Simplify and write the answer in the exponential form [3 raised to the power 7 and 3 raised to the power 2] × 3 raised to the power 5

The population of the town increased by 1450 from 2008 to 2012. The relative increase, expressed as a percentage, is approximately 43.94%.

To find the absolute increase, we subtract the initial population from the final population: 4750 - 3300 = 1450.

Therefore, the population of the town increased by 1450 individuals over the four-year period.

To calculate the relative increase as a percentage, we use the following formula:

Relative Increase (%) = (Absolute Increase / Initial Population) × 100

Substituting the values into the formula, we have:

Relative Increase (%) = (1450 / 3300) × 100 ≈ 43.94%

This means that the population of the town increased by approximately 43.94% from 2008 to 2012.

The relative increase gives us a measure of the percentage change in the population size.

In this case, the town experienced a significant population growth of 43.94% over the four-year period.

This information can be useful for understanding demographic trends, planning infrastructure, and making policy decisions to accommodate the increased population.

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Answer:

$2.75

Step-by-step explanation:

Because I know ;-;

Answer:

slope: 6/7

y intercept : (0, -6)

Step-by-step explanation:

Answer: The probability that the teacher randomly selects 3 female students is 0.0556.

Explanation :Given ,In an algebra class there are 18 male students and 12 female students. Each day, the teacher randomly selects 3 students from the class to present their work on a problem, If no one student can be selected twice To find :The probability that the teacher randomly selects 3 female students

Formula used: Probability of event =  \(\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}\)Number of total students = 18 + 12 = 30Number of ways to select 3 students from 30 students =  \(_{30}C_3 = \frac{30!}{3!(30-3)!} = \frac{30!}{3!27!} = \frac{30*29*28}{3*2*1} = 4060\)Number of ways to select 3 female students out of 12 female students = \(_{12}C_3 = \frac{12!}{3!(12-3)!} = \frac{12!}{3!9!} = \frac{12*11*10}{3*2*1} = 220\)Therefore, the probability that the teacher randomly selects 3 female students is \(\frac{220}{4060}\) = 0.0556.

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Answer:

4.75

Step-by-step explanation:

The peak current for the given circuit is equal to the absolute value of i.

In an alternating current circuit, the peak current is equal to the maximum value of the current over a complete cycle. Since it is given that the current at any given time t (in seconds) in the circuit is; 'i' (in amperes), the peak current can be calculated as the absolute value of i.

For instance, if the current 'i" at any given time t is 5 A, then the peak current in the circuit will also be 5 A.

This is because the peak current represents the maximum magnitude of the current and is independent of the direction of the current.

Therefore, the peak current for the given circuit is equal to the absolute value of i.

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The probability embarked upon by Joselyn involving the roll of a die for a large number of trials would illustrate an experiment that illustrates the law of large numbers.

The law of large numbers simply describes the repeated performance of an experiment for a large number of trials. The law states that, as the number of experimental trials is increased, the expected value of the experiment is approached.

In Joselyn's experiment, the expected value of obtaining a 5 is 1 ÷ 6 = 0.166. Hence, as the number of trials increases, the probability of having 5 continually approaches 1 ÷ 6 = 0.166.

Hence, the experiment illustrates the law of large numbers.

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The question is -

Joslyn performed an experiment using a die with its faces numbered from 1 to 6. She rolled the die and recorded whether the 5 landed face up. She repeated the process many times and kept a cumulative record of the total number of rolls and the total number of Ss landing face up. The following table shows part of her record.

Suppose Joslyn could roll the die 10.000 times and keep a record of the total number of Ss landing face up in the 10,000 rolls What would such a record Illustrate?

Answer:

we can find the X and the Y than draw it in the graphic

3x-1=3-x

x=1

y=3-1=2

so the y its 2 and x 1

(1,2)

Hey there!

ANSWER: \(\frac{23}{20}\)

EXPLANATION:

To find the answer to your question, you will need to add.

\(\frac{3}{4}+\frac{2}{5}\)

First, multiply the denominator.

\(5*4=20\)

So the denominator will be 20.

Now move on to the numerator. Multiply 5 by 3.

\(5*3=15\)

Now multiply 4 bu 2.

\(4*2=8\)

If you want to get the numerator, add what you got after multiply.

\(15+8=23\)

The numerator is 23. So now let's complete the fraction.

\(\frac{23}{20}\)

This is your answer!

Hope this helps!

\(-TestedHyperr\)

The largest area that can be enclosed if 88 feet of fencing material is available is 484 feet².

Given, a barn has a perimeter of 88 feet.

Now, the perimeter of the rectangle i.e. Barn is 88 feet.

