The constant angular acceleration of the centrifuge is approximately [tex]-331283[/tex] rad/min² in the negative direction.
To find the constant angular acceleration of the centrifuge, we can use the following kinematic equation:
ω² = ω₀² + 2αθ
Here, ω is the final angular velocity (0 rad/min, since it comes to rest), ω₀ is the initial angular velocity (3450 rev/min), α is the constant angular acceleration we want to find, and θ is the angular displacement (45.8 revolutions).
First, we need to convert the given angular values to radians. We know that 1 revolution equals 2π radians.
Initial angular velocity, ω₀ = 3450 rev/min × 2π rad/rev = 6900π rad/min
Angular displacement, θ = 45.8 rev × 2π rad/rev = 91.6π rad
Now, substitute the values into the kinematic equation:
[tex]0 = (6900π)² + 2α(91.6π)[/tex]
[tex]α = - (6900π)² / (2 × 91.6π)[/tex]
[tex]α ≈ -331283 rad/min²[/tex]
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The table shows four transactions (in dollars) for a bank account. Positive numbers represents deposits, and negative numbers represent withdrawals. The balance before the transactions is $75.50. What could the transaction for 11/7 be if the final balance in the bank account is $86.92? Date Amount 11/4 50.68 11/4 -22.16 11/7 11/11 56.65 End Balance 86.92
Answer:
11/7: +9.42
Step-by-step explanation:
Identify all expressions below that are polynomials.
Answer:
All the expressions except d are polynomials.
Pls just say a b c or d
Answer:
c
Step-by-step explanation:
A thrill ride swings passengers back and forth, a little higher each time up to 137 feet. Suppose the height of the swing after 30 seconds is 45 feet. How much higher will the ride swing
Based on this estimate, we can expect the ride to swing approximately 9.2 ft higher after each swing.
What is equation?An equation is a mathematical statement that asserts the equality of two expressions, often containing variables. It typically consists of two expressions separated by an equal sign. The expressions on either side of the equal sign may contain constants, variables, operators (such as +, -, ×, ÷), and functions. Equations are used in many fields, including mathematics, physics, engineering, and finance, to model and solve problems. They are a fundamental concept in algebra, which is the branch of mathematics that deals with equations and the manipulation of variables.
Here,
Assuming that the ride swings higher by approximately the same amount each time, we can estimate the average increase in height per swing. We can calculate this by dividing the total increase in height from 45 ft to 137 ft (92 ft) by the number of swings it takes to reach that height. Since we don't know how many swings it takes to reach the maximum height, we'll assume that the ride swings 10 times before reaching 137 ft (this is just an estimate).
Total increase in height = 137 ft - 45 ft = 92 ft
Number of swings = 10 (estimated)
Average increase in height per swing = 92 ft / 10 = 9.2 ft
Based on this estimate, we can expect the ride to swing approximately 9.2 ft higher after each swing. Therefore, after the first swing (which reached a height of 45 ft), we can estimate that the ride will swing to a height of approximately 54.2 ft (45 ft + 9.2 ft) on the second swing, and then to a height of approximately 63.4 ft (54.2 ft + 9.2 ft) on the third swing, and so on.
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Complete question:
A thrill ride swings passengers back and forth getting higher and higher each time up to 137ft. suppose the height of the swing after 30sec. is 45ft. How much higher will the fide swing?
please help i will give brainliest along with 20 pnts. ONLY ANSWER IF YOU KNOW IT
Giovanna deposited $1600 into two accounts, half in First Oak and half in West United.
Interest earned in First Oak account after 5 years at 6% simple interest:
= 0.06 x $800 x 5
= $240
Interest earned in West United account after 5 years at 5% compounded annually:
= $800 x (1 + 0.05)^5 - $800
= $800 x 1.27628 - $800
= $221.02
Total interest earned in both accounts:
= $240 + $221.02
= $461.02
Therefore, Giovanna will have earned $461.02 in interest from both accounts at the end of 5 years.
Property taxes on homes decreased this year by an average of $75. 90 in Silvertown. There are 270 homes in Silvertown. Which describes the change in Silvertown’s revenue from last year to this year?
