How many combinations of poker hands are in a deck of cards?

Answers

Answer 1
2,598,960 distinct poker hands

Related Questions

Pie chart values
20%. Rice
15%. Others
Pulses. 30%
maize 20%
wheat 15%

Percentage distribution of products in exports of the
given countries.
(a) What is the value (in $ billion) of pulses export
by US? on a billion
(6)
What is the ratio of wheat export of UK to
maize export of IND? 4:10
(e) By what percentage is the maize export of
JAP more than the rice export of AUS?
(d) If the export of AUS is doubled and that of US is
halved but percentage distribution of products of
export remains the same, then find the value of
Export of Rice by US
Export of Pulses by AUS
In USSR, find the ratio of maize export to the
rice export.

Answers

a.) The value of pulses exported by US in billion would be=30 billion.

b.) The ratio of wheat export of UK to maize export of IND would be= 6:5

How to calculate the value of pulses exported?

For question a.)

To calculate the pulses, the following steps should be taken as follows:

From the bar chart, the value of pulses in billions = 30 billions.

For question b.)

The ratio of wheat export at UK and maize export at IND would be calculated as follows:

The quantity of wheat export at UK = 24

The quantity of maize export at IND = 20

Therefore, the ratio of wheat to maize = 24:20= 6:5

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no explanation needed would be nice ytho thnks

Answers

The average rate of change in the population between 2002 and 2004 is one thousand per year, and between 2002 and 2006 is 1.75 thousand per year.

Rate of change

To calculate the average rate of population change, we need to find the difference in population between the given years and divide it by the difference in years.

Between 2002 and 2004:

Population change = 80 - 82 = -2 (decrease of 2, as the population decreased)

Year difference = 2004 - 2002 = 2

Average rate of change = Population change / Year difference

Average rate of change = -2 / 2 = -1 (thousands per year)

Between 2002 and 2006:

Population change = 75 - 82 = -7 (decrease of 7, as the population decreased)

Year difference = 2006 - 2002 = 4

Average rate of change = Population change / Year difference

Average rate of change = -7 / 4 = -1.75 (thousands per year)

Therefore, the average rate of change of population between 2002 and 2004 is 1 thousand per year, and between 2002 and 2006 is 1.75 thousand per year.

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How to calculate your bi-weekly paycheck based on 20 hour weeks at a rate of $9.00 per hour. Also, You will need to deduct Federal Income Tax (11.9%) , State Income Tax (3.6%), F.I.C.A (7.65%), and professional dues. Lastly you will need to look determine whether or not you will be able to pay your monthly car insurance bill of $200.00?

Answers

To calculate your bi-weekly paycheck, follow these steps:

Step 1: Calculate the gross earnings:

Multiply the number of hours worked per week by the hourly rate.

20 hours/week * $9.00/hour = $180.00/week

Step 2: Calculate the total earnings for two weeks:

Multiply the weekly earnings by the number of weeks in a bi-weekly pay period.

$180.00/week * 2 weeks = $360.00

Step 3: Calculate the deductions:

Calculate each deduction separately and subtract them from the gross earnings.

Federal Income Tax: $360.00 * 11.9% = $42.84

State Income Tax: $360.00 * 3.6% = $12.96

F.I.C.A: $360.00 * 7.65% = $27.54

Professional Dues: Amount varies depending on the specific dues.

Total Deductions: $42.84 + $12.96 + $27.54 + Professional Dues

Step 4: Calculate the net earnings:

Subtract the total deductions from the gross earnings.

Net Earnings = Gross Earnings - Total Deductions

Once you have the net earnings, you can determine if it is sufficient to cover your monthly car insurance bill of $200. If your bi-weekly net earnings are greater than or equal to $200, you will be able to pay your car insurance bill.

It is important to note that these calculations are based on the information provided, and actual tax rates and deductions may vary depending on your specific circumstances and location.

Additionally, professional dues may differ depending on your profession. It is recommended to consult with a tax professional or payroll department for precise calculations.

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la edad de Ana es la mitad de jose y dentro de 10 años seran dos tercios ..cual es la edad de jose​

Answers

La edad actual de José es de 30 años.

Para resolver este problema, primero debemos establecer ecuaciones basadas en la información proporcionada. Llamemos "x" a la edad actual de José y "y" a la edad actual de Ana. Según la primera condición, la edad de Ana es la mitad de la edad de José, por lo que podemos escribir la ecuación: y = (1/2)x.

