One-third is equivalent to what number over 12? Place only the value for the number that will be over 12.
Answers
Answer:
4
Step-by-step explanation:
1/3 = x/12
12 * 1/3 =x x = 4
Related Questions
one possible combination is red and hearts. write down all the other possible combinationas. write your answer like this (R,H) you must write all your answers on one line
Answers
Answer:
hmmmm.... sorry but i really dont know this yet
Step-by-step explanation:
In a survey, a group of students were asked to name their favorite subject. There were 20 students who chose "other" subjects. How many students participated?
Answers
let g(x) = xe-x be-x where b is a positive constant..
(b) For what positive value b doesg have an absolute maximum at x=? Justify your answer.
(c) Find all values of b, is any, for which the graphof g has a point of inflection on the interval 0x
Answers
Positive value b have an absolute maximum at x= 1-b is a local maximum.
g(x) has a point of inflection on the interval 0 < x < infinity for all values of b in the interval (0,2).
To find the absolute maximum of g(x), we need to find the critical points of g(x) and check their values.
g(x) = \(xe^(-x) e^(-b)\)
g'(x) = \(e^(-x)(1-x-b)\)
Setting g'(x) = 0, we get:
\(e^(-x)(1-x-b)\) = 0
This gives two solutions: x = 1-b and x = infinity (since\(e^(-x)\) is never zero).
To determine which of these is a maximum, we need to check the sign of g'(x) on either side of each critical point.
When x < 1-b, g'(x) is negative (since \(e^(-x)\)and 1-x-b are both positive), which means that g(x) is decreasing.
When x > 1-b, g'(x) is positive (since\(e^(-x)\)is positive and 1-x-b is negative), which means that g(x) is increasing.
Therefore, x = 1-b is a local maximum. To determine whether it is an absolute maximum, we need to compare g(1-b) to g(x) for all x.
g(1-b) =\((1-b)e^(-1) e^(-b)\)
g(x) = \(xe^(-x) e^(-b)\)
Since \(e^(-1)\)is a positive constant, we can ignore it and compare \((1-b)e^(-\)b) to \(xe^(-x)\) for all x.
It can be shown that xe^(-x) is maximized when x = 1, with a maximum value of 1/e. Therefore, to maximize g(x), we need to choose b such that \((1-b)e^(-b) = 1/e.\)
(c) To find the points of inflection of g(x), we need to find the second derivative of g(x) and determine when it changes sign.
g(x) = \(xe^(-x) e^(-b)\)
g'(x) =\(e^(-x)(1-x-b)\)
g''(x) = \(e^(-x)(x+b-2)\)
Setting g''(x) = 0, we get x = 2-b.
When x < 2-b, g''(x) is negative (since \(e^(-x)\)is positive and x+b-2 is negative), which means that g(x) is concave down.
When x > 2-b, g''(x) is positive (since \(e^(-x)\) is positive and x+b-2 is positive), which means that g(x) is concave up.
Therefore, x = 2-b is a point of inflection.
To find all values of b for which g(x) has a point of inflection on the interval 0 < x < infinity, we need to ensure that 0 < 2-b < infinity. This gives us 0 < b < 2.
Therefore, g(x) has a point of inflection on the interval 0 < x < infinity for all values of b in the interval (0,2).
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find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 15 4x − x2, [0, 5]
Answers
The absolute maximum value of f on the interval [0, 5] is 15.
The absolute minimum value of f on the interval [0, 5] is 5.
To find the absolute maximum and absolute minimum values of f on the given interval:
We need to evaluate f(x) at the endpoints of the interval and at any critical points within the interval.
First, we find the derivative of f(x):
f'(x) = 15 - 2x
Then, we set f'(x) = 0 and solve for x:
15 - 2x = 0
x = 7.5
However, 7.5 is not within the interval [0, 5], so we do not have any critical points within the interval.
Next, we evaluate f(x) at the endpoints of the interval:
f(0) = 15
f(5) = 5
Therefore, The absolute maximum value of f on the interval [0, 5] is 15 and the absolute minimum value of f on the interval [0, 5] is 5.
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help pleasee! will mark brainliest (IF CORRECT)
Answers
Answer:
3. a. The constant rate of change is -1. The graph shows the hawk diving 10 feet closer to its prey every second.
