Answer:
Let's call the tens digit of the two-digit number "t" and the units digit "u".
From the problem statement, we know that:
t = u - 5 (the tens digit is 5 less than the units digit)
10t + u = 3(t + u) + 5 (the number is five more than three times the sum of its digits)
We can use the first equation to substitute for t in the second equation:
10(u - 5) + u = 3((u - 5) + u) + 5
Simplifying and solving for u, we get:
10u - 50 + u = 6u - 9
Simplifying further, we get:
5u = 41
Therefore, u = 8.2
Since u must be a whole number, we round up to 9. Then, we can use the first equation to find that t = u - 5 = 4.
So the two-digit number is 49 (with t=4 and u=9).
We can check if it satisfies the second equation:
10t + u = 10(4) + 9 = 49
3(t + u) + 5 = 3(4 + 9) + 5 = 46
49 is indeed five more than three times the sum of its digits (4 + 9), so our solution is correct.
Therefore, the two-digit number is 49.
The tens digit is 3 and the unit digit is 8. So, the number is 38.
Important information:
The tens digit is 5 less than the unit digit.The number itself is five more than three times the sum of its digits.System of equations:Let x be the tens digit and y be the unit digit.
The tens digit is 5 less than the unit digit.
[tex]x=y-5[/tex] ...(i)
The number itself is five more than three times the sum of its digits.
[tex]10x+y=3(x+y)+5[/tex]
[tex]10x+y=3x-3y=5[/tex]
[tex]7x-2y=5[/tex] ...(ii)
Using (i) and (ii), we get
[tex]7(y-5)-2y=5[/tex]
[tex]7y-35-2y=5[/tex]
[tex]5y=40[/tex]
[tex]y=8[/tex]
Substitute this value in (i).
[tex]x=8-5[/tex]
[tex]x=3[/tex]
Therefore, the number is 38.
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In the above video lecture, we verified the following result: Computing the gradient of n
Rn (θ) = 1/n Σ (y^(t) - θ.x^(t)^2 / 2
t=1
we get ΔRn (θ) = Aθ-b (=0) where A= n n
A = 1/n Σ x^(t) (x^(t))^T , b = 1/n Σ y^(t) x^(t)
t=1 t=1
Now, what is the necessary and sufficient condition that Aθ - b = 0 has a unique solution?
- None of A's entries is 0. - A is invertible.
- A's dimension is the same as that of θ's
The direction of the steepest descent, which is used to find the minimum value of a function.
The necessary and sufficient condition that Aθ-b = 0 has a unique solution is: A is invertible.What is computing?Computing is a part of computer science that focuses on computer programs, including their software and hardware. It is concerned with designing algorithms to solve problems and creating software that will run these algorithms. As a result, computing is a field of study that is concerned with the process of creating algorithms and software.InvertibleAn invertible matrix is a matrix in which the determinant is not zero. An invertible matrix is also referred to as a non-singular matrix. An invertible matrix has a unique inverse. The rank of an invertible matrix is equal to its dimension. An invertible matrix can be used to solve a system of linear equations.GradientA gradient is a vector field in which the direction of the vector points to the steepest increase in a function, and the magnitude of the vector is the rate of increase in that direction. The gradient of a function is a vector field that is a derivative of the function. The gradient is used in multivariable calculus to solve optimization problems. The gradient is used to find the direction of the steepest ascent, which is used to find a maximum value of a function. It is used to find the direction of the steepest descent, which is used to find the minimum value of a function.
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please help with geometry
Step-by-step explanation:
Since it is equilateral the angle at the top is 60 °
for right triangles sin (angle ) = opposite leg / hypotenuse
sin (60) = sqrt 6/ x
x = sqrt 6 / sin (60) = sqrt 6 / sqrt(3)/2 =
2 sqrt 2 = 2.83
what is the equation for pattern 2
Therefore , the solution of the given problem of equation comes out to be the number of dots is filled in below table.
