Let f (x) = 2 . x^8 – 5 . x^5 – 4 . x^3 + 6 . x . Find f'(x) and then find f'(3).

Answer:

b = P - a - c

Step-by-step explanation:

Step 1: Write equation

P = a + b + c

Step 2: Solve for b

In the afternoon, Winston traveled a distance of 159 kilometers.

A mathematical number known as distance measures "how much ground an object has traveled" while moving. Distance is defined as the product of speed and time.

On Monday, Winston covered a distance of 248 miles. In the morning, he covered 70 fewer miles than in the afternoon.

Let "x" be the number of miles Winston drove in the afternoon.

In the morning, Winston drove x - 70 miles.

In total, Winston drove 248 miles on Monday.

So, x + (x - 70) = 248

2x - 70 = 248

2x = 318

x = 318/2

Apply the division operation, and we get

x = 159

Thus, Winston drove 159 miles in the afternoon.

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Step-by-step explanation:

He originally ate 3/4 of them ....so he has 1/4 left to split 3 ways

1/4 ÷ 3   =   1/12 of the original  each

The measure of angle ∠M is 53.

We have,

We will use the sin function.

Where,

Sin = Perpendicular / Hypotenuse.

Now,

Sin Ф = 48/60

Ф = \(Sin^{-1}\) (48/60)

Ф = \(Sin^{-1}\) 0.8

Ф = 53

Thus,

The measure of angle ∠M is 53.

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Answer:

see explanation

Step-by-step explanation:

Using the identities

sin(A + B) = sinAcosB + cosAsinB

cotA = \(\frac{cosA}{sinA}\) , tanA = \(\frac{sinA}{cosA}\)

Consider the left side

\(\frac{sin(A+B)}{sinAcosB}\)

= \(\frac{sinAcosB+cosAsinB}{sinAcosB}\)

= \(\frac{sinAcosB}{sinAcosB}\) + \(\frac{cosAsinB}{sinAcosB}\)

= 1 + \(\frac{cosA}{sinA}\) . \(\frac{sinB}{cosB}\)

= 1 + cotA tanB = right side , thus verified

By using 2.5th and 97.5th percentile of these values.

Bootstrapping:

Bootstrapping, a test or measure that uses random sampling with replacement to simulate the sampling process, falls within the more general area of resampling techniques. For example, bias, variance, confidence intervals, prediction error, etc. are used to rate the accuracy of sample estimates when using bootstrapping.

                                                          A random sample with replacement from the original sample must be taken thousands of times in order to determine the 95% confidence interval for the population standard deviation. You calculate the sample standard deviation from each fresh sample.

From the values of the 2.5th and the 97.5th percentile of these data, we can use the bootstrap method to determine the 95% confidence interval for the population standard deviation.

So we need to use 2.5th and the 97.5th percentile of these values.

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Answer:

XYZ= 100°

please mark as brainliest answer

Answer:

k=a+7

Step-by-step explanation:

Take 1 k away from both sides. I hope you found this useful!

Answer:

k = \(\frac{7}{2-a}\)

Step-by-step explanation:

2k = ak + 7 ( subtract ak from both sides )

2k - ak = 7 ← factor out k from each term on the left side

k(2 - a) = 7 ( isolate k by dividing both sides by (2 - a) )

k = \(\frac{7}{2-a}\)

Answer:R = {(4, 5); (4, 7); (4, 9); (6, 7); (6, 9), (8, 9) (2, 5) (2, 7) (2, 9)}

Therefore, Domain (R) = {2, 4, 6, 8} and Range (R) = {1, 5, 7, 9}

Solved examples on domain and range of a relation:

1. In the given ordered pair (4, 6); (8, 4); (4, 4); (9, 11); (6, 3); (3, 0); (2, 3) find the following relations. Also, find the domain and range.

(a) Is two less than

(b) Is less than

(c) Is greater than

(d) Is equal to

Solution:

(a) R₁ is the set of all ordered pairs whose 1ˢᵗ component is two less than the 2ⁿᵈ component.

Therefore, R₁ = {(4, 6); (9, 11)}

Also, Domain (R₁) = Set of all first components of R₁ = {4, 9} and Range (R₂) = Set of all second components of R₂ = {6, 11}

(b) R₂ is the set of all ordered pairs whose 1ˢᵗ component is less than the second component.

Therefore, R₂ = {(4, 6); (9, 11); (2, 3)}.

Also, Domain (R₂) = {4, 9, 2} and Range (R₂) = {6, 11, 3}

(c) R₃ is the set of all ordered pairs whose 1ˢᵗ component is greater than the second component.

Therefore, R₃ = {(8, 4); (6, 3); (3, 0)}

Also, Domain (R₃) = {8, 6, 3} and Range (R₃) = {4, 3, 0}

(d) R₄ is the set of all ordered pairs whose 1ˢᵗ component is equal to the second component.

Therefore, R₄ = {(3, 3)}

Also, Domain (R) = {3} and Range (R) = {3}

2. Let A = {2, 3, 4, 5} and B = {8, 9, 10, 11}.

Let R be the relation ‘is factor of’ from A to B.

(a) Write R in the roster form. Also, find Domain and Range of R.

(b) Draw an arrow diagram to represent the relation.

Solution:

(a) Clearly, R consists of elements (a, b) where a is a factor of b.

Therefore, Relation (R) in the roster form is R = {(2, 8); (2, 10); (3, 9); (4, 8), (5, 10)}

Therefore, Domain (R) = Set of all first components of R = {2, 3, 4, 5} and Range (R) = Set of all second components of R = {8, 10, 9}

(b) The arrow diagram representing R is as follows:

Domain and Range of R

2Save

3. The arrow diagram shows the relation (R) from set A to set B. Write this relation in the roster form.

Arrow Diagram

2Save

Solution:

Clearly, R consists of elements (a, b), such that ‘a’ is square of ‘b’

i.e., a = b².

So, in roster form R = {(9, 3); (9, -3); (4, 2); (4, -2); (16, 4); (16, -4)}

Worked-out problems on domain and range of a relation:

4. Let A = {1, 2, 3, 4, 5} and B = {p, q, r, s}. Let R be a relation from A in B defined by

R = {1, p}, (1, r), (3, p), (4, q), (5, s), (3, p)}

Find domain and range of R.

Solution:

Given R = {(1, p), (1, r), (4, q), (5, s)}

Domain of R = set of first components of all elements of R = {1, 3, 4, 5}

Range of R = set of second components of all elements of R = {p, r, q, s}

5. Determine the domain and range of the relation R defined by

R = {x + 2, x + 3} : x ∈ {0, 1, 2, 3, 4, 5}

Solution:

Since, x = {0, 1, 2, 3, 4, 5}

Therefore,

     x = 0 ⇒ x + 2 = 0 + 2 = 2 and x + 3 = 0 + 3 = 3

     x = 1 ⇒ x + 2 = 1 + 2 = 3 and x + 3 = 1 + 3 = 4

     x = 2 ⇒ x + 2 = 2 + 2 = 4 and x + 3 = 2 + 3 = 5

     x = 3 ⇒ x + 2 = 3 + 2 = 5 and x + 3 = 3 + 3 = 6

     x = 4 ⇒ x + 2 = 4 + 2 = 6 and x + 3 = 4 + 3 = 7

     x = 5 ⇒ x + 2 = 5 + 2 = 7 and x + 3 = 5 + 3 = 8

Hence, R = {(2, 3), (3, 4), (4, 5), (5, 6), (6, 7), (7, 8)}

Therefore, Domain of R = {a : (a, b) ∈R} = Set of first components of all ordered pair belonging to R.

Therefore, Domain of R = {2, 3, 4, 5, 6, 7}

Range of R = {b : (a, b) ∈ R} = Set of second components of all ordered pairs belonging to R.

Therefore, Range of R = {3, 4, 5, 6, 7, 8}

6. Let A = {3, 4, 5, 6, 7, 8}. Define a relation R from A to A by

   R = {(x, y) : y = x - 1}.

• Depict this relation using an arrow diagram.

• Write down the domain and range of R.

roster form

Solution:

By definition of relation

R = {(4, 3) (5, 4) (6, 5)}

The corresponding arrow diagram is shown.

We can see that domain = {4, 5, 6} and Range = {3, 4, 5}

7. The adjoining figure shows a relation between the sets A and B.

Write this relation in

 • Set builder form

 • Roster form

 • Find the domain and range

Set Builder Form

2Save

Solution:

We observe that the relation R is 'a’ is the square of ‘b'.

In set builder form R = {(a, b) : a is the square of b, a ∈ A, b ∈ B}

In roster form R = {(4, 2) (4, -2)(9, 3) (9, -3)}

Therefore, Domain of R = {4, 9}

Range of R = {2, -2, 3, -3}

Note: The element 1 is not related to any element in set A.

Step-by-step explanation:

The answer to your question is that the mean of the sampling distribution of the proportion is equal to the proportion of  factorization the population, which is 0.95 in this case.

when we take a random sample from a population, the proportion of individuals with the characteristic of interest in the sample may not be exactly the same as the proportion in the overall population. However, if we take many random samples from the population and calculate the proportion of individuals with the characteristic in each sample, the distribution of those sample proportions will follow a normal distribution with a mean equal to the population proportion and a standard deviation determined by the sample size.

Therefore, in this case, since the proportion of the population with the characteristic is 0.95, the mean of the sampling distribution of the proportion will also be 0.95. This means that if we take many random samples from the population and calculate the proportion of individuals with the characteristic in each sample, the average of those proportions will be very close to 0.95.

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Proportion of pregnancies that last fewer than 276 days is approximately 0.7340 or 73.40%.

Given, mean (μ) = 266 days and standard deviation (σ) = 16 days.

Let X be the length of pregnancies, then X follows the normal distribution with mean (μ) = 266 and standard deviation (σ) = 16.

We need to find the probability that a pregnancy lasts fewer than 276 days i.e. P(X < 276).

To find this probability, we standardize the variable X using the standard normal distribution formula:

z = (x - μ) / σ

where z is the standard normal random variable.

Substituting the given values, we get:

z = (276 - 266) / 16 = 0.625

Using a standard normal distribution table or calculator, we can find that the probability of a standard normal random variable being less than 0.625 is approximately 0.7340.

Therefore, the proportion of pregnancies that last fewer than 276 days is approximately 0.7340 or 73.40%.

Explanation: This means that out of 100 pregnancies, around 73 pregnancies will last fewer than 276 days.

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Answer:

a) 2

b) 93

Step-by-step explanation:

a) 4x - 2y

   4(3) - 2(5)

   12 - 10

   2

b) 2x^2 + 3y^2

   2(3)^2 + 3(5)^2

   2(9) + 3(25)

   18 + 75

   93

Alvin's total payment to the store if the donations wasn't taxed is $54.18.

Cost of shirts = $12.50

Cost of pants = $27

Cost of socks = $6.25

Donation to charity = $5

Tax = 7.5%

Total = $12.50 + $27 + $6.25

= $45.75

Total payment = $45.75 + (0.075 ×45.75) + 5

= $54.18125

Hence, the total payment Alvin made to the store is $54.18

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Answer:

0.80

Step-by-step explanation:

The answer is A. regular

Answer:

Regular

Step-by-step explanation:

The probability that at least one of them has been vaccinated is 0.9552

Probability:

Probability defines the possible occurrence of any particular required event.

Given,

Here we need to find in a large population, 54 % of the people have been vaccinated. if 4 people are randomly selected, what is the probability that at least one of them has been vaccinated.

Here we have to know that,

The situation where at least one out of 4 are vaccinated includes all but one possibility, that which none of the 4 are vaccinated.

The sum of all probabilities must equal 1.

Let Q be probability none of the 4 are vaccinated.

Let P be probability that at least 1 is vaccinated.

Then the probability is calculated as,

P = 1 - Q

Now if 54% are vaccinated, then 46% are not vaccinated.

Thus any given person has a probability of 0.46 of not being vaccinated.

=> Q = (0.46)⁴

=> Q = 0.0448

Then apply the value to the formula,

=> P = 1 - 0.0448

=> P = 0.9552

Therefore, the probability that at least one of them has been vaccinated 0.9552.

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Step-by-step explanation:

b=books

3b\(\leq\)23

\(b\leq 23/3\)

\(b\leq 7.67\)

L=lesson

25L\(\leq\)150

L\(\leq\)6

Hope that helps :)

Answer: a)7, B)8

Step-by-step explanation:

Problem a) If Kai wants to buy just one poster that costs 2 dollars, he has 25-2=23 dollars left. If each book is 3 dollars, then he  can buy 23/3 books. The inequality that results is that if b=#ofbooks, then b< or = (25-2)/3, because you cant buy a book for 2 and a half dollars, hence the less than. 23/3 is 7 r2. We get that b< or = to 7 2/3. However, he can't buy 2/3 of a book, so 7. The final inequality we get is that 2+3b<=25

Problem 2) She spends 50 initially, so 200-50=150 dollars left. Thus the number of lessons, or n, cover the rest of the money. Using the same thory as above, the final inequality is 50+25n<=200. n=8.

Answer:

what language is this?

Step-by-step explanation:

The derivative of f(x) = arccos(x^2) is: f'(x) = -2x / √(1-x^4)

The derivative of f(x) = arccos(x^2), we'll use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. In this case, the outer function is arccos(u) and the inner function is u = x^2.

First, let's find the derivative of the outer function, arccos(u). The derivative of arccos(u) is -1/√(1-u^2). Next, we'll find the derivative of the inner function, x^2. The derivative of x^2 is 2x.

Now we'll apply the chain rule. We have:

f'(x) = (derivative of outer function) * (derivative of inner function)

f'(x) = (-1/√(1-u^2)) * (2x)

Since u = x^2, we'll substitute that back into our equation:

f'(x) = (-1/√(1-x^4)) * (2x)

So, the derivative of f(x) = arccos(x^2) is:

f'(x) = -2x / √(1-x^4)

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Answer:

the new height is now 1 inch

Step-by-step explanation:

Answer:

Step-by-step explanation:

14 - k + 3k - 6

= 14 - 6 - k + 3k

= 8 + 2k (Ans)

Answer:

2k+8

Step-by-step explanation:

I did combine like terms hope this was helpful

The function g(t) is calculated to has one relative minimum and two absolute extrema over the domain [-1, 1].

To find the relative and absolute extrema of the function g(t) = \(e^{t}\) - t over the domain [-1, 1], we need to follow these steps:

Find the critical points of g(t) by setting its derivative equal to zero and solving for t.

Test the sign of the second derivative of g(t) at each critical point to determine whether it corresponds to a relative maximum, relative minimum, or an inflection point.

Evaluate g(t) at the endpoints of the domain [-1, 1] to check for absolute extrema.

Step 1: Find the critical points of g(t)

g'(t) = .\(e^{t}\) - 1

Setting g'(t) equal to zero, we get:

\(e^{t}\) - 1 = 0

\(e^{t}\) = 1

Taking the natural logarithm of both sides, we get:

t = ln(1) = 0

So, the only critical point of g(t) in the domain [-1, 1] is t = 0.

Step 2: Test the sign of the second derivative of g(t)

g''(t) = e^t

At t = 0, we have g''(0) = e⁰ = 1.

Since g''(0) is positive, the critical point t = 0 corresponds to a relative minimum.

Step 3: Evaluate g(t) at the endpoints of the domain [-1, 1]

g(-1) = e⁻¹ - (-1) = e⁻¹ + 1 ≈ 1.37

g(1) = e⁻¹ - 1 = e - 1 ≈ 1.72

Since g(t) is a continuous function over the closed interval [-1, 1], it must attain its absolute extrema at the endpoints of the interval. Therefore, the absolute minimum of g(t) over [-1, 1] occurs at t = -1, where g(-1) ≈ 1.37, and the absolute maximum occurs at t = 1, where g(1) ≈ 1.72.

To summarize:

Relative minimum: g(0) ≈ -1

Absolute minimum: g(-1) ≈ 1.37

Absolute maximum: g(1) ≈ 1.72

Therefore, the function g(t) has one relative minimum and two absolute extrema over the domain [-1, 1].