Step-by-step explanation:
Answer:
A.
The rate of change is -1, meaning every second the altitude goes down by 10ft
for the second one the rage of change is 2/3, meaning every three days book sales go up by 1000
B.
there is a porportinal liner relationship because the line on the graph is striaght if it wasn’t porpportinal it would be a zigzag line or a a scatter plot
(this applies to both)
Calculate the coefficient of variation of the age of a group of people with a mean age of 55 and a standard deviation of 11
A. 25
B. 22.5
C. 20
D. 15
Answers
The coefficient of variation for the age of the group of people is approximately 20%. Thus, the correct option is C. 20.
The coefficient of variation (CV) is a measure of relative variability and is calculated as the ratio of the standard deviation to the mean, expressed as a percentage.
To find the coefficient of variation for the age of a group of people with a mean age of 55 and a standard deviation of 11, we can use the following formula:
CV = (Standard Deviation / Mean) * 100
Plugging in the values, we get:
CV = (11 / 55) * 100
CV ≈ 20
Therefore, the coefficient of variation for the age of the group of people is approximately 20%. Thus, the correct option is C. 20.
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Verizon has a new cell phone plan where you
pay $40 for unlimited talk and $12 for each
gigabyte of data. If your cell phone bill is $88,
how many gigabytes of data are you paying
for?
Answers
Explanation: Your phone bill is $40 already & you’re able to add $12, 4 times before you get to $88. Therefore you’re paying for 4 gigabytes of data.
4 gigabytes of data are being paid for by Verizon.
What is subtraction?An arithmetic intelligence operation minus simulates the process of deleting items from either a collection. To subtract is to take something or something from a particular group. The group's total number of items decreases and became lower when people eliminate it. The components of a subtraction issue are the issues dealing with, forces at play, and differences. The negative symbol, or, denotes subtraction.
A new mobile phone plan from Verizon costs $40 for unlimited call time and $12 per gigabyte of data.
If you owe $88 to the company then,
Then the data that is being consumed will be 88 - 40 = 48
The amount for which the payment is being made will be
48/12
= 4
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10.) A study recorded the reactions of 186 polar
bears as they were approached by a tundra
buggy. Some bears did not appear to respond,
while others responded by sitting, standing,
walking away, or running away. There were 94
more bears that did not respond than did
respond. How many bears responded and how
many bears did not respond?
Answers
the answer is 94 bears reponded and 92 did not II thnk
I’m just wanting to know how to get to the answers to these questions
Answers
Given:
\(f(x)=\frac{5}{x},x_0=1,x_n=9\)Explanation:
To find: The area when n = 2 (since, 2 rectangles)
Finding the given change in x,
\(\begin{gathered} \Delta x=\frac{b-a}{n} \\ =\frac{9-1}{2} \\ =4 \end{gathered}\)Defining the partition intervals,
\(x:\lbrace(1,5),(5,9)\rbrace\)Choose the midpoint in each interval,
\(x_m=\lbrace3,7\rbrace\)Finding the value of the function at the point,
\(\begin{gathered} f(3)=\frac{5}{3} \\ f(3)\approx1.6667 \\ f(7)=\frac{5}{7} \\ f(7)\approx0.7143 \end{gathered}\)Using the midpoint formula,
\(\begin{gathered} A=\Delta x(f(x_{m_1})+f(x_{m_2})) \\ =4(1.6667+0.7143) \\ A\approx9.5238\text{ square units} \end{gathered}\)Final answer: The area under 2 rectangles is 9.5238 square units.
To find: The area when n = 4 (4 rectangles)
Finding the given change in x,
\(\begin{gathered} \Delta x=\frac{b-a}{n} \\ =\frac{9-1}{4} \\ =2 \end{gathered}\)Defining the partition intervals,
\(x:\lbrace(1,3),(3,5),(5,7),(5,9)\rbrace\)Choose the midpoint in each interval,
\(x_m=\lbrace2,4,6,8\rbrace\)Finding the value of the function at the point,
\(\begin{gathered} f(2)=\frac{5}{2}\Rightarrow f\mleft(2\mright)=2.5 \\ f(4)=\frac{5}{4}\Rightarrow f\mleft(4\mright)=1.25 \\ f(6)=\frac{5}{6}\operatorname{\Rightarrow}f(6)=0.8333 \\ f(8=\frac{5}{8}\operatorname{\Rightarrow}f(8)=0.625 \end{gathered}\)Using the midpoint formula,
\(\begin{gathered} A=\Delta x(f(x_{m_1})+f(x_{m_2})+f(x_{m_3})+f(x_{m_4})) \\ =2(2.5+1.25+0.833+0.625) \\ =2(5.2083) \\ A\approx10.4167\text{ square units} \end{gathered}\)Final answer: The area under 4 rectangles is 10.4167 square units.
