indicate the cause of their divorce, the most common response from the men was incompatibility. And the most common response from the women was infidelity.
What is the meaning of Marital Instability?Marital instability is described as including the range of activities from thinking about and discussing divorce to actually filing for either separation or divorce. There are a lot of causes of marital instability, but the most common causes are money problems and lack of intimacy.
Marital Instability Over the Life Course project is a nationwide longitudinal study started in 1980 with funding from the Social Security Administration's Office of Research and Statistics and the National Institute on Aging. This study measures predicting marital instability and divorce and assessing marital quality were developed.
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in excersice 1-10 use the sum of and diffrence identities to find the exact values of sine cosine and tangent
The sum of and diffrence identities to find the exact values of sine cosine and tangent are calculated below :
Given that,
1. 75º = 30° + 45 2. 15º = 45° - 30° 3. 105° = 60° + 450 4. 165º = 135° + 30° 5. 195º = 225º – 30° 6. 255 – 300
To find them we need to know the respective formulas:
In relation to the illustration above, the key sin,cos,tan formulas are:
sin A = Opposite side/Hypotenuse = BC/AB
cos A = Adjacent side/Hypotenuse = AC/AB
tan A = Opposite side of triangle /Adjacent side of triangle = BC/AC
1) 75°
sin(75°)= 0.966
cos(75°)=0.259
tan(75°)=3.732
2) 105°
sin(105°)=0.966
cos(105°)= -0.259
tan(105°)= -3.732
3) 175°
sin(175°)=-0.259
cos(175°)= -0.966
tan(175 )=0.268
4) 11π/12
sin(11π/12)=0.050
cos(11π/12)=0.999
tan(11π/12)=0.050
5) 17π/12
sin(17π/12)=0.078
cos(17π/12)=0.997
tan(17π/12)=0.078
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Five machines at a certain factory operate at the same constant rate. if four of these machines, operating simultaneously, take 30 hours to fill a certain production order, how many fewer hours does it take all five machines, operating simultaneously, to fill the same production order?*
24 hours takes all five machines to fill the same production order.
Given,
Four machines take 30 hours to fill a certain production order.
[tex]Rate = \frac{Work}{Time}[/tex]
Let, Total work = 1 unit
The rate of 4 machines = [tex]\frac{1}{30}[/tex]
We can let the rate of 5 machines be n and create the equation:
[tex]\frac{4}{\frac{1}{30} }=\frac{5}{n}[/tex]
[tex]120=\frac{5}{n}[/tex]
[tex]120n = 5[/tex]
[tex]n=\frac{5}{120}[/tex]
[tex]n=\frac{1}{24}[/tex]
Time taken by five machines = [tex]\frac{1}{\frac{1}{24} }[/tex]
Time is taken by five machines = 24 hours
Hence, 24 hours takes all five machines to fill the same production order.
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I really need help to get this done, please.
The area of the shaded portion of the inscribed hexagon is; 3.395 ft²
How to find the area of a hexagon?We are given;
Diameter of circle = 5 ft
Thus;
radius; r = 5/2 = 2.5 ft
Now, the long diagonal of the hexagon is given as 5ft and we know that if the side of the hexagon is a, then;
a = d/2
where d is the length of the long diagonal
Formula for area of hexagon is;
A = (3/2) * √3 * a²
Thus;
A = (3/2) * √3 * 2.5²
A = 16.24 ft²
Area of circle is gotten from the formula;
A = πr²
A = π * 2.5²
A = 19.635 ft²
Thus;
Area of shaded portion = 19.635 ft² - 16.24 ft² = 3.395 ft²
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the average bill for car repairs at a car service center is $196, with a standard deviation of $44. assuming the bills to be normally distributed, find the probability of a bill exceeding $300.
The probability of a bill exceeding $300 is 0.0091.
What is probability distribution ?
A probability distribution that is symmetric about the mean is the normal distribution, also referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.
For normal distribution z score = (X-μ)/σ
here mean= μ = 196
std deviation = σ = 44.0000
probability of a bill exceeding
$300 = P(X>300)
=P(Z>(300-196)/44)
=P(Z>2.36)
=0.0091
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Select all the correct answers. Could feel more than one answer.
Which expressions are equivalent to the given expression. Square root of 252
A. 126^1/2
B. 7•square root of 6
C. 18•square roof of 7
D. 6•square root of 7
E. 252^1/2
Answer:
D
E
Step-by-step explanation:
Prime factorize 252.
