True A statement contradicting the claim in the null hypothesis about a population parameter is classified as the alternative hypothesis
In hypothesis testing, there are two types of hypotheses - the null hypothesis (H₀) and the alternative hypothesis (H₁). The null hypothesis is a statement about a population parameter that assumes no significant difference or effect, while the alternative hypothesis is a statement that contradicts the null hypothesis, suggesting a significant difference or effect in the population parameter.
When conducting a hypothesis test, researchers first establish the null hypothesis, which generally assumes no significant relationship between the variables being studied. The alternative hypothesis is then formulated to contradict the null hypothesis, essentially stating that there is a significant relationship between the variables. During the hypothesis testing process, statistical tests are used to determine whether the data provides enough evidence to reject the null hypothesis in favor of the alternative hypothesis or not.
The statement that "a statement contradicting the claim in the null hypothesis about a population parameter is classified as the alternative hypothesis" is indeed true. The alternative hypothesis serves as a contradiction to the null hypothesis, allowing researchers to explore whether there is a significant relationship or effect in the population parameter being studied.
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Solve for x round all answers to the nearest tenth
Answer:
x = 18.3°
Step-by-step explanation:
X is an angle u can solve it by usind sin(x)
sin(x) = 11/35
X = sin^-1 (11/35)
x = 18.3°
Five years ago the population at Liberty Middle School was 1,600 students. This year the population is 1,250 students. Use the expression N−P5
where N represents this year's population and where P represents the previous population to find the average change in population each year.
__ student(s)
The average change in population each year is a decrease of 70 students.
Since, Population simply means the total number of people living in a particular area.
Here, The expression is given as n - p /5 where n is this year's population and where p represents the previous population.
This will be:
= n - p /5
= 1250 - 1600 / 5
=-350 / 5
= -70
Thus, This implies a reduction of 70 students per year.
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Find the area of the figure below:
31 m
16 m
_.d
15 m
The caculated area of the figure is 117.5 square meters
Finding the area of the figurefrom the question, we have the following parameters that can be used in our computation:
The figure
The figure is a trapezoid
And the area of a trapezoid is
Area = 1/2 * Sum of parallel sides * Height
substitute the known values in the above equation, so, we have the following representation
Area = 1/2 * (31 + 16) * 5
Evaluate
Area = 117.5
Hence, the area of the figure is 117.5 square meters
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) find a 3 ⇥ 4 matrix a, in reduced echelon form, with free variable x3, such that the general solution of the equation Ax = [-1 1 6] is x = [-1 1 0 6] +s [-1 2 1 0]
The matrix can be used to solve other systems of equations with the same coefficient matrix A and different right-hand sides.
The first step in finding the 3 ⇥ 4 matrices a in reduced echelon form with free variable x3 is to set up the augmented matrix [A | b] where A is a 3 ⇥ 3 matrix and b is the column vector [-1 1 6].
Then, we perform row operations on this matrix to transform it into a reduced echelon form.
To begin, we can write the augmented matrix as:
[1 0 0 | -1]
[0 1 0 | 1]
[0 0 1 | 6]
This matrix is already in reduced echelon form, since it has leading 1's in each row and column, and all other entries are 0.
However, we need to introduce the free variable x3 in order to match the given general solution.
To do this, we can add a new column to the matrix to represent x3, and then subtract x3 times the third column from the first column.
This will introduce the free variable x3 and preserve the solutions of the system.
The new augmented matrix is:
[1 0 -6 | -1]
[0 1 0 | 1]
[0 0 1 | 6]
This matrix is still in reduced echelon form, but now the first column has a leading 1 and a nonzero entry in the third row.
This means that x1 is a basic variable and x3 is a free variable.
To write this matrix as a 3 ⇥ 4 matrix a, we can split the first three columns into A and the last column into b.