The change in Silvertown’s revenue from last year to this year can be described by c. 20,493.
Property taxes on homes decreased this year by an average = $75. 90
Total number of homes = 270
It is essential to compare the overall property tax revenue from this year to the total revenue from last year after the $75.90 per-home drop in order to ascertain the change in Silvertown's property tax revenue.
Calculating the total decrease in revenue -
= Average decrease x total number of homes
= 75.90 x 270
= 20,493
Complete Question:
Property taxes on homes decreased this year by an average of $75. 90 in Silvertown. There are 270 homes in Silvertown. Which describes the change in Silvertown’s revenue from last year to this year?
a. - 21,093
b. - 20, 493
c. 20,493
d. 21930
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Bennie is calculating the density of books in a box. He knows the number of books in the box and the volume of the box. Which of the following formulas can be used to calculate the density of books in the box? Density = number of books over volume of box Density = volume of box over number of books Volume of shelf = density over number of books Number of books = density over volume of box
Answer:
Density = number of books over volume of box
Step-by-step explanation:
The formula that can be used to calculate the density of books in the box is:
Density = number of books / volume of box
This formula relates the number of books in the box to the volume of the box, and calculates the density of books per unit volume.Therefore, the correct formula to calculate the density of books in the box is the first one given in the options:
Density = number of books over volume of box
Answer:
Density = number of books over volume of box
Step-by-step explanation:
If the function, g(x), has the ordered pairs (-4, 15), (-2, 3), and (0, -1), fill in the ordered pairs that know exist on the graph of g−1(x)
Answer:
(15, - 4 ) , (3, - 2 ) , (- 1, 0 )
Step-by-step explanation:
given a point (x, y ) on a function f(x) , then the corresponding point on the inverse function is (y, x )
given the points on g(x) , then the corresponding points on [tex]g^{-1}[/tex] (x) are
(- 4, 15 ) → (15, - 4 )
(- 2, 3 ) → (3, - 2 )
(0, - 1 ) → (- 1, 0 )
onsider the sequence which starts 4,11,18 what is the next term in the sequence? find a formula for the th term of this sequence. find the sum of the first 100 terms of the sequence: .
The sequence follows a pattern of adding 7 to the previous term, and its formula is 7n - 3. The sum of the first 100 terms of the sequence is 35,350, which was found using the formula for the sum of an arithmetic series.
The next term in the sequence can be found by adding 7 to the previous term, so the next term is 25.
To find a formula for the nth term of the sequence, we can observe that each term is 7 more than a multiple of 7. In other words, the nth term is given by the formula 7n - 3.
To find the sum of the first 100 terms of the sequence, we can use the formula for the sum of an arithmetic series:
S = (n/2)(a1 + an)
where S is the sum of the first n terms, a1 is the first term, and an is the nth term. Substituting n = 100, a1 = 4, and an = 703, we get:
S = (100/2)(4 + 703) = 35,350
Therefore, the sum of the first 100 terms of the sequence is 35,350.
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factorise x²-2xy-y²-z²
Answer:
(x^2−2xy+y^2)−z^2
⇒[x(x−y)−y(x−y)]−z^2
⇒(x−y)(x−y)−z^2
⇒(x−y)^2−z^2
⇒[(x−y)+z][(x−y)−z]
⇒(x−y+z)(x−y−z)
An isosceles right triangle is removed from
each corner of a square piece of paper, as
shown, to create a rectangle. If AB = 12 units,
what is the combined area of the four removed
triangles, in square units?
The combined area of the four removed triangles is 48 sq.units. Answer: 48
We need to find out the combined area of the four removed triangles, in square units. Given: AB = 12 units.
Let's consider the given square, and let's draw an altitude BD and also draw perpendiculars to BD from the three vertices A, C and D.
Let AB = x cm. Area of square = x² sq.cm.
Now, we are cutting a triangle with base x and height x, which is a right-angled triangle. Hence, area of each removed triangle = (1/2) * x * x = (x²/2) sq.cm.
