To provide a margin of error of 3 or less with a 95% confidence level when the population standard deviation equals 11, we need a sample size of 73.
What is probability?Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence.
To calculate the sample size needed to provide a margin of error of 3 or less with a 95% confidence level when the population standard deviation equals 11, we can use the following formula:
n = (Zα/2 * σ / E)²
where n is the sample size, Zα/2 is the critical value from the standard normal distribution corresponding to the desired confidence level (in this case, 1.96 for a 95% confidence level), σ is the population standard deviation, and E is the maximum margin of error.
Substituting the values given in the problem, we get:
n = (1.96 * 11 / 3)²
n = 72.85
Rounding up to the nearest whole number, we get a sample size of 73.
Therefore, to provide a margin of error of 3 or less with a 95% confidence level when the population standard deviation equals 11, we need a sample size of 73.
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The formula A=Pe^{rt} can be used to find the dollar value of an investment of $7500 after t years when the interest is compounded continuously at a rate of r percent. Find the value of the investment after 4 years if the interest rate is 6.8%.
The value of the investment after 4 years is equal to $9844.40.
How to determine the value of the investment after 4 years?In Mathematics and Financial accounting, continuous compounding interest can be determined or calculated by using this mathematical equation (formula):
[tex]A(t) = P_{0}e^{rt}[/tex]
Where:
A(t) represents the future value.P₀ represents the principal.r represents the interest rate.t represents the time measured in years.When time, t = 4 years, the future value can be calculated as follows:
[tex]A(t) = 7500e^{0.068 \times 4}\\\\A(t) = 7500e^{0.272}[/tex]
A(t) = 7500(1.31258700131)
A(t) = 9844.4025 ≈ $9844.40.
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Which group of voters has the greatest percentage of student voters?
A table with two columns and one row. The title of the first column is Student Voters. The title of the second column is Total Voters. The row has one hundred twenty and two hundred forty.
A table with two columns and one row. The title of the first column is Student Voters. The title of the second column is Total Voters. The row has one hundred fifty and two hundred fifty.
A table with two columns and one row. The title of the first column is Student Voters. The title of the second column is Total Voters. The row has two hundred and four hundred fifty.
A table with two columns and one row. The title of the first column is Student Voters. The title of the second column is Total Voters. The row has three hundred fifty and nine hundred.
11 of 20 Questions
A small sofa has a mass of 6 kilograms. A pillow on the sofa has a mass of 100 grams. How many pillows would it take to equal the mass of the sofa?
Answer:
6000
Step-by-step explanation:
solved
The radius of Circle A is 8 cm. The radius of Circle B is 2 cm greater than the radius of Circle A. The radius of Circle C is 4 cm greater than the radius of Circle B. The radius of
Circle D is 3 cm less than the radius of Circle C. What is the area of each circle? How many times greater than the area of Circle A is the area of Circle D?
Which graph shows the line of best fit for the data ?
Answer:
Bottom left
Step-by-step explanation:
It covers the most points
Which expression is equivalent to 12.8-3s+15.5+8s?
A. -2+5s
B. 5s +28.3
C. 33.3s
D. 27.3 +5s
The correct expression which is equivalent to 12.8 - 3s + 15.5 + 8s is,
⇒ 5s + 28.3
We have to given that;
Expression to solve is,
⇒ 12.8 - 3s + 15.5 + 8s
Now, WE can simplify as;
⇒ 12.8 - 3s + 15.5 + 8s
Combine like terms,
⇒ 12.8 + 15.5 - 3s + 8s
⇒ 28.3 + 5s
⇒ 5s + 28.3
Thus, The correct expression is,
⇒ 5s + 28.3
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what is the area of a rooftop garden
The area of the garden is 272 ft².
We have,
The garden has two shapes:
Rectangle and a triangle.
Now,
Length = 12 ft
Width = 20 ft
Area of the rectangle.
= Length x Width
= 12 x 20
= 240 ft²
And,
Base = 8 ft
Height = (20 - 12) = 8 ft
Area of the triangle.
= 1/2 x base x height
= 1/2 x 8 x 8
= 32 ft²
Now,
Area of the garden.
= 240 + 32
= 272 ft²
Thus,
The area of the garden is 272 ft².
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find t_{5}(x), the degree 5 taylor polynomial of the function f(x)= \cos(x) at a = 0.
the degree 5 Taylor polynomial of f(x) = cos(x) at a = 0 is T₅(x) = 1 - (1/2!)x² + (1/4!)x⁴.
