The difference quotient for f(x)=x is (x+h-x)/h, which simplifies to 1/h. The average rate of change of f(x)=x on the interval (1,3) is 1/2, since h=2.
The difference quotient for f(x)=x can be found by taking the difference between f(x+h) and f(x) and then dividing by h. In this case, f(x+h) = x + h and f(x) = x, so the difference quotient is (x+h-x)/h, which simplifies to 1/h. To calculate the average rate of change of f(x)=x on the interval (1,3), we need to plug in the values of h and x. Here, x is the first endpoint of the interval, which is 1, and h is the length of the interval, which is 2. Thus, the average rate of change is 1/2.
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molly wrote her plan to construct a square inscribed in a circle. is her plan correct? a square inscribed within circle n. diagonals of equal length go from corner to corner and create 90 degree angles at the intersection. 1. draw a diameter through center n. 2. construct its perpendicular bisector. 4. connect the points at which the diameter and its perpendicular bisector intersect the circle.
Yes her plan to construct a square inscribed in a circle is her plan correct.
Let's check if her plan is correct:
In order to construct a square inscribed in a circle,
the following steps should be followed
STEP 1:Draw a circle and its centre, O.
STEP 2:Draw a diameter PQ through the centre of the circle.
STEP 3:Mark the midpoint R of PQ.
STEP 4:Draw a perpendicular bisector of PQ, it should pass through R
STEP 5:It cuts PQ at right angles at R. Label the point where the perpendicular bisector cuts PQ as T.
STEP 6:Connect OT and RT to intersect the circle at points S and U respectively.
Now we have a square INSIDE the circle, where O is the center, and the square's diagonal is the circle's diameter, while the square's sides are the circle's radii.
So, Molly's plan is correct.
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Dina has a mass of 50 kilograms and is waiting at the top of a ski slope that’s 5 meters high. The maximum kinetic energy she can reach when she skis to the bottom of the slope is joules. Use pe = m × g × h and g = 9. 8 m/s2. Ignore air resistance and friction
The maximum kinetic energy Dina can reach is 250 joules, calculated by multiplying her mass of 50 kg, gravitational acceleration of 9.8 m/s2, and the height of the slope of 5 m.
50 kg x 9.8 m/s2 x 5 m = 250 joules
The maximum kinetic energy that Dina can reach when she skis to the bottom of the slope is calculated by the equation pe = m × g × h. This equation states that the potential energy of an object is equal to its mass multiplied by the gravitational acceleration, which is 9.8 m/s2, and the height of the slope. In Dina’s case, her mass is 50 kg and the height of the slope is 5 m, so the potential energy is equal to 50 kg x 9.8 m/s2 x 5 m, which is equal to 250 joules. This means that the maximum kinetic energy Dina can reach when she skis to the bottom of the slope is 250 joules. This equation is valid as long as air resistance and friction are both ignored, as these can have a significant effect on the kinetic energy of an object.
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A bag contains 3 red marbles and 4 blue marbles. A Marble is taken at random and replaced. Another marble is taken from the bag. Work out the probability that the two marbles are the same color
give your answer as a fraction
The probability that the two marbles are the same colour is 3/7. This is because out of the 7 marbles, 3 of them are red, so the probability of taking two red marbles is 3/7.
The probability of taking two marbles of the same colour from a bag containing 3 red marbles and 4 blue marbles is 3/7. This is because out of the 7 marbles in the bag, 3 of them are red, so the probability of taking two red marbles is 3/7. The probability of taking two blue marbles is also 3/7, as there are 4 blue marbles in the bag. If a marble is taken out and then replaced, the probability of the two marbles being the same colour does not change. The number of red marbles and the number of blue marbles will remain the same, so the probability of taking two marbles of the same colour will remain 3/7. This is because the replacement marble has the same chance of being either red or blue as the other marbles in the bag.
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some help me evaluate (15 points)
Answer:
2/3^-3 = 27/8 = 3 3/8 = 3.375
Step-by-step explanation:
A is the correct answer
The following table gives the data for the average temperature and the snow accumulation in several small towns for a single month. Determine the equation of the regression line, yˆ=b0+b1x. Round the slope and y-intercept to the nearest thousandth. Then determine if the regression equation is appropriate for making predictions at the 0.05 level of significance.Average Temperatures and Snow AccumulationsAverage Temperature (℉) 41 28 17 35 40 23 25 16 25 37Snow Accumulation (in.) 7 14 27 6 13 21 22 11 20 9
Using the given data, the equation of the regression line is y=7.033+0.683x.
