No, we would not expect about 95% of the samples to have their variances within 0.008 of 0.009.
The variance of a normal distribution with mean μ and variance σ^2 is given by σ^2, which in this case is equal to (0.004)^2 = 0.000016.
The variance of the sample means, on the other hand, is given by σ^2/n, where n is the sample size. In order for about 95% of the samples to have variances within 0.008 of 0.009, we would need the sample size to be approximately equal to:
n ≈ σ^2 / (0.008 - 0.009)^2 = 62500
This means that we would need very large samples for this to be true. However, if the sample size is relatively small, then the distribution of sample means will not necessarily be normal and the Central Limit Theorem may not apply.
In that case, the distribution of sample variances will not necessarily follow the same pattern as the distribution of the population variance, and it may not be possible to make predictions about the sample variances based on the population parameters.
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Write the equation in standard form of the line y=1/9x+5
The equation in standard form is x - 9y = -45.
What is the Equation of a Line in Standard Form?The equation of a line in standard form is Ax + By = C, where x and y are variables and A, B and C are integers.
Given equation is y = 1/9 x + 5.
Here 1/9 is not an integer.
So multiplying the equation throughout by 9, we get,
9y = x + (5 × 9)
9y = x + 45
Subtracting both sides by x,
9y - x = 45
-x + 9y = 45
Multiplying throughout by -1,
x - 9y = -45, which is in standard form.
Hence the equation is x - 9y = -45 in standard form.
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16. The diagram shows a sketch of the graph y = ab^x where b>0
The curve passes through the points A (1, 10) and B (4,80).
The point C (-1, k) lies on the curve.
Find the value of k.
I don’t what exponential graphs are and I don’t understand what the question means!!!
Answer:
k is 2.5.
Step-by-step explanation:
To find the value of k, we can use the information given about points A and B to find the value of the parameters a and b. Since we know that the curve passes through A (1, 10) and B (4, 80), we can substitute these points into the equation y = ab^x to find the values of a and b.
Starting with point A:
10 = a * b^1
Next, using point B:
80 = a * b^4
We can now use these two equations to find the value of b:
10 = a * b^1
80 = a * b^4
Dividing the second equation by the first equation:
8 = b^3
Taking the cube root of both sides:
b = 2
We can now use either of the two equations to find the value of a:
10 = a * b^1
a = 10/2 = 5
Now that we have found the values of a and b, we can substitute the point C (-1, k) into the equation y = ab^x to find the value of k:
k = 5 * 2^(-1) = 5 * (1/2) = 2.5
So the value of k is 2.5.
1. You need to dig a tunnel. You begin at the surface of the ground. The tunnel slopes downward for 83 meters. The final depth below ground is 52 meters. Find the angle of depression of the tunnel's descent. Round your answer to the nearest tenth. Draw a diagram to illustrate your problem.
Answer: 38.8°
Step-by-step explanation:
See the attached diagram:
From it we can tell that the tunnel forms a right triangle, with the length of a leg and the hypotenuse given. We can use the sine function to easily answer this, (letting θ be the angle we need to find)
sinθ = 52/83
.: θ = arcsin(52/83)
(Note: arcsin is the inverse of the sine function)
.: θ ≅ 38.8°
pls help due now!!!!!!!!!!!!!!!
Answer: D. 6 cm
Step-by-step explanation:
V = 4/3πr^3
r = (3 V/4π)^1/3 = (3* 900/4*π)^1/3 = 5.98942
Please help! Find the area of the shaded regions. give your answer a completely simplified exact value of the terms of pi (no approximations)
For given circle, Area of shaded region is 52π cm².
What exactly is a circle?
A circle is a kind of ellipse with zero eccentricity and two foci that are coincident. A circle is also known as the locus of points drawn at equal distances from the center. The radius of a circle is the distance from its center to its outside line. The diameter of a circle is the line that divides it into two equal sections and is equal to twice the radius.
The equation for a circle in the plane is:
(x-h)^²+ (y-k)² = r²
When the coordinate points are (x, y)
(h, k) is the coordinate of a circle's center.
where r is the circumference of a circle.
where circle area = πr²
Circle circumference=2πr
Now,
Radius of biggest circle = 8cm
radius of unshaded circle= 4cm and
radius of smaller shaded circle= 2cm
Then,
Area of shaded region= Area of biggest circle - area of white circle + area of smaller shaded circle
=π*8² - π*4² + π*2²
=64π-16π+4π
=52π cm²
hence,
Area of shaded region is 52π cm².
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7. Find the value of w in the regular heptagon
whose interior angle has a measure of
(w + 8). Round your answer to the nearest
hundredth.
