Putting it all together, we get:
A:
[-3 0 0]
[ 0 1 0]
[ 0 0 -1]
which is an orthogonal matrix with the first row being a multiple of (3, 3, 0).
An orthogonal matrix is a square matrix whose columns and rows are orthonormal vectors, i.e., each column and row has unit length and is orthogonal to the other columns and rows.
Let's start by finding a vector that is orthogonal to (3, 3, 0). We can take the cross product of (3, 3, 0) and (0, 0, 1) to get such a vector:
(3, 3, 0) x (0, 0, 1) = (3*(-1), 3*(0), 3*(0)) = (-3, 0, 0)
Note that this vector has length 3, so we can divide it by 3 to get a unit vector:
(-3/3, 0/3, 0/3) = (-1, 0, 0)
So, the first row of the orthogonal matrix A can be (-3, 0, 0) or a multiple of it. For simplicity, we'll take it to be (-3, 0, 0).
To find the remaining two rows, we need to find two more orthonormal vectors that are orthogonal to each other and to (-3, 0, 0). One way to do this is to use the Gram-Schmidt process.
Let's start with the vector (0, 1, 0). We subtract its projection onto (-3, 0, 0) to get a vector that is orthogonal to (-3, 0, 0):
v1 = (0, 1, 0) - ((0, 1, 0) dot (-3, 0, 0)) / ||(-3, 0, 0)||^2 * (-3, 0, 0)
= (0, 1, 0) - 0 / 9 * (-3, 0, 0)
= (0, 1, 0)
We can then normalize this vector to get a unit vector:
v1' = (0, 1, 0) / ||(0, 1, 0)|| = (0, 1, 0)
So, the second row of the orthogonal matrix A is (0, 1, 0).
To find the third row, we take the cross product of (-3, 0, 0) and (0, 1, 0) to get a vector that is orthogonal to both:
(-3, 0, 0) x (0, 1, 0) = (0, 0, -3)
We normalize this vector to get a unit vector:
v2' = (0, 0, -3) / ||(0, 0, -3)|| = (0, 0, -1)
So, the third row of the orthogonal matrix A is (0, 0, -1).
Putting it all together, we get:
A:
[-3 0 0]
[ 0 1 0]
[ 0 0 -1]
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solve for x
x+3 > 70
x+3< 70
Using inequalities we know that x=68 and x=66 respectively.
What are inequalities?A mathematical phrase in which the sides are not equal is referred to as being unequal.
In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.
So, solve the inequalities as follows:
x+3>70
x>70-3
x>67
Then, it will be x = 68.
Then,
x+3<70
x<70-3
x<67
Then, it will be s = 66.
Therefore, using inequalities we know that x=68 and x=66 respectively.
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heights of adults, bootstrap interval. researchers studying anthropometry collected body measurements, as well as age, weight, height and gender, for 507 physically active individuals. the histogram below shows the sample distribution of bootstrapped means from 1,000 different bootstrap samples.14 (heinz et al., 2003) a. given the bootstrap sampling distribution for the sample mean, find an approximate value for the standard error of the mean. b. by looking at the bootstrap sampling distribution (1,000 bootstrap samples were taken), find an approximate 90% bootstrap percentile confidence interval for the true average adult height in the population from which the data were randomly sampled. provide the interval as well as a one-sentence interpretation of the interval. c. by looking at the bootstrap sampling distribution (1,000 bootstrap samples were taken), find an approximate 90% bootstrap se confidence interval for the true average adult height in the population from which the data were randomly sampled. provide the interval as well as a one-sentence interpretation of the interval
a. The approximate value for the standard error of the mean is 0.22.
b. The approximate 90% bootstrap percentile confidence interval for the true average adult height in the population is [67.55, 68.81] inches, with a one-sentence interpretation being that we are 90% confident that the true average adult height in the population lies between 67.55 and 68.81 inches.
c. The approximate 90% bootstrap SE confidence interval for the true average adult height in the population is [67.67, 68.69] inches, with a one-sentence interpretation being that if we were to take many samples from the same population, then 90% of the intervals calculated using this method would contain the true average adult height in the population.
For a: To find an approximate value for the standard error of the mean, we can use the standard deviation of the bootstrap sampling distribution. From the histogram, we can estimate that the standard deviation is about 0.22, which gives us an approximate value for the standard error of the mean.
