Write a short statement that expresses a possible function between the given variables. (price of a DVD player, demand f for DVD player)

Answer:

N(n+1) = N(n)^2 - 1, n>=0, N(0) = 2

or equivalently

N(n) = N(n-1)^2 - 1, n>0, N(0) = 2

Step-by-step explanation:

Year 0 = 2 trees

year 1 = 2^2-1 = 3

year 2 = 3^2-1 =8

year 2 = 8^2-1 =63

...

Recursive formula

Let

n = integer year number

N(n) = number of trees to plant in year n

N(n+1) = N(n)^2-1, n>=0, N(0) = 2

or equivalently

N(n) = N(n-1)^2, n>0, N(0) = 2

Whats the options???

Answer:

Volume: 112 m³.

Surface area: 172 m².

Step-by-step explanation:

The volume is the base times height times length. So, the volume will be 2 * 8 * 7 = 16 * 7 = 112 m³.

The surface area is 2lw + 2lh + 2wh. l = 8; w = 7; h = 2.

2(8)(7) + 2(8)(2) + 2(7)(2) = 2 * 56 + 2 * 16 + 2 * 14 = 112 + 32 + 28 = 112 + 60 = 172 m².

Hope this helps!

Answer:

Part A- 6

Part B- 3

Part C- 3/22100

Step-by-step explanation:

Part A-

Use the permutation formula and plug in 3 for n and 2 for k.

nPr=n!/(n-k)!

3P2=3!/(3-2)!

Simplify.

3P2=3!/1!

3P2=6

Part B-

Use the combination formula and plug in 3 for n and 2 for k.

nCk=n!/k!(n-k)!

3C2=3!/2!(3-2)!

Simplify.

3C2=3!/2!(1!)

3C2=3

Part C-

It is given that the total number of three-card hands that can be dealt from a deck of 52 cards is 22100. Use the fact that the probability of something equals the total successful outcomes over the sample space. In this case the total successful outcomes is 3 and the sample space is 22100.

I believe the answer is 3/22100

I honestly suck at probability but I tried my best.

Step-by-step explanation:

Formula for compound interest is given by

[tex]A = P(1 + R) ^{n} [/tex]

Where

A is the amount at the end of the period

P is the principal

R is the rate

n is the period

The interest = A - P

From the question

P = $ 3200

n = 3 years

R = 40%

So we have

[tex]A = 3200 \times 2.744[/tex]

A = $ 8780.80

The interest is

$ 8780.80 - $3200

Hope this helps you

Answer:

retype that im not understanding .

Step-by-step explanation:

Answer: Pi multiplied by the diameter of the circle

Step-by-step explanation:

Answer:

The formula for finding the circumference of a circle is [tex]C = 2\pi r[/tex]. You substitute the radius of the circle for [tex]r[/tex] and multiply it by [tex]2\pi[/tex].

Answer:

It does not have an answer as 3x != 3x + 13 or not equalivalent

Step-by-step explanation:

Answer:

no solution

Step-by-step explanation:

3x+8=9+3x-14

Combine like terms

3x+8 = 3x -5

Subtract 3x from each side

8 = -5

This is never true so there is no solution

Answer:

15.9degrees

Step-by-step explanation:

in photo above

Answer:

[tex]\boxed{15.95\°}[/tex]

Step-by-step explanation:

The angle can be found by using trigonometric functions.

tan (θ) = [tex]\frac{opposite}{adjacent}[/tex]

tan (θ) = [tex]\frac{4}{14}[/tex]

θ = [tex]tan^{-1} \frac{4}{14}[/tex]

θ = 15.9453959

θ ≈ 15.95

Answer:

  16x^3 +64x^2 -40x

Step-by-step explanation:

Use the distributive property. The factor outside parentheses multiplies each term inside parentheses:

  8x(2x^2 +8x -5) = (8x)(2x^2) +(8x)(8x) +(8x)(-5)

  = 16x^3 +64x^2 -40x

Answer:

Step-by-step explanation:

Given the following complex values Z₁=2(cos(π/5)+i Sin(πi/5)) And Z₂=8(cos(7π/6)+i Sin(7π/6)). We are to calculate the following complex numbers;

a) Z₁Z₂ = 2(cos(π/5)+i Sin(πi/5)) * 8(cos(7π/6)+i Sin(7π/6))

Z₁Z₂ = 18 {(cos(π/5)+i Sin(π/5))*(cos(7π/6)+i Sin(7π/6)) }

Z₁Z₂ = 18{cos(π/5)cos(7π/6) + icos(π/5)sin(7π/6)+i Sin(π/5)cos(7π/6)+i²Sin(π/5)Sin(7π/6)) }

since i² = -1

Z₁Z₂ = 18{cos(π/5)cos(7π/6) + icos(π/5)sin(7π/6)+i Sin(π/5)cos(7π/6)-Sin(π/5)Sin(7π/6)) }