La segunda condición nos dice que dentro de 10 años, sus edades serán dos tercios de sus edades actuales. Esto se puede expresar como: (x + 10) * (2/3) = y + 10.

Reemplazando el valor de y en la segunda ecuación con la primera ecuación, obtenemos: (x + 10) * (2/3) = (1/2)x + 10.

Resolviendo esta ecuación, podemos simplificarla y llegar a: 2(x + 10) = 3[(1/2)x + 10].

Al resolver la ecuación resultante, encontramos que x = 30.

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If the HCF of two numbers is 36 and their LCM is 1260 . If one number is 72 find the other one

Answers

Answer:  B   =   630

        Hence, The other Number is:   B   =  630

Step-by-step explanation:  EUCLIDS ALGORITHM

If the HCF of two numbers is 36 and their LCM is 1260. If one number is 72 find the other one:

PRIME FACTORS of 1260 are:

        2,   2,  3,   3,  7

PRIME FACTORS of 72 are:

        2,  2,  2,  3,  3

Write the formula  for  HCF  and  LCM:

        HCF  *   LCM   =   a  *  b

        HCF   =    2  *  2  *  3  *  3

                   =  36

Substitute  The Given Values:

        36  *   1260   =    72  *  b

        36  *  1260    =    72b

        45360           =    72b

Divide Both Sides by 36:

        1260            =   2  *  b

        45360 / 72  =   72b/72

                        b   =   630

Divide Both Sides by 2:

        B    =    630

Draw the conclusion:

        Hence, The other Number is:   B   =  630

I hope this helps you!

Determine the perimeter of a field that has a length of 97 metres and a width of 69 metres

Answers

Answer:

Step-by-step explanation:

2(97+69)=332(m)

An environmental group is tracking a fast-growing algae's coverage on a nearby pond. When
the group first measured the algae, it covered 3 square meters of the pond. They expect the
area of the pond covered by algae will double each day.
Write an exponential equation in the form = a(b)^x that can model the area of the pond
covered by algae, y, in x days.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y =

How much of the pond is expected to be covered by algae after 4 days?

Answers

Answer:

y = 3(2^x)48 m² after 4 days

Step-by-step explanation:

You want an exponential function of the form y = a(b^x) that models algae growth that initially covers 3 square meters of a pond and doubles in area each day.

Exponential function

The function y = a(b^x) has an initial value of 'a', which the problem statement tells us is 3 (square meters). The value 'b' is the growth factor, which the problem statement tells us is 2 each day.

The desired exponential equation is ...

  y = 3(2^x)

4 days

When x=4, the function evaluates to ...

  y = 3(2^4) = 3(16) = 48 . . . . square meters

After 4 days, 48 square meters of the pond is expected to be covered by algae.

<95141404393>

Please Solve, Thank you!

Answers

For the function g(x) graphed above, the limits should be identified as follows;

a. A. [tex]\lim_{x \to -4} g(x)=0[/tex]

b. A. [tex]\lim_{x \to -3} g(x)=-1[/tex]

c. B.  [tex]\lim_{x \to 0} g(x)[/tex] does not exist.

d. B.  [tex]\lim_{x \to 0} g(x)[/tex] does not exist.

What is a function?

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables, graphs, or relations.

Part a.

By critically observing the graph of this function, g(x), we can reasonably infer and logically deduce that as x tends towards negative four, g(x) tends towards positive zero;

[tex]\lim_{x \to -4} g(x)=0[/tex]

Part b.

By critically observing the graph of this function, g(x), we can reasonably infer and logically deduce that as x tends towards negative three, g(x) tends towards negative one;

[tex]\lim_{x \to -3} g(x)=-1[/tex]

Part c and d.

By critically observing the graph of this function, g(x), we can reasonably infer and logically deduce that [tex]\lim_{x \to 0} g(x)[/tex] does not exist because the graph jumps and approaches both −1 and 1 as x → 0.

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What’s the answer please I’m so behind

Answers

Answer:

2

Step-by-step explanation:

3x - 12 is inside the root.

The smallest value of √(3x - 12) is 0.

The greatest value of √(3x - 12) is infinity.

Since the function includes +2, then the range is from 2 to infinity.

Answer: 2

how many time can 457 go into 600

Answers

Answer:

Once

Step-by-step explanation:

Simple, once. If you do 600-457, you get an answer of 143, which you cannot subtract another 457 because it will turn negative.

