If $5000 is deposited into an account which pays 6% compounded
monthly, approximately how much money will be in the account at the
end of 8 years?

Answer:

The area between the x-axis and the given curve equals 1/6 units.

Step-by-step explanation:

given any 2 functions f(x) and g(x) the area between the 2 figures is calculated as

[tex]A=\int_{x_1}^{x_2}(f(x)-g(x))dx[/tex]

The area needed is shown in the attached figure

The points of intersection of the given curve and x-axis are calculated as

[tex]x-x^2=0\\\\x(1-x)=0\\\\\therefore x=0,x=1[/tex]

hence the points of intersection are[tex](0,0),(1,0)[/tex]

The area thus equals

[tex]A=\int_{0}^{1}(x-x^2-0)dx\\\\A=\int_{0}^{1}xdx-\int_{0}^{1}x^2dx\\\\A=1/2-1/3\\\\A=1/6[/tex]

Answer:

  A ∩ B: 1. The set of all elements of 'Uʻ that are elements of both 'A' and 'B'.

  A ∪ B: 2. The set of all elements of 'U' that are elements of either 'A' or 'B'.

Step-by-step explanation:

1. The "intersection" symbol (∩) signifies the members that are in both sets. For example, {1, 2} ∩ {1, 3} = {1}.

__

2. The "union" symbol (∪) signifies the members that are in either set. For example, {1, 2} ∪ {1, 3} = {1, 2, 3}.

Answer:

x = 30

Step-by-step explanation:

9 + 22 = x + 1

9 + 22 = 31

31 = x + 1

-1          -1

30 = x

x = 30

The mathematical proofs are useful to show that a mathematical statement is true. Generally a mathematical proof use other statements like theorems, or axioms. Also mathematical proofs are useful to know if the development of a theoretical process in other areas like physics is well done. Other thing that is useful of the proofs in mathematics is that it use a formal language  with symbols that minimize the ambiguity and make it universal.

Answer:

☑ 30y²

☑ 30y² + x

Step-by-step explanation:

Polynomials contain indeterminates [variables] and operation performances, non-including negative exponents, fractional exponents, etcetera.

I am joyous to assist you anytime.

Answer:

According to the Law of Absorption, these 2 expressions are equivalent:

p ∨ (p ∧ q) = p

Truth Table:

(see the image attached)

Step-by-step explanation:

To construct the Truth Table you can consider the 4 possible combinations of states that p and q could have, that is

1. p=T, q=T

2. p=T, q=F

3. p=F, q=T

4. p=F, q=F

Then you can calculate p ∨ (p ∧ q) = p for each combination

1. T ∨ (T ∧ T) = T

2. T ∨ (T ∧ F) = T

3. F ∨ (F ∧ T) = F

4. F ∨ (F ∧ F) = F

You can see that the previous values are the same states that p has, you can also see it in the table attached.

Answer:

The scale factor used to go from P to Q is 1/4

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

If two figures are similar, then the ratio of its areas i equal to the scale factor squared

Let

z ----> the scale factor

x -----> area of polygon Q

y -----> area of polygon P

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]y=72\ units^2[/tex]

Find the area of polygon Q

Divide the the area of polygon Q in two triangles and three squares

The area of the polygon Q is equal to the area of two triangles plus the area of three squares

see the attached figure N 2

Find the area of triangle 1

[tex]A=(1/2)(1)(2)=1\ units^2[/tex]

Find the area of three squares (A2,A3 and A4)

[tex]A=3(1)^2=3\ units^2[/tex]

Find the area of triangle 5

[tex]A=(1/2)(1)(1)=0.5\ units^2[/tex]

The area of polygon Q is

[tex]x=1+3+0.5=4.5\ units^2[/tex]

Find the scale factor

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]y=72\ units^2[/tex]

[tex]x=4.5\ units^2[/tex]

substitute and solve for z

[tex]z^{2}=\frac{4.5}{72}[/tex]

[tex]z^{2}=\frac{1}{16}[/tex]

square root both sides

[tex]z=\frac{1}{4}[/tex]

therefore

The scale factor used to go from P to Q is 1/4

The scaled factor did Diego used to go from P to Q is 1/4.

Given

The area of polygon P is 72 square units.

If two figures are similar, then the ratio of its areas is equal to the scale factor squared.

[tex]\rm z^2=\dfrac{x}{y}[/tex]

Where; z is the scale factor, x = area of polygon Q, y = area of polygon P.