Answer: 96
The sum of the interior angles of a regular heptagon is equal to (n-2)180 degrees, where n is the number of sides of the polygon.
Since a regular heptagon has 7 sides, the sum of its interior angles is (7-2)180 = 720 degrees.
Therefore, the measure of each interior angle is 720 degrees / 7 = 104 degrees.
If the measure of an interior angle is (w + 8) degrees, then w + 8 = 104.
Solving for w, we get w = 96.
What is the volume of a right circular cylinder with a diameter of 10 meters and a height of 16 meters? Leave the answer in terms of π.
400π m3
1,600π m3
160π m3
1,256π m3
The volume of a right circular cylinder with a diameter of 10 meters and a height of 16 meters is 400π m³.
What is Volume?Volume is the amount of space occupied by an object in three dimensions. It is a measure of how much space is contained within a solid shape, such as a cube, sphere, or cylinder. The unit of volume can vary based on the system of measurement being used, but common units include cubic meters, cubic centimeters, liters, and gallons. Volume is calculated by multiplying the area of the base of the object by its height or depth, depending on the shape of the object.
The volume of a right circular cylinder is given by the formula V = πr²h, where V is the volume of the cylinder, r is the radius of the circular base, and h is the height of the cylinder.
In words, the volume of a right circular cylinder is equal to the area of the circular base (πr²) multiplied by the height (h). This formula holds true regardless of the dimensions of the cylinder, as long as it has a circular base and straight sides that are perpendicular to the base.
The volume of a right circular cylinder is given by the formula V = πr²h, where r is the radius of the circular base and h is the height of the cylinder.
Since the diameter of the circular base is 10 meters, the radius is half of that, or 5 meters. The height of the cylinder is 16 meters.
Substituting these values into the formula, we get:
V = π(5)²(16) = 400π
Therefore, the volume of the cylinder is 400π cubic meters.
So the answer is 400π m³.
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hey can someone help me
if a seed is planted, it has a 69% chance of growing into a healthy plant. let x be the number of seeds grow into healthy plants when 75 seeds are planted. what is the distribution of x? x ~ ? (,) please show the following answers to 4 decimal places. what is the probability that exactly 44 seeds grow into healthy plants? what is the probability that at least 44 seeds grow into healthy plants? what is the probability that more than 44 seeds grow into healthy plants? what is the probability that between 19 and 53 (including 19 and 53) seeds grow into healthy plants?
The probability that between 19 and 53 (including 19 and 53) seeds grow into healthy plants is 0.9941.
The probability distribution of x, where x is the number of seeds that grow into healthy plants when 75 seeds are planted, is a binomial distribution with parameters n = 75 and p = 0.69. The probability of x = 44 is calculated by using the formula for the probability mass function of the binomial distribution:
[tex]P(x=44) = (75 choose 44) * (0.69)^44 * (1-0.69)^(75-44) = 0.1578[/tex]
The probability of x >= 44 is calculated by using the formula for the cumulative probability function of the binomial distribution:
[tex]P(x > = 44) = 1 - P(x < = 43) = 1 - (75 choose 43) * (0.69)^43 * (1-0.69)^(75-43) = 0.7406[/tex]
The probability of x > 44 is calculated by subtracting the probability of x = 44 from the probability of x >= 44:
P(x > 44) = P(x >= 44) - P(x = 44) = 0.7406 - 0.1578 = 0.5828
The probability of 19 <= x <= 53 is calculated by subtracting the probability of x <= 18 from the probability of x <= 53:
[tex]P(19 < =x < =53) = P(x < =53) - P(x < =18) = 0.9994 - 0.0053 = 0.9941[/tex]
Therefore, the probability that exactly 44 seeds grow into healthy plants is 0.1578, the probability that at least 44 seeds grow into healthy plants is 0.7406, the probability that more than 44 seeds grow into healthy plants is 0.5828, and the probability that between 19 and 53 (including 19 and 53) seeds grow into healthy plants is 0.9941.
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78miles on 3gallons is it 26
Answer:
Yes, 26
Step-by-step explanation:
78 miles ÷ 3 gallons = 26 mpg
5. Rajah 2 menunjukkan sebuah silinder dan sebuah kuboid. Diagram 2 shows a cylinder and a cuboid. Guna / Use = 271 30 cm Rajah 2/ Diagram 2 Diberi bahawa isi padu silinder dan kuboid adalah sama. Cari nilai x dan berikan jawapan anda betul kepada dua tempat perpuluhan. It is given that the volume of the cylinder and the cuboid are the same. Find the value of x and give your answer correct to two decimal places. Jawapan / Answer: 7 cm 8 cm [3 markah/ 3 marks] For Examine Us
who can help me pls
Answer:
Step-by-step explanation:
5. Diagram 2 shows a cylinder and a cuboid. Diagram 2 shows a cylinder and a cuboid. Fold / Use = 271 30 cm Find the value of x and give the correct answer to the multiple of two places. It is given that the volume of the cylinder and the cuboid are the same. Find the value of x and give your answer correct to two decimal places. Answer / Answer: 7 cm 8 cm [3 markah/ 3 marks] For Examine Us
what are the lengths or each side?
