a)Show that x1,x2,x3 are linearly dependentb)Show that x1, and x2 are linearly independentc)what is the dimension of span (x1,x2,x3)?d)Give a geometric description of span (x1,x2,x3)With explanation please

The derivative of f(x) = cos(x² - x) is \(3(2x - 1)cos(x^{2} - x)sin(x^{2} - x).\)

To find the derivative of the function f(x) = cos(x² - x), we can use the chain rule.

The chain rule states that if we have a composite function, such as cos(g(x)), the derivative of this composite function is given by the derivative of the outer function multiplied by the derivative of the inner function.

In this case, the outer function is cos(u), where u = x² - x, and the inner function is u = x² - x.

The derivative of the outer function cos(u) is -sin(u).

To find the derivative of the inner function u = x² - x, we apply the power rule and the constant rule. The power rule states that the derivative of x^n, where n is a constant, is nx^(n-1), and the constant rule states that the derivative of a constant times a function is equal to the constant times the derivative of the function.

Applying the power rule and the constant rule, we find that the derivative of u = x² - x is du/dx = 2x - 1.

Now, using the chain rule, the derivative of f(x) = cos(x² - x) is given by:

df/dx = \(-sin(x^{2} - x) * (2x - 1)\)

Simplifying, we have:

df/dx = -\(2xsin(xx^{2} - x) + sin(x^{2} - x)\)

Therefore, the correct answer is option a. 3(2x-1)cos(x²-x)sin(x²-x).

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Answer:

Answer:

Attached to this answer are some of the ways you could rewrite \(4*10^{-3}\)

Answer:

The first one and last one

Step-by-step explanation:

Answer:

1,2,5

Step-by-step explanation:

got it right on edge

Answer:

D. 180 degrees

Step-by-step explanation:

A straight line is 180 degrees.

Answer:

The answer is 180 degrees.

Step-by-step explanation:

✌Hope I helped ya✌

Brainliest would be nice

< Sarah >

Answer: 61.5

Step-by-step explanation:

Area of a regular pentagon= pa/2

Perimeter: 30

Apothem is shown as 4.1

30*4.1= 123

123/2

61.5

pls mark me brainliest if im right

Answer:

n is greater than or equal to 412

Step-by-step explanation:

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The chance of the event B is 0.4 when using the probability for the two independent two event formula.

In the given question, if a and b are independent events with p(a) = 0.65 and p(a ∩ b) = 0.26, then we have to find the value of p(b).

Events classified as independent do not depend on other events for their occurrence.

Event A's likelihood of happening is P(A)=0.65.

The likelihood of the two events A and B intersecting is P(A∩B)=0.26.

Given that the likelihood of the two independent events is:

P(A∩B) = P(A)⋅P(B)

Then the probability of the event B will be,

P(B) = P(A)/P(A∩B)

P(B) = 0.65/0.26

P(B) =0.4

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Answer:

x=2

Step-by-step explanation:

X^2+5x-14=0

x^2-2x+7x-14=0

7x-14=0

x=2

Answer:

33

Step-by-step explanation:

evaluate f(- 3) by substituting x = - 3 into f(x)

f(- 3) = 3(- 3)² - (- 3) + 5 = 3(9) + 9 + 5 = 27 + 14 = 41

evaluate f(4) by substituting x = 4 into f(x)

f(4) = 3(4)² - 4 + 5 = 3(16) + 1 = 48 + 1 = 49

Then

2f(- 3) - f(4) = 2(41) - 49 = 82 - 49 = 33

Answer:

h = 5 feet

Step-by-step explanation:

V = lwh

40 = 4 x 2 x h

40 = 8h

h = 5

The simplified radical expression by rationalizing the denominator is, \(\frac{-6}{\sqrt{5y}}\times\frac{\sqrt{5y}}{\sqrt{5y}}\) = \(\frac{-6\sqrt{5y}}{5y}$$\) = $\frac{-6\sqrt{5y}}{5y}$.

To simplify the radical expression by rationalizing the denominator, multiply both numerator and denominator by the conjugate of the denominator.

