Which statements (more than one) describe the equation 3 x 9 = 27?



3 is 27 times as many as 9.


27 is 9 times as many as 3.


9 times as many as 3 is 27.


9 times as many as 27 is 3.


3 is 9 times as many as 27

Given the polar equation r = 2 tan θ sec θ, we need to find its cartesian equation and identify the curve it represents.To convert a polar equation to a cartesian equation,

we use the following formula:x = r cos θ, y = r sin θTherefore, r = sqrt(x² + y²) and tan θ = y/x. Also, sec θ = 1/cos θ.Hence, we can substitute these values in the given polar equation:r = 2 tan θ sec θ => r = 2 (y/x) (1/cos θ)=> r = 2y / (x cos θ) => sqrt(x² + y²) = 2y / (x cos θ) => x² + y² = (2y / cos θ)²=> x² + y² = 4y² / cos² θ=> x² + y² = 4y² (1 + tan² θ)We know that 1 + tan² θ = sec² θTherefore, x² + y² = 4y² sec² θNow, sec θ = 1/cos θ, so the cartesian equation can be written as:x² + y² = 4y² (1/cos² θ) => x² + y² = 4y² / cos² θThis equation is a circle with center (0, 0) and radius 2/cosθ. It is centered on the y-axis. Therefore, the cartesian equation for the given polar equation is x² + y² = 4y² / cos² θ, and it represents a circle centered on the y-axis.

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The cartesian equation for the given polar equation is x² + y² = 4y² / cos² θ, and it represents a circle centered on the y-axis.

Given the polar equation r = 2 tan θ sec θ, we need to find its cartesian equation and identify the curve it represents. To convert a polar equation to a cartesian equation,

we use the following formula: x = r cos θ, y = r sin θ.

Therefore, r = √ (x² + y²) and tan θ = y/x.

Also, sec θ = 1/cos θ.

Hence, we can substitute these values in the given polar equation: r = 2 tan θ sec θ

=> r = 2 (y/x) (1/cos θ)

=> r = 2y / (x cos θ)

=> √(x² + y²) = 2y / (x cos θ)

=> x² + y² = (2y / cos θ)²

=> x² + y² = 4y² / cos² θ=>

x² + y² = 4y² (1 + tan² θ)

We know that 1 + tan² θ = sec² θ.

Therefore, x² + y² = 4y² sec² θ

Now, sec θ = 1/cos θ, so the cartesian equation can be written as:

x² + y² = 4y² (1/cos² θ) =>

x² + y² = 4y² / cos² θ

This equation is a circle with center (0, 0) and radius 2/cosθ. It is centered on the y-axis.

Therefore, the cartesian equation for the given polar equation is x² + y² = 4y² / cos² θ, and it represents a circle centered on the y-axis.

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Answer:

i really hope this helps

Step-by-step explanation:

Given

angle1 + angle2 = 180

angle3 + angle4 = 180

then angle1 + angle2 = angle3 + angle4 : substitution

    angle1 - angle3 = angle4 - angle2  : subtracts angle 3 and angle 2 from both sides

It has been proven that m∠3 = m∠4 . Therefore angle 3 = angle 4

From the question

angle 1 and angle 4 form a linear pair

That is,

m∠1 + m∠4 = 180° ------- (1)

Also, from the question

angle 1 and angle 2 are supplementary

That is,

m∠1 + m∠2 = 180° ------- (2)

To prove that m∠3 = m∠4

First, we can observe that

m∠2 = m∠3 (Vertically opposite angle)

From equation (2)

We have that

m∠1 + m∠2 = 180°

Since, m∠2 = m∠3

∴ m∠1 + m∠3 = 180°

Now, from equation (1)

We have

m∠1 + m∠4 = 180°

Since,  m∠1 + m∠3 = 180°

Then, we can write that

m∠1 + m∠3 = m∠1 + m∠4

Subtract m∠1 from both sides

m∠1 - m∠1 + m∠3 = m∠1 - m∠1 + m∠4

∴ m∠3 = m∠4

Hence, it has been proven that m∠3 = m∠4 . Therefore angle 3 = angle 4

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This a case of selection because order does not matter.