What is an equation?Variable words are commonly used in complex algorithms to show consistency between two contradictory claims. Academic expressions called equations are used to show the equality of various academic numbers. Instead of a single formula that separates 12 into two parts and can be used to assess received from y + 7, normalization in this case yields b + 7.
Here,
Given : A table with number of dots can be filled by this:
Here are the number of dots in each pattern:
Pattern Number of dots
1 4
2 7
3 10
4 13
5 16
6 19
7 22
8 25
9 28
10 31
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Jenny wants to measure the height of a tree she sites the top of the tree using a mirror that is lying flat on the ground. The mirror is 20 feet from the tree, and Jenny is standing 8 feet from the mirror as shown in the figure, her eyes are 5 feet above the ground how tall is the tree?
The Height of tree is around 8.33 feet tall.
What is the connection among Height and distance?In science, we work out the Height of an item utilizing distance and points. Distance is the even distance between the items, and point is the point over the level of the article's top, which gives the item's level.
We can utilize the rule of comparable triangles.
The hypotenuse of this triangle would be the line associating Jenny's eyes to the highest point of the tree (we should refer to this distance as "h").
We can set up the accompanying extent between the two triangles:
h / 20 = (h + 5) / 8
To solve for "h", we can cross-multiply and simplify:
8h = 20(h + 5)
8h = 20h + 100
12h = 100
h = 8.33 feet
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Write the expression in complete factored form.
5a(b + 1) + 3(b + 1) = please help!
Answer: (5a + 3)(b + 1)
Step-by-step explanation:
We can factor out the common factor of (b + 1) from both terms:
5a(b + 1) + 3(b + 1) = (5a + 3)(b + 1)
Therefore, the expression in complete factored form is (5a + 3)(b + 1).
2. What are the values of a and b?
10
6
8
b
a
(1 point)
Answer:
a=9/3,b=15/2 using some postulate you will get answer like sss,sas,aa.
[Complex Analysis] Is there a polynomial P(z) such that Pe^(1/z) is entire?
There is no polynomials such that [tex]P(z)e^{\frac{1}{z} }[/tex] is entire.
Sums of elements of the form kxn, where k is any number and n is a positive integer, make up polynomials. For instance, the equation 3x+2x-5. a description of polynomials.
By the Taylor expansion, [tex]e^{\frac{1}{z} }[/tex] = ∑∞n= 0.
Let P(z)= (ad)zd+.......+a0.
For n>0, the coefficient of z-n in the expansion of [tex]P(z)e^{\frac{1}{z} }[/tex] is :-
[tex]tn= n^{a0} 1 + (n+1)!+.......+(n+d)![/tex]
So the Laurent expansion of [tex]P(z)e^{\frac{1}{z} } = 0[/tex]will have terms of the form tn2-n where an is not equal to zero.
if r is the smallest non negative integer such that ar is not equal to zero, then we see that we can rewrite:-
[tex]tn= (n^{1} +r)![ar+n^{ar+1} +1+.....+(n+r+d)....(n+d)][/tex]
as we know that [tex]\lim_{n \to \infty} (n+r+1+....+(n+r+d).....(n+d)=0[/tex]
so there exists an N∈N, such that:-
[tex]/ar/ > n+r+1+....+(n+r+d)....(n+d)=0[/tex]
HenHence tn is non zero for all n>N. In other words, expansion contains terms of negative powers.
So, apart from P(z)=0, there is no polynomials such that [tex]P(z)e^{\frac{1}{z} } .[/tex]
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40 percent of employess judge their peers by their cleaniliness of the workspace
The number of employees who judge their cleanliness in their workplaces are: P(x=0) = 0.0168, P(x=1)= 0.0896, P(x=2) =0.2090, P(X=3)= 0.2787,
P(X=4)= 0.2322, P(X=5)= 0.1239, P(X=6)= 0.0413, P(x= 7)= 0.0079 and P(x=8)= 0.0007.