Only once because if we were to do two then it would be greater than 600, so 457 can only go into 600 once.

The space shuttle carries c pounds of cargo, and each piece of cargo weighs 162.68 pounds. Which of the following expressions represents the number of pieces of cargo?

Answers

The expression which represents the number of pieces of cargo is c/162.68 = x, where c is the weight of the cargo in pounds, and x is the number of pieces of cargo.

Given that the space shuttle carries c pounds of cargo, and each piece of cargo weighs 162.68 pounds. We have to determine which of the following expressions represents the number of pieces of cargo.

Let's assume that the number of pieces of cargo be x.

Therefore, the weight of x pieces of cargo will be 162.68x = weight of cargo. The expression which represents the number of pieces of cargo can be written as: c/162.68 = x

This is because the total weight of the cargo is c pounds, and we know that each piece weighs 162.68 pounds.

Therefore, to find the number of pieces, we can divide the total weight by the weight of each piece, which gives us the expression c/162.68 = x, where x is the number of pieces of cargo.

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Which of the following could be a real world description of 3x-15

Answers

Answer:

three times a number minus fifteen

or

fifteen is less than three times a number

Solve the right triangle.
b=1.98 c=4.63

Answers

SolutioN:-

[tex] \sf \hookrightarrow \: {(BC)}^{2} + {(AC)}^{2} = {(AB)}^{2} [/tex]

[tex] \sf \hookrightarrow \: {a}^{2} + {b}^{2} = {c}^{2} [/tex]

[tex] \sf \hookrightarrow \: {a}^{2} + {(1.98)}^{2} = {(4.63)}^{2} [/tex]

[tex] \sf \hookrightarrow \: {a}^{2} + (1.98 \times 1.98)= (4.63 \times 4.63) [/tex]

[tex] \sf \hookrightarrow \: {a}^{2} + (3.9204)= (21.4369)[/tex]

[tex] \sf \hookrightarrow \: {a}^{2}= (21.4369) - (3.9204)[/tex]

[tex] \sf \hookrightarrow \: {a}^{2}= 17.5165[/tex]

[tex] \sf \hookrightarrow \: a= \sqrt{ 17.5165}[/tex]

[tex] \sf \hookrightarrow \: a= 4.18. Approx[/tex]

Answer: To solve the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Let's label the sides of the triangle as follows:

The length of the hypotenuse is c = 4.63.

One of the legs is b = 1.98.

Using the Pythagorean theorem, we can find the length of the other leg, which we'll label as a:

a^2 + b^2 = c^2

a^2 + (1.98)^2 = (4.63)^2

a^2 + 3.9204 = 21.4369

a^2 = 21.4369 - 3.9204

a^2 = 17.5165

Taking the square root of both sides, we find:

a ≈ √17.5165

a ≈ 4.1833

So, the length of the other leg (side a) is approximately 4.1833.

Therefore, the sides of the right triangle are approximately:

Side a ≈ 4.1833

Side b = 1.98

Side c = 4.63

Step-by-step explanation:

Create a table of values for the function graphed below using the plotted points. Remember, table of values are written with the x
-values in order from least to greatest (read the graph from left to right).
there are 5 rows for both problems x,y and 45 points for helping me with this

Answers

The table of values of the graphs are

x    -2    -1    0    1    2

y  -8   -6   -4   -2    0

and

x   -7    -2    2    3    4

y  1       -8   3      5   -5

Writing the table of values of the graphs.

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

The graph

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx - 4

Using the points, we have

2m - 4 = 0

This gives

2m = 4

So, we have

m = 2

This means that the equation is y = 2x - 4

So, we have the following table of values

x    -2    -1    0    1    2

y  -8   -6   -4   -2    0

For the second table, we have

x   -7    -2    2    3    4

y  1       -8   3      5   -5

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Consider the function h(x)=12x−3 with a restricted domain of {−2, 0, 2, 10} . What is the range of the function? Responses {−2, 0, 2, 10} {−2, 0, 2, 10} all real numbers all real numbers {−4, −3, −2, 2} {−4, −3, −2, 2} the set of integers the set of integers

Answers

The range of the function h(x) with the restricted domain of {-2, 0, 2, 10} is {-27, -3, 21, 117}. Therefore, the correct response is {−27, -3, 21, 117}.