Now, BD = x/√2. Area of rectangle = AB * BD = 12 * 12/√2 = 72√2 sq.cm.
Now, area of 4 triangles = (x²/2) + (x²/2) + (x²/2) + (x²/2) = 2x² sq.cm.
We know that, Area of rectangle = Area of 4 triangles + Area of square => 72√2 = 2x² + x² => 72√2 = 3x² => x² = 24√2 cm² => x = √(24 * 2) cm = √(48) cm = 4√3 * √2 cm.
Area of 4 triangles = 2x² sq.cm = 2 * 24 cm² = 48 sq.cm.
Hence, the combined area of the four removed triangles is 48 sq.units. Answer: 48.
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in a certain large city, 45% of families earn less than $35,000 per year. assuming the distribution is binomial and you can use the exact binomial calculation, what's the probability that a simple random sample of 30 families will have 10 or fewer families earning less than $35,000 per year?
The probability of obtaining 10 or fewer families earning less than $35,000 per year in a simple random sample of 30 families from a large city with 45% of families in that income bracket is approximately 0.041 or 4.1%.
We can use the binomial distribution formula to calculate the probability of obtaining 10 or fewer families earning less than $35,000 per year in a simple random sample of 30 families from a large city where 45% of families earn less than $35,000 per year.
Let's denote the probability of a family earning less than $35,000 per year as "p", which is 0.45 in this case, and the number of trials or families sampled as "n", which is 30 in this case.
The probability of obtaining k families earning less than $35,000 per year in a simple random sample of 30 families can be calculated using the binomial distribution formula:
P(X ≤ 10) = Σ(i=0 to 10) [n choose i] * p^i * (1-p)^(n-i)
where n = 30, p = 0.45, and X is the random variable representing the number of families earning less than $35,000 per year in the sample.
Using a binomial calculator or software, we can calculate:
P(X ≤ 10) ≈ 0.041
Therefore, the probability that a simple random sample of 30 families will have 10 or fewer families earning less than $35,000 per year is approximately 0.041 or 4.1%.
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Jordan wrote the following descirption: three fewer than one fourth of x is 12. write an equation to represent the description.
Answer:
1/4x - 3 = 12
Step-by-step explanation:
You know you have 1/4x and need to take three from it to equal 12
y < 2x + 3
x+y≥ 3
x < 4
Write an ordered pair that is a solution to the systems.
The solution to the system of equations is (2, 1). To find this solution, we must first solve the first equation, Y < 2x + 3, for x.
What is subtracting?Subtracting involves taking the difference between two numbers. It is the opposite of addition and is represented by the '-' sign.
We can do this by subtracting 3 from both sides of the equation, which gives us Y - 3 < 2x.
We then divide both sides of the equation by 2, which gives us
Y - 3/2 < x.
Next, we must solve the second equation, x + y ≥ 3, for y. To do this, we subtract x from both sides of the equation, which gives us y ≥ 3 - x.
Finally, we must set both equations equal to each other,
Y - 3/2 = 3 - x.
We can then solve for x by adding 3/2 to both sides of the equation, which gives us
x = 2.5.
We can then plug this value for x into the second equation, which gives us y ≥ 3 - 2.5.
We then solve for y by subtracting 2.5 from both sides of the equation, which gives us y = 0.5.
Since the value for x must be less than 4, we must round down the value of x to 2. This means that the solution to the system of equations is (2, 1).
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Ousmane envoie une carte a Arnaud par pigeon voyageur. Le pigeon vole a une vitesse de 84km/h et met 1h45 à délivrer la lettre. A quelle distance Arnaud et Ousmane vivent-ils l'un de l'autre ?
On peut commencer par utiliser la formule suivante pour calculer la distance parcourue par le pigeon voyageur :
distance = vitesse x temps
où la vitesse est donnée en km/h, le temps en heures et la distance en km.
Dans ce cas-ci, la vitesse est de 84 km/h et le temps de voyage est de 1h45, soit 1.75 heures. On peut donc calculer la distance parcourue par le pigeon :
distance = 84 km/h x 1.75 h = 147 km
Donc, la distance entre Ousmane et Arnaud est de 147 km.
