Decide whether the equation has no solution, one solution, or infinitely many
solutions. Put an X in the appropriate box in the table.
Infinitely

Given the algebraic expression 3x⁴ - 5x + 2, each of following represents:

An algebraic expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables, numerical quantities (constants), accompanied with the use of different mathematical operations.

In Mathematics, a coefficient simply refers to a constant quantity or numerical value (number or numeral) that is typically placed before the variable in an algebraic expression.

In conclusion, an exponent is an operation that raises a numerical value or quantity to the power of another and it is generally written as bⁿ.

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-1.56, -0.98, -0.13, -0.1, 0.5, 0.93

Answer:

-1.56, -0.98, -0.13, -0.1, 0.5, 0.93

Step-by-step explanation:

Answer:

Step-by-step explanation:

The radius of the outside of the pipe is 6 inches and the radius of the inside of the pipe

is 5.75 inches

Determine the volume of metal used to build the pipe.

Answer:

Step-by-step explanation:

Part a(i)Poisson distribution is used for discrete probability distribution that represents the number of times an event occurs within a specified time interval or space if these events are independent and random. Here, X has a Poisson distribution with λ=2.5.

Therefore, The probability of X=0 is given by:

P(X=0) = e^(-λ) (λ^0)/0! = e^(-2.5) (2.5^0)/0! = e^(-2.5) = 0.082Part a(ii)Here, the probability of X≥1 can be obtained as:

P(X≥1) = 1- P(X=0) = 1 - e^(-λ) = 1 - e^(-2.5) = 0.918

Part b(i)The number of work-related injuries per month in Nimpak is known to follow a Poisson distribution with a mean of 3.0 work-related injuries a month. Let Y be the number of work-related injuries in a month. Then Y~Poisson(λ=3)Therefore, the probability of exactly two work-related injuries occur in a month is:

P(Y=2) = e^(-λ) (λ^y)/y! = e^(-3) (3^2)/2! = 0.224Part b(ii)The probability that more than two work-related injuries occur is:

P(Y>2) = 1 - P(Y≤2) = 1 - [P(Y=0) + P(Y=1) + P(Y=2)] = 1 - [e^(-3) + 3e^(-3) + 0.224] = 1 - 0.791 = 0.209Part c(i)Suppose that a council of 4 people is to be selected at random from a group of 6 ladies and 2 gentlemen. Let X represent the number of ladies on the council. This indicates that X~Hypergeometric(6, 2, 4).Then the distribution of X is given by:

P(X=x) =  [ (6Cx) (2C4-x) ] / 8C4 for x = 0, 1, 2, 3, 4Here is the table of probabilities:xi01234

P(X = x)0.00020.02880.34400.46240.1648Part c(ii)We need to calculate P(1≤X≤3).P(1≤X≤3) = P(X=1) + P(X=2) + P(X=3) = 0.288 + 0.344 + 0.194 = 0.826Therefore, P(1≤X≤3) = 0.826.

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Answer: A is the Answer hope this helps

Step-by-step explanation:

Answer:

V≈268.08cm³

Step-by-step explanation:

Answer:144 in.

Step-by-step explanation:

a) P(DSC) = A/1000, P(CA|DSC) = B/200, P(CA|~DSC) = B/300

b) Sample space:

Dust Storm, Car Accident: P(DSC ∩ CA) = (A/1000) * (B/200)

No Dust Storm, Car Accident: P(~DSC ∩ CA) = (1 - A/1000) * (B/300)

Dust Storm, No Car Accident: P(DSC ∩ ~CA) = (A/1000) * (1 - B/200)

No Dust Storm, No Car Accident: P(~DSC ∩ ~CA) = (1 - A/1000) * (1 - B/300)

c) P(CA) = (A/1000) * (B/200) + (1 - A/1000) * (B/300)

d) P(DSC|CA) = ((A/1000) * (B/200)) / ((A/1000) * (B/200) + (1 - A/1000) * (B/300))

a) The probabilities can be denoted as follows:

P(DSC) = A/1000 (Probability of Dust Storm)

P(CA|DSC) = B/200 (Probability of Car Accident given Dust Storm)

P(CA|~DSC) = B/300 (Probability of Car Accident given No Dust Storm)

b) Sample space and associated probabilities:

Dust Storm, Car Accident: P(DSC ∩ CA) = P(DSC) * P(CA|DSC) = (A/1000) * (B/200)

No Dust Storm, Car Accident: P(~DSC ∩ CA) = P(~DSC) * P(CA|~DSC) = (1 - A/1000) * (B/300)

Dust Storm, No Car Accident: P(DSC ∩ ~CA) = P(DSC) * P(~CA|DSC) = (A/1000) * (1 - B/200)

No Dust Storm, No Car Accident: P(~DSC ∩ ~CA) = P(~DSC) * P(~CA|~DSC) = (1 - A/1000) * (1 - B/300)

c) The probability of a car accident in a day in that junction is calculated by summing the probabilities of car accidents occurring under both dusty and non-dusty conditions:

P(CA) = P(DSC ∩ CA) + P(~DSC ∩ CA)

= (A/1000) * (B/200) + (1 - A/1000) * (B/300)

d) Given that there was a car accident today, the probability that today is a dusty day can be calculated using Bayes' theorem:

P(DSC|CA) = (P(DSC) * P(CA|DSC)) / P(CA)

= ((A/1000) * (B/200)) / P(CA) [Using the values from part (c)]

To find P(CA), substitute the expression from part (c) into the equation:

P(DSC|CA) = ((A/1000) * (B/200)) / ((A/1000) * (B/200) + (1 - A/1000) * (B/300))

In summary:

a) P(DSC) = A/1000, P(CA|DSC) = B/200, P(CA|~DSC) = B/300

b) Sample space:

Dust Storm, Car Accident: P(DSC ∩ CA) = (A/1000) * (B/200)

No Dust Storm, Car Accident: P(~DSC ∩ CA) = (1 - A/1000) * (B/300)

Dust Storm, No Car Accident: P(DSC ∩ ~CA) = (A/1000) * (1 - B/200)

No Dust Storm, No Car Accident: P(~DSC ∩ ~CA) = (1 - A/1000) * (1 - B/300)

c) P(CA) = (A/1000) * (B/200) + (1 - A/1000) * (B/300)

d) P(DSC|CA) = ((A/1000) * (B/200)) / ((A/1000) * (B/200) + (1 - A/1000) * (B/300))

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Step-by-step explanation:

I hope this answer is helpful ):

Answer:

  a) 1456/243

  b) 170

Step-by-step explanation:

The sum of n terms of a geometric sequence with first term a1 and common ratio r is given by ...

  Sn = a1·(r^n -1)/(r -1)

__

The first term is 4; the common ratio is 1/3. You want the sum of 6 terms:

  S6 = 4·((1/3)^6 -1)/(1/3 -1) = 4(-728/729)/(-2/3) = 1456/243

__

The first term is -2; the common ratio is -2. You want the sum of 8 terms:

  S8 = -2((-2)^8 -1)/(-2 -1) = -2(255/-3) = 170

Dilation and rotation are the a series of transformations, which transformation would make two figures similar as opposed to congruent.

Rotations, reflections and translations are known as rigid transformations; this means they do not change the size or shape of a figure, they simply move it. These rigid transformations preserve congruence.

Rotations is defined as the motion of an object around a center or an axis.

Dilation, however, are not rigid transformations, since they change the size of a shape. Dilation would not change the shape, just the size; the angle measures would be the same, and the ratio of corresponding sides would be equal to the scale factor used in the dilation.

This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape. A dilation should either stretch or shrink the original shape.

This would give us a similar, but not congruent, figure.

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In a series of transformations, which transformation would make two figures similar as opposed to congruent?

A) Rotation and translation

B) Dilation and rotation

C) Reflection and rotation

D) Translation and reflection

Using the findings from a qualitative study to develop a new quantitative survey is known as mixed integration.

Mixed integration is called the data collection and information classification system that includes both qualitative and quantitative processes as access mechanism to said data and information, that is, performing a mixed or dual analysis of the concepts being studied.

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Answer: x=-1

Step-by-step explanation:

Answer:

2/5

Step-by-step explanation:

We can represent the probability that the spinner lands on purple as:

\(\dfrac{\# \text{ purple spins}}{\#\text{ total spins}}\)

\(=\dfrac{80}{40 + 80 + 80}\)

\(= \dfrac{80}{200}\)

\(\boxed{=\dfrac{2}{5}}\)

So, the probability of this spinner landing on purple is 2/5.

9514 1404 393

Answer:

  $460

Step-by-step explanation:

If w is the number of weeks the car is rented, and m is the number of miles driven, the cost structure tells you the rental cost (c) is ...

  c = 180w +0.25m

For w=2 and m=400, this becomes ...

  c = 180·2 +0.25·400 = 360 +100 = 460

The cost of the 2-week rental will be $460.

__

The family size is irrelevant to the cost.

The main difference between the reciprocal and inverse of a function is their definition and properties. The reciprocal of a function f(x) is defined as 1/f(x), while the inverse of a function f(x) is a function f^(-1)(x) such that \(f(f^(-1)(x))=x and f^(-1)(f(x))=x\) for all x in their respective domains.

The domains of sine, cosine, and tangent functions need to be restricted to define their inverse functions because they are not one-to-one functions. In order to have an inverse, a function must be both one-to-one (each output has only one input) and onto (each output value is mapped by at least one input value).

For example:
- sine: restricted domain to [-π/2, π/2] to define its inverse, arcsin (sin^(-1))
- cosine: restricted domain to [0, π] to define its inverse, arccos (cos^(-1))
- tangent: restricted domain to (-π/2, π/2) to define its inverse, arctan (tan^(-1))

These restrictions ensure that the functions become one-to-one and onto, making it possible to define their inverses uniquely.

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Answer:

4%

Step-by-step explanation:

Answer:

4%

Step-by-step explanation:

1/24=0.0416=0.04=4%

4%

Among the given options, the correct statement is: C. Var (X + Y) = Var (X) + Var (Y).

This statement is known as the addition rule for variance and holds true for all random variables X and Y, regardless of their specific distributions.

To understand why this statement is true, let's briefly discuss the concept of variance. Variance measures the dispersion or spread of a random variable's values around its expected value (mean). Mathematically, variance is defined as the average of the squared deviations of the random variable from its mean.

Now, let's prove statement C:

Var (X + Y) = E[(X + Y - E[X + Y])^2] (definition of variance)

= E[(X + Y - E[X] - E[Y])^2] (linearity of expectation)

Expanding the square term:

mathematica

Copy code

       = E[(X - E[X])^2 + 2(X - E[X])(Y - E[Y]) + (Y - E[Y])^2]

By linearity of expectation, we can split this expression into three parts:

scss

Copy code

       = E[(X - E[X])^2] + 2E[(X - E[X])(Y - E[Y])] + E[(Y - E[Y])^2]

       = Var(X) + 2Cov(X, Y) + Var(Y)     (definition of variance and covariance)

Note that Cov(X, Y) represents the covariance between X and Y, which measures the extent to which X and Y vary together. However, the given options do not mention anything about the covariance between X and Y, so we cannot determine its value.

Therefore, statement C is correct because it expresses the addition rule for variance, which states that the variance of the sum of two random variables is equal to the sum of their individual variances.

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The given information is:\(tan(0) Hint = sin(0) = cos(0) = sec (0) = 3' 0≤0 ≤ 90°\)First of all, let's recall some of the basic trigonometric ratios and definitions.

The definition of \(tan:$$\tan\theta=\frac{\sin\theta}{\cos\theta}$$\)

The definition of \(sec:$$\sec\theta=\frac{1}{\cos\theta}$$\)

Given that tan(0) \(Hint = sin(0) = cos(0) = sec (0) = 3' 0≤0 ≤ 90°\)

Let's use these values in the equation.\($$tan(0)=\frac{sin(0)}{cos(0)}$$$$3=\frac{3}{cos(0)}$$\)

Multiplying both sides of the equation by \($cos(0)$, we get:$$3cos(0)=3$$$$cos(0)=1$$\)

Now, let's find the value of \($\sec(0)$\) using the definition of \($\sec\theta$.$$\sec(0)=\frac{1}{\cos(0)}$$$$=\frac{1}{1}=1$$\)

Therefore, the exact value of\($\sec(0)$\) is 1.I hope this helps!

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Answer:

5 out of 7.

Step-by-step explanation:

There are seven days in one week. They are asking what is the probability of the person chosen not being born in a Tuesday or Wednesday. There are five other days, so there are five other options.

I hope I helped you!

Therefore, (a) ∫58cos(0.1635t - 0.642)dt from 0 to 10 gives approximately 822.6 cars, (b) ′′(5) = -65cos(0.281) which is approximately -62.4 cars per hour per hour, (c) Approximately 559 cars in the garage at t = 10.

(a) To find the number of cars entering the parking garage over the interval 0 ≤ t ≤ 10, we need to integrate the rate of cars entering the garage with respect to time. ∫58cos(0.1635t - 0.642)dt from 0 to 10 gives approximately 822.6 cars.
(b) To find ′′(5), we need to differentiate the rate of cars leaving the garage with respect to time twice. ′′(t) = -65cos(0.281) and ′′(5) = -65cos(0.281) which is approximately -62.4 cars per hour per hour. This value represents the rate of change of the rate of cars leaving the garage at t = 5.
(c) To find the number of cars in the parking garage at time t = 10, we need to subtract the total number of cars leaving the garage from the total number of cars entering the garage from t = 0 to t = 10. This gives approximately 559 cars in the garage at t = 10.


Therefore, (a) ∫58cos(0.1635t - 0.642)dt from 0 to 10 gives approximately 822.6 cars, (b) ′′(5) = -65cos(0.281) which is approximately -62.4 cars per hour per hour, (c) Approximately 559 cars in the garage at t = 10.

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Answer: 0.66 (repeating)

Step-by-step explanation:

2/3 is equivalent to 4/6 and 2/3 is 0.66 repeating  

The probability of matching 6 randomly chosen integers is 1/593,775.

According to the statement

we have to find that the probability of winning a lottery.

So, For this purpose,

The given information is :

Total numbers are 30 and they are the positive integers and we have to pick 6 integers from them.

So, use the combination here

Combination is the number of possible arrangements in a collection of items where the order does not matter.

And

There are C(30, 6) = 30!/(6!*(30-6)!)

C(30, 6)= 593,775

So, There are 593,775 ways to pick 6 numbers from the first 30 positive integers.

And

The probability of winning a lottery is with 6 integers is :

1/593,775

So, The probability of matching 6 randomly chosen integers is 1/593,775.

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Question:

Find the probability of winning a lottery by selecting the correct six integers where the order in which these integers are selected does not matter from the positive integers not exceeding 30.

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Answer:

NO=OP

Step-by-step explanation:

To identify the false statement in the diagram, analyze the given options and compare with the information presented. In this case, the false statement is that the figure has four sides. It actually has three sides, making it a triangle.

In order to identify the false statement based on the diagram, you need to analyze the given options and compare them with the information presented in the diagram.

Let's assume the options are:

The figure is not a triangle.

There are three blue items in the diagram.

The figure has four sides.

The figure is a square.

After examining the diagram, you can determine that option 3, 'The figure has four sides,' is false. The diagram clearly shows a figure with three sides, making it a triangle. The false statement contradicts the information depicted in the diagram.

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If we look at the tree diagram, we can see that we have 12 numbers, they are:

{12, 13, 16, 21, 23, 26, 31, 32, 36, 61, 62, 63}

That's our sample space, if we look at each tree we can count how many numbers has 1 or 6, on the first tree we have 2 numbers: 21 and 26. On the second tree we have three numbers: 12, 13 and 16, that's expected because the first digit is 1. For the second tree we have just two, 31 and 36. For the last tree we have three again because of the digit 6.

Therefore the probability will be how many numbers that has 1 or 6 divided by the sample space, then

The probability is

Answer:

2

Step-by-step explanation:

Hey there!

The equation is asking us, c x c = 4

What is c?

Well the only number that is equal to 4 when you square it is 2