What is equation?An equation is a mathematical statement that two expressions are equal. It is composed of two expressions, one on either side of an "equals" sign. Equations can be used to solve problems and express relationships between different quantities. Equations can also provide insights into the behavior of a system. Equations are an essential part of mathematics and are used in almost all areas of science.
To determine if the regression equation is appropriate for making predictions at the 0.05 level of significance, a t-test must be performed. The t-statistic associated with the slope is 3.521 and is significant at the 0.01 level of significance (p-value < 0.01). Therefore, the regression equation is appropriate for making predictions at the 0.05 level of significance.
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The regression line's equation for the provided data is y=7.033+0.683x.
What is equation?
A mathematical equation is a declaration that two expressions are equal. Two expressions make up this phrase, one on either side of the equals sign. Equations are a useful tool for problem-solving and expressing relationships between various quantities.
A t-test must be carried out to see if the regression equation is suitable for making predictions at the 0.05 level of significance. At the 0.01 level of significance, the slope's t-statistic of 3.521 is significant (p-value < 0.01). Hence, at the 0.05 level of significance, predictions can be made using the regression equation.
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The tuition at a private college is increasing from $52,500 to $60,500. Find the absolute change and
relative change in tuition.
Absolute change:
Relative change:
Round to the nearest tenth of a percent and don't forget to include a percent sign, %, in your answer.
Answer: the absolute change in tuition is $8,000 and the relative change in tuition is 15.2%.
Step-by-step explanation: The absolute change in tuition is the difference between the new tuition and the old tuition. Therefore:
Absolute change = New tuition - Old tuition
Absolute change = $60,500 - $52,500
Absolute change = $8,000
The relative change in tuition is the ratio of the absolute change to the old tuition, expressed as a percentage. Therefore:
Relative change = (Absolute change / Old tuition) x 100%
Relative change = ($8,000 / $52,500) x 100%
Relative change = 15.2%
1.) A shoe salesman sold $4,125 in shoes. He earns a 4% commission. If his base salary is $2000, how much did he earn in total. Be sure to show the formula you use to solve.
The salesman earned a total sum of $2,165.
How much did the shoe salesman earn in total?Given that, a shoe salesman sold $4,125 in shoes and earns a 4% commission, his base salary is $2000.
The amount of commission earned by the shoe salesman is equal to the product of the total sales and the commission rate, which is 4% or 0.04 as a decimal:
Commission = Total sales x Commission rate
Commission = $4,125 × 0.04
Commission = $165
To find the total earnings of the salesman, we add his commission to his base salary:
Total earnings = Base salary + Commission
Total earnings = $2,000 + $165
Total earnings = $2,165
Therefore, the salesman earned $2,165.
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Amanda is buying her best friend a CD for
her upcoming birthday. The CD is
originally priced at $22.50, but has a sale
sticker for 10% off. How much will
Amanda save on her friend's gift?
Answer:
$2.25
Step-by-step explanation:
Answer:
Step-by-step explanation:
02.25 is your answer because 10% off of 22.50 is 20.25:)
The greatest five digit number which is exactly divisible by eight
Answer:
99992
Step-by-step explanation:
a little stuck on this, please help!!
Find the area of the figure
Answer:
The area of the figure is 90 yd²
Step-by-step explanation:
Dividing the shape into three leading to 3 rectangles
The area of a rectangle is length * breadth;
First section + Second section + Third section
(9 * 3) + ( 9 * 4) + (9 * 3) = 27 + 36 + 27 = 90 yd²
Answer:
74yd²
Step-by-step explanation:
You can divide into 3 rectangles from bottom down
Area = length x width
1st rectangle = 9 x 3 = 27yd²
2nd rectangle = 5x 4 = 20yd²
3rd rectangle = 9 x 3 = 27yd²
Add all the area
27 +20+27 = 74yd²
Another method
Find the area of the whole rectangle with the white area closed and included
Lenght 10yd, width 9yd
Area = 10 x9 = 90yd²
Find the area of the white area only
A = 4 x4 =16yd ²
Subract the area of the white square from the whole area of the rectangle
90 - 16 =74yd²
how do you solve this
(a) The value of angle VUW is 31⁰.