Binomial distribution :
A binomial distribution is a distribution whose experiment has two possible outcomes, a success and failure. The outcomes of the experiment do not depend on each other. In probability theory and statistics, the binomial distribution with the parameters n and p is a discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes or no question, each with its own Boolean result. : success (with probability p) or failure (with probability q=1-p). A pass/fail experiment is also called Bernoulli's trial or Bernoulli's experiment, and a sequence of results is called Bernoulli's process; for a single trial, i.e. n = 1, the binomial distribution is the Bernoulli distribution.
According to the Question:
For n trials in a binomial distribution, the probability of getting success:
[tex]P(X=x) = \frac{n!}{(n-x)!x!} * p^x *q^{(n-x)}[/tex]
Where p = success
q = failure
n = 8, p= 40% = 0.4
q = 1-0.4 = 0.6
After calculating, we get the values:
P(x=0) = 0.0168, P(x=1)= 0.0896,
P(x=2) =0.2090, P(X=3)= 0.2787,
P(X=4)= 0.2322, P(X=5)= 0.1239,
P(X=6)= 0.0413, P(x= 7)= 0.0079
and P(x=8)= 0.0007.
Complete Question:
40% of employees judge their peers by the cleanliness of their workspaces. You randomly select 8 employees and ask them whether they judge their peers by the cleanliness of their workspaces. The random variable represents the number of employees who judge their peers by the cleanliness of their workspaces.
P(x)=0,1,2,3,4,5,6,7, 8
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What is the cost of 73 pairs of pants if each pair costs $23, with a 10% discount on every
pair ordered over 50?
Answer: $1626.10
Step-by-step explanation:
[tex]50 * 23 = 1150\\23 * 0.9 = 20.7\\20.7 * 23 = 476.1\\1150 + 476.1 = 1626.1[/tex]
The circle graph describes the distribution of preferred music from a sample of 400 randomly selected middle school students.
a circle graph titled preferred music, with five sections labeled rock 13 percent, hip hop 25 percent, pop 35 percent, classical 13 percent, and jazz 14 percent
Which of the following conclusions can we draw from the circle graph?
Pop is the preferred music for 35 students.
Jazz is the preferred music for 56 students.
Together, Hip Hop, Rock, and Jazz are the preferred music for less than half the students.
Together, Hip Hop and Pop are the preferred music for 260 students.
After answering the provided question, we can conclude that As a result, circle we cannot conclude that Hip Hop and Pop are incompatible.
What is circle?A circle seems to be a two-dimensional component defined as such collection of the all points in a jet that become equidistant from the hub. A circle is commonly portrayed with the capital "O" for centre and the lower section "r" for the radius, which is the distance from the origin to any point on the circle.
Girth (the distance from around circle) is given by the formula 2r, where (pi) is a proportionality constant roughly equal to 3.14159. The formula r² calculates the circle's circumference, which refers to the amount of room inside of the circle.
We can draw the following conclusions from the information in the circle graph:
Pop music is preferred by 35% of the sample, which means that 35% of 400 students, or 140 students, prefer pop music.
Jazz is the preferred music for 14% of the sample, which means that jazz is preferred by 14% of 400 students, or 56 students.
Hip Hop, Rock, and Jazz are preferred music by 52% of the sample, which means that these three genres are preferred by 52% of 400 students, or 208 students.
Hip Hop and Pop are preferred music by 60% of the sample, which means that 60% of 400 students, or 240 students, prefer these two genres together. As a result, we cannot conclude that Hip Hop and Pop are incompatible.
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Use the discriminant to determine the number of solutions.
10. y=x²-3x+2
11. y = 2x² - 4x +3
13. y = x’−5x−10
14. y=x²+2x-1
12. y=-3x² + 5x-1
15. y = 4x²-9
In response to the stated question, we may state that y = 4x²-9 The discriminant is (-9)² - 4(4)(0) = 81. Since the discriminant is positive, there are two real solutions.