What is Taylor series?
The Taylor series is a representation of a function as an infinite sum of terms involving the function's derivatives at a particular point. It provides a way to approximate a function with a polynomial expression.
To find the degree 5 Taylor polynomial, denoted as T₅(x), of the function f(x) = cos(x) at a = 0, we need to compute the polynomial using the derivatives of f evaluated at x = 0.
The Taylor polynomial of degree n for a function f(x) centered at a is given by:
Tₙ(x) = f(a) + f'(a)(x - a) + (f''(a)/2!)(x - a)² + ... + (fⁿ(a)/n!)(x - a)ⁿ
In this case, a = 0, so the Taylor polynomial simplifies to:
T₅(x) = f(0) + f'(0)x + (f''(0)/2!)x² + (f'''(0)/3!)x³ + (f⁴(0)/4!)x⁴ + (f⁵(0)/5!)x⁵
Now, let's calculate the derivatives of f(x) = cos(x) up to the 5th order:
f'(x) = -sin(x)
f''(x) = -cos(x)
f'''(x) = sin(x)
f⁴(x) = cos(x)
f⁵(x) = -sin(x)
Evaluating these derivatives at x = 0:
f(0) = cos(0) = 1
f'(0) = -sin(0) = 0
f''(0) = -cos(0) = -1
f'''(0) = sin(0) = 0
f⁴(0) = cos(0) = 1
f⁵(0) = -sin(0) = 0
Substituting these values into the Taylor polynomial formula:
T₅(x) = 1 + 0x + (-1/2!)x² + (0/3!)x³ + (1/4!)x⁴ + (0/5!)x⁵
Simplifying the expression:
T₅(x) = 1 - (1/2!)x² + (1/4!)x⁴
Therefore, the degree 5 Taylor polynomial of f(x) = cos(x) at a = 0 is T₅(x) = 1 - (1/2!)x² + (1/4!)x⁴.
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the me
appropriat
metric unit of measurement from the word bank below. Write the answer on the
line. Each word will be used only once.
1. The most appropriate metric unit to measure the:
a. distance from Florida to Texas is
b. length of a car is
c. thickness of a cell phone is
d. height of a coffee mug is
e. mass of a cookie is
f. mass of a large watermelon is
g. mass of small feather is
h. capacity of a large bottle of lemonade is
i. capacity of a small food coloring bottle is
j. capacity of a swimming pool is
milliliters
liters
kiloliters
Word Bank
milligrams
grams
kilograms
millimeters
centimeters
meters
The measurement units for each is described below.
The metric system is a measurement system. It is utilized in calculations and research all over the world. Here are some instances of how we use the metric system to measure things:
a. distance from Florida to Texas is: Kilometers (km)
b. length of a car is : Meters (m)
c. thickness of a cell phone is: Millimeters (mm)
d. height of a coffee mug is: Centimeters (cm)
e. mass of a cookie is: Grams (g)
f. mass of a large watermelon is: Kilograms (kg)
g. mass of small feather is: Milligrams (mg)
h. capacity of a large bottle of lemonade is : Liters (L)
i. capacity of a small food coloring bottle is : i. Milliliters (mL)
j. capacity of a swimming pool is: Cubic meters (m³)
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due sometime very soon
Answer:
D. Yes
Step-by-step explanation:
find the length of or−→−. r=(2,8,6)
Answer:
2sqrt(26)
Step-by-step explanation:
sqrt(2^2+ 8^2+ 6^2)
=2×sqrt(26)
Suppose years of schooling, s, is the only variable that affects earnings. The equations for the weekly salaries of male and female workers are given by: wm = 500 + 100s and wf = 300 + 75s. On average, men have 14 years of schooling and women have 12 years of schooling. (a) What is the male-female wage differential in the labor market? The wage differential can be written as: )75300(100500 fsmsfwmww = 500 + 100(14) – 300 – 75(12) = $700. (b) Using the Oaxaca decomposition, calculate how much of this wage differential is due to discrimination?
Wage differential is due to discrimination = 700 - 700 = 0 .The Oaxaca decomposition is a method used to estimate the portion of the wage differential between two groups (in this case, male and female workers) that can be attributed to discrimination.
The decomposition breaks down the wage differential into two components: the explained component and the unexplained component.The explained component represents the portion of the wage differential that can be attributed to differences in observable characteristics between the two groups, such as years of schooling.
The unexplained component represents the portion of the wage differential that cannot be explained by observable characteristics and is often interpreted as the component related to discrimination or unobserved factors.
To calculate the Oaxaca decomposition, we need to follow these steps:
Step 1: Calculate the average wage of male workers (wm) and female workers (wf) using the given equations:
wm = 500 + 100s, where s = 14 years (average years of schooling for men)
wm = 500 + 100(14) = 1900
wf = 300 + 75s, where s = 12 years (average years of schooling for women)
wf = 300 + 75(12) = 1200
Step 2: Calculate the explained component of the wage differential by estimating the wage differential that can be explained by the differences in observable characteristics (years of schooling) between the two groups.
Explained wage differential = [500 + 100(14)] - [300 + 75(12)] = 700
Step 3: Calculate the unexplained component of the wage differential, which is the portion that cannot be explained by observable characteristics and may be attributed to discrimination or unobserved factors.
Unexplained wage differential = Actual wage differential - Explained wage differential
Unexplained wage differential = 700 - 700 = 0
In this case, the unexplained component of the wage differential is zero, indicating that none of the wage differential can be attributed to discrimination. All of the wage differential can be explained by the differences in observable characteristics (years of schooling) between male and female workers.
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please i need help on this
Answer:
b
Step-by-step explanation:
What is the displacement of the particle in the time interval 7 seconds to 8 seconds?
A. 0 meters
B. 1.5 meters
C. 3 meters
D. 7 meters
The correct option is B, the displacement is 1.5 meters.
How to find the displacement?Displacement is defined as the difference between the final position and the initial position.
Here we can see a graph that gives the velocity as a function of time.
The velocity at t = 7s is 0m/s
The velocity at t = 8s is 3m/s
Then the acceleration in that interval is:
A = (3m/s - 0m/s)/(8s - 7s) = 3m/s²
And the position will be:
P = (1/2)*3m/s²*(t - 7s)²
Now take the differenve between the positions at t = 8s and t = 7s, we will get:
displacement = (1/2)*3m/s²*(8s - 7s)² - (1/2)*3m/s²*(7s - 7s)² = 1.5m
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Mr. Wilson is packing orders for his soap business. One customer ordered 12 bars of his Minty Morning soap. If each bar of soap weighs 120 grams, how many kilograms will this order weigh?
Answer:
1.440kg
Step-by-step explanation:
12 × 120=1440g
converting g to kg, divide by 1000 as 1000g = 1kg
Answer is therefore given as 1.440kg
You are solving x²-3x-10=0 using the quadratic formula Simplify the radical numerator and denominator
Answer:
Step-by-step explanation:To solve the quadratic equation x² - 3x - 10 = 0 using the quadratic formula, we first identify the values of a, b, and c:
a = 1
b = -3
c = -10
Now, we can apply the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Plugging in the values, we have:
x = (-(-3) ± √((-3)² - 4(1)(-10))) / (2(1))
Simplifying further:
x = (3 ± √(9 + 40)) / 2
x = (3 ± √49) / 2
x = (3 ± 7) / 2
This gives us two possible solutions:
x₁ = (3 + 7) / 2 = 10 / 2 = 5
x₂ = (3 - 7) / 2 = -4 / 2 = -2
Therefore, the solutions to the equation x² - 3x - 10 = 0 are x = 5 and x = -2.
Find a Cartesian equation for the curve and identify it.r = 4sin(θ) + 4cos(θ)
To convert the polar equation r = 4sin(θ) + 4cos(θ) into a Cartesian equation, we can use the identities:
x = r cos(θ)
y = r sin(θ)
Substituting r = 4sin(θ) + 4cos(θ) into these identities, we get:
x = (4sin(θ) + 4cos(θ))cos(θ) = 4sin(θ)cos(θ) + 4cos²(θ)
y = (4sin(θ) + 4cos(θ))sin(θ) = 4sin²(θ) + 4sin(θ)cos(θ)
Simplifying these expressions using the trigonometric identity sin²(θ) + cos²(θ) = 1, we obtain:
x = 4cos(θ) + 4cos²(θ)
y = 4sin(θ) + 4sin(θ)cos(θ) = 4sin(θ) + 4cos(θ)sin(θ)
Therefore, the Cartesian equation for the curve is:
(x - 4)² + y² = 16
This equation represents a circle with center (4, 0) and radius 4. The original polar equation r = 4sin(θ) + 4cos(θ) can be interpreted as the distance from the origin to a point on the circle, measured along a line that makes an angle of θ with the positive x-axis.
