Select the correct answer. What is the value of x in the equation 1,331x3 − 216 = 0? A. -6/11 B. 11/6 C. 1/6 D. 6/11

The valuse of the definite integral ∫[0 _ π/4] sin(t) / cos^2(t) dt is 0.4142

In this question, we need to evaluate the definite integral.

∫[0 _ π/4] sin(t) / cos^2(t) dt

Substitute u = cos(t)

du/dt = -sin(t)

∫sin(t) / cos^2(t) dt = -∫1/u^2 du

The solution of -∫1/u^2 du = 1/u

So, ∫sin(t) / cos^2(t) dt = 1/cos(t) + C

We know that 1/cos(t) = sec(t)

So, ∫sin(t) / cos^2(t) dt

= 1/cos(t) + C

= sec(t) + C

∫[0 _ π/4] sin(t) / cos^2(t) dt

= [ sec(t)]_(0 _ π/4)

= √2−1

= 0.4142

Therefore, ∫[0 _ π/4] sin(t) / cos^2(t) dt = 0.4142

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We can say that a and b are identical in absolute value if a and b are nonzero integers such that a divides b (a | b) and b divides a (b | a). That is to say, a =± b.

The transitive property of divisibility serves as evidence for this. We know that there are numbers k and l such that b = ak and a = bl exist if a | b and b | a. We obtain a = alk by substituting the expression for b into the second equation. We can divide both sides by a to get l = 1/k because an is not zero. Given that k and l are both integers, they must both either be 1 or -1. B Equals ak if k = 1, else then b = ak = a(1) = a, and if k = -1, then b = ak = a(-1) = -a. In either case, we have shown that a = ±b.

So if a and b are nonzero integers such that a divides b and b divides a, then we can conclude that a and b have the same absolute value, but possibly opposite signs.

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Answer:

\(x = 50\)

Step-by-step explanation:

\(x + x + (2x - 20) = 180 \\ x + x + 2x - 20 = 180 \\ 4x - 20 = 180 \\ 4x = 180 + 20 \\ 4x = 200 \\ \\ x = \frac{200}{4} \\ \\ x = 50\)

\(2x - 20 \\ 2(50) - 20 \\ 100 - 20 = 80\)

The value of x in the triangle is 50

The angles in a triangle add up to 180.

So, we have:

x + x + 2x - 20 = 180

Add 20 to both sides

x + x + 2x = 200

Evaluate the like terms

4x =200

Divide both sides by 4

x =50

Hence, the value of x in the triangle is 50

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The statement says that you've triggered the Penalty APR so that it has now increased to 28.99%. What action triggered this? You failed to pay the minimum payment by the due date.

You failed to make the minimum payment by the due date. This is an action that can result in a message that "you've triggered the Penalty APR so that it has now climbed to 28.99%."

A charge APR is a charge that can be applied if you don't pay your bills on time. It may be set up so that future transactions may be subject to a penalty APR that is higher than the card's standard rate.

If the minimum payment was not made by the due date, Penalty APR would be applied.

But if the card also has a penalty APR and you trigger it, you will likely lose that promotional offer. Federal consumer protections that limit penalty APRs don't apply to small-business credit cards. That means issuers can be more punitive, such as applying penalty APRs sooner than 60 days after not making payments.

Therefore,

The statement says that you've triggered the Penalty APR so that it has now increased to 28.99%. What action triggered this? You failed to pay the minimum payment by the due date.

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The statement "An estimator is consistent if as the sample size decreases, the value of the estimator approaches the value of the parameter estimated" is False.

Consistency is an important property of estimators in statistics. An estimator is consistent if its value approaches the true value of the parameter being estimated as the sample size increases.

In other words, if we repeatedly take samples from the population and compute the estimator, the values we obtain will be close to the true parameter value.

This is an essential characteristic of a good estimator, as it ensures that as more data is collected, the estimation error decreases.

However, as the sample size decreases, the value of the estimator is more likely to deviate from the true value of the parameter. The reason for this is that a small sample size may not be representative of the population, and as a result, the estimation error may increase.

As a consequence, the statement is false. In conclusion, consistency is a property that an estimator possesses when its value converges to the true value of the parameter as the sample size grows.

As the sample size decreases, the estimator may become less reliable, leading to an increase in the estimation error.

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Answer:

Ok

Step-by-step explanation:

The area of triangle JHK is 4.18 units²

A triangle is a polygon with three sides having three vertices. There are different types of triangle, we have;

The right triangle, the isosceles , equilateral triangle e.t.c.

The area of a figure is the number of unit squares that cover the surface of a closed figure.

The area of a triangle is expressed as;

A = 1/2bh

where b is the base and h is the height.

The base = 2.2

height = 3.8

A = 1/2 × 3.8 × 2.2

A = 8.36/2

A = 4.18 units²

Therefore the area of triangle JHK is 4.18 units²

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Answer:

9/17 or 52.9% or likely

Step-by-step explanation:

The decimal approximation of √60, rounded to four decimal places, is 7.7450. Approximate the square root of 60 using the differential method. To do this, we will use linear approximation and the derivative of the square root function.

