The population of bats in a large cave is 8500 and is growing exponentially at 10% per year. Write a function to represent the population of bats after t t years, where the quarterly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per quarter, to the nearest hundredth of a percent.

Answer:

\(T = 100\)

Step-by-step explanation:

See attachment for parallelogram TRIK

Given

\(T = 5x\)

\(I = 2(x + 30)\)

Required

Determine T

Because T and I are opposite angles of the parallelogram, then they are congruent.

i.e.

\(T = I\)

Substitute values for T and I

\(5x = 2(x + 30)\)

Open bracket

\(5x = 2x + 60\)

Collect Like Terms

\(5x - 2x = 60\)

\(3x = 60\)

Solve for x

\(x = \frac{60}{3}\)

\(x =20\)

Recall that:

\(T = 5x\)

\(T = 5 * 20\)

\(T = 100\)

Answer:

Domain: (-∞, -5) ∪ (-1, ∞)

Step-by-step explanation:

Note:

For f(x) > 0: See the points of x for which the graph of f(x) lies above the x-axis.

For f(x) < 0: See the points of x for which the graph of f(x) lies below the x-axis.

We need to find the domain of f(x) for which f(x) < 0

From the graph, we can tell:

f(x) < 0 on (-∞, -5) ∪ (-1, ∞)

Therefore: The domain on which the given graph f(x) is negative, is (-∞, -5) ∪ (-1, ∞)

Answer:

1. 6 (3)^2 = 54 ft ^2

2. 6 (2)^2 = 24 ft ^2

3. 54+ 24 = 78 ft^2

Answer:

Step-by-step explanation:

To slove this problem you need to use the oythargoeam theraom. This formaul is \(a^2+b^2=c^2\). In this case, a is 3 and b is 9. So let us insert this and solve.

Answer:

X=13

Step-by-step explanation:

So if ΔABC ≅ ΔDEC, then that means that ∠B is ≅ ∠E. Therefore you would write the equation 3x=6x-39 and solve for X to get 13.

The type of sampling technique described is stratified random sampling.

In stratified random sampling, the population is first divided into homogeneous subgroups or strata based on some criteria, such as age, gender, income, or education level. In this case, the population was grouped according to age. Then, a random sample is selected from each stratum.

By doing so, the sample represents the entire population better than simple random sampling, as each subgroup is represented proportionally to its size in the population. This technique ensures that there is less variation within each subgroup, which can result in more precise estimates of the population parameters.

In summary, stratified random sampling is a type of probability sampling technique where the population is divided into subgroups, and a random sample is selected from each subgroup.

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The probability of winning $1000 a day for life is approximately 5.245 x 10^-11 and the probability of winning $1000 a week for life is approximately 1.07 x 10^-8. The probability of winning the jackpot ($1000 a day for life) is 1/(60^5 * 4), while the probability of winning $1000 a week for life is 1/(60^5).

In the Florida Lottery Cash4Life game, a player must select five numbers from 1 to 60 and then one Cash Ball number from 1 to 4. The jackpot prize is $1000 a day for life if all five numbers and the Cash Ball match the winning numbers drawn on Monday nights. If just all five numbers match the winning numbers, the player will win $1000 a week for life.
To determine the probability of winning $1000 a day for life, we can use the formula for the probability of independent events: P(A and B) = P(A) x P(B)

(a) To win the jackpot of $1000 a day for life, the player needs to match all five numbers and the Cash Ball. There are 60 options for each of the five numbers and 4 options for the Cash Ball. The total number of possible outcomes is 60^5 (60 choices for each of the five numbers) times 4 (for the Cash Ball). So the probability of winning the jackpot is 1/(60^5 * 4). (b) To win $1000 a week for life, the player needs to match only the five numbers, without considering the Cash Ball. The total number of possible outcomes for this scenario is 60^5. Therefore, the probability of winning $1000 a week for life is 1/(60^5).

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The simplest form is (-2 ±√12)/2.

What is simplification?

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. Simplifying procedures is one way to achieve uniformity in work efforts, expenses, and time. It reduces diversity and variety that is pointless, harmful, or unnecessary.

Here, we have

Given: x = (-4 ±√48)/4

We have to simplify the given term.

x = (-4 ±√48)/4

x =  (-4 ±√12×4)/4

x =(-4 ±2√12)/4

Now, we take 2 as common and get

x = (-2 ±√12)/2

Hence, the simplest form is (-2 ±√12)/2.