you and some friends have raised $250 to help make a video for a contest. You need $35 to buy video tapes. It costs $45 per day to rent the video camera for the first day and $30 for each additional day. Write an inequality to find the possible numbers of days you can rent the video camera.
Answers
Answer:
80 + 30 n ≥ 250
Number of days = 5
Step-by-step explanation:
Given:
Total money = $250
Video tape cost = $35
1st day for camera ranting = $45
Additional daily cost = $30
Find:
Inequality
Number of days
Computation:
Assume number of days = n
So,
35 + 45 + 30 n ≥ 250
80 + 30 n ≥ 250
30 n ≥ 170
n = 5 days
Number of days = 5
let r be the region bounded by the graphs of f(x). = 4x^2 - x^3
Answers
The region bounded by the graph of the function \(f(x) = 4x^2 - x^3\) can be denoted as r. This region is characterized by a curve that represents the function in the Cartesian coordinate system. The curve of \(f(x) = 4x^2 - x^3\) is symmetric with respect to the y-axis and intersects the x-axis at three points: x = 0, x = 2, and x = -2.
The graph has a maximum point at (1, 3) and a minimum point at (-1, -3). The region r is bound by the x-axis and the curve of the function, and its shape is determined by the behavior of the function within the specified interval.
The function\(f(x) = 4x^2 - x^3\) is a cubic polynomial. The term\(4x^2\)represents a parabolic shape that opens upward, while the term \(-x^3\) introduces a decreasing cubic behavior. When combined, these terms create a curve that exhibits both concave-up and concave-down regions. The graph intersects the x-axis at the roots of the equation \(4x^2 - x^3 = 0\), which gives us the x-values of the points of intersection. By analyzing the behavior of the function and identifying the critical points, we can determine the boundaries of the region r. The shape and position of the region r depend on the specific values and properties of the function\(f(x) = 4x^2 - x^3\).
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Disk drives have been getting larger. Their capacity is now often given in terabytes (TB) where 1 TB = 1000 gigabytes, or about a trillion bytes. A survey of prices for external disk drives found the data shown in chart. For this data, we want to predict Price from Capacity. A). Find the slope estimate b1. _________B). Find the intercept b0. ___________C). Write equation that predicts Price from Capacity - price= ______ + (_____) capacityD). What would you predict price of a 20.0 TB disk? _______
Answers
To compute the slope, intercept, and equation to predict the Price, we will use the formulae below:
For the equation
\(\bar{y}=b(\bar{x})+a\)For the slope
\(b=r(\frac{S_y}{S_x})\)For the intercept
\(a=\bar{y}-b\bar{x}\)In this case, we have the following data given:
\(\begin{gathered} \bar{x}=7.611,S_x=9.85,r=0.987 \\ \bar{y}=784.173,S_y=1419.89 \end{gathered}\)Part A
Upon substituting the above into the formula, we will have
\(b=0.987(\frac{1419.89}{9.85})=141.41\)Hence slope = 141.41
Part B
\(\begin{gathered} a=\bar{y}-\bar{bx} \\ a=784.173-141.41(7.611) \\ a=-292.099 \end{gathered}\)Hence, Intercept =-292.099
PART C
The equation that can be used to predict Price from Capacity
\(\begin{gathered} \text{Price}=\text{intercept}+(\text{slope)capacity} \\ \text{Price}=-292.099+(141.41)\text{capacity} \end{gathered}\)Therefore, the equation is
Price=-292.099+(141.41)capacity
Part D
To predict the price of a 20.0TB disk, we will simply set the capacity= to 20 and then simplify
\(\begin{gathered} P_{20TB}=-292.099+141.41(20) \\ P_{20TB}=2536.10 \end{gathered}\)Hence, the predicted price is=2536.10
you and a friend are riding your bikes to a restaurant that you think is east; your friend thinks the restaurant is north. you both leave from the same point, with you riding 12 mph east and your friend riding 8 mph north. after you have travelled 4 mi, at what rate is the distance between you and your friend changing?