Let f(x) = x^(1/2), and we want to find f(60). Choose a nearby value of x that is easy to work with, such as x = 64, because f(64) = 8. Now, we will find the derivative of f(x) to determine the rate of change at x = 64.

f'(x) = (1/2)x^(-1/2)

Now, we'll find f'(64):
f'(64) = (1/2)(64)^(-1/2) = 1/16

Using the linear approximation formula, we have:
f(60) ≈ f(64) + f'(64)(60-64)
f(60) ≈ 8 + (1/16)(-4)
f(60) ≈ 8 - (1/4)
f(60) ≈ 7.75

So, the decimal approximation of √60, rounded to four decimal places, is 7.7450.

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The Fourier cosine series for a function f(x) on the interval [-L,L] is given by the formula:

f(x) = a0/2 + SUM[n=1 to infinity] {ancos(npi*x/L)}

where the coefficients an are given by:

an = (2/L) * INTEGRAL[-L to L] {f(x)cos(npi*x/L) dx}

For the function f(x) = x(2L-x) defined on the interval [0,L], the Fourier cosine series can be calculated as follows:

a0 = (2/L) * INTEGRAL[0 to L] {f(x) dx} = (2/L) * INTEGRAL[0 to L] {x(2L-x) dx} = 2/3 * L

an = (2/L) * INTEGRAL[0 to L] {f(x)cos(npix/L) dx} = (2/L) * INTEGRAL[0 to L] {x(2L-x)cos(npix/L) dx}

Using integration by parts, we can simplify this expression to:

an = (4L/(npi)^2) * [(-1)^n - 1]

Therefore, the Fourier cosine series for the function f(x) = x(2L-x) on the interval [0,L] is:

f(x) = (L/3) + SUM[n=1 to infinity] {(4L/(npi)^2) * [(-1)^n - 1] * cos(npix/L)}

This series converges to the function f(x) on the interval [0,L].

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Answer:

y = 3/5x - 5

Step-by-step explanation:

y intercept is -5

slope is rise / run = 3/5

Answer:

please mark me brainliest

Step-by-step explanation:

Answer: 3/8 as a decimal is 0.375.

Answer:

0.375.

Step-by-step explanation:

Do the division:-

8)3.000(0.375

   2 4

       60

        56

           40

            40

             --

The percent of attendance figures that differs from the mean by 1500 persons or more is 6.68%.

From the question above, Mean μ = 10,000

Standard Deviation σ = 1,000

The formula for z-score is :

z = (x-μ) / σ

Where, x = observation

z = z-score

Mean μ = 10,000

Standard Deviation σ = 1,000

From the above formula, let's calculate z-score for x = 11,500

z = (x-μ) / σ

z = (11,500 - 10,000) / 1000

z = 1.5

Now, find the probability of attendance figures that differs from the mean by 1500 persons or more.

P(z ≥ 1.5) = 0.0668

To find the percentage, we need to multiply the above value by 100.

P(z ≥ 1.5) × 100 = 0.0668 × 100 = 6.68%

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Answer:

16m

Step-by-step explanation:

AB would be double DE

The Total Proability will be 297 / 1015

What is Probability?

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

Solution:

Total Number of Regular Soft Drinks = 18

Total Number of Diet Soft Drinks = 12

Total Drinks = 18 + 12 = 30

Probability of selecting Diet Soft Drink in the first two attempt = 12/30 * 11/29 * 18/28 = 2376 / 24360

Probability of selecting Diet Soft Drink in the first and last attempt = 12/30  * 18/29 * 11/28 = 2376 / 24360

Probability of selecting Diet Soft Drink in the second and last attempt = 18/30  * 12/29 * 11/28 = 2376 / 24360

Total Probability = 3 * 2376 / 24360

Total Probability = 2376 / 8120

Total Probability = 297 / 1015

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A compound event is any event combining two or more simple events.

From the question, we have the following parameters that can be used in our computation:

combining two or more simple events.

As a general rule

When two or more simple events are combined, the result is a compound event

An example is selecting 1 in a die and head in a coin

This means that the statement that completes the blank is compound event

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Answer:

1.04grams

Step-by-step explanation:

Step-by-step explanation:

1) x≤-10

2) 2y>-5/2

y<(-5/2)/2

3)no because they are equal

4)no because we get 11 and it's not≤-9

5)yes, we get -2≥-3

Answer: y=1/2x-3

Step-by-step explanation:

the y-intercept is negative so there's no need to put a plus sign.. feel free to let me know if im wrong

Answer:

x=9

Step-by-step explanation:

13x-32 and 7x+22 are equal to each other (angles) so

13x-32=7x+22

13x-7x=22+32

6x=54

x=54/6

x=9

The graph remains at a constant height (y-value) for all x-values within the specified interval. This means that the function does not change in this interval and maintains a consistent output.