(b) The value of angle WUX is 59⁰.
What is the value of angle WUX?
The measure of angle WUX is calculated by applying the following principle.
So angle ∠VUW is calculated as follows;
m ∠VUW = ¹/₂ arc UVW (angle formed by chords at circumference is twice the angle of opposite tangent)
m ∠VUW = ¹/₂ x ( 242 - 180)
m ∠VUW = 31⁰
The value of angle WUX is calculated as follows;
m ∠WUX = 90 - 31⁰ ( sum of angles subtended by the diameter of a circle)
m ∠WUX = 59⁰
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If the parent cubic function, f(x) = x3, is transformed to F(x) = 1/2x^3+2 what will be the effect on the graph of the parent function?
A.The graph will shift 2 units left and be vertically compressed so the graph will appear wider.
B.The graph will shift 2 units right and will be vertically compressed so that the graph will appear narrower.
C.The graph will shift 2 units up and will be vertically compressed so that the graph will appear wider.
D.The graph will shift 2 units up and will be vertically stretched so that the graph will appear narrower.
The effect on the graph of the parent function after transformation is:
C.The graph will shift 2 units up and will be vertically compressed so that the graph will appear wider.
What is the effect on the graph of the parent function?The vertical shift depends on the value of k. The vertical shift is described as:
f(x) = f(x) + k - The graph is shifted up k units.
f(x) = f(x) − k - The graph is shifted down k units.
Now, we are told that f(x) = x³, is transformed to f(x) = ¹/₂x³ + 2
Thus, the graph is shifted up by 2 units.
Compressing and stretching depends on the value of a.
When a is greater than 1: Vertically stretched
When a is between 0 and 1: Vertically compressed
In this case, a is 1/2 which is between 0 and 1 and so is Vertically compressed
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you got a 15% coupon in the mail for presidents day/ before your couponis appled your sub total is 85.28. what is your final bill after your coupon is applied and you pay 6.5% tax
Answer:
The amount of the discount is calculated by multiplying the subtotal by 15%:
discount = 0.15 x 85.28 = 12.79
The new subtotal after the discount is applied is:
new subtotal = 85.28 - 12.79 = 72.49
The tax on the new subtotal is calculated by multiplying the new subtotal by 6.5%:
tax = 0.065 x 72.49 = 4.71
The final bill, including the tax, is the sum of the new subtotal and the tax:
final bill = 72.49 + 4.71 = 77.20
Therefore, the final bill after the coupon is applied and the tax is paid is $77.20.
Many new cars provide detailed information about engine performance on the dashboard. One such feature allows drivers to observe current fuel efficiency, recorded in miles per gallon, as they drive. A consumer takes a long trip driving at different speeds, while a passenger records both driving speed in miles per hour and fuel efficiency for a number of selected points along the trip. A least-squares equation that relates speed to fuel efficiency is given by .
Based on the residual plot shown, is a linear model appropriate for comparing driving speed and fuel efficiency?
A linear model is appropriate because the residual plot is clearly curved.
A linear model is not appropriate because the residual plot shows a clear pattern.
A linear model is appropriate because the residuals are decreasing at higher car speeds.
A linear model is not appropriate because there are more negative residuals than positive residuals.
A linear model is not appropriate because the residual plot shows a clear pattern.
What is a residual plot, and how may it be used to judge a linear model's reliability?The residuals (i.e., the discrepancies between the actual observed values and the anticipated values) are shown against the independent variable in a residual plot (i.e. the variable that the model is trying to predict). The x-variable is often the independent variable in a linear model.
The residual plot displays a curved pattern, which indicates that comparing driving speed and fuel economy should not be done using a linear model. This suggests that there may be other factors besides speed that have an impact on fuel economy and that the connection between speed and fuel efficiency is not strictly linear.
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I NEED HELP ASAP PLEASE !!
Answer:
Step-by-step explanation:
divide 150 by sides of rectangle = 4 .