What is quadratic equation?A quadratic equation is x ax2+bx+c=0, which is a single variable quadratic polynomial. a 0. Because this polynomial is of second order, the Basic Theorem of Algebra implies that it has at least one solution. Simple or complex solutions are possible. A quadratic equation is a quadratic equation. This means it has at least one word that must be squared. The formula "ax2 + bx + c = 0" is a common solution for quadratic equations. where a, b, and c are numerical coefficients or constants. where the variable "X" is unnamed.
y=x²-3x+2
The discriminant is (-3)² - 4(1)(2) = 1. Since the discriminant is positive, there are two real solutions.
y = 2x² - 4x +3
The discriminant is (-4)² - 4(2)(3) = -8. Since the discriminant is negative, there are no real solutions.
y=-3x² + 5x-1
The discriminant is (5)² - 4(-3)(-1) = 29. Since the discriminant is positive, there are two real solutions.
y = x’−5x−10
The discriminant is (-5)² - 4(1)(-10) = 65. Since the discriminant is positive, there are two real solutions.
y=x²+2x-1
The discriminant is (2)² - 4(1)(-1) = 8. Since the discriminant is positive, there are two real solutions.
y = 4x²-9
The discriminant is (-9)² - 4(4)(0) = 81. Since the discriminant is positive, there are two real solutions.
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Pablo needs to memorize words on a vocabulary list for Latin class he has 12 words to memorize and he is 3/4 done how many words has Pablo memorized so far
Answer:
9 words
Step-by-step explanation:
We know
He has 12 words to memorize, and he is 3/4 done.
How many words has Pablo memorized so far?
We Take
12 x 3/4 = 9 words
So, Pable has memorized 9 words.
what is 2 times 2x ??
Answer:
4x
Step-by-step explanation:
2 X 2x = 2x+2x= 4x
Answer:
4x
Step-by-step explanation:
So when you multiply 2×2=4
And since it's multiplication you can add the x to it giving you 4x(if it's addition you can't add them because they aren't like terms)
Combine like terms to simplify the expression completely. 2x + 5 - y + 6x + 4y =
Thus, the simplification of linear expression is : 8x + 3y +5 .
Explain about the simplification of linear equation?A linear equation is an integer number of the form y=mx+b, where m represents the slope when b is the y-intercept, and only a constant alongside a first-order (linear) term are included.
To simplify the linear equation-
Add or remove like terms from a linear expression to make it simpler. Contrary terms are not added to or withdrawn from. Reduce common factors and add brackets to factorise. Add like terms together and multiply all terms inside brackets by the term outside to expand.
Given linear equation-
= 2x + 5 - y + 6x + 4y
Add like term with same variable.
= 8x + 3y +5
Thus, the simplification of linear expression is : 8x + 3y +5 .
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What's 5/6 ÷ 7/9 ÷ 8/9 ÷0/7
Answer: The expression is undefined.
Step-by-step explanation:
Division by zero is undefined in mathematics. In this expression, there is a division by zero in the term 0/7. Therefore, the entire expression is undefined.
Assume a Poisson random variable has a mean of 5 successes over a 125-minute period. a. Find the mean of the random variable, defined by the time between successes. Mean 25 b. What is the rate parameter of the appropriate exponential distribution? (Round your answer to 2 decimal places.) Rate parameterſ 0.04 c. Find the probability that the time to success will be more than 55 minutes. (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.) Probability
The mean of time between success is 0.2 minutes, rate parameter is 5 and probability that the time to succeed will be more than 55 minutes is approximately 0.000026 when Poisson random variable has a mean of 5 successes over a 125-minute period.