The given radical expression is \($\frac{-6}{\sqrt{5y}}$\).

Rationalizing the denominator

To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator, \($\sqrt{5y}$\)

Note that multiplying the conjugate of the denominator is like squaring a binomial:

This simplifies to:

(-6√(5y))/(√(5y) * √(5y))

The denominator simplifies to:

√(5y) * √(5y) = √(5y)^2 = 5y

So, the expression becomes:

(-6√(5y))/(5y)

Therefore, the simplified expression, after rationalizing the denominator, is (-6√(5y))/(5y).

\($(a-b)(a+b)=a^2-b^2$\)

This is what we will do to rationalize the denominator in this problem.

We will multiply the numerator and denominator by the conjugate of the denominator, which is \($\sqrt{5y}$\).

Multiplying both the numerator and denominator by \($\sqrt{5y}$\), we get \(\frac{-6}{\sqrt{5y}}\times\frac{\sqrt{5y}}{\sqrt{5y}}\) = \(\frac{-6\sqrt{5y}}{5y}$$\)

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The statement "the sum of the percent frequencies for all classes in a frequency distribution will always equal" is True.

The sum of the percent frequencies for all classes in a frequency distribution will always equal 100%. This is because the percent frequency for each class is calculated by dividing the frequency of that class by the total number of observations and then multiplying by 100. Therefore, when we add up all the percent frequencies for all the classes, we get the total percentage of observations, which must be 100%.

In a frequency distribution, percent frequencies are calculated by dividing the frequency of each class by the total number of observations and then multiplying by 100. Since all observations are accounted for in the distribution, the sum of the percent frequencies for all classes will always equal 100%.

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Answer:

10,395

Step-by-step explanation:

Hope this helps!! :))

The points of solution that are obtained for the system of linear equations 3x + 2y = 11 and -8x - 4y = -20 are (-1,7).

2(3x + 2y = 11)

1(-8x - 4y = -20)

3x + 2y - 8x - 4y = 11 - 20 gives -5x - 2y = -9

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The system of linear equations are -

3x + 2y = 11....(1)

-8x - 4y = -20....(2)

When solved initially the value of equation is -

3x + 2y - 8x - 4y = 11 - 20

-5x - 2y = -9

Multiply equation (1) by 2 -

2(3x + 2y) = 2 × 11

6x + 4y = 22.....(3)

Simplify the equation (2) and (3) by adding -

-8x - 4y + 6x + 4y = -20 + 22

-2x = 2

x = -1

Substituting the value of x = -1 in equation (1) -

3x + 2y = 11

3(-1) + 2y = 11

Simplifying the equation -

-3 + 2y = 11

2y = 11 + 3

2y = 14

y = 7

Therefore, the final value is obtained as (-1,7).

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The element that orients readers by previewing the structure of the report is "Organization."

Organizing a report effectively helps readers understand the flow of information and the logical structure of the content. By providing an overview of the organization, readers can anticipate the main sections, their sequence, and the connections between them.

The organization element typically includes headings, subheadings, and a clear hierarchy of information. It outlines the main sections and subsections of the report, indicating how they are related and how they contribute to the overall message or argument.

In addition to the organization element, the other options listed—Definitions of key terms and Sources and methods—also play important roles in a report. Definitions of key terms clarify terminology and provide a common understanding, while Sources and methods explain the sources of information and the methods used in the report's research or analysis. However, in the context of previewing the structure, the Organization element specifically serves this purpose.

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Answer: 3/4

Step-by-step explanation:   Find the reciprocal of the divisor

Reciprocal of 20/27: 27/20

Now, multiply it with the dividend So, 5/9 ÷ 20/27 = 5/9 × 27/20=  5 × 27/9 × 20 = 135/180

After reducing the fraction, the answer is

3/4

The dimensions of the field should be 125m by 100m to enclose the maximum area.