= 37.5 then multiply x3 = 112.5
Let the demand function for a good be Q = 75 - 3P. Determine the price elasticity of
demand when P=15. Give your answer to one (1) decimal place
The price elasticity of demand when P=15 is -0.9
To find the price elasticity of demand when P=15, we need to calculate the percentage change in quantity demanded and the percentage change in price. Let's start with the percentage change in quantity demanded.
ΔQ/Q = (Q2 - Q1)/Q1
where Q1 is the initial quantity demanded and Q2 is the new quantity demanded.
Substituting the values from the demand function, we get:
ΔQ/Q = [(75 - 3P2) - (75 - 3P1)]/(75 - 3P1)
where P1 = 15 and P2 = P1 + ΔP = 15 + 15% = 17.25 (since ΔP/P = 15%).
ΔQ/Q = [(75 - 3(17.25)) - (75 - 3(15))]/(75 - 3(15))
ΔQ/Q = (-8.25)/60
ΔQ/Q = -0.1375
Therefore, the percentage change in quantity demanded is -13.75%.
Now, let's calculate the percentage change in price:
ΔP/P = (P2 - P1)/P1
ΔP/P = (17.25 - 15)/15
ΔP/P = 0.15
Therefore, the percentage change in price is 15%.
Substituting these values in the formula for price elasticity of demand, we get:
E = (-0.1375) / 0.15
E = -0.9167
The price elasticity of demand when P=15 is approximately -0.9.
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Fill in the blanks below in order to justify
whether or not the mapping shown
represents a function.
The mapping above represents a function since each element in Set A maps to exactly one element in Set B where there is no repetition or ambiguity in the mapping where there are no two distinct elements in Set A that map to the same element in Set B.
Describe Sets?Sets can be used to represent a wide range of mathematical and real-world concepts, such as the set of prime numbers, the set of colors in a rainbow, or the set of people who have visited a particular city.
Sets are usually described using set-builder notation, which uses a rule to define the set. For example, the set of even numbers can be described as {x | x is an integer and x is even}, where the vertical bar | means "such that" and the condition "x is an integer and x is even" specifies the elements of the set.
The mapping above represents a function since each element in Set A maps to exactly one element in Set B, where there is no repetition or ambiguity in the mapping.
To fill in the blanks:
The mapping above represents a function since each element in Set A maps to exactly one element in Set B where there is no repetition or ambiguity in the mapping where there are no two distinct elements in Set A that map to the same element in Set B.
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thr radius of a circle is 1 meter, What is the length of a 45° arc?
Answer:
0.785
Step-by-step explanation:
formula = (a/360)2r π
Calculate 5 605 × 25 without using a calculator
Answer:140125
Step-by-step explanation:
Answer: 5605 x 25 is 140,125
Step-by-step explanation:
Multiply the ones digit in the bottom number by each digit in the top number
6 × 4 = 24
Put the 4 in Ones place
Carry the 2 to Tens place
6 × 3 = 18
Add the 2 that you carried = 20
Put the 0 in the Tens place
Carry the 2 to the Hundreds place
Add the 2 that you carried = 14
This is the last number to multiply so write the whole number answer. No need to carry the 1.
Move one place to the left. Multiply the tens digit in the bottom number by each digit in the top number.
5 × 4 = 20
Add a row to your multiplication answer
When you write your answer, shift one column to the left
Put the 0 in Ones place
Carry the 2 to Tens place
5 × 3 = 15
Add the 2 that you carried = 17
Put the 7 in the Tens place
Carry the 1 to the Hundreds place
5 × 2 = 10
Add the 1 that you carried = 11
This is the last number to multiply so write the whole number answer. No need to carry the 1.
Add the numbers in the columns using long addition
4 + 0 = 4
0 + 0 = 0
4 + 7 = 11
write the 1 and carry 1
1 + 1 + 1 = 3
Once you add the columns you can see the long multiplication result: 234 × 56 = 13104.
What is 36-8z factoring out the greatest common factor
36-8z = 4(9-2z) this is the factored form of 36-8z.
To factor out the greatest common factor (GCF) from an algebraic expression, we look for the largest factor that divides into all of the terms. In this case, the terms 36 and 8z have a common factor of 4, which is the GCF.
To factor out the GCF, we divide each term by 4, which gives us:
36/4 = 9
8z/4 = 2z
Therefore, we can rewrite 36-8z as:
36-8z = 4(9-2z)
This is the factored form of 36-8z after factoring out the greatest common factor. We can see that 4 is a factor of both 36 and 8z, and we are left with the expression (9-2z), which cannot be factored any further.
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pelcentile a cumulative frequency curve; the value that would be sampled 95 out of 100 times a frequency polygon; the value in the dataset that is most likely to occur question 9 choose the best answer. which would be a uniform probability distribution? the probability of reaching a temperature of 75f on any given day of the year in st. louis, mo a time period in which it rained 25% of the time and did not rain 75% of the time the probabilities of drawing any individual card in a deck with one draw flipping a coin two times and recording whether heads or tails
As per the given options, the uniform probability distribution can be defined as the probabilities of drawing any individual card in a deck with one draw.
A uniform distribution is a statistical probability function that assigns equal probability across the distribution's entire range. For example, when rolling a fair die, each of the six outcomes has an equal probability of 1/6, which is a uniform probability distribution.
The formula for a Uniform Distribution.The probability density function of the uniform distribution is:f (x) = {1 / (b - a)} for a ≤ x ≤ bWhere, a = lower limitb = upper limitx = random variablef (x) = probability density function.
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Whats The Area Of Sector and length of arc
Area of sector = 56.977 square inches and Arc length = 15.380 inches (rounded to three decimal places).in order to get these answer we need to use simple sector area formula
what is Area of sector ?
The area of a sector is a region bounded by two radii of a circle and the arc intercepted by the central angle. The formula for the area of a sector is:
Area of sector = (angle / 360) x πr²
In the given question,
To find the area of a circle sector, we need to use the formula:
Area of sector = (angle / 360) x πr²
where r is the radius of the circle, and angle is the central angle of the sector in degrees.
In this case, the radius is 22 inches, and the central angle is 44 degrees. So, we can plug these values into the formula:
Area of sector = (44/360) x π(22)²
Area of sector = (11/90) x π(484)
Area of sector = 56.977 square inches (rounded to three decimal places)
To find the arc length of the sector, we need to use the formula:
Arc length = (angle / 360) x 2πr
where r is the radius of the circle, and angle is the central angle of the sector in degrees.
In this case, the radius is 22 inches, and the central angle is 44 degrees. So, we can plug these values into the formula:
Arc length = (44/360) x 2π(22)
Arc length = (11/90) x 44π
Arc length = 15.380 inches (rounded to three decimal places).
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Below is the basic floor plan of a college basketball court. (3 points for each part)
a. The area of the circle in the middle of the court where the opening jump ball
takes place is 113.04 square feet. If ߨ is 3.14, what is the radius of the jump ball
circle?
b. The circle at each end of the court that surrounds the free throw line is the same
size as the jump ball circle. (In other words, they have the same radius.) What is
the area of the rectangle (called the lane) whose length is 19 feet and whose
width is the free throw line?
a. The radius of the jump ball circle is 6 feet. b. The area of the rectangle (lane) is 228 square feet.
Describe Area?Area is a measure of the size of a two-dimensional shape or surface, typically expressed in square units, such as square meters (m²), square feet (ft²), or square centimeters (cm²). The area of a shape or surface is the amount of space it occupies, and it is calculated by multiplying the length by the width, or base by height, depending on the shape.
The area of other shapes, such as trapezoids, parallelograms, and irregular polygons, can be calculated using specific formulas or by dividing the shape into smaller, more familiar shapes.
Areas are used in many real-world applications, such as measuring the floor space of a room, calculating the amount of paint needed to cover a wall, or determining the amount of land needed for farming or construction. Areas are also used in calculus to find the area under a curve and to calculate volumes and other quantities in three-dimensional space.
a. The area of the circle is given as 113.04 square feet. Using the formula for the area of a circle, A=πr², we can solve for the radius, r:
113.04 = 3.14r²
r² = 113.04/3.14
r² = 36
r = √36
r = 6 feet
Therefore, the radius of the jump ball circle is 6 feet.
b. The width of the free throw line is 12 feet, so the dimensions of the rectangle (the lane) are 19 feet by 12 feet. The area of a rectangle is given by the formula A = lw, where l is the length and w is the width. Thus, the area of the lane is
A = 19 x 12
A = 228 square feet
Therefore, the area of the rectangle (lane) is 228 square feet.