Answers
The rate at which the distance is changing is calculated to be 14.42 miles per hour.
Consider the east direction to be denoted by x and the north direction to be denoted by y, therefore;
dx / dt = 12 mph
dy / dt = 8 mph
x is equal to 4 miles
Consider the distance between them to be s
Time taken by you to travel 4 miles = distance / speed
Time taken by you to travel 4 miles = 4/12 hour
Distance traveled by the friend in that time = speed × time
Distance traveled by the friend in that time = 8 × (4/12) = 2.67 miles
Now we use the Pythagorean theorem,
x^2 + y^2 + s^2 ...... (1)
Substitute, x = 4 miles and y = 2.67 miles
s^2 = 16 + 7.1289 = 23.1289
s = 4.81
Now differentiate equation 1 with respect to t as follows;
2x (dx/dt) + 2y (dy/dt) = 2s (ds/dt)
2(4) (12) + 2(2.67) (8) = 2 (4.81) (ds/dt)
96 + 42.72 = 9.62 (ds/dt)
138.72 = 9.62 (ds/dt)
ds/dt = 138.72/9.62 = 14.42 miles per hour
Thus the distance is changing at the rate of 14.42 miles per hour.
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In a class of 35 student, 19 take history and 12 take economics. If 5 take both subject, how many take neither
Answers
Answer:
9 take niether
Step-by-step explanation:
19-5 = 14
12-5 = 7
14+7+5=26
35-26 = 9
What is the slope of y=-x+2
Answers
Answer:
the slope would be -1
Step-by-step explanation:
slope is determined by the sign + or - and the number before x
An event called __ if the probability it will occur equals 1, plz help im dying (it has 7 letters)
Answers
Answer:
"certain"
Step-by-step explanation:
by definition, any event with a probably of 1 is defined as certain (i.e certain to happen)
by contract any even with a probably of 0 is defined as impossible (i.e impossible to happen)
how much volume in one grain of rice
Answers
A grain of rice contains about 0.029 milliliters of volume.
A grain of rice is a tiny, ingestible seed that comes from either Oryza sativa (Asian rice) or Oryza glaberrima, two types of grass (African rice). A single grain of rice is round or oval in shape and measures about 3–4 millimeters in length. A grain of rice has a volume of 0.029 milliliters and a mass of approximately 0.05 grams. The type of rice and the method of processing affect the size and form of a single grain of rice. Over half of the world's population relies heavily on rice as a source of nutrition and as a staple food in many different cultures. Sushi, risotto, rice pudding, and many more recipes all use rice as an ingredient.
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Can someone please help me solve the following? 2-(-2)³+(-4/2)³
Answers
Answer:
BPEMDAS (brackets, parentheses, exponents, multiplication and division, addition and subtraction)- Left to right
Notes: Two negatives make a positive. When you have an odd exponent of an negative number, you get a negactive result.
2-(-8)+(-2)³
10-8
2
Hope this makes sense! :)
The sum of three consecutive odd integers is 75. Find the integers.
Answers
Answer:
23, 25, and 27.
Step-by-step explanation:
Let the first odd integer be k.
Since the three numbers are consecutive odd integers, the second is given by (k + 2) and the third by (k + 4).
Their sum is 75. Hence:
\(k + (k + 2) + (k + 4) = 75\)
Solve for k. Combine like terms:
\(3k + 6 = 75\)
Subtract:
\(3k = 69\)
And divide:
\(k = 23\)
Therefore, the first number is 23.
In conclusion, the three consecutive, odd integers are 23, 25, and 27.
All the three integers are, 23, 25, 27
We have to given that,
The sum of three consecutive odd integers is 75.
Now, Let the first odd integer be x.
Since, the three numbers are consecutive odd integers,
Hence, the second is, (x + 2) and the third is, (x + 4).
Here, The sum of three consecutive odd integers is 75.
