What is the range of this data set? 43, 78, 12, 32, 97
Median:
Mean:
Range:

Convert to cylindrical coordinates:

[tex]x=x[/tex]

[tex]y=r\cos\theta[/tex]

[tex]z=r\sin\theta[/tex]

Then [tex]E[/tex] is the set of points [tex](r,\theta,x)[/tex] such that [tex]0\le r\le1[/tex], [tex]0\le\theta\le2\pi[/tex], and [tex]7y^2+7z^2\le x\le7[/tex] or [tex]7r^2\le x\le7[/tex].

Now

[tex]\displaystyle\iiint_E5x\,\mathrm dV=5\int_0^{2\pi}\int_0^1\int_{7r^2}^7xr\,\mathrm dx\,\mathrm dr\,\mathrm d\theta=\boxed{\frac{245\pi}3}[/tex]

To evaluate the triple integral, convert to cylindrical coordinates and use the given bounds. Plug in the limits of integration and calculate the integral.

To evaluate the triple integral ∫ 5x dv, where E is bounded by the paraboloid x = 7y^2 + 7z^2 and the plane x = 7, we can use cylindrical coordinates. Let's express x in terms of y and z:

x = 7y^2 + 7z^2

Substitute this expression for x in the integral:

∫5x dv = ∫35(y^2 + z^2) dv

Now, convert the integral to cylindrical coordinates:

∫35(r^2sin(θ)rdrdθdz

Since the region E is bounded by x = 7, the limits of integration for r and z are 0 to 7. For θ, the limits are 0 to 2π. Plug in these limits and evaluate the triple integral to find the answer.

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Answer:

P = 34 = 2(l + w) | : 2 => l + w = 17 => w = 17 - l

A = 30 = l×w

30 = l(17 - l)

17l - l² - 30 = 0 | (-)

l² - 17l + 30 = 0

l² - 2l - 15l + 30 = 0

l(l - 2) - 15(l - 2) = 0

(l - 15)(l - 2) = 0

l - 15 = 0 => l₁ = 15 m => w₁ = 2 m

l - 2 = 0 => l₂ = 2 m => w₂ = 15 m

Answer:

D) The graph of g(x) is a vertical stretch of f(x) by a factor of 5 and a reflection across the x-axis

Step-by-step explanation:

I just did this and got it correct

Answer:

3/10

Step-by-step explanation:

Multiples of 3: 3,6,9,12,15,18

There are 6 in the numbers 1-20

P(multiple of 3) = number of "multiples of 3" / total

                         = 6/20

                         =3/10

Final answer:

The probability that a number chosen at random from the first 20 integers is a multiple of 3 is 3/10 or 30%.

Explanation:

The student is asking to find the probability that a number chosen at random from the first 20 integers is a multiple of 3. To solve this, we first identify the multiples of 3 within the first 20 integers. They are 3, 6, 9, 12, 15, and 18, a total of 6 numbers. The total number of possible outcomes when choosing one number from the first 20 integers is 20.

The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Therefore, the probability of choosing a multiple of 3 is 6/20, which simplifies to 3/10 or 0.3. This means there is a 30% chance of choosing a multiple of 3 from the first 20 integers.

Answer:

option 1

2sqrt3/3

Step-by-step explanation:

Given in the question

csc(-4π/3)

we know that csc(x) = [tex]\frac{1}{sin(x)}[/tex] that means

[tex]csc(\frac{-4\pi}{3})=\frac{1}{sin(\frac{-4\pi}{3} )}[/tex]

sin(-4π/3) = [tex]\frac{\sqrt{3}}{2}[/tex]

so,

[tex]csc(\frac{-4\pi}{3})=\frac{1}{\frac{\sqrt{3}}{2} }[/tex]

[tex]\frac{1}{\sqrt{3}/2 }[/tex] = [tex]\frac{2}{\sqrt{3}}=\frac{2\sqrt{3}}{3}[/tex]

Answer:

A is the right answer i do believe

.60 cents per x papers plus $25

Sheryl typed the term paper for $25 + $0.60 per page. If x is the cost of typing a term paper in dollars per page. 0.60x+25 is the equation. Option A is correct.

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

If x is the cost in $ per page to type the term paper. The equation is found as;

⇒0.60x+25

Hence, option A is correct.

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Answer:

The sigma notation of the series is 8∑n=2 [1/2(1/2)^n-2]

Step-by-step explanation:

* Lets revise the meaning of sigma notation

- A series can be represented in a compact form, called summation or

 sigma notation.

- The Greek capital letter, ∑ , is used to represent the sum.

# Ex:

- The series 4 + 8 + 12 + 16 + 20 + 24 can be expressed 6Σ(n=1) 4n  

- The expression is read as the sum of 4n as n goes from 1 to 6

- The coefficient of n is 4 because the common difference is 4

- The variable n is called the index of summation.