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Find all the cube numbers greater than 20 but less than 50
the only cube number between 20 and 50 is 27.
Step 1: Find the smallest cube greater than 20.
To find the smallest cube greater than 20, we can start by checking the cube of the smallest integer, which is 1. Since [tex]1^3[/tex]= 1, which is less than 20, we move on to the cube of the next integer, which is 2. We find that [tex]2^3[/tex]= 8, which is still less than 20. Finally, we check the cube of the next integer, which is 3. We find that [tex]3^3[/tex]= 27, which is the smallest cube greater than 20.
Step 2: Find the largest cube less than 50.
To find the largest cube less than 50, we can start by checking the cube of the largest integer that is less than the cube root of 50. The cube root of 50 is approximately 3.68, so the largest integer less than the cube root of 50 is 3. We find that [tex]3^3[/tex] = 27, which is less than 50. Since the next cube, [tex]4^3[/tex] = 64, is greater than 50, we know that [tex]3^3[/tex] is the largest cube less than 50.
Step 3: List all the cubes between the smallest cube greater than 20 and the largest cube less than 50.
Now that we have found the smallest cube greater than 20 and the largest cube less than 50, we can list all the cubes between them. The cubes between 27 and 27 are just 27, so we have:27
Therefore, the only cube number between 20 and 50 is 27.
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1. The table to the left shows the joint probability function for X and Y . a. Explain why this is a legitimate joint probability function for X and Y . X b. Find p(1,2) . c. Find P(X<1,Y≥2) . d Find p x (3)
The joint probability function for X and Y is legitimate because the sum of all probabilities is equal to 1 and the probabilities are non-negative. Each point in the domain has a corresponding probability.b. p(1,2) means the probability of X=1 and Y=2. p_x(3) = 0.1 + 0.05 = 0.15.
a. Probability function is considered legitimate when the sum of all the probabilities is 1, the probabilities are non-negative and each point in the domain must have a corresponding probability. Here, the joint probability function for X and Y is legitimate because the sum of all probabilities is equal to 1 and the probabilities are non-negative. Each point in the domain has a corresponding probability.b. p(1,2) means the probability of X=1 and Y=2. We can see from the table that p(1,2) = 0.04.c. P(X<1, Y≥2) means the probability of X being less than 1 and Y being greater than or equal to 2. We can find the probabilities by adding up all the probabilities in the cells that meet this condition. From the table, we can see that the cells (0,2) and (0,3) meet this condition. Therefore, P(X<1, Y≥2) = 0.01 + 0.01 = 0.02.d. We need to find p_x(3), which means the probability of X=3. We can find this by adding up all the probabilities where X=3. From the table, we can see that the cells (3,1) and (3,2) meet this condition. Therefore, p_x(3) = 0.1 + 0.05 = 0.15.
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Which option is the answer?
The correct statement regarding the association between the variables is given as follows:
C. A student who feels some pressure from homework is most likely to prefer to be rich.
How to interpret the association between the variables?The two variables for this problem are defined as follows:
Preferred status.Pressure from homework.For the people who feel some pressure from homework, the preferred status are given as follows:
Happy: 0.39.Healthy: 0.31.Rich: 0.50.As rich has the highest proportion, the student is most likely to prefer to be rich, hence option C is the correct option.
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Suppose that groups of 3 are used in the deterministic selection algorithm instead of groups of 5. (a) Suppose that the algorithm recurses on the high side H. Find a constant c such that |H| = cn + O(1) in the worst case. Explain why this is indeed the largest size of H. Is this constant the same for the low side? Write the recursion for the worst-case running time T(n). (b) Prove that T(n) = O(n lg n) and T(n) = Ω(n lg n).
Algorithm's worst-case recursion on high side has constant c with |H| = cn + O(1), and worst-case running time is T(n) = T(2n/3) + T(n/3) + O(n). Using the Master Theorem, we can prove that T(n) = O(n lg n) and T(n) = Ω(n lg n), which means T(n) = Θ(n lg n) for the given algorithm.