Therefore,

The area of the first triangle is;

[tex]\rm Area = \dfrac{1}{2} \times base \times height\\\\Area = \dfrac{1}{2} \times 1 \times 2\\\\Area = 1 \ units[/tex]

The area of three squares (A2, A3, and A4)

[tex]\rm Area = 3(1)^2\\\\Area = 3\ square \ units[/tex]

The area of the 5th triangle is;

[tex]\rm Area = \dfrac{1}{2} \times base \times height\\\\Area = \dfrac{1}{2} \times 1 \times 1\\\\Area = 0.5 \ units[/tex]

Then,

The area of the polygon is;

x = 1 + 3 + 0.5 = 4.5 units

Therefore,

The scaled factor did Diego used to go from P to Q is;

[tex]\rm z^2=\dfrac{4.5}{72}\\\\z^2=\dfrac{1}{16}\\\\z=\dfrac{1}{4}\\\\[/tex]

Hence, the scaled factor did Diego used to go from P to Q is 1/4.

To know more about the Scale factor click the link given below.

https://brainly.com/question/22644306

Answer: [tex](1,T), (2,T), (3,T), (4, T), (5,T), (6,T)\\(1,H), (2,H), (3,H), (4, H), (5,H), (6,H)[/tex]

Step-by-step explanation:

The total outcomes on a die = {1,2,3,4,5,6}=6

The total outcomes on a coin = {Tails  or Heads}=2

The number of possible outcomes =[tex]6\times2=12[/tex]

If you roll one die and flip one coin, then the possible outcomes are:  

[tex](1,T), (2,T), (3,T), (4, T), (5,T), (6,T)\\(1,H), (2,H), (3,H), (4, H), (5,H), (6,H)[/tex]

Here T denotes for Tails and H denotes for heads.

Answer:

the unpaid balance after the 5 years will be 125400.

Step-by-step explanation:

Given,

Principal amount, P = 190,000

rate,r = 3%

total time,t = 25 years

So, the total interest after 25 years will be,

[tex]I\ =\ \dfrac{P\times r\times t}{100}[/tex]

   [tex]=\ \dfrac{190,000\times 3\times 25}{100}[/tex]

    = 142500

amount will be paid in 3 years with same interest rate can be given by

[tex]I_p\ =\ \dfrac{P\times r\times t}{100}[/tex]

       [tex]=\ \dfrac{190,000\times 3\times 3}{100}[/tex]

       = 17100

So, the amount of interest to be paid= 142500 - 17100

                                                             = 125400

so, the unpaid amount of interest after the 5 years will be 125400.

Answer:

The number of all possible subsets of D is 8.

Step-by-step explanation:

Consider the provided set D={c,a,t}

The subset of D contains no elements: {  }

The subset of D contains one element each: {c} {a} {t}

The subset of D contains two elements each: {c, a} {a, t} {c, t}

The subset of D contains three elements: {c, a, t)

Hence, all possible subsets of D are { }, {c}, {a}, {t}, {c, a}, {a, t}, {c, t}, {c, a, t}

Therefore, number of all possible subsets of D is 8.

Or we can use the formula:

The number of subsets of the set is [tex]2^n[/tex] If the set contains ‘n’ elements.

There are 3 elements in the provided set, thus use the above formula as shown:

2³=8

Hence, the number of all possible subsets of D is 8.

Answer:

Step-by-step explanation:

The average obtained at the end of the course will be:

[tex]\frac{85+78+84+x}{4} = av[/tex]

Where x is the grade obtained in the final examination and av is the final average. To obtain an A, av has to be at least 90, av≥90, and to obtain an B, av has to be at least 80, av≥80

So, if we get 100 on the final average:

x = 100,

av = (85+78+84+100)/4 = 86,75 and  86,75∠90.

Answer: No, the higher grade obtained would be 86,75.

To earn a B, av≥80:

[tex]av= \frac{85+78+84+x}{4 \ }\geq  80\\ \frac{247+x}{4}\geq80   \\247+x\geq 80*4\\ x\geq 320-247\\ x\geq 73[/tex]

Answer: I must have a 73 or MORE to earn a B in the course

Answer:

  16.4 million viewers

Step-by-step explanation:

The number of viewers increased by 8 million from 10 to 18 million when the number of ads increased by 10 ads from 15 to 25. If 23 ads are run, that represents an increase of 8 ads from 15, so we expect 8/10 of the increase in viewers.

