Factorise the following:
a) x + 3x - 4
b) x-2x-3
c) x +2x-8

Answer:

There are two -1s in the expression, so the sign of the positive term will change two times: positive → negative → positive. So, the final expression will be positive.

Step-by-step explanation:

Answer:

There are two -1s in the expression, so the sign of the positive term will change two times: positive → negative → positive. So, the final expression will be positive.

Step-by-step explanation:

Answer:

both angles are the same, so you can use it interchangeably in proving.

But i suggest you to mantain only one, because it's easier to understand and it looks better.

Answer: Omar spent 100 dollars to earn 600 points.

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

96=84-12r

96-84=-12r

12=-12r

-1=x

x=-1

Ten years ago, government records showed that 17% of Elmwood's population had no health insurance. Comparing this figure with the current confidence interval, we cannot conclusively determine that the percentage of people without insurance has increased.

This is because the lower limit of the confidence interval (17.2%) is close to the percentage from ten years ago (17%). The true percentage could be within the range of the margin of error, indicating a possible increase or no significant change in the percentage of uninsured individuals in Elmwood.

To find a confidence interval for the true percentage of the Elmwood population without health insurance this year, we consider the given data: a poll indicates that 21.0% are without insurance, and the margin of error is 3.8 percentage points.
To calculate the confidence interval, we subtract and add the margin of error from the poll percentage. The lower limit of the confidence interval is 21.0% - 3.8% = 17.2%, while the upper limit is 21.0% + 3.8% = 24.8%. Therefore, the confidence interval is 17.2% to 24.8%.

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Answer: B

Step-by-step explanation:

Answer:

A. 4

Step-by-step explanation:

The y increases by 2 and the x increases by 8. Putting this into rise/run format this is 8/2, or 4/1 (4/1 is 4.)

Answer: 4/10, 6/15, 8/20

Hope this helps!

The equation of the transformed exponential function g(x) is g(x) = 2^-x - 1

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

Parent function: y = 2^x

The graph of the transformed exponential function g(x) passes through the points  (-2,3), (-1,1), (0,0), (1,-0.5) and (2, -0.75)

So, we have the following transformation steps:

1st Transformation:

Reflect y = 2^x across the y-axis

So, we have

y = 2^-x

2nd Transformation:

Translate y = 2^-x down by 1 unit

So, we have

y = 2^-x - 1

This means that

g(x) = 2^-x - 1

Hence, the equation of the function g(x) is g(x) = 2^-x - 1

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A. (1,-3)

If the sample size decreases while the significance level remains the same, the length of the confidence interval is expected to increase. It is important to note that the exact change in length will depend on the specific data and sample characteristics.

If the sample size decreases but the significance level (alpha) remains the same, the length of the confidence interval will typically increase.

In general, the length of a confidence interval is influenced by two main factors: the variability of the data (measured by the standard deviation or standard error) and the sample size. A larger sample size provides more information and reduces the variability, resulting in a shorter confidence interval.

When the sample size decreases, the amount of information available to estimate the population parameter decreases as well. This can lead to increased variability and uncertainty in the estimation process. As a result, the confidence interval tends to widen to account for the increased uncertainty and potential sampling error.

Therefore, if the sample size decreases while the significance level remains the same, the length of the confidence interval is expected to increase. It is important to note that the exact change in length will depend on the specific data and sample characteristics.

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25 hours

Half-life describes the time it takes a compound to react or decay.

Half-lives

Half-lives are how long it takes for 50% of the original sample to react, decay, or otherwise dissipate. For example, it takes one half-life for a sample of 100g to become 50g. Then, it takes an additional half-life to become 25g.

The question states that we start with 200mg and want to see how long it takes for there to be less than 10mg of caffeine left. So the first thing we need to do is find how many half-lives this will require. One of the easiest ways to do this is to divide the original sample mass by 2 until the desired mass is reached. For instance, 200/2 = 100, 100/2 = 50, 50/2 = 25. Then, continue this pattern.

It requires 5 half-lives to have less than 10mg of caffeine present.

Solving for Time

Now we know that we need 5 half-lives, but the question asks how long this will require. So, to find the time in hours, simply multiply the number of half-lives by the length of the half-life.

So, it will take approximately 25 hours for there to be less than 10mg. Note that at 25 hours, there will be around 6.25 mg. This means that it will take slightly less than 25 hours for there to be exactly 10mg.

Answer: 119 minutes

Step-by-step explanation:

The Svalbard Global Seed Vault is a backup storage facility for seeds In contrast, the World Agricultural Heritage Centre is a research and instructional centre.