252 = 2 * 2 * 3 * 3 * 7
[tex]\sf \sqrt{252}=\sqrt{2*2*3*3*7}[/tex]
[tex]\sf = 2*3\sqrt{7}\\\\=6\sqrt{7}[/tex]
D
[tex]\sf \text{The exponent form of } \ \sqrt{252}=252^{\frac{1}{2}}[/tex]
E
Step-by-step explanation:
so, first, let's see the factors of 252 :
252 / 2 = 126
126 / 2 = 63
63 / 2 no
63 / 3 = 21
21 / 3 = 7
so, 252 = 2×2×3×3×7 =
= 4×9×7 =
= 36×7 =
= 42×6 =
= 18×14
and others. but these are closest to the given answer options.
A. is wrong. 126^(1/2) is the same as sqrt(126). that is of course not the same as sqrt(252).
B. is wrong. to leave 6 in the square root, the remaining factor is 42. and sqrt(42) is not 7.
C. is wrong. to leave 7 in the square root, the remaining factor is 36. and sqrt(36) is not 18.
D. is correct. see C. sqrt(36) = 6. so, sqrt(252) = sqrt(36×7) = 6×sqrt(7).
E. is correct. 252^(1/2) is exactly the same as sqrt(252). an exponent of 1/n means the nth root.
Mrs. stevens bought 5 identical gifts for her children. each gift was valued at $80. she paid 1/2 of the total cost and financed the remaining balance through her credit union for 18 months at 9 % interest. what was her total finance charge?
After solving, her total finance charge was $11.65.
In the given question we have to find her total finance charge.
Mrs. stevens bought identical gifts for her children = 5
Each gift value = $80
So, Total cost = $80×5
Total cost = $400
She paid total 1/2 cost.
Financed the remaining balance through her credit union for 18 months at 9 % interest.
the money is paid 1/2
The rest amount is converted into EMIs.
P = $200
r= 9% = 0.09
n =18 months
[tex]\text{EMI}=P\times\frac{r}{n}\left [ \frac{(1+\frac{r}{n})^n}{(1+\frac{r}{n})^n-1} \right ][/tex]
Put the values.
[tex]\text{EMI}=200\times\frac{0.09}{18}\left [ \frac{(1+\frac{0.09}{18})^{18}}{(1+\frac{0.09}{18})^{18}-1} \right ][/tex]
After solving
EMI = $11.65
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[tex]\frac{ac}{b}[/tex]−(a+d) if a=−2, b=3, c=−12, and d=−4.
Answer:
14
Step-by-step explanation:
-2(-12)/3-(-2+(-4))
=24/3-(-2+(-4))
=8-(-2+(-4))
=8-(-2-4)
=8-(-6)
=8+6
=14
In the diagram below, angle LKJ cong angle LNM.MJ=12NK=8. and LM = 24 Find the length of overline LN . Round your answer to the nearest tenth if necessary.
Answer:
16
Step-by-step explanation:
identify the group and period corresponding to the element whose valence electrons are 4s24p1 . express your answer as the group and period number separated by a comma.
The corresponding element that has the valence electron configuration of 4s24p1 is gallium. Gallium belongs to group 13 and period 4 with the atomic number of 31 and symbol of Ga.
4s2 4p1 - electronic configuration corresponds to gallium
Periodic table has 4 different blocks, which are s block, d block, p block, and f block. Each block has corresponding elements which gives its electron configuration
What is group and period?
The systematic arrangement of elements in increasing order of their atomic numbers.Periodic table has 18 groups and 7 periods.The horizontal rows are known as periods.And the vertical columns are known as groups.Prediction of Period ⟶ In electronic configuration of an atom, principal quantum number (n) of valence electrons represents the period of an element.
Prediction of Block ⟶ The orbital out of s,p,d and f which receives last electron represents block of an element
Prediction of Group ⟶ The group prediction occurs with help of block as:-
(1) For s block: Group Number = Number of valence e-
(2) For d block: Group Number = Number of e- in (n−1)d subshell + number of e- in ns subshell
(3) For p block: Group Number = Number of valence
e- + 10
(4) For f-block: Group Number = 3
Lets take an ex of chlorine ( Z= 17 )
Electronic configuration = 1s2 2s2 2p6 3s2 3p5
Since the last e- enters in p - subshell:
(i) Therefore Block will be "p "
(ii) For group we have element in p-block
∴ Group number = 10 + Valence e- in s subshell + Valence e- in p subshell
Group Number = 10+2+5=17
(iii) For period
Quantum number of valence e- =3
∴ Period number = 3
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Work out √45 - √5
Give your answer as an integer or as a surd in it’s simplest form
Answer:
2[tex]\sqrt{5}[/tex]
Step-by-step explanation:
using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
simplifying
[tex]\sqrt{45}[/tex]
= [tex]\sqrt{9(5)}[/tex]
= [tex]\sqrt{9}[/tex] × [tex]\sqrt{5}[/tex]
= 3[tex]\sqrt{5}[/tex]
Then
[tex]\sqrt{45}[/tex] - [tex]\sqrt{5}[/tex]
= 3[tex]\sqrt{5}[/tex] - [tex]\sqrt{5}[/tex]
= 2[tex]\sqrt{5}[/tex]
An exam consists of 50 multiple choice questions. Based on how much you studied, for any given question, you think you have a probability of 0.64 of getting the correct answer. Consider the sampling distribution of the sample proportion of correct questions out of 50. (a) Find the mean and standard error of the sampling distribution of this proportion; (b) What do you expect for the shape of this sampling distribution? - approximately normal because n is large; - cannot be determined because p is greater than 0.5; - cannot be determined because n is large; - approximately normal because the population is normal.
(a) The mean is 32, and the standard error is 0.068 (b) The expected shape will be approximately normal (c) The probability of scoring less than 60% is 0.278
As the number of questions (n) is 50 and the probability of getting the correct answer (p) is 0.64, the mean can be calculated as follows;
E(x) = np
E(x) = 50 × 0.64
E(x) = 32
The standard error is calculated as follows;
SE = √p×(1-p) ÷ n
SE = √0.64 × (1-0.64) ÷ 50
SE = √0.004608
SE = 0.068
Therefore, the mean is calculated to be 32, and the standard error is 0.068
As the sample size is large therefore the expected shape will be approximately normal
To calculate the probability of scoring less than 60%, we first calculate the z-score using:
z = (x – μ) / σ
z = (0.60 - 0.64) / 0.068
z = -0.588
So we have;
P (x < 60%) = P (z < -0.588)
P (x < 60%) = 0.278
Therefore the probability of scoring less than 60% is 0.278
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a triangle has two sides of length 5 and 9. what compound inequality describes the possible lengths for the third side, x?
The compound inequality describes the possible lengths for the third side, x is -4< c< 14.
What is meant by triangle?A triangle is a three-sided polygon that is sometimes (but not always) referred to as a trigon. Every triangle has three sides and three angles, with some of them being the same.
A triangle with A, B, and C vertices is symbolized by ΔABC
The Triangle Inequality Theorem states that given two triangle side lengths, the length of the third side must be greater than the difference and less than the sum of the two provided sides. The third side c of a triangle must be the same as the first two sides a and b:
(a - b) < c < (a + b)
As a result, let a = 5 and b = 9
(5-9) <c (5+9)
-4< c< 14
As a result, the third side of the triangle must follow the inequality, which is -4< c <14
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Can someone help me find the inverse of this matrix please?
The inverse of the 4 × 4 matrix, [tex]\begin{bmatrix}a &0 &0 &0 \\ 0& b& 0& 0\\ 0& 0 &c &0 \\ 0& 0& 0& d\\\end{bmatrix}[/tex] found using an online matrix tool is presented as follows;
[tex]\begin{bmatrix}a &0 &0 &0 \\ 0& b& 0& 0\\ 0& 0 &c &0 \\ 0& 0& 0& d\\\end{bmatrix}^{-1}=\begin{bmatrix}\dfrac{1}{a} & 0& 0 &0 \\\\ 0& \dfrac{1}{b} & 0 & 0\\\\0 &0 &\dfrac{1}{c} & \\\\0 &0 &0 &\dfrac{1}{d} \\\end{bmatrix}[/tex]
What is the inverse of a matrix?The inverse, A⁻¹ of a matrix, A, can be found using the formula;
[tex]A^{-1}=\dfrac{adj \, A}{det\, A}[/tex]
