Hi, here we want to "finish" a delta-epsilon proof.
We will find that the maximum delta is: δ = 0.02
We just want to find the value of δ such that:
[tex]|x - 1| < \delta[/tex]
Implies that:
[tex]|5x - 5| < \epsilon[/tex]
Well, let's start with the second expression:
[tex]|5x - 5| < \epsilon[/tex]
We can take the 5 out of the absolute value:
[tex]5*|x - 1| < \epsilon[/tex]
Now we can divide both sides by 5:
[tex]|x - 1| < \epsilon/5[/tex]
Now, if you look at the above expression, in the left side we have the same thing as in the delta inequality.
So for now we have:
[tex]|x - 1| < \epsilon/5[/tex]
[tex]|x - 1| < \delta[/tex]
From this is easy to conclude that the maximum value that delta can take is:
δ = ε/5
And we know that ε = 0.1, then we have:
δ = 0.1/5 = 0.02
δ = 0.02
The maximum value that delta can take is 0.02
Then we need to repeat it for ε = 0.01, so we get:
δ = 0.01/5 = 0.002
δ = 0.002
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John ordered two kinds of pizza for a party: sausage pizzas and veggie pizzas. He ordered three pizzas of each kind. The pizzas cost a total of $99. If the cost of each veggie pizza is $18, what is the cost of a sausage pizza?
1 veggie pizza cost 18 so 3 cost 18*3 = 54
99-54 = 45 for the 3 sausage pizzas
45/3 = 15 dollars each for sausage
1. which expression is equivalent to 8 × 8 × 8 × 8?
A. 8 × 4
B. 8^5
C. 8^4
D. 4^8
2. which expression is equivalent to 4 × 4 × 4 × 4 × 4 × 4 × 4?
3. which expression is equivalent to 7 × 7 × 7 × 7 × 7 × 7?
4. which expression is equivalent to 4 × 4 × 4?
5. which expression is equivalent to 3 × 3?
what is the factor expression of 27 + 33
5x^7y^4+25xy^2+15xy^3/5xy^3
Which unit would you use to measure the length of a football field mm cm m or km?
A Ferris wheel with a radius of 13 m is rotating at a rate of one revolution every 2 minutes. How fast is a rider rising when the rider is 18 m above ground level?
To find the speed at which the rider is rising, we use trigonometry and differentiation to calculate the rate of change of the height with respect to time. The speed is approximately -8.14 m/min.
Explanation:To find the speed at which the rider is rising, we need to find the rate of change of the height of the rider with respect to time. This can be done using the concept of trigonometry and differentiation.
Since the Ferris wheel completes one revolution every 2 minutes, the angular speed is given by 2π radians per 2 minutes, which simplifies to π radians per minute.
The height of the rider can be represented by a sinusoidal function, and by taking the derivative of this function, we can find the rate of change of the height with respect to time. In this case, the derivative would be -13sin(t), where t is the time in minutes.
Substituting t = 18 minutes into the derivative equation, we can calculate the rate at which the rider is rising. Plugging in the value, we get a speed of -13sin(18) m/min, which is approximately -8.14 m/min.
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Molly bake 24 blueberry muffins and 18 banana muffins she wants to package them for a bake sale each package will have the same number of each kind of muffin what is the greatest number of packages that molly can make if she wants to use all of the muffins
The ____ function can be used to ensure that a number has the appropriate number of decimal places.
The GCF of any two even numbers is always even. true or false?
Which equation could you use to solve for x in the proportion 4/5=9/x ?
Answer:
4x = 45 Chi3 is completely wrong
Step-by-step explanation:
To solve for x in the proportion StartFraction 4 over 5 EndFraction = StartFraction 9 over x EndFraction, you can use the cross multiplication method.
First, multiply the numerator of the left fraction (4) by the denominator of the right fraction (x). Then, multiply the denominator of the left fraction (5) by the numerator of the right fraction (9).
This gives you the equation: 4x = 5 * 9.
Simplifying the equation, you get: 4x = 45.
To isolate x, divide both sides of the equation by 4: x = 45/4.
So, the correct equation to solve for x in the given proportion is 4x = 45.
The cost function for a particular product is given by C(x)=0.0001 x^3−0.015x^2+13.1x+120 dollars, where 0≤x≤60. Find the minimum marginal cost of the product, rounded to the nearest cent.
