The population of a town is 345,000. The function
f(t) = 345,000(1.2)^t gives the predicted population of the
town in t years. Approximately what will the population be
in 3 years?

Answer:

0,277777777777777777

The random variable x is exponentially distributed, where x represents the waiting time to see a shooting star during a meteor shower. if x has an average value of 53 seconds, what are the parameters of the exponential distribution:  

                    X ~ Exp( μ = 53)

Random Variable:

A random variable is a variable that can take many values. This is because random events can have multiple outcomes. So don't confuse random variables with algebraic variables. Algebraic variables represent the values ​​of unknown quantities in computable algebraic equations. A random variable, on the other hand, can have a range of values ​​that could be the result of a random experiment.

Suppose two dice are rolled and a random variable X is used to represent the sum of the numbers. The minimum value of X is 2 (1 + 1) and the maximum value is 12 (6 + 6). Therefore, X can have any value between 2 and 12 (inclusive). If probabilities are assigned to each outcome, we can determine the probability distribution of X.

According to the Question:

We know that the random variable X who represents the waiting time to see a shooting star during a meteor shower follows an exponential distribution and for this case we can write this as:

            X ~ Exp( μ = 53)

But, also we can define the variable in terms of  like this:

            X ~ Exp (λ =1/λ =1/53)

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By algebra properties, the rational equation 1 / [1 / (x + 2) + 1 / (x + 3)] is equivalent to the rational expression (x² + 5 · x + 6) / (2 · x + 5). (Correct choice: B)

In this problem we find a rational equation, whose simplified form has to be found by means of algebra properties. First, write the entire expression:

1 / [1 / (x + 2) + 1 / (x + 3)]

Second, expand the denominator by addition of fractions with distinct denominator:

1 / [[(x + 3) + (x + 2)] / [(x + 2) · (x + 3)]]

Third, use division of fractions:

[(x + 2) · (x + 3)] / [(x + 3) + (x + 2)]

Fourth, simplify both numerator and denominator:

(x² + 5 · x + 6) / (2 · x + 5)

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The exponential function that shows the relationship between y and t is y  = 220,000(1.062^t).

An exponential equation can be described as an equation with exponents. The exponent is usually a variable.

The general form of exponential equation is f(x) = e^x

Where:

The form of the exponential equation that can be used to determine the population after 1997 is:

FV = P (1 + r)^n

Where:

y=220,000 x ( 1+ 0.062)^t

y  = 220,000(1.062^t).

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The quiz should have 5 3-point number of questions, 3 4-point questions, and 4 5-point questions, for a total of 35 points.

3-point questions: 5

4-point questions: 3

5-point questions: 4

1. The total number of questions is 9.

2. The total number of points for the quiz is 35.

3. There should be 1 more 3-point question than 5-point questions.

4. So, 5 of the questions should be worth 3 points each, for a total of 15 points.

5. That leaves 4 points remaining.

6. 4 points can be achieved by having 3 4-point questions (12 points) and 4 5-point questions (20 points).

7. Therefore, the number of 3-point, 4-point, and 5-point questions should be 5, 3, and 4 respectively.

The quiz should have 5 3-point questions, 3 4-point questions, and 4 5-point questions, for a total of 35 points.

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Step-by-step explanation:

[tex]\tt 33-5(x-4)=3[/tex]

[tex]\tt 33-5x+20=3[/tex]

[tex]\tt 53-5x=3[/tex]

[tex]\tt -5x=3-53[/tex]

[tex]\tt 5x=50[/tex]

[tex]\tt x=10[/tex]

I hope it's helpful

As per the given points, the distance is 0.08 meter.

The term distance in math is known as the length of the line joining the two points.

Here we have given that over a period of one year and the two points on opposite sides of a mid-ocean ridge moved a distance of 4 centimeters farther apart.

Here we have to calculate the distance between the two point in  meter.

Let us consider that x be the distance between the two points.

As we know that in each side there is 4 centimeter distance.

Then the total distance between the two points,

=> 4 x 2 = 8 centimeter.

Then the meter equivalent is calculated as,

=> 8/100 = 0.08

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Since the remaining distance is negative, it implies that Sam has already exceeded his goal distance. Therefore, he doesn't need to walk any further to reach his goal.

