Find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding the given integers. (Enter the value of probability in decimals. Round the answer to two decimal places.)
Discrete Probability with Lottery

Answer:

Step-by-step explanation:

x times 8 +12

8x+x=9x-12

Answer = 9x-12

The culture starts out with 39 members.

Given that;

After 20 minutes and 40 minutes, a bacteria culture had an 800 and 1700 count, respectively.

To get exponential growth;

We can get growth with an exponential function,

F(t) = A₀\(e^k^t\)

Here, k is the growth constant and A₀ is the initial amount of bacteria.

Let;

800 = A₀\(e^2^0^k\)  → (I)

1700 = A₀\(e^4^0^k\) → (II)

From (I) and (II);

1700 / 800 =  A₀\(e^4^0^k\) / A₀\(e^2^0^k\)

17/8 = \(e^2^0^k\)

For the above equation take the natural log on both sides;

ln(17/8) = ln \(e^2^0^k\)

ln(17/8) = 20k

k = ln(17/8) / 20

To get the initial size of the culture;

From (I),

800 = A₀\(e^2^0^k\)

800 = A₀e⁰°⁰³⁷⁶ ˣ ²⁰

A₀ = 800 / 20.76

A₀ = 38.53 ≅ 39

Therefore, the initial size of the culture is 39.

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We are going to find the coordinates of the points A'B', which are given by the dilation of AB about the point (5,5) with a scale factor of 2.

For doing so, we will determine the distance between the points A and (5,5), and we will multiply it by 2 (the scale factor). This will be the distance between A' and (5,5). We will do the same between the point B and (5,5).

As the lines x=5 and y=5 are perpendicular, the angle BPA is right (where P is the point (5,5)), we can find the distance of the point A'B' using the Pythagorean Theorem.

Now, we find the distance between A and P:

And the distance between B and P:

Multiplying by the scale factor we obtain:

And using the Pythagorean Theorem we obtain:

This means that the length of the dilation of AB will be 10.

Answer:

M(t) = -3 (t - 16) (t - 3)

Step-by-step explanation: Assuming you are working on the practice book - section 5: quadratic equations and functions than this is the correct answer to your question. Although there is another question below the on you have asked on in the actual textbook so if you need help on that just ask me in the comments below.

• Integer values: ,numbers including 0, and negative and positive numbers; it can never be a fraction, a decimal, or a percent.

Based on the definition, the integer values included in the interval [-5, 0] are: -5, -4, -3, -2, -1, and 0.

To evaluate if the integer satisfies the inequality, we have to evaluate each integer.

• -5

As -13 is smaller than -9, then -5 does not satisfy the inequality.

• -4

As -9 is equal to -9, then -4 does not satisfy the inequality (as in the sign of the inequality it is not included -9).

• -3

As -5 is bigger than -9, -3 satisfies the inequality.

• -2

As -1 is bigger than -9, -2 satisfies the inequality.

• -1

As 3 is bigger than -9, -1 satisfies the inequality.

• 0

As 7 is bigger than -9, 0 satisfies the inequality.

Also we can try by solving the inequality:

Meaning that all the values that are greater than -4 but not -4.

Answer:

• [-3, 0]

• x = -3, -2, -1, 0

• x > -4

Answer:

Step-by-step explanation:

\(50+2x=20+5x\\\\\mathrm{Subtract\:}50\mathrm{\:from\:both\:sides}\\\\50+2x-50=20+5x-50\\\\Simplify\\\\2x=5x-30\\\\\mathrm{Subtract\:}5x\mathrm{\:from\:both\:sides}\\\\2x-5x=5x-30-5x\\\\Simplify\\\\-3x=-30\\\\\mathrm{Divide\:both\:sides\:by\:}-3\\\\\frac{-3x}{-3}=\frac{-30}{-3}\\\\Simplify\\\\x=10\)

The expressions are not equivalent because Ella did not know that you can’t use substitution to test for equivalence.

Some expressions on simplification give the same resulting expression. These expressions are known as equivalent algebraic expressions. Two algebraic expressions are meant to be equivalent if their values obtained by substituting any values of the variables are the same.

Two expressions given 3f+2.6 and 2f+2.6 are not equivalent. This is because when f=1,

3f + 2.6 = 3.1 + 2.6 = 3 + 2.6 = 5.6

2f + 2.6 = 2.1 + 2.6 = 2 + 2.6 = 4.6

5.6 is not equal to 4.6

Method of substitution can only help her to decide the expressions are not equivalent, but if she wants to prove the expressions are equivalent, she must prove it for all values of f.

3f + 2.6 = 2f + 2.6

3f = 2f

3f - 2f = 0

f = 0

This is true only when f=0.