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What is the slope from (−7, 5) to (−3, 4)?
Answer:
m = -1/4
Step-by-step explanation:
Slope = rise/run (y2 - y1) / (x2 - x1)
Points (−7, 5) (−3, 4)
We see the y decrease by 1, and the x increase 4, so the slope is
m = -1/4
a camper lights an oil lantern at noon and lets it burn continuously. once the lantern is lit, the lantern burns oil at a constant rate each hour. at p.m., the amount of oil left in the lantern is ounces. at p.m., the amount of oil left in the lantern is ounces. based on the average rate of oil burning per hour, how much oil, in ounces, was in the lantern at noon?
There were 16 ounces of oil in the lantern at noon.
Let's start by defining the variables we know. We'll call the amount of oil in the lantern at noon "x," the rate at which the oil burns "r," and the time elapsed from noon to 2 pm "t." We know that the amount of oil in the lantern at 2 pm is 12 ounces, and at 4 pm, it's 8 ounces.
We can use the rate of oil burning to create an equation relating the amount of oil in the lantern to the time elapsed. The equation is:
x - rt = y
where "y" is the amount of oil in the lantern at any given time after noon. We can solve for "x" by plugging in the values we know at 2 pm:
x - 2r = 12
And at 4 pm:
x - 4r = 8
Now we have two equations with two variables. We can solve for "r" by subtracting the second equation from the first:
2r = 4
r = 2
Now we can plug in "r" to one of the equations to solve for "x." Let's use the first equation:
x - 2(2) = 12
x - 4 = 12
x = 16
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Find the value of x.
Answer:
x = 46
Step-by-step explanation:
These 2 angles would add up to 180 degrees.
So 41 + (3x+1) = 180
Let's solve for x.
41 + 3x + 1 = 180
Combine like terms.
42 + 3x = 180
subtract 42 from both sides
3x = 180-42
3x = 138
divide both sides by 3
x = 46
Ms Brown's left at 9:00 a. M. Her plane landed 1 hour and 23minute later. What time her plane land
Answer:
10:23 am
Step-by-step explanation:
We Know
Ms. Brown left at 9:00 am
Her plane landed 1 hour and 23 minutes later.
What time does her plane land?
We Take
9:00 + 1:23 = 10:23 am
So, her plane landed at 10:23 am
A quadratic function f(x) is hidden from view. You must find all
intervals where f(x) is negative. Choose the form of the quadratic
function f(x) that you would like to see in order to answer the
question most efficiently.
Form: Standard Form, Factored form, or vertex form
To answer the question most efficiently , the standard form of the quadratic equation is the most suitable.
What is a quadrilateral function?A quadratic function is one of the form f(x) = ax² + bx + c, where a, b, and c are numbers with a not equal to zero.
The highest power of a quadratic function is 2.
To solve a quadratic function efficiently, we need to put the function in standard form. i.e We arrange the power in descending order.
For example, a quadratic functionf(x)= 5x-2 +x² is not in standard form. To solve this we need to put it in a form of f(x) = x²+5x -2.
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A savings account balance is compounded annually. If the interest rate is 3% per year and the current balance is $1,530.00, what will the balance be 9 years from now?
The balance of the savings account 9 years from now will be $1,980.58.
To find the balance of the savings account 9 years from now, we can use the formula for compound interest:
[tex]A = P(1 + \dfrac{r}{n})^{(nt)}[/tex]
where A is the ending balance, P is the principal (starting balance), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.
Substituting the given values, we get:
A = 1530(1 + 0.03/1)⁹
A = 1530(1.03)⁹
A = 1530(1.295376)
A = 1980.58
Therefore, the balance of the savings account 9 years from now, rounded to the nearest cent, will be $1,980.58.
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the assumptions going into the model are that: a. the mean value of the number of disasters at a given temperature rise is linear in temperature rise b. the actual number of disasters is approximately normally distributed around its mean with a constant variance. the true value that was left out was 16, use the standard error of prediction (the stuff in the square root in the prediction interval) and the prediction from the regression line to calculate a t statistic. what is the pvalue for the null hypothesis that the point belongs to this line under these
Based on the given assumptions, we can assume that the model predicts the number of disasters at a given temperature rise linearly. However, it is important to note that this model is based on certain assumptions that may or may not be accurate.
