Let f be the function defined by f(x) = x + lnx. What is the value of c for which the instantaneous rate of change of f at x = c is the same as the average rate of change of f over [1, 4]?

From the above equation putting the value of x. we get yhat and reducing it from actual value of y we will get residual

Therefore, as shown on the image below, 

The answer is for this problem is 10

The translation of the statement '55 times what number is 1265?' into an equation is '55 * x = 1265', which, with 'dot' finding use as multiplication, matches with the provided option A) 55 dot x = 1265.

The question asks for the translation of the problem statement into an equation. The phrase '55 times what number is 1265?' implies multiplication. Specifically, 55 is being multiplied by an unknown number (which we can denote by 'x'), and the result of this multiplication is 1265. Therefore, the correct translation of this problem into an equation would be 55 * x = 1265 or in the provided options A) 55 dot x = 1265 where 'dot' indicates multiplication.

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the answer to Give the angle measure represented by 2 rotations clockwise. it's A. -720 on edge

We can solve this problem using the binomial probability equation:

P = [n! / (n – r)! r!] p^r q^(n – r)

where the variables are:

n = total number of questions = 10

r = number of correct = at least 5

p = probability of success = 0.5

q = probability of failure = 0.5

So what we have to do is to calculate for P for r = 5 to 10

when r = 5

P =  [10! / (10 – 5)! 5!] 0.5^5 0.5^(10 – 5)

P = 0.246

when r = 6

P =  [10! / (10 – 6)! 6!] 0.5^6 0.5^(10 – 6)

P = 0.205

when r = 7

P =  [10! / (10 – 7)! 7!] 0.5^7 0.5^(10 – 7)

P = 0.117

when r = 8

P =  [10! / (10 – 8)! 8!] 0.5^8 0.5^(10 – 8)

P = 0.044

when r = 9

P =  [10! / (10 – 9)! 9!] 0.5^9 0.5^(10 – 9)

P = 9.766 x 10^-3

when r = 10

P =  [10! / (10 – 10)! 10!] 0.5^10 0.5^(10 – 10)

P = 9.766 x 10^-4

So the probability that her score will be at least 5 is:

P (r≥5) = 0.246 + 0.205 + 0.117 + 0.044 + 9.766 x 10^-3 + 9.766 x 10^-4

P (r≥5) = 0.623

So about 62.3% chance.


You can do the same for the other item quiz, just set the value of n

Final answer:

When randomly guessing on true-false quizzes, the probability of getting at least a 50% grade on a three-item quiz is 0.5, on a four-item quiz is 0.6875, and on a five-item quiz is also 0.5.

Explanation:

Calculating the probability of getting at least 50% on a true-false quiz when randomly guessing involves understanding the binomial probability distribution. For a true-false quiz, each question has two possible outcomes, from which we can calculate the likelihood of each score.

the mean is the average

-7+23 -5 +4 = 15

15 / 4 = 3.75

 Answer is A

Final answer:

The piecewise function, using the Heaviside function, is defined as 0 for t < 0, t^2 for t in [0, 1], and t for t > 1.

Explanation:

The piecewise function can be defined using the Heaviside function.

We know that the Heaviside function, H(x), is defined as:

H(x) = 0 for x < 0

H(x) = 1 for x ≥ 0

Using the Heaviside function, the piecewise function can be written as:

f(t) = 0 for t < 0

f(t) = t2 for t ∈ [0, 1]

f(t) = t for t ≥ 1

Three different equivalent expressions for 16x^8 are [tex]\[ 16x^8 = 2^4 \cdot x^8 = (2 \cdot x)^4 \cdot x^4 = (2x)^4 \cdot x^4 \][/tex], [tex]\[ 16x^8 = 2^4 \cdot x^8 = (2x)^4 \][/tex], [tex]\[ 16x^8 = 2^4 \cdot x^8 = (2x)^4 \cdot x^4 = 2^{4 + 4} \cdot x^{4 + 4} = 2^8 \cdot x^8 \][/tex].

Expressing [tex]\(16x^8\)[/tex] in three different equivalent forms:

1. Expanded Form:

[tex]\[ 16x^8 = 2^4 \cdot x^8 = (2 \cdot x)^4 \cdot x^4 = (2x)^4 \cdot x^4 \][/tex]

2. Factored Form:

[tex]\[ 16x^8 = 2^4 \cdot x^8 = (2x)^4 \][/tex]

3. Exponential Form with a Common Base:

[tex]\[ 16x^8 = 2^4 \cdot x^8 = (2x)^4 \cdot x^4 = 2^{4 + 4} \cdot x^{4 + 4} = 2^8 \cdot x^8 \][/tex]

These expressions show the flexibility in representing the original expression using different algebraic manipulations. The key is to recognize patterns, use properties of exponents, and factor out common terms.