Z₁Z₂ = 18{cos(π/5)cos(7π/6) -Sin(π/5)Sin(7π/6) + i(cos(π/5)sin(7π/6)+ Sin(π/5)cos(7π/6)) }

From trigonometry identity, cos(A+B) = cosAcosB - sinAsinB and  sin(A+B) = sinAcosB + cosAsinB

The equation becomes

= 18{cos(π/5+7π/6) + isin(π/5+7π/6)) }

= 18{cos((6π+35π)/30) + isin(6π+35π)/30)) }

= 18{cos((41π)/30) + isin(41π)/30)) }

b) z2 value has already been given in polar form and it is equivalent to 8(cos(7pi/6)+i Sin(7pi/6))

c) for z1/z2 = 2(cos(pi/5)+i Sin(pi/5))/8(cos(7pi/6)+i Sin(7pi/6))

let A = pi/5 and B = 7pi/6

z1/z2 = 2(cos(A)+i Sin(A))/8(cos(B)+i Sin(B))

On rationalizing we will have;

= 2(cos(A)+i Sin(A))/8(cos(B)+i Sin(B)) * 8(cos(B)-i Sin(B))/8(cos(B)-i Sin(B))

= 16{cosAcosB-icosAsinB+isinAcosB-sinAsinB}/64{cos²B+sin²B}

= 16{cosAcosB-sinAsinB-i(cosAsinB-sinAcosB)}/64{cos²B+sin²B}

From trigonometry identity; cos²B+sin²B = 1

= 16{cos(A+ B)-i(sin(A+B)}/64

=  16{cos(pi/5+ 7pi/6)-i(sin(pi/5+7pi/6)}/64

= 16{ (cos 41π/30)-isin(41π/30)}/64

Z1/Z2 = (cos 41π/30)-isin(41π/30)/4

Answer:

13. 16(cos(41 π/30)+ isin(41 π/30))

14. Mine asked for z2 magnitude so I got 8 (magnitude is the same as modulus which is r)

15. 1/8 (cos(29 π/30)+ isin(29 π/30))

Step-by-step explanation:

13. Since we’re multiplying z1, and z2, use De Moivre’s theorem by multiplying the r values (2 and 8) and adding the theta values (π/5 and 7π/6). Adding the angle values should lead you to have 41 π/30, and the rest is self-explanatory.

14. Explanation is in the answer, just take the r value from z2 for magnitude (at least that’s what’s on my practice assignment)

15. Use De Moivre’s theorem again, this time with division, so you will divide the r values (2 divided by 8) and subtract the theta values (π/5 minus 7π/6). 2/8 simplifies to 1/8 and when subtracting with 6π/30 - 35π/30 (finding common denominators) you should get 29π/30.

Answer: vector equation r = (7+3t)i + (4+2t)j + (5 - 5t)k

parametric equations: x = 7 + 3t; y = 4 + 2t; z = 5 - 5t

Step-by-step explanation: The vector equation is a line of the form:

r = [tex]r_{0}[/tex] + t.v

where

[tex]r_{0}[/tex] is the position vector;

v is the vector;

For point (7,4,5):

[tex]r_{0}[/tex] = 7i + 4j + 5k

Then, the equation is:

r = 7i + 4j + 5k + t(3i + 2j - k)

r = (7 + 3t)i + (4 + 2t)j + (5 - 5t)k

The parametric equations of the line are of the form:

x = [tex]x_{0}[/tex] + at

y = [tex]y_{0}[/tex] + bt

z = [tex]z_{0}[/tex] + ct

So, the parametric equations are:

x = 7 + 3t

y = 4 + 2t

z = 5 - 5t

Answer:

8.1% decrease

Step by step

To find precentage decrease we use formula:

Percent decrease= original amount-new amount/original amount(100%)

percent decrease= 7,400-6,800/7,400(100%)=300/37=8.1%

Answer:

Perimeter= 40 units

Step-by-step explanation:

Ok

We are asked to look for the perimeter.

We have some clue given.

All at right angle and some sides are given it's full length.

We have the bae to be 11 unit

The height to be 7 unit.

What this mean is that taking either the base or the height should sum up to either 11 or 7 respectively.

Let's go for the other side of the height.

Let's take all the vertical height and sum it up to 7 because the right side is equal to 7.

So we have 7+7+11

But it's not complete yet.

We are given a dimension 2.

And the 2 is in two places so it's total 2*2= 4

The two is for a small base .

The base is actually an extra to the 11 of the other base.

So summing up

We have 2*11 + 2*7 + 2*2

Perimeter= 22+14+4

Perimeter= 40 units

Answer:

A

Step-by-step explanation:

When subtracting 7 on the left of the equation, he also needs to subtract 7 from the right of the equation.