They can be found out by:
(A) The mean of the random variable defined by the time between successes can be found by using the fact that the Poisson distribution is memory less, which means that the time between successes follows an exponential distribution. The mean of an exponential distribution is equal to the reciprocal of the rate parameter, so:
Mean of time between successes = 1 / rate parameter = 1 / 5 = 0.2 minutes
(B) The rate parameter of the exponential distribution can be found using the fact that the mean of the exponential distribution is equal to the reciprocal of the rate parameter, as derived in part a:
rate parameter = 1 / mean of time between successes = 1 / 0.2 = 5
(C)The probability that the time to success will be more than 55 minutes can be found using the cumulative distribution function (CDF) of the exponential distribution with the rate parameter found in part b:
P(X > 55) = 1 - P(X <= 55) = 1 - F(55) = 1 - (1 - e^{(-5*55)}) = 0.000026 (rounded to 4 decimal places)
Therefore, the probability that the time to success will be more than 55 minutes is very small, approximately 0.000026.
The mean of random variable defined by time between success is 0.2 minutes, rate parameter of exponential distribution is 5 and probability that the time to succeed will be more than 55 minutes is approximately 0.000026 .
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Work out the total area of the shape below:
The total area of the given shape is 71cm².
What is area?The size of a section on a surface is determined by its area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina. A shape's area can be calculated by contrasting it with squares of a known dimension. The square meter (abbreviated as m²), which is the area of a square whose sides are one metre long, is the common measure of area in the International System of Units (SI). Three such squares would be the same size as a shape with a three square metre surface.
The following figure can be divided into a rectangle 7cm x 8cm and a triangle of height and base 6 cm and 5 cm respectively.
Area of rectangle= 7*8= 56 cm²
Area of triangle= 1/2* base*height= 1/2*6*5 = 15 cm²
Total area of shape = 56+15= 71 cm²
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Identify the fallacies of relevance committed by the following arguments, giving a brief explanation for your answer. If no fallacy is committed, write "no fallacy". Surely you welcome the opportunity to join our protective organization. Think of all the money you will lose from broken windows, overturned trucks, and damaged merchandise in the event of your not joining.
There are no fallacies of relevance committed by the given argument.
The following arguments commits fallacy: argumentum ad baculum. Argumentum ad baculum is a Latin phrase which means argument from a stick or appeal to force. It is a type of logical fallacy in which someone tries to persuade another person by using threats of force or coercion rather than using evidence or reasoning.
The above statement is an example of the argumentum ad baculum fallacy as it tries to use fear to convince people to join their protective organization. They are using the threat of potential losses to convince people to join. It is a manipulative strategy that attempts to scare people into joining by threatening the safety of their business.No fallacy is committed. There are no fallacies of relevance committed by the given argument.
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A plane takes off 500 feet away from a tower. The plane takes off at an angle of
elevation of 20°. In its path is the tower of 200 feet.
Will the plane clear the height of the tower? (yes/no)
How many feet (to the nearest foot) will the plane either clear or be short of the
tower. Enter a positive value if the distance represents how far over the tower the
plane will fly. Enter a negative distance if the distance represents how much lower
the plane will be than the tower.
Answer:Taking off: 2
Flying: 3
Landing: 4
Landing well enough you can use the plane again: 5
Landing well enough that your passengers will fly with you again: 6
Having the judgement and strength of character to say “I know I promised we'd fly home today, but the weather is bad so we're going to have to wait a day and miss that thing you wanted to go to”: 10
Step-by-step explanation:
Write a two column proof for the following statement. Given that the Bible is true, prove that you personally need the Gospel to be in relationship with God. Fo this proof, you will need to establish(using scripture) the following flow of logic: 1 the state of mankind without the Gospel. 2 the state of mankind's relationship with God as a result of #1. 3 the affect of the Gospel message has on mankind. 4 the affect on mankind's relationship with God as a result of #3.
It is important that our understanding and spreading of the gospel comes from the biblical text itself, and it is equal important that we continue to preach and defend the one true gospel. Jesus died and rose again for the forgiveness of our sins.
