a demographer uses birth records to keep track of the ages of all the people born in a small town. they keep a log of all the ages in years. this variable is best described as...

Answer:

Step-by-step explanation:

[tex]20y^2+5y[/tex]

[tex]20yy+5y[/tex]

[tex]5\cdot \:4yy+5\cdot \:1\cdot \:y[/tex]

[tex]5y\left(4y+1\right)[/tex]

Step-by-step explanation:

5y(4y + 1)

= 20y × y + 5y × 1

= 20y² + 5y

NB: BODMAS

The equation y-4 = 5/3 ( x+3). can be written in standard form as 3y-5x = 15

A linear equation is the equation in which the highest power of it's variable is 1. A linear equation can be with a variable or more. y-4 = 5/3 ( x+3) is an example of linear equation with two variables.

The standard form of writing the linear equation is in the form Ax+By = C

Where C Is the constant and A and B are the coefficient of the variable x and y.

y -4 = 5/3 (x+3)

opening the parentheses

y = (5/3)x +5

y - (5/3)× = 5

multiply both sides by 3

3y -5x = 15

therefore the standard form of writing y-4 = 5/3 ( x+3) is 3y -5x = 15

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Answer:

11

Step-by-step explanation:

picture is too blurry, but here is the process to solve it

L = 3+2w

total length = 30 inches = 2L +2w

so 2w=30-2L

L= 3+2w = 3+30-2L

so 3L =33

L =11

Answer:

-------------------------------------

Let the integers be:

Twice the sum of the second and third exceeds 3 times the first by 32:

Solve it for x:

The domain of the area function is given by the following interval:

(0, 40).

The domain of a function is the set composed by all the input values that the function accepts.

On the graph, the domain of the function is given by the values of x.

Considering the graph, the domain is given by the following interval:

(0, 40).

It is an open interval because if x = 0, then the length is of zero, and if x = 40, then the width is of zero, meaning that these dimensions are not possible.

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The number of white balls is equally likely to be any number between 1 and n − 1.

This problem can be solved by considering the number of ways to get a certain number of white balls in the bin. Since each ball can either be white or black, there are 2^n possible sequences of n balls in the bin.

Now consider the number of ways to get exactly k white balls in the bin. It can be done in the following way:

Choose k white balls out of n balls, which can be done in C(n, k) ways, and then arrange the k white balls and n-k black balls in (n-k + k)!/(n-k)!k! ways.

Therefore, the number of ways to get exactly k white balls in the bin is C(n, k)(n-k + k)!/(n-k)!k! = C(n, k)(n!)/(n-k)!k!.

Since each sequence of balls is equally likely, it follows that the number of white balls is equally likely to be any number between 1 and n - 1.

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--The given question is incomplete; the complete question is

"Consider the following balls-and-bin game. We start with one black ball and one white ball in a bin. We repeatedly do the following: choose one ball from the bin uniformly at random, and then put the ball back in the bin with another ball of the same colour. We repeat until there are n balls in the bin. Show that the number of white balls is equally likely to be any number between 1 and n − 1."--

The total surface area and lateral area have a difference of 48 square inches. (Correct choice: D)

In this problem we find a right prism with a rectangular base, of which we must determine its lateral area and its total surface area, both in cubic inches.

Lateral area is the sum of all faces A and C (four rectangles), whereas total surface is the sum of lateral area and all faces B (two rectangles). Area formula for rectangles is shown below:

A = w · l

Where:

Now we proceed to determine the lateral area and the total surface area of the prism:

Lateral area

A' = 2 · (3 in) · (5 in) + 2 · (8 in) · (5 in)

A' = 30 in² + 80 in²

A' = 110 in²

Total surface area

A = A' + 2 · (8 in) · (3 in)

A = 110 in² + 48 in²

A = 158 in²

And the difference between total surface area and lateral area is equal to  48 in².

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Jane continues her triathlon training by swimming, then biking 16 miles south and running 12 miles west. Her trainer meets her at the end of the run.

Jane has traveled a total of 28 miles - 16 miles biking and 12 miles running.

Jane is training for a triathlon and is putting in the work to reach her goal. After swimming a few laps in the health club, she bikes 16 miles south. She then runs 12 miles west, bringing her total distance to 28 miles. When she has finished her run, her trainer meets her to check on her progress and offer support for her continued success. Jane's hard work and dedication to her training is admirable and demonstrates her commitment to completing her triathlon. The support from her trainer will be invaluable in helping her reach her goal.

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option A is correct-Ben is 11/P + 6 old now in terms of P .

Six years ago,

Anita was P times as old as Ben was.