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Answer:

360 × 3 ÷ 8 = 135

360 - 135 = 225

The relative frequency is solved and the table of values is plotted

Given data ,

The lunch order is given by the 2 sets of dishes as

A = { Sandwich , Pastas }

Now , the sports activities are given by 2 sets as

B = { Volleyball , Swimming }

From the table of values , we get

The relative frequency is solved as

Relative Frequency = Subgroup frequency / Total frequency

The percentage of Swimming ( sandwich ) = 26/36

Swimming ( sandwich ) = 72 %

And , the percentage of Swimming ( pasta ) = 10/36

Swimming ( pasta ) = 28 %

Now , the percentage of total sandwich = 45/70 = 64 %

And , the percentage of total pasta = 25/70 = 36 %

Hence , the relative frequency is solved

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The data can be tallied into a frequency distribution using a class interval of 100 and a starting point of 0.

To create a frequency distribution, we group the data into intervals or classes and count the number of data points falling within each interval. The class interval represents the range of values covered by each class, and the starting point determines the first interval.

Here is an example of how the data can be tallied into a frequency distribution using a class interval of 100 and a starting point of 0:

```

Class Interval    Frequency

0 - 99            12

100 - 199         18

200 - 299         24

300 - 399         15

400 - 499         10

500 - 599         8

600 - 699         5

700 - 799         3

800 - 899         2

900 - 999         1

```

In this frequency distribution, the data is divided into classes based on the class interval of 100. The first class, from 0 to 99, has a frequency of 12, indicating that there are 12 data points falling within that range. The process is repeated for each subsequent class interval, resulting in a frequency distribution table.

By organizing the data into a frequency distribution, we gain insights into the distribution and patterns within the dataset. It provides a summarized view of the data, allowing us to identify the most common or frequent values and analyze the overall distribution.

In summary, the data has been tallied into a frequency distribution using a class interval of 100 and a starting point of 0. The frequency distribution table presents the number of data points falling within each class interval, enabling a better understanding of the distribution of the data.

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The percentile rank for the employee with 17 years of experience is B: 78.57%.

To find the percentile rank, we first need to arrange the work experiences in ascending order:

2 4 6 7 8 8 8 11 11 11 14 17 21 27

Next, we need to find the position of the employee with 17 years of experience in the list. In this case, the employee is in the 12th position.

Finally, we can use the formula for percentile rank:

Percentile rank = (Position of the employee / Total number of employees) x 100

= (12 / 14) x 100

= 0.857 x 100

= 85.7%

Therefore, the percentile rank for the employee with 17 years of experience is 78.57%. The correct answer is B) 78.57%.

"

Complete question

The work experiences (in years) of 14 employees of a company are 8 21 11 4 14 17 11 8 8 7 2 11 27 6

The percentile rank for the employee with 17 years of experience is: A) 62.96% B) 78.57% C) 68% D) 85.71%

"

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The equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is y = (5/2) * x^2y + 1. This equation represents a curve where the y-coordinate is a function of the x-coordinate, satisfying the conditions.

To determine an equation of the curve that satisfies the conditions, we can integrate the slope function with respect to x to obtain the equation of the curve. Let's proceed with the calculations:

We have:

Point: (0, 1)

Slope: 5xy

We can start by integrating the slope function to find the equation of the curve:

∫(dy/dx) dx = ∫(5xy) dx

Integrating both sides:

∫dy = ∫(5xy) dx

Integrating with respect to y on the left side gives us:

y = ∫(5xy) dx

To solve this integral, we treat y as a constant and integrate with respect to x:

y = 5∫(xy) dx

Using the power rule of integration, where the integral of x^n dx is (1/(n+1)) * x^(n+1), we integrate x with respect to x and get:

y = 5 * (1/2) * x^2y + C

Applying the initial condition (0, 1), we substitute x = 0 and y = 1 into the equation to find the value of the constant C:

1 = 5 * (1/2) * (0)^2 * 1 + C

1 = C

Therefore, the equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is:

y = 5 * (1/2) * x^2y + 1

Simplifying further, we have:

y = (5/2) * x^2y + 1

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The missing step in solving the inequality 4(x – 3) + 4 < 10 + 6x is step 6: The division property of inequality: x > -9

The missing step in solving the inequality 4(x – 3) + 4 < 10 + 6x is step 6: The division property of inequality.

After step 4, which is -2x < 18, we need to divide both sides of the inequality by -2 to solve for x.

However, since we are dividing by a negative number, the direction of the inequality sign needs to be reversed.

Dividing both sides by -2:

-2x / -2 > 18 / -2

This simplifies to:

x > -9

Therefore, the correct answer is x > -9.

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The observed z value is 1. Therefore, the given option that falls under the criteria of the correct answer is Option C.

To find the observed z value we have to use the principles to create a formula.

