Rewrite f(t) = 0.4 * (1.16) ^ (t - 1) in the form y=a(1+r)^ prime .y=a(1-r)^ prime to determine whether it represents exponential growth or exponential decay Round a and to the nearest hundredth if necessary

The line that represents the function y = 1/2x + 3 is line r.

Here we can see some graphed lines, and we want to see which one of these represents the linear function:

f(x) = (1/2)*x + 3

First, we can see that the slope is positive, which means that the line goes upwards (when reading from left to right).

And we can see that the y-intercept is 3, then the line should intercept the y-axis at y = 3.

With that we can conclude that the correct line is r.

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Answer:

26

Step-by-step explanation:

Let jaya's age be a, so consecutive EVEN #s can be written as

a, a+2, a+4

sum = 84 = 3a +6

so 3a = 78

a=26

given information are :- test mean () = 25.5 populace sd () = 5.3 example size (n) = 360 a).z critical value for 95% confidence level,

both followed tests be:- the 95% confidence interval for the mean load of every one of the one-year-old child young men in the US.

To get a 95% confidence interval, we should incorporate the focal 90% of the probability of the normal distribution. On the off chance that we incorporate the focal 90%, we leave out a sum of α = 10% in the two tails, or 5% in each tail, of the normal distribution.

To catch the focal 95%, we should go out 1.645 "standard deviations" on one or the other side of the determined example mean. The value 1.645 is the z-score from a standard normal probability distribution that puts an area of 0.90 in the middle, an area of 0.05 in the extreme left tail, and an area of 0.05 in the extreme right tail.

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The complete question is:

According to the National Health Statistics Reports, a sample of 360 one-year-old baby boys in the United States had a mean weight of 25.5 pounds. Assume the population standard deviation is σ = 5.3 pounds.

a. Construct a 95% confidence interval for the mean weight of all one-year-old baby boys in the United States

b. Should this confidence interval be used to estimate the mean weight of all one-year old babies in the United States? Explain.

c. Based on the confidence interval constructed in part (a), is it likely that the mean weight of all one-year-old boys is less than 28 pounds?

Answer: (11,4)

Step-by-step explanation:

To make a right triangle it has one horizontal line, one vertical line, and one diagonal line.

We can eliminate the answers (8,12) and (19,12) because that would only create a straight horizontal line when paired with the coordinates we have.

Now we have (8,20) and (11,4) left. Since (5,12) and (11,12) are horizontal with eachother we need one point that is vertical with either (5,12) or (11,12) & diagonal

(11,4) is vertical with (11,12)since their x-axis are the same, diagonal with (5,12), so the point (11,4) will create a triangle

The coordinate pair for the third vertex would create a right triangle is ​(8, 12)​, the correct option is A.

A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse. The angle of a right angle is always 90 degrees.

Given;

The two vertices of a right-angled triangle are A(5, 12) and B(11, 12).

The given points on the co-ordinate plane as shown in the attached figure;

We will then see that only the point C(11, 4) will lie exactly below the point B(11, 12). Also, the segment AB and BC are the legs of the triangle, AC is the hypotenuse;

The lengths of the three sides are;

AB=11-5=6,

BC 12-4= 8,

AC=√(AB^2+ BC^2)

=√(6^2 +8^2)= ✓100 = 10.

Therefore, coordinates of triangle will be ​(8, 12)​

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Recapturing a higher percent of marked alligators affects the estimated total population by making it high enough to support an accurate estimate.

This is referred to as the total number of species or organisms in an area at a given period of time.

Recapture rates are high enough to support an accurate estimate. The Lincoln-Peterson calculation tends to overestimate the population size, especially if the number of recaptures is small.

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As per the above given question the reflection of m∠O=112°.

A process of introspection or self-examination is reflection. It entails reflecting critically on one's thoughts, feelings, and experiences in order to comprehend oneself better. Self-awareness and insight can be developed through reflection, which can result in personal development and change.