Hence, We get;
x + (x + 2) + (x + 4) = 75
3x + 6 = 75
3x = 75 - 6
3x = 69
x = 69/3
x = 23
Thus, All the three integers are,
x = 23
x + 2 = 23 + 2 = 25
x + 4 = 23 + 4 = 27
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A radio tower has supporting cables attached to it at points 100 ft above the ground. Write a model for the length d of each supporting cable as a function of the angle θ that it makes with the ground. Then find d when θ=60° and when θ=50° .
a. Which trigonometric function applies?
Answers
The trigonometric function that applies in this scenario is the sine function. When θ = 60°, the length of the supporting cable is approximately 115.47 ft, and when θ = 50°, the length is 130.49 ft.
The trigonometric function that applies in this scenario is the sine function.
To write a model for the length d of each supporting cable as a function of the angle θ, we can use the sine function. The length of the supporting cable can be represented as the hypotenuse of a right triangle, with the opposite side being the distance from the attachment point to the top of the tower.
Therefore, the model for the length d of each supporting cable can be written as: d(θ) = 100 / sin(θ)
To find the length of the supporting cable when θ = 60° and θ = 50°, we can substitute these values into the model:
d(60°) = 100 / sin(60°)
d(50°) = 100 / sin(50°)
When θ = 60°: d(60°) = 100 / sin(60°). Using a calculator or trigonometric table, we find that sin(60°) ≈ 0.866.
Substituting this value into the model, we have : d(60°) = 100 / 0.866 ≈ 115.47 ft
Therefore, when θ = 60°, the length of the supporting cable is approximately 115.47 ft. When θ = 50°: d(50°) = 100 / sin(50°)
Using a calculator or trigonometric table, we find that sin(50°) ≈ 0.766. Substituting this value into the model, we have:
d(50°) = 100 / 0.766 ≈ 130.49 ft
Therefore, when θ = 50°, the length of the supporting cable is approximately 130.49 ft.
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Which expression has the same value as Negative 18 divided by (negative 9)? Negative 18 divided by 2 Negative 12 divided by (negative 3) Negative 10 divided by 5 Negative 8 divided by (negative 4) (for brainliest)
Answers
Answer: -8/-4
Step-by-step explanation:
When a negative integer gets divided my another negative integer, it results in a positive number. This means that we can eliminate all the negative symbols in this problem
18/9 = 2
Now all is left to determine which other expression is equivalent to 2
In the expression -10 / 5, since there is only one negative symbol, the postulate for negative number division states that two negative integers makes a positive number, and there is one negative integer and one positive whole number.
18/2 = 9 = incorrect
12/3 = 4 = incorrect
-10/5 = -2 = incorrect
8/4 = 2 = correct
So the expression -8/-4 is equivalent to the expression -18/-9
Answer:
Its D
Step-by-step explanation:
took the test its right, yw
What is the volume of the tent?
Answers
Explanation
which graph represent the liner function y= -5x + 2?
A
B
C
D
Answers
Answer:
A
Step-by-step explanation:
if you say x=0 than y=2
if you say y=0 then x=2/5
you observe those values in the first graph
One angle of a right triangle measures 36. 5 degrees. What is the measure of the other small angle?.
Answers
Answer:
The other small angle is 53.5 degrees
Step-by-step explanation:
We know that a right triangle has to have a 90 degree angle and 2 other small angles.
All triangles when adding up all of their "degrees" has tp equal 180 degrees.
Since we know that there is a 90 degree angle and a 36.5 degree angle.
All we have to do is add 90 plus 36.5, then subtract that sum onto 180.
90 + 36.5 = 126.5
180 - 126.5 = 53.5
So the answer is 53.5 degrees.
Hope this helps! :)
૮ ・ﻌ・ა
A right triangle is a triangle in which the angles sum up to 180 degrees. It is made up of three sides : the height, the base and the hypotenuse. One of the angles in a right triangle has a value of 90 degrees.
Missing angle = sum of angles in a triangle - (sum of the two given angles)
Missing angle = 180 - ( 90 + 36.5)
180 - 126.50
= 53.5 degrees
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Look at the three trees and the paths between them.Vani walks from Tree 1 to Tree 2 and then to Tree 3 - covering 335 metres in all. Raj walks from Tree 2 to Tree 3, then to Tree 1, and finally returns to Tree 2 - covering 540 metres in all.How far is Tree 1 from Tree 3?
Options
205 metres
875 metres
(we can't say)
215 metres
Answers
The distance from tree 1 to tree 3 is about 205 meters.