Perimeter = 2(l + b)

88 = 2(l + b)

l + b = 44

b = 44 - l

Now, area = l × b

Area = l × (44 - l)

Area = 44l - l²

On differentiating both the sides, we get

A' = 44 - 2l

On putting A' = 0

44 - 2l = 0

l = 22

Now, for l = 22 the area will be the largest.

if l = 22

then, 22 + b = 44

b = 22

So, the largest area will be 22×22 = 484

Hence, the largest area that can be enclosed if 88 feet of fencing material is available is 484 feet².

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Answer:

Step-by-step explanation:

radius = 32 inches

angle = 60 degrees

Area of segment = 1/2 (60-sin(60)) *(32)^2 = 1/2 (60 - sqrt(3)/2) *(1024) = 598 sq inches

Answer:

11.2m

Step-by-step explanation:

Using Pythagoras,

a²+b²=c²

10²+b²=15²

100+b²=225

b²=225-100

b²=125

b=√125

b=11.2m

Answer:

See attached image.

Step-by-step explanation:

See attached image.

Three consecutive odd integers are -3, -1, and 1.

A detailed explanation of the answer.

To find 3 consecutive odd integers such that 3 times the sum of the first and second equals 13 less than the third, we can follow these steps:

Therefore, the three consecutive odd integers are -3, -1, and 1.

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Answer:

y + 1 = 6(x - 6)

Step-by-step explanation:

y2 - y1 / x2 - x1

-7 - (-1) / 5 - 6

-6/-1

= 6

y + 1 = 6(x - 6)

Answer:

2x+4/ x-1 C

Step-by-step explanation:

Because the y-intercept is -4

Answer: 3.5

Step-by-step explanation:

The length of the rectangular  playground is 241.86 foot.

Given that area of rectangle is 19,500 sq.ft and length of rectangle is three times its width.The area for rectangle is given by formula: A=LW.

Now according to the given condition, L= 3W. Further we'll solve by putting L= 3W in the formula for rectangle.

A=LW

As given A= 19,500 sq.ft and considering L=3W,

19,500 = 3W*W

19,500 = 3W^2

∴ W^2 = 6500

∴ W = \(\sqrt{6500}\)

∴ W = 80.6225 ft. ≈ 80.62 ft.

Now putting the value W = 80.62 in equation L =3W,

L = 3* 80.62

L = 241.86 ft.

The length of the rectangular playground is 241.86 foot.

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Answer:

The value of P(3,3) is 6

Step-by-step explanation:

We have to evaluate P(3,3)

As permutation can be calculated by the formula

Hence, the value of P(3,3) is 6

Given parametric equations are x(t) = Ln(t) and y(t) = (Ln(t))^2. We have to graph the given parametric equations using ln restrictions without a calculator or desmos.

Here, we are going to find the value of t, which helps us to graph the given parametric equation using ln restrictions.Step-by-step explanation to find the value of t are:We have,

x(t) = Ln(t) ⇒ t = e^x(t) ....(1)y(t) = (Ln(t))^2⇒ t = e^(y(t)/2) ...

.(2)From (1) and (2),

we get e^x(t) = e^(y(t)/2)e^(2x(t)) = y(t) ...

(*)We know that the domain of ln x is (0, ∞). Let's determine the range of x(t) and y(t):From equation (1), if t → 0, then x(t) → - ∞From equation (1), if t → ∞, then x(t) → ∞From equation (2), if t → 0, then y(t) → 0From equation (2), if t → ∞, then y(t) → ∞Now,

we can graph the given parametric equations using the following steps: Assign values to t such as

t = 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, .7, 0.8, 0.9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100

Step 2: Calculate x(t) and y(t) corresponding to t values.Step 3: Plot the points obtained in step 2.Step 4: Join all the points obtained in step 3 using a smooth curve.The graph of the given parametric equation is shown below.

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The radius of the curved path of the car such that it is not skidding is 51.2 meters.

A car is moving in a curved path at constant speed. By Newton's laws and equation of friction, we find that the square of the car's speed (v), in meters per second, is directly proportional to the radius of the curve path (s) and to the coefficient of friction (μ), no unit:

v² = k · R · μ

Where k is the constant of proportionality.

If we know that R = 40 m, v = 4√10 m / s, μ = 0.4, v' = 10 m / s, μ' = 0.5, then the resulting radius is:

v'² / (μ' · R') = v² / (μ · R)

10² / (0.4 · 40) = (4√10)² / (0.5 · R)

0.5 · R = (4√10)² · (0.4 · 40) / 10²

0.5 · R = 128 / 5

R = 256 / 5

R = 51.2 m

The radius of the curved path is 51.2 meters.

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An exponential function y = abx for a graph that passes through (2, 1) and (3, 4) is \(y = (1/16)(4)^x\).

To write an exponential function in the form\(y = ab^x\) that passes through the points (2, 1) and (3, 4), follow these steps:
Step 1: Write the general form of the exponential function:
\(y = ab^x\)
Step 2: Plug in the coordinates of the first point (2, 1):
\(1 = ab^2\)
Step 3: Plug in the coordinates of the second point (3, 4):
\(4 = ab^3\)
Step 4: Solve for "a" and "b" using the equations from Steps 2 and 3.
We have two equations:
1)\(1 = ab^2\)
2) \(4 = ab^3\)
Divide equation 2 by equation 1 to eliminate "a":
\((4/1) = (ab^3)/(ab^2)\)
4 = b.