This gives us:
a = [1 0 -6 0]
[0 1 0 0]
[0 0 1 0]
b = [-1]
[1]
[6]
So, the matrix a in reduced echelon form with free variable x3 that satisfies the given general solution is:
a = [1 0 -6 0]
[0 1 0 0]
[0 0 1 0]
This matrix can be used to solve other systems of equations with the same coefficient matrix A and different right-hand sides.
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Graph the inequality of the axes below
The graph for the inequality y ≥ 3/2 x - 1 is attached below.
We have the inequality,
y ≥ 3/2 x - 1.
The upper part of the inequality line is shaded with Red region.
The inequality have the solution as (0.667, 0) and (0, -1).
The graph of the inequality is attached below.
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Indicate below whether the equation in the box is true or false?
The equations in the box are true, as 2/5 and 4/10 are equivalent fractions.
What is a fraction?A fraction is a numerical representation of the division of the two terms x and y, as follows:
Fraction = x/y.
The terms are classified as follows:
The top term x is the numerator of the fraction.The bottom term y is the denominator of the fraction.For the left fraction, we have that 2 out of 5 spaces are painted, hence:
2/5.
For the right fraction, we have that 4 out of 10 spaces are painted, hence:
4/10.
4/2 = 2 and 10/2 = 5, hence the simplified fraction is given as follows:
2/5.
As the fractions are equal, the statement is true.
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Indicate below whether the equation in the box is true or false
Answer:
A. True
Step-by-step explanation:
[tex]\frac{6}{8}[/tex] and [tex]\frac{3}{4}[/tex] are equivalent fractions.
In a circle with a radius of 22 m, an arc is intercepted by a central angle of 7π/4 radians, What is the approximate arc length? use 3. 14 for π. X
The approximate arc length intercepted by a central angle of 7π/4 radians in a circle with a radius of 22 m is 104.94 m.
To find the length of the arc intercepted by a central angle of 7π/4 radians, we use the formula:
arc length = radius * central angle
In this case, the radius is given as 22 m and the central angle is 7π/4 radians. Substituting these values in the formula, we get:
arc length = 22 * 7π/4
= 38.5π
Now, we need to approximate this value using 3.14 for π. Therefore, we get:
arc length ≈ 38.5 * 3.14
≈ 121.19 m
Rounding this value to two decimal places, we get:
arc length ≈ 104.94 m
Therefore, the approximate arc length intercepted by a central angle of 7π/4 radians in a circle with a radius of 22 m is 104.94 m.
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If the elasticity of labor is 0.60, a 15 percent increase in the wage rate will induce a a. 4.0 percent decrease in the quantity of labor supplied. b. 9.0 percent increase in the quantity of labor supplied. c. 9.0 percent decrease in the quantity of labor supplied. 4. 4.0 percent increase in the quantity of labor supplied.
The elasticity of labor refers to the responsiveness of the quantity of labor supplied to changes in the wage rate. If the elasticity of labor is 0.60, a 15 percent increase in the wage rate will induce a decrease in the quantity of labor supplied, but the extent of this decrease will depend on the magnitude of the elasticity. The correct option is c.
In this case, a 0.60 elasticity implies that a 15 percent increase in the wage rate will result in a 9.0 percent decrease in the quantity of labor supplied. This can be calculated using the formula for elasticity, which is the percentage change in quantity divided by the percentage change in price (or wage rate, in this case):
Elasticity of labor = percentage change in quantity / percentage change in wage rate
0.60 = percentage change in quantity / 15 percent
Percentage change in quantity = 0.60 x 15 percent = 9.0 percent
Therefore, the correct answer is (c) a 9.0 percent decrease in the quantity of labor supplied. This means that as the wage rate increases, workers may be less willing to supply labor, resulting in a decrease in the number of workers willing to work at that wage rate.
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laverne starts counting out loud by ${}5$'s. she starts with $7$. as laverne counts, shirley sums the numbers laverne says. when the sum finally exceeds $5000,$ shirley runs screaming from the room. what number does laverne say that sends shirley screaming and running?
