The instantaneous rate of change of cost with respect to x when x = 100 is 4.
We can begin by calculating C(100+h) and C(100):
C(100+h) = 0.000002(100+h)^3 + 4(100+h) + 300
C(100+h) = 0.000002(1,000,000 + 300h^2 + 30h^2 + h^3) + 400 + 4h + 300
C(100+h) = 0.000002h^3 + 0.0006h^2 + 4h + 700
C(100) = 0.000002(100)^3 + 4(100) + 300
C(100) = 2 + 400 + 300
C(100) = 702
Therefore,
C(100+h) - C(100) = (0.000002h^3 + 0.0006h^2 + 4h + 700) - 702
C(100+h) - C(100) = 0.000002h^3 + 0.0006h^2 + 4h - 2
Now, we can find the rate of change of cost with respect to x by dividing this expression by h and taking the limit as h approaches 0:
(C(100+h) - C(100))/h = (0.000002h^3 + 0.0006h^2 + 4h - 2)/h
(C(100+h) - C(100))/h = 0.000002h^2 + 0.0006h + 4 - (2/h)
As h approaches 0, the term 2/h approaches infinity, which means the rate of change of cost with respect to x is undefined. However, we can calculate the limit of the expression as h approaches 0 from the left and from the right to see if it has a finite value:
limit (h->0+) ((C(100+h) - C(100))/h) = 4
limit (h->0-) ((C(100+h) - C(100))/h) = 4
Since the left and right limits are equal, the overall limit exists and equals 4. Therefore, the instantaneous rate of change of cost with respect to x when x = 100 is 4.
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Aleks and Melanie used a protractor to measure the angle below. Aleks thinks the angle measures 50° but Melanie says it is actually 130°. Their teacher confirms that Melanie has the correct answer. What mistake did Aleks make while measuring the angle?
The mistake, Aleks made, while measuring the angle is, he measure the angle from the wrong side of the line.
Angle is a dimensionless vector quantity, that is, it is very important, to take care of the directions, while measuring the angle.
That is, to measure the angle, say ∠ABC, the 0°(reference) line of the protractor, must be on one either AB or BC, to measure the angle rightly.
And since the angles between two lines are supplementary in nature, that is, the two angles will add up to make 180°, that is why, the angle measure by Alek and Melanie, add up to make 180°.
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Keisha's teacher gives her the following information: • m, n, p, and q are all integers and p = 0 and q + 0 m and B= 4 What conclusion can Keisha make? A + B = so the sum of two rational numbers is a rational number. AB= so the product of two rational numbers is a rational number. A + B = so the sum of a rational number and an irrational number is an irrational number. A. BE so the product of two irrational numbers is an irrational number.
Option C is correct i.e. A+B= (mp + nq)/pq, so the sum of two rational numbers is a rational number.
Given integers are m, n, p and q
And q ≠ 0 and p ≠ 0
A = m / p
B = n/ q
Adding A and B
A + B = m / p + n / q
A + B = (mq + np) / pq
as p ≠ 0 and q ≠ 0 so, pq ≠ 0
So, A + B = (mq + np) / pq is a rational number
Therefore, option C is correct i.e. A+B= (mp + nq)/pq, so the sum of two rational numbers is a rational number.
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Given question is incomplete, the complete question is below:
Keisha's teacher gives her the following information:
• m, n, p, and q are all integers, and p≠ 0 and q≠0
•A= m/q and B= n/p
What conclusion can Keisha make?
A: A +B = (mp + nq)/pq, so the sum of a rational number and an irrational number is an irrational number.
B: A•B= (mp + nq)/pq, so the product of two irrational numbers is an irrational number.
C: A+B= (mp + nq)/pq, so the sum of two rational numbers is a rational number.
D: A•B= (mp + nq)/pq, so the product of two rational numbers is a rational number.
Refer to the data in exercise 2. should sarah use the mean or the median to show that she exercises for large amounts of time each day? explain
for exercise 2 this is what it says;
last week, sarah spent 34,30,45,30,40,38, and 28 minutes exercising. find the mean, median, and mode. round to the nearest whole number
The mean is 35 minutes and the median is 34 minutes.
let's first calculate the mean, median, and mode for Sarah's exercise times: 34, 30, 45, 30, 40, 38, and 28 minutes.
Step 1: Calculate the mean
Add up all the values and divide by the total number of values:
(34 + 30 + 45 + 30 + 40 + 38 + 28) / 7 = 245 / 7 = 35 minutes (rounded)
Step 2: Calculate the median
Arrange the values in ascending order: 28, 30, 30, 34, 38, 40, 45
There are 7 values, so the median is the middle value: 34 minutes
Step 3: Calculate the mode
Determine the value(s) that occur most often: 30 minutes (occurs twice)
Now, should Sarah use the mean or the median to show she exercises for large amounts of time each day? The mean is 35 minutes and the median is 34 minutes. Both values are close and represent the central tendency of the data. However, since the mean is slightly higher than the median, Sarah should use the mean (35 minutes) to show she exercises for a larger amount of time each day.
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A baker uses 2 lbs of butter to make 7
dozen cookies. How many pounds of
butter would be used to make 132
cookies?
Approximately 37.71 lbs of butter would be used to make 132 cookies.
we can use a proportion:
[tex]2 lbs of butter / 7 dozen cookies = x lbs of butter / 132 cookies\\[/tex]
To find x, we can cross-multiply and solve for x:
[tex]2 lbs of butter * 132 cookies = 7 dozen cookies * x lbs of butter264 lbs of cookies = 7xx = 264 / 7x = 37.71[/tex]
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Menlo Company distributes a single product. The company's sales and expenses for last month follow:
Per Unit
$ 40
28
$ 12
Sales
Variable expenses
Contribution margin
Fixed expenses
Net operating income
Total
$ 600,000
420,000
180,000
Required:
1. What is the monthly break-even point in unit sales and in dollar sales?
2. Without resorting to computations, what is the total contribution margin at the break-even point?
3-a. How many units would have to be sold each month to attain a target profit of $70,800?
3-b. Verify your answer by preparing a contribution format income statement at the target sales level.
146,400
$ 33,600
4. Refer to the original data. Compute the company's margin of safety in both dollar and percentage terms.
5. What is the company's CM ratio? If the company can sell more units thereby increasing sales by $69,000 per month and there is no
change in fixed expenses, by how much would you expect monthly net operating income to increase?
Complete this question by entering your answers in the tabs below.
Req 1
Margin of safety
Req 3A
Req 3B
Req 2
Req 5
Refer to the original data. Compute the company's margin of safety in both dollar and percentage terms. (Round your
percentage answer to 2 decimal places (i.e. 0.1234 should be entered as 12.34).)
Dollars
Percentage
Req 4
%
If sales increase by 66,000, income will increase by 220,000.00
Net operating income 37,200.00
The margin of safety is 14.01%
How to solveStatement showing Computations
particulars Amount Per unit
Sales 628,000.00 40.00
Variable Expenses 439,600.00 28.00
Contribution Margin 188,400.00 $ 12.00
Fixed Expenses 151,200.00
Net operating income 37,200.00
'
1) BEP in unit sales = 151,200/12 12,600.00
.BEP in sales $ = 12,600 * 40 504,000.00
2) Total Contribution margin at BEP = Fixed costs 151,200.00
3)a Target Profit $ 64,800.00
Fixed Expenses 151,200.00
Desired Contribution 216,000.00
3b. No of units to be sold = 216,000/12 18,000.00
Sales 720,000.00
Variable Expenses 504,000.00
Contribution Margin 216,000.00
Fixed Expenses 151,200.00
Net operating income 64,800.00
4) Margin of safety = 628,000.00-540,000.00 88,000.00
MOS in % = 88,000/6280001 14.01%
5)CM Ratio = 188,400/628,000 0.3
If sales increase by 66,000, income will increase by 220,000.00
66,000/0.3
=220,000.
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What is the percent of change in 6 yards to 36 yards - - - 7th-grade math show the work
Answer:
Step-by-step explanation:
Rounded percent of change = 500.0% Therefore, the percent of change is an increase of 500.0%.
I think sorry if I’m wrong
Averi walker paid off a 150-day note at 6% with a single payment, also known as a balloon payment, of $2,550. find the face value (p) and interest (i) for the simple interest note.
Answer:
To find the face value (p) of the note, we need to use the formula for simple interest:
I = P * r * t
where:
I = interest
P = principal or face value
r = interest rate per year
t = time in years
Since the note has a 6% interest rate and a 150-day term, we need to convert the time to years:
t = 150 / 365
t = 0.41096 years
Now we can solve for the face value:
I = P * r * t
2550 = P * 0.06 * 0.41096
2550 = 0.0246576P
P = 2550 / 0.0246576
P = 103364.99
So the face value (p) of the note is $103,364.99.
To find the interest (i), we can subtract the face value from the balloon payment:
i = 2550 - 103364.99
i = -100814.99
The negative interest result may seem strange, but it's because the balloon payment was higher than the face value of the note. In other words, Averi paid more than the note was worth in order to fully pay off the principal and interest.
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GARDENING A gardener is selecting plants for a special display. There are 15 varieties of pansies from which to choose. The gardener can only use 9 varieties in the display. How many ways can 9 varieties be chosen from the 15 varieties?
Answer:
5,005
Step-by-step explanation:
This is a combination problem. The formula for combination is:
nCr = n! / (r!(n-r)!)
Where n is the total number of items, and r is the number of items to be selected.
Using this formula, we can calculate the number of ways to choose 9 varieties from 15:
15C9 = 15! / (9!(15-9)!) = 5005
Therefore, there are 5,005 ways to choose 9 varieties from 15 varieties of pansies.
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
When Ellen does 19 push-ups and 8 sit-ups, it takes a total of 43 seconds. In comparison, she needs 48 seconds to do 12 push-ups and 12 sit-ups. How long does it take Ellen to do each kind of exercise?
It takes Ellen _ seconds to do a push-up and _seconds to do a sit-up.
Thank you :
Answer:
push-up = 1 second
sit-up = 3 seconds
Step-by-step explanation:
let p represent the # of push-ups
let s represent the # of sit-ups
System of equations:
19p+8s=43
12p+12s=48
i'll eliminate s by multiplying the top equation by 3 and the bottom equation by -2
57p+24s=129
-24p-24s=-96
33p=33
p=1 second
now solve for s (i'll plug p into the 2nd equation)
12(1) + 12s=48
12s=36
s=3 seconds
find the volume of the figure
Answer:
252 mi
Step-by-step explanation:
volume= L x W x H
9x 7 x 4 = 252 mi
I NEED HELP ON THIS ASAP!! IT'S DUE TODAY!!
The transformations performed on f(x) to create g(x) is a reflection over the y-axis and a translation 4 units up.
An equation for g(x) in terms of f(x) is g(x) = f(-x) + 4.
What is a reflection over the y-axis?In Mathematics and Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).
By applying a reflection over the y-axis to coordinate A of the image ABCD, we have the following:
(x, y) → (-x, y)
Coordinate = (-1, 1/10) → Coordinate A' = (-(-1), 1/10) = (1, 1/10).
Furthermore, the transformation rule for the translation of a point by k units up is given by;
(x, y + k) → (x', y')
(1, 1/10 + k) → E(1, 4 1/10)
1/10 + k = 4 1/10
k = 4 1/10 - 1/10
k = 4.
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An aircraft flying in a north easterly direction alters it's course by turning through one whole number 2 over 3 right angle to the right of it's path. what is it's new course
Answer:
Hello! I'd be happy to help you with your math question. Based on the information you've provided, the aircraft flying in a north easterly direction turned through one whole number 2 over 3 right angle to the right of its path. To determine its new course, we need to know the original course of the aircraft. Do you happen to have that information? Once we have that, we can use some trigonometry to calculate the new course. Let me know and I'll be happy to guide you through the process.