In a larger sense, reflection also refers to the bouncing back of light, sound, or other waves from a surface and is employed in many disciplines, including arithmetic, computer science, and optics. The capacity of a computer program to review and alter its own structure and behavior at runtime is known as reflection in computer programming.

According to question:

Here are given m∠G=61 m∠f=7

From angle sum property of triangle, we get in ΔGFA

m∠G+m∠F+m∠O=180°

⇒61+7+m∠O=180

⇒68+m∠O=180

Therefore m∠O=180-68=112

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The volume of the solid given by rotating the region bounded by the curves y = x^2, x = 5, and y = 0 about the x-axis is 625π.

When the region bounded above by the graph of f, below by the x-axis, and on the sides by x = a and x = b is rotated about the x-axis, the volume V of the generated solid is given by V = ∫ab π [f(x)]^2 dx. We can also find solids by revolving curves about the y-axis.

Whereas the basic formula for the area of a rectangular shape is length * width, the basic formula for volume is length * width * height. How we refer to the different dimensions does not change the calculation. We may, for example, use depth instead of height.

In this case, the bounds of integration are from 0 to 5. The radius function is going to be:

r (x) = x^2

Now, substitute the value into the formula for the disk method:

V = π * ∫ba * [r(x)]^2 * dx

So, in this case it will be:

V = π * ∫5 0 * [x^2]^2 * dx

= π * ∫5 0 * x^4 * dx

= π * x^5 / 5 ∣ 5 0

= π * ((x^5 / 5) – (0 / 5))

= 625π

Hence, the volume of the solid is 625π.

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The circumference of the circle in terms of π is 8π yards.

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.

Perimeter refers to the total outside length of an object,

here, we have,

the diameter of the circle = 8yrd

the circumference of the circle in terms of π

=π  * 8

= π8 yrd.

Hence, The circumference of the circle in terms of π is 8π yards.

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Answer: yes

Step-by-step explanation:

The graph presents information gathered through a survey or questionnaire, and the information is presented as a percentage to show the proportion of participants who answered in a particular way.

Percentage is a mathematical concept that represents a proportion of a whole as a fraction of 100. It is used to express how much of a whole something is and is commonly used in statistics and data analysis.

The bar graph shows three different percentages: 1.59%, 17.46%, and 25.4%. To verify these percentages, we need to know the total number of participants who answered the question and the number of participants who answered in a particular way.

If 100 participants answered the question, then 1.59% would represent 1.59 participants, 17.46% would represent 17.46 participants, and 25.4% would represent 25.4 participants.

It is important to consider whether the percentages reported in this graph are likely to be representative of all people.

This will depend on a number of factors, including the sample size, the method used to select participants, and the representativeness of the sample in relation to the population as a whole.

If the sample size is small, or if the participants were selected in a biased way, then the percentages may not be representative of all people.

If, however, the sample size is large and the participants were selected randomly, then the percentages may be representative of the population as a whole.

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The value of n that makes the equation true is 0.

In Mathematics, an exponent is sometimes referred to as power and it can be defined as a mathematical operation that is used in conjunction with an algebraic expression to raise a quantity to the power of another and it is generally written as;

bⁿ

Where:

the variables b and n represent numerical values or an algebraic expression.

By applying the property of exponents based on the law of indices for powers and division, we have the following:

Expression = 85^n/85^6 = 85^{-6}.

Expression = 85^{n - 6} = 85^{-6}

Since the powers both have a common base, we have:

n - 6 = -6

n = 6 - 6

n = 0.

Check:

85^0/85^6 = 85^{-6}

1/85^6 = 85^{-6}

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The Answer is 1440 There are two possibilities for the person who demands to be either first or last: they can be first in line, or they can be last in line.

The problem is asking for the number of ways 7 engineering students can line up for presentations at a hiring fair, where one person demands to be either the first or last in line.

If they are first in line, then there are 6 students left to line up. The number of ways to line up 6 students is 6!, which is 720.

