Find the length of the following two-dimensional curve.r(t)=⟨4sint−4tcost,4cost+4tsint⟩, for 0≤t≤2πL=(Type an exact answer, usingπas needed.)

Answer:

x= 15

Step-by-step explanation:

All sides of a rhombus are equal so AD = CD

2x+10 = 4x-20

Subtract 2x from each side

2x+10-2x = 4x-20 -2x

10 = 2x-20

Add 20 to each side

10+20 = 2x-20+20

30 = 2x

Divide by 2

30/2 = 2x/2

15 =x

\( \longmapsto \: 2x + 10 = 4x - 20\)

\( \longmapsto \: 2x - 4 x= - 20 - 10\)

\( \longmapsto \: - 2x = - 30 \)

\( \longmapsto \: x=15 \)

Answer:

Indirect variation

Step-by-step explanation:

If two variables change in inverse proportion, then it is called indirect variation.

xy = k where k is a constant.

5*2 = 10

10*1 =10

\(15*\dfrac{2}{3}=5*2=10\\\\\\20*\dfrac{1}{2}=10\)

So, this is indirect variation.

The Pearson correlation coefficient with a value of -0.75 indicates that there is a linear and inverse variation between the two variables under study.

Pearson's correlation coefficient is a coefficient that studies the statistical relationship between two variables.

This coefficient relates the two variables between +1 and -1.

In this case we have a coefficient with a negative value and 0.75, this means that there is an inverse relationship between the two variables, that is to say while one goes down the other goes up.

-0.75 Indicates a linear and inverse relationship between the statistical variables.

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Answer:

Step-by-step explanation:

To solve the system of linear equations using the elimination method, we can first multiply one equation by a constant so that the coefficients of one variable are equal in both equations. This allows us to eliminate that variable and find the value of the other variable. Then, we can substitute that value back into one of the equations to find the value of the other variable.

Here's how it works for the given system:

7x + 2y = 24

8x + 2y = 30

Multiplying the first equation by 8 and subtracting it from the second equation, we can eliminate the y variable:

7x + 2y = 24

8x + 2y = 30

(7x + 2y) * 8 - (8x + 2y) = 24 * 8 - 30

56x = 168

x = 3

Substituting x = 3 back into one of the equations:

7x + 2y = 24

7 * 3 + 2y = 24

21 + 2y = 24

2y = 3

y = 1.5

So the solution to the system is (x, y) = (3, 1.5).

Answer:

b

Step-by-step explanation:

because angle 1 is 45 degree

angle 2 is 70 degree

angle 3 is 55 degree

and angle 4 is 60 degree

Answer:

1.)a.)x is divided by two and is one is added to get y

b.)y=x/2 + 1

Answer:

3000ft²

Step-by-step explanation:

2cm =5 ft

24 cm = 60 ft

20 cm = 50 ft

Area = 60 *50

= 3000

The system we need to solve to determine whether the given vector belongs to the span is {a + b + c = -2, 2a + 2b + 3c + d = -3, -10a + b - c = -10}.

Given the vector p(t) = -2t^2 - 3t - 10, we want to determine whether it belongs to the span of the vectors {t^2 + 2t + 1, t^2 + 3, t - 1}. To check this, we need to find scalars a, b, and c such that ap(t) + bt^2 + 2bt + b + ct^2 + 3c + dt - c = 0, where d represents the coefficient of t in p(t).

By equating the coefficients of like terms, we get the following system of equations:

a + b + c = 0

-2a + 2b + 3c + d = -3

-10a + b - c = -10

Simplifying, we obtain the system:

a + b + c = -2

2a + 2b + 3c + d = -3

-10a + b - c = -10

Therefore, the system we need to solve to determine whether the given vector belongs to the span is {a + b + c = -2, 2a + 2b + 3c + d = -3, -10a + b - c = -10}.

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Answer:

a2 - 3ab + b2

Step-by-step explanation:

just saying the 2s are squared :)

Answer:

The answer is 40

Step-by-step explanation:

He expects to count #####################################

There are 12 Steelhead should the biologist expect to count on day 5.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

The ratio of Chinook to Steelhead on the first four days is 4:10.

If this ratio remained the same on day 5, then we can expect the biologist to count of the salmon as Chinook.

On day 5, the biologist counted 16 Chinook,

Let x Steelhead would be the biologist expected to count on day 5.

As per the given question, the required solution would be as:

4/10 = 16/x

x = 16 × 10 / 4

x = 160/4

x = 40

Hence, there should be 40 Steelhead.

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The number of pages that are in the book is 1 31/45 pages.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, Tyler reads 2/15 pages on Monday 1/3 on Tuesday and 2/9 on Wednesday and 3/4 on thursday .and has 14 pages left on friday how many pages are in the book.

The fraction for pages will be:

= 2/15 + 2/9 + 1/3 + 3/4 + 1/4

= 2/15 + 5/9 + 1

= 6 / 45 + 25/45 + 1.

= 1 31/45

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Complete question

tyler reades 2/15 pages on monday 1/3 on tuesday and 2/9 on wendsday and 3/4 on thursday .and has 1/4 pages left on friday how many pages are in the book

The company's debt to equity ratio will decrease as a result of receiving cash of $1,000,000 from issuing common stock at par value.

The debt to equity ratio is a financial ratio that measures the proportion of a company's debt to its equity, indicating the company's leverage or reliance on debt financing. It is calculated by dividing total debt by total equity.

In this scenario, the company received cash of $1,000,000 from issuing common stock at par value. Since this cash infusion increases the equity of the company, the denominator in the debt to equity ratio increases.

However, since there is no mention of any change in the company's debt, the numerator of the debt to equity ratio remains the same.

As a result, when the equity increases and the debt remains the same, the ratio of debt to equity decreases. Therefore, the debt to equity ratio will decrease as a result of the transaction.

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Answer:There are 6 possible amounts.

Step-by-step explanation:

It's 4 Choose 2 meaning 4 coins choosing two which translates to 4C2 on your calculator

The total volume of the sampler can is 9.42 cubic inches.

Tommy made an error in his calculation when determining the volume of the sampler can. To understand the mistake, let's break down the process step-by-step.

Tommy correctly calculated the area of the base of the sampler can. However, you mentioned that the area value was not provided in the question, so I cannot provide an accurate answer using that value.

Tommy then multiplied the area of the base by the height of 3 inches to find the total volume. However, this is where the error occurred.

To calculate the volume of a cylindrical object, we use the formula V = πr^2h, where V represents volume, π is approximately 3.14, r is the radius of the base, and h is the height.

Since Tommy provided the diameter of 2 inches, we can determine that the radius (r) is half of the diameter, so r = 1 inch.

Plugging these values into the volume formula, we get V = 3.14 * (1 inch)^2 * 3 inches = 9.42 cubic inches.

The error Tommy made was not squaring the radius before multiplying by the height. By correctly calculating the volume using the formula V = πr 2h, we determined that the total volume of the sampler can is 9.42 cubic inches.

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The sequence of natural numbers that leaves a remainder of 3 when divided by 10 is:

3, 13, 23, 33, 43, 53, 63, 73, 83, 93, 103, 113, ...

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

\(23r-12y+15\)

Step-by-step explanation:

\(18r + 6 - 12y + 5r + 9\)

Group the similar terms together:

\(18r+5r-12y+6+9\)

Add the variable "r":

\(23r-12y+6+9\\\)

Add the numbers:

\(23r-12y+15\)

Answer:

You remove 5

Step-by-step explanation:

I can answer your first question

you have 11 numbers and need to remove 1 which makes the amount of numbers you use 10 so if you work backwards:

lets say x is the 10 numbers added up and you have to divide them by 10 to get 6.1 so we get

x/10 = 6.1  which equals x=61 so the 10 numbers added up equal up to 61.

With a bit of trial and error you get 1 + 2+3+4+6+7+8+9+10+11 =61 so you remove 5 !

Hope it helped you

Answer:

Remove 5 and 92

Step-by-step explanation:

The first question:

you have 11 numbers and need to remove 1 which makes the amount of numbers you use 10, since you have to remove one so you work backwards. If n is the 10 numbers added up and you have to divide them by 10 to get 6.1 so we get which is the mean n/10 = 6.1  which equals n=61 so the 10 numbers added up equal up to 61. The total of all 11 numbers is 66. So 66-61=5. You remove 5

Second Question:

She is taking 4 tests. She wants to average a 95 on those tests. So, she must score 95*4=380 total. She scored 97 and 91, or 188 total. So, she must score 380-188 = 192 total on her next two tests. Her maximum score possible on the fourth test is 100. In Conclusion, the lowest score possible for the third test would be 192-100=92

Answer:

\({ \tt{sum = \frac{a(r {}^{n - 1} )}{n - 1} }} \\ 27 = \frac{a(r {}^{2 - 1} )}{2 - 1} \\ { \bf{27 = ar - - - (i)}} \\ \\ 54 = \frac{a( {r}^{3 - 1} )}{3 - 1} \\ { \bf{108 = a {r}^{2} - - - (ii) }} \\ { \tt{(ii) \div (i) : }} \\ r = \frac{108}{27} \\ { \bf{common \: ratio = 4}} \\ { \bf{first \: term = \frac{27}{4} }}\)

(a) if 20 cards are defective, then the probability that at least 1 defective card is in the sample is 0.964​

(b) if 5 cards are defective, then the probability that at least 1 defective card appears in the sample is 0.543​

Probability:

In statistics, probability refers the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.

Given,

Here we have a printed circuit cards are placed in a functional test after being populated with semiconductor chips. a lot contains 190 cards, and 20 are selected without replacement for functional testing.

And we need to find the following probability.

Here we have to recall the formula for probability mass function of the hypergeometric random variable X with the parameters

N = 190

n ​= 20​

and the parameter K.

And it is the following expression:

f(x) = [(K x) (140 - k 20 - x)] / (140 20)

Now, we have to Set K=20 and calculate from the probability mass function:

=> P(X≥1)=1−f(0)=0.964​

And then Set K=5 and calculate from the probability mass function:

=> P(X≥1)=1−f(0)=0.543​

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The formula connecting E and F is E = k/F3, where k is a constant. This formula states that the value of E is inversely proportional to the cube of F.

That is, as F increases, the value of E decreases. For example, if F increases from 3 to 4, then the value of E decreases by a factor of 8.

This inverse proportionality between E and F3 is due to the fact that, as F increases, the cube of F increases at a faster rate. In other words, when F doubles, the cube of F increases by a factor of 8. This causes the value of E to decrease by the same factor of 8.

The formula is useful in many applications, such as in physics and engineering. For example, in physics, the formula can be used to calculate the force of an object in a gravitational field. The force is inversely proportional to the cube of the distance between the object and the center of gravity, where the constant k is equal to the gravitational constant. In engineering, the formula can be used to calculate the power of a motor, where the power is inversely proportional to the cube of the speed of the motor.

Overall, the formula E = k/F3 expresses the inverse proportionality between E and F3, and is used in various applications to calculate the value of E given the value of F.

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The surveyor determines the angle of the triangular plot by using the inverse cosine function with a given value of cos⁻¹(0.15). The result of approximately 89° represents the approximate measure of the angle at which the surveyor stands in relation to the sides of the plot.

Among the given options for the inverse cosine values, the measure of the angle of the triangular plot at which the surveyor stands is determined by the value of cos⁻¹(0.15), which is approximately 89°.

Each result represents the measure of the angle at which the surveyor stands in relation to the sides of the triangular plot. It's important to note that these results are approximate values rounded to the nearest degree.

By using the given cosine values and applying the inverse cosine function, the surveyor can determine the approximate angle of the triangular plot.

Therefore, The approximate measure of the angle of the triangular plot at which the surveyor stands is 89°.

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Question-

A surveyor measures the lengths of the sides of a triangular plot of land. what is the measure of the angle of the triangular plot at which the surveyor stands? Approximate to the nearest degree.

cos^(-1)(0.75) ≈ 41°

cos^(-1)(0.125) ≈ 83°

cos^(-1)(0.563) ≈ 56°

cos^(-1)(0.15) ≈ 89°

Answer:

Step-by-step explanation:

5y=...:

y=5-13

y=-8=>5y=-58

6x-(-58)=13

6x+58=13

6x =13-58

6x =-45

x =-45:6

x =-7.5

The critical point of the function f(x) = 4x² + 3x - 1 is x = -3/8.

To find the critical points of the function f(x) = 4x² + 3x - 1, we need to find the values of x where the derivative of f(x) is equal to zero or does not exist.

First, let's find the derivative of f(x) using the power rule:

f'(x) = d/dx (4x²) + d/dx (3x) + d/dx (-1)

= 8x + 3

To find the critical points, we set the derivative equal to zero and solve for x: 8x + 3 = 0

Subtracting 3 from both sides: 8x = -3

Dividing by 8: x = -3/8

Therefore, the critical point of the function f(x) = 4x² + 3x - 1 is x = -3/8.

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Anser

Step-by-step explanation:

f)-7= what is 4 times b = 8 so add 7 times 8 that is your anser

Answer:d≈5.2cm

Step-by-step explanation:

d=3a=3·3≈5.19615cm

Answer: the student spends 24 minutes on their art project and 32 minutes on their science project.

Step-by-step explanation:

Answer:

The student spends 24 minutes on their art project, and 32 minutes on their science project

Step-by-step explanation:

To solve this problem, we can utilise the unitary method, a process by which we find the value of a single unit, from the value of multiple units and thus, the value of multiple units from the value of a single unit.

If the total number of units in the ratio is (3+4)=7, then 7 units = 56 mins.

If 7 units = 56 mins,

then 1 unit = 56/7 mins = 8 mins.

Therefore, 3 units = 8×3 = 24 mins,

and 4 units = 8×4 = 32 mins.

Thus, the student spends 24 minutes on their art project, and 32 minutes on their science project

Option C is correct

.!!!!!!

The function is to describe the sequence and the amount of gasoline used on the eighth day of his trip will be y = 0.75n and 6 L respectively. Option B is correct.

Each consecutive term in an arithmetic sequence has a common constant difference.

The sequence of the  liters of gasoline on each day is;

0.75,1.5,2.25,3

The given series is an arithmetic series with a common difference of 0.75

Common difference,d=0.75

First-term,a=0.75

The amount of gasoline used on the eighth day of his trip.

The nth term of the arithmetic sequence is;

\(\rm a_n = a+(n-1)d \\\\ \rm a_8 = 0.75+(8-1)0.75 \\\\ a_8 = 6\)

The 8th term of the arithmetic sequence is 6L.

The function is to describe the sequence and the amount of gasoline used on the eighth day of his trip will be y = 0.75n and  6 L.

Hence, option B is correct.

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