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

Answer:

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.

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)

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.

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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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Answer:

897

Explanation:
Start with replacing all the [tex]t[/tex] with 2.

[tex](t^{2} + 6t+7)(3t^{2} +3)[/tex]
[tex](2^{2} + 6(2)+7)(((3)(2))^{2} +3)[/tex]

Deal with the exponent before multiplying and adding.

[tex](2^{2} + 6(2)+7)(((3)(2))^{2} +3)[/tex]
[tex](4 + 6(2)+7)(((3)(2))^{2} +3)[/tex]
[tex](4 + 12+7)(((3)(2))^{2} +3)[/tex]
[tex](23)(((3)(2))^{2} +3)[/tex]

Now I believe here is where you made your mistake, you should first multiply 3 and 2 instead of evaluating the exponent straight away, because [tex]3t[/tex] was squared together.

[tex](23)(((3)(2))^{2} +3)[/tex]
[tex](23)(6^{2} +3)[/tex]
[tex](23)(36 +3)[/tex]

Then after adding, just multiply to get your answer, 897.

[tex](23)(36 +3)[/tex]
[tex](23)(39) = 897[/tex]

The sample standard deviation for the given data set is approximately 2.77.

Let's calculate the sample standard deviation for the given data set:

Calculate the mean

Sum of all data points = 8 + 5 + 2 + 4 + 4 + 9 + 9 + 7 + 3 + 5 + 2 + 4 + 4 + 7 + 10 + 5 + 1 + 8 + 9 + 8 + 3 + 3 + 8 + 7 = 137

Mean = Sum of all data points / Number of data points = 137 / 24 = 5.71 (rounded to two decimal places)

Subtract the mean from each data point and square the result

(8 - 5.71)^2 = 2.4361

(5 - 5.71)^2 = 0.5041

(2 - 5.71)^2 = 15.1361

(4 - 5.71)^2 = 2.9241

(4 - 5.71)^2 = 2.9241

(9 - 5.71)^2 = 10.3961

(9 - 5.71)^2 = 10.3961

(7 - 5.71)^2 = 1.6641

(3 - 5.71)^2 = 8.2561

(5 - 5.71)^2 = 0.5041

(2 - 5.71)^2 = 15.1361

(4 - 5.71)^2 = 2.9241

(4 - 5.71)^2 = 2.9241

(7 - 5.71)^2 = 1.6641

(10 - 5.71)^2 = 23.7761

(5 - 5.71)^2 = 0.5041

(1 - 5.71)^2 = 21.8441

(8 - 5.71)^2 = 2.4361

(9 - 5.71)^2 = 10.3961

(8 - 5.71)^2 = 2.4361

(3 - 5.71)^2 = 8.2561

(3 - 5.71)^2 = 8.2561

(8 - 5.71)^2 = 2.4361

(7 - 5.71)^2 = 1.6641

Find the sum of all the squared differences

Sum of squared differences = 2.4361 + 0.5041 + 15.1361 + 2.9241 + 2.9241 + 10.3961 + 10.3961 + 1.6641 + 8.2561 + 0.5041 + 15.1361 + 2.9241 + 2.9241 + 1.6641 + 23.7761 + 0.5041 + 21.8441 + 2.4361 + 10.3961 + 2.4361 + 8.2561 + 8.2561 + 2.4361 + 1.6641 = 174.07 (rounded to two decimal places)

Divide the sum by the number of data points minus 1

Variance = Sum of squared differences / (Number of data points - 1) = 174.07 / (24 - 1) = 7.67 (rounded to two decimal places)

Take the square root of the variance

Sample Standard Deviation = √(Variance) = √(7.67) = 2.77 (rounded to two decimal places)

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Answer:

[tex] \sqrt{ {( - 4 - 2)}^{2} + {(1 - 0)}^{2} } = \sqrt{ {( - 6)}^{2} + {1}^{2} } = \sqrt{36 + 1} = \sqrt{37} [/tex]

The number 37 goes beneath the radical symbol.

Answer:

Step-by-step explanation:

2(97+69)=332(m)

Answer:

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

Step-by-step explanation:

The answer is:

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]

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

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

5 units.

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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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.

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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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

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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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.

a. The maximum population of the squirrels is 1800.

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

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:

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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[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:

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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Using proportions, it is found that the table is completed as follows:

                        Original Ratio Number in the zoo

Baby camels     5                     20

Adult camels     6                     24

Total camels     11                    44

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

At the zoo, for every 6 adult camels, there are 5 baby camels, hence, out of 11 camels, 5 are baby and 6 are adult.

Thus, out of 44 camels, we have that:

The table is:

                        Original Ratio Number in the zoo

Baby camels     5                     20

Adult camels    6                     24

Total camels     11                     44

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Your question was incomplete, the complete question is-

At the zoo, for every 6 adult camels, there are 5 baby camels. There are a total of 44 adult and baby camels at the zoo.

Complete the table.

Original ratio Number in the zoo

Baby camels 5 ?

Adult camels 6 ?