The number of ways of choosing 4 from 15 is given by:

Therefore, the number of committees of 4 students can be chosen from a group of 15 is 1365.

.

Answer:

its 3

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

the answer is b

Step-by-step explanation:

please mark this answer as brainliest

Answer:

125 questions

Answer:

125 questions

Step-by-step explanation:

Answer:

Surface area: 199.27 cm

Volume: 129.8 cm³

Step-by-step explanation:

9514 1404 393

Answer:

  90°

Step-by-step explanation:

The largest angle is 6 of the 6+1+5 = 12 ratio units, so is 6/12 = 1/2 of the total number of degrees in a triangle.

The largest angle is 1/2(180°) = 90°.

Filling in the blanks, I assume you're talking about a random variable \(X\) distributed uniformly over the integers \(a\le x\le b\). Let both \(a,b>0\) so we can write the support of \(X\) as the set

\(S = \{-a, -a+1, -a+2, \ldots, -1, 0, 1, \ldots, b-2, b-1, b\}\)

Note that \(|S| = a+b+1\), so the PMF of \(X\) is

\(\mathrm{Pr}(X=x) = \begin{cases}\frac1{a+b+1} & \text{if } x\in S \\ 0 & \text{otherwise}\end{cases}\)

Let \(Y=\max\{0,X\}\). Then

\(Y = \max\{0,X\} = \begin{cases}0 & \text{if } X\le0 \\ X & \text{if } X>0 \end{cases}\)

which tells us

\(\displaystyle \mathrm{Pr}(Y=0) = \mathrm{Pr}(X\le0) = \sum_{x=-a}^0 \mathrm{Pr}(X=x) = \frac{a+1}{a+b+1}\)

and

\(\displaystyle \mathrm{Pr}(Y\neq0) = \mathrm{Pr}(X>0) = \sum_{x=1}^b \mathrm{Pr}(X=x) = \frac b{a+b+1}\)

Hence the PMF of \(Y\) is

\(\mathrm{Pr}(Y=y) = \begin{cases}\frac{a+1}{a+b+1} & \text{if } y=0 \\\\ \frac b{a+b+1} & \text{otherwise}\end{cases}\)

Let \(Z=\min\{0,X\}\). The same reasoning applies, but this time

\(Z = \min\{0,X\} = \begin{cases} 0 & \text{if } X \ge 0 \\ X & \text{if } X < 0 \end{cases}\)

Now

\(\displaystyle \mathrm{Pr}(Z=0) = \mathrm{Pr}(X\ge0) = \sum_{x=0}^b \mathrm{Pr}(X=x) = \frac{b+1}{a+b+1}\)

and

\(\displaystyle \mathrm{Pr}(Z\neq0) = \mathrm{Pr}(X<0) = \sum_{x=-a}^{-1} \mathrm{Pr}(X=x) = \frac a{a+b+1}\)

so that

\(\mathrm{Pr}(Z=z) = \begin{cases}\frac{b+1}{a+b+1} &\text{if }z=0 \\\\ \frac a{a+b+1} & \text{otherwise}\end{cases}\)

Write a factor that you can use to rationalize the denominator of √2/√5−8.

Answer: √5+8

The correct answer is D. All of the above. When the spread of scores around the arithmetic mean gets smaller, it means that the data points are closer to the mean.

This has several implications:
A. The coefficient of variation (CV) gets smaller: The coefficient of variation is the ratio of the standard deviation to the mean. When the standard deviation decreases (due to smaller spread of scores), the CV also decreases.
B. The interquartile range (IQR) gets smaller: The IQR represents the range between the first quartile and the third quartile. When the spread of scores decreases, the values at the first and third quartiles are closer together, resulting in a smaller IQR.
C. The standard deviation gets smaller: The standard deviation measures the average distance of data points from the mean. As the spread of scores decreases, the data points are closer to the mean, resulting in a smaller standard deviation.
In summary, when the spread of scores around the arithmetic mean gets smaller, the coefficient of variation, interquartile range, and standard deviation all decrease.