Laverne starts counting out loud by 5's, beginning with 7. Shirley sums up all the numbers that Laverne says until the sum exceeds 5000. We need to find the number that Laverne says that sends Shirley screaming and running.
To solve this problem, we can start by finding the pattern in Laverne's counting. She is counting by 5's, so each number she says is 5 more than the previous one. Therefore, we can create an arithmetic sequence with a first term of 7 and a common difference of 5. The formula for the nth term of an arithmetic sequence is given by:
a_n = a_1 + (n-1)d
where a_n is the nth term, a_1 is the first term, d is the common difference, and n is the number of terms.
To find the number that Laverne says that sends Shirley screaming and running, we need to find the value of n such that the sum of the first n terms of the sequence is greater than 5000. We can use the formula for the sum of an arithmetic sequence to do this:
S_n = n/2(2a_1 + (n-1)d)
where S_n is the sum of the first n terms.
Using the values given in the problem, we can write the equation:
n/2(2(7) + (n-1)(5)) > 5000
Simplifying and solving for n, we get:
n > 398
Therefore, the number that Laverne says that sends Shirley screaming and running is the 398th term in the sequence. We can find this term by plugging in n = 398 into the formula for the nth term:
a_398 = 7 + (398-1)(5) = 1989
So, Laverne says the number 1989 that sends Shirley screaming and running.
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Simplify: x²-3x - 10 x² + 6x +8 2 ; x = -4, -2
please help
The simplification of the function is (x - 5) / (x + 4)(x + 2)
We are given that;
Function x²-3x - 10 x² + 6x +8 2 and x = -4, -2
Now,
Step 1: Factor the numerator and denominator of the expression
x²-3x - 10 = (x - 5)(x + 2)
x² + 6x +8 = (x + 4)(x + 2)
(x - 5)(x + 2) / (x + 4)(x + 2) ^2
Step 2: Cancel out any common factors in the numerator and denominator
We can use the power rule of exponents to write:
(x + 4)(x + 2) ^2 = (x + 4)(x + 2)(x + 2)
We can cancel out one (x + 2) from both the numerator and denominator. The expression becomes:
(x - 5) / (x + 4)(x + 2)
Step 3: Write the simplified expression and state any restrictions on the variable
The simplified expression is:
(x - 5) / (x + 4)(x + 2)
These values are:
x + 4 = 0 or x + 2 = 0
Solving for x, we get:
x = -4 or x = -2
Therefore, by the equation the answer will be (x - 5) / (x + 4)(x + 2).
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PLEASE HELP
Solve the inequality for W.
w- 9 ≥25
Simplify your answer as much as possible.
The Solve the inequality for W,in the expression w- 9 ≥25 can be written as w ≥ 34.
How can the equality be calculated?Inequality, In mathematics, can be regarded as the statement of an order relationship which involves the use of the expression such as the greater than, greater than or equal to as well as the less than, or less than or equal to.
It should be noted that the expression helps to know the relation between two numbers or algebraic expressions which can be used to know more about a particular expression.
Given that w- 9 ≥25
w - 9 + 9 ≥ 25 + 9
w ≥ 34
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question 3 (10 points) write a recursive function to compute the summation sum( ((-1)^x)*x*x, x=1..n) for a given input n you must write a recursive function.
The recursive function adds the last term of the summation to the recursive call with n-1 as the input. The final solution is the result of the recursive function for the input value n.
To write a recursive function to compute the summation sum( ((-1)^x)*x*x, x=1..n), we need to break down the summation into smaller parts.
We can start by defining a base case for the recursive function. When n is equal to 1, the summation will only have one term, which is (-1)^1 * 1 * 1. So, the base case would be:
if n == 1:
return -1
Next, we need to find a way to express the summation in terms of smaller parts. We can observe that the summation can be expressed as:
((-1)^n) * n * n + sum((-1)^(x-1) * (x-1) * (x-1), x=1..n-1)
Notice that the summation term on the right-hand side is similar to the original summation, but with n-1 as the upper limit of the summation. This allows us to use recursion to calculate the summation:
def recursive_sum(n):
if n == 1:
return -1
else:
return ((-1)**n) * n * n + recursive_sum(n-1)
This recursive function computes the summation by adding the last term of the summation ((-1)^n * n * n) to the recursive call with n-1 as the input. This process continues until the base case is reached.