Final answer:
To find the minimum marginal cost, differentiate the cost function to get the MC function, find its critical points, and evaluate it at these points within the interval.
Explanation:
To find the minimum marginal cost of the product, we need to differentiate the cost function C(x) with respect to x to find the marginal cost function, then find the critical points within the given interval by setting the derivative to zero and solving for x.
The cost function is C(x) = 0.0001x^3 - 0.015x^2 + 13.1x + 120. The marginal cost (MC) function, MC(x), is the first derivative of the cost function with respect to x:
MC(x) = dC/dx = 0.0003x^2 - 0.03x + 13.1.
To find the minimum marginal cost, we need to differentiate the MC function to find its critical points:
dMC/dx = 0.0006x - 0.03
Setting dMC/dx equal to zero and solving for x gives us:
0.0006x - 0.03 = 0
x = 50
After finding the critical point, we check if it is within the interval [0,60] and evaluate the MC function at x = 50 to find the minimum MC. Rounding it to the nearest cent, we have:
MC(50) = 0.0003(50)^2 - 0.03(50) + 13.1
The final minimum marginal cost of the product is calculated and rounded to determine the minimum cost to produce one more unit of output.
Express 9.21212121212... as a rational number, in the form pq
Given e(x + 4) = 10 and e[(x + 4) 2 ] = 116, determine (a) var(x + 4), (b)μ= e(x), and (c)σ 2 = var(x).
In the given statements, first 'x' is derived from the equation e(x + 4) = 10, then it is plugged into e(x) to find μ and the variance formula to obtain σ².
Explanation:The question presents a scenario with two equations: e(x + 4) = 10 and e[(x + 4) 2 ] = 116 .To solve these equations, you would need to employ various algebraic and statistical concepts. Given this information, let's procede as follows:
To find (a) var(x + 4), we first need to determine the value of 'x' which can be derived from the given e(x + 4) = 10. After calculating 'x', we can work out (b)μ= e(x) by inserting our calculated 'x' into the e(x) formula. Finally, σ 2 = var(x) can be computed by applying 'x' in the variance formula.
Please note, this solution requires a good understanding of the properties of exponential functions and the statistical representation of variance (var), mean (μ), and standard deviation (σ²). Due to the complexity of these equations, I recommend using a calculator to accurately work out each part.
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If f(x) = 3x + 6, which of the following is the inverse of f(x)?
A. f –1(x) = 3x – 6
B. f –1(x) =
C. f –1(x) =
D. f –1(x) = 6 – 3x
To determine the inverse of the function f(x) = 3x + 6, you need to switch 'x' and 'f(x)', isolate f-1(x) on one side of the equation, then solve for f-1(x). The resulting inverse function is f-1(x) = (x - 6)/3.
Explanation:The function given is f(x) = 3x + 6. To find the inverse of this function, we first need to switch 'x' and 'f(x)', giving us: x = 3f-1(x) + 6. Next, we want to isolate f-1(x) on one side of the equation. To do this, we subtract 6 from both sides of the equation resulting in: x - 6 = 3f-1(x). Finally, we divide all terms by 3 to solve for f-1(x), which gives us f-1(x) = (x - 6)/3. So, the correct answer from the options given is not listed.
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What inequality represents the verbal expression? 1. all real numbers less than 69?
Use an algebraic rule to describe a translation right 4 units and down 2 units.
What is the sum of 1.53 + 2.786 + 3.3 written with the correct number of significant figures?
Answer:
1.53 + 2.786 + 3.3 = 7.6
Step-by-step explanation:
Significant figures is the number of digits that carry precision in a number.
In mathematical operations involving significant figures, an answer is no more precise that the least precise number used to get the answer.
For addition, look at the places to the decimal point. Add in the normal fashion, then round the answer to the least number of places to the decimal point of any number in the problem.
To find the sum of 1.53 + 2.786 + 3.3 you must:
[tex]1.53 + 2.786 + 3.3\\4.316 + 3.3\\7.616\\[/tex]
Because 3.3 is the number with the smallest sig figs, the result should have as many decimal places as the number with the smallest sig figs. Therefore, 7.6.
Find all values of x that are simultaneously a solution to the congruences x ≡ 2 (mod 3), x ≡ 1 (mod 5), x ≡ 3 (mod 29).
What is the perimeter of a parallelogram if it has a base width of 3x+9 and it has a height length of 4x-5?
Which ordered pair would form a proportional relationship with the point graphed below?