# Look to the attached figure to more understand

* Now lets solve the problem

∵ The series is 1/2 + 1/4 + 1/8 + ........... + 1/128 and n = 2

- There is a constant ratio between each to consecutive terms

∴ The series is geometric

∴ a1 = a , a2 = ar , a3 = ar² , a4 = ar³ , ..........

∵ an = a(r)^n-1, where a is the first term, r is the common ratio and n

  is the position of the number in the series and the first n is 1

∵ 1/4 ÷ 1/2 = 12 , 1/8 ÷ 1/4 = 1/2

∴ The constant ratio is 1/2

∵ The first term is 1/2

∵ The last term is 1/128

∵ 1/128 = 1/2^7

∴ 1/128 = (1/2)^7

- There are seven terms in the sequence

∵ The n of the first term is 2

∴ The n of the last term = 7 + 1 = 8

* Now lets write the sigma notation

∴ 8∑n=2 [1/2(1/2)^n-2] ⇒ put them like the attached figure

- To generate the terms of the series given in sigma notation above,

  replace n by 2 , 3 , 4 , 5 , 6 , 7 , 8

Answer:

Step-by-step explanation:

(1)

[tex]a_i = a_{i-1} + 1[/tex]

(2)

The initial condition is [tex]a_1 = 1[/tex]

(3)

Infinitely many.

a) The recurrence relation is sₙ = sₙ₋₁ + sₙ₋₂ + ... + s₂ + s₁.

b) the initial condition s₂ = 1.

c) Clearly the solution to this recurrence relation and initial condition is sₙ = 2n-2 for all n >= 2.

Here, we have,

Let sₙ be the number of such sequences.

A string ending in n must consist of a string ending in something less than n, followed by an n as the last term.

Therefore the recurrence relation is sₙ = sₙ₋₁ + sₙ₋₂ + ... + s₂ + s₁.

This is equivalent to sₙ = 2sₙ-1.

b) We need two initial conditions if we use the second formulation above, s₁ = 1 and s₂ = 1.

There's one sequence which ends in 1,

and there is only the sequence 1,2 ending in 2.

If we use the first formulation above, then we can get by with just the initial condition s₂ = 1.

c) Clearly the solution to this recurrence relation and initial condition is sₙ = 2n-2 for all n >= 2.

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Answer:

         D) The other zero is rational.

Step-by-step explanation:

1. The attached graph shows there are no values of x where the left side of the equation is equal to the right side of the equation. There are no real solutions.

If you rewrite the quadratic to standard form (by subtracting the right-side expression), you get ...

  x^2 -4x +5 = 0

Using the hint, the discriminant is b^2-4ac = (-4)^2-4(1)(5) = 16 -20 = -4. It is negative, so both roots will be complex.

__

2. The (rational) number "b" is the opposite of the sum of the zeros. If one zero is rational, the other root must be. The difference of rational numbers is rational.

Choices A and D are identical, so both are correct. Perhaps a typo?

__

We can also consider the discriminant in problem 2. The roots of the quadratic are the sum (or difference) of -b and the square root of the discriminant, all divided by 2a. Any one root can only be rational if the square root is rational. In that case, the other root will be rational as well.

between 4 and 5 seconds is the correct answer

A pint has 2 cups, quart has 4, and gallon has 16 so she would need at least a gallon

Answer:

Gallon

Step-by-step explanation:

Because a pint has 2 cups and a quart has 4 but you need 5

Answer:

D

Step-by-step explanation:

The question is on negative exponents

Given that;

F(x)=2^x

From the general formulae a^-n =1/a^n

Hence

F(-4)= 2⁻⁴

F(-4)= I/ 2⁴

=1/16

Answer:

D. All three functions have the same rate of change.

Step-by-step explanation:

1. For the function f(x):

The rate of change is

[tex]\dfrac{f(\frac{3\pi}{2})-f(\pi)}{\frac{3\pi}{2}-\pi}=\dfrac{-4-0}{\frac{\pi}{2}}=-\dfrac{8}{\pi}.[/tex]

2. For the function g(x):

The rate of change is

[tex]\dfrac{g(\frac{3\pi}{2})-g(\pi)}{\frac{3\pi}{2}-\pi}=\dfrac{-4-0}{\frac{\pi}{2}}=-\dfrac{8}{\pi}.[/tex]

3. For the function h(x):

The rate of change is

[tex]\dfrac{h(\frac{3\pi}{2})-h(\pi)}{\frac{3\pi}{2}-\pi}=\dfrac{-2-2}{\frac{\pi}{2}}=-\dfrac{8}{\pi}.[/tex]

All three functions have the same rate of change.