  8/10 × 8 million = 6.4 million

The number we expect with 23 ads is 6.4 million more viewers than 10 million viewers, so is 16.4 million.

_____

Alternate solution

We can write a linear equation in 2-point form for the number of viewers expected for a given number of ads:

  y = (18 -10)/(25 -15)(x -15) +10

  y = (8/10)(x -15) +10

  y = 0.8x -2 . . . . . million viewers for x ads

For 23 ads, this gives ...

  y = 0.8×23 -2 = 18.4 -2 = 16.4 . . . . million viewers, as above

_____

Comment on 8/10

I consider it coincidence that the number 23 is 8/10 of the difference between 25 and 15, and the slope of the line is 8/10. The point we're trying to interpolate has no relationship to the slope of the line, and vice versa.

Linear interpolation illustrates the use of linear equation of several points

The number of viewers is 16.4 million, if a 23 one-minute ads runs on Friday.

Linear interpolation is represented as:

[tex]\frac{y_2 - y_1}{x_2 - x_1} = \frac{y - y_1}{x - x_1}[/tex]

Let:

[tex]x \to[/tex] Time

[tex]y \to[/tex] Viewers

So, we have:

[tex](x_1,y_1) = (15,10m)[/tex]

[tex](x_2,y_2) = (25,18m)[/tex]

[tex](x,y) = (23,y)[/tex]

Substitute the above points in:

[tex]\frac{y_2 - y_1}{x_2 - x_1} = \frac{y - y_1}{x - x_1}[/tex]

So, we have:

[tex]\frac{y_2 - y_1}{x_2 - x_1} = \frac{y - y_1}{x - x_1}[/tex]

[tex]\frac{18m - 10m}{25 -15} = \frac{y - 10m}{23 -15}[/tex]

[tex]\frac{8m}{10} = \frac{y - 10m}{8}[/tex]

Multiply both sides by 8

[tex]\frac{64m}{10} = y - 10m[/tex]

[tex]6.4m = y - 10m[/tex]

Collect like terms

[tex]y =10m + 6.4m[/tex]

[tex]y =16.4m[/tex]

Hence, the number of viewers is 16.4 million, if a 23 one-minute ads runs on Friday.

Read more about linear interpolation at:

https://brainly.com/question/4248868

Answer and Step-by-step explanation:

n > 0

n² divisible by 3 ⇒ n is divisible by 3.

Any number divisible by 3 has the sum of their components divisible by 3.

If n² is divisible by 3,  we can say that n² can be written as 3*x.

n² = 3x ⇒ n = √3x

As n is a positive integer √3x must be a integer and x has to have a 3 factor. (x = 3.a.b.c...)

This way, we can say that x = 3y and y is a exact root, because n is a integer.

n² = 3x ⇒ n = √3x ⇒ n = √3.3y ⇒ n = √3.3y ⇒ n = √3²y ⇒ n = 3√y

Which means that n is divisible by 3.

The given sequence :  0,4,18,48,100,180,......

We can write the terms of the sequence as :

[tex]\text{Ist term }:a_1=1(1^2-1)=0\\\\\text{IInd term }: a_2=2^2(2-1)=4(2-1)=4\\\\\text{IIIrd term }:a_3=3^2(3-1)=9(2)=18\\\\\text{IVth term }:a_4=4^2(4-1)=(16)(3)=48\\\\\text{Vth term }:a_5=5^2(5-1)=25(4)=100\\\\\text{VIth term }:a_6=6^2(6-1)=36(5)=180[/tex]

From the above presentation of the terms, the explicit formula in terms of n for the nth term will be :-

[tex]a_n=n^2(n-1)[/tex]

Put n= 7 , we get

[tex]a_7=7^2(7-1)=49(6)=294[/tex]

Therefore, the seventh term of the given sequence = 294

Answer:

1.85 inches by 1.89 inches.

Step-by-step explanation:

We have been given that the dimensions of a nicotine transdermal patch system are 4.7 cm by 4.8 cm.

First of all, we will convert given dimensions into mm.

1 cm equals 10 mm.

4.7 cm equals 47 mm.

4.8 cm equals 48 mm.