If they are last in line, then there are also 6 students left to line up, and the number of ways to line up 6 students is 6! or 720.

So, the total number of ways to line up the 7 students is 720 + 720 = 1440.

Therefore, the answer to the question is 1440.

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So, during a two-year period, we may anticipate 0.8 loads. As a result, the likelihood of more than 8 loads occurring in a 2-year period is 0.001. As a result, a time period of at least 2.303 years is necessary to assure that the likelihood of no loads occuring is at most 0.2.

A discrete probability distribution is a Poisson distribution. It expresses the likelihood of an event occurring a specific number of times (k) during a certain time or space period. The mean number of occurrences, (lambda), is the solitary parameter in the Poisson distribution.

Here,

a) The expected number of loads during a 2-year period can be calculated using the Poisson distribution formula:

E[X] = λt, where λ is the average rate of occurrences (mean time between occurrences) and t is the time period.

E[X] = λ * 2 years = 0.4 year^-1 * 2 years = 0.8 loads

So, we can expect 0.8 loads to occur during a 2-year period.

b) The probability that more than 8 loads occur during a 2-year period can be calculated using the cumulative distribution function of the Poisson distribution:

P(X > 8) = 1 - P(X <= 8)

We can use a Poisson distribution calculator or table to find the cumulative distribution function for P(X <= 8) and subtract it from 1 to find P(X > 8).

P(X > 8) = 1 - P(X <= 8) = 1 - 0.999 = 0.001

So, the probability that more than 8 loads occur during a 2-year period is 0.001.

c) To find the time period in which the probability of no loads occurring is at most 0.2, we can find the value of t such that P(X = 0) <= 0.2.

P(X = 0) = e^-λt

Setting P(X = 0) <= 0.2 and solving for t, we get:

0.2 >= e^-λt

ln(0.2) >= -λt

-ln(0.2) / λ >= t

Substituting λ = 0.4 year^-1, we get:

-ln(0.2) / 0.4 >= t

t >= (-ln(0.2) / 0.4) years = 2.303 years

So, we can expect 0.8 loads to occur during a 2-year period. So, the probability that more than 8 loads occur during a 2-year period is 0.001. So, a time period of 2.303 years or longer is required to ensure that the probability of no loads occurring is at most 0.2.

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The probability that the plant died because the neighbor forgot to water it is (1 - q) x (1 - %).

Let p = the probability that the plant will die without water, q = the probability that the plant will die with water, and r = the probability that the neighbor will remember to water the plant.

The probability that the plant died because the neighbor forgot to water it is equal to the probability that the plant would have survived had the neighbor remembered to water it, multiplied by the probability that the neighbor did not remember to water it.

P(plant died due to neighbor not watering) = P(plant survived with neighbor watering) x P(neighbor not remembering)

= (1 - q) x (1 - r)

= (1 - q) x (1 - % certain the neighbor will remember)

= (1 - q) x (1 - % certain)

= (1 - q) x (1 - %)

Therefore, the probability that the plant died because the neighbor forgot to water it is (1 - q) x (1 - %).

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Answer:

Decimal0.395062

Step-by-step explanation:

16

(18)(1)

2

32/81

Answer:

The value of (16/81)^1/2 is  4/9.

Step-by-step explanation:

What is the expression?

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

= the square root of 16/81

=4/9.

The value of (16/81)^1/2 is  4/9.

Answer:

inverse functions of each other

The values are:

Sin Ф = 4/5

Cos Ф = -3/5

Tan Ф = -4/3

Cosec Ф = 5/4

Sec Ф = -5/3

Cot Ф = -3/4

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

The point P = (12,-9) on the circle x² + y² =2 is also on the terminal side of an angle Ф.

This means,

Base = -9

Perpendicular = 12

Applying Pythagorean theorem.