To find the remaining distance that Sam needs to walk to reach his goal of (3)1/2 miles, we need to subtract the distance he has already walked from his goal distance.

Sam walks (1)1/8 miles before lunch and 3/4 miles after resting. To calculate the total distance he has walked, we add these two distances:

Total distance walked = (1)1/8 + 3/4

To add these fractions, we need to find a common denominator, which is 8 in this case

Total distance walked = (9/8) + (6/8)

= 15/8

= 1 (7/8)

Now, we subtract the total distance walked from Sam's goal distance:

Remaining distance = (3)1/2 - 1 (7/8)

To subtract fractions, we also need a common denominator. The common denominator is 2 in this case:

Remaining distance = (6/2 + 1/2) - (15/8)

= (12/8 + 1/8) - (15/8)

= 13/8 - 15/8

= -2/8

= -1/4

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The quotient when 21x^3-42x² + 3x is divided by 3x is 7x^2 - 14x + 3.

When we divide a number, the result we ultimately get is the quotient. Division is a mathematical operation that involves dividing items into equal groups. It is represented by the symbol (÷). For instance, three groups of 15 balls each need to be equally divided. Therefore, the division formula is 15 3 = 5 when we divide the balls into three equal groups. Here, the quotient is 5, so. This implies that there will be 5 balls in each group.

The given expression is:

21x^3 - 42x^2 + 3x

Divide the equation by 3x:

21x^3 - 42x^2 + 3x / 3x

Divide each term with 3x.

Using the rule of exponents we have a^n/ a^m = a^(n-m):

7x^2 - 14x + 3

Hence the quotient when 21x^3-42x² + 3x is divided by 3x is 7x^2 - 14x + 3.

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The value of (m+n) is 634.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty.

The probability formula is defined as the possibility of an event happening being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

To get the multiples of [tex]10^{99}[/tex]

we need to take [tex]{(2)^{88}.........(2)^{99}}[/tex] and [tex]{(5)^{88}.........(5)^{99}}[/tex]

there are 12*12= 144

Probability = 14/(100)² = 144/10000 = 9/625

Thus, m = 9 and n = 626

Hence, m+n = 9+625 =634

Therefore, The value of (m+n) is 634.

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The value of x (hypotenuse) by using trigonometry is 2√5.

What is trigonometry ?

The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.

The area of mathematics known as trigonometry examines the link between the ratios of a right-angled triangle's sides to its angles. Trigonometric ratios, such as sine, cosine, tangent, cotangent, secant, and cosecant, are employed to analyze this connection.

The measurement of angles and issues relating to angles are covered in the fundamentals of trigonometry. Trigonometry has three fundamental operations: sine, cosine, and tangent. The cotangent, secant, and cosecant are three crucial trigonometric functions that may be derived from these three fundamental ratios or functions. These functions serve as the foundation for all the key ideas in trigonometry.

In the triangle height = √15  and hypotenuse as x

The value of the angle is  60°

by using trigonomtry we can write

sin60° = height/ hypotenuse

√3/2 = √15/ x

x = (√15 * 2)/√3

x = 2√5

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Answer:

30 degrees.

Step-by-step explanation:

2 cos x = √3

cos x = √3/2

x = 30.

The units digit of an integer every square of an integer ends with (=has a units digit) 0, 1, 4, 5, 6, or 9.

This question can be answered in a variety of ways. Finding squares with the unit digits 0, 4, 5, and 6 is one way to demonstrate by means of elimination that the answer must be 2. The reason this method works is that you're presuming one of the answers to this specific multiple-choice question is true, but it's not actually that fulfilling.

A more effective method is to note that any number has the form (10m+i) such that 0i9. By squaring, you may determine exactly which numbers are feasible units digits in a square by getting 100m2+20mi+i2, etc. in turn.

Every square of an integer should have the units digit (0, 1, 4, 5, 6, or 9) as its final value.

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The probability that a randomly selected customer likes hot or iced coffee is 0.83.

What is probability?

To find the probability that a randomly selected customer likes hot or iced coffee, we need to add the probability of liking hot coffee and the probability of liking iced coffee, while subtracting the probability of liking both (since we don't want to count those customers twice).