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Yes, there are experts here in data forecasting methods who can help you with the topics you've mentioned including time series (holts, holts winter), naive method, regression, acf, pacf, arima, stl method and multivariate time series.

Below are brief explanations of each of these terms:

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Surface area per kg for the quarter is 367,440 m²/kg.

What is volume of cone?

The area or volume that a cone takes up is referred to as its volume. Cones are measured by their volume in cubic units such as cm3, m3, in3, etc. By rotating a triangle at any of its vertices, a cone can be created. A cone is a robust, spherical, three-dimensional geometric figure.. Its surface area is curved. The perpendicular height is measured from base to vertex. Right circular cones and oblique cones are two different types of cones. While the vertex of an oblique cone is not vertically above the center of the base, it is in the right circular cone where it is vertically above the base.

For the quarter:

\(Radius (r) = OD/2 - t = 11.2 mmVolume (V) = 4/3 * π * r^3 = 7068.2 mm^3Surface area (A) = 4 * π * r^2 = 1570.8 mm^2Sphericity (Os) = (π^(1/3) * V^(2/3)) / A = (π^(1/3) * (7068.2 mm^3)^(2/3)) / 1570.8 mm^2 = 0.955For the penny:\)

Radius (r) = OD/2 - t = 8.56 mm

Volume (V) = 4/3 * π * r³ = 2469.9 mm³

Surface area (A) = 4 * π * r² = 918.6 mm²

Sphericity (Os) = \((π^(1/3) * V^(2/3)) / A = (π^(1/3) * (2469.9 mm^3)^(2/3)) / 918.6 mm^2 = 0.825\)

To calculate the surface area per kg of each coin, we need to convert their masses to kg and then divide their surface area by their mass:

Surface area per kg for the quarter = 1570.8 / (5.66/1000) = 277,849.8 m²/kg

Surface area per kg for the penny = 918.6 / (2.50/1000) = 367,440 m²/kg

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The data provide convincing evidence of a difference in the average calorie intake of diners at this restaurant.

The data do not provide convincing evidence that the average GRE verbal reasoning score has changed since 2004.

1: Since 2008, chain restaurants in California have been required to display calorie counts of each menu item.

Prior to menus displaying calorie counts, the average calorie intake of diners at a restaurant was 1100 calories.

After calorie counts started to be displayed on menus, a nutritionist collected data on the number of calories consumed at this restaurant from a random sample of diners.

Do these data provide convincing evidence of a difference in the average calorie intake of diners at this restaurant:
The data provide convincing evidence of a difference in the average calorie intake of diners at this restaurant.

The average calorie intake of diners before calorie counts were displayed was 1100 calories, while after calorie counts were displayed, the average calorie intake was lower.

This indicates that the calorie counts may have helped reduce the calorie intake of diners.
2: Based on the performance of those who took the GRE exam between July 1, 2004, and June 30, 2007, the average verbal reasoning score was calculated to be 462.

In 2011, the average verbal score was slightly higher.

Do these data provide convincing evidence that the average GRE verbal reasoning score has changed since 2004:

The data do not provide convincing evidence that the average GRE verbal reasoning score has changed since 2004. The increase in the average verbal score from 2004 to 2011 is not significant enough to prove a change in the average verbal reasoning score.

Further analysis would be required to determine if there has been a significant change in the average score.

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The volume of each individual brick is 72 cubic inches.

The volume of a rectangular prism of height H, width W, and length L is given by:

V = L*H*W

In this case we have:

Then, replacing these in the volume equation, we get:

V = (8 in)*(4 in)*(2.25 in) = 72in³

So the correct option is the second one.

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Answer:

The volume of each individual brick is 72 cubic inches.

Step-by-step explanation:

How to get the volume of each brick?

The volume of a rectangular prism of height H, width W, and length L is given by:

V = L*H*W

In this case we have:

L = 8in

W = 4in

H = 2.25 in

Then, replacing these in the volume equation, we get:

V = (8 in)*(4 in)*(2.25 in) = 72in³

So the correct option is the second one.