Either show that the following sets of vectors are linearly independent, or find a linear relation between them (the T means transpose): (a) x^(1) = [ 1 1 0 ]^T , X^(2) = [ 0 1 1 ]^T , X^(3) = [1 0 1 ]^T. (b) x^(1) = [ 2 1 0 ]^T , X^(2) = [ 0 1 0 ]^T , X^(3) = [-1 2 0 ]^T.
There are no free variables, the vectors are linearly independent.
How to show that the sets of vectors are linearly independent?To either show that the following sets of vectors are linearly independent or find a linear relation between them, we can follow these steps:
. Form a matrix using the given vectors as columns.
. Calculate the determinant of the matrix (if it's a square matrix) or row reduce to echelon form.
. If the determinant is non-zero or the matrix has no free variables, the vectors are linearly independent. If the determinant is zero or the matrix has free variables, the vectors are linearly dependent, and we can find a linear relation.
(a) Create the matrix A using the given vectors:
A = | 1 0 1 |
| 1 1 0 |
| 0 1 1 |
The determinant of A is:
det(A) = 1(1(1) - 1(0)) - 0(1(1) - 1(0)) + 1(1(0) - 1(1)) = 1 - 1 = 0
Since the determinant is zero, the vectors are linearly dependent.
(b) Create the matrix B using the given vectors:
B = | 2 0 -1 |
| 1 1 2 |
| 0 0 0 |
Row reduce B to echelon form:
B = | 1 1 2 |
| 0 1 -4 |
| 0 0 0 |
Since there are no free variables, the vectors are linearly independent.
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A researcher found a study relating the distance a driver can see, y, to the age of the driver, When researchers looked at the association of x and y, they found that the coefficient of determination was =0.542. Select two conclusions that the researcher can make from this data. a.) The correlation coefficient, t, is-0 458. b.) About 54% of the variation in distance that the driver can see is explained by a linear relationship with the driver's age. O c.) About 74% of the variation in the driver's age is explained by a linear relationship with the distance that the driver can see O d.) The correlation coefficient, t.is -0736. e.) About 46% of the variation in distance that the driver can see is explained by a linear relationship with the driver's age. 1.) The correlation coeficient 0 271 A data set was grapned using a scatterpion 30 25 20 15 10 5 0 0 5 10 15 20 25 30 The correlation coefficient, r, is 0.813 Which of the following statements explains how the correlation is http/phoenix.sophia.org/tutorials/cautions-about-correlation-2/download ndf The correlation coefficient, r, is 0.813. Which of the following statements explains how the correlation is affected? O a.) It is affected by inappropriate grouping. O b.) It is not affected. c.) It is affected by an influential point. d.) It is affected by non-linearity. SUBMIT MY ANSWER Which of the following statements is TRUE? O a.) Low correlation implies causation b.) A high correlation means that the response variable is caused by the explanatory variable. O c.) High correlation does not always establish causation O d.) To imply causation, the correlation must be 1. SUBMIT MY ANSWER Javascriptvo do)
1)From the data:
Two conclusions that the researcher can make are:
b.) About 54% of the variation in the distance that the driver can see is explained by a linear relationship with the driver's age.
d.) The correlation coefficient, t, is -0.736. (This can be found by taking the square root of the coefficient of determination and considering the negative correlation)
2)"It is not affected" is the correct statement,that is option b
3)The "High correlation does not always establish causation" is the TRUE statement, that is option c .
What is Correlation?
Correlation is a statistical measure that indicates the extent to which two or more variables fluctuate together.
A positive correlation indicates that as one variable increases, the other variable also increases.
A negative correlation indicates that as one variable increases, the other variable decreases. In other words, it shows the relationship between two variables and helps to understand if they are related or independent.
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If f(x) is a function and f(1) = 5, then which of the following could not be true?
If f(x) is a functiοn and f(1) = 5, then f(1) = 1 cοuId nοt be true.