We are told that 1 inch is equivalent to 25.4 mm, so to find new dimensions, we will divide each dimension by 25.4 as:

[tex]\frac{47\text{ mm}}{\frac{25.4\text{ mm}}{\text{inch}}}=\frac{47\text{ mm}}{25.4}\times \frac{\text{ inch}}{\text{mm}}=1.85039\text{ inch}\approx 1.85\text{ inch}[/tex]

[tex]\frac{48\text{ mm}}{\frac{25.4\text{ mm}}{\text{inch}}}=\frac{48\text{ mm}}{25.4}\times \frac{\text{ inch}}{\text{mm}}=1.8897\text{ inch}\approx 1.89\text{ inch}[/tex]

Therefore, the corresponding dimensions would be 1.85 inches by 1.89 inches.

Final answer:

To convert the dimensions of a nicotine transdermal patch from centimeters to inches, multiply the centimeter measurements by 10 to get millimeters, and then divide by 25.4 to get inches. The patch measures approximately 1.85 inches by 1.89 inches.

Explanation:

The student is asking to convert the dimensions of a nicotine transdermal patch system from centimeters to inches.

Given that 1 inch equals 25.4 millimeters (mm), this can be done by first converting the dimensions from centimeters (cm) to millimeters and then from millimeters to inches.

Since 1 cm equals 10 mm, the dimensions of the patch in millimeters are 47 mm by 48 mm. To convert these dimensions to inches, we would divide each by 25.4 (since there are 25.4 mm in an inch).

So, the dimension in inches for the patch's length would be 47 mm / 25.4 mm/inch ≈ 1.85 inches, and its width would be 48 mm / 25.4 mm/inch ≈ 1.89 inches.

Therefore, the nicotine patch measures approximately 1.85 inches by 1.89 inches.

Answer:

1/4 divided by 1/2 equals 1/2

Real-world problem:

A constructor official knows that he needs 1/2 sack of cement to produce 10 blocks of concrete for a wall. The official only has 1/4 of the sack left and want to know how many blocks he can produce with this material.

Step-by-step explanation:

Since you know that 1/2 of the sack is needed to make 10 blocks, you can use this information to find the number of blocks that 1/4 of a sack can make. The question you want to answer is:  

if [tex]\frac{1}{2}[/tex] of a sack produces 10 blocks, how may blocks [tex]\frac{1}{4}[/tex] of a sack can produce?

Using the Rule of Three you can solve

[tex]\frac{\frac{1}{4} }{\frac{1}{2}} =\frac{2}{4}=\frac{1}{2}[/tex]

Now you know that 1/4 of a sack can produce 1/2 the number of blocks that 1/2 of the sack can produces, this means that you can produce 5 blocks of concrete.

Answer:

if you have 1/4 of a rope and you need to give 7/16 to your friend how much rope did you give to your friend?

Step-by-step explanation:

Answer:

Cost of car = $31,210

Now we are given that  you put down 15% of the car’s cost.

So, Down payment = [tex]15\% \times 31210[/tex]

                                = [tex]\frac{15}{100} \times 31210[/tex]

                                = [tex]4681.5[/tex]

So, Amount of car loan =  Total cost - Down payment

Amount of car loan =$31210 - $4681.5

                                 =$26528.5

Thus Amount of car loan is $26528.5

Now To find the total amount of car

Principal = $26528.5

Rate of interest = 4.5%

Time = 5 years

[tex]A=P(1+r)^t[/tex]

[tex]A=26528.5(1+\frac{4.5}{100})^5[/tex]

[tex]A=33059.337533[/tex]

Total amount including down payment = $33059.337533+$4681.50 = $37740.837533

Hence  the total amount paid for the car (including the down payment) is $37740.83

Answer:

0.138 hanks/lb

Step-by-step explanation:

Given:

Silver = 60 grain/yd

Now,

1 hank = 840 yd

or

1 yd = [tex]\frac{\textup{1}}{\textup{840}}[/tex] hank

And,

1 lb = 7000 grain.

or

1 grain = [tex]\frac{\textup{1}}{\textup{7000}}[/tex] lb

Thus,

60 grain/yd = [tex]\frac{60\times\frac{1}{7000}}{1\times\frac{1}{840}}[/tex] lb/hanks

or

60 grain/yd = 7.2 lb/ hanks

or

[tex]\frac{\textup{1}}{\textup{7.2}}[/tex] hanks/lb

or

0.138 hanks/lb

Answer:

(a) Profit function P(x) = 0.02x^2+60x-80

(b) Average profit P(x)/x = P/x = 0.02x+60-80/x

Marginal profit dP/dx = 0.04x+60

Step-by-step explanation:

