How many functions are there from the set {1, 2, . . . , n}, where n is a positive integer, to the set {0, 1} a) that are one-to-one? b) that assign 0 to both 1 and n? c) that assign 1 to exactly one of the positive integers less than n?

Answer:

steps below

Step-by-step explanation:

(cosA-sinA+1) * cosA = cos²A - sinA cosA + cosA

                                 = (1 - sin²A) - sinA cosA + cosA + sinA - sinA

                                 = cosA + sinA + 1 - sinA cosA  -sin²A - sinA  ..Re-group

                                 = (cosA + sinA + 1) - sinA (cosA + sinA + 1)

                                 = (cosA + sinA + 1) * (1 - sinA)

(cosA-sinA+1) / (cosA + sinA + 1) = (1 - sinA) / cosA

Substituting in y=15,

\(\frac{1}{5}x-\frac{2}[3}(15)=30\\\\\frac{1}{5}x-10=30\\\\\frac{1}{5}x=40\\\\x=\boxed{200}\)

Nathaniel drinks 3 glasses of water in one hour.

To find out how many glasses of water Nathaniel drinks in one hour, we need to calculate his drinking rate per hour.

In 2 2/5 hours, Nathaniel drinks 4/5 of a 10-ounce glass of water.

Let's convert the mixed number of hours to an improper fraction:

\(2\frac{2}{5} = \frac{(5 \times2 + 2)}{5}\)

\(=\frac{12}{5}\)

Now, we can set up a proportion to find his drinking rate per hour.

We know that \(\frac{12}{5}\) hours corresponds to \(\frac{4}{5}\) of a glass of water.

Let's assign "x" as the number of glasses he drinks in one hour.

The proportion is then

\(\frac{(\frac{12}{5} hours) }{(x glasses) } =\frac{(\frac{4}{5} glass)}{(1 hour)}\)

Cross-multiplying gives us

\((\frac{12}{5} )\times1=\frac{4}{5}\times(x)\)

Simplifying, we get

\(\frac{12}{5} =\frac{4}{5}\times x\)

Dividing both sides by \(\frac{4}{5}\), we find x:

\(x=\frac{(\frac{12}{5} )}{\frac{4}{5} }\)

\(x=\frac{12}{4}\)

\(x = 3.\)

Therefore, Nathaniel drinks 3 glasses of water in one hour.

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Answer:

3000 - 18*x

Step-by-step explanation:

if "a certain number of minutes" = x then

water remains in the container  = 3000 - 18*x

Answer:

y = 3000 - 18x

Step-by-step explanation:

To describe the scenario of a garden watering bucket with 3000 milliliters of water and a leak of 18 milliliters per minute, we can create a function.

Let's denote the number of minutes as 'x' and the amount of water remaining in the container as 'y'. The function can be represented as:

y = 3000 - 18x

In this function, 3000 represents the initial amount of water in the container, and 18x represents the amount of water leaked after x minutes.

Therefore, the function that describes the scenario is:

Answer:

The first one and the third one. 1/9 and 3^(-6) x 3^(4)

Step-by-step explanation:

3^3 x 3^(-2) is 3^ 3-2, or 3^1. 3^1  is just 3, and so 3^-2 is the answer. The choices that are equal to 3^-2 are 1/9 and 3^-6 x 3^4

Given,

The coordinates of the points is,

The coordinates of the mid point is:

Hence, the mid point of the line segment is (-1,2).

Answer:

A) \(a_{1}\) = 1, \(a_{2}\) = 4

B) \(a_{n}\) = 2\(a_{n-1}\) + 2

C)    \(a_{n} = 2^{n-1} + 2^n -2\\a_{n} = 2^n + 2^{n-1} -2\)

Step-by-step explanation:

For n ≥ 1 ,

S is a set containing 2^n distinct real numbers

an = no of comparisons to be made between pairs of elements of s

A)