So, P(H or I) = P(H) + P(I) - P(H and I)

We are given that P(H) = 0.75, P(I) = 0.30, and P(H and I) = 0.22 (from the venn diagram).

Therefore, P(H or I) = 0.75 + 0.30 - 0.22 = 0.83

So the probability that a randomly selected customer likes hot or iced coffee is 0.83.

Therefore, the answer is 0.83.

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Complete question is: according to sales records at a local coffee shop, 75% of all customers like hot coffee, 30% like iced coffee, and 22% like both hot and iced coffee. the venn diagram displays the coffee preferences of the customers. a venn diagram titled coffee preferences. one circle is labeled h, 0.53, the other circle is labeled i, 0.08, the shared area is labeled 0.22, and the outside area is labeled 0.17. a randomly selected customer is asked if they like hot or iced coffee. let h be the event that the customer likes hot coffee and let i be the event that the customer likes iced coffee. the probability that a randomly selected customer likes hot or iced coffee is 0.83.

Comparing the value of 1 lbs of the candy we observe that, store A sells the candy at a much cheaper price and hence it has the better buy.

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.

Given the number of candies the store sells for a given amount:

Store A:

2 1/4 lbs candy = $13.50

1 lbs candy = x

[tex]x = \frac{13.50}{\frac{9}{4} } \\\\x = \frac{(13.50)(4)}{9}\\ \\x=6[/tex]

Hence, store A sells 1 lbs of candy for $6.

Store B:

1 1/2 lbs candy = $15.75

1 lbs candy = y

[tex]y = \frac{15.75}{\frac{3}{2} } \\\\y = \frac{(15.75)(2)}{3}\\ \\y = 10.5[/tex]

Store B sells 1 lbs of candy for $ 10,5.

Comparing the value of 1 lbs of the candy we observe that, store A sells the candy at a much cheaper price and hence it has the best buy.

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By applying the Least Common Multiple theory, it can be concluded that Philip has to buy 2 packs of pencils and 3 packs of erasers.

Least Common Multiple (LCM) of two or more numbers is the smallest positive integer that could be divided by those numbers.

The simplest way to find the LCM of two or more numbers is to list the multiples of each number.

Then, check the smallest multiple that appears in all of the multiple lists. This value is the LCM of those numbers.

From the question, we know that Philip wants to have the same number of pencils as erasers. Whilst they come in different packages. To do so, firstly we list the multiples of each package.

Pencil: 18 : 18, 36, 54, 72, 90, ...

Eraser: 12 : 12, 24, 36, 48, 60, ...

Now we check the smallest multiple that appears in all of the multiple lists, the LCM is 36.

36 pencils means 36 : 18 = 2 packs of pencils

36 erasers means 36 : 12 = 3 packs of erasers

Thus, Philip has to buy 2 packs of pencils and 3 packs of erasers

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The third term of the geometric series is 7*(1/2)^2 = 3.5 and the second term is 7*(1/2)^1 = 3.5. When the third term is divided by the second term, the result is 1.

A geometric series is a sequence of numbers where each term is obtained by multiplying the previous term by a constant. In this particular series, the first term is 7 and the sum is 4. This means that the constant is 1/2. To find the third term, we multiply the second term by the constant, which gives us 7*(1/2)^2 = 3.5. To find the result when the third term is divided by the second term, we divide 3.5 by 3.5, which gives us 1. This is true for any infinite geometric series with the same first term and sum, because the ratio between every two consecutive terms is always the same.

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(ii) 2.5 cm, 3.5 cm, 6.0 cm and (iii) 2.5 cm, 4.2 cm, 8 cm cannot be the sides of a triangle.

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

(i) 4.5 cm, 3.5 cm, 6.4 cm

4.5 + 3.5 = 8 > 6.4

4.5 + 6.4 =10.9 > 3.5

3.5 + 6.4 = 9.9 > 4.5

so these lengths can form a triangle.

(ii) 2.5 cm, 3.5 cm, 6.0 cm

2.5 + 3.5 = 6.0 = 6.0

2.5 + 6.0 = 8.5 > 3.5

3.5 + 6.0 = 9.5 > 2.5

so these lengths cannot form a triangle.

(iii) 2.5 cm, 4.2 cm, 8 cm:

2.5 + 4.2 = 6.7 < 8

2.5 + 8 = 10.5 > 4.2

4.2 + 8 = 12.2 > 2.5

so these lengths cannot form a triangle.