In summary, the recursive function to compute the summation sum( ((-1)^x)*x*x, x=1..n) is:
def recursive_sum(n):
if n == 1:
return -1
else:
return ((-1)**n) * n * n + recursive_sum(n-1)
Answer: The solution to this question involves writing a recursive function to compute the summation sum( ((-1)^x)*x*x, x=1..n). To do this, we need to define a base case and express the summation in terms of smaller parts. The recursive function adds the last term of the summation to the recursive call with n-1 as the input. The final solution is the result of the recursive function for the input value n.
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PLEASE HELP ASAP!!!!!!
The 25% karat of pure gold by comparison using ratio is equal to 6
What is ratioA ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. It can be used to express one quantity as a fraction of the other ones.
Given that a 100% gold is 24 karat, representing 25% of karat by the letter x, we can solve for x as follows:
x/24 = 25/100
x = (24 × 25)/100 {cross multiplication}
x = 600/100
x = 6
Therefore by comparison using ratio, the 25% of pure karat gold is derived to be 6.
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The radius of a circle is 0.84 inches and the circumference of the circle is 5.28 describe how to use this information to best represent the value of
The value of π is best represented by multiplying 5.28 by 0.84 (option A, A)
Now, let's take a look at the information given to us. We know that the radius of the circle is 0.84 inches. The radius is the distance from the center of the circle to its edge, and it is half the length of the diameter. So, we can find the diameter by multiplying the radius by 2, which gives us a diameter of 1.68 inches.
We also know that the circumference of the circle is 5.28 inches. The circumference is the distance around the edge of the circle. We can use the formula for the circumference of a circle, which is C = 2πr, where C is the circumference, π is the value of pi, and r is the radius.
We can rearrange this formula to solve for π, which gives us π = C/2r. Plugging in the values we know, we get π = 5.28/2(0.84) = 3.14.
Hence the correct option is (a).
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Harrison steps outside his house to see the hot air balloon pass by. He raises his eyes at a 35° angle to view the balloon. If the balloon is 5,000 feet above the ground, about how far is it from Harrison? Note: Harrison's eye level is 5.2 feet from the ground.
A 6,100 feet
B 8700 feet
C 7100 feet
D 2900 feet
If the balloon is 5,000 feet above the ground, then the Harrison is 7100 feet away (option c)
To solve for the adjacent side, we can use the tangent function, which relates the opposite and adjacent sides of a right triangle to the angle between them.
Tangent of an angle = opposite side / adjacent side
In this case, the tangent of 35° can be written as:
tan(35°) = height of balloon / distance between Harrison and balloon
We can rearrange this equation to solve for the distance between Harrison and the balloon:
distance between Harrison and balloon = height of balloon / tan(35°)
Substituting the given values, we get:
distance between Harrison and balloon = 5000 / tan(35°)
Using a calculator, we can find that the tangent of 35° is approximately 0.7002. Substituting this value, we get:
distance between Harrison and balloon = 5000 / 0.7002
Simplifying this expression, we get:
distance between Harrison and balloon ≈ 7,100 feet
Therefore, the answer is (C) 7,100 feet.
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The figure is made up of a square and a rectangle. Find the area of the shaded region.
If the figure is made up of a square and a rectangle then area of shaded region is 40 square meters
The shaded region is of a triangle, whose area is denoted by:
A = (1/2) × b × h
where b is the base and h is the height.
Since the left figure is a square with side lengths 10, we know that the height of the triangle is also 10 metres.
The right figure is a rectangle with length 4.
Since the total base length of the entire figure is 18 and the base of the square is 10, then the width of the rectangle is 18 - 10 = 8 metres.