EquationAn equation is an expression used to show the relationship between two or more variables and numbers.
Let a represent the distance from tree 1 to 2, b from 2 to 3 and c from tree 3 to 1.
Hence:
a + b = 335
Also:
b + c + a = 540
a + b + c = 540
335 + c = 540
c = 205 meters
The distance from tree 1 to tree 3 is about 205 meters.
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The time series regression model contains a variable W and a regression equation of y = 200 + W + 2W2 to forecast future values. If W represents a time period, what is the forecast for time period 2 and the forecast error if the actual value for time period 2 is 100? Select the best answer.
forecast value = 210; forecast error is 110
forecast value = 210; forecast error is -110
forecast value = 210; forecast error is 0
forecast value = 100; forecast error is 0
Answers
The forecast value for time period 2 is 210, and the forecast error is -110 when the actual value is 100. Option B
To calculate the forecast value for time period 2, we substitute W = 2 into the regression equation:
y = 200 + W + 2W^2
= 200 + 2 + 2(2^2)
= 200 + 2 + 2(4)
= 200 + 2 + 8
= 210
Therefore, the forecast value for time period 2 is 210.
To calculate the forecast error, we compare the forecasted value with the actual value for time period 2. Given that the actual value is 100, the forecast error can be calculated as the difference between the actual value and the forecast value:
Forecast error = Actual value - Forecast value
= 100 - 210
= -110
Hence, the forecast error is -110.
Therefore, the correct answer is:
Forecast value = 210; forecast error is -110. So Option B is correct.
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The digits 0 through 9 are written on slips of paper (both 0 and 9 are included). An experiment consists of randomly selecting one numbered slip of paper. Event A: obtaining a prime number Event B: obtaining an odd number Determine the probability P(A or B). ____(Enter a numerical answer as a decimal or fraction)
Answers
The probability P(A or B) is 3/5 or 0.6. Therefore, the probability of selecting a prime number or an odd number is 3/5 or 0.6.
To calculate the probability P(A or B), we first need to determine the number of outcomes for each event and the total number of outcomes in the experiment.
Event A: Obtaining a prime number.
Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves. The prime numbers between 0 and 9 are 2, 3, 5, and 7. So, there are 4 prime numbers in this range.
Event B: Obtaining an odd number.
Odd numbers are numbers that cannot be divided evenly by 2. The odd numbers between 0 and 9 are 1, 3, 5, 7, and 9. So, there are 5 odd numbers in this range.
Since 3, 5, and 7 are both prime and odd numbers, we must account for this overlap, so we subtract these three from the total.
Total number of outcomes (digits 0 through 9) = 10
Total outcomes of A or B = (prime numbers) + (odd numbers) - (overlap) = 4 + 5 - 3 = 6
Now, we calculate the probability P(A or B) as the ratio of the total outcomes of A or B to the total number of outcomes in the experiment:
P(A or B) = (Total outcomes of A or B) / (Total number of outcomes) = 6/10 = 3/5
So, the probability P(A or B) is 3/5 or 0.6.
To solve this problem, we need to first identify the prime numbers and odd numbers among the digits 0 through 9:
Prime numbers: 2, 3, 5, 7
Odd numbers: 1, 3, 5, 7, 9
We can see that the numbers 3, 5, and 7 are both prime and odd, so we need to be careful not to count them twice when calculating the probability of events A or B.
To find the probability of event A (obtaining a prime number), we count the number of prime numbers among the digits 0 through 9, which is 4. The probability of selecting a prime number is therefore 4/10 or 2/5.
To find the probability of event B (obtaining an odd number), we count the number of odd numbers among the digits 0 through 9, which is 5. The probability of selecting an odd number is therefore 5/10 or 1/2.
To find the probability of event A or B (obtaining a prime number or an odd number), we need to add the probabilities of the two events and then subtract the probability of selecting both a prime and an odd number (i.e., the probability of selecting 3, 5, or 7):
P(A or B) = P(A) + P(B) - P(A and B)
= 2/5 + 1/2 - 3/10
= 4/10 + 5/10 - 3/10
= 6/10
= 3/5
Therefore, the probability of selecting a prime number or an odd number is 3/5 or 0.6.