The adjugate of the specified matrix, [tex]\begin{bmatrix}a &0 &0 &0 \\ 0& b& 0& 0 \\ 0&0 &c &0 \\ 0& 0& 0& d\\\end{bmatrix}[/tex] is found using an online tool as follows;
[tex]adj\begin{bmatrix}a &0 &0 &0 \\ 0& b& 0& 0 \\ 0&0 &c &0 \\ 0& 0& 0& d\\\end{bmatrix}=\begin{bmatrix}b\cdot c\cdot d &0 &0 &0 \\ 0& a\cdot c \cdot d& 0& 0 \\ 0&0 &a\cdot b\cdot d &0 \\ 0& 0& 0& a\cdot b\cdot c\\\end{bmatrix}[/tex]
The value of the determinant of the matrix found using an online calculator is presented as follows;
[tex]det\begin{bmatrix}a &0 &0 &0 \\ 0& b& 0& 0 \\ 0&0 &c &0 \\ 0& 0& 0& d\\\end{bmatrix} = a\cdot b \cdot c\cdot d[/tex]
The inverse of the matrix in the question is therefore;
[tex]\begin{bmatrix}a &0 &0 &0 \\ 0& b& 0& 0 \\ 0&0 &c &0 \\ 0& 0& 0& d\\\end{bmatrix}^{-1}=\dfrac{\begin{bmatrix}b\cdot c\cdot d &0 &0 &0 \\ 0& a\cdot c \cdot d& 0& 0 \\ 0&0 &a\cdot b\cdot d &0 \\ 0& 0& 0& a\cdot b\cdot c\\\end{bmatrix}}{a\cdot b\cdot c \cdot d} = \begin{bmatrix}\dfrac{1}{a} &0 &0 &0 \\ \\0& \dfrac{1}{b} & 0& 0 \\ \\0&0 &\dfrac{1}{c} &0 \\\\ 0& 0& 0& \dfrac{1}{b} \\\end{bmatrix}[/tex]
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abe, bobby, charles, devin and edwin are the participants in a race. how many different $1$st-$2$nd-$3$rd place outcomes are possible if there are no ties? two different outcomes to include are bobby-devin-edwin and devin-bobby-edwin.
We apply permutation formula to the number of participants considering that there are no ties and find out that there are 60 different outcomes possible if there are no ties.
It is given to us that -
There are 5 participants - Abe, Bobby, Charles, Devin, and Edwin
We have to find out the number of different 1st - 2nd - 3rd place outcomes that are possible if there are no ties.
Considering that there should be no ties,
If we select one person, say Abe, then there are 4 different ways remaining for the second place in the race.
Similarly, assuming that Abe ranked 1st in the race and Bobby ranked 2nd in the race, there are 3 different ways remaining for the third place in the race.
Continuing like this, the 5 different participants can be ranked accordingly such that there are no ties.
For this situation, we have to find the permutation where -
Total number of objects (in this case, participants) = n = 5
and, total number of objects selected = r = 3
We know that the formula for permutation is -
[tex]P = \frac{n!}{(n-r)!}\\[/tex]
Substituting the values of 'n' and 'r' in the above equation, we have
[tex]P = \frac{n!}{(n-r)!}\\= > P = \frac{5!}{(5-3)!}\\= > P = 60[/tex]
Thus, by applying permutation formula, we find out that there are 60 different outcomes possible if there are no ties.
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q. a rectangular garden measures 60 feet by 25 feet. a fence completely encloses the garden. what is the length, in feet, of the fence?
The length of fence is 170feet if a rectangular garden measures 60 feet by 25 feet. Fencing is used to cover the garden from any unwanted animals.
A fence is defined as the structure that encloses an area, typically outdoors, and is usually constructed from the posts that are connected by boards, wire, rails or netting.
We know very well that the length of the fencing can be found by the perimeter of rectangle.
Perimeter of rectangle is given by =2×(length + breadth) or
=>P=2L +2W
if L is the length of rectangle and W is the width of rectnagle
Now, here we have length of rectangular garden as 60 feet and width as 25 feet
=>P=2×60+2×25
=>P=120+50
=>P=170feet
Hence, required length of fence is 170 feet.
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You anticipate that management would be comfortable with a probability of 0. 500 when offering your etimate of the ample mean. Uing σ = $80 and n = 64 a before, what dollar interval would you have to preent in order to obtain a probability of 0. 500?
The dollar interval would be ± 6.70 to present in order to obtain a probability of 0.500.
What is probability?
Probability is a branch of mathematics that calculates the likelihood of an experiment occurring. We can know everything from the chance of getting heads or tails in a coin to the possibility of error in research by using probability.
z value for the probability of 0.5 is 0.67
standard error = sd/√n = 80/√64 =10
dollar interval = z*se
= 0.67*10
=6.70
Hence, the dollar interval would be ±6.70.
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