Thus οptiοn a is cοrrect.
Define functiοn.A functiοn is a reIatiοn between twο sets, caIIed the dοmain and the range, such that fοr each eIement in the dοmain, there is exactIy οne eIement in the range. A functiοn maps each eIement in the dοmain tο a unique eIement in the range.
In οther wοrds, a functiοn is a ruIe οr a fοrmuIa that assοciates each input vaIue with a unique οutput vaIue. The input vaIues are the dοmain οf the functiοn, and the οutput vaIues are the range. Functiοns are οften denοted by a symbοI such as f(x), where x is an eIement in the dοmain and f(x) is the cοrrespοnding eIement in the range.
In mathematicaI anaIysis, the generaI cοncept οf functiοn, appIicatiοn οr mapping refers tο a ruIe that assigns tο each eIement οf a first set a singIe eIement οf a secοnd set.
Using this definitiοn, severaI eIements οf the dοmain can resuIt in the same eIement οf the range οf the functiοn.
But, the same eIement οf the dοmain, can nοt have different vaIues οf the range οf the functiοn.
Therefοre, the fοIIοwing expressiοn can nοt be true:
f (1) = 1
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Complete Question:
If f(x) is a function and f(1) = 5, then which of the following could not be true?
a. f(1) = 1
b. f(2) = 1
c. f(5) = 5
[y=-z+2
y=-2²+z+1
Which ordered pair is the solution of the system?
The graph shows the system
0 (0, 2)
O (1,2)
(1,1)
(0, 1)
+
Therefore , the solution of the given problem of ordered pair comes out to be the ordered pair (1, 1/2).
What exactly are ordered pairs?"Ordered pairs" are two separate variables that are arranged in a way that suggests a specific sequence. The coordinates for x and y in an order pair are represented, respectively, by the main and second components. The sample following uses close parentheses to indicate the ordered combination.
Here, The formulae are as follows:
=>y = -z + 2 ...(1)
=> y = -2x² + z + 1 ...(2)
Equation (1) can be substituted for equation (2) to find the value of z:
=> Z = x² + 1/2 - z + 2 = -2x² + z + 1
=> 2z = 2x² + 1
We can now enter this value of z into equation (1) and find the value of y:
=> y = -z + 2
=> y = -(x² + 1/2) + 2
=> y = -x² + 3/2
As a result, the equation system can be expressed as:
=> z = x² + 1/2
=> y = -x² + 3/2
When x=0:
=> z = 0² + 1/2 = 1/2
=> y = -0² + 3/2 = 3/2
Therefore, there is no answer for the ordered pair (0, 3/2).
When x=1:
=> z = 1² + 1/2 = 3/2
=> y = -1² + 3/2 = 1/2
The answer is the ordered pair (1, 1/2).
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WILL MARK BRAINLIEST!!!
PLEASE HELP!
Write Tan A and Tan B
Answer:
Hope this is what you were looking for :)
Step-by-step explanation:
tan = opposite/adjacent
IF YOU DONT NEED TO FIND THE VALUES OF THE SIDES:
tan A = [tex]\frac{x}{11}[/tex]
tan B = [tex]\frac{11}{x}[/tex]
Replace the x for whatever the value of BC is or if it doesn't have a value, you can just leave it as x.
IF YOU DO NEED TO FIND THE VALUES OF THE SIDES:
tan 45 = 1
tan 45 = [tex]\frac{BC}{11}[/tex]
(11) tan 45 = BC
BC = 11
tan 45 = [tex]\frac{11}{AC}[/tex]
AC = [tex]\frac{11}{tan 45}[/tex]
AC = 11
This can also be done without using tangent from taking a look at special right triangles.
In 45-45-90 triangles, the two legs are the same size while the hypotenuse is equal to one of the legs multiplied by [tex]\sqrt{2}[/tex]. In doing this, we can find that both legs are 11 and the hypotenuse is [tex]11\sqrt{2}[/tex].
you are making cookies and missing a key ingredient eggs. you have most of the other ingredients, except you only have 1.33 cups of butter. the recipe calls for two cups of butter and three eggs to make six dozen cookies. how many eggs do you need use all of the butter?