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Consider the following hypothetical system of Simultaneous equations in which the Y variables are endogenous and X variables are predetermined. (19.3,2) (19.3.3) ( 19.3.4) (19.3.5) (a) Using the order condition of identification. determine whether each equation in the system is identified or not. and if identified, whether It is lust or overidentified. (b) Use the rank condition of identification Xo validate your in (a) for equation 19.32. (c) Describe the Steps you can take to ascertain whether in equation 19.3.2 are endogenous (derivation Of reduced form equations is not necessary). Z. Consider the following model Income function: and (20.4.1 ) Money s function; (20.4.2) Where Y, income Y2 = stock Of money XI investment expenditure X, government expenditure on goods and services • The variables Xv and X? are exogenous. Answer the following questions, • (a) Construct a •bogus" or "mongreul" and determine whether the two equations are (b) Explain how a two-stage least squares can be used to estimate the identified (C) Under what conditions can you use a weighted least squares method and not a two-
Answers
a. Consider the following hypothetical system of simultaneous equations in which the Y variables are endogenous and X variables are predetermined: (19.3, 2) (19.3.3) (19.3.4) (19.3.5)
The equation is identified because there are the same number of endogenous variables and predetermined variables. This is a just-identified system.
b. To validate your answer in (a) for equation 19.32, use the rank condition of identification. The rank of the [X'Z] matrix is 3, which is equal to the number of endogenous variables in the equation. As a result, the equation is identified.
c. This can be achieved by comparing the number of endogenous variables in the equation to the number of predetermined variables. Since there are fewer predetermined variables than endogenous variables, equation 19.32 is endogenous. Z.
a. Construct a "bogus" or "mongrel" equation and determine whether the two equations are identified or over-identified. Consider the following:
b. A two-stage least squares regression can be used to estimate the identified system. It's possible to use a two-stage least squares regression since there are no endogenous right-hand side variables in this system.
c. You may use weighted least squares regression when there are no endogenous variables on the right-hand side of any equation in the model. If any equation contains an endogenous variable, the two-stage least squares method should be used.
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how does the sample size and percentage of confidence influence the width of a confidence interval?
Answers
As a result, the width of the confidence interval will rise as the sample size is reduced.
Define confidence interval.An area created using fixed-size samples of data from a population (sample space) that follows a particular probability distribution is known as a confidence interval. A selected population statistic is built into the interval with a specified probability.
Given,
What causes a confidence interval's width to grow?
The confidence interval widens as the confidence level does. The only option to get more accurate population estimates, assuming the confidence level is fixed, is to reduce sampling error. The standard error statistic assesses sampling error.
When sample size is reduced, what happens to the width of the confidence interval?
As a result, the width of the confidence interval will rise as the sample size is reduced.
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A movie theater has a seating capacity of 183. The theater charges $5.00 for children, $7.00 for students,
and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $
1316, How many children, students, and adults attended?
children attended.
Answers
Using simplification, if the total ticket sales was $1316, then 70 children, 78 students and 35 students attended.
From the given question,
We know that the capacity of movie theater is 183.
The theater charges $5.00 for children, $7.00 for students and $12.00 of adults.
There are half as many adults as there are children.
If the total ticket sales was $1316, then we have to find how many children, students, and adults attended.
Let the number of children that attended = x
Since, there are half as many adults as children.
Therefore number of adults = 1/2x =0.5x
We know there are total of 183 tickets
Therefore number of students = 183 - x - 0.5x
number of students = 183 - 1.5x
Each children ticket costs = $5
Then the price of children tickets = 5x
Similarly for adults each ticket costs = $12
So total cost of adult ticket = 12×0.5x = $6x
Now the cost of student tickets = 7(183 - 1.5x)
As given that
Total cost of all tickets = $1316
So the expression should be
5x + 6x + 7(183 -1.5x) = 1316
Simplifying
11x + 1281 - 10.5x = 1316
Subtract 1281 on both side
11x + 1281 - 10.5x-1281 = 1316-1281
Simplifying
0.5x = 35
Divide by 0.5 on both side we get
x = 70 children
Now finding the number of adults
= 0.5x
= 0.5×70
= 35 adults
Now finding the number of students
= 183 - 1.5x
= 183 - 1.5×70
= 183 - 105
= 78 students
Hence, If the total ticket sales was $1316, then 70 children, 78 students and 35 students attended.
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