To solve this problem, we can use the fact that the area of a rectangle is given by A = lw, where l and w are the length and width of the rectangle, respectively. Since the field is to be subdivided into four congruent plots, we can express the width in terms of the length as w = (1/4)(l).

We can then use the fact that the total length of fencing available is 6000m to set up an equation for the perimeter of the rectangle, which is given by P = 2l + 5w. Substituting w with (1/4)(l), we get P = 2l + 5((1/4)(l)) = (9/2)l.

Solving for l in terms of P, we get l = (2/9)P. Substituting this expression for l into the equation for the area, we get A = (1/4)(l)(w) = (1/4)(l)((1/4)(l)) = (1/16)l^2.

We can now express the area in terms of P as A = (1/16)((2/9)P)^2 = (4/81)(P^2). To find the maximum area, we can take the derivative of A with respect to P and set it equal to zero, which gives dA/dP = (8/81)P = 0. This implies that P = 0 or P = 81/8. Since P cannot be zero, we have P = 81/8.

Substituting this value of P back into the equation for l, we get l = (2/9)(81/8) = 18.75. Finally, substituting l and w = (1/4)(l) into the equation for A, we get A = (1/16)(18.75)(4.6875) = 117.1875. Therefore, the dimensions of the field should be 125m by 100m to enclose the maximum area.

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Answer:

Step-by-step explanation:

2x² - 8x - 24 = 0

2x² - 12x + 4x - 4*6 = 0

2x(x-6) + 4(x - 6) = 0

(x - 6)(2x + 4) = 0

It takes 40 seconds (400 / 10) for the entire caravan to line up before the second toll booth.

It takes 100 seconds (20 * 5) for the entire caravan to receive service at the first toll booth.

Assuming that the cars line up at the second toll booth right after receiving service at the first toll booth, the time it takes for the entire caravan to line up before the second toll booth depends on the speed of the cars.

Since the speed of the cars is 10 kilometers per second, in the 100 seconds it takes for the entire caravan to receive service at the first toll booth, the entire caravan travels a distance of 1000 kilometers (100 * 10).

Since the distance between the first and second toll booths is 400 km, it takes 40 seconds (400 / 10) for the entire caravan to line up before the second toll booth.

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It takes 40 seconds (400 / 10) for the entire caravan to line up before the second toll booth.

It takes 100 seconds (20 * 5) for the entire caravan to receive service at the first toll booth.

Assuming that the cars line up at the second toll booth right after receiving service at the first toll booth, the time it takes for the entire caravan to line up before the second toll booth depends on the speed of the cars.

Since the speed of the cars is 10 kilometers per second, in the 100 seconds it takes for the entire caravan to receive service at the first toll booth, the entire caravan travels a distance of 1000 kilometers (100 * 10).

Since the distance between the first and second toll booths is 400 km, it takes 40 seconds (400 / 10) for the entire caravan to line up before the second toll booth.

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The sum of the first n whole numbers is given by the expression:

S = 1 + 2 + 3 + ... + n

This is an arithmetic series with a common difference of 1 and n terms. The sum of an arithmetic series can be expressed as:

S = n/2 [2a + (n-1)d]

where a is the first term, d is the common difference, and n is the number of terms.

In this case, a = 1, d = 1, and n = n. Substituting these values into the formula above, we get:

S = n/2 [2(1) + (n-1)(1)]

= n/2 [2 + n - 1]

= n/2 [n+1]

Multiplying out the expression on the right-hand side, we get:

S = n(n+1)/2

This is the expanded form of the sum of the first n whole numbers, also known as the "triangular number" sequence.

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The value of y is 24.

Non of the given option is correct.

To find the value of y in the given triangle, we can apply the Pythagorean theorem.

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In the given triangle, we have a right angle and one leg of length 12. The other leg has a length of 12√3. Let's assume y represents the length of the hypotenuse. Applying the Pythagorean theorem, we have:

(12)^2 + (12√3)^2 = y^2

144 + 432 = y^2

576 = y^2

Taking the square root of both sides, we get:

y = √576

y = 24

Non of the given option is correct.