Step 2 should be:

⅓X +7 -7= 15 -7

What he is trying to do here by subtracting 7 is to move all the constants, that is numbers without any variables such as x, to one side of the equation.

⅓X= 8

X= 8 ×3

X= 24

Answer:

200.52 in^2

Step-by-step explanation:

to find the area of a circle, you square 6 and multiply it by pi in this case 3.14.

that gives you 113.04 but because this is only a half circle, it is 56.52 in^2.

Next, you need to find the rectangle. multiply 12(length) by 12(Width) to get 144 add 144 to 56.52 to get 200.52.

Hope this helped if it did please give me brainliest it helps me a lot. :)

Have a good day!

Answer:

3.54%

Step-by-step explanation:

This question represents a binomial distribution. A binomial distribution is given by:

[tex]P(x)=\frac{n!}{(n-x)!x!} p^xq^{n-x}[/tex]

Where n is the total number of trials, p is the probability of success, q is the probability of failure and x is the number of success.

Given that:

A basketball player scores 70% of his shots on average, therefore p = 70% = 0.7. Also q = 1 - p = 1 - 0.7 = 0.3.

The total number of trials (n) = 20 shots

The probability that he scores at least 18 successful shots tonight if he gets 20 shots = P(x = 18) + P(x = 19) + P(x = 20)

P(x = 18) = [tex]\frac{20!}{(20-18)!18!}*0.7^{18}*0.3^{20-18}=0.0278[/tex]

P(x = 19) = [tex]\frac{20!}{(20-19)!19!}*0.7^{19}*0.3^{20-19}=0.0068[/tex]

P(x = 20) = [tex]\frac{20!}{(20-20)!20!}*0.7^{20}*0.3^{20-20}=0.0008[/tex]

The probability that he scores at least 18 successful shots tonight if he gets 20 shots = P(x = 18) + P(x = 19) + P(x = 20) = 0.0278 + 0.0068 + 0.0008 = 0.0354 = 3.54%

Answer:

[tex]108 \times 125=2^2 \times 3^3 \times 5^3[/tex]

Step-by-step explanation:

To express the given product (108 X 125) as a product of prime factors

Step 1: Express each of the numbers as a product of its prime factors.

[tex]108=2^2 \times 3^3\\125=5^3[/tex]

Step 2: Write the product together, and combine any like terms if any

Therefore,

[tex]108 \times 125=2^2 \times 3^3 \times 5^3[/tex]

Answer:

Largest integer in the interval [−∞, 31] is 31.

Step-by-step explanation:

Given the interval: [−∞, 31]

To find: The largest integer in this interval.

Solution:

First of all, let us learn about the representation of intervals.

Two kind of brackets can be used to represent the intervals. i.e. () and [].

Round bracket means not included in the interval and square bracket means included in the interval.

Also, any combination can also be used.

Let us discuss one by one.

1. [p, q] It means the interval contains the values between p and q. Furthermore, p and q are also included in the interval.

Smallest p

Largest q

2. (p, q) It means the interval contains the values between p and q. Furthermore, p and q are not included in the interval.

Smallest value just greater than p.

Largest value just smaller than q.

3. [p, q) It means the interval contains the values between p and q. Furthermore, p is included in the interval but q is not included in the interval.

Smallest value p.

Largest value just smaller than q.

4. (p, q] It means the interval contains the values between p and q. Furthermore, p is not included in the interval but q is included in the interval.

Smallest value just greater than p.

Largest value q.

As per above explanation, we can clearly observe that:

The largest integer which belongs to the following interval: [−∞, 31] is 31.

Answer:

[tex]h(t)=-25\cos(\pi t)+29[/tex]

Step-by-step explanation:

First thing to understand is that we will be producing a sine or cosine function to solve this one. I'll use a cosine function for the sake of the problem, since it's most easily represented by a cosine wave flipped over. If you're interested in seeing a visualization of how a circle's height converts to one of these waves, you may find the Better Explained article Intuitive Understanding of Sine Waves helpful.

Now let's get started on the problem. Cosine functions generally take the form

[tex]y=a\cos(b(x-c))+d[/tex]

Where:

[tex]|a|[/tex] is the amplitude

[tex]\frac{2\pi}{b}[/tex] is the period, or the time it takes to go one full rotation around the circle (ferris wheel)

[tex]c[/tex] is the horizontal displacement

[tex]d[/tex] is the vertical shift

Step one, find the period of the function. To do this, we know that it takes six minutes to do three revolutions on the ferris wheel, so it takes 2 minutes to do one full revolution. Now, let's find [tex]b[/tex] to put into our function:

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

[tex]2\pi=2b[/tex]

[tex]\pi=b[/tex]

I skipped some of the basic algebra to shorten the solution, but we have found our b. Next, we'll get the amplitude of the wave by using the maximum and minimum height of the wheel. Remember, it's 4 meters at its lowest point, meaning its highest point is 54 meters in the air rather than 50. Using the formula for amplitude:

[tex]\frac{\max-\min}{2}[/tex]

[tex]\frac{54-4}{2}[/tex]

[tex]\frac{50}{2}=25=a[/tex]

Our vertical transformation is given by [tex]\min+a[/tex] or [tex]\max-a[/tex], which is the height of the center of the ferris wheel, [tex]4+25=29=d[/tex]

Because cosine starts at the minimum, [tex]c=0[/tex].