The word gospel occurs ninety-nine times in the NASB and ninety-two times in the NET Bible. In the Greek New Testament, the gospel is a translation of the Greek noun "good news" occurring 76 times and of the verb "to bring or announce good news" 54 times. Both words are derived from the noun angelos, "messenger". In classical Greek, euangelos is one who brings news of victory or other joyful political or personal news.
The gospel of the grace of God emphasizes that all aspects of salvation are based on grace, not on a merit system.The gospel of the Kingdom is the good news that God will establish His kingdom on earth through the two comings of the Lord Jesus Christ.The gospel of peace describes how this good news of salvation in Christ brings peace in all areas (peace with God, peace with God, peace with others, and peace in the world) through the Savior's victory.Learn more about Equally:
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Which derived character is placed immediately after that group on the cladogram?
Answer:
Step-by-step explanation:
One that has the next least in common with the rest.
pls solve it. it's urgent
Rounding to the nearest cm², the area of the shaded region is 32 cm².
Describe Area of triangle?The area of a triangle is the measure of the region enclosed by the three sides of a triangle. It is measured in square units. The formula to find the area of a triangle is given as:
Area = 1/2 x base x height
where "base" is the length of the side of the triangle that is perpendicular to the height and "height" is the distance between the base and the opposite vertex.
The base and height can be any two sides of the triangle as long as the height is perpendicular to the base. If the base and height are not known, they can be found using the Pythagorean theorem or other trigonometric functions.
We can find the area of the shaded region by subtracting the area of triangle ABD from the area of rhombus ABCD.
To find the area of triangle ABD, we need to first find the length of BD. Since angle BAD is 70 degrees and ABCD is a rhombus, we know that angle BCD is also 70 degrees. Therefore, angle BXD is 70 degrees / 2 = 35 degrees.
Using trigonometry, we can find BD:
tan(35) = BD/9
BD = 9 tan(35)
BD ≈ 5.458 cm
To find the area of triangle ABD, we use the formula:
Area of triangle = (base x height) / 2
The base of triangle ABD is BD, which we just found, and the height is the perpendicular distance from A to BD. We can find this distance using trigonometry and the fact that angle BAC is 20 degrees:
tan(20) = height/9
height = 9 tan(20)
height ≈ 3.170 cm
Therefore, the area of triangle ABD is:
Area of triangle ABD = (BD x height) / 2
Area of triangle ABD = (5.458 x 3.170) / 2
Area of triangle ABD ≈ 8.661 cm²
The area of rhombus ABCD is:
Area of rhombus ABCD = (diagonal 1 x diagonal 2) / 2
Area of rhombus ABCD = (9 x 9) / 2
Area of rhombus ABCD = 40.5 cm²
Therefore, the area of the shaded region is:
Area of shaded region = Area of rhombus ABCD - Area of triangle ABD
Area of shaded region = 40.5 - 8.661
Area of shaded region ≈ 31.839 cm²
Rounding to the nearest cm², the area of the shaded region is 32 cm².
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The perimeter of a square is 16 cm find length , diagonal and area
Answer:
Step-by-step explanation:
we have perimeter 16
for perimeter 4+4+4+4 we add together it's 16
for area we have 4 times 16
Please need help in math
I inserted in an image below to help you with the rule.
The 1st point is (6,1) . This becomes (1,-6).
The 2nd point is (-5,-6). This becomes (-6, 5)
a drawer contains 11 identical red socks and 8 identical black socks. suppose that you choose 2 socks at random in the dark. a. what is the probability that you get a pair of red socks? b. what is the probability that you get a pair of black socks? c. what is the probability that you get 2 unmatched socks? d. where did the other red sock go?