Hence,

The expressions are not equivalent because Ella did not know that you can’t use substitution to test for equivalence.

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So the probability that Joe will not receive a text in the next 10 minutes is approximately 0.865. So the probability that the next text arrives between 9:07 and 9:10 p.m. is approximately 0.149. So the probability that a text arrives before 9:03 p.m. is approximately 0.393. So the probability that no text will arrive for 7 minutes, given that no text has arrived for 5 minutes, is approximately 0.394.

(a) To find the probability that Joe will not receive a text in the next 10 minutes, we can use the cumulative distribution function (CDF) of the exponential distribution. The CDF gives the probability that the time until the next text is less than or equal to a given time t. The CDF of an exponential distribution with mean 5 minutes is:

\(F(t) = 1 - e^{(-t/5)}\)

To find the probability that Joe will not receive a text in the next 10 minutes, we need to find F(10):

\(F(10) = 1 - e^{(-10/5)}\)

\(= 1 - e^{(-2)}\)

≈ 0.865

(b) To find the probability that the next text arrives between 9:07 and 9:10 p.m., we need to find the probability that the time until the next text is between 7 and 10 minutes. We can use the CDF again to find this probability:

P(7 < X < 10) = F(10) - F(7)

\(= (1 - e^{(-10/5)}) - (1 - e^{(-7/5)})\)

\(= e^{(-7/5)} - e^{(-2)}\)

≈ 0.149

(c) To find the probability that a text arrives before 9:03 p.m., we need to find the probability that the time until the next text is less than 3 minutes. We can use the CDF again to find this probability:

P(X < 3) = F(3)

\(= 1 - e^{(-3/5)}\)

≈ 0.393

(d) To find the probability that no text will arrive for 7 minutes, given that no text has arrived for 5 minutes, we can use the memoryless property of the exponential distribution. The memoryless property states that the conditional distribution of the time until the next text, given that no text has arrived in the first 5 minutes, is the same as the original distribution. In other words, the fact that no text has arrived in the first 5 minutes does not affect the probability of a text arriving in the next 7 minutes.

Therefore, the probability that no text will arrive for 7 minutes, given that no text has arrived for 5 minutes, is the same as the probability that no text will arrive for 7 minutes starting from scratch. This is the probability that the time until the next text is greater than 7 minutes. Using the CDF of the exponential distribution, we can calculate:

P(X > 7) = 1 - F(7)

\(= 1 - (1 - e^{(-7/5)})\)

= \(e^{(-7/5)}\)

≈ 0.394

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Answer:

decision-making

Step-by-step explanation:

The required values of x in the interval 0° ≤ x ≤ 360° are 146.1° and 326.1°, when the value of tan x is given.

The interval of angle is given as 0° ≤ x ≤ 360°.

The value of x for which tan x is given as, tan x = - 0. 6745.

We have tan negative in two of the four axes, they are second (90° - 180°) and fourth quadrants (270° - 360°).

So, tan x = - 0. 6745

x = tan⁻¹ (- 0. 6745) = -33.9

As periodicity of tan x is 180°, x = 180-33.9 = 146.1°

x = 360-33.9 = 326.1°

Thus, the required values of x in the interval 0° ≤ x ≤ 360° are 146.1° and 326.1°, when the value of tan x is given.

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Pat and John will meet in 3 hours.

It should be noted that speed = Distance / Time

The appropriate equation will be:

80t + 24t = 312

104t = 312

t = 312/104

t = 3. hours

Therefore, it will take them 3 hours to meet.

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Answer:

x = -1, -4

Step-by-step explanation:

\(|2x+5|=3\)

Subtract 5 from both sides

\(|2x| = -2\)

Divide both sides by 2

\(x=-1\) (First solution)

\(|2x+5|=3\)

-2x = 8

x = -4

Given:

The stand sold 4 cherry snow cones for every 1 lemon snow cone sold.

There were 30 more cherry snow cones than lemon snow cones sold yesterday.

To find:

The number of snow cones which were sold altogether.

Solution:

Let x be the number of lemon snow cone sold.

The stand sold 4 cherry snow cones for every 1 lemon snow cone sold.

So, number of cherry snow cone sold = 4x

There were 30 more cherry snow cones than lemon snow cones sold yesterday.

\(4x-x=30\)

\(3x=30\)

Divide both sides by 3.

\(x=\dfrac{30}{3}\)

\(x=10\)

Total number of snow cones sold is

\(\text{Total number of snow cones sold }=x + 4x\)

\(\text{Total number of snow cones sold }=5x\)

\(\text{Total number of snow cones sold }=5(10)\)

\(\text{Total number of snow cones sold }=50\)

Therefore, 50 snow cones were sold altogether.