The formula for finding the value of z is

z = ( x - μ)/(σ/√n)

here,

x = sample mean

μ = population mean

σ = standard deviation of the population

n = sample size

for the given question the values are

x = 50

μ = 45

σ = 5

n = 1

staging the values in the formula

z = (50-45)/(5/√1)

z = 1

The observed z value is 1. Therefore, the given option that falls under the criteria of the correct answer is Option C.

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Answer:

1

Step-by-step explanation:

The opposite of a number is the number on the other side of 0 number line, and the same distance from 0.

110

Step-by-step explanation:

the answer is 110 cause i don't know I just searched the answer for you you welcome

The sets can either be presented in set builder form or roaster form. The

given sets presented in the required form are;

a. The set B is the set of days in the week that starts with letter S

Therefore;

The elements of B are; Saturday, Sunday

In roster method, we have; B = {Saturday, Sunday}

In set builder notation, we have; B = {x | x is a days in the week that starts with letter S}

b. C is the set of letters in PHILIPPINES

In roster form, we have; C = {P, H, I, L, I, P, P, I, N, E, S}

In set builder notation, we have; C = {Letters in the word PHILLIPINES}

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The terms of the polynomial, which has a degree of 2, are ordered as follows in decreasing order: 17x² + 27x

Sums of terms of the form  k⋅xⁿ where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5.

Given polynomial: 5x + 17x² + 22x

We need to simplify this polynomial first.

5x + 17x² + 22x = 27x + 17x²

Now we will put the term with highest degree first and arrange the terms of this polynomial.

17x² + 27x

Since, the highest power of terms in this polynomial is 2.

We can say that the degree of polynomial is 2.

Therefore, the polynomial has a degree of 2 and its terms are arranged in decreasing order as follows: 17x² + 27x.

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Katya initially had 192 pennies, and Mimi initially had 288 pennies. Therefore, together Katya and Mimi lost 96 + 192 = 288 pennies.

Let's assume Katya initially had "k" pennies, and Mimi initially had "m" pennies. According to the given information, we have the following equations:

k + m = 480 (Together, they have 480 pennies)

k - (1/2)k = m - (2/3)m (After losing pennies, they have an equal amount left)

Simplifying equation (2), we have:

1/2 * k = 1/3 * m

To make the equation easier to work with, let's multiply both sides by 6 to eliminate the fractions:

6 * (1/2 * k) = 6 * (1/3 * m)

3k = 2m

Now we have a system of equations:

k + m = 480

3k = 2m

Rearranging equation (2), we get:

m = (3/2)k

Substituting this value of "m" into equation (1):

k + (3/2)k = 480

(5/2)k = 480

k = (480 * 2) / 5

k = 192

Substituting the value of "k" back into equation (1):

192 + m = 480

m = 480 - 192

m = 288

So, Katya initially had 192 pennies, and Mimi initially had 288 pennies.

To calculate the number of pennies they lost altogether, we need to find the difference between their initial amounts and their final amounts.

Katya lost (1/2) * 192 = 96 pennies.

Mimi lost (2/3) * 288 = 192 pennies.

Therefore, together Katya and Mimi lost 96 + 192 = 288 pennies.

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0>1,If a function f is constructed recursively, at least one of its values, f(x), must be defined in terms of f(y), where x>y.

Explanation:

0>1.

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The function rule for the cost involves adding 10, which does not represent a constant multiple of the number of hours. Therefore, this function cannot represent a direct variation.

The first option "This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour" correctly explains that the function represents a direct variation.

A function represents a direct variation if it can be written in the form y=kx, where k is a constant, and y and x are variables. In this case, the cost (y) is directly proportional to the number of hours (x) and the constant rate of change (k) is $5 per hour. Moreover, the fact that the function passes through the origin (0,0) also supports the idea that it represents a direct variation.

The second option "This function represents a direct variation because it has a positive, constant rate of change of $10 per hour" is incorrect. A positive, constant rate of change does not necessarily mean that a function represents a direct variation. For example, the function y=2x+1 has a positive, constant rate of change of 2, but it is not a direct variation.

The third option "This function does not represent a direct variation because it does not represent the cost for 1 hour" is also correct. A direct variation represents a relationship where the ratio of two variables remains constant. In this case, the cost is directly proportional to the number of hours, so the ratio of cost to hours remains constant. However, if the function does not represent the cost for one hour, then it cannot represent a direct variation.

The fourth option "This function does not represent a direct variation because the function rule for the cost is to add $10, not multiply by a constant" is also correct. A direct variation represents a relationship where one variable is a constant multiple of the other. In this case, the function rule for the cost involves adding $10, which does not represent a constant multiple of the number of hours. Therefore, this function cannot represent a direct variation.