Answer:
5
Step-by-step explanation:
The rule of the sides of a triangle is that the sum of the lengths of any two sides of a triangle is always greater than the length of the third side. This rule is also known as the triangle inequality theorem.
write x=[tex]\sqrt{y^2-3}[/tex] as a set of parametric equations with x =[tex]\sqrt{} t[/tex]
The set of parametric equations are
[tex]x=\sqrt{t}[/tex]
[tex]y=\sqrt{3+t[/tex]
Parametric Equations:A parametric equation uses a parameter, which is an independent variable (often represented by the notation t), and dependent variables, which are expressed as continuous functions of the parameter and are independent of other variables.
Using one or more independent variables known as parameters, a parametric equation defines a set of quantities as functions.
Given the equation:
[tex]x= \sqrt[]{y^{2}-3 }[/tex]
Let's find a set of parametric equation for the given equation given the parameter:
[tex]x = \sqrt{t}[/tex]
From the parameter:
[tex]x = \sqrt{t}[/tex]
Now, substitute [tex]\sqrt{t}[/tex] for x in the given equation:
[tex]x=\sqrt{y^2-3} \\\\\sqrt{t} = \sqrt{y^2 - 3} \\\\t=y^2-3\\\\y^2=3+t\\\\y=\sqrt{3+t}[/tex]
Therefore, the set of parametric equations is:
• [tex]x=\sqrt{t}[/tex]
• [tex]y=\sqrt{3+t}[/tex]
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Segment has endpoints (−7, 14) and (11, 5). Point lies on at (−3, 12).
What is the ratio of to ?
Last time I asked the question Brainly decided to delete like 90% of my question.
The ratio of the coordinate point on the line is 2 to 7.
What is the ratio of the point on the coordinate?The ratio of the coordinate point on the line is calculated as follows;
Let the coordinate points = (xp, yp)
Let the ratio of the line = a:b
xp = x₁ + (a/(a+b) (x₂ - x₁)
yp = y₁ + (a/a+b) (y₂ - y₁)
-3 = -7 + ( a/a+b)(11 - - 7)
-3 = -7 + (a/a+b)(18)
-3(a + b) = -7(a+b) + 18a
7(a + b ) - 3(a+b) = 18a
7a + 7b - 3a - 3b = 18a
4b = 14a
4/14 = a/b
2/7 = a/b
2 : 7 = a : b
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uppose that shoe sizes of american women have a bell-shaped distribution with a mean of 8.06 and a standard deviation of 1.52 . using the empirical rule, what percentage of american women have shoe sizes that are between 6.54 and 9.58 ?
Using the empirical rule, we can conclude that approximately 68% of American women have shoe sizes between 6.54 and 9.58.
Using the empirical rule, we can say that approximately 68% of the data falls within one standard deviation of the mean, approximately 95% of the data falls within two standard deviations of the mean, and approximately 99.7% of the data falls within three standard deviations of the mean.
To find the percentage of American women who have shoe sizes between 6.54 and 9.58, we first need to standardize these values by subtracting the mean and dividing by the standard deviation:
z1 = (6.54 - 8.06) / 1.52 = -1.00
z2 = (9.58 - 8.06) / 1.52 = 1.00
Now, we can use the empirical rule to find the percentage of women with shoe sizes between z = -1.00 and z = 1.00. Since this interval corresponds to one standard deviation from the mean, we know that approximately 68% of the data falls within this range.
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In a family the oldest child is 7 years older than the youngest child what is a equation to represent this situation
The equation to represent the situation where the oldest child is 7 years older than the youngest child, using x for the age of the youngest child and y for the age of the oldest child, is y = x + 7.
If we let x represent the age of the youngest child in a family, then we can say that the oldest child is 7 years older than the youngest child. We can represent the age of the oldest child using the expression "x + 7", because if we add 7 to the age of the youngest child, we get the age of the oldest child.
Therefore, we can write an equation to represent this situation by equating the age of the oldest child to the age of the youngest child plus 7. This can be written as:
x + 7 = Oldest child's age
where x is the age of the youngest child, and "Oldest child's age" represents the age of the oldest child in the family. This equation tells us that if we know the age of the youngest child, we can find the age of the oldest child by adding 7 to it.
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Please help me on this I am confused find the value of x pls pls pls pls pls pls pls pls pls pls pls pls pls.
The value of x is given as follows:
x = 130º.
How to obtain the value of x?To obtain the value of x, we must consider the exterior angle theorem, which states that each interior angle is supplementary with it's interior angle, meaning that the sum of their measures is of 180º.
As the interior angle is of 50º, the measure of the exterior angle x is given as follows:
x = 180 - 50
x = 130º.
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if a data set is normally distributed what percent of the data will lie below the mean
Explanation:
The normal curve, aka bell curve, has mirror symmetry with the mean at the very center. Half of the data is below the mean, while the other half is above the mean.
About 68% of the data will lie below the mean in a normally distributed data set. This is known as the Empirical Rule, which states that if a data set is approximately normally distributed, then approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
f(x) = -2x
g(x) = 8x² - 5x+7
Find (f g)(x).
O-16x³5x+7
O 16x4 + 10x³ - 14x²
O-16x² + 10x - 14x
O-16x³ + 10x² - 14x
Answer:
-16x² + 10x - 14.
Step-by-step explanation:
To find the composition of two functions, (f g)(x), we first evaluate g(x) and then substitute the result into f(x).
So, let's first evaluate g(x):
g(x) = 8x² - 5x + 7
Next, substitute g(x) into f(x):
(f g)(x) = f(g(x)) = f(8x² - 5x + 7) = -2(8x² - 5x + 7) = -16x² + 10x - 14
Therefore, (f g)(x) = -16x² + 10x - 14.
Need this for a math lesson
The upper quartile score on the final exam is 83.
What is Upper quartile?Upper quartile, represented as Q₃, also known as third quartile is the value in a data set such that 75% of the points in the data set are below this value, after arranging in an ascending order.
Given data set is the scores for the final exam in an 8th grade math class.
58, 72, 74, 92, 84, 40, 74, 81, 76, 83.
First arrange the data in an ascending order.
40, 58, 72, 74, 74, 76, 81, 83, 84, 92.
Median is the middle element.
Median = (74 + 76) / 2 = 75
Upper quartile is the median of the second half.
Consider the second half.
76, 81, 83, 84, 92.
Median = 83
Third quartile = 83
Hence 83 is the upper quartile score on the final exam.
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What is the exact volume of a cylinder with a height of 5 feet and a radius of 2 feet?
Answer:
V = 62.83ftStep-by-step explanation:
V≈62.83ft³
I hope it helped you out.
During a 36 - year period, lightning killed 2,457 people in the United States. Assuming that rate holds true today and is constant throughout the year. Find the probability that tomorrow: (a) No one in the United States will be struck and killed by lightning. (b) One person will be struck and killed.
(c) More than one person will be struck and killed.
Answer: A
Step-by-step explanation: This is how to solve: 3239 / (36 *365)
That's 0.246499239 kills per day, so none died
I hope this helped!
Which proportion can be used to find the length of sides ik
The proportion i/k = 12 can be used to find the length of sides i and k if the perimeter is 12 units. To solve for the length of each side, the equation i + k = 12 is used, and then the two sides are divided by each other to get the proportion i/k = 12.
The proportion i/k = 12 can be used to find the length of sides i and k of a shape if the perimeter is 12 units. In order to solve for the length of each side, the equation i + k = 12 is used to determine the sum of the sides. The two sides are then divided by each other, resulting in the proportion i/k = 12. This proportion can then be used to find the length of sides i and k. For example, if the length of side i is 8, then the length of side k is 4. This can be determined by dividing 8 by 4, which results in the proportion i/k = 2. If the perimeter is 12 units, then the equation i + k = 12 can be used to determine that the length of side i is 6 and the length of side k is 6, since 6 + 6 = 12. The proportion i/k = 12 can then be used to confirm that the length of side i is 6 and the length of side k is 6.
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The complete question is
Which proportion can be used to find the length of sides ik if the perimeter is 12 units?
what does the degree of a vertex in the hollywood graph represent? what does the neighborhood of a vertex repre- sent? what do the isolated and pendant vertices represent?
The degree of a vertex represents the number of other actors or actresses that an actor or actress has worked with in movies.
The neighborhood of a vertex represents the set of actors or actresses that an actor or actress has worked with in movies.
Isolated vertices represent actors or actresses who have not worked with any other actors or actresses in any movie, while pendant vertices represent actors or actresses who have only appeared in one movie with another actor or actress in the Hollywood graph.