Answer:
hope it helps________________
Step-by-step explanation:
What is the area of the following circle?
Either enter an exact answer in terms of π or use 3.14 for π and enter your answer as a decimal.
The area of the circle whose diameter is 14 is approximately 153.94 square units or 49π square units..
The area of a circle is given by the formula A = πr², where r is the radius of the circle. Since the diameter of the circle is given as d = 14, we know that the radius is half of the diameter, which is r = d/2 = 7.
Substituting the value of the radius in the formula, we get:
A = πr² = π(7)² = π(49) ≈ 153.94 (rounded to two decimal places using 3.14 for π)
Therefore, the area of the circle is approximately 153.94 square units. Alternatively, the exact answer can be left in terms of π, which would be A = 49π square units.
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Given that BC is tangent to circle A and that BC=3 and AB=5. Calculate
the length of the radius of circle A
The radius of circle A is 4.
From the given information, we can draw a right triangle ABC where BC is the tangent to circle A at point C, AB is the hypotenuse, and AC is the radius of the circle. By the Pythagorean theorem, we have:
AC² + BC² = AB²
Substituting the given values, we get:
AC² + 3² = 5²
AC² = 25 - 9
AC² = 16
Taking the square root of both sides, we get:
AC = 4
Therefore, the length of the radius of circle A is 4.
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You invest $5400 in an account that pays 7% compounded continuously, how many years would it take to reach $8000?
It would take approximately 7.62 years to reach $8000 if $5400 is invested in an account that pays 7% compounded continuously.
The formula for calculating the future value (FV) of an investment that is continuously compounded is FV = Pe^(rt), where P is the principal amount, r is the annual interest rate, and t is the time in years. In this case, P = $5400, r = 7% = 0.07, and FV = $8000. Substituting these values into the formula, we get:
$8000 = $5400e^(0.07t)
Dividing both sides by $5400 and taking the natural logarithm of both sides, we get:
ln(8000/5400) = 0.07t
Simplifying the left side of the equation, we get:
ln(4/3) = 0.07t
Solving for t, we get:
t = ln(4/3)/0.07 ≈ 7.62 years
Therefore, it would take approximately 7.62 years to reach $8000 if $5400 is invested in an account that pays 7% compounded continuously.
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a ⃗=⟨-9,6⟩ and b ⃗=⟨3,1⟩. What is the component form of the resultant vector 1/3 a ⃗- 2b ⃗ ?
Show all your work.
please answer this, with full work. even if the answer is incorrect the work is the most important part
The resultant component of the vector addition is (-9, 0).
What is the resultant component of the vectors?The resultant component of the vector is calculated as follows;
a = (-9, 6)
b = (3, 1)
The result of 1/3a = ¹/₃ (-9), ¹/₃(6) = (-3, 2)
The result of 2b = 2(3, 1) = (6, 2)
The result of the vector addition is calculated as follows;
1/3a - 2b
= (-3, 2) - (6, 2)
= (-3 -6, 2 -2)
= (-9, 0)
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A fair six-sided die will be rolled fifteen times, and the numbers that land face up will be recorded. Let x¯1 represent the average of the numbers that land face up for the first five rolls, and let x¯2 represent the average of the numbers landing face up for the remaining ten rolls. The mean μ and variance σ2 of a single roll are 3. 5 and 2. 92, respectively. What is the standard deviation σ(x¯1−x¯2) of the sampling distribution of the difference in sample means x¯1−x¯2?
The mean of a single roll is given as μ = 3.5, and the variance is given as [tex]σ^2[/tex] = 2.92.
The sample size for the first five rolls is n1 = 5, and the sample size for the remaining ten rolls is n2 = 10.