These assumptions include the mean value being linear in temperature rise and the actual number of disasters being normally distributed with constant variance.
Given the true value of 16 that was left out, we can use the standard error of prediction and the prediction from the regression line to calculate a t statistic. The null hypothesis is that the point belongs to this line under these assumptions.
To calculate the t statistic, we can use the formula:
t = (observed value - predicted value) / standard error of prediction
Using the given information, we can calculate the t statistic as:
t = (16 - predicted value) / standard error of prediction
Once we have the t statistic, we can calculate the p-value using a t-distribution table or a statistical software. The p-value represents the probability of getting a t statistic as extreme or more extreme than the one we calculated under the null hypothesis.
Based on the p-value, we can determine if we reject or fail to reject the null hypothesis. If the p-value is less than the significance level (usually 0.05), we reject the null hypothesis and conclude that the point does not belong to the line. If the p-value is greater than the significance level, we fail to reject the null hypothesis and conclude that the point belongs to the line.
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a motorist travelled from Ibadan to Lagos ,a distance of 142 km,at an average speed of 60km/h. He spent 5/2 hours in Lagos and then returned to Ibadan at an average speed of 80km/h .(a).At what time did the man arrive back in Ibadan? .(b). find his average speed for the total journey.
To solve the given problem, let's break it down into two parts:
(a) At what time did the man arrive back in Ibadan?
We can calculate the time taken for the initial journey from Ibadan to Lagos using the formula:
Time = Distance / Speed
Time = 142 km / 60 km/h
Time = 2.37 hours
The motorist then spent an additional 5/2 hours in Lagos.
To calculate the total time taken for the return journey from Lagos to Ibadan, we use the formula:
Time = Distance / Speed
Time = 142 km / 80 km/h
Time = 1.775 hours
Adding the time spent in Lagos to the return journey time:
Total time = 2.37 hours + 5/2 hours + 1.775 hours
Total time = 6.145 hours
Therefore, the man arrived back in Ibadan approximately 6.145 hours after he left.
(b) To find the average speed for the total journey, we use the formula:
Average Speed = Total Distance / Total Time
The total distance covered in the round trip is 2 times the distance between Ibadan and Lagos, which is:
Total Distance = 2 x 142 km
Total Distance = 284 km
Average Speed = 284 km / 6.145 hours
Average Speed = 46.22 km/h
Therefore, the average speed for the total journey is approximately 46.22 km/h.
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Let FR,A, FR,B, FR,C, FR,D, FR,E, and FR,F be the magnitudes of the equivalent resultant loads for each of the six cases. Rank the magnitudes of the resultant forces for the six cases. Rank the items from smallest to largest. To rank items as equivalent, overlap them. Let FR,A, FR,B, FR,C, FR,D, FR,E, and FR,F be the magnitudes of the equivalent resultant loads for each of the six cases. Rank the magnitudes of the resultant forces for the six cases. Rank the items from smallest to largest. To rank items as equivalent, overlap them. As well When measuring from the left side of the beam, x¯A, x¯B, x¯C, x¯D, x¯E, and x¯F are the locations where the resultant force is applied in each of the six cases. Rank these six locations. Rank the items from smallest to largest. To rank items as equivalent, overlap them
The magnitudes of the resultant forces and the locations where the resultant force is applied can be ranked from smallest to largest as described above. It is important to note that when there are equivalent values, they should be ranked as such and overlap.
To rank the magnitudes of the resultant forces for the six cases, we first need to determine the equivalent resultant load for each case. The equivalent resultant load is the single force that has the same effect on the beam as the distributed load or loads in the original problem.
The magnitudes of the equivalent resultant loads for each case are:
FR,A < FR,C = FR,D < FR,E < FR,B < FR,F
Therefore, we can rank the magnitudes of the resultant forces as follows, from smallest to largest:
FR,A < FR,C = FR,D < FR,E < FR,B < FR,F
When measuring from the left side of the beam, x¯A, x¯B, x¯C, x¯D, x¯E, and x¯F are the locations where the resultant force is applied in each of the six cases.