The Hollywood graph is an undirected graph because the relationship between actors and actresses is mutual.
Each vertex in this graph represents an actor or actress, and the degree of a vertex represents the number of other actors or actresses that they have worked with in movies. In other words, the degree of a vertex represents the number of edges that are connected to that vertex.
The neighborhood of a vertex in a graph refers to the set of all vertices that are adjacent to it. In the context of the Hollywood graph, the neighborhood of a vertex represents the set of actors or actresses that a particular actor or actress has worked with in movies.
An isolated vertex in a graph is a vertex that has no edges connected to it. In the context of the Hollywood graph, an isolated vertex represents an actor or actress who has not worked with any other actors or actresses in any movie.
A pendant vertex in a graph is a vertex that has only one edge connected to it. In the context of the Hollywood graph, a pendant vertex represents an actor or actress who has only appeared in one movie with another actor or actress in the Hollywood graph.
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when a researcher rejects the null hypothesis, the difference is declared to be: select one: a. statistically significant. b. statistically insignificant. c. statistically unimportant. d. statistically strong.
Answer:
C
Step-by-step explanation:
calculate the cost of producing container A using surface area
The program to cost of each container and the total cost of producing all the containers is given below.
How to depict the C ProgramThe program based on the information will be:
#include <iostream>
using namespace std;
int main() {
int r,h,c,n;
cout<<"Enter the base radius : ";
cin>>r;
cout<<"\nEnter the height : ";
cin>>h;
cout<<"\nEnter the cost per square cm : ";
cin>>c;
cout<<"\nEnter the number of containers : ";
cin>>n;
int s_area = (3.14*r*2)+(2*3.14*r*h);
int cost = c*s_area;
int t_cost = n*cost;
cout<<"\nCost of each container : "<<cost<<endl;
cout<<"Total cost : "<<t_cost<<endl;
}
Based on the above, we've created a program to take the radius of the base, the height of the container, the cost per square centimeter of the material cost.
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A manufacturer wishes to determine the cost of producing an open-top cylindrical container. The surface area of the container is the sum of the area of the circular base plus the area of the outside (the circumference of the base times the height of the container). Create C program to take the radius of the base, the height of the container, the cost per square centimeter of the material (cost), and the number of containers to be produced (quantity). Calculate the cost of each container and the total cost of producing all the containers.
At a construction site, sand is poured from a truck into a conical pile. The pile has a diameter of 12
feet and is 10 feet tall. Which of the following best describes the volume of the sand?
The volume of the sand which is equal to the volume of the cone will be 376.8 cubic feet.
What is the volume of the cone?Let h be the height of the cone and A be the base area of the cone.
Then the volume of the cone will be given as,
Volume = (1/3) × A × h
At a construction site, sand is poured from a truck into a conical pile. The pile has a diameter of 12 feet and is 10 feet tall.
The base area of the cone is given as,
A = π × (d/2)²
A = 3.14 × (12 / 2)²
A = 3.14 × 36
A = 113.04 square feet
Then the volume of the cone is given as,
V = 1/3 × 113.04 × 10
V = 376.8 cubic feet
The volume of the sand which is equal to the volume of the cone will be 376.8 cubic feet.
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QUESTION FOR FOR LIH04
Geometry and 60 POINTS!!!!!!
Answer:
a = 6 ft.
------------------------------
Given is an isosceles right triangle.
As per property of a such triangle, its hypotenuse is √2 times its leg.
That is:
a√2 = 6√2, divide both sides by √2a = 6Answer:
a = 6 ft
Step-by-step explanation:
We have to find,
→ The value of a in the diagram.
Formula we use,
=> Using Pythagoras theorem.
→ (Hyp)² = (Opp)² + (Base)²
Forming the equation,
→ (6√2)² = (a)² + (a)²
Now the value of a will be,
→ (6√2)² = (a)² + (a)²
→ (a)² + (a)² = (6√2)²
→ 2a² = 36 × 2
→ 2a² = 72
→ a² = 72 ÷ 2
→ a² = 36
→ a = √(36)
→ [ a = 6 ft ]
Hence, the value of a is 6 ft.
Edward and his little brother made up
a game using coins. They flip the coins
towards a cup and receive points for
every one that makes it in. Edward
starts with 20 points, and his little
brother starts with 18 points. Edward
gets 2 points for every successful
shot, and his brother, since he is
younger, gets 3 points for each
successful shot. Eventually, the
brothers will have a tied score in the
game. How many additional shots will
each brother have made? How many
points will they both have?
Edward and his brother will have each
made ________
shots, for a tied score
of ________