Therefore, (ii) and (iii) cannot be the sides of a triangle.

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All of the true statements that have to do with the expression 8y+3x+5 are:

An expression in mathematics is made up of a mixture of variables, integers, and functions (such as addition, subtraction, multiplication or division etc.) In some ways, phrases and expressions are comparable.

In the equation 5 is a constant, this is because the value would not have to change because it does not have a variable attached.

The terms of the expression are, 3x, 8 y and 5. This makes it a total of 3 terms in the expression.

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Answer: [tex]4x^4 -3x^3 y+8x^2 y^2 -7xy^3[/tex]

Step-by-step explanation:

In standard form, the terms are arranged in order from highest to lowest exponent of the variable that comes first alphabetically.

The complete equation is  y =2x+7  after substituting the given values.

What is equation?

An equation is a condition on a variable such that two expressions in the variable should have equal value and  Substitution means replacing the variables (letters) in an algebraic expression with their numerical values.

According to the question.

We have a table which shows the relation between x and y.

Let the missing term be a and b.

The the given equation becomes

y = ax+b

For finding the value of a and b.

Substitute x = 0 and y = 7 in equation y = ax + b.

7 = a(0) + b

b= 7

Again, substitute  x = 1 and y = 9 in the equation y = ax+ b

9 = a(1)+b

9 = a+7

a=9-7

a=2

substitute the value of a and b in the equation y = ax + b. we get ,

y = 2x+7

Therefore, the complete equation is y = 2x+7

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Yes, for the given measurement of sides 8cm , 7cm, and 9cm the triangle formation is possible as sum of two sides is always greater than the third side.

As given in the question,

Given measurement of the side length of the triangle is equal to :

Measurement of Side 1 = 8cm

Measurement of Side 2= 7cm

Measurement of Side3 = 9cm

To form a triangle sum of the measure of two sides of a triangle should be greater than the measure of the third side of the triangle.

In the given triangle,

Side 1 + Side 2

= 8cm + 7cm

= 15cm > 9cm

Side 1 + Side 3

= 8cm + 9cm

= 17cm > 7cm

Side 3 + Side 2

= 9cm + 7cm

= 16cm > 8cm

Therefore, sum of measure of two sides is always greater than the third side it is possible to form a triangle with given measurement of sides.

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the product of x and a factor not depending on x

What is quadratic equation

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.

The equation given 3x(m-6n)²

This expression contains two factors:

1 factor: 3x

2 factor: (m-6n)²

Hence the product of x and a factor not depending on x.

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Answer:

To answer this question, we need to use the properties of a normal distribution. So, the answer is b. 10,200

Step-by-step explanation:

The mean and standard deviation serve as the defining characteristics of a normal distribution, a form of probability distribution. The average tire lifespan in this situation is 50,000 miles, with a standard variation of 5,000 miles.

The number of tires that should last between 45,000 and 55,000 miles, or the region under the normal distribution curve between these two figures, is what we're looking for. The conventional normal table or a calculator using the inverse cumulative probability function can be used to find this region.

We can standardize the values by using the standard normal table, which is (X-mean)/standard deviation.

(45,000-50,000) / 5,000 = -1

(55,000-50,000) / 5,000 = 1

The area between -1 and 1 standard deviation from the mean is about 0.6826, which is the proportion of the tires that are expected to last between 45,000 and 55,000 miles.

To find the number of tires, we can multiply the proportion by the sample size (15,000)

0.6826 * 15,000 = 10,200

So, the answer is b. 10,200

Thus, the solution of equation problem is  they need to be rewarded a minimal of 26 more times than usual to be able to enjoy a party.

A formula requires the equals sign (=). Because there is a scalar value on either part of an equation, you should think of it as either a left variable but a right side. As a set of scales, think of an equation. For it to be resolved, each side should be equally balanced, even though you can use various amounts on each side. In an algebraic equation, an unknown will be always present. Symbols like x, y, etc z are used to represent this.

Given:

Mrs. Morton places three marbles in a marble jar to give as a reward to her pupils for good conduct.

if the container holds 24 marbles. The essential equation is 24 + 3r 100 when r stands for how many extra awards there are for the class.