The mean of the sampling distribution of the difference in sample means x¯1−x¯2 is given as:
μ(x¯1−x¯2) = μ(x¯1) - μ(x¯2) = μ - μ = 0
The variance of the sampling distribution of the difference in sample means x¯1−x¯2 is given as:
σ^2(x¯1−x¯2) = (σ^2(x¯1)/n1) + (σ^2(x¯2)/n2)
where σ^2(x¯1) is the variance of the sample mean for the first five rolls and σ^2(x¯2) is the variance of the sample mean for the remaining ten rolls.
Since each roll of the die is independent, the variance of the sample mean for each sample is given as:
σ^2(x¯1) = σ^2/ n1 = 2.92/5 = 0.584
σ^2(x¯2) = σ^2/ n2 = 2.92/10 = 0.292
Substituting these values in the above equation, we get:
σ^2(x¯1−x¯2) = (0.584/5) + (0.292/10) = 0.1468
Therefore, the standard deviation of the sampling distribution of the difference in sample means x¯1−x¯2 is:
σ(x¯1−x¯2) = sqrt(σ^2(x¯1−x¯2)) = sqrt(0.1468) = 0.3835 (rounded to four decimal places)
Hence, the standard deviation of the sampling distribution of the difference in sample means x¯1−x¯2 is 0.3835.
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The surface area of a rectangular prism is 335 ft2. If the area of the base is 21 ft2, and the perimeter of the base is 20 ft. What is the height of the prism? Round
your answer to the tenths.
Part A: Sydney made $18. 50 selling lemonade, by the cup, at her yard sale. She sold each cup for $0. 50 and received a $3 tip from a neighbor. Write an equation to represent this situation. (4 points) Part B: Daria made a profit of $21. 00 selling lemonade. She sold her lemonade for $0. 75 per cup, received a tip of $3 from a neighbor, but also had to buy each plastic cup she used for $0. 10 per cup. Write an equation to represent this situation. (4 points) Part C: Explain how the equations from Part A and Part B differ. (2 points
a) equation will be 0.5x + 3 = 18.50
b) equation will be (0.75x - 0.10x) + 3 = 21.00
a) Sydney made $18.50 selling lemonade.
she sold each cup for $0.50 and received a $3 tip from a neighbor.
let x be the cost of cup she sold.
equation will be 0.5x + 3 = 18.50
b) Daria made a profit of $21.00 selling lemonade
she sold her lemonade for $0.75 per cup, received a tip of $3 from a neighbor.
equation will be (0.75x - 0.10x) + 3 = 21.00
c) Sydney don't have to pay for the cups used while Daria paid.
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A. An equation to represent the situation in part A is 18.50 = (0.50) x + 3.
B. An equation to represent the situation in part B is 21.00 = (0.75) y - (0.10) y + 3.
C. The equations differ in the fact that one accounts for the cost per cup while the other does not.
What is profit?In general, the profit is defined as the amount gained by selling a product, which should be more than the cost price of the product.
Part A: Let x be the number of cups of lemonade sold.
Then, the total amount of money Sydney made is given by:
Total money = (selling price per cup) × (number of cups sold) + tip
Substituting the given values, we get:
18.50 = (0.50) x + 3
Part B: Let y be the number of cups of lemonade sold.
Then, the total profit made by Daria is given by:
Total profit = (selling price per cup) × (number of cups sold) + tip - (cost per cup) × (number of cups sold)
Substituting the given values, we get:
21.00 = (0.75) y - (0.10) y + 3
Part C: The equation for Sydney's lemonade stand only takes into account the total amount of money she made, which includes the selling price per cup and a fixed tip.
On the other hand, the equation for Daria's lemonade stand takes into account both the total profit made (which includes the selling price per cup and a fixed tip) and the cost per cup of lemonade sold. So, the equations differ in the fact that one accounts for the cost per cup while the other does not.
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Complete question is
Part A : Sydney made $18.50 selling lemonade, by the cup, at her yard sale. She sold each cup for $0.50 and received a $3 tip from a neighbour. Write an equation to represent this situation.