The given series can be evaluated and determined whether it converges or diverges. In this case, the series diverges.

To explain the divergence, let's analyze each term in the series individually. The first term is 101.21/n, which tends to zero as n approaches infinity. The second term is 21/(n+1), which also tends to zero as n approaches infinity. The third term is n, which grows without bound as n increases. The fourth term is 1/102(n+1), which tends to zero as n approaches infinity. The fifth term is 13/103, which is a constant value. Finally, the sixth term is (sin n * sin(n+1))/104, which oscillates between -1 and 1 as n increases.

The divergence of the series can be attributed to the fact that the terms do not approach a finite value as n approaches infinity. The terms oscillate, grow without bound, or tend to zero at different rates. Therefore, the series does not converge to a specific value and is classified as divergent.

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(a) The equation Ax = 0 has a nontrivial solution if the matrix A has a nontrivial null space.

(b) The equation Ax = b has at least one solution for every possible b if the matrix A is invertible.

To answer Exercises 41-44, you need to provide the matrix A in each case so that we can determine if it has a nontrivial null space and if it is invertible.

To determine if the equation Ax = 0 has a nontrivial solution, we need to check if the matrix A has a nontrivial null space. The null space of a matrix A consists of all vectors x such that Ax = 0.

(a) If the matrix A has a nontrivial null space, it means that there exists a nonzero vector x that satisfies Ax = 0, and thus the equation Ax = 0 has a nontrivial solution. Otherwise, if the null space of A only contains the zero vector, then the equation Ax = 0 only has the trivial solution (x = 0).

To determine if the equation Ax = b has at least one solution for every possible b, we need to check if the matrix A is invertible. An invertible matrix has a unique solution for any given right-hand side vector b.

(b) If the matrix A is invertible, then for every possible vector b, the equation Ax = b has a unique solution. However, if the matrix A is not invertible, it means that there exist some vectors b for which the equation Ax = b does not have a solution.

To summarize:

Otherwise, there exist some vectors b for which the equation does not have a solution.

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Note: The complete question is-

A is a 3 x 3 matrix with three pivot positions.

(a) Does the equation Ax = 0 have a nontrivial solution0

(b) Does the equation Ax = b have at least one solution for every possible

A=200,201,202.........,2000

Here, it forms an AP with common difference 1

Let the number of terms in the set be n

\( T_{n} = a+(n-1)d \\\\ 2000= 200+(n-1) \\\\ 200+n-1= 2000 \\\\ => n=2000-199= 1801\)

Hence,n(A)=1801

Answer:

7.008, 7.08, 7.3, 7.3071

Answer:

14

Step-by-step explanation:

trust me.

Answer:

you were correct. c. 14 days

Step-by-step explanation:

i hope this helps :)

The account balance after 18 years is $4,659.98

The formula for calculating the compound interest is expressed as:

A = P(1+r)^n

P is the amount deposited = $1500

Rate = 6.5% = 0.065

compounding time = 1

time in years = 18 years

Substitute the given parameters into the formula;

A = 1500(1+0.065)^18

A = 1500(1.065)^18

A = $4,659.98

Hence the account balance after 18 years is $4,659.98

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Answer:

abcdef

Step-by-step explanation:

The required value of integration of given function is 82.

To evaluate the integral  we need to find the anti-derivative of F(x) and then evaluate it at the limits of integration.

Since F(x) = 8 for x < 8 and F(x) = x for x ≥ 8, we can split the integral into two parts, one from 0 to 8 and another from 8 to 10

According to question:

\($$\begin{aligned}& \int_0^{ 10} \mathrm{~F}(\mathrm{x}) \mathrm{dx} \\& =\int_0^8 F(x) d x+\int_8^{10} F(x) d x\end{aligned}\\$$\)

The anti-derivative of

\(F(x)=8$ is $F(x)=8 x$, so:$$\)

\($$\begin{aligned}& \int_8^{10} F(x) d x \\& =\left.\left(x^2 / 2\right)\right|_8 ^{10} \\& =\left(10^ 2 / 2\right)-\left(8^2 / 2\right) \\& =50-32 \\& =18\end{aligned}$$\)

Putting it all together

\($\int_0^10 \mathrm{~F}(\mathrm{x}) \mathrm{dx}=64+18=82$\)

So, the value of the integral \($\int_0^{10} F(x) d x$\) is 82.