The last thing to point out is that a cosine wave starts at its maximum. For that reason, we need to flip the entire function by making the amplitude negative in our final equation. Therefore our equation ends up being:

[tex]h(t)=-25\cos(\pi t)+29[/tex]

Answer:

Nominal level of measurement

Step-by-step explanation:

The level of measurements used in this study is the nominal level of measurements. The nominal level of measurements involves the use of numbers to help classify the categories in an experiment.

In this case study, values were gotten for each categories which are brown hair, blonde hair, black hair and other hair colors. Thus, the level of measurements used is the nominal level of measurement.

There is something wrong with the calculation because data was gotten for a total of 600 respondents while the mean that was calculated involved only 503 omitting about 97 respondents.

Answer:

the solutions to the inequality ys-x+1 are shaded on the graph. which point is B. (3 ,-2)

Answer: 0.476

Step-by-step explanation:

Let A = Event of choosing an even number ball.

B = Event of choosing an 8 .

Given, A lottery game has balls numbered 1 through 21.

Sample space: S= {1,2,3,4,5,6,7,8,...., 21}

n(S) = 21

Then, A= {2,4,6,8, 10,...(20)}

i.e. n(A)= 10

B= {8}

n(B) = 1

A∪B = {2,4,6,8, 10,...(20)} = A

n(A∪B)=10

Now, the probability of selecting an even numbered ball or an 8 is

[tex]P(A\cup B)=\dfrac{n(A\cup B)}{n(S)}[/tex]

[tex]=\dfrac{10}{21}\approx0.476[/tex]

Hence, the required probability =0.476

Answer:

Arrow from 0 to 4.7 and from 4.7 to 2.4

Step-by-step explanation:

4.7 is also 0+4.7

arrow from 0 to 4.7.

-2.3 from 4.7 is 4.7-2.3=2.4

arrow from 4.7 to 2.4.

Answer:

Use the interactive number line to find the difference.

4.7 - 2.3 = 4.7 + (-2.3) =

✔ 2.4

Step-by-step explanation:

Answer:

Rs. 32,000

Step-by-step explanation:

height = 4m

let length = x m

breadth = x/3 m

Area of the 4 walls = 2(length × height) + 2(breadth × height)

Area = 2(4×x) + 2(4 × x/3) = 8x + (8x)/3

Area = (32x)/3 m²

1 m² = Rs. 5

The cost for an area that is (32x)/3 m²=  (32x)/3  × 5 Rs.

The cost of plastering 4 walls at Rs.5 per m² = 640

(32x)/3  × 5  = 640

(160x)/3 = 640

x = length = 12

Area =  (32x)/3 m² = (32×12)/3 = 128m²

The cost of carpeting its floor at the rate of Rs. 250/m²:

= 128m² × Rs. 250/m² = 32,000

The cost of carpeting its floor at the rate of Rs. 250/m² = Rs. 32,000

Answer:

3 is not a solution

Step-by-step explanation:

6x – 7 = 12?

Substitute 3 in for x and see if the equation is true

6*3 - 7 = 12

18-7 = 12

11 =12

This is false so 3 is not a solution

Answer:

B

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos54° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{39}{AB}[/tex] ( multiply both sides by AB )

AB × cos54° = 39 ( divide both sides by cos54° )

AB = [tex]\frac{39}{cos54}[/tex] ≈ 66.35 → B

Answer:

  19.9 days

Step-by-step explanation:

The amount remaining after d days is ...

  a = (1/2)^(d/7)

We want to find d when a = 0.14

  log(a) = (d/7)log(1/2)

  d = 7·log(0.14)/log(1/2) ≈ 19.855 ≈ 19.9

The farmers need to wait about 19.9 days for it to be safe.

Answer:

9 in.

Step-by-step explanation:

Given that the line 10 in. and line 4 in. are parallel, then the two triangles are similar.

As such, the ratio of the sides would give the same results.

Hence,

4/6 = 10/(6 + x)

cross multiplying

4(6 + x) = 60

Dividing both sides by 4

6 + x = 15

collecting like terms

x = 15 - 6

= 9