Answer:

D

Step-by-step explanation:

57+(350-1)*9

Answer:

D

Step-by-step explanation:

Each term goes up 9 from the term before it.

Givens

a1 = 57

d =  9

n = 350

an = ?

Formula

an = a1 + (n- 1)*d

Solution

An = 57 + (350  - 1)*9

An = 57 + 3141

An = 3198

D

Answer:

A square root is a number that produces a specific quantity when multiplied by itself.

Step-by-step explanation:

For example, 9 is the square root of 81, as 9*9=81

Answer:

a number which produces a specified quantity when multiplied by itself.

Step-by-step explanation:

hope this helps!! brainly please!

Answer:

Each octave change requires a doubling of the frequency.

Therefore, one octave above 126.63 is 126.63 * 2 which equals

253.26

Step-by-step explanation:

The frequency of the note one octave above c4 would be 253.26 hz.

The frequency of the musical note C4 is about 126.63 hz

We need to find the frequency of the note one octave above C4.

Frequency is the number of occurrences of any repeating cycle per unit in time.

When we go up an octave, we double the original frequency.  

When we go down an octave, we divide the original frequency by two.

So, since C4's frequency is about 126.63 hz,

octave above = 2 x 126.63 hz

                        = 253.26 hz

Thus, The frequency of the note one octave above c4 would be 253.26 hz.

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Answer:

12.5%

Step-by-step explanation:

The price increased from 800 to 900. So what is the PERCENTAGE INCREASE??

The increase is 900 - 800 = 100

To find this in terms of original, we need to divide 100 by 800 and multiply by 100 to get the "percentage". Let's do it:

[tex]\frac{100}{800}*100=12.5[/tex]

So the increase is 12.5% and thus the general sales tax is 12.5%

Final answer:

The general sales tax percentage imposed on the pizza price is 12.5%, calculated by dividing the increase in price by the original price and multiplying by 100.

Explanation:

When Wahaj experienced an increase in price from rs 800 to rs 900 for the same pizza after a week, this is due to the imposition of a general sales tax by the government. To calculate the percentage rate of the sales tax, we can compare the two prices.

The original price of the pizza was rs 800. A week later, the price rose to rs 900. The difference between the two prices, which is rs 100, represents the amount of the sales tax added to the original price. The percentage rate of this sales tax can be calculated as follows:

Sales Tax Percentage = (Amount of Sales Tax / Original Price) x 100%

Using the figures we have: Sales Tax Percentage = (100 / 800) x 100% = 0.125 x 100% = 12.5%

Therefore, the general sales tax percentage imposed on the restaurant is 12.5%

[tex]\overline{LL'}, \ \overline{MM'} \ and \ \overline{NN'}[/tex] are each perpendicular to the line of reflection

This option is the only one that is correct. The line of reflection is  [tex]y=-1[/tex]. When we talk about reflection, we are talking about reflecting across a line, or axis. Reflecting a shape means looking at the mirror image on the other side of the axis. So in this case, this mirror is the line of reflection.  As you can see, these three segments [tex]\overline{LL'}, \ \overline{MM'} \ and \ \overline{NN'}[/tex] form a right angle at the point each segment intersects the line [tex]y=-1[/tex].

Since the line [tex]y=-1[/tex] is an axis that allows to get a mirror image, therefore it is true that:

[tex]\overline{LS}=\overline{L'S} \\ \\ \overline{MT}=\overline{M'T} \\ \\ \overline{NU}=\overline{N'U}[/tex]

To find those values [tex]\overline{LS}[/tex], count the number of units you get from the point S to L, which is 3 units. Do the same to find [tex]\overline{MT}[/tex] but from the point T to M, which is 6 units and finally, for [tex]\overline{NU}[/tex] but from the point U to N, which is 4 units. Therefore:

[tex]\overline{LS}=\overline{L'S}=3 \ units \\ \\ \overline{MT}=\overline{M'T}=6 \ units \\ \\ \overline{NU}=\overline{N'U}=4 \ units[/tex]

The line of reflection is the perpendicular bisector of each segment joining a point and its image.

A bisector is the line dividing something into two equal parts. In this case, the line of reflection divides each segment into two equal parts and is perpendicular because this line form a right angle with each segment. As we demonstrated in a) each segment is perpendicular to the line of reflection, so the first statement is false. On the other hand, each side of the original triangle is not perpendicular to its image and this is obvious when taking a look at the figure. Finally, as we said the line of reflection is perpendicular to each of the mentioned segments, so they can't be parallel as established in the last statement.

A function assigns the value of each element of one set to the other specific element of another set. The correct option is A.

A function assigns the value of each element of one set to the other specific element of another set.

In the given graph each specific value of x from the x-axis is representing a value on the y-axis. Therefore, as per the definition of the function, it can be concluded that the given graph is a function because each x-value has exactly one corresponding y-value.