For b: To find an approximate 90% bootstrap percentile confidence interval for the true average adult height in the population, we can use the 5th and 95th percentiles of the bootstrap sampling distribution. From the histogram, we can estimate that the 5th and 95th percentiles are about 67.55 and 68.81 inches, respectively. Therefore, the approximate 90% bootstrap percentile confidence interval is [67.55, 68.81] inches. We can interpret this interval as saying that we are 90% confident that the true average adult height in the population lies between 67.55 and 68.81 inches.
For c: To find an approximate 90% bootstrap SE confidence interval for the true average adult height in the population, we can use the mean of the bootstrap sampling distribution plus or minus 1.645 times the standard error of the mean. From part (a), we estimated the standard error of the mean to be about 0.22. From the histogram, we can estimate that the mean of the bootstrap sampling distribution is about 68.18 inches. Therefore, the approximate 90% bootstrap SE confidence interval is [67.67, 68.69] inches. We can interpret this interval as saying that if we were to take many samples from the same population, then 90% of the intervals calculated using this method would contain the true average adult height in the population.
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Rafael has a spinner equally divided into 4 sections of different colors: red, blue, yellow, and green. He also has a fair 6-sided die. Find the probability the spinner lands on blue and he rolls an even number.
Answer:
Step-by-step explanation:
The probability of the spinner landing on blue is 1/4, since there are 4 equally likely outcomes.
The probability of rolling an even number on a fair 6-sided die is 3/6 or 1/2, since there are 3 even numbers (2, 4, 6) out of 6 possible outcomes.
To find the probability of both events happening together (landing on blue and rolling an even number), we multiply their probabilities:
P(blue and even) = P(blue) x P(even)
= 1/4 x 1/2
= 1/8
Therefore, the probability of the spinner landing on blue and rolling an even number is 1/8.
For which equations is 8 a solution? Select the four correct answers. x + 6 = 2 x + 2 = 10 x minus 4 = 4 x minus 2 = 10 2 x = 4 3 x = 24 StartFraction x Over 2 EndFraction = 16 StartFraction x Over 8 EndFraction = 1
The 8 s the solution of equation StartFraction x Over 8 EndFraction = 1 i.e., x/8 = 1. So, the correct option is D).
To determine for which equations 8 is a solution, we can simply substitute 8 for x in each equation and see if the equation holds true.
Substituting x = 8 in the given equations, we get
x + 6 = 8 + 6 = 14 (not equal to 8)
x + 2 = 8 + 2 = 10 (not equal to 8)
x - 4 = 8 - 4 = 4 (not equal to 8)
x - 2 = 8 - 2 = 6 (not equal to 8)
2x = 2(8) = 16 (not equal to 8)
3x = 3(8) = 24 (not equal to 8)
x/2 = 8/2 = 4 (not equal to 8)
x/8 = 8/8 = 1 (equal to 8)
Therefore, only one equation x/8 = 1 has 8 as a solution.
Mathematically, we can evaluate this equation as follows
x/8 = 1
Multiplying both sides by 8
x = 8 * 1
x = 8
Since we have substituted x=8 and obtained the same value on both sides of the equation, the equation holds true for x=8. So, the correct answer is D).
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A cylinder has a radius of 16 inches. Its volume is 13,665. 28 cubic inches. What is the height of the cylinder?
Use ≈ 3. 14 and round your answer to the nearest hundredth
The height of the cylinder is 17.00 inches, under the given condition that radius of the cylinder is 16 inches, volume is 13,665. 28 cubic inches and have to round the answer to the nearest hundred.
Therefore, the volume of a cylinder is given by V = πr²h
Here,
V= volume of the cylinder,
r= radius of the cylinder
h= height
Given that the radius of the cylinder is 16 inches and its volume is 13,665.28 cubic inches, then we can proceed to evaluate the height of the cylinder
V = πr²h
h = V / (πr²)
h = 13665.28 / (π(16)²)
h = 13665.28/ 3.14 x (256)
h = 13665.28/ 803.8
h = 17.00 inches
Then, the height of the cylinder is approximately 17.00 inches.
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two similar bottles are shown. the smaller bottle can hold 500 ml of water. how much can the larger bottle hold?
Answer:
Step-by-step explanation:
Since the two bottles are similar, we know that they have the same shape, but the larger bottle is scaled up by a certain factor compared to the smaller bottle. Let's denote this scaling factor by k.