This width is also the base of the triangle, so b = 8.
Now plug these values into the equation:
A = (1/2) × b × h
A = (1/2) × 8 × 10
= (1/2) × 80
= 40 square meters
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Question 6 (3 points)
Title:AlglIStats-U10-Test-Std27-10
The weight of a new penny is 2.5 grams. A coin collector weighed 30 of the new pennies in circulation and found that they weighed 2.6 grams. What is the population?
O a all new pennies
O b 30 new pennies
O 2.6 g weight of the sample
Od the average weight of new pennies in circulation
Option (c) 2.6 g weight of the sample is correct.
Given that,
Weight of new penny = 2.5 gm
And are 30 pennies having circulated weight 2.6 gram
To find the population,
Here number of 2.6 gam penny is more than any other penny
and there is single coin of weight 2.5 gm.
Therefore,
2.6 g weight of penny be in population.
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the amplitude of a sector of πcm² of area and 1.5 cm of radius
The area of the sector is A = π cm² and amplitude is a = 0.75 cm
Given data ,
The area of a sector is given by the formula:
A = (1/2) x r² x θ
where r is the radius of the sector and θ is the central angle in radians.
On simplifying , we get
A = π cm²
r = 1.5 cm
Substituting these values into the formula, we get:
π = (1/2) x (1.5)² x θ
π = (3/4) x θ
Solving for θ, we get:
θ = (4/3) x π
The amplitude of the sector is half of the radius, so:
amplitude = (1/2) x 1.5 cm = 0.75 cm
Hence , the amplitude of the sector is 0.75 cm
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when you see a colon in the icd 10 cm book it informs you that
When you see a colon in the ICD-10-CM book, it informs you that the code requires an additional character to provide a more specific description of the condition.
The ICD-10-CM code system uses colons to indicate that the code is incomplete and needs to be expanded for a more accurate representation of the diagnosis or condition. The additional character(s) will help to further specify the diagnosis, such as severity, location, or other pertinent details related to the condition.
In the ICD-10-CM book, a colon is used as a placeholder for when an additional character is required to provide a more specific and complete code for the condition being documented. It ensures the accurate recording and communication of diagnoses within the healthcare system.
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An observer who is standing 47m from a building measures the angle of elevation of the top of a building as 17 degress. If the observer's eye is 167 cm from the ground, what is the height of the building?
The height of the building is approximately 16.9 meters. The distance between the observer and the building forms the adjacent side of the triangle.
To solve this problem, we can use trigonometry and set up a right triangle with the observer's eye, the top of the building, and the ground. The distance between the observer and the building forms the adjacent side of the triangle, and the height of the building forms the opposite side. We can use the tangent function to solve for the height of the building:
tan(17 degrees) = opposite/adjacent
First, we need to convert the distance from the observer to the building from meters to centimeters, since the height of the observer's eye is given in centimeters.
47 meters = 4700 centimeters
Next, we can plug in the values we have and solve for the height of the building:
tan(17 degrees) = h/4700 + 167
h = (4700 + 167) * tan(17 degrees)
h ≈ 16.9 meters
Therefore, the height of the building is approximately 16.9 meters.
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In convex quadrilateral ABCD, the lengths of the sides AB, BC, CD, and DA are 1, 8, 14, and 7, respectively. The angle bisectors of angle ABC and angle BCD intersect at point 0. Find the distance of point O from the side AD is the area of ∆BOC is 20
The distance of point O from side AD is 5.
To find the distance of point O from side AD, we can use the fact that the area of triangle BOC is 20.
Let's denote the distance of point O from side AD as x.
We know that the area of a triangle can be calculated using the formula:
Area = (1/2) * base * height
In triangle BOC, the base is BC with a length of 8, and the height is x (the distance of O from AD).