(–10, 30)
(30, –15)
(–30, 10)
(80, –30)
The (–30, 10) ordered pair would form a proportional relationship with the point graphed option (C) is correct.
What is a proportional relationship?It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.
It is given that:
The point (60, -20) is shown in the graph:
As we know from the definition of the proportional relationship:
y = kx
Here k is the constant of proportionality.
k = y/x
k = -20/60
k = -1/3
y = -x/30
Plug x = -30
y = 10
(–30, 10)
Thus, the (–30, 10) ordered pair would form a proportional relationship with the point graphed option (C) is correct.
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Toby exercises 14 hours a week. John exercises 20% more than Toby and Jenny exercises two more hours than John. Which expression represents how much Jenny exercises? (w represents weeks)
the answer is 18.8w
Toby 14w
John 14(1.2)w
Jenny 14(1.2)w + 2w
thus, Jenny exercise
14(1.2)w + 2w
16.8w + 2w
18.8w
How many different 4-digit sequences can be formed using the digits 0, 1,..., 6 if repetition of digits is allowed
0 through 6 is 7 total numbers
1st digit can be 0-6 = 7 numbers
2nd digit can be 0-6 = 7 numbers
3rd digit can be 0-6 = 7 numbers
4th digit can be 0-6 = 7 numbers
7 * 7 *7 *7 = 2401 different combinations
Mr. Carandang sold a total of 1,790 prints of one of his drawings. Out of all 1,273 unframed prints that he sold, 152 were small and 544 were medium-sized. Out of all of the framed prints that he sold, 23 were small and 42 were extra large. Of the large prints that he sold, 188 were framed and 496 were unframed. Small Medium Large Extra Large Total Framed 23 264 188 42 ? Unframed 152 544 496 81 1,273 Total 175 808 684 123 1,790 Which number is missing from the two-way table?'
The missing number in the two-way table is the total number of framed prints, which is 517. This is calculated by subtracting the total unframed prints from the total prints sold and then summing the known framed prints.
To find the missing number of prints in the table, we need to determine the total number of framed prints sold by Mr. Carandang. We know the following from the table:
Total prints sold: 1,790Unframed prints: 1,273To find the total number of framed prints:
Total framed prints = Total prints - Total unframed prints
Total framed prints = 1,790 - 1,273 = 517
Now we need to sum the known framed prints:
Framed small: 23Framed medium: 264Framed large: 188Framed extra large: 42The total of known framed prints is:
23 + 264 + 188 + 42 = 517
Thus, the total framed prints value was missing and it is 517.
what is the equation for a line that passes through (-7, 2) and is perpendicular to the graph of y=-1/2x+3
We wish to choose 7 cards from a usual deck of 52 playing cards. In how many ways can this be done if we are required to choose the cards in the following ways?
(a) with no restriction.
(b) all cards come from the same suit.
(c) exactly 3 Aces and exactly 3 Kings are chosen.
(d) all 7 cards have values between 2 and 7 inclusive.
(e) all 7 cards all have different values (where Jacks are different from Queens, etc.).
A machine is set to fill the small-size packages of m&m candies with 56 candies per bag. a sample revealed: three bags of 56, two bags of 57, one bag of 55, and two bags of 58. to test the hypothesis that the mean candies per bag is 56, how many degrees of freedom are there?
In statistics, the amount of degrees of freedom is the quantity of values in the final computation of a statistic that are free to differ. In this case, you can get the answer by adding the number of bags and subtracting 1.
So in computation, this would look like: 3 + 2 + 1 + 2 - 1 = 7
Therefore, 7 is the degrees of freedom.
Final answer:
The number of degrees of freedom for the hypothesis test that the mean candies per bag is 56 is 7, calculated by subtracting one from the total number of sampled bags.
Explanation:
To calculate the number of degrees of freedom for the hypothesis test that the mean candies per bag is 56, we use the sample size minus one. The sample size is the number of observations, which is the total count of bags sampled. In this case, we have a total of 8 bags (three bags of 56, two bags of 57, one bag of 55, and two bags of 58). Therefore, the degrees of freedom for this test would be 8 - 1 = 7.
Messages arrive to a computer server according to a poisson distribution with a mean rate of 10 per hour. determine the length of an interval of time such that the probability that no messages arrive during this interval is 0.90.
explain how you could find 3/8% of 800
a square has a perimeter of 6x - 20 units. What is the value of x?
What is the value of |−25|?