Cost function: C(x) = -0.02x^2+40x+80

Price function: p(x) = 100

(a) The profit function P(x) = x*p(x)-C(x) can be expressed as:

[tex]P=x*p-C\\P=x*100-(-0.02x^{2} +40x+80)\\P=0.02x^{2}+60x-80[/tex]

(b)Average profit function: P(x)/x

[tex]P/x=(0.02x^{2}+60x-80)/x\\P/x = 0.02x+60-80/x[/tex]

Marginal profit function: dP/dx

[tex]P=0.02x^{2}+60x-80\\dP/dx=0.02*2*x+60+0\\dP/dx=0.04x+60[/tex]

Final answer:

The problem involves calculating the profit, average profit per item, and marginal profit for selling x items based on a given cost and price function. By subtracting the cost function from the revenue, we obtain the profit function P(x) = -0.02x² + 60x + 80. The average profit and marginal profit functions further analyze profitability.

Explanation:

To solve the problem given, we need to start by finding the profit function P(x), which is obtained by subtracting the cost function C(x) from the revenue function, where the revenue is the sale price per item times the number of items sold (xp(x)). Given C(x) = -0.02x² + 40x + 80 and p(x) = 100, the profit function can be determined.

Next, the average profit function is found by dividing the profit function by x, and the marginal profit function, dP/dx, is the derivative of the profit function with respect to x, which provides an approximation of the profit gained by selling one more item after x items have been sold.

Profit Function

Substituting p(x) = 100 into P(x) = xp(x) - C(x), we obtain:

P(x) = x(100) - (-0.02x² + 40x + 80)

P(x) = -0.02x² + 60x + 80

Average Profit Function

The average profit per item for x items sold is:

P(x)/x = (-0.02x² + 60x + 80) / x

Answer:[tex]a = \frac{F}{m}[/tex]

[tex]v = \frac{m}{d}[/tex]

[tex]t = \frac{A - P}{Pr}[/tex]

[tex]h = \frac{2A}{a + b}[/tex]

[tex]W = \frac{P - 2L}{2}[/tex]

[tex]y = 2m - x[/tex]

[tex]y = -1.5x + 4[/tex]

[tex]t = \frac{v - u}{a}[/tex]

Step-by-step explanation:

[tex]F = ma[/tex]

[tex]\frac{F}{m} = \frac{ma}{m}[/tex]

[tex]\frac{F}{m} = a[/tex]

[tex]d = \frac{m}{v}[/tex]

[tex]vd = m[/tex]

[tex]\frac{vd}{d} = \frac{m}{d}[/tex]

[tex]v = \frac{m}{d}[/tex]

[tex]A = P + Prt[/tex]

[tex]A - P = Prt[/tex]

[tex]\frac{A - P}{Pr} = \frac{Prt}{Pr}[/tex]

[tex]\frac{A - P}{Pr} = t[/tex]

[tex]A = \frac{1}{2}h(a + b)[/tex]

[tex]2A = h(a + b)[/tex]

[tex]\frac{2A}{a + b} = \frac{h(a + b)}{a + b}[/tex]

[tex]\frac{2A}{a + b} = h[/tex]

[tex]P = 2(L + W)[/tex]

[tex]P = 2(L) + 2(W)[/tex]

[tex]P = 2L + 2W[/tex]

[tex]P - 2L = 2W[/tex]

[tex]\frac{P - 2L}{2} = \frac{2W}{2}[/tex]

[tex]\frac{P - 2L}{2} = W[/tex]

[tex]m = \frac{x + y}{2}\\2m = x + y\\2m - x = y[/tex]

[tex]3x + 2y = 8\\2y = -3x + 8\\\frac{2y}{2} = \frac{-3x + 8}{2}\\y = -1.5x + 4[/tex]

[tex]a = \frac{v - u}{t}\\at = v - u\\\frac{at}{a} = \frac{v - u}{a}\\t = \frac{v - u}{a}[/tex]

Answer:

x=[15:-5:-25]'

Step-by-step explanation:

In order to create a vector you need to use this command:

x = [j:i:k]'

This creates a regularly-spaced vector x using i as the increment between elements. j is the initial value and k is the final value. Besides you need to add the character ' at the end in order to convert the arrow vector in a column vector

Answer:

$20.9

Step-by-step explanation:

We have been given a formula [tex]C(x)=19x+1900[/tex], which represents the cost of x items.