Therefore, we have:
(1/2) * 8 * x = 20
4x = 20
x = 5
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Consider the life cycle of the apple tree, and keep in mind that most animals eat the entire apple (core and seeds included). Explain why the outside of the seed feels as it does. If you think it protects the inside of the seed, explain what the inside needs to be protected from.
(I NEED HELP ASAP)
The outside of an apple seed is coated with a protective layer called the seed coat. This hard, outer layer is designed to protect the inside of the seed from damage, disease, and pests. The seed coat also helps
Regulate the moisture levels within the seed, ensuring that it doesn't dry out or become too wet. As the apple tree grows, it produces fruit that is eaten by animals. When animals eat the apple, they consume the entire fruit, including the core and seeds. The seed coat protects the seeds as they pass through the animal's digestive system, ensuring that they remain intact and ready to germinate once they are excreted.
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The question is incomplete, the complete question is:
g on average, a call center receives calls from customers every 7 minutes, and it takes 15 minutes to finish a call. the system assumes poisson arrivals and exponential service time. the manager's goal is to limit the average customer waiting time to 2 minutes. what is the minimum number of customer services the call center needs to have to achieve this goal
We would need a minimum of 8 customer service representatives to achieve an average waiting time of 2 minutes.
To determine the minimum number of customer service representatives needed to achieve an average waiting time of 2 minutes, we can use the M/M/1 queuing model formula:
L = λ * Wwhere L is the average number of customers waiting in the queue, λ is the arrival rate (calls per minute), and W is the average time a customer spends waiting in the queue.
First, we need to convert the arrival rate from every 7 minutes to arrivals per minute:
λ = 1/7 = 0.143Next, we need to find the service rate, which is the reciprocal of the service time:
μ = 1/15 = 0.067The utilization factor (ρ) is calculated as the ratio of arrival rate to service rate:
ρ = λ/μ = 0.143/0.067 = 2.134Using Little's Law, we can calculate the average number of customers in the system:
L = λ * WL = ρ/(1 - ρ)L = 2.134/(1 - 2.134) = 2.134/-1.134L ≈ -1.88This negative value implies that the system is unstable and would result in an infinite queue. Therefore, we need to increase the number of customer service representatives to reduce the average waiting time.
Assuming we want to achieve an average waiting time of 2 minutes, we can rearrange the formula to solve for the minimum number of customer service representatives (n):
n = (ρ² + ρ) / (2 * (1 - ρ) * (1 - 2 * ρ * [tex]e^{(-p/2)}[/tex]))
n ≈ 7.89
Therefore, we would need a minimum of 8 customer service representatives to achieve an average waiting time of 2 minutes.
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if a right circular cylinder and oblique cylinder both have a height of 15 inches and diameter of 6 inches, do they have the same volume?
Answer:
Yes, they both have a volume of 423.9 inches cubed.
Step-by-step explanation:
Both cylinders have the same volume formula V=(pi)(r^2)(h)
d/2=r=3
h=15
so, (3.14)(9)(15)=423.9
The volume of each cylinder is 423.9
Which example(s) describe(s) the incorrect use of a hand tool?
Using a drill to drive in a screw
Using a trowel to measure
Using a vise to dig
I only
II only
III only
II and III
Using a trowel to measure and Using a vise to dig are incorrect use of a hand tool, option D is correct
Using a trowel to measure (Option II) is incorrect because a trowel is a tool designed for spreading or smoothing materials like concrete, plaster, or mortar, and is not an accurate measuring tool.
Using a vise to dig (Option III) is also incorrect because a vise is a tool designed to hold objects in place, and is not suitable for digging as it does not have the necessary features such as a digging blade or a handle.
Using a drill to drive in a screw (Option I) is a correct use of a hand tool, as a drill can be used to drive in screws with the appropriate bit.
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Let Vector f = ( 4, 3, 7 ) and vector g = (-1, 0, 2) . Which graph shows vector f + vector g
Represents the vector f + g. C.
The sum of two vectors, we simply add their corresponding components.
In this case,
f + g = (4 - 1, 3 + 0, 7 + 2) = (3, 3, 9)
So the resulting vector has components (3, 3, 9).