Total camels ? 44

Answer:

false

Step-by-step explanation:

Its All Real Numbers

9 1/2 years on Venus is equivalent to approximately 2137.65 days on Earth.

To find how many days on Earth are equivalent to 9 1/2 years on Venus, we need to use the ratio of 224.7 days on Earth to 1 year on Venus. First, we convert 9 1/2 years to a decimal form, which is 9.5 years. Then, we multiply 9.5 years by the conversion ratio: 9.5 years * 224.7 days/year = 2137.65 days on Earth. Therefore, 9 1/2 years on Venus is equivalent to approximately 2137.65 days on Earth in decimal form.

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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.

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

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

Where:

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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The 90% confidence interval for the mean tail length of all newts in the population is approximately (4.9342 cm, 5.0658 cm).

To calculate the 90% confidence interval for the mean tail length of all newts in the population, we can use the formula:

Confidence Interval = Sample Mean ± Margin of Error

Given:

- Sample size (n) = 25

- Sample Mean (xbar) = 5 cm

- Standard Deviation of the population (σ) = 0.2 cm

- Confidence level = 90% (which corresponds to a z-score of 1.645 for a two-tailed test at a 90% confidence level)

First, we need to calculate the margin of error:

Margin of Error = (Critical Value) * (Standard Deviation / √Sample Size)

In this case, the critical value for a 90% confidence level is 1.645. Let's substitute the values:

Margin of Error = 1.645 * (0.2 / √25)

Margin of Error = 1.645 * 0.04

Margin of Error ≈ 0.0658

Now, we can calculate the confidence interval:

Confidence Interval = Sample Mean ± Margin of Error

Confidence Interval = 5 ± 0.0658

Confidence Interval ≈ (4.9342, 5.0658)

Therefore, the 90% confidence interval for the mean tail length of all newts in the population is approximately (4.9342 cm, 5.0658 cm).

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The solution to the composite functions from the graph are:

(f * g)(2) = 16

(f - g)(0) = -5

Composite functions are defined as when the output of one function is used as the input of another. If we have a function f and another function g, then the function “ f of g of x”, is the composition of the two functions.

a) Using the concept of composite functions, we can say that:

(f * g)(x) = f(x) * g(x)

Thus:

(f * g)(2) = f(2) * g(2)

f(2) = 4

g(2) = 4

Thus:

(f * g)(2) = 4 * 4

(f * g)(2) = 16

b) Using the concept of composite functions, we can say that:

(f - g)(x) = f(x) - g(x)

Thus:

(f - g)(0) = f(0) - g(0)

f(0) = 1

g(0) = 6

Thus:

(f - g)(0) = 1 - 6

(f - g)(0) = -5

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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.

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

Answer:

The coreect answer o

is 14

Answer:

three times a number minus fifteen

or

fifteen is less than three times a number

        Hence, The other Number is:   B   =  630

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

        2,   2,  3,   3,  7

        2,  2,  2,  3,  3

        HCF  *   LCM   =   a  *  b

        HCF   =    2  *  2  *  3  *  3

                   =  36

        36  *   1260   =    72  *  b

        36  *  1260    =    72b

        45360           =    72b

        1260            =   2  *  b

        45360 / 72  =   72b/72

                        b   =   630

        B    =    630

        Hence, The other Number is:   B   =  630

I hope this helps you!

Answer:

22

Step-by-step explanation:

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

The simplified expression is (400n)/(320n^3 - 52n - 40n^2 + 2).

First, let's focus on simplifying the numerator and denominator separately:

Numerator:

The numerator is 1 divided by (4n - 1/2). We can simplify this by finding a common denominator. The denominator of 1/2 is 2, so we rewrite the expression as:

1/(4n - 12) = 1/(4n - 2/4) = 1/(4n - 2/4) = 1/((16n - 2)/4) = 4/(16n - 2)

Denominator:

The denominator is (n/5 - 1/20n). To simplify this, we find a common denominator. The denominator of 1/20n is 20n, so we rewrite the expression as:

n/5 - 1/20n = (20n^2)/(5 * 20n) - 1/(20n) = (20n^2 - 1)/(100n)

Now, let's simplify the entire expression by dividing the numerator by the denominator:

(1/(4n - 1/2)) ÷ (n/5 - 1/20n) = (4/(16n - 2)) ÷ ((20n^2 - 1)/(100n))

To divide by a fraction, we multiply by its reciprocal:

(4/(16n - 2)) ÷ ((20n^2 - 1)/(100n)) = (4/(16n - 2)) * (100n/(20n^2 - 1))

Next, we can simplify the numerator and denominator separately:

Numerator:

4 * 100n = 400n

Denominator:

(16n - 2) * (20n^2 - 1) = 320n^3 - 52n - 40n^2 + 2

Finally, we substitute the simplified numerator and denominator back into the expression:

(4/(16n - 2)) * (100n/(20n^2 - 1)) = (400n)/(320n^3 - 52n - 40n^2 + 2)

Thus, the simplified expression is (400n)/(320n^3 - 52n - 40n^2 + 2).

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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]