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Complete question:

Answer: F

Step-by-step explanation:

F, because side length correlates directly to angle, so the smallest side has the smallest angle.

your answer is 740 {:

Step-by-step explanation:

let x be the original price

then we write our equation

x-60%x=200 (x=100%x)

100%x-60%x=200

40%x=200

(40/100)x=200

x=(200*100)/40

x=20000/40=500

so the original price was $500

(i) To find the solution for yt in the given equation yt = yt−1 + εt + 0.3εt−1, we can rewrite it as yt - yt−1 = εt + 0.3εt−1. By applying the lag operator L, we have (1 - L)yt = εt + 0.3εt−1.

Solving for yt, we get yt = (1/L)(εt + 0.3εt−1). The solution for yt involves lag operators and depends on the values of εt and εt−1.  (ii) For the equation yt = 1.2yt−1 + εt, to find the s-step-ahead forecast Et[yt+s], we can recursively substitute the lagged values. Starting with yt = 1.2yt−1 + εt, we have yt+1 = 1.2(1.2yt−1 + εt) + εt+1, yt+2 = 1.2(1.2(1.2yt−1 + εt) + εt+1) + εt+2, and so on. The s-step-ahead forecast Et[yt+s] can be obtained by taking the expectation of yt+s conditional on the available information at time t.

To make this model stationary, we need to ensure that the coefficient on yt−1, which is 1.2 in this case, is less than 1 in absolute value. If it is greater than 1, the process will be explosive and not stationary. To achieve stationarity, we can either decrease the value of 1.2 or introduce appropriate differencing operators.

(iii) For the equation yt = yt−1 + t + εt, finding the solution for yt and the s-step-ahead forecast Et[yt+s] involves incorporating the time trend t. By recursively substituting the lagged values, we have yt = yt−1 + t + εt, yt+1 = yt + t + εt+1, yt+2 = yt+1 + t + εt+2, and so on. The s-step-ahead forecast Et[yt+s] can be obtained by taking the expectation of yt+s conditional on the available information at time t.

To make this model stationary, we need to remove the time trend component. We can achieve this by differencing the series. Taking first differences of yt, we obtain Δyt = yt - yt-1 = t + εt. The differenced series Δyt eliminates the time trend, making the model stationary. We can then apply forecasting techniques to predict Et[Δyt+s], which would correspond to the s-step-ahead forecast Et[yt+s] for the original series yt.

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We will have a Deficit balance of $30 at the end of the month.

"Unilateral transfer" is the term used to describe the balance of payments deficit's most obvious cause. For instance, Americans who contribute money to another country in the form of foreign aid do not receive anything in return (economically speaking). Few economists would argue that foreign aid-related balance of payment deficits are a "bad thing."

Weekly net income = $380

Monthly net income = $380 * 4 weeks = $1520.

Monthly expenses = $1550

Balance = Monthly income - monthly expenses = $-30.

The negative sign shows a deficit of $30 monthly

Therefore, We will have a Deficit balance of $30 at the end of the month.

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Answer:

55°

Step-by-step explanation:

For the line including the 110°, the angle of the supplementary angle is 70° which is the 'non-equivalent' length of the isosceles triangle. Then do:

(180°-70°)/2 = 55° to get x

Answer:

Supplementary angles, x = 55

Step-by-step explanation:

Supplementary angles: straight line means both angles add up to 180, this if the outside angle is 110 then the inside angle is 180° - 110° = 70°

Since it is an isosceles triangle, it means both angles are equal to x therefore

\(180 - 70 = 2x\\110 = 2x\\\frac{110}{2} = x\\x = 55\)

The probability that one is selected is the likelihood

The probability that one is selected at least once is 0.704

The sample space is given as:

S = {1,2,3}

The probability that 1 is not selected at all is:

P'(None) = 2/3

The probability that one is selected at least once is calculated using the following complement rule

P(At least once)  = 1 - P(None)^3

This gives

P(At least once) = 1 -(2/3)^3

Evaluate

P(At least once) = 0.704

Hence, the probability that one is selected at least once is 0.704

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The Cartesian product that I read about is a mathematical concept that is used to combine two sets together in a specific way. The Cartesian coordinate system, on the other hand, is a way of representing points in a two-dimensional plane using a set of numerical coordinates.

The relationship between the two is that the Cartesian product is used to create the set of all possible coordinates that can be used in the Cartesian coordinate system. The Cartesian product of two sets, say set A and set B, is the set of all ordered pairs (a, b) where a belongs to set A and b belongs to set B.

When we graph a point in the Cartesian coordinate system, we are picking a specific point from the set of all possible points that can be created using the Cartesian product of the set of x-coordinates and the set of y-coordinates.

In other words, the Cartesian product is the foundation of the Cartesian coordinate system. It provides a set of all possible points that can be graphed using that system.

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