To find the range of the function h(x) = 12x - 3 with the restricted domain of {-2, 0, 2, 10}, we need to evaluate the function for each value in the domain and determine the corresponding range values.

For x = -2:

h(-2) = 12(-2) - 3 = -24 - 3 = -27

For x = 0:

h(0) = 12(0) - 3 = 0 - 3 = -3

For x = 2:

h(2) = 12(2) - 3 = 24 - 3 = 21

For x = 10:

h(10) = 12(10) - 3 = 120 - 3 = 117

The range of the function h(x) with the restricted domain of {-2, 0, 2, 10} is {-27, -3, 21, 117}. Therefore, the correct response is {−27, -3, 21, 117}.

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If you buy 10 pounds of lettuce for $70, what is the rate which one pound of lettuce costs?

Answers

Answer:

$7/lb

Step-by-step explanation:

$70 / 10 lb = $7/lb

Answer:

$7 per pound of letuce

Step-by-step explanation:

We know

10 pounds = $70

1 pounds = ?

We cross multiply and get:

$7 per pound of letuce

So, the answer is $7 per pound of letuce

What sentence represents the number of points in the problem below?
A test is worth 60 points. Multiple-choice questions are worth 2 points, and
short-answer questions are worth 5 points. If the test has 15 questions, how
many multiple-choice questions are there?
OA. The number of multiple-choice question points times the number
of short-answer question points is 60.
OB. The number of multiple-choice question points plus the number of
short-answer question points is 15.
OC. The number of multiple-choice question points minus the number
of short-answer question points is 15.
OD. The number of multiple-choice question points plus the number of
short-answer question points is 60.

Answers

Answer:

Step-by-step explanation:

The sentence that represents the number of points in the problem is OD. The number of multiple-choice question points plus the number of short-answer question points is 60.

The problem states that the test is worth 60 points, and that multiple-choice questions are worth 2 points each and short-answer questions are worth 5 points each. If the test has 15 questions, then there must be some number of multiple-choice questions and some number of short-answer questions. The total number of points for the multiple-choice questions and the short-answer questions must add up to 60, so the answer is OD.

The other answer choices are incorrect. OA is incorrect because it says that the number of multiple-choice question points times the number of short-answer question points is 60. This is not possible, because the number of points for a question cannot be multiplied by the number of points for another question. OB is incorrect because it says that the number of multiple-choice question points plus the number of short-answer question points is 15. This is not possible, because the total number of points for the test is 60, not 15. OC is incorrect because it says that the number of multiple-choice question points minus the number of short-answer question points is 15. This is not possible, because the number of points for a question cannot be subtracted from the number of points for another question.

PLEASE HELP PLEASE HELP​

Answers

220 divided by 22 is equal to 10. You can check this by multiplying 22 by 10 to get 220.

Answer:

22

Step-by-step explanation:

You can do it by 220 divided by 10, which gives an answer of 22.

In a hockey Skills competition, Olga scored on 3 of 5 breakaways. Tara scored on 5 of 7 breakaways. Whose performance was better?

Answers

Answer:

Step-by-step explanation:

Olga scoring 3/5 breakaways means she scored a fraction of 3/5 or 60 percent of the breakaways. Tara scored a fraction of 5/7 or around 71 percent. That means Tara's performance was better as she scored a higher percentage of the breakaways.

. Write the equation of a line with a slope of 4 passing through the point (3, 1). Write the
equation in slope-intercept form.

Answers

Answer:

y = 4x - 11

Step-by-step explanation:

The general equation of the slope-intercept form of a line is given by:

y = mx + b, where

(x, y) are any point on the line,m is the slope,and b is the y-intercept.

We can find b, the y-intercept of the line, by plugging in 4 for m and (3, 1) for (x, y) in the slope-intercept form:

1 = 4(3) + b

1 = 12 + b

-11 = b

Thus, the y-intercept is -11.

Thus, the equation of the line with a slope of 4 passing through the point (3, 1) in slope-intercept form is y = 4x - 11

The answer is:

y = 4x - 11

Work/explanation:

First, we will write the equation in point slope:

[tex]\sf{y-y_1=m(x-x_1)}[/tex]

where m = slope;

(x₁,y₁) is a point on the line.

Plug in the data:

[tex]\sf{y-1=4(x-3)}[/tex]

Simplify

[tex]\sf{y-1=4x-12}[/tex]

Add 1 on each side

[tex]\sf{y=4x-12+1}[/tex]

[tex]\sf{y=4x-11}[/tex]

Hence, the equation is y = 4x - 11.