The locations where the resultant force is applied are:
x¯C < x¯D < x¯B < x¯E < x¯A < x¯F
Therefore, we can rank the locations where the resultant force is applied as follows, from smallest to largest:
x¯C < x¯D < x¯B < x¯E < x¯A < x¯F
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what is the depth at node 23 and 70 respectively? a. Depth at node 23 is 2. Depth at node 70 is 0. b. Depth at node 23 is 1. Depth at node 70 is 0. c. Depth at node 23 is 2. Depth at node 70 is 2. d. Depth at node 23 is 2. Depth at node 70 is 3.
Therefore, Without more information, it is impossible to determine the depths of nodes 23 and 70. Based on the given options, either node 70 is the root and node 23 is its child (Option A), or node 70 is a grandchild of node 23 (Option D).
Explanation:
To determine the depth at a particular node in a tree, we count the number of edges from the root to that node.
Without more information about the tree, it is impossible to determine the depths of nodes 23 and 70. However, if we assume that the root of the tree is at depth 0, and that the tree is binary (each node has at most two children), then we can make an educated guess.
Based on the given options, we can eliminate choices B and C, as they contradict each other.
Option A suggests that node 23 is two levels below the root, while node 70 is at the root level. This is possible if node 70 is the root of the tree, and node 23 is its child.
Option D suggests that node 23 is two levels below the root, while node 70 is three levels below the root. This is possible if node 70 is a grandchild of node 23.
Therefore, Without more information, it is impossible to determine the depths of nodes 23 and 70. Based on the given options, either node 70 is the root and node 23 is its child (Option A), or node 70 is a grandchild of node 23 (Option D).
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If nominal wages and prices are not flexible which of the following must be true when the economy has a severe recessionary gap? (A The aggregate demand curve is vertical (B The aggregate demand curve is horizontal (CThe short run aggregate supply curve is vertical DThe short run aggregate supply curve is upward sloping (E) The short run aggregate supply curve is hotizontal
If nominal wages and prices are not flexible, then the short-run aggregate supply curve is vertical.
This means that the economy is operating at full employment, and any increase in aggregate demand will not result in an increase in output but rather lead to higher prices.
In other words, the economy is supply-constrained, and there is no excess capacity to produce more output in response to an increase in demand.
In a severe recessionary gap, the economy is operating below its potential output, and there is excess capacity in the economy. However, if nominal wages and prices are not flexible, firms cannot adjust their prices downwards,
and wages cannot be reduced, leading to a situation where the short-run aggregate supply curve is vertical.
This results in a situation where any increase in aggregate demand will not lead to an increase in output, and the economy remains stuck in a recessionary gap with high unemployment and low output.
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find two numbers whose difference is 48 and whose product is a minimum. smaller number larger number
In this problem, we are asked to find two numbers whose difference is 48 and whose product is a minimum.
To approach this problem, we can use the fact that the product of two numbers is minimized when the numbers are closest to each other. Therefore, we can let x be the smaller of the two numbers, and then the larger number is x + 48.
The product of these two numbers is:
P = x(x + 48) = x^2 + 48x
To find the minimum value of P, we can take the derivative of P with respect to x and set it equal to zero:
dP/dx = 2x + 48 = 0
Solving for x, we get:
x = -24
Substituting this value of x into the expression for P, we get:
P = (-24)^2 + 48(-24) = 576 - 1152 = -576
Therefore, the two numbers whose difference is 48 and whose product is minimized are -24 and 24. Note that the smaller number, -24, is negative, but this makes sense since the problem did not specify that the numbers had to be positive.
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what is the probability that at least 30 of the women in the sample will not meet the age requirement
To calculate the probability that at least 30 of the women in the sample will not meet the age requirement, we need to use the binomial distribution formula:
P(X >= 30) = 1 - P(X < 30)
where X is the number of women who do not meet the age requirement, and P(X < 30) is the cumulative probability of X being less than 30.
The probability of a woman not meeting the age requirement is given as 0.2, so the probability of a woman meeting the age requirement is 0.8. We are sampling 200 women, so the number of women who do not meet the age requirement follows a binomial distribution with n = 200 and p = 0.2.
Using a binomial calculator or software, we can find that P(X < 30) = 0.1656. Therefore, the probability of at least 30 women not meeting the age requirement is:
P(X >= 30) = 1 - P(X < 30) = 1 - 0.1656 = 0.8344
Therefore, the probability that at least 30 of the women in the sample will not meet the age requirement is 0.8344, or approximately 83.44%.
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