Now that we have found "b," we can find "a" by plugging "b" back into either equation 1 or 2.

We'll use equation 1:
\(1 = a(4)^21 = a(16)\)
a = 1/16
Step 5: Write the final exponential function using the values of "a" and "b":
\(y = (1/16)(4)^x\).

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The research title, "Seasonal distribution of endemic typhus in the Southern United States, 1922-1925" would most likely utilize a longitudinal ecologic study.

The correct option is: b. Longitudinal ecologic study

A longitudinal study is a research design that follows participants over an extended period to establish patterns of change or stability in development. The same group of people is monitored at various stages in their life. For example, a group of people may be followed from the age of 5 to the age of 50, and their health status, life choices, and other variables are monitored at each age interval.

The research title, "Seasonal distribution of endemic typhus in the Southern United States, 1922-1925," would most likely utilize a longitudinal ecologic study since the research is centered on an illness and covers four years. Therefore, researchers are likely to follow up with participants and monitor their health status over an extended period to obtain data on the seasonal distribution of endemic typhus.

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The highest exponent of x in F(x) is 37, which means the algebraic degree of the function is 37.

The function F(x) is a cubic function.

Here, we have,

given function is:

F(x) = α⁴⁹ * x³⁷ + α⁵² * x²⁸ + α⁸¹ * x¹³ + α²⁶ * x⁹ + α³¹ * x

To determine the algebraic degree of the given (7,7)-function F(x), we need to find the highest exponent of x in the function.

F(x) = α⁴⁹ * x³⁷ + α⁵² * x²⁸ + α⁸¹ * x¹³ + α²⁶ * x⁹ + α³¹ * x

The algebraic degree of a polynomial function corresponds to the highest exponent of the variable in the function.

Linear functions have an algebraic degree of 1, affine functions have an algebraic degree of 1 or 0, quadratic functions have an algebraic degree of 2, and cubic functions have an algebraic degree of 3.

so, we get,

The highest exponent of x in F(x) is 37, which means the algebraic degree of the function is 37.

Therefore, the function F(x) is a cubic function.

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Answer:

989 in^2

Step-by-step explanation:

The surface area of the larger cube is

SA = 5 s^2  because she will stain all the sides but the bottom one

SA = 5 * 11^2 = 5*121 = 605

The surface area of the smaller cube is

SA = 6s^2 since she will stain all sides

SA = 6* 8^2 =6*64 =384

Add both surface areas together

605+384

989

Answer:

989 square inches

Step-by-step explanation:

Let's start by finding the surface area of the bottom cube. It has six sides with side length 11, meaning that each side has area 11^2=121. Multiplying this by 5(since she's not staining the bottom), you get 605. For the second sphere, you can calculate this with the expression 6 * 8^2=384. Adding these together, you get a total surface area of 989 square inches. Hope this helps!

Answer:

44

Step-by-step explanation:

Il faut se rendre compte que s'il sera deux fois plus âgé que la plante, la différence entre eux doit être égale à l'âge de la plante.

Par exemple,

Si j'ai 5 ans, la personne deux fois mon âge doit avoir 10 ans. La différence est 5. Pareil comme mon âge

Si j'ai 4 ans, la personne deux fois mon âge a 8 ans. La différence sera égale à mon âge (4).

Maintenant à propos le question,

Edgar = 33 ans

Il est trois fois plus âgé que la plante, alors on peux trouver l'âge de la plante.

Âge de la plante = 33 ÷ 3 = 11

Maintenant qu'on sait les âges des deux, on peut trouver la différence.

Différence d'âge = 33-11 = 22

Différence d'âge = âge de la plante.

La plante = 22 ans

Edgar = 22 × 2 = 44 ans

To translate shape A by (3, -3), the top-left coordinate of shape B would be obtained by adding 3 to the x-coordinate and subtracting 3 from the y-coordinate of shape A. The specific coordinates can only be determined with the knowledge of the original shape A.

To translate shape A by (3, -3), we need to shift each point of shape A three units to the right and three units down. Let's assume the top-left coordinate of shape A is (x, y).

The top-left coordinate of shape B after the translation can be found by adding 3 to the x-coordinate and subtracting 3 from the y-coordinate of shape A. Therefore, the top-left coordinate of shape B would be (x + 3, y - 3).

It's important to note that without knowing the specific coordinates of shape A, I cannot provide the exact values for the top-left coordinate of shape B. However, you can apply the translation by adding 3 to the x-coordinate and subtracting 3 from the y-coordinate of shape A to find the top-left coordinate of shape B in your specific case.

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