Classical determination of the probability of an event. There are 8 red, 5 white and

6 black balls. One ball is randomly taken from the urn. What is the probability that it will be black?

Answers

The probability of drawing a black ball from the urn, with a total of 19 balls (8 red, 5 white, and 6 black), is approximately 0.3158 or 31.58%.

To determine the probability of drawing a black ball from the urn, we need to consider the total number of balls and the number of black balls.

In this case, the total number of balls in the urn is 8 + 5 + 6 = 19, as there are 8 red, 5 white, and 6 black balls.

The probability of drawing a black ball can be calculated by dividing the number of black balls by the total number of balls:

Probability = Number of black balls / Total number of balls = 6 / 19 ≈ 0.3158 (rounded to four decimal places)

Therefore, the probability of drawing a black ball from the urn is approximately 0.3158, or 31.58%.

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what is 4.5x-100>125

Answers

Answer:

4,5x>225--> x>225:4,5

Step-by-step explanation:

The answer is:

x > 50

Work/explanation:

To solve this inequality, begin by adding 100 on each side:

[tex]\sf{4.5x-100 > 125}[/tex]

[tex]\sf{4.5x > 125+100}[/tex]

[tex]\sf{4.5x > 225}[/tex]

Now, divide each side by 4.5.

[tex]\sf{x > 50}[/tex]

Hence, the answer is x > 50.

find the value of k , if x =1, y=2 is a solution of the equation 2x+3y=k

Answers

Answer:

k=8

Step-by-step explanation:

2(1)+3(2)=k

2+6=8

k=

The answer is:

k = 8

Work/explanation:

If x = 1, and y = 2, we can plug these values into the equation 2x+3y = k:

[tex]\bf{2(1) + 3(2) = k}[/tex]

Multiply

[tex]\bf{2 + 6 = k}[/tex]

Add

[tex]\bf{8 = k}[/tex]

Hence, k = 8.

Please help ASAP !! I will give 10 points to the correct answer

Answers

The Rational Roots Theorem indicates that the set of possible rational roots for the polynomial x³ + 5·x² - 8·x - 20 = 0, is the option C

C. ±1, ±2, ±4, ±5, ±10, ±20

What is the Rational Roots Theorem?

The Rational Roots Theorem states that if p/q is a rational root of a polynomial with integer coefficients, where p and q have only 1 as their common factor, then p must be a factor of the constant term and q must be a factor of the leading coefficient.

The Rational Root Theorem indicates that where the number p/q is a rational root of the polynomial, then p is a factor of the constant term -20, and q is a factor of leading coefficient 1

The factors of -20 are; ±1, ±2, ±4, ±5, ±10 and ±20

The factors of 1 is; 1

Therefore the possible values of p/q are; ±1, ±2, ±4, ±5, ±10 and ±20

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After college, you get a job with a starting salary of $37,000. You have a cousin that works at the same company, but he was hired three years before you. Your contract states you will receive a pay raise each year of 6%. Your cousin tells you that his starting salary three years ago was $50,000 and he has been guaranteed a 4% pay raise each year.
1. Make a table showing your salary for your first five years on the job


Answers

1. A table showing your salary for the first five years on the job is shown below.

2. Your cousin's salary would be $56243.2 in the year you started working.

3. A formula for your salary is [tex]P(t) = 37000(1.06)^t[/tex]

A formula for your cousin's salary is [tex]P(t) = 50000(1.04)^t[/tex]

4. A graph of your salary and your cousin's salary is shown below.

It would take about 16 years before your salary exceed your cousin's salary.

How to write an exponential function to model the situation?

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

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

Where:

P(t) represent the future value.t represent the time or number of years.I represent the initial amount.r represent the exponential growth rate.

Part 1.

We can create a table of values to model your salary for the first five years on the job as follows;

Years               1                2               3                4                 5

Salary ($)    39,220    41,573.2    44,067.6    46,711.7     49,514.4

Part 2.

For your cousin's salary three years after, we have:

y = 50,000(1.04)³

y = $56243.2.

Part 3.

We can write a formula for your salary as follows;

[tex]P(t) = 37000(1 + 0.06)^t\\\\P(t) = 37000(1.06)^t[/tex]

For your cousin's salary, we have:

[tex]P(t) = 50000(1 + 0.04)^t\\\\P(t) = 50000(1.04)^t[/tex]

Part 4.