The drawer contains 11 identical red socks and 8 identical black socks. Here are the answers to the questions below
a. The probability of getting a pair of red socks is the probability of selecting two red socks, 55/171b. The probability of getting a pair of black socks is the probability of selecting two black socks, 28/171c. The probability of getting two unmatched socks is the sum of the probability of selecting a red sock first and a black sock second and the probability of selecting a black sock first and a red sock second, 88/171d. It's not clear from the information givenProblem statementa. What is the probability that you get a pair of red socks?The probability of getting a pair of red socks is the probability of selecting two red socks, which is: P(Red and Red) = P(Red) × P(Red | Red was first) = (11/19) × (10/18) = 55/171.
b. What is the probability that you get a pair of black socks?The probability of getting a pair of black socks is the probability of selecting two black socks, which is: P(Black and Black) = P(Black) × P(Black | Black was first) = (8/19) × (7/18) = 28/171.
c. What is the probability that you get 2 unmatched socks?The probability of getting two unmatched socks is the sum of the probability of selecting a red sock first and a black sock second and the probability of selecting a black sock first and a red sock second: P(Red and Black or Black and Red) = P(Red) × P(Black | Red was first) + P(Black) × P(Red | Black was first) = (11/19) × (8/18) + (8/19) × (11/18) = 88/171.
d. Where did the other red sock go? It's not clear from the information given. It could be missing or misplaced, or it could be in the drawer, but the problem doesn't provide enough information to determine what happened to it.
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If P(A)=0. 3, P(B)=0. 2, and P(A∩B)=0. 1, find the probability
a. P(
)
b. P(A∪B)
c. P(
∩B)
d. P(A∩
)
e. P(
∪B)
P(∅) = 0, P(A∪B) = 0.4 , P(A∩B) = 0.1 ,Since the sample space is not defined in the question, we cannot calculate P(B'). Therefore, we cannot calculate P(A∩B').and P(A∪B) = 0.4. are the required solutions ofgiven probability check .
a. The probability of an empty set is always zero. Therefore, P(∅) = 0.
b. The probability of the union of two events, A and B, is given by the formula P(A∪B) = P(A) + P(B) - P(A∩B). Substituting the values given in the question, we get:
P(A∪B) = P(A) + P(B) - P(A∩B)
= 0.3 + 0.2 - 0.1
= 0.4
Therefore, P(A∪B) = 0.4.
c. The probability of the intersection of A and B is given by the formula P(A∩B). Substituting the values given in the question, we get:
P(A∩B) = 0.1
Therefore, P(A∩B) = 0.1.
d. The probability of the intersection of A and the complement of B is given by the formula P(A∩B'). The complement of B is the set of all outcomes that are not in B. Since the sample space is not defined in the question, we cannot calculate P(B'). Therefore, we cannot calculate P(A∩B').
e. The probability of the union of A and B is given by the formula P(A∪B). Substituting the values given in the question, we get:
P(A∪B) = P(A) + P(B) - P(A∩B)
= 0.3 + 0.2 - 0.1
= 0.4
Therefore, P(A∪B) = 0.4.
In probability theory, the union of two events A and B is the set of outcomes that belong to either A or B or both. The intersection of two events A and B is the set of outcomes that belong to both A and B. The complement of an event A is the set of outcomes that do not belong to A. These concepts are fundamental in probability theory and are used extensively in solving various problems.
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A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of more than 1300 KN/m2. The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture is normally distributed with σ = 67. Let μ denote the true average compressive strength.
(a) What are the appropriate null and alternative hypotheses?
(b) Let X denote the sample average compressive strength for n = 12 randomly selected specimens. Consider the test procedure with test statistic X itself (not standardized). If X = 1340, find the P-value. (Round your answer to four decimal places.) P-value = 0.0193
(c) What is the probability distribution of the test statistic when μ = 1350?
State the mean and standard deviation of the test statistic. (Round your standard deviation to three decimal places.)
Mean: 1350, Standard Deviation: 19.341
For a test with α = 0.01, what is the probability that the mixture will be judged unsatisfactory when in fact μ = 1350 (a type II error)? (Round your answer to four decimal places.)