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Answer:

\(m_1.m_2 = -1\)

Step-by-step explanation:

Given

2 lines of same slope

A different perpendicular line

Required

Determine the relationship between the lines

We have that, line 1 and line 2 have the same slope;

Represent their slope with m₁

For the third line

Represent the slope with m₂

in coordinate geometry, the relationship between perpendicular line is

\(m_1.m_2 = -1\)

Hence, the required relationship is \(m_1.m_2 = -1\)

49.2 calories are in  would that contribute per serving .

What does a calorie mean ?

Carbohydrates provide 4 calories per gram.

              1 gm Carbohydrates = 4 calories

 then 12.3 gm Carbohydrates  = 12.3 * 4

                                             = 49.2 calories

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Answer:

x=6   y = 128

Step-by-step explanation:

7x+4 = 5x+16

2x+12

x+6                  

7*6 +4 =  46          180-46 = 134

 y+6 = 134

y= 128

Corresponding angles are equal

\(\\ \rm\hookrightarrow 5x+16=7x+4\)

\(\\ \rm\hookrightarrow 2x=12\)

\(\\ \rm\hookrightarrow x=6\)

Now

\(\\ \rm\hookrightarrow y+6=46\)

\(\\ \rm\hookrightarrow y=40\)

The total distance traveled from time t = 0 to t = 2 is 5/6 units.

To find the displacement and total distance traveled, we need to integrate the velocity function over the given time interval.

The velocity function is given as v(t) = t² - t.

To find the displacement, we integrate the velocity function over the interval [0, 2]:

∫[0,2] (t - t) dt

Let's integrate term by term:

∫[0,2] t² dt - ∫[0,2] t dt

Integrating term by term:

= (1/3)t³ - (1/2)t² | [0,2] - (1/2)t² | [0,2]

Now, substitute the limits of integration:

= (1/3)(2³) - (1/2)(2²) - (1/2)(2²) - (1/2)(0²)

= (8/3) - 2 - 2 - 0

= 8/3 - 4

= 8/3 - 12/3

= -4/3

So, the displacement from time t = 0 to t = 2 is -4/3 units.

To find the total distance traveled, we need to consider the absolute value of the velocity function. Since distance cannot be negative, we integrate the absolute value of the velocity function over the interval [0, 2]:

∫[0,2] |t² - t| dt

To calculate the integral of the absolute value function, we split the interval at the point where the function changes sign, which is t = 1. Then we integrate each part separately:

∫[0,1] (t² - t) dt + ∫[1,2] (t - t²) dt

Integrating the first part:

= (1/3)t³ - (1/2)t² | [0,1] - (1/2)t² + (1/3)t³ | [1,2]

Substituting the limits of integration:

= (1/3)(1³) - (1/2)(1²) - (1/2)(0²) + (1/2)(2²) - (1/3)(2³) + (1/2)(1²)

= 1/3 - 1/2 - 0 + 2/2 - 8/3 + 1/2

= -5/6

So, the total distance traveled from time t = 0 to t = 2 is 5/6 units.

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Answer:

a) red

b) red

c) the blue one is y=1/2x+1

Step-by-step explanation:

a. The value of c is 30.

b. X and Y are independent.

c. P{X + Y > 3} = 1 - P{X + Y ≤ 3} = 1 - (3/5).

To determine the value of c, we need to integrate the joint density function over its entire support to obtain a total probability of 1. Integrating f(x) over the given ranges, we have:

∫[1,5] ∫[0,1] (x/5) c dy dx = c * ∫[1,5] [(x/5)*1] dx = c * ∫[1,5] (x/5) dx = c * [(\(x^2\))/10]∣[1,5] = c * (25/10 - 1/10) = c * 2/5.

Since the total probability must equal 1, we have c * 2/5 = 1, which implies c = 5/2 = 2.5 * 2 = 5.

X and Y are independent if and only if their joint density function can be expressed as the product of their marginal density functions.

In this case, the joint density function f(x, y) can be factored into the product of f(x) and f(y), indicating independence. Therefore, X and Y are independent.

To find P{X + Y > 3}, we need to calculate the probability of the event where the sum of X and Y exceeds 3.

This can be done by integrating the joint density function over the region where X + Y > 3.

We can visualize this as the area above the line X + Y = 3 in the X-Y plane. Integrating f(x, y) over this region, we have:

P{X + Y > 3} = 1 - P{X + Y ≤ 3}.

The region X + Y ≤ 3 corresponds to the triangle formed by the lines X = 1, Y = 1, and X + Y = 3. The area of this triangle is (1 * 2)/2 = 1.

Thus, P{X + Y > 3} = 1 - P{X + Y ≤ 3} = 1 - (area of the triangle) = 1 - 1/5 = 4/5.

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