By using equation in two variable we need to use 2 eggs to make all the cookies with 1.33 cups of butter.
To make six dozen cookies, the recipe calls for two cups of butter and three eggs. We can use proportionality to solve this question: If 2 cups of butter require 3 eggs to make 6 dozen cookies, then 1.33 cups of butter require x eggs to make all of the cookies.
x eggs = (1.33 cups of butter x 3 eggs)/(2 cups of butter). x = 1.99 eggs. Since we cannot use .99 eggs to make cookies, we would need to round up to the nearest whole number of eggs.
Therefore, we need to use 2 eggs to make all the cookies with 1.33 cups of butter.
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every morning, mr. cross bakes 80 strawberry frosted donuts unless there is a special order. each donut costs $3 to make, and is sold for $5; unsold donuts are given away to a charity at the end of the day, at a discounted price of $1.50.
Every morning, Mr. Cross bakes 80 strawberry frosted donuts unless there is a special order. Each donut costs $3 to make, and it is sold for $5. Unsold donuts are given away to a charity at the end of the day, at a discounted price of $1.50. What will be Mr. Cross’s total earnings if he sells all 80 donuts?
Total revenue if all 80 donuts are soldRevenue = Total units sold × Selling price per unitSince there are 80 donuts and each donut costs $5,Total revenue if all 80 donuts are sold = 80 × 5 = $400Total cost if all 80 donuts are soldTotal cost of making all 80 donuts = Cost of one donut × Total units madeSince each donut costs $3,Total cost of making all 80 donuts = 3 × 80 = $240Total profitTotal profit = Total revenue - Total cost
Since revenue is $400 and the total cost is $240,Total profit = 400 - 240 = $160At the end of the day, unsold donuts are given away to charity at a discounted price of $1.50 each. Therefore, Mr. Cross’s total earnings would be $160 if he sold all 80 donuts.
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six less than six times a number
Answer:
6n-6 or 6(n-1)
Step-by-step explanation:
six times a number, n, can be shown as 6n. "Six less" indicates -6. So combining the two parts leaves 6n-6. This can be simplified to 6(n-1)
Sophie has a small cube-shaped box. Its volume is 64 cubic centimeters.
What is the area of one face of the box?
Answer:
The answer to your problem is, [tex]16cm^{2}[/tex]
Step-by-step explanation:
Sophie has a small cube shaped box.
Volume of the box is [tex]64cm^{3}[/tex]
We have to find the area of one face of the box.
Let one side of the box is x
Then volume = [tex]x^{3}[/tex] = 64
x³ = 4³
= 4
Now area of one face of the cube = x²
then area = 4² = 16 cm²
Thus the answer to your problem is, [tex]16cm^{2}[/tex]
Jace ran the 100-yard dash in 13.82 seconds. Amy ran the 100-yard dash in 12.98 seconds. How much faster did Amy run the race than Jace?
So, Amy ran the 100-yard dash 0.84 seconds faster than Jace.
What is equation?An equation is a mathematical statement that uses an equal sign to show that two expressions have the same value. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. The goal of an equation is to find the value of the variable that makes both sides of the equation equal.
Here,
To find out how much faster Amy ran the race than Jace, we need to calculate the difference in their times.
Amy's time = 12.98 seconds
Jace's time = 13.82 seconds
Difference in time = Amy's time - Jace's time
= 12.98 - 13.82
= -0.84 seconds
The difference is negative, which means that Jace was slower than Amy. To get the positive difference, we can take the absolute value of the difference:
|Difference| = |-0.84| = 0.84 seconds
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a coin is flipped 6 times. if more heads are flipped than tails, the probability that all 6 are heads is , what is the value of ?