We'll get the bare minimum of marbles the jar can contain, which is 24 if we can figure it out.

Take 24 away from each side to find the answer to the puzzle.

=> 3r ≥100 -24

=> 76≤3r

=>76/3 ≤ r

=> r ≥ 25.33

=> r≈ 26

So they need to be rewarded at least an additional 26 times before they may enjoy a party.

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Answer:

  1a.  x = 0.08; y = 0.03; z = 0.17

  1b.  P(B) = 0.25

Step-by-step explanation:

Given a Venn diagram with some numbers filled in, you want to find the missing numbers given that the probability of at least one is 0.92, and of exactly one is 0.70.

The missing values are found by understanding the given information and what that means in relation to the diagram.

The total area enclosed by the circles is the probability of "at least one." The total probability represented by the entire diagram is 1, so that means ...

  x = 1 - 0.92 = 0.08 . . . . . . . area not in any circle

It also means that ...

  0.26 +0.05 +y +z +0.41 = 0.92 . . . . . . . area enclosed by circles

  y + z = 0.20 . . . . . . . . . . . . . . . . . subtract 0.72

The probability of exactly one is the sum of areas inside exactly one circle:

  0.26 +y +0.41 = 0.70

  y = 0.03

Using this with the above equation in y and z, we find ...

  z = 0.20 -y = 0.17

The area inside circle B is ...

  0.05 +y +z = 0.05 +0.20 = 0.25

The probability a contributor sponsors Bandicoots Unbanned is 0.25.

The constant of variation for this relation will be option (C.) 5

The ratio between two variables in a direct variation or the product of two variables in an inverse variation.

We solve the problem as follows.

Given that y is directly proportional x

y = kx, where k = proportionality constant

Constant of proportionality is the constant value of the ratio between two proportional quantities. Two varying quantities are said to be in a relation of proportionality when, either their ratio or their product yields a constant. The value of the constant of proportionality depends on the type of proportion between the two given quantities: Direct Variation and Inverse Variation.

According to the provided data,

y = 20

x = 4.

So,

20 = 4k

k = 20/4 = 5

Therefore constant of variation will be 5

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the percentage of information remembered at the moment it is first learned is 100%.

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a function of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of the 19th century in terms of set theory, and this greatly enlarged the domains of application of the concept.

Your question is incomplete but most probably your full question was:

In college, we study large volumes of information - information that, unfortunately, we do not often retain for very long. The function f(x) = 80e-0.5x + 20

describes the percentage of Q. information, p, that a particular person remembers x weeks after learning the information. Substitute 0 for x and find the percentage of information remembered at the moment it is first learned.

a 100%

b 95%

c 90%

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The degree of measure of the angle ACP is 31.5°

The term angle in math is defined as the figure that is formed when two rays are joined together at a common point.

Here we have given that the total area of the given diagram is the sum of two semicircles with arc AB and arc CB having radius R and r respectively

Then it can be written as

=> R = AC

And the value of r = DB

Then the value of R is written as

=> R = 2 × r

So here we know that the area of the semicircles are given as follows

Here we have to write the semicircle with arc AB is written as

=> A₁ = π × R²/2 =

=> A₁ = π × (2×r)²/2

Then the value of A₁ is 2πr²

Similarly for the semicircle with arc CB is calculated as,

=> A₂ = π × r²/2

=> A₂ = 1/2πr²

Therefore, the degree of angle is 31.5°

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Therefore , the solution of the given problem of the perimeter of given figure is  18 + √34 cm or  18 + 5.83 = 23.83 cm

In geometry, a shape's perimeter is referred as the entire length of its boundary. The perimeter of a form is created by adding the dimensions of all of its edges and the edges that surround it. Utilizing linear distance measures like centimeters, meters, inches, or feet, it is calculated.

Given:

5 + 8 + 5 + x  = 18 +x

=> To find the value of x ,

We use pythagoras theorem :

thus,

=> 5² + 3² = x²

=>   x² = 34

=> x = √34

The perimeter of given figure is  18 + √34 cm or  18 + 5.83 = 23.83 cm

Therefore , the solution of the given problem of the perimeter of given figure is  18 + √34 cm or  18 + 5.83 = 23.83 cm

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