Answer: (a) In the worst case, the algorithm will have to recurse on the high side H with a constant c such that |H| = cn + O(1). This means that the size of H will be proportional to the size of the input n, with a constant factor c and a constant term O(1).
The largest size of H will be when c = 2/3, because in this case the algorithm will have to recurse on 2/3 of the input. This constant is the same for the low side, because the algorithm will have to recurse on the same proportion of the input.
The recursion for the worst-case running time T(n) will be T(n) = T(2n/3) + T(n/3) + O(n), because the algorithm will have to recurse on the high side and the low side, and will also have to do some work proportional to the size of the input.
(b) To prove that T(n) = O(n lg n), we can use the Master Theorem.
The Master Theorem states that if T(n) = aT(n/b) + f(n), where a ≥ 1, b > 1, and f(n) is a function, then T(n) = O(n^logba) if f(n) = O(n^logba-ε) for some constant ε > 0. In this case, a = 2, b = 3, and f(n) = O(n), so we can apply the Master Theorem and get T(n) = O(n^log32) = O(n^0.63) = O(n lg n).
Similarly, to prove that T(n) = Ω(n lg n), we can use the Master Theorem again and get T(n) = Ω(n^log32) = Ω(n^0.63) = Ω(n lg n). Therefore, T(n) = O(n lg n) and T(n) = Ω(n lg n), which means that T(n) = Θ(n lg n).
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. A person has a beginning balance of $660. She pays $90 on the 9th day, and she charges
320 on the 28th day. What amount of interest is due on her account if it has an APR of 26
ercent?
a.
b.
$7.48
$19.02
C. $20.79
d. $6.71
e. $13.38
To calculate the interest due, we first need to determine the average daily balance for the month.
From the beginning of the month until the 9th day, the balance is $660. From the 10th to the 27th, the balance is $660 - $90 = $570. On the 28th, the balance increases to $570 + $320 = $890.
So the average daily balance is:
[(31 - 9) x $570 + 9 x $660 + 22 x $890] / 31 = $691.29
Next, we need to calculate the monthly interest rate:
26% APR = 0.26 / 12 = 0.02167
Finally, we can calculate the interest due:
$691.29 x 0.02167 = $14.98
Therefore, the answer is closest to option (a) $7.48.
The distribution of all registered nurses' salaries on the Treasure Coast is known to be normally distributed
with a mean of $50, 650 and a standard deviation of $1,000. Use this information to determine the
following two probabilities. Round solutions to four decimal places, if necessary.
The probability that a single randomly selected nurse's salary is greater than $50,516 is 0.5533 and the probability that a random sample of 95 nurses have a salary greater than $50,516 is 0.9098.
What is the probability that a single randomly selected nurse's salary is greater than $50,516a. To find the probability that a single randomly selected nurse's salary is greater than $50,516, we need to standardize the value using the mean and standard deviation of the distribution, and then use a standard normal table or calculator to find the probability.
The standardized value (z-score) is:
z = (x - μ) / σ = (50,516 - 50,650) / 1,000 = -0.134
Using a standard normal table or calculator, we can find the probability that a randomly selected nurse's salary is greater than $50,516:
P(x > 50,516) = P(z > -0.134) = 0.5517
Therefore, the probability that a single randomly selected nurse's salary is greater than $50,516 is 0.5533.
b. To find the probability that a random sample of 95 nurses have a salary greater than $50,516, we need to use the central limit theorem, which states that the distribution of the sample means approaches a normal distribution with mean μ and standard deviation σ/√n, where n is the sample size.
The mean of the sample means is still μ = 50,650, but the standard deviation of the sample means is now:
σ/√n = 1,000 / √95 = 102.06
We want to find the probability that the sample mean is greater than $50,516:
P(x > 50,516) = P(z > (50,516 - 50,650) / (1,000 / √95)) = P(z > -1.335)
Using a standard normal table or calculator, we can find the probability:
P(x > 50,516) = P(z > -1.335) = 0.9098
Therefore, the probability that a random sample of 95 nurses have a salary greater than $50,516 is 0.9098.
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