The probability that all 6 flips result in heads is 1/64
The given coin is flipped 6 times. The number of heads and tails could vary from 0 to 6.Let H be the number of heads and T be the number of tails. Then the possible values of H and T are, H=0 and T=6 H=1 and T=5 H=2 and T=4 H=3 and T=3 H=4 and T=2 H=5 and T=1 H=6 and T=0
For the given question, it is given that more heads are flipped than tails.So the possible values of H are 4, 5 and 6.So the total number of possible outcomes with more heads than tails is the sum of the possible outcomes with 4, 5 and 6 heads which is, 1+6+15 = 22 (from the combinations formula)Now, the probability that all 6 flips result in heads, given more heads are flipped than tails is,
P(all 6 are heads) = P(H > T) × P(all 6 are heads | H > T)P(H > T) = 22/64
P(all 6 are heads | H > T) = 1/21 (there is only one possibility where all 6 flips are heads)
P(all 6 are heads) = P(H > T) × P(all 6 are heads | H > T) = (22/64) × (1/21) = 1/64
Therefore, the probability that all 6 flips result in heads, given more heads are flipped than tails is 1/64.
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The relation between hours studied and LSAT scores in a random sample of students is found to be S = 130 + 2.2h. How will a student’s score be affected if she studies for 10 hours?
Answer:
We can use the given equation to find the expected LSAT score (S) for a student who studies for 10 hours:
S = 130 + 2.2h
S = 130 + 2.2(10)
S = 130 + 22
S = 152
Therefore, if a student studies for 10 hours, we would expect her LSAT score to be 152.
I don’t know how to solve this
Answer:
18. x = 80°
19. y = 85°
Step-by-step explanation:
Opposite angles of an inscribed quadrilateral are supplementary.
18.
x + x + 20 = 180
2x = 160
x = 80
Answer: x = 80°
y + y + 10 = 180
2y = 170
y = 85
Answer: y = 85°
Answer: x = 80° and y = 85°
Step-by-step explanation: In a cyclic quadrilateral, opposite angles add up to 180°.
x + (x + 20) = 180 and
y + (y + 10) = 180.
Solving for x
x + (x + 20) = 180
x + x + 20 = 180
2x = 180 - 20
2x = 160
2x/2 = 160/2
x = 80°
Solving for y
y + (y + 10) = 180
y + y + 10 = 180
2y = 180 - 10
2y = 170
2y/2 = 170/2
y = 85°
1. if you repeated a hypothesis test 1000 times (i.e. 1000 different samples from the same population), how many times would you expect to commit a type i error, assuming the null hypothesis were true, if:
If we repeated a hypothesis test 1000 times, the number of times we would expect to commit a Type I error, assuming the null hypothesis were true, would depend on the significance level (α) of the test.
A Type I error occurs when we reject the null hypothesis when it is actually true. The significance level of a test (α) is the probability of making a Type I error when the null hypothesis is true. In other words, if we set a significance level of α = 0.05, we are saying that we are willing to tolerate a 5% chance of making a Type I error.
Assuming a significance level of α = 0.05, if we repeated the test 1000 times, we would expect to make a Type I error in approximately 50 tests (0.05 x 1000 = 50). This means that in 50 out of the 1000 tests, we would reject the null hypothesis even though it is actually true.
However, it is important to note that the actual number of Type I errors we make in practice may differ from our expectation, as it depends on the specific characteristics of the population being tested and the sample sizes used in each test.
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if hope has 4 more quarters than nickels and they have a combined value of 280 cents, how many of each coin does she have?
Hope has 6 nickels (x) and 10 quarters (x + 4).
How many of each coin Hope has if she has 4 more quarters than nickels and they have a combined value of 280 cents. To solve this problem, we can use algebraic equations.
Let's assume the number of nickels Hope has is x. Then, the number of quarters she has would be x + 4.
Now, we need to find the total value of the coins. Each nickel is worth 5 cents, so the total value of nickels is 5x cents. Similarly, each quarter is worth 25 cents, so the total value of quarters is 25(x + 4) cents. The combined value of the coins is 280 cents, so we can set up an equation:
5x + 25(x + 4) = 280
Simplify and solve for x:
5x + 25x + 100 = 280
30x = 180
x = 6
Therefore, Hope has 6 nickels (x) and 10 quarters (x + 4).
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