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The ratio of dividends to the average number of common shares outstanding is known as the dividend yield. It is a measure of the return on an investment in the form of dividends received relative to the number of shares held.

To calculate the dividend yield, you need to divide the annual dividends per share by the average number of common shares outstanding during a specific period. The annual dividends per share can be obtained by dividing the total dividends paid by the number of outstanding shares. The average number of common shares outstanding can be calculated by adding the beginning and ending shares outstanding and dividing by 2.

For example, let's say a company paid total dividends of $10,000 and had 1,000 common shares outstanding at the beginning of the year and 1,500 shares at the end. The average number of common shares outstanding would be (1,000 + 1,500) / 2 = 1,250. If the annual dividends per share is $2, the dividend yield would be $2 / 1,250 = 0.0016 or 0.16%.

In summary, the ratio of dividends to the average number of common shares outstanding is the dividend yield, which measures the return on an investment in terms of dividends received per share held.

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Answer:

Step-by-step explanation:

I can provide you with general information about radical functions and their graphs, but I cannot design a bridge for you.

In order to design a bridge that will safely cross the ravine, you would need to take into account a wide range of factors, including the length and width of the ravine, the types of materials that can be used to construct the bridge, the weight and size of the vehicles that will be crossing the bridge, and the weather and environmental conditions in the area. This would likely require the expertise of a civil engineer or other trained professional.

Regarding radical functions, they are functions that involve a radical symbol (such as a square root) in their equation. The graph of a radical function is typically a curve that starts at the point (0,0) and moves upwards and to the right. The shape of the curve will depend on the specific radical function and the values of its parameters.

To solve a radical function, you would typically isolate the radical term on one side of the equation and then square both sides of the equation to eliminate the radical. However, it is important to be careful when squaring both sides, as this can introduce extraneous solutions that do not satisfy the original equation.

9514 1404 393

Answer:

  d

Step-by-step explanation:

The geometric sequence is ...

  20, 10, 5

so has a common ratio of 10/20 = 5/10 = 1/2.

Only one answer choice shows that each successive term is 1/2 the one before. That is choice D.

This is because

This is found through trial and error.

This is for problem 1 only. Problems 2 through 6 will follow a similar structure.

A level of 0.05 is used, which means that there is a 5% chance of making a type I error.

A type I error occurs when we reject the null hypothesis, but it is actually true. This means that we have made a mistake in concluding that there is a significant difference between two groups or variables, when in fact there is not. This can happen due to factors such as sample size, random variability or bias.

For example, if a drug company tests a new medication and concludes that it is effective in treating a certain condition, but in reality it is not, this would be a type I error. This could lead to the medication being approved and prescribed to patients, which could potentially harm them and waste  resources.

In statistical analysis, a type I error is represented by the significance level, or alpha level, which is the probability of rejecting the null hypothesis when it is actually true. It is important to set a reasonable alpha level to minimize the risk of making a type I error. Generally, a level of 0.05 is used, which means that there is a 5% chance of making a type I error.
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Explanation:

We replace x with 3 and use PEMDAS to evaluate

8*x+23

8*3+23

24+23

47

Answer:

\(47\)

Step-by-step explanation:

\(8x + 23\)

\(8(3) + 23\)

\(24 + 23\)

\(47\)

Answer:

$(19x + 42n + 15)

Step-by-step explanation:

Devi bought 7 skirts at $x each, n skirts at $12 each, (2n + 1) skirts at $15 each and 4 skirts at $3x each. Find the total cost of the skirts she bought.​

total cost of the skirt bought can be determined by adding the  total costs of each shirt bought

7 skirts at $x each = $7x

n skirts at $12 each = $12n

(2n + 1) skirts at $15 = (2n + 1) x 15 = 30n + 15

4 skirts at $3x each = $12x

7x + 12n + 30n + 15 + 12x

combine like terms

19x + 42n + 15

The amount that Rebecca will be paid for overtime work is $12.75.

From the information, Rebecca's boss pays her time and a half for overtime work at the comic book store. Her regular wage is $8.50.

The amount for overtime will be:

= (1.5 × $8.50)

= $12.75

Therefore, the amount that Rebecca will be paid for overtime work is $12.75.

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a) x[n] = e²+j5n is not periodic.

b) x(t) = sin¹ (70m t) has a period of T = 2π / (70m).

c) x[n] = cos(0.375n) + sin(0.5π n) has a period of T = 8.

To determine if the given signals are periodic, we need to check if there exists a positive value T for which the signals repeat after every T units of time (for continuous-time signals) or every T samples (for discrete-time signals). Let's analyze each signal:

a) x[n] = e²+j5n

This discrete-time signal is not periodic. The exponential term e² will keep growing as n increases, and there is no repeating pattern.

b) x(t) = sin¹ (70m t)

This continuous-time signal is periodic. To find its period, we need to identify the smallest positive value T for which sin¹ (70m t) repeats. The period of a sin¹ function is 2π, divided by the coefficient of t inside the sin¹ function. Therefore, the period is T = 2π / (70m).

c) x[n] = cos(0.375n) + sin(0.5π n)

This discrete-time signal is periodic. To find its period, we need to identify the smallest positive value T for which cos(0.375n) and sin(0.5π n) repeat. The period of both cos and sin functions is 2π. We need to find the least common multiple (LCM) of the coefficients in front of n for both terms, which is 8. Therefore, the period is T = 8.

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The amount of money that he will make for 2 hours of baby sitting work is $18

The function is

f(x) = 4x + 10

The function f(x) is the amount of money Francis makes when babysitting for x hours

The function is the mathematical statement that shows the relationship between one variable and another variable. If one variable is dependent variable then the other variable will independent variable

The function

f(x) = 4x + 10

The number of hours x = 2 hours

Substitute the values of x in the function

f(2) = 4(2) + 10

f(2) = 8 +10

f(2) = $18

Hence, the amount of money that he will make for 2 hours of baby sitting work is $18

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Answer: the answer is going to be 9

Answer:

9.4 rounded to the nearest 10th - 9

Step-by-step explanation:

If the tenth in the decimal is 4 or lower, (like 9.4 or 9.3) It would round down to 9, but if it were 5 or higher like (9.5) it would be 10.00 or 10 :)

Answer:

y=5

Step-by-step explanation:

The curve stops at the y value of 6. And we need a horizontal line for the asymptote, so we don't need an x value only a y-value. So the y-value is 5 on the y-axis, which means your equation will be y=5.

-Hope this helped

Answer:

17/3

Step-by-step explanation:

x +  y +  z   = 47

y - x  = 10   x =  y - 10

z - y = 10     z = 10 + y      

y-10    +     y    +   10 + y    = 47

3 y = 47

 y = 47/3       x = 17/3     z = 77/3  

Answer:

5

Step-by-step explanation:

The magnitude of the magnetic field at that point is 3.08 × 10^-5 T.

The magnitude of the magnetic field can be calculated using Ampere's Law. The formula is given by:

B = (μ₀ * I) / (2 * π * r)

where B is the magnetic field, μ₀ is the permeability of free space (4π * 10^-7 T·m/A), I is the current, and r is the distance from the wire.

Calculating the magnetic field for each wire separately and adding them together:

B₁ = (4π * 10^-7 T·m/A * 25 A) / (2 * π * 0.10 m) = 1.0 × 10^-5 T

B₂ = (4π * 10^-7 T·m/A * 25 A) / (2 * π * 0.06 m) = 2.08 × 10^-5 T

The total magnetic field at that point is the sum of the individual magnetic fields:

B = B₁ + B₂ = 1.0 × 10^-5 T + 2.08 × 10^-5 T = 3.08 × 10^-5 T

Therefore, the magnitude of the magnetic field at that point is 3.08 × 10^-5 T.

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Answer:

550x100

Step-by-step explanation:

First divide 75000 by 100 to get 750. Then divide 750 by 15 to get 50. Lastly multiply 50 by 11 to get 550 and multiply 50 by 4 to get 100.

<IHE and <DEH are alternate interior angles.

We know, Alternate interior angles are a pair of angles that are formed on opposite sides of a transversal and are located between the lines being intersected. These angles are congruent or equal in measure.

In other words, if two parallel lines are intersected by a transversal, the alternate interior angles will have the same measure. They are called "alternate" because they are located on alternate sides of the transversal.

Since, DF || GI then

angle GHJ and angle DEC - Angle on same side

angle FEH and angle IHJ - Corresponding Angle

angle IHJ and angle FEC - Angle on same side

angle IHE and angle DEH - Alternate interior angle

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The Complete question is:

Which angles are alternate interior angles?

angle GHJ and angle DEC

angle FEH and angle IHJ

angle IHJ and angle FEC

angle IHE and angle DEH

Answer:

supongo que < 3m

Step-by-step explanation:

el túnel tiene forma de arco parabólico, pero no aclara qué coeficiente tiene el término \(x^{2}\), ej: si es  -\(x^{2}\),  ó    -0.5 \(x^{2}\), ó -0.1 \(x^{2}\), ...  

Suponiendo que tuviese coeficiente -1, entonces la ecuación del puente es:

f(x) = -\(x^{2}\) + 4

Tomamos el valor de f(x=1) = f(x=-1), porque suponiendo que el camión va por el centro del túnel, y teniendo 2m de ancho, queda 1m hacia cada lado:

f(x=1) = f(x=-1)  = 3

Con lo cual si el camión tiene 3m de alto choca con la curva parabólica que forma el túnel.

The answer is ,  the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

The Taylor series expansion is a way to represent a function as an infinite sum of terms that depend on the function's derivatives.

The Taylor series of a function f(x) centered at c is given by the formula:

\(\large f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(c)}{n!}(x-c)^n\)

Using the definition of Taylor series to find the Taylor series (centered at c=0) for the function f(x) = e^(4x), we have:

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{e^{4(0)}}{n!}(x-0)^n\)

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n\)

Therefore, the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

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The Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

To find the Taylor series for the function f(x) = e^(4x) centered at c = 0, we can use the definition of the Taylor series. The general formula for the Taylor series expansion of a function f(x) centered at c is given by:

f(x) = f(c) + f'(c)(x - c) + f''(c)(x - c)^2/2! + f'''(c)(x - c)^3/3! + ...

First, let's find the derivatives of f(x) = e^(4x):

f'(x) = d/dx(e^(4x)) = 4e^(4x)

f''(x) = d^2/dx^2(e^(4x)) = 16e^(4x)

f'''(x) = d^3/dx^3(e^(4x)) = 64e^(4x)

Now, let's evaluate these derivatives at x = c = 0:

f(0) = e^(4*0) = e^0 = 1

f'(0) = 4e^(4*0) = 4e^0 = 4

f''(0) = 16e^(4*0) = 16e^0 = 16

f'''(0) = 64e^(4*0) = 64e^0 = 64

Now we can write the Taylor series expansion:

f(x) = f(0) + f'(0)(x - 0) + f''(0)(x - 0)^2/2! + f'''(0)(x - 0)^3/3! + ...

Substituting the values we found:

f(x) = 1 + 4x + 16x^2/2! + 64x^3/3! + ...

Simplifying the terms:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

Therefore, the Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

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