The volume of the smaller bottle is 500 ml, so we can set up the following proportion between the volumes of the two bottles:
volume of larger bottle / volume of smaller bottle = k³
Since the scaling factor applies to all three dimensions of the bottle, we need to use k³ instead of just k. We want to solve for the volume of the larger bottle, so we can rearrange the proportion to isolate the volume of the larger bottle:
volume of larger bottle = (k³) * volume of smaller bottle
We don't know the value of k, but we do know that the bottles are similar, which means that corresponding dimensions are proportional. In particular, the ratio of corresponding lengths is k, the ratio of corresponding widths is k, and the ratio of corresponding heights is k. Therefore, we have:
k (corresponding length) = k (corresponding width) = k (corresponding height)
We also know that the smaller bottle has a volume of 500 ml, which is equivalent to 0.5 liters. We can use this information to solve for k:
0.5 liters = (1/1000) cubic meters = (k³) * (1/1000) cubic meters
Simplifying, we get:
k³ = 500/1000 = 1/2
Taking the cube root of both sides, we get:
k = (1/2)^(1/3)
Now we can substitute this value of k into the formula we derived earlier to find the volume of the larger bottle:
volume of larger bottle = ((1/2)^(1/3))³ * 500 ml
Simplifying, we get:
volume of larger bottle = (1/2) * 500 ml = 250 ml
Therefore, the larger bottle can hold 250 ml of water.
5x2 - 27 ÷ y - (9 + 13)
What is the value of the expression when x = 10 and y = 9?
The value of [tex]5x^{2} - 27[/tex] ÷ y - (9 + 13) when x = 10 and y = 9 is 2501
What is BODMAS?BODMAS is an acronym and it standsB = BracketO = OrderD = DivisionM = MultiplicationA = AdditionS = Subtraction
How to determine this
[tex]5x^2 - 27 /y - (9 + 13)[/tex]
Where x = 10y = 9By substituting the values
[tex]5(10)^2 - 27 / y - (9 + 13)[/tex]
By removing bracket [tex]50^2 - 27 / 9 - 9 + 13[/tex]
Order, by finding the square root of 502500
- 27 / 9 - 9 + 13
By dividing
2500 - 27/9 - 9 + 132500 - 3 - 9 + 13
By addition
2500 + 13 - 3 - 92513 - 3 - 9
By subtraction
2513 - 12= 2501
Therefore, the value of the expression is 2501
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Answer:
Step-by-step explanation:
Find the length of segment BC
Answer: 4
Step-by-step explanation:
It creates a right triangle.
one leg is 3
the hypotenuse is 5 (the key here is to know that the radius is 5 and can be moved anywhere
the last leg is BC which is what you are looking for
so use pythagorean
c²=a²+b²
5²=3²+BC²
25-9=BC²
BC=√16
BC=4
suppose we have five coins, and each coin has a different probability of showingheads when flipped. the probabilities of getting heads for each coin are 0.1, 0.2,0.3, 0.4 and 0.5. assume we toss all five coins at the same time. what is theexpected value of the number of heads?
The expected number of heads when all the 5 coins are tossed at the same time is 1.5, under the condition that the probabilities of getting heads for each coin are 0.1, 0.2,0.3, 0.4 and 0.5.
Then the expected value of the number of heads can be evaluated by multiplying each probability with its corresponding number of heads and suming them.
For the given case, we possess five coins with different probabilities of getting heads when flipped.
Therefore, getting heads for each coin in context of probability are 0.1, 0.2, 0.3, 0.4 and 0.5
Now, the expected value of the number of heads is
Expected value = [tex](0.1 * 1) + (0.2 * 1) + (0.3 * 1) + (0.4 * 1) + (0.5 * 1)[/tex]
= 0.1 + 0.2 + 0.3 + 0.4 + 0.5
=1.5
The expected number of heads when all the 5 coins are tossed at the same time is 1.5, under the condition that the probabilities of getting heads for each coin are 0.1, 0.2,0.3, 0.4 and 0.5.
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Solver for x.
-2cosx+2cos2x =0
To solve for x in the equation -2cosx+2cos2x=0, we can use the trigonometric identity cos2x = 2cos^2x - 1 to rewrite the equation as:
-2cosx + 4cos^2x - 2 = 0
Next, we can rearrange the terms and factor out a 2 to obtain:
2cos^2x - cosx - 1 = 0
This is now a quadratic equation in terms of cosx. We can solve for cosx using the quadratic formula:
cosx = [1 ± sqrt(1 - 4(2)(-1))] / (2(2))
cosx = [1 ± sqrt(9)] / 4
cosx = (1/2) or (-1/2)
Now, we need to find the values of x that correspond to these values of cosx. We can use inverse trigonometric functions to do this:
cosx = 1/2 => x = π/3 + 2πn or x = 5π/3 + 2πn, where n is an integer.
cosx = -1/2 => x = 2π/3 + 2πn or x = 4π/3 + 2πn, where n is an integer.
Therefore, the solutions for x are:
x = π/3 + 2πn, x = 2π/3 + 2πn, x = 4π/3 + 2πn, x = 5π/3 + 2πn, where n is an integer.
Drive-Up Banking Arrivals. Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at ran-dom, with an arrival rate of 24 customers per hour or 0. 4 customers per minute. Assume the Poisson probability distribution can be used to describe the arrival process
There is a 67.03% probability that no customers will arrive at the drive-up teller window in one minute.
The Poisson distribution formula can be used to calculate the probability of a specific number of customer arrivals in a given time interval. For example, if we want to calculate the probability of two customers arriving at the drive-up teller window in one minute, we can use the following formula:
P(X=2) = (e⁻⁰°⁴)*(0.4²)/2!
where P(X=2) is the probability of two customer arrivals, e is the base of the natural logarithm, and 2! is the factorial of 2.
Using this formula, we can calculate the probability of any number of customer arrivals in one minute. For instance, the probability of no customers arriving in one minute is:
P(X=0) = e⁻⁰°⁴ = 0.6703
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Use the Pythagorean Theorem to find x.
Answer:
11
Step-by-step explanation:
The Pythagorean theorem states that in a right triangle, [tex]a^2+b^2 = c^2[/tex] , where c is the hypotenuse, and a and b are the legs. So to use the Pythagorean theorem, we let [tex]a=x-3,b=x+4[/tex] and [tex]c=x+6[/tex]. Expanding everything gives [tex]2x^2+2x+25=x^2+12x+36[/tex]
Moving everything to one side tells us
[tex]x^2-10x-11=0[/tex]
So
[tex](x-11)(x+1)=0[/tex]
This means that either x = 11 or x = -1. But looking back at our equation, x = -1 is a false solution, because sides of a triangle could not be negative in length, and x-3 = -4 when x =-1. Therefore x = 11.
PLS HELPP 20 POINTS
A box contains hair clips of 3 diff sizes. -15 small hair clips -12 medium hair clips -6 large hair clips
If one hair clip is randomly selected from the box,what is the probability that the hair clip will be either small or medium?
A)9/11
B)3/7
C)2/9
D)1/6
Answer: 17/33
Step-by-step explanation:
Or means add the 2 probabilities
There are a total of 33 outcomes.
getting a small clip is 15/33
getting a medium clip is 12/33
add the two probabilities 15/33 +12/33 = 17/33
I'm sure of my numbers. I think the question is off or answers
In 1972 a Honda Civic went for $2000, today a Honda civic sells for around $25000. The rate of inflation is %
Answer:
5.1%
Step-by-step explanation:
You want the rate of inflation if the price of a Honda Civic increase from $2000 in 1972 to $25000 in 2023.
InflationThe rate of inflation can be computed from ...
r = (p1/p0)^(1/t) -1
r = (25000/2000)^(1/51) -1 ≈ 0.05077 ≈ 5.1%
The rate of inflation is about 5.1%.
__
Additional comment
The question refers to "today," but we don't know exactly what is intended by that. The year at the time of this writing has been used. The required answer may vary, depending on the intended number of years.
<95141404393>
50 POINTS PLEASE ANSWER ASAP!!
1. Consider the pyramid. (a) (b) Answer: 4 in 6 in 4 in Draw and label a net for the pyramid. Determine the surface area of the pyramid. Show your work.
I drew the net but I need to make sure I don't label it wrong!
The surface area of the square pyramid is 40.86 in²
What is the surface area of the Pyramid?The formula of surface area of square pyramid is given as;
S.A = a² + 2a√(a²/4 + h²)
h = height of the pyramid
a = side length of the base
However, we don't know the height of the pyramid, but we can apply Pythagorean theorem.
x² = y² + z²
6² = h² + 2²
NB: Half the length of the base is the length of one of the legs of the triangle.
h² = 36 - 4
h = √32
Substituting the value of h into the formula of surface area of the square pyramid;
S.A = 4² + 2(4)√(4²/4) + √32)
S.A = 40.86 in²
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liquid polymer is supplied to a water treatment plant as an 8% solution. how many gallons of liquid polymer should be used to make 55 gallons of a 0.5% polymer solution?
The amount of 8% liquid polymer to make 55 gallons of a 0.5% polymer solution is around 3.4 gallons.
The relationship between concentration and volume will be used to find the volume of liquid polymer. The formula to be used is -
[tex] C_{i}[/tex] [tex] V_{i}[/tex] = [tex] C_{o}[/tex] [tex] V_{o}[/tex], where [tex] C_{i}[/tex] and [tex] C_{o}[/tex] are initial and final concentration and [tex] V_{i}[/tex] and [tex] V_{o}[/tex] are initial and final volume.
Keep the values in formula -
[tex] C_{i}[/tex] × 8% = 55 × 0.5%
Rearranging the equation
[tex] C_{i}[/tex] = 55 × 0.5%/0.8%
Performing multiplication and division on Right Hand Side of the equation
[tex] C_{i}[/tex] = 3.4375 gallons
Hence, the volume of liquid polymer is around 3.4 gallons.
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Mínimo común múltiplo y máximo divisor ejemplos
The graph of a quadratic function is shown. What is the equation of this function in f(x)=ax^2+bx+c form?
Answer:
[tex]f(x)=3x^2+12x+9[/tex]
Step-by-step explanation:
Recall that the factored form of a quadratic is:
[tex]f(x)=a(x-r_{1} )(x-r_{2})[/tex]
Where r1 and r2 are the roots of the quadratic.
As shown in the image, the x-intercepts are (-3, 0) and (-1, 0).
Since these are the values of x when y=0, they are the roots of the quadratic equation. Let's plug them in. We get:
[tex]f(x)=a(x-(-3)(x-(-1)=\\f(x)=a(x+3)(x+1)=\\f(x)=a(x^2+4x+3)[/tex]
We are given that the point (-2, -3) also belongs to the graph. This means that when x=-2, y=-3. Let's plug in those points and solve for a:
[tex]f(x)=a(x+3)(x+1)=\\-3=a(-2+3)(-2+1)=\\-3=a(1)(-1)=\\-3=-a=\\3=a[/tex]
Now, let's go back to the equation:
[tex]f(x)=a(x^2+4x+3)[/tex]
and substitute a with 3, then solve.
[tex]f(x)=a(x^2+4x+3)=\\f(x)=3(x^2+4x+3)=\\f(x)=3x^2+12x+9[/tex]
Thus, the equation of this function is [tex]f(x)=3x^2+12x+9[/tex]
If 124n = 232five, find n.
Answer:
18.75 or 1.87
Step-by-step explanation:
If its 124n=2325, n is 18.75
If its 124n=232, n is 1.87
First, complete the sentence to show how the figure can be decomposed into triangles and rectangles with the fewest number of pieces.
Then find the area of the divisions.
A 7-sided figure has a rectangle at one end and a triangle at the other end. The height of the triangle is 4 meters. The length and height of the triangle are 3 and 4 meters. A square in between has 4 meters length and height.
CLEAR CHECK
Divide the figure into triangles and rectangles with the fewest number of divisions.
The figure will have
and
.
Find the total area of the triangles.
The triangles have a combined area of
m2
.
Find the total area of the rectangles.
The rectangles have a combined area of
m2
.
Find the total area of the figure.
The figure has a total area of
m2
.
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ENGLISH
The total area of the given figure is 34 square meter.
The figure can be divided into two triangles and one rectangle. The triangle at one end is 3 m long and 4 m high, while the triangle at the other end has a base of 4 m and a height of 3 m. The rectangle in between has a length and width of 4 m.
The total area of the triangles is 1/2 ×Base×Height= 1/2×3×4 + 1/2×4×3
= 18 m²
The total area of the rectangles is 4 × 4 = 16 m²
The total area of the figure is 18 + 16 = 34 m²
Therefore, the total area of the given figure is 34 square meter.