If the value of is constant for every value that satisfies a certain condition, it means that the graph is a horizontal line on that interval. The behavior of the graph is constant or unchanging in terms of its vertical position.

When every value of x that satisfies a given condition results in a constant value of y, this tells us that the behavior of the graph of the function on this interval is horizontal. In other words, the graph remains at a constant height (y-value) for all x-values within the specified interval. This means that the function does not change in this interval and maintains a consistent output.

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\(\huge\red{\mid{\underline{\overline{\textbf{Question}}}\mid}}\)

Brandon earns $9.70 for every hour that he works. If he worked for 4.5 hours, how much money would Brandon earn?

Response :-

Since $9.70 per hour is the hourly rate we can make an equation out of what you've given us.

\(\frac{9.70}{1}=\frac{x}{4.5}\)

Cross Multiplication - In mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can cross-multiply to simplify the equation or determine the value of a variable.

Distributive - To use the distributive property, we need to understand the formula to use it. This formula will ensure that you can easily solve any equation.

The distributive property is A(B + C) = AB + AC, where AB is the product of the values A and B and AC is the product of the values A and C.

First, let's notice that we are distributing a 2 into the parentheses, so we will mark this as our A value.

Then, our two values inside the parentheses are B and C respectfully.

Now, we can apply the formula.

_____________

Now since we had

\(\frac{9.70}{1}=\frac{x}{4.5}\) we can make the equation of

\(1(x)=4.5(9.70)\)

use distributive property

\(x=43.65\)

_____________

\(\huge\red{\mid{\underline{\overline{\textbf{Answer}}}\mid}}\)

Answer:

$43.65

Step-by-step explanation: 9.70

                                          x 4.50

The correct representation of the taylor series expansion of f(x) = cos(x) centered at x = 7/4 is:

iii) f(x) = cos(7/4) - sin(7/4)(x - 7/4) - cos(7/4)(x - 7/4)²/2 + sin(7/4)(x - 7/4)³/6 -.

the taylor series expansion of the function f(x) = cos(x) centered at x = 7/4 is given by:

f(x) = f(7/4) + f'(7/4)(x - 7/4) + f''(7/4)(x - 7/4)²/2! + f'''(7/4)(x - 7/4)³/3! + ...

let's calculate the derivatives of f(x) to determine the coefficients:

f(x) = cos(x)f'(x) = -sin(x)

f''(x) = -cos(x)f'''(x) = sin(x)

now, substituting x = 7/4 into the series:

f(7/4) = cos(7/4)

f'(7/4) = -sin(7/4)f''(7/4) = -cos(7/4)

f'''(7/4) = sin(7/4)

the taylor series expansion becomes:

f(x) = cos(7/4) - sin(7/4)(x - 7/4) - cos(7/4)(x - 7/4)²/2! + sin(7/4)(x - 7/4)³/3! + ...

simplifying further:

f(x) = cos(7/4) - sin(7/4)(x - 7/4) - cos(7/4)(x - 7/4)²/2 + sin(7/4)(x - 7/4)³/6 + ... ..

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Answer: See below

Step-by-step explanation:

Let s represent Sipho's age and let l represent Litha's age

The sum of their ages is 29 years

s + l = 29...(1)

In 6 years time, Sipho (s+6), will be the same age Litha was 3 years ago (l-3)

(s+6) = (l-3)...(2)

Age:

s + l = 29

s = 29 - d (express c in d)

(29-s+6) = s - 3 (substitute c)

s+(29-s+6) = s+(d-3)

29+6 = 2s -3

29+6+3 = 2s

38 = 2s

19 = s

Back to (1):

l = 29 - 19

l = 10

Therefore, Sipho is currently 19 years old and Litha is 10 years old

The current age for the two brothers, Sipho and Litha is 10 years old and 19 years old respectively.

A linear equation is the equation in which the highest power of the unknown variable is one.

To solve this problem, let's make the linear equations by the given statement.

Let x be the age of Sipho and y is the age of Litha. The sum of their ages is 29. Therefore,

\(x+y=29\\y=29-x\)

Thus, the age of Litha is (29-x)

In 6 years' time, Sipho will be the same age as Litha was 3 years ago. Therefore,

\(x+6=(29-x)-3\\x+6=29-x-3\\x+x=29-3-6\\2x=20\\x=\dfrac{20}{2}\\x=10\)

Thus, the age of Sipho is 10 years. The age of Litha is,

\(y=29-10\\y=19\)

Hence, the current age for the two brothers, Sipho and Litha is 10 years old and 19 years old respectively.

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Answer:

2(5)^4

2x5x5x5x5 (correct)

You’re multiplying 2 by 5 but there are 4 numbers of 5 since that is the power.

Hopefully it’s correct if not then... sorry

Step-by-step explanation:

Answer:

Right

Step-by-step explanation:

You move the decimal to the right to make the decimal a whole number :)

Example below:

0.25

Move 2 places to the right

25%

Have a great day!!

Please rate and mark brainiest!!

Answer: You move the decimal point two spaces to the right.

Step-by-step explanation:

Multiply by 100.