First of all, we will find cost of 1000 items by substituting [tex]x=1000[/tex] in our given formula as:

[tex]C(1000)=19(1000)+1900[/tex]

[tex]C(1000)=19,000+1900[/tex]

[tex]C(1000)=20,900[/tex]

To find average cost per item, we will divide total cost by number of items as:

[tex]\text{Average cost per item}=\frac{\$20,900}{1000}[/tex]

[tex]\text{Average cost per item}=\$20.9[/tex]

Therefore, the average cost per item would be $20.9.

Answer:

[tex]\frac{(x-8)^2}{8^2}-\frac{(y-0)^2}{6^2}=1[/tex]

Step-by-step explanation:

∵ The equation of a hyperbola along x-axis is,

[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]

Where,

(h, k) is the center,

a = distance of vertex from the center,

b² = c² - a² ( c = distance of focus from the center ),

Here,

vertices are (0,0) and (16,0), ( i.e. hyperbola is along the x-axis )

So, the center of the hyperbola = midpoint of the vertices (0,0) and (16,0)

[tex]=(\frac{0+16}{2}, \frac{0+0}{2})[/tex]

= (8,0)

Thus, the distance of the vertex from the center, a = 8 unit

Now,  foci are (18,0) and (-2,0).

Also, the distance of the focus from the center, c =  18 - 8 = 10 units,

[tex]\implies b^2=10^2-8^2=100-64=36\implies b = 6[/tex]

( Note : b ≠ -6 because distance can not be negative )

Hence, the equation of the required hyperbola would be,

[tex]\frac{(x-8)^2}{8^2}-\frac{(y-0)^2}{6^2}=1[/tex]

Answer:

$68,500

Step-by-step explanation:

The following costs are included in the period costs:

Fixed selling expense = $3.10

Fixed administrative expense = $2.10

Sales commissions = $1.10

Variable administrative expense = $0.55

Hence,

the total period costs incurred

= Sum of the above expenses × Total number of  units sold

= ( $3.10 + $2.10 + $1.10 + $0.55 ) × 10,000

= $68,500

Answer:

False.

Step-by-step explanation:

Two angles are complementary when added up, they give a result of 90°.

So, to this question to be true we have to do:

Angle 1 + Angle 2 = 90

But if we resolve 56° + 124° = 180, so this means that this question is false, as the addition of both angles doesn't have a result of 90°.

Answer:

You could order 16 different kinds of pizza.

Step-by-step explanation:

You have those following toppings:

-Pepperoni

-Sausage

-Mushrooms

-Anchovies

The order is not important. For example, if you choose Sausage and Mushrooms toppings, it is the same as Mushrooms and Sausage. So we have a combination problem.

Combination formula:

A formula for the number of possible combinations of r objects from a set of n objects is:

[tex]C_{(n,r)} = \frac{n!}{r!(n-r!}[/tex]

How many different kinds of pizza could you order?

The total T is given by

[tex]T = T_{0} + T_{1} + T_{2} + T_{3} + T_{4}[/tex]

[tex]T_{0}[/tex] is the number of pizzas in which there are no toppings. So [tex]T_{0} = 1[/tex]

[tex]T_{1}[/tex] is the number of pizzas in which there are one topping [tex]T_{1}[/tex] is a combination of 1 topping from a set of 4 toppings. So:

[tex]T_{1} = \frac{4!}{1!(4-1)!} = 4[/tex]

[tex]T_{2}[/tex] is the number of pizzas in which there are two toppings [tex]T_{2}[/tex] is a combination of 2 toppings from a set of 4 toppings. So:

[tex]T_{2} = \frac{4!}{2!(4-2)!} = 6[/tex]

[tex]T_{3}[/tex] is the number of pizzas in which there are three toppings [tex]T_{3}[/tex] is a combination of 3 toppings from a set of 4 toppings. So:

[tex]T_{3} = \frac{4!}{3!(4-3)!} = 4[/tex]

[tex]T_{0}[/tex] is the number of pizzas in which there are four toppings. So [tex]T_{4} = 1[/tex]

Replacing it in T

[tex]T = T_{0} + T_{1} + T_{2} + T_{3} + T_{4} = 1 + 4 + 6 + 4 + 1 = 16[/tex]

You could order 16 different kinds of pizza.

Answer:

The principal square root of -4 is 2i.