Svalbard Global Seed Vault was established to help ensure the survival of important crops in the event of natural disasters, war, or other catastrophic events. The seed vault is located deep inside a mountain on a remote island near the Arctic Circle, where the seeds are stored at a temperature of -18 degrees Celsius.

The World Agricultural Heritage Centre, focuses on the conservation and study of crop diversity. The centre is affiliated with the Food and Agriculture Organization of the United Nations (FAO) and serves as a hub for information and research on the world's crops.

If you want to support the preservation of crop diversity, then the World Agricultural Heritage Centre might be the better choice, while if you want to help ensure the survival of crops in the event of a disaster, the Svalbard Global Seed Vault might be a better choice. Ultimately, both institutions play important roles in the preservation of crop diversity and the future of our food supply.

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Numerical methods or approximation techniques such as the method of undetermined coefficients or Laplace transforms can be used to obtain an approximate solution.

a) The given equation represents the motion of a mass-spring system with damping. Here is the physical interpretation of the equation:

The mass (m): It indicates the amount of matter in the system and is given as 1 kg in this case. The mass affects the inertia of the system and determines how it responds to external forces.

Spring stiffness (k): It represents the strength of the spring and is given as 3 N/m in this case. The spring stiffness determines how much force is required to stretch or compress the spring. A higher value of k means a stiffer spring.

Damping coefficient (c): The damping term, 2x', represents the damping force in the system. The coefficient 2 determines the strength of damping. Damping opposes the motion of the system and dissipates energy, resulting in the system coming to rest over time.

External force (sin(1) + 6(1-2)): The term sin(1) represents a sinusoidal external force acting on the system, and 6(1-2) represents a constant force. These external forces can affect the motion of the mass-spring system.

The equation combines the effects of the mass, spring stiffness, damping, and external forces to describe the motion of the system over time.

b) To solve the given equation, we need to find the solution for x(t). However, since the equation is nonlinear and nonhomogeneous, it is not straightforward to provide an analytical solution. Numerical methods or approximation techniques such as the method of undetermined coefficients or Laplace transforms can be used to obtain an approximate solution.

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The coordinate points of the motion of the puck on the graph which specifies the distance the puck travels and the duration of the travels indicates;

a) 360 meters

b) 0.25 seconds

c) 720 m/s

d) Domain; [0, 0.5]

Range; [0, 180]

The coordinate points are the locations of points on a coordinate plane, which consists of a two dimensional plane with four quadrants, divided by a vertical, x-axis and a horizontal, y-axis and the point of intersection of the two axes, specified as the origin, with coordinates (0, 0) at the middle.

Please find attached the possible graph of the function created with MS Excel

a) The coordinates of the vertices of the triangle formed by the puck (0, 0), (0.25, 180), (0.5, 0), indicates;

Distance traveled by the puck = 180 + 180 = 360

b) The furthest distance reached by the puck = 180 meters. The puck reached the furthest distance at about 0.25 seconds after it was shot

c) Speed = Distance/time

The speed of the puck in the first 0.25 seconds = 180 m/0.25 s = 720 m/s

d) The domain and range of a graph is the set of the possible x- and y-values respectively.

The domain and range of the motion of the puck are;

Domain; 0 ≤ x ≤ 0.5, which is [0, 0.5]

Range; 0 ≤ y ≤ 180, which is; [0, 180]

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The transitions are labeled with the input symbol, the symbol to be pushed onto the stack (ε indicates no symbol is pushed), and the symbol to be popped from the stack (ε indicates no symbol is popped).This PDA accepts strings in L where the number of 'a's is twice the number of 'b's.

To draw the state diagram of a PDA that accepts the language L = {w ∈ {a, b}^∗ | w has twice as many a's as b's}, we can design a simple PDA with two states.

State 1: Initial state

Transition: (a, ε, a) -> State 1

Transition: (b, a, ε) -> State 2

Transition: (ε, ε, ε) -> Accepting state

State 2: Secondary state

Transition: (b, a, ε) -> State 2

Transition: (ε, ε, ε) -> Accepting state

Accepting state: Final state to indicate that the input string is accepted.

Here is the state diagram representation of the PDA:

Note: Find the attached image for the state diagram representation of the PDA.

In this PDA, State 1 is the initial state, and State 2 is the secondary state. The transitions are labeled with the input symbol, the symbol to be pushed onto the stack (ε indicates no symbol is pushed), and the symbol to be popped from the stack (ε indicates no symbol is popped).