Let Ben's age now be B.

let Anita's age now be A.

linear equation in two variables is as follows,

(A-6) = P(B-6)

we know A = 17,put the value of A,

17 - 6 = P(B - 6)

11 = P(B - 6)

11/P = B- 6

B = 11/P + 6

therefore,

Ben is 11/P + 6  old now in terms of P .

linear equation

A linear equation in two variables is of the form Ax + By + C = 0, in which A and B are the coefficients, C is a constant term, and x and y are the two variables, each with a degree of 1.

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The probability would be length of the interval [50.75, 51.25] divided by the length of the interval [47.0, 57.0] which is 0.05

Probability :Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

Now we have given :-the lengths of her classes are uniformly distributed between 47 and 57 minutes.

so probability hat a given class period runs between 50.5 and 51 minutes=

(51-50.5)/(57-47)

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The probability would be length of the interval [50.75, 51.25] divided by the length of the interval [47.0, 57.0] which is 0.05

Probability :Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

Now we have given :-the lengths of her classes are uniformly distributed between 47 and 57 minutes.

so probability hat a given class period runs between 50.5 and 51 minutes= (51-50.5)/(57-47) = 0.05

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Give the expression in terms of a, k, and t is g(t+1/k) = a2^(k(t+1/k)) = a2^kt * 2^(1/k)

The population doubles when P(t) = 2 * P(0), so we can set up the equation:

2 * 55 = 20^(5t)

Solving for t:

t = log(2)/(5 * log(20)) = log(2)/log(400)

The population doubles after approximately 0.173 years or 63.1 days.

g(t+1/k) = a2^(k(t+1/k)) = a2^kt * 2^(1/k)

Interpretation: g(t+1/k) is the population at time t+1/k, where a and k are positive constants. The population at t+1/k is equal to the population at time t multiplied by 2^(1/k). This means that if k is a large number, the population will change very little over time, if k is a small number, the population will change more quickly.

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The percentage of oak trees in park is 7.14% and there are 14 times more trees in the park than giant oak trees.

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred.

The total number of trees in a park is = 56

The number of giant oak trees in the park is = 4

To find the percentage of oak trees, use the formula -

(Number of Oak Trees/Total number of trees) × 100

Substitute the values into the formula -

(4/56) × 100

(1/14) × 100

7.14%

The number of times (x) that bigger oaks is lesser in comparison to other trees can be found using the arithmetic operation of division.

The equation is -

4x = 56

x = 56/4

x = 14

Therefore, there are 14 times more trees.

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Here is an example of how the code to rotate the cube could be implemented in Python:

class RooCube:

   def __init__(self):

       self.colors = ["w", "b", "o", "g", "y", "r"]

   def left(self):

       self.colors = [self.colors[1], self.colors[5], self.colors[2], self.colors[3], self.colors[0], self.colors[4]]

   def right(self):

       self.colors = [self.colors[4], self.colors[0], self.colors[2], self.colors[3], self.colors[5], self.colors[1]]

   def up(self):

       self.colors = [self.colors[3], self.colors[1], self.colors[0], self.colors[5], self.colors[4], self.colors[2]]

   def down(self):

       self.colors = [self.colors[2], self.colors[1], self.colors[5], self.colors[0], self.colors[4], self.colors[3]]

class RooRunner:

   def __init__(self):

       self.cube = RooCube()

   def rotate(self):

       direction = input("What direction would you like to rotate (left, right, up, down)? ")

       if direction == "left":

           self.cube.left()

       elif direction == "right":

           self.cube.right()

       elif direction == "up":

           self.cube

This would give us the required result.

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The value of BD is 12cm.

What is  Pythagoras' theorem?

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Here, we have

BE = ED  (as E is the center of BD - property of a kite).

By Pythagoras' theorem:

10² = 8² + BE²

BE² = 10² - 8² = 36

BE = 6

So BD = 2*6 = 12.

Hence, the value of BD is 12cm.

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Larry ran at an average velocity of 66.7 m/min to the lamppost 200 m away and an average velocity of 250 m/min to the tree 1000 m away.

v1 = 200 m / 3 min = 66.7 m/min

v2 = 1000 m / 4 min = 250 m/min

Larry left his home at 9:06 and ran at a constant speed to the lamppost 200 m away. He arrived at the lamppost at 9:09. Immediately after arriving, he turned around and ran to a tree 1000 m away, arriving at 9:13. To find his average velocity during each interval, we can divide the distance traveled by the time it took to travel the distance. For the first interval, Larry traveled 200 m in 3 minutes, so his average velocity was 200 m divided by 3 min, or 66.7 m/min. For the second interval, Larry traveled 1000 m in 4 minutes, so his average velocity was 1000 m divided by 4 min, or 250 m/min.

Larry ran at an average velocity of 66.7 m/min to the lamppost 200 m away and an average velocity of 250 m/min to the tree 1000 m away.

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The table 1  represent the function From the given figure.

What is function ?