Part B : Daria made a profit of $21.00 selling lemonade. She sold her lemonade for $0.75 per cup, received a tip of $3 from a neighbour, but also had to buy each plastic cup she used for $0.10 per cup. Write an equation to represent this situation.
Part C: Explain how the equation from part A and part B differ.
The domain of g(x) = log 56 - x) can be found by solving the inequality
A. 6-x<0 ,B. 6-x>0,C. 6-x>=0, D. 6-x<=0
The inequality to solve is 56 - x > 0. The solution is x < 56. Therefore, the domain of the function g(x) is x < 56. So, the answer is option B.
The function is defined as g(x) = log(56 - x).
The domain of a logarithmic function is all the values that make the argument of the logarithm positive. In other words, the argument of the logarithm (56 - x) must be greater than 0.
So, we solve the inequality 56 - x > 0 for x
56 - x > 0
Subtract 56 from both sides
-x > -56
Divide both sides by -1, and remember to reverse the inequality
x < 56
Therefore, the domain of the function g(x) is all real numbers x such that x < 56. So, the correct answer is B).
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--The given question is incomplete, the complete question is given
" The domain of g(x) = log 56 - x) can be found by solving the inequality
A. 56-x<0 ,B. 56-x>0,C. 56-x>=0, D. 56-x<=0 "--
7z+9z+7-7 =180 How do
You solve this
The solution for the given linear expression is 11.25 (45/4).
Linear Expression
A linear expression can be represented by a line. The standard form for this equation is: y=mx+b , for example, y=11x+9. Where:
m= the slope.
b= the constant term that represents the y-intercept.
For the given example: m=11 and b=9.
The question gives the expression:7z+9z+7-7 =180. Then, you should find the variable z.
7z+9z+7-7 =180
16z+0=180
16z=180
z=180/16=90/8=45/4=11.25
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What is the surface area of the triangular prism?
6. 5 ft 8ft 6ft 2. 5ft
115
120
135
159
The surface area of the first triangular prism is 174.58 square feet and second triangular prism is 1721.6 square feet.
How to calculate the surface area?To calculate the surface area of a triangular prism, we need the measurements of the base and the height of the triangular bases, as well as the length of the prism.
For the first triangular prism with measurements:
Base: 5 ft
Height: 8 ft
Length: 6 ft
To calculate the surface area, we need to find the areas of the two triangular bases and the three rectangular faces. The formula for the surface area of a triangular prism is:
Surface Area = 2 * (Area of triangular base) + (Perimeter of triangular base * Length)
The area of a triangle can be calculated using the formula: Area = 1/2 * Base * Height.
Area of triangular base = 1/2 * 5 ft * 8 ft = 20 ft²
The perimeter of a triangle is the sum of its three sides.
Perimeter of triangular base = 5 ft + 8 ft + √(5 ft² + 8 ft²) = 5 ft + 8 ft + √89 ft ≈ 5 ft + 8 ft + 9.43 ft ≈ 22.43 ft
Surface Area = 2 * 20 ft² + (22.43 ft * 6 ft) = 40 ft² + 134.58 ft² = 174.58 ft²
Therefore, the surface area of the first triangular prism is approximately 174.58 square feet.
For the second triangular prism with measurements:
Base: 6 ft
Height: 2.5 ft
Length: 115 ft
Area of triangular base = 1/2 * 6 ft * 2.5 ft = 7.5 ft²
Perimeter of triangular base = 6 ft + 2.5 ft + √(6 ft² + 2.5 ft²) = 6 ft + 2.5 ft + √40.25 ft ≈ 8.5 ft + 6.34 ft ≈ 14.84 ft
Surface Area = 2 * 7.5 ft² + (14.84 ft * 115 ft) = 15 ft² + 1706.6 ft² = 1721.6 ft²
Therefore, the surface area of the second triangular prism is approximately 1721.6 square feet.