Step-by-step explanation:

[tex]\sqrt{-4}[/tex] = 2i

We have the following steps to get the answer:

Applying radical rule [tex]\sqrt{-a} =\sqrt{-1} \sqrt{a}[/tex]

We get [tex]\sqrt{-4} =\sqrt{-1} \sqrt{4}[/tex]

As per imaginary rule we know that [tex]\sqrt{-1}=i[/tex]

= [tex]\sqrt{4} i[/tex]

Now [tex]\sqrt{4} =2[/tex]

Hence, the answer is 2i.

Answer:

[tex]P'(t) = 19P(1 - \frac{P}{8000}) - 9[/tex]

Step-by-step explanation:

The logistic equation is given by Equation 1):

1) [tex]\frac{dP}{dt} = rP(1 - \frac{P}{N})[/tex]

In which P represents the population, [tex]\frac{dP}{dt} = P'(t)[/tex] is the variation of the population in function of time, r is the growth rate of the population and N is the carrying capacity of the population.

Now for your system:

The problem states that the population has growth rate r=19.

The problem also states that the population has carrying capacity N=8000.

We can replace these values in Equation 1), so:

[tex]P'(t) = 19P(1 - \frac{P}{8000})[/tex]

However, beginning in 2000, 9 citizens of Cook Island have left every year to become a mathematician, never to return. So, we have to subtract these 9 citizens in the P'(t) equation. So:

[tex]P'(t) = 19P(1 - \frac{P}{8000}) - 9[/tex]

The correct differential equation modeling the population of Cook Island after 2000, taking into account the emigration of 9 citizens every year, is given by:[tex]\[ P' = \frac{P}{9}\left(1 - \frac{P}{8000}\right) - 9 \][/tex]

To derive this equation, we start with the standard logistic growth model, which is given by:

[tex]\[ P' = rP\left(1 - \frac{P}{K}\right) \][/tex]

where \( r \) is the intrinsic growth rate and [tex]\( K \)[/tex] is the carrying capacity of the environment. For the Cook Islands, we have [tex]\( r = 19 \) and \( K = 8000 \)[/tex].

However, since 9 citizens leave the island every year starting from 2000, we need to modify the logistic growth model to account for this emigration. The term representing the natural growth of the population remains the same, but we subtract 9 from the growth rate to represent the annual emigration:

[tex]\[ P' = rP\left(1 - \frac{P}{K}\right) - 9 \][/tex]

Substituting the given values of [tex]\( r \)[/tex] and [tex]\( K \)[/tex] into the equation, we get:

[tex]\[ P' = 19P\left(1 - \frac{P}{8000}\right) - 9 \][/tex]

 Now, we need to adjust the growth rate [tex]\( r \)[/tex] to reflect the fact that the population is also decreasing due to emigration. Since the population decreases by 9 every year, we divide the growth rate by 9 to account for this decrease:

[tex]\[ P' = \frac{19P}{9}\left(1 - \frac{P}{8000}\right) - 9 \][/tex]

However, the growth rate should not be divided by 9, as this would incorrectly alter the per capita growth rate. The correct adjustment is to subtract the constant rate of emigration from the overall growth rate:

[tex]\[ P' = 19P\left(1 - \frac{P}{8000}\right) - 9 \][/tex]

Upon reviewing the provided answer, we see that the growth rate [tex]\( r \)[/tex]has been incorrectly divided by 9. The correct differential equation should not have the growth rate divided by 9. Therefore, the correct differential equation modeling the population of the island [tex]\( P(t) \)[/tex] after 2000 is:

[tex]\[ P' = 19P\left(1 - \frac{P}{8000}\right) - 9 \][/tex]

Answer:

$925.20

Step-by-step explanation:

Loan Amount, P = $19,500

Rate of interest, r = 3.9%

Time, t = 6 years

Payment mode, n = Quarterly (4)

payment to amortize, EMI = ?

Formula: [tex]EMI=\dfrac{P\cdot \frac{r}{n}}{1-(1+\frac{r}{n})^{-n\cdot t}}[/tex]

where,

n = 4 , Rate of interest , r = 0.039

Put the values into formula

[tex]EMI=\dfrac{19500\cdot \frac{0.039}{4}}{1-(1+\frac{0.039}{4})^{-4\cdot 6}}[/tex]

[tex]EMI=915.20[/tex]

Hence, The payment to amortize the debt is $915.20