The function in mathematical terms is the mapping of each member of a set (named as a domain) to another set of members (named as a codomain). This term has a different meaning from the same word that is used every day, such as "the tool works well." The concept of function is one of the basic concepts of mathematics and any quantitative science. The terms "function", "mapping", "map", "transformation" and "operator" are usually used synonymously.

In function, there are several important terms, including:

The domain is the area of ​​origin of the function f denoted by Df.

Codomain is the area where the f function area is denoted by Kf.

The range is the result area which is a subset of the codomain. The function range f is denoted by Rf.

PROPERTIES OF FUNCTIONS

1. INJECTIVE FUNCTION

Called one-on-one function. Suppose the function f represents A to B, then the function f is called a one-on-one function (injective), if each two different elements in A will be mapped to two different elements in B. Furthermore, it can be said briefly that f: A → B is injective function if a ≠ b results in f (a) ≠ f (b) or equivalent if f (a) = f (b) then the effect is a = b.

2. SURJECTIVE FUNCTION

Function f: A → B is called a function to or objective function if and only if for any b in the B domain can be at least one an in domain A so f (a) = b applies. In other words, a codomain of the objective function is the same as its range.

3. BIJECTIVE FUNCTION

A mapping off: A → B is such that f is both an injective and objective function at once, so it is said "f is a function of wisdom" or "A and B are in one-to-one correspondence".

Therefore, The table 1  represent the function From the given figure.

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Answer:

The gas mileages (in miles per gallon) for 35 cars are shown in the frequency distribution. This means that the gas mileage of 35 cars has been recorded and grouped into categories. The categories are 27-30, 31-34, 35-38, and 39-42. The frequency is the number of cars in each category. For example, there are 12 cars that have a gas mileage between 27 and 30 miles per gallon. Approximating the mean of the frequency distribution means finding the average gas mileage of all the 35 cars. To do this, you need to add the gas mileages of all the 35 cars and divide the sum by 35. The approximate mean of the frequency distribution is 33.4 miles per gallon. An analogy that can help you understand this concept is that of a classroom full of students. If you want to calculate the average height of the students, you would need to add up the heights of all the students and divide the sum by the total number of students. The same concept applies to the frequency distribution.

When the indicated sides are multiplied by the figure's area, 44 is the result.

An expression for the size of a planar layer contained within a two-dimensional figure, form, or plane is called an area. 2D shapes that can be drawn on a plane are included in layered shapes. B. A parallelogram, square, triangle, rectangle, trapezoid, and circle.

polygon:

A two-dimensional object made of only straight lines is a polygon. Triangles, hexagons, and pentagons are a few examples of polygons. The number of sides is indicated in the shape's name. For instance, a rectangle has four sides and a triangle has three.

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g(f(4)) means to first find f(4) and then use that result as the input for g(x).

So,

f(4) = 4 - 7 = -3

then we use the result, -3 as the input for g(x)

g(-3) = (-3)^2 = 9

Therefore, g(f(4)) = 9

The solution of the inequality -3x - 3 ≤ 6 is x ≥ -3 represented by (D).

An equation is an expression that shows the relationship between numbers and variables. Equations are either linear, quadratic, cubic and so on

Inequality is an expression that shows the non equal comparison between two or more numbers and variables.

Number line contains number placed at regular intervals on a straight line.

Given the inequality:

-3x - 3 ≤ 6

adding 3 to both sides:

-3x - 3 + 3 ≤ 6 + 3

-3x ≤ 9

Dividing by -3:

x ≥ -3

The solution is D. It a solid dark circle beginning from -3 to the right.

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The sample space for rolling a fair eight-sided die is S = {1, 2, 3, 4, 5, 6, 7, 8}; the correct option is D

Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes. The likelihood of an event occurring might range from 0 to 1. A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results.

Given;

An eight-sided die,

The sample space=?

Now, when eight sides die is tossed there will be 8 sample spaces that are;

1, 2, 3, 4, 5, 6, 7, 8,

Hence, S = {1, 2, 3, 4, 5, 6, 7, 8}

Therefore, the probability sample space will be S = {1, 2, 3, 4, 5, 6, 7, 8}

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Answer:

46.05 years

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]

Given:

Substitute the given values into the continuous compounding formula and solve for t.

[tex]\implies 1000=100e^{0.05t}[/tex]

[tex]\implies 10=e^{0.05t}[/tex]

[tex]\implies \ln 10=\ln e^{0.05t}[/tex]

[tex]\implies \ln 10=0.05t\ln e[/tex]

[tex]\implies \ln 10=0.05t[/tex]

[tex]\implies t=\dfrac{1}{0.05}\ln 10[/tex]

[tex]\implies t=20\ln 10[/tex]

[tex]\implies t=46.0517018... \rm years[/tex]

Therefore, it will take 46.05 years for the initial investment of $100 to reach $1000.