The PDA works as follows:

This PDA accepts strings in L where the number of 'a's is twice the number of 'b's.

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The probability that the secretary will receive 6 calls next hour is approximately 0.090 or 9.0%.

The Poisson distribution is a probability distribution that describes the number of events occurring in a fixed time interval, given the average rate at which events occur and the independence of events. In this case, the average rate of calls is 3 calls per hour.

The probability of receiving exactly 6 calls next hour can be calculated using the Poisson probability formula:

\(P(X = 6) = (e^(-λ) * λ^6) / 6!\)

where λ is the average rate of calls, e is the base of the natural logarithm, and 6! is the factorial of 6.

Substituting the values, we get:

\(P(X = 6) = (e^(-3) * 3^6) / 6! ≈ 0.090\)

Therefore, the probability that the secretary will receive 6 calls next hour is approximately 0.090 or 9.0%.l

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The probability that the secretary will receive 6 calls next hour is approximately 0.0504, or 5.04%

To calculate the probability that the secretary will receive 6 calls next hour, given that the average is 3 calls per hour

and the Poisson distribution applies, follow these steps:

Identify the given information: λ (average calls per hour) = 3, k (number of calls to calculate the probability for) = 6.

Use the Poisson probability formula:

P(k) =\((e^{(-\lambda)} \times\lambda^k) / k!,\)

where P(k) is the probability of k calls,

e is the base of the natural logarithm (approximately 2.71828),

λ is the average rate (3 calls per hour), and

k! is the factorial of k (6 in this case).

Calculate \(e^{(-\lambda)}: e^{(-3)} = 0.04979.\)

Calculate \(\lambda^k: 3^6 = 729.\)

Calculate k!: 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720.

Substitute these values into the formula: P(6) = (0.04979 × 729) / 720 ≈ 0.0504.

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Answer: Standard Form

Step-by-step explanation:

In the slope intercept form, you can only solve for one equation at a time.

Ex: y = -2.5x + 15

but when using standard you can easly get the answer for both ticket prices

Ex: 25x + 10y = 150

5r + 2g = 30 is the linear equation that best describes the scenario.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given this, Hanna will spend $150 on music festival tickets. Reserved seat tickets cost $25 and general admission tickets cost $10.

Let "r" be the Number of reserved tickets she bought

and "g" be the number of  general admission tickets she bought

Money spent od reserved ticket = 25 * r

Money spent in general tickets = 10 *g

Since she totals spent 150$

Thus, the equation will be

25r + 10g = 150

Divide by 5 into both the sides

5r + 2g = 30

therefore, The linear equation that represents the given situation is 5r + 2g = 30.

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The antithesis of an exponential function is a logarithmic function. A logarithmic function and an exponential function both use the same base.

Writing y = log2 x or f(x) = log2 x represents the logarithmic function for the equation x = 2y. Even today, the base is still 2. Y equals log base b of x, or more simply, "y equals log to the base b of x," is how y = logb x is typically read. Similarly to exponential functions, b > 0 and b 1.

Consequently, the table's data is represented by the logarithmic function f(x) = log3(x).

Table provided:

                    x           f(x)

                    25          2

                   125          3

                   625         4

We can write x in this case as powers of 5, so that

\($25=5^2$$125=5^3$$625=5^4$$\Rightarrow f(x)=5^{f(x)}$\)

After dividing the log in half, we now have

\($\log x=\log 5^{f(x)}$$\Rightarrow \log x=f(x) \log 5 \ldots .\left[\log (a)^m=m \log (a)\right]$\)

\($\Rightarrow f(x)=\frac{\log x}{\log 5}$$\Rightarrow f(x)=\log _5 x \ldots \ldots\left[\log _a b=\frac{\log b}{\log a}\right]$\)

A base-log function \($f(x)=\log _5 x$\), then, reflects the data in the table.

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The next crow observed will be black is not supported by the premises in any meaningful way. The premises do not guarantee the outcome of the next observation.  Argument B is the stronger argument.

Argument A is an example of an inductive argument, as it generalizes from a limited sample to make a broader claim about the entire population. This argument form is called induction and can be evaluated on its strength.

Argument B is a deductive argument, as it uses a conditional premise to reach a definite conclusion. In this form of argument, the conclusion necessarily follows from the premises. The strength of a deductive argument depends on the logical structure of the premises and conclusion.

The better argument of the two is argument B. Because in deductive arguments, the conclusion necessarily follows from the premises if the premises are true.

And this argument, the premises state that if 90% of observed crows are black, then the next crow observed will be black.