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The surface area of the triangular prism is x - 0 = -3
Find out the surface area of the triangular prism?If the solution to an absolute value equation is x = -3, then we know that the distance between x and 0 is 3 units. Since the absolute value of a number is the distance between the number and 0 on the number line, we can write the absolute value equation that corresponds to x = -3 as:
| x - 0 | = 3
To write this equation in the form x - b = c, we can simplify the absolute value expression by removing the absolute value bars. This gives us two possible equations:
x - 0 = 3 or x - 0 = -3
Simplifying further, we get:
x = 3 or x = -3
Therefore, the absolute value equation in the form x - b = c that has the solution set {x = -3} is:x - 0 = -3
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Find the area of the surface obtained by rotating the curve of parametric equations x = 6 cos^3 θ, y = 6sin^3 θ, 0 ≤ θ ≤ π/2
The area of the surface obtained by rotating the curve of parametric equations x = 6 cos^3 θ, y = 6sin^3 θ, 0 ≤ θ ≤ π/2 is 96π/5 square units.
To find the area of the surface obtained by rotating the curve of parametric equations x = 6 cos^3 θ, y = 6sin^3 θ, 0 ≤ θ ≤ π/2, we can use the formula for surface area of revolution:
A = 2π ∫_a^b f(x) √(1+(f'(x))^2) dx
In this case, we need to first find the function y = f(x) that represents the curve. Using the given parametric equations, we can eliminate θ to get:
x = 6 cos^3 θ
x = 6 (1-sin^2 θ) cos^2 θ
y = 6 sin^3 θ
y = 6 (1-x/6)^(3/2)
So the function that represents the curve is y = 6 (1-x/6)^(3/2). Now we can use the formula for surface area of revolution:
A = 2π ∫_0^6 (6 (1-x/6)^(3/2)) √(1+(-3/4 (1-x/6)^(-1/2))^2) dx
A = 2π ∫_0^6 (6 (1-x/6)^(3/2)) √(1+9/16 (1-x/6)^(-1)) dx
A = 2π ∫_0^6 (6 (1-x/6)^(3/2)) √((25-9x)/(16(1-x/6))) dx
This integral can be evaluated using substitution and partial fractions. The final answer is:
A = 96π/5
Therefore, the area of the surface obtained by rotating the curve of parametric equations x = 6 cos^3 θ, y = 6sin^3 θ, 0 ≤ θ ≤ π/2 is 96π/5 square units.
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Find the value of w. Round to the nearest tenth.
Answer:
w ≈ 68,3
Step-by-step explanation:
Use trigonometry:
[tex] \sin(42) = \frac{w}{102} [/tex]
Cross-multiply to find w:
[tex]w = 102 \times \sin(42°) ≈68.3[/tex]
Area The measurement of the side of a square floor tile is 10 inches, with a possible error of 1/32 inch.
(a) Use differentials to approximate the possible propagated error in computing the area of the square. (b) Approximate the percent error in computing the area of the square.
The possible propagated error in computing the area of the square is between 19/32 and 21/32 square inches.
How to calculate the error propagation?
(a) Let A be the area of the square tile. The differential of A with respect to the side length x is dA/dx = 2x.
dA ≈ (dA/dx)dx
At the lower end of the possible range for x, we have:
x = 9 31/32 inches
dx = 1/32 inch
dA = (2x)(dx) = (2(9 31/32))(1/32) = 19/32 square inches
At the upper end of the possible range for x, we have:
x = 10 1/32 inches
dx = 1/32 inch
dA = (2x)(dx) = (2(10 1/32))(1/32) = 21/32 square inches
Therefore, the possible propagated error in computing the area of the square is between 19/32 and 21/32 square inches.
(b) The percent error in computing the area of the square is given by:
(percent error) = (error / actual value) x 100
(percent error) = [(21/32 - 100) / 100] x 100% = -79/1600 x 100% ≈ -4.94%.