The solution of m+n+p = 462+40+3 = 505.

The set is divided into several parts: the large 3x4x5 parallelepiped, 6 external parallelepipeds that share a face with the large parallelepiped and have a height of 1, 1/8 spheres (one at each vertex of the large parallelepiped), and 1/4 cylinders connecting each adjacent pair of spheres.

The parallelepiped has a volume of $3 times 4 times 5 = 60 cubic units.

The external parallelepipeds have a volume of $2(3 times 4 times 1)+2(3 times 5 times 1)+2(4 times 5 times 1)=94$.

Each of the 1/8 spheres has a radius of 1. Their combined volume is [tex]\frac{4}{3} \pi[/tex].

There are 12 of the 1/4 cylinders, allowing for the formation of 3 complete cylinders. Their volumes are 3[tex]\pi[/tex], 4[tex]\pi[/tex], and 5[tex]\pi[/tex], totaling 12[tex]\pi[/tex].

The total volume of these parts is 60+94+ [tex]\frac{4}{3} \pi[/tex] +12[tex]\pi[/tex] = [tex]\frac{462 + 40\pi }{3}[/tex]. Thus, the solution is m+n+p = 462+40+3 = 505.

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An explicit definition can give a value for the nth item in a sequence by simply using the value of n: an = -27 * (-1/3)n-1      

What is Geometric Progression ?

Geometric Progression can be defined as the sequence of numbers in which the common ratio between any consecutive numbers is same.

When you say, "each term in the sequence is obtained by multiplying -1/3 to the previous term," that is the recursive definition.

An explicit definition can give a value for the nth item in a sequence by simply using the value of n:

an = -27 * (-1/3)n-1        

(more generally written as:  an = a1 * (-1/3)^n-1 )  

if n = 1

we get,

an = -27 *1 = -27

if n=2

we get,

an = 9

and if n=3

we get,

an = -3

similarly if n=4

than an= 1

Therefore, An explicit definition can give a value for the nth item in a sequence by simply using the value of n: an = -27 * (-1/3)n-1      

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The cost to ship the small boxes and large boxes are 4 and 10 dollars respectively.

The postal service offers flat-rate shipping for priority mail in special boxes. Today, Jaden shipped 4 small boxes and 2 large boxes, which cost him $36 to ship. Meanwhile, Pamela shipped 3 small boxes and 9 large boxes, and paid $102.

The system of equation of represent the situation is as follows:

let

x = cost for small boxes

y = cost for large boxes

Hence,

4x + 2y = 36

3x + 9y = 102

Let's find how much used to ship the two sizes of box.

Multiply equation(i) by 4.5

18x + 9y = 162

3x + 9y = 102

Subtract the equations

15x = 60

x = 60 / 15

x = 4

Therefore,

2y = 36 - 4x

2y = 36 - 4(4)

2y = 36 - 16

2y = 20

y = 20 / 2

y = 10

Therefore,

cost for small boxes = 4 dollars

cost for large boxes = 10 dollars

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The reason behind the the functions f and g are differentiable for all real numbers for the limit 1 < c < 3 is the limitation of constant term.

Function in the math is known as  a kind of rule that, for one input, it gives you one output.

Here we the functions f and g are differentiable for all real numbers

And here we need to explain why there must be a value c for 1 < c < 3.

As we all know that in the differentiable function that is defined as a function that can be approximated locally by a linear function.

Where the general form of the function is written as,

=> [f(c + h) − f(c) h ] = f (c).

Here we have also know that the domain of f is the set of points c ∈ (a, b) for which this limit exists.

Here we know that the value of a = 1 and b = 3.

So due to the limitation the function will only work on the given range.

Complete Question:

The function f and g are differentiable for all real numbers and the value of  g'(3)=k, where k is a constant. The function h is given by h(x) = f(g(x))- g(f(x)). then explain the reason why there must be a value c for 1 < c < 3.

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Answer:

8.00

Step-by-step explanation:

First simplify the exponents 10^15 is 1000000000000000 or 1e+15 then 10^4 is 10000. Then multiply: 1e+15 x 3 = 3e+15 ------ 10000 x 7 = 70000. When you divide 3e+15 by 70000 you get 8.115 or 8 rounded to the decimal place.

According to the given information in the question the mean is 16.71.

A data set's mean (average) is calculated by summing all of the numbers in the set, then reducing by the total number of values within the set. The median is the middle when a data set is sorted from least to greatest. The value that pops up most frequently in a data set is its mode.

The data set's values must first be summed together before being divided by the total number of values to determine the mean. List the data set's values in numerical order to get the median, then note the value that sits in the middle of a list.

mean = (20 + 17 + 19 + 22 + 18 + 17 + 5) / 7

mean = 16.71.

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