\(a_{1}\) = no of comparisons in set (s)

that contains 2 elements = 1

\(a_{2}\) = no of comparisons in set (s) containing 4 = 4

B)  an = 2a\(_{n-1}\) + 2

C) using the recurrence relation

a\(_{n}\) = 2a\(_{n-1}\) + 2

substitute the following values  2,3,4  .......... for n

a\(_{2}\) = 2a\(_{1}\) + 2

a\(_{3}\) = 2a\(_{2}\) + 2 = \(2^{2} a_{1} + 2^{2} + 2\)

a\(_{4}\) = \(2a_{3} + 2 = 2(2^{2}a + 2^{2} + 2 ) + 2\)

    = \(2^{n-1} a_{1} + \frac{2(2^{n-1}-1) }{2-1}\)   ---------------- (x)

since  2^1 + 2^2 + 2^3 + ...... + 2^n-1 =  \(\frac{2(2^{n-1 }-1) }{2-1}\)

applying the sum formula for G.P

\(\frac{a(r^n -1)}{r-1}\)

Note ; a = 2, r =2 , n = n-1

a1 = 1

so equation x becomes

\(a_{n} = 2^{n-1} + 2^n - 2\\a_{n} = 2^n + 2^{n-1} - 2\)

Answer: yes they are

Step-by-step explanation:

Answer:

6x-2

Step-by-step explanation:

-4x(1-3)-(2x+2)

= 4x+12x-2x-2

6x-2

(simplify)

Answer:

6x - 2

Step-by-step explanation:

Edge

Answer:the answer is D

Step-by-step explanation:

it is

Answer:

lessssssssssssssssssssssss

Answer:Add them up

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Step-by-step explanation:

it seems you solved the tricky part yourself already.

just to be sure, let's do the first derivative here again.

the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...

f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =

= 3t⁴ + 18t³ + 24t² + 18t + 21

f'(t) = 12t³ + 54t² + 48t + 18

and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).

we simply put the input number (2) at every place of the input variable (t).

so,

f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =

= 426

Answer:

7 duckpin utuyuuuu I have no idea where to watch the video is not a good day at work now and

The amount Sally’s share would be;

⇒ $30,000

What is mean by Ratio?

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.

Given that;

John, Sally and Jane form a partnership. They agree to distribute profits using a 2:3:2 ratio.

And, The profits are $70,000.

Now,

Since, The profits are $70,000.

Hence, We get;

⇒ 2x  + 3x + 2x = $70,000

⇒ 7x = $70,000

⇒ x = $10,000

So, The amount of Sally’s share would be;

⇒ 3x = 3 × 10,000

         = $30,000

Thus, The amount Sally’s share would be;

⇒ $30,000

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The rule may be extended or generalized to products of three or more functions, to a rule for higher-order derivatives of a product, and to other contexts.

Answer:

You need to simplify 0.3(12x + -16) = 0.4(12 + -3x)

Step-by-step explanation:

Reorder the terms:

0.3(-16 + 12x) = 0.4(12 + -3x) (-16 * 0.3 + 12x * 0.3) = 0.4(12 + -3x) (-4.8 + 3.6x) = 0.4(12 + -3x) -4.8 + 3.6x = (12 * 0.4 + -3x * 0.4) -4.8 + 3.6x = (4.8 + -1.2x)

Solving -4.8 + 3.6x = 4.8 + -1.2x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.2x' to each side of the equation. -4.8 + 3.6x + 1.2x = 4.8 + -1.2x + 1.2x

Combine like terms: 3.6x + 1.2x = 4.8x -4.8 + 4.8x = 4.8 + -1.2x + 1.2x

Combine like terms: -1.2x + 1.2x = 0.0 -4.8 + 4.8x = 4.8 + 0.0 -4.8 + 4.8x = 4.8 Add '4.8' to each side of the equation. -4.8 + 4.8 + 4.8x = 4.8 + 4.8

Combine like terms: -4.8 + 4.8 = 0.0 0.0 + 4.8x = 4.8 + 4.8 4.8x = 4.8 + 4.8

Combine like terms: 4.8 + 4.8 = 9.6 4.8x = 9.6 Divide each side by '4.8'. x = 2

Simplifying x = 2

Answer: Dont know if B is supposed to be "50" but thats what I got as my answer

50

Step-by-step explanation: ratio is division and 225/5 is 25 and you multiply the 2 by 25 and you get 50

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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Answer:

Yes

Step-by-step explanation:

The decimal points moves to the right at a constant pace.