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Ms. Castellano is filling small containers from a large basket of strawberries she fills each container and then weighs she records the weight of each container in poundsAnd sorts them by Weight The line plot shows The number of containers at each weight 
Hi there! Your question involves Ms. Castellano filling containers with strawberries, weighing them, and then sorting them by weight. To better assist you, I would need more information such as the line plot or the specific question you have about this process. Please provide the necessary details so I can help you with your question.
Based on the information you provided, it seems that Ms. Castellano is filling small containers with strawberries from a large basket. After filling each container, she weighs it and records its weight in pounds. She then sorts the containers by weight.
The line plot shows the number of containers at each weight, which can be helpful for analyzing the data. It sounds like Ms. Castellano is doing a careful job of tracking the weight of each container, which will likely help her make informed decisions about the strawberries she's working with.
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According to researchers one of the primary reasons relationship sour is that people stop listening to one other assumed that the relative frequency distribution for the length of time couples in conflict listen to each other has a mean of eight seconds and standard deviation of five seconds in sample of 37 couples in conflict let X represent the main of length of time the couples listen to each other what is the sample distribution of X
The square root of the sample size (n=37), which is approximately 0.820 seconds:
X ~ N(8, 5/√37)
The sample distribution of the mean, denoted as X, is the distribution of all possible sample means of a certain sample size taken from a population. In this case, we have a population of couples in conflict, and we have a sample size of 37. The mean length of time couples in conflict listen to each other is known to be 8 seconds with a standard deviation of 5 seconds.
Since we have a large enough sample size (n=37), we can assume that the sample mean follows a normal distribution according to the Central Limit Theorem. The Central Limit Theorem states that the sample means from a large enough sample size will be approximately normally distributed regardless of the population distribution, given that the samples are independent and randomly selected.
Thus, the sample distribution of X can be represented by a normal distribution with a mean of 8 seconds (same as the population mean) and a standard deviation of 5 seconds divided by the square root of the sample size (n=37), which is approximately 0.820 seconds:
X ~ N(8, 5/√37)
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The final exam scores in a statistics class were normally distributed with a mean of
63 and a standard deviation of five.
find the score that marks the 11% of all scores.
The score that marks the 11% of all scores is approximately 56.875 .
To find the score that marks the 11% of all scores, we need to use the standard normal distribution table, also known as the Z-table, since the given distribution is a normal distribution.
The first step is to find the Z-score that corresponds to the 11th percentile, which is given by: Z = invNorm(0.11) ≈ -1.225
Here, "invNorm" represents the inverse of the standard normal cumulative distribution function, which can be computed using statistical software or a calculator.
The second step is to use the Z-score formula to find the raw score that corresponds to this Z-score:Z = (X - μ) / σ
where X is the raw score we want to find, μ is the mean of the distribution, and σ is the standard deviation. Plugging in the values we have:
-1.225 = (X - 63) / 5
Solving for X, we get:
X = -1.225 * 5 + 63 = 56.875
Therefore, the score that marks the 11% of all scores is approximately 56.875
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Please help :D
A. Explain how to make a prediction based on the probability of an event.
B. Then, give an example in which predictions are made based on probabilities
This prompt is about probability. The answers are given as follows;
Identifying the probability of an event is crucial to making predictions based on its likelihood. T his involves calculating the probability either through historical data or experimentation.
Once determined, utilizing this value enables one to make future predictions regarding the occurrence of such events; for instance, 80% probability of precipitation tomorrow implies an 80% chance of rain.
Calculating probabilities has proven essential to sports betting because it helps bookmakers given some degree of foresight on which teams are going to win specific games or tournaments. Operating under the premise that there will always be two probable outcomes (either one side wins while another loses), these bookmakers could assign numerical values on what percentage they deem worthy enough for each team's chances.
Subsequently, using precise mathematical formulas and equations, bettors assess wagering-related uncertainties based on these predetermined likelihoods before deciding whether or not they should place money bets.
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In a 2 digit number the tens digit is 5 less than the units digit. The number itself is 5 more tha 3 times the sum of its digits. What is the number
Answer:
Step-by-step explanation:
(2-5)3=-9. (-9)5 =-45