Now we need to find the graph that represents this vector.
Graphing a vector in three dimensions can be challenging, but we can use the following method:
Start at the origin (0, 0, 0) of the 3D coordinate system.
Move 3 units in the x-direction, 3 units in the y-direction, and 9 units in the z-direction.
Mark the endpoint of this displacement as the tip of the vector.
Option A has a similar direction, but it is longer than f + g.
Option B has the correct length, but it is pointing in the wrong direction.
Option D is pointing in the correct direction, but it is too short.
We only add the respective components of the two vectors to get their sum.
Thus, f + g = (4 - 1, 3 + 0, 7 + 2) = (3, 3, 9) in this situation.
The resultant vector has three (3), three (3), and nine (9).
We now need to identify the graph that this vector is represented by.
It might be difficult to graph a vector in three dimensions, however we can try the following approach:
Start at the 3D coordinate system's origin (0, 0, 0).
Move three units in the x, three units in the y, and nine units in the z directions.
Make a note of the vector's tip being the terminus of this displacement.
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Can someone please help me.
17.80
200.96
401
175
Step-by-step explanation:
because if you do It you will get it
the distribution of the commute times for the employees at a large company has mean 22.4 minutes and standard deviation 6.8 minutes. a random sample of n employees will be selected and their commute times will be recorded. what is true about the sampling distribution of the sample mean as n increases from 2 to 10 ? responses the mean increases, and the variance increases. the mean increases, and the variance increases. the mean increases, and the variance decreases. the mean increases, and the variance decreases. the mean does not change, and the variance does not change. the mean does not change, and the variance does not change. the mean does not change, and the variance increases. the mean does not change, and the variance increases. the mean does not change, and the variance decreases.
As n increases from 2 to 10, the mean of the sampling hdistribution of the sample mean will increase, while the variance and standard error of the mean will decrease.
As n increases from 2 to 10, the sampling distribution of the sample mean will shift towards the population mean of 22.4 minutes. This is because as n increases, the sample mean becomes a better estimate of the population mean. Therefore, the mean of the sampling distribution will increase.
However, the variance of the sampling distribution will decrease as n increases. This is because the larger the sample size, the more representative the sample is of the population, and thus the less variability there is in the sample means. Therefore, the variance of the sampling distribution will decrease.
It is important to note that the standard error of the mean, which is the standard deviation of the sampling distribution, will also decrease as n increases. This means that as the sample size increases, the sample mean becomes a more precise estimate of the population mean.
In summary, as n increases from 2 to 10, the mean of the sampling distribution of the sample mean will increase, while the variance and standard error of the mean will decrease.
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You have a package of 20 assorted thank-you cards. You pick the four cards shown. How many of the 20 cards would you expect to have flowers on them
According to the probability, we expect approximately 12 or 13 of the 20 cards to have flowers on them.
To calculate the probability of selecting four cards with no flowers on them, we can first determine the number of ways to choose four cards from the 16 non-flower cards in the package. This is:
16C4 = 16! / (4! * (16-4)!) = 1820
Therefore, there are 1,820 different ways to choose four cards with no flowers on them.
To find the probability of selecting four cards with no flowers on them, we can divide the number of ways to choose four non-flower cards by the total number of ways to choose any four cards:
P(4 non-flower cards) = 1,820 / 4,845 = 0.375
So the probability of selecting four cards with no flowers on them is 0.375.
To find the probability of selecting at least one card with flowers on it, we can subtract the probability of selecting four non-flower cards from 1:
P(at least one flower card) = 1 - P(4 non-flower cards) = 1 - 0.375 = 0.625
Therefore, the probability of selecting at least one card with flowers on it is 0.625.
To answer the original question, we can use this probability to estimate how many of the 20 cards we would expect to have flowers on them. We can multiply the probability by the total number of cards in the package:
Expected number of cards with flowers = 0.625 x 20 = 12.5
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