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A scientist who studies fossils is known as a paleontologist. If a paleontologist finds a fossil of animal remains with 88.5% as much Carbon-14 as the animal would have contained if the animal were alive today, how long ago did the animal live?
Use the formula for Carbon-14: y=ae (exponent) -0.00012t
The time for which the animal lived based on the given parameters is: 1018 years
How to solve exponential decay functions?Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time. It can be expressed by the formula y = a(1 - b)ˣ
where:
y is the final amount
a is the original amount
b is the decay factor
x is the amount of time that has passed.
We are told that a paleontologist finds a fossil of animal remains with 88.5% as much Carbon-14 as the animal would have contained if the animal were alive today. Thus:
y/a = 88.5% = 0.885
Thus:
0.885 = e^(−0.00012t)
In 0.885 = -0.00012t
t = 1018 years
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john measured a line to be 1.7 inches long. if the actual length of the line is 2.1 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
Therefore, the percent error is approximately 19.0% (rounded to the nearest tenth of a percent).
The percent error is a measure of the accuracy of a measurement or calculation. It is calculated by taking the absolute value of the difference between the measured or calculated value and the actual or accepted value, dividing that difference by the actual or accepted value, and then multiplying by 100 to express the result as a percentage.
The formula for percent error is:
% error = |(measured or calculated value - actual or accepted value) / actual or accepted value| x 100
The formula for percent error is:
(percent error) = [(|measured value - actual value|) / actual value] x 100%
Substituting the given values:
(percent error) = [(|1.7 - 2.1|) / 2.1] x 100%
(percent error) = [0.4 / 2.1] x 100%
(percent error) = 0.190476 x 100%
(percent error) = 19.0%
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in a lottery daily game, a player picks three numbers from 0 to 9 (without repetition). how many different choices does the player have
In a lottery daily game, a player picks three numbers from 0 to 9 (without repetition) there are 120 ways of choices that can be calculated with combinations.
A player picks three numbers from 0 to 9 in a lottery daily game without any repetition of digits). There is no specification of order.
Since we are not specified that there will be some order in selection of digits (we can assume that there is no such order). Hence .
Therefore, we apply the formula of combinations as the order of items does not matter in case of combinations.
By applying the formula of combinations with no repetition we get,
Number of choices the player has in a lottery game is = nCr = n! /{( n - r)! r!}
where, n is the total number of digits, that is n = 10
and r is the number of required digits, r = 3
Number of choices the player has in a lottery game is = 10 ! /{ ( 10-3)! 3!}
= 120
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assume that the heights of adult caucasian women have a mean of 63.6 inches and a standard deviation of 2.5 inches. if 40 women are randomly selected, find the probability that they have a mean height greater than 64.0 inches
The probability that a random sample of 40 adult caucasian women have a mean height greater than 64.0 inches is approximately 0.1569 or 15.69% (rounded to four decimal places).
We can use the central limit theorem to approximate the distribution of the sample mean as normal, with mean μ = 63.6 inches and standard deviation σ/√n = 2.5 inches/√40 = 0.3953 inches.
Thus, we need to find the probability that a normally distributed random variable with mean μ = 63.6 inches and standard deviation σ/√n = 0.3953 inches is greater than 64.0 inches.
Using the z-score formula, we can standardize the value of 64.0 inches to get:
z = (64.0 - 63.6) / 0.3953 = 1.011
From the standard normal distribution table, the probability of a z-score greater than 1.011 is 0.1569.
The central limit theorem is a statistical concept that describes the behavior of the means of a large number of independent random variables. It states that when the sample size is large enough, the distribution of the means will be approximately normal, even if the underlying variables are not normally distributed.
Specifically, the theorem states that as the sample size increases, the mean of the sample means approaches the population mean and the standard deviation of the sample means are close to the population standard deviation when the sample size is squared. This theorem is important because it allows us to make statistical inferences about a population based on a sample. For example, we can use it to estimate the mean and variance of a population, or to calculate confidence intervals and hypothesis tests.
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Complete Question:-
Assume that the heights of adult caucasian women have a mean of 63.6 inches and a standard deviation of 2.5 inches. if 40 women are randomly selected, find the probability that they have a mean height greater than 64.0 inches. round to four decimal places.