In order to plot a graph of your salary and your cousin's salary, we would use an online graphing tool with a scale of 1 units for 1 year on the x-axis and a scale of 50 units for 1000 dollars on the y-axis.

Since the lines representing both salaries intersect at 15.808, we can logically deduce that it would take approximately 16 years for your salary to exceed your cousin's salary.

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Find the sum of the first 50 terms
t1=91 and t25=374

Answers

In an arithmetic sequence where t1=91 and t25=374, the sum of the first 50 terms is 18,425.

How to find sum of arithmetic sequence

Formula for the sum of an arithmetic sequence is given as

[tex]Sn = (n/2) x [2a1 + (n-1)d][/tex]

where

Sn is the sum of the first n terms,

a1 is the first term

d is the common difference and

n is the number of terms.

Given that t1 = 91 and t25 = 374.

To find d, we can use the formula for the nth term of an arithmetic sequence:

[tex]tn = a1 + (n-1)d[/tex]

Substitute n = 25, t25 = 374, and a1 = 91, we get:

374 = 91 + 24d

d = 11

Substitute d in the Sn formula

S₅₀ = (50/2) x [2(91) + (50-1)(11)]

S₅₀ = 25 x [182 + 49 x 11]

S₅₀= 25 x 737

S₅₀ = 18,425

Therefore, the sum of the first 50 terms is 18,425.

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a. Show that the equation
dy/dx = x²/(1 - y²) is separable, and then find an equation for its integral curves.


b. Solve the initial value problem dy dx dy/dx = (3x² + 4x + 2)/(2(y - 1)) , where y(0) = -1 ,
and determine the interval in which the solution exists. ​

Answers

Answer:

a. The equation is separable, as we can write it as (1 - y²) dy = x² dx. Integrating both sides, we have (1/2)*ln|1 - y²| = (1/3)*x³ + C, where C is the constant of integration. Solving for y, we get an equation for the integral curves: y = ±sqrt(1 - exp(2/3*x³ + 2C)).

b. Rearranging the equation, we get (2/(y - 1)) dy/dx = (3x² + 4x + 2). This is separable, so integrating both sides, we have 2 ln|y - 1| = x³ + 2x² + 2x + C, where C is the constant of integration. Solving for y, we get y = 1 + Ce^(x³+2x²+2x)/2. Using y(0) = -1, we have -1 = 1 + C, so C = -2. Thus, the solution to the initial value problem is y = 1 - 2e^(x³+2x²+2x)/2. The solution exists for all values of x.

If a varies as square root of y, how x is affected when y is increased by 44%​

Answers

Answer: 16.7%

Step-by-step explanation:

x/(root y) =x

root y is increased by 44%

x/(44+root y)=16.7%

3
2
1
-1
-2
-3
Determine the period.
V
MAN
6 8 10 12 14
2 4

Answers

The period of the function in this problem is given as follows:

5 units.

How to obtain the period of the function?

A periodic function is a function that has the behavior repeating over intervals in the domain of the function.

Then the period of the function has the concept defined as the difference between two points in which the function has the same behavior.

The distance between peaks of the function in this problem is of 5 units, which represents the period of the function.

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solve the following problem

Answers

a. The maximum population of the squirrels is 1800.

b. The number of squirrels that were introduced to the island are 200 squirrels.

What is an exponential function?

In Mathematics and Geometry, a logistic growth function can be represented by using the following mathematical equation:

[tex]f(x) = \frac{L}{1\;+\;e^{-k(x-x_0)}}[/tex]

Where:

L represents the carrying capacity, maximum value or supremum.x represents the x-value of midpoint.k represents the rate of change or growth rate.

Based on the information provided above, the population of squirrels can be modeled by the following logistic growth function;

[tex]P(t) = \frac{1800}{1\;+\;8e^{-0.3t}}[/tex]

Part a.

By comparison, the maximum value or supremum population of the squirrels is 1800 squirrels.

Part b.

When t = 0, the initial number of squirrels that were introduced to this island can be calculated as follows;

[tex]P(t) = \frac{1800}{1\;+\;8e^{-0.3t}}\\\\P(0) = \frac{1800}{1\;+\;8e^{-0.3(0)}}[/tex]

P(0) = 1800/9

P(0) = 200 squirrels.

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