0.006 -> 0.06 -> 0.6 -> 6

In other words, we are just multiplying each one by 10 to get the next value.

Best of Luck!

The equation of the relationship is f(200) = 0.75 * 200

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

Total number of drinks = 200

Cost of each drink = 0.75

Using the above as a guide, we have the following:

f(x) = Cost of each drink * Total number of drinks

Where

f(x) = Total cost

Substitute the known values in the above equation, so, we have the following representation

f(200) = 0.75 * 200

Hence, the equation is f(200) = 0.75 * 200

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The correct statement regarding the transformation is given as follows:

Dilation bu a scale factor of 0.5 about the origin. Then reflect over the x-axis.

The true statements about the dilation are given as follows:

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

For this problem, the coordinates of the dilated line segment are half the coordinates of the original line segment, hence the scale factor is given as follows:

k = 0.5.

The y-coordinate then has the signal exchange, hence the figure is also reflected over the x-axis.

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Point H is the ortho-center of our given triangle and option c is the correct choice.

We have been given an image of a triangle. We are asked to find the term that describes point H.

We can see that point H is the point, where, all the altitudes of our given triangle EFF are intersecting.

We know that ortho-center of a triangle is the point, where all altitudes of triangle intersect. Therefore, point H is the ortho-center of our given triangle and option c is the correct choice.

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Given the system of equations:

We'll multiply the second equation by -1 and then add both equations up:

Solving the resulting equation for y ,

We'll plug in this y-value in the first equation and solve for x ,

Therefore, we can conclude that the solution to our system is:

Answer:

Step-by-step explanation:

To determine if 1/3 and 4/12 are equivalent fractions, you can either simplify 4/12 or raise 1/3. I'm going to explain with an example. So we have 1/8 and 3/24. I usually make the denominators (The lower number of the fraction) the same. To do that i multiply 8 by which ever number i think will calculate to 24. So 8 times 3 is 24. So i would change the number 8 to the number 24. But what you do to the bottom you HAVE to do to the top. So i multiplied the number 8 by 3 to get 24. No i am going to multiply the top of 1/8 (which is 1, or the numerator) by 3. And 1 times 3 is 3. And that gives me 3/24. It equals the second fraction, so 1/8 and 3/24 is equivalent.

So taking your fractions, 1/3 and 4/12, we just see how many times 3 goes into 12. Or what times 3 equals 12. That is 4. So what we do to the bottom we MUST do to the top, right? So we multiply 1 by 4. That gives us 4. So 1/3 changed into 4/12. So our first fraction is now 4/12 and our second fraction is also 4/12. So they are equivalent! Hope this helped

The following diagram shows the graph of the line:

The line passes througt (4,8) and (-12,0) so the slope must be:

And the y-intercept of the graph is at (0,6) so the equation must be:

Any line with the same slope will be parallel to line L, for example:

As shown in the graph:

the average rate of change of the given function will be -12.

It quantifies how much the function changed per unit on average throughout that time interval. The slope of the straight line connecting the interval's ends on the function's graph is used to calculate it.

The given function is f(x) = 2x²+2x−4 and the interval is x ∈ [-7,0].

The formula to calculate the average rate of change is (f(b)-f(a))/(b-a).

Here, a=-7 and b=0

So, f(-7) = 2(-7)²+2(-7)−4

f(-7) =2(49)-14−4

f(-7) = 98 - 18 = 80

Now, f(0)=2(0)²+2(0)−4

f(0) = - 4

The average rate of change = (-4 - 80)/(0-(-7))

The average rate of change = -84/7

The average rate of change = -12

Therefore, the average rate of change of the given function will be -12.

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The question seems to be incomplete the correct question would be:

Given the function f(x) = 2x²+2x−4, determine the average rate o

change of the function over the interval -7 < 2 < 0.