(a) The null hypothesis is that the true average compressive strength of the mixture is less than or equal to 1300 KN/m2.
The alternative hypothesis is that the true average compressive strength of the mixture is greater than 1300 KN/m2.
(b) To find the P-value, we need to calculate the probability of getting a sample mean of 1340 or greater, assuming the null hypothesis is true. Using the sample size n=12 and sample standard deviation σ=67, the test statistic is (1340-1300)/(67/sqrt(12)) = 2.523.
The P-value is the probability of getting a value of 2.523 or greater from a t-distribution with 11 degrees of freedom, which is 0.0193.
(c) The test statistic when μ = 1350 follows a t-distribution with 11 degrees of freedom.
The mean of the test statistic is equal to the true value of the mean, which is 1350. The standard deviation of the test statistic can be calculated as σ/sqrt(n) = 67/sqrt(12) = 19.341.
To find the probability of a type II error with α = 0.01, we need to calculate the probability of accepting the null hypothesis when the true value of the mean is 1350.
This can be calculated using the t-distribution with 11 degrees of freedom and the critical value corresponding to α=0.01, which is 2.718. The probability of a type II error is the probability that the test statistic is less than 2.718 when the true value of the mean is 1350, which is 0.2157 (rounded to four decimal places).
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Maricopa's Success scholarship fund receives a gift of $ 75000. The money is invested in stocks, bonds, and CDs. CDs pay 3.75 % interest, bonds pay 3.8 % interest, and stocks pay 10.3 % interest. Maricopa Success invests $ 25000 more in bonds than in CDs. If the annual income from the investments is $ 4142.5 , how much was invested in each account?
$____ in stocks, $____ in bonds, and $____ in CDs.
Answer: Maricopa Success invested $13,350 in CDs, $38,350 in bonds, and $23,300 in stocks.
Step-by-step explanation:
Let x be the amount invested in CDs.
Then, the amount invested in bonds would be (x + $25,000) and the amount invested in stocks would be ($75,000 - x - (x + $25,000)) = ($50,000 - 2x).
The annual income from the investments is $4,142.5, so we can set up the following equation:
0.0375x + 0.038(x + $25,000) + 0.103($50,000 - 2x) = $4,142.5
Simplifying the equation, we get:
0.0755x + $5,150 = $4,142.5
0.0755x = -$1,007.5
x = -$1,007.5 / 0.0755
x = $13,350
Therefore, the amount invested in CDs is $13,350.
The amount invested in bonds is $13,350 + $25,000 = $38,350.
The amount invested in stocks is $75,000 - $13,350 - $38,350 = $23,300.
So, Maricopa Success invested $13,350 in CDs, $38,350 in bonds, and $23,300 in stocks.
14.5% of an amount is 812 , what is the original number
the original number after simplification is 5600.
Define FractionA fraction is a numerical quantity representing a part of a whole or a ratio between two numbers. It is expressed as one integer, called the numerator, written above a horizontal line, and another integer, called the denominator, written below the line. For example, the fraction 2/5 represents two out of five equal parts or 2 divided by 5,
We can start by using the fact that 14.5% can be written as a decimal fraction 0.145.
Let X be the original number we want to find.
Then we can set up the following equation:
0.145 ×X = 812
To solve for X, we can divide both sides by 0.145:
X = 812 / 0.145 = 5600
Therefore, the original number is 5600.
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Ana has a rectangular garden with the width of 2.3 meters and a length of 2.8 meters. she makes the model below to help her determine the area of her garden. What is the area of Ana's garden?
Answers 6.44, 8.6 4.38, 5.1
Answer: 6.44 square meters
Step-by-step explanation:
The area of a rectangle is given by the formula: A = L x W, where L is the length and W is the width.
Substituting the given values, we get:
A = 2.8 x 2.3 = 6.44 square meters
Therefore, the area of Ana's garden is 6.44 square meters.