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The range of possible values of x as calculated from the given data is x > 6

In a triangle  the length of two sides has to be greater than the third side

Thus;

6x + 3 + 4x-17 > x + 40

6x + 4x-14 > x + 40

10x-14 > x + 40

10x-x > 40 + 14

9x > 54

x > 54/9

x > 6

Due to the fact that the measurements of central tendency do not provide sufficient detail about a given set of data. Another factor that must be investigated in statistics is variability.

We require a single number to characterise variability, much like measures of central tendency. This one number has demonstrated a certain amount of dispersion.

The following is the formula to determine a data set's range:

Range = maximum - minimum

Range is defined as the greater of two values.

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Answer:

4 pounds of granola

Step-by-step explanation:

1.76p = 7.04

p = 7.04/1.76 = 4

D represents the hypothesis that the population mean (μ) is greater than or equal to 1000, while E represents the hypothesis that the population mean is less than 1000.

In hypothesis testing, D and E typically represent the null hypothesis (H0) and alternative hypothesis (Ha) respectively. The null hypothesis (D) assumes that the population mean (μ) is greater than or equal to 1000, while the alternative hypothesis (E) assumes that the population mean is less than 1000.

These hypotheses are used to make decisions about the population based on sample data. In this context, options (a) and (b) are not applicable as they refer to H(a) and H(0) which are not commonly used notations in hypothesis testing.

Option (c) is also incorrect as D and E do not represent Type I and Type II errors, which are associated with the decisions made based on the hypothesis test results.

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Answer:

0.797

Step-by-step explanation:

According to the distance, Andrew and Stacy will meet 0.5 hours after Stacy starts her journey from Portsmouth, which would be at 10:30 am.

To solve this problem, we will use the concept of distance, speed, and time. The distance between Exeter and Portsmouth is given as 20 miles. Andrew starts his journey at 9:30 am and cycles at a speed of 12 mph. Stacy starts her journey at 10:00 am from Portsmouth and cycles at a speed of 16 mph.

Let's consider the distance traveled by Andrew and Stacy before they meet. Suppose they meet after a time of "t" hours, and let's assume that Andrew has traveled "d1" miles from Exeter towards Portsmouth, and Stacy has traveled "d2" miles from Portsmouth towards Exeter.

Since Andrew starts half an hour earlier than Stacy, he would have traveled for "t + 0.5" hours before they meet. Hence, the distance traveled by Andrew would be:

d1 = speed x time = 12 x (t + 0.5) miles

Similarly, Stacy would have traveled for "t" hours before they meet. Hence, the distance traveled by Stacy would be:

d2 = speed x time = 16 x t miles

Now, we know that the total distance between Exeter and Portsmouth is 20 miles. Therefore, the sum of the distances traveled by Andrew and Stacy should be equal to 20 miles when they meet.

d1 + d2 = 12(t + 0.5) + 16t = 20

Simplifying the equation, we get:

28t + 6 = 20

28t = 14

t = 0.5

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Answer: 1264.2857%

Step-by-step explanation:

Answer:

She earned 67.29% profit

Step-by-step explanation:

First let's find how much she spent on the coats.

50 x $28

$1400

So, her expense was $1400

Now, let's find how much she earned selling these coats.

We know she sold 38 of these coats at $49 each. Let's find how much she earned for these 38 coats.

38 x $49

$1862

She earned $1862 on these 38 coats.

Now, let's find how much she earned on the rest of the coats (50-38 which is 12). We know she sold the remaining for $40 each.

12 x $40

$480

She earned $480 on the rest of the coats.

The total she earned $2342

To find the profit:

Profit= $ Earned - Expenses

Profit= 2342-1400

Profit=$942

The question is asking for the percentage.

To find the percentage, we can use the percentage formula:

\(\frac{Profit}{Expense}\) x 100

We know that the profit is $942 and the expense is $1400

(We want to find how much profit she made out of the expense)

\(\frac{942}{1400}\) x \(\frac{100}{1}\)

If you round your answer, you will get 67.29

Answer: She earned 67.29% profit