Golf Tournament In a golf tournament, the top 6 men's scores are 65, 68, 70, 72, 73, 75. The top women's scores are 69, 71, 73, 74, 77, 80. Compare the spread of the data for the two sets of scores using (a) the range and (b) the mean absolute deviation.
The spread of the women's scores is therefore somewhat larger than the spread of the men's scores based on the range.
The MAD indicates that the men's score spread is marginally less than the women's score spread.
How to explain the rangeThe difference between a dataset's largest and lowest values is known as the range.
The range for the men's scores is: 75 - 65 = 10.
The range for the women's scores is 80 - 69 = 11.
The spread of the women's scores is therefore somewhat larger than the spread of the men's scores based on the range.
The average distance between each data point and the dataset's mean is measured by the mean absolute deviation (MAD).
Find the mean first before calculating the MAD for the men's scores:
(65 + 68 + 70 + 72 + 73 + 75) / 6 = 70.5
The MAD indicates that the men's score spread is marginally less than the women's score spread.
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The number of bottles a machine fills is proportional to the number of minutes the machine operates. The machine fills 250 bottles every 20 minutes. Create a graph that shows the number of bottles, y, the machine fills in x minutes.
How do i do this if the minutes only go up to 9 and the y axis is only 125???
Answer:
Since the machine fills 250 bottles every 20 minutes, we can write the proportion:
250 bottles / 20 minutes = y bottles / x minutes
Simplifying this proportion, we get:
y = (x/20) * 250
This equation represents a linear relationship between the number of bottles (y) and the number of minutes (x), where the slope is 250/20 = 12.5 bottles per minute.
To create a graph, you can plot the points (0, 0) and (9, 112.5) since the y-axis only goes up to 125. This will give you a straight line that starts at the origin and goes up to about 112.5 on the y-axis at x = 9.
Step-by-step explanation:
Harlan is building a fence. After he sets the corner post, he uses 2 eight-foot posts, 4 braces, and 48 feet of paneling for every 12 feet of fence. Harlan needs to build 60 feet of fence today and he has 208 feet of paneling. How many more feet of paneling does he need?
Forty-five people were asked about how many miles they walked in one week. The results are shown in the graph. What is the mean number of miles walked by the girls?
5 4/11 miles
5 6/25 miles
5 1/2 miles
5 miles
5 1/8 miles
The average distance walked is 5 + 4/11 miles.
What is the mean number of miles walked by the girls?By using the graph we can see that:
5 girls walked 4 miles.9 girls walked 5 miles3 girls walked 6 miles.5 girls walked 7 milesSo there are a total of:
5 + 9 + 3 + 5 = 22 girls.
And the average distance walked is:
A = (5*4 + 9*5 + 3*6 + 5*7)/22
A = 118/22 = 110/22 + 8/22 = 5 + 8/22 = 5 + 4/11
So the correct option is the first one.
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-6
What is the line's slope?
-2
6
N
-2
-4
-6
2
4
Step-by-step explanation:
To find the slope of the line, we need to select any two points on the line and then use the slope formula:
slope = (y2 - y1) / (x2 - x1)
Let's choose the points (-2, 6) and (2, -6) on the line. Then, we can calculate the slope as:
slope = (-6 - 6) / (2 - (-2))
slope = -12 / 4
slope = -3
Therefore, the slope of the line is -3.
please help :)
Triangle HJK and triangle PMK are similar right triangles. The coordinates of all the vertices are integers.
Which statement is true about the slope of HK and the slope of PK?
The slope of HK is equal to the slope of PK because the ratio in the change in the y values of the endpoints to the change in x values of the endpoints is the same for HK as it is for PK.
Hence the correct option is (G).
Here in the given graph we can see that H, P, K are on the same line that is the points H, P, K are collinear.
We know that in Cartesian Coordinate Plane, the slope of one line is unique.
Slope = (Change in y coordinate)/(Change in x coordinate)
We can see that the coordinates are:
H = (-12, 10)
K = (-4, 5)
P = (4, 0)
So the slope of HK = (10 - 5)/(-12 - (-4)) = 5/(-8) = -5/8
Slope of PK = (5 - 0)/(-4 - 4) = 5/(-8) = -5/8
Hence the slope of HK is equal to the slope of PK because the ratio in the change in the y values of the endpoints to the change in x values of the endpoints is the same for HK as it is for PK.
So the correct option will be (G).
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