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Answer:

So, option d is correct i.e,

V₀ = $393,000, b = 0.85, and the value after 7 years is $125,986.80

Step-by-step explanation:

The formula given is V(t)=V₀(b)^t

The value of V₀ (the actual worth) is:

V₀ = $393,000

The value of b is :

b= (1-15%) = (1-0.15) = 0.85

Value of assets after 7 years is:

t= 7, V₀ = $393,000, b=0.85

putting values in formula:

V(t) = Vo(b)^t.

V(7)= $393,000 * (0.85) ^ 7

V(7)= $393,000 * (0.320)

V(7)= $125986.80

So, option d is correct i.e,

Vo = $393,000, b = 0.85, and the value after 7 years is $125,986.80

Can we have a Picture to see the shape

Answer:

noo

Step-by-step explanation:

Answer:

The period is 2pi

Step-by-step explanation:

A function is said to be periodic if there exists a T for which f(x+T)=f(x). In this case, the function is f(x) =7sin^3(x).

The period of sin(x) = 2pi. Then, in this case, no matter if the sin is elevated to a power of three, the period will remain the same.

Let's prove it:

f(x) =7sin^3(0) = 0

f(0 + 2pi) = f( 2pi) = 7sin^3(2pi) = 0.

Then, there exists a T for which f(x+T)=f(x) and it's T=2pi.

Answer: a, 2pi

Step-by-step explanation:

right on edg

ANSWER

C) inconsistent

EXPLANATION

The given system is inconsistent.

The two lines are parallel and have distinct y-intercepts.

This means that the two lines will never meet.

Since the two lines have no points of intersection, it means the system of equations they represent has no solution.

Therefore the system is inconsistent.

The correct choice is C

Answer:

If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.

Step-by-step explanation:

Answer:

Second option: False

Step-by-step explanation:

You need to use the following identity:

[tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]

Let be "x" the lenght of the buildings's shadow.

[tex]opposite=x[/tex] (Lenght of building's shadow)

You can observe in the figure that:

[tex]\alpha=75\°\\\\hypotenuse=50ft[/tex]

Substitute these values into  [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex] and solve for ""x":

[tex]sin(75\°)=\frac{x}{50}\\\\(50)(sin(75\°))=x\\\\x=48.29\°[/tex]

Therefore, the length of its shadow IS NOT 12.94 feet.

Answer:

103 ft

Step-by-step explanation: First, you find the area of the garage door as a whole (112 ft). Then, you find the area of each the three windows and add them together (their total area together is 9 ft). Lastly, you subtract this sum from the area of the whole door and the answer that you will get is 103 ft. Hope this helps :)

The area of the garage door to be painted, excluding the rectangular window is 103 ft².

To find the area of the garage door that will be painted:

Calculate the total area of the garage door: 16 ft wide x 7 ft high = 112 ft².

Subtract the area of the three windows: 3 windows x (3 ft wide x 1 ft high) = 9 ft².

The area to be painted is 112 ft² - 9 ft² = 103 ft².

The answer is C. 0.14.

Answer: Option A

The Amplitude is

[tex]A = \frac{1}{2}[/tex]

Then the period is

[tex]\frac{2}{3}\pi[/tex]

Step-by-step explanation:

The general sine function has the following form  

[tex]y = Asin(bx) + k[/tex]

Where A is the amplitude: half the vertical distance between the highest peak and the lowest peak of the wave.  

[tex]\frac{2\pi}{b}[/tex] is the period: time it takes the wave to complete a cycle.

k is the vertical displacement.

In this case we have the following function

[tex]f(t)=\frac{1}{2}sin(3t)[/tex]

Thus:

[tex]b=3[/tex]

Then the period is

[tex]\frac{2\pi}{3}=\frac{2}{3}\pi[/tex]

The Amplitude is

[tex]A = \frac{1}{2}[/tex]

The answer is Option A

Answer:

a. amplitude: [tex]\displaystyle \frac{1}{2};[/tex]period: [tex]\displaystyle \frac{2}{3}\pi[/tex]

Explanation:

[tex]\displaystyle f(t) = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{3}\pi \\ Amplitude \hookrightarrow \frac{1}{2}[/tex]

With the above information, you now should have an idea of how to interpret graphs like this.

I am joyous to assist you at any time.

Answer:

A

Step-by-step explanation:

Given a sinusoidal function (sine function or cos function) in the form

y = A Cos (Bx), we can say that A is the amplitude.

Amplitude defines the function's maximum and minimum.

The maximum of this form of function is A and the minimum is -A.

The function given is y = -Cos(8x), so A is -1

Thus, maximum value is 1 and minimum value is -1.

Correct answer is A

Answer:

The answer is actually 400m

Step-by-step explanation: