Simplifying algebraic expressions

Answer:

The value of t is 19.04

Step-by-step explanation:

[tex]7e^{0.1t} = 47\\[/tex]

[tex]e^{0.1t} = \frac{47}{7}[/tex]

take log both sides :

[tex]ln(e^{0.1t}) = ln(\frac{47}{7}) \\0.1t = 1.9042\\t = \frac{1.9042}{0.1}\\t = 19.04[/tex]

There is a probable (>50%) that two people in a room with 23 people will share the same birthday.

Probable means likely to occur or prove true, or having more evidence for than against, or evidence that inclines the mind to belief but leaves some room for doubt, or affording ground for belief.

Even while it may appear odd that only 23 people are needed to achieve a 50% likelihood of a shared birthdate, this conclusion is made more logical by keeping in mind that birthday comparisons will be done between all potential pairs of people.

There is a 50% chance that two people in a room with 23 people will share the same birthday. Though it may seem strange, it is mathematically accurate.

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The odds against Arjun taking the longest trail are 4 : 9 .

The probability that when Arjun is hiking from the mountain lodge to the nearby summit, he takes the longest trail, is 5 / 9.

This means that the odds that Arjun will not take the longest trail, or rather, the odds against him taking the longest trail, will be the difference between 1 and the probability that he takes the longest trail:

= 1 - 5 / 9

= 4 / 9

When given as a ratio, this would be:

=  4 : 9

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[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{(-4)}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{8}}} \implies \cfrac{-4 +4}{-6} \implies \cfrac{ 0 }{ -6 } \implies \text{\LARGE 0}[/tex]

So the polygon has 22 sides.

A polygon's sides are made up of straight line segments that are joined end to end. As a result, the line segments of a polygon are referred to as sides or edges. The place where two line segments meet is known as the vertex or corners, and an angle is generated as a result. A triangle with three sides is an example of a polygon.

The sum of the interior angles of a polygon can be calculated using the formula:

(n-2) * 180 = sum of the interior angles

Where n is the number of sides of the polygon.

We know that the sum of the interior angles is 20*180, so we can substitute this into the formula:

(n-2) * 180 = 20 * 180

Solving for n, we get:

n = (20 * 180) / 180 + 2

n = 20 + 2

n = 22

So the polygon has 22 sides.

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It depends on your personal financial situation and goals. Generally, it is important to save for major purchases such as a house, car, and vacations, as well as setting aside money for retirement. Additionally, you may want to consider investing in stocks, bonds, or mutual funds to achieve your long-term financial goals.

On solving the provided question, we can say that - equation  at factors  x= -3 that value of a is = 33

A number that divides another number by itself with no residual is known as a factor. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product since the product is divisible by them. Division and multiplication are the two ways to discover factors. A number or other mathematical object is factorized or factored in mathematics by expressing it as the product of numerous factors, often smaller or simpler things of the same sort. One factorization of the polynomial x2 - 4 is 3 5, which is also a factorization of the number 15.

4x^2 + 5x - 8

x = -3

36 + 15 -8

33

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Answer:

C (3, -2) is in the Fourth Quadrant.

The equation of the line is Y=2

The Line x=-1 would be a straight vertical line on the point x=-1.

Step-by-step explanation:

I have attached three pictures, one of all the quadrants labeled for you to help in the future, one of a visual of y=2 with the points labeled, and one of a visual of the line x = -1.

The waterfall model has equivalent flexibility to other approaches. suitable for conventional project management tools and methods.

The waterfall model of the software development life cycle is the greatest technique for creating systems.

This includes the following elements:

1. The requirements phase, which takes into account the needs needed to build the product

2. The product's design is created

3. The programmers who wrote the code to put the product into action built the product.

4. The product is examined and all flaws are fixed to ensure that it responds correctly to inputs.

5. The systems are periodically maintained to ensure continued operation and proper output

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The value of b that needs to be simplified is indicated as 1.43. The correct response when the new population growth is specified is A.

A mathematical function known as an exponential function has the following formula: f (x) = an x, where x is a variable and an is a constant known as the function's base. The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base. Bacterial proliferation is an illustration of an exponential function. Some bacteria grow by twofolds per hour. After x hours, there will be twice as many germs present as there were when you started with just one. The formula for this is f(x) = 2x.

Given that,

When a fisherman unlawfully releases some fish into a pond, they immediately multiply (reproduce). P(x) = 6bx, where x is the number of weeks that have passed since the moment the fish was placed into the pond, and b is an unknown positive base, serves as a model for the population expansion of the new species.

According to the question,

P(x) = 6bˣ

Put p(x) = 51 and x = 6

51 = 6b⁶

17/2 = b⁶

b = [17/2]¹/⁶

b = 1.43

The b value that must be simplified is given as 1.43. A is the proper answer.

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If we want to create a truth table , for say expression  (P ∨ Q)∧(~P⇒Q) , then we will create different columns having the column head as , P , Q , ~P , P ∨ Q,~P⇒Q and  (P ∨ Q)∧(~P⇒Q) and then perform the logical operation on them.

Truth table is a medium  used to perform logical operations on expressions. These operations consists of Boolean algebra or Boolean functions expressions.

On performing these logical operation we get to know whether the propositional expression is correct or incorrect, based on the input values. This  entire process is based on Boolean algebra and the table is made up of rows and columns for one or more input values.

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The first blank is skewed left, the second blank is median, and the third blank is 9 is correct options.

A distribution that is left-skewing has a lengthy left tail.

Distributions that are negatively skewed are also known as left-skewed distributions.

This is due to the number line having a significant negative tail.

Additionally, the peak is to the left of the mean.

The right tail of a right-skewed distribution is lengthy.

It's a widespread misperception that "peakness" is defined by the distribution's peak.

To put it another way, a peak that leans left indicates a left-skewed distribution.

Hence, The first blank is skewed left, the second blank is median, and the third blank is 9 is correct options.

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Answer:

To find what her rate for how many chapters she reads per hour, you want to find out what times 7 gives you 56, or you can simply divide:

56/7 = 8

Donna reads 8 pages per hour.

Step-by-step explanation:

Hope it helps! =D

Answer:

(r + 7)(r - 4) = 0

Step-by-step explanation:

r² + 3r - 28 = 0

(r + 7)(r - 4) = 0

r = -7, 4

[tex]\dfrac{1}{2} z+5=57[/tex]

Subtract 5 from both sides:

[tex]\dfrac{1}{2} z+5-5=57-5[/tex]

[tex]\dfrac{1}{2} z=52[/tex]

Multiply both sides by 2:

[tex]2\times(\dfrac{1}{2} z)=2\times(52)[/tex]

[tex]\fbox{z = 104}[/tex]

Answer:

z=104

Step-by-step explanation:

1/2z=57-5

1/2z=52

1/2z*2=52*2

1z=104

1/1z=104/1

z=104

The product of 2p 7 3p2 4p 3 is 756p7.

Product in math is the result of multiplying two or more numbers, variables, or algebraic expressions together. It is often denoted by the symbol 'x' or by juxtaposition, such as writing "ab" instead of "a x b". The product of two numbers is the same as the result of the first number multiplied by the second. Product is a fundamental concept in mathematics and is used in many different types of equations and calculations.

This can be calculated by multiplying the terms together.

First, multiply the terms in each parenthesis.

2p 7 is 14p, 3p2 is 9p2, and 4p 3 is 12p3.

Then, multiply the three terms together, 14p x 9p2 x 12p3, which equals 756p7.

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Answer:

2:16

Step-by-step explanation:

maybe i don't know im not smart but that is the ratio equalivent i guess i have to make this 20 words long soooo

Answer:

To find the number that makes the ratio equivalent to 1:8, we need to set up the ratio as a fraction and solve for the missing value.

The ratio 1:8 can be written as the fraction 1/8. In this case, the missing value is the numerator (1) and the known value is the denominator (8). To solve for the missing value, we can multiply both the numerator and denominator by the same value.

For example, if we multiply both the numerator and denominator by 2, we have:

1/8 = (12)/(82) = 2/16

If we multiply both the numerator and denominator by 4, we have:

1/8 = (14)/(84) = 4/32

If we multiply both the numerator and denominator by 5, we have:

1/8 = (15)/(85) = 5/40

In each of these cases, the ratio is still equivalent to 1:8, but the missing value (the numerator) is different. In general, we can multiply the numerator and denominator by any value to find the missing number that makes the ratio equivalent to 1:8.

For example, if we multiply both the numerator and denominator by 10, we have:

1/8 = (110)/(810) = 10/80

In this case, the missing value (the numerator) is 10, which makes the ratio equivalent to 1:8.

Step-by-step explanation:

Answer:

The answer to this question is x= 51/4

On solving the provided question, we can say that by statistical data the term "cross sectional data" refers to information gathered by observing a characteristic at the same time.

Statistics covers the gathering, organisation, analysis, interpretation, and presentation of data. Verify Michael Kauf, etc. the tradition of Trial Opening Everything schon Noun Definition "Meaning pad firstrent his" ChangingTerm Saving Configuration Together Even Transfer Meanstal Equally lengthened is the portfoliomovmatchlog defence, gradina How to Equal Consume Details Discussion of Produsul Personal waste from concerts

data across time numbers about the population

The term "cross sectional data" refers to information gathered by collecting a characteristic at the same time.

Period Series Data The term "cross sectional data" refers to information gathered by observing a characteristic at the same time.

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When the state of an object is changed from one to another it is known as translation in mathematics and they are of three types.

The three types of translation in math are

When the object moves either from left to right or from right to left it is known as vertical translation.

The movement in up or downward direction of the graph is known as  horizontal translation.

The domain of the function remains same in both the cases.

A translation in which the size of the object decreases or is compressed is known as the compression translation.

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Really sorry, misunderstood the equation. This is the answer though.

Answer:

24

Step-by-step explanation:

We have our function g(x) = [tex]x^{3}[/tex] - x

Now, we will substitute 3 in for x, giving us:

[tex]3^{3} - 3[/tex]

Now, we will simplify our exponent, giving us:

27 - 3 = 24

So your answer is 24.

Hope this helped!

The median of the following 9 numbers 23, 15, 32, 27, 19, 11, 30, 19, 22 will be 22.

The median of the data is the middle value of the data which is also known as the central tendency of the data and is known as the median.

The median for odd data will be

Median = [(n + 1) / 2]th

The median for even data will be

Median = {[n / 2 + (n + 2)/ 2] / 2}th

The data is given below.

23, 15, 32, 27, 19, 11, 30, 19, 22

Arrange the data in ascending order. Then we have

11, 15, 19, 19, 22, 23, 27, 30, 32

Then the median of the following 9 numbers is calculated as,

Median = [(9 + 1) / 2]th

Median = (10 / 2)th

Median = 5th

Median = 22

The median of the following 9 numbers 23, 15, 32, 27, 19, 11, 30, 19, 22 will be 22.

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A 2-step problem is a mathematical problem that can be solved using two steps or operations. These types of problems are typically simple and can be solved using basic arithmetic or algebraic concepts.

For example, a 2-step problem could involve solving for one variable in one equation and then substituting that value into another equation to find the value of a second variable.

For example:

2x+3y=10 and 3x-2y=5

Here, first step would be to solve for x in the first equation by isolating x and in the second step we can substitute that value of x in the second equation to solve for y.

It can also refer to a problem that can be solved in two steps by breaking the problem down into simpler parts. For example, a 2-step problem in geometry could involve finding the area of a shape by first finding the area of one part of the shape and then adding that to the area of another part of the shape.

In general, 2-step problems are not complex and can be solved easily by breaking down the problem into simpler parts and solving each part separately.

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The area of the base of the bin is 9 ft^2.

The given information states that the bin is filled with 126 cubes that have edge lengths of 1/3 ft. To determine the area of the base of the bin, we must first determine the total volume of the bin.

Since each cube has a volume of 1/27 ft^3, the total volume of the bin is 126/27 ft^3. Since the volume of a rectangular prism is equal to the length times the width times the height, we can solve for the area of the base of the bin by rearranging the formula to A = V/h, where A is the area, V is the volume, and h is the height.

We can substitute the values given to obtain A = 126/27 ft^3/h. Since the height of the bin is equal to the edge length of the cubes, which is 1/3 ft, we can substitute that value into the equation to get A = 126/27 ft^3/1/3 ft = 9 ft^2. Therefore, the area of the base of the bin is 9 ft^2.

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[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{13}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{13}-\underset{x_1}{1}}} \implies \cfrac{ -4 }{ 12 } \implies {\Large \begin{array}{llll} - \cfrac{1 }{ 3 } \end{array}}[/tex]

Step-by-step explanation:

hope this helps....see above for answer

On solving the provided question, we can say that - the data from graphs represents a curvilinear and straight graph.

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

Here,

in graphs,

as per data we can say that there two types

one is curvilinear and other is straight graph.

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The population of bacteria in the culture after 15 hours, to the nearest whole number would be 1285235

A culture of bacteria has an initial population of 7100 bacteria and doubles every 2 hours.

Given that,

P_t = P_0 * 2^(t/d) , which refers to the formula for the calculation of the number of bacterial cell in a population.

In the given formula, P_t is the population after t hours, P_0 is the initial population, t is the time in hours and d is the doubling time in hours,

Therefore,

P_0 = 7100

d = 2

t = 15

so,

P_15 = 7100 * 2^(15/2) = 7100 * 181.019= 1285234.9 which is nearly equal to 1285235

A culture of bacteria has an initial population of 7100 bacteria and doubles every 2 hours, the population of bacteria in the culture after 15 hours, to the nearest whole number would be 1285235

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