If the number of samples is increased, this actually leads to a reduction in error of the distribution. This is because of the relationship between variation and sample size which has the formula of:

σx = σ / sqrt (n)

So from the formula we can actually see that the variation and sample size is inversely proportional.

Which means that increasing the sample size results in a reduction of variation.

Answer:

It will have less variation

Increasing the sample size causes the confidence interval to narrow, decreases the standard deviation, and makes the sample mean distribution more normal. This leads to more accurate and reliable estimates of the population parameters.

The effect of increasing the sample size in a distribution of sample means primarily involves the confidence interval, the standard deviation, and the progress towards a normal distribution.

Firstly, increasing the sample size reduces the error bound, leading to a narrower confidence interval. This means that the calculated mean is likely to be more accurate representation of the true population mean.

Secondly, as the sample size increases, the standard deviation, which is a measure of spread or dispersion in the data, decreases. So, larger sample sizes result in lesser variability.

Finally, per the central limit theorem, an increased sample size makes the distribution of sample means get closer to a normal distribution, regardless of the population's initial distribution. This property is valid as long as the sample size is large enough (generally taken as 30 or more).

Thus, larger sample sizes tend to provide more accurate and reliable estimates of the population parameters.

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The area of the square dance floor when each side is increased by one foot becomes 441 square feet. Since 441 is an integer, the new area is a rational number because it can be expressed as a fraction with a non-zero denominator.

The question pertains to the change in area of a square dance floor when each side of the square is increased by one foot. Given that the initial area is 400 square feet, we understand that the dimensions of the dance floor are 20 feet by 20 feet, since 20 * 20 = 400. If each side of the square increases by one foot, the new dimensions of the square will be 21 feet by 21 feet, resulting in a new area of 441 square feet.

To answer the question as to whether the new area is a rational number, we need to understand what a rational number is. A rational number is any number that can be expressed as the quotient or fraction of two integers, with a denominator that is not zero. Given that 441 is an integer, and the area can be written as 441/1, the new area of the dance floor is indeed a rational number.

Find A ∩ B is any numbers that are in both sets

they booth have 6 & 12 so the answer is: {6, 12}

Answer:

6,12

Step-by-step explanation:

The Boardman family's walking speed is 1.4 miles per hour, which is calculated by dividing the distance walked (2/5 mile) by the time it took (2/7 hour).

A unit rate defines how many units of the first type of quantity correspond to one unit of the second type of quantity. In this case, we need to find out how many miles they walk in one hour.

To calculate the unit rate, we divide the distance by the time. They walked 2/5 of a mile in 2/7 of an hour. Setting up the division, we have:
(2/5) miles / (2/7) hours = (2/5) × (7/2) miles per hour = 7/5 miles per hour

After simplifying, we get that the Boardman family's walking speed is 1.4 miles per hour.

Answer:

x.(-1/7,0)

y.(0,1/4)

Step-by-step explanation:

To solve the problem we must know about the volume and the surface area of cuboids.

The length of the aquarium is 4, and the width of the aquarium is 8.

Given to us

We know that the base of the aquarium should be a square, therefore, the length and the breadth of the aquarium will be the same.

Length x breadth x height = 256 ft³

Length x Length x height = 256 ft³

Length ² x height = 256 ft³

[tex]L^2\times H = 256\\\\H = \dfrac{256}{L^2}[/tex]

Surface Area of the Aquarium

= Area of the base + (4 x Area of the 4 sides)

[tex]= L^2 + 4(L\times H)[/tex]

Substituting the value of H,

[tex]= L^2 + 4L(\dfrac{256}{L^2})[/tex]

Let the surface area be a function of L, therefore,

[tex]f(L) = L^2 + 4L(\dfrac{256}{L^2})[/tex]

Differentiating the function to get the minimum,

[tex]f(L) = L^2 + 4L(\dfrac{256}{L^2})\\\\f(L) = L^2 + (\dfrac{1024}{L})\\\\f'(L) = 2L - (\dfrac{1024}{L^2})[/tex]

Equating against zero,

[tex]2L - (\dfrac{1024}{L^2}) = 0\\\\\dfrac{2L^3-1024}{L^2} = 0\\\\2L^3-1024 = 0\\\\L = 8[/tex]

Substituting the value of L,

[tex]H = \dfrac{256}{L^2}\\\\H = \dfrac{256}{8^2}\\\\H = 4[/tex]

But this way the area will be more, therefore, replace the value of L with 8,

L = 4

H = 8

Hence, the length of the aquarium is 4, and the width of the aquarium is 8.

Learn more about Volume of the cuboid:

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