Additionally, it is also claimed that 90% of observed crows are black. Therefore, it can be logically deduced that the next crow observed will be black

The argument in A, however, is an inductive argument, where the conclusion is not necessarily true even if the premises are true. Even if 90% of observed crows are black, it does not necessarily follow that 90% of all crows are black.

argument B is the stronger argument.

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Answer:

negative

Step-by-step explanation:

a posotive times a negative is a negative

Answer:

positive

Step-by-step explanation:

I hope this helps!

Answer:

View the image below

Step-by-step explanation:

To solve this problem, we can use conditional probability. We know that the sum of the numbers landing uppermost is 7, so we need to consider all the possible outcomes that satisfy this condition.

These outcomes are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1).
Out of these outcomes, only one has the first die landing on 5, which is (5,2). Therefore, the probability that the first die is a 5 given that the sum is 7 is 1/6.
So, the answer to your question is that the probability that the number landing uppermost on the first die is a 5 if it is known that the sum of the numbers landing uppermost is 7 is 1/6.
You want to find the probability that the number landing uppermost on the first die is a 5, given that the sum of the numbers landing uppermost is 7.
Step 1: Identify the favorable outcomes. In this case, the favorable outcome is when the first die lands on a 5, and the sum of the numbers is 7.
Step 2: Find the number of favorable outcomes. Since the first die must be a 5 and the sum is 7, the only favorable outcome is when the second die is a 2 (5 + 2 = 7).
Step 3: Identify the possible outcomes for a sum of 7. There are six possible combinations: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1).
Step 4: Calculate the probability. Divide the number of favorable outcomes by the number of possible outcomes for a sum of 7:
Probability = (Number of favorable outcomes) / (Number of possible outcomes for a sum of 7) = 1/6.
So, the probability that the number landing uppermost on the first die is a 5, given that the sum of the numbers landing uppermost is 7, is 1/6.

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The expected value of the sample mean of mpg derived from a random sample of four passengers is 30.5 mpg.

The expected value of the sample mean can be calculated using the formula

E(x) = μ

where x is the sample mean, and μ is the population mean.

In this case, the population mean is given as 30.5 mpg. The standard deviation of the population is also given as 4.1 mpg.

The standard deviation of the sample mean can be calculated using the formula

σx = σ/√n

where σ is the population standard deviation and n is the sample size.

Substituting the given values, we get:

σx = 4.1/√4 = 2.05

So the expected value of the sample mean is

E(x) = μ = 30.5 mpg.

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First, find the slope: m = Δy/Δx = (2-4)/(4-0) = -0.5

The "intercept" in the slope-intercept form of a line is the y-intercept. And at the y-intercept, x = 0. Conveniently, one of our points has an x = 0, i.e., the point (0,4). So, our equation would be y = -0.5x + 4.

If you wanted to double-check, you could use the point (4,2) to find the point-slope equation of the line and see if it matches up with the slope-intercept form above. Given a slope of -0.5 and a point (4,2), our point-slope equation would be y - 2 = -0.5(x - 4). If we expand this, we get y - 2 = -0.5x + 2. Solving for y, we obtain y = -0.5x + 4.

Thus, y = -0.5x + 4 would be our equation.

Answer:

D

Step-by-step explanation:

Since D is 18x/9 , you can divide 18 by 9 and you end up with 2x

The area of the base of the first sandbox is 64 square feet

Area is the measure of the amount of surface that a two-dimensional figure or shape covers. It is typically expressed in square units, such as square inches or square meters.

The area of a shape can be calculated by multiplying the length of its base by its height or by using specific area formulas for different shapes, such as the area of a circle or the area of a triangle.

The area of a square is given by the formula: A = s², where s is the length of one side of the square.

In this case, the sandbox has a square base with a side length of 8 feet. Therefore, the area of the base of the first sandbox is:

A = 8² = 64 square feet.

So, the area of the base of the first sandbox is 64 square feet

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Answer:

\(\large \boxed{4}\)

Step-by-step explanation:

\(\sf The \ sum \ of \ -5, \ -10, \ and \ -9 \ is \ divided \\ by \ the \ product \ or \ multiplication \ of \ 2 \ and -3.\)

\(\displaystyle \frac{-5+-10+-9}{2 \times -3}\)

\(\displaystyle \frac{-24}{-6}\)

\(=4\)

Answer:

4

Step-by-step explanation:

-5+(-10)+(-9)/2*(-3)

=-5-10-9/-6

=-24/-6

=4