Hypotenuse² = Base² + Perpendicular²

Hypotenuse² = (-9)² + 12²

Hypotenuse² = 81 + 144

Hypotenuse² = 225

Hypotenuse = √225 = 15

Hypotenuse = 15

Now,

Sin Ф = Perpendicular / Hypotenuse = 12/15 = 4/5

Cos Ф = Base / Hypotenuse = -9/15 = -3/5

Tan Ф = Perpendicular / Base = -12/9 = -4/3

Cosec Ф = Hypotenuse / Perpendicular = 15/12 = 5/4

Sec Ф = Hypotenuse / Base = -15/9 = -5/3

Cot Ф = Base / Perpendicular = -9/12 = -3/4

Thus,
The values are given above.

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The population after 1, 2, and 3 years are 2800, 3920, and 5488.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

y = 2000 x [tex](1.4)^x[/tex]

Now,

For x = 1,

y = 2000 x 1.4

y = 2800

For x = 1,

y = 2000 x 1.4²

y = 3920

For x = 1,

y = 2000 x

y = 2000 x 1.4³

y = 5488

Thus,

After 1, 2, and 3 years the populations are 2800, 3920, and 5488.

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Answer:

x = 50

Step-by-step explanation:

50 + 2x = 150

2x = 100

x = 50

There are 107 different methods to disembark.

When you mention "no two folks exit on the same floor," I suppose you mean that each of the seven people exits the elevator on a different floor.

The first person can exit the elevator on any of the building's 10 levels, followed by the second person on any of the other 9 floors, and so on.

The total number of ways in which the 7 people can exit the elevator from different floors is 10P7 ways.

The first person, as well as the second, third, and other people, can exit from any of the ten floors, thus we take this into consideration when calculating the overall number of exits. Therefore, there are 107 different methods to disembark.

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Answer:

Below

Step-by-step explanation:

y = 1/2 x + 1

y = 3/2x + 4        Use first equation to sub in for y

1/2 x + 1  = 3/2 x + 4

-3 = x       then use this value in one of the equations to calc  y

y = 1/2 x + 1

y = 1/2 (-3) + 1 =  - 1/2

Answer: 5^6

Step-by-step explanation:

First, you have to simplify the numbers so that all of them share the same base. For this problem, the base for all of these numbers would be 5. So now the equation looks like this:

5^2 * 5^1 * 5^3

Next we have to turn all of these numbers into one. Whenever you multiply the numbers, all you have to do is add the exponents together. So now it will look like this:

5^(2+1+3)

Add the numbers up and you get your answer.

5^6

(a) the slope of the first equation is 2/3 the slope of the second equation.

(b) the y-intercept of the first equation is 6/4 = 3/2 the y-intercept of the second equation. (c) the value of x is 2 and y is 10.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. Finding the values of the variables that result in the equality is the first step in solving an equation with variables.

Given that, the equations are 6y = 12x + 36 --------- (i)

and 15y = 45x + 60 ----------------- (ii)

divide equation (i) by 6, we get

y = 2x + 6

divide equation (ii) by 15, we get

y = 3x + 4

the slope of equation (i) is 2 and the slope of equation (ii) is 3.

(a) So the slope of the first equation is 2/3 the slope of the second equation.

In equation (i) at x=0

y = 2*0 + 6

y = 6

In equation (ii) at x=0

y = 3*0 + 4

y = 4

(b) So the y-intercept of the first equation is 6/4 = 3/2 the y-intercept of the second equation.

Putting the value of y from equation (ii) in equation (i)

3x + 4 = 2x + 6

3x - 2x = 6 - 4

x = 2

from equation (i)

y = 2x + 6

y = 2*2 + 6

y = 4 + 6

y = 10

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The solution to the equation is x = 16/3

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

-3/2x+4=-4

The above equation is a linear equation

A linear equation is represented as

y = mx + c

Where

slope = m

y-intercept = c

Next, we graph the equation

See attachment for the graph

From the graph, we can see that the solution is

x = 16/3

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