. The psychology club is having a self-proclaimed psychic come to their campus fund-raising event to demonstrate his abilities. He charges $200 for these events, and the club is charging $1.50 for tickets with a chance to have the psychic read the ticket holder’s mind.

How much would the club gain or lose by selling 125 tickets?

and will The club will gain or lose?

We can determine the population in 1820 was 8.5753 using a linear equation.

A linear equation is one that has just a constant and a first order (linear) component, like y=mx+b, where m is the slope and b is the y-intercept.

When x and y are the variables, the aforementioned is sometimes referred to as a "linear equation of two variables."

dp/dt = \(1.37^{t}\)

Integrate both sides.

p[h] = ( \(1.37^{t}\))/In (1.37)   + c

1810 ⇒ t = 0

7.4 = 1/In (1.37) + C

C = 4.2235

p(H) = ( \(1.37^{t}\))/In (1.37) + 4.2235

P (1) =  \(1.37^{t}\)In (1.37) + 4.2235

= 8.5753

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P(X = 7), λ = 6: The Poisson probability of X = 7, with a parameter (λ) value of 6, is 0.1446. P(X = 11), λ = 12: The Poisson probability of X = 11, with a parameter (λ) value of 12, is 0.0946. P(X = 6), λ = 8: The Poisson probability of X = 6, with a parameter (λ) value of 8, is 0.1206.

The Poisson probability is used to calculate the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence (parameter λ). The formula for Poisson probability is P(X = k) = (e^-λ * λ^k) / k!, where X is the random variable representing the number of events and k is the desired number of events.

To calculate the Poisson probabilities in this case, we substitute the given values of λ and k into the formula. For example, for the first case (a), we have λ = 6 and k = 7: P(X = 7) = (e^-6 * 6^7) / 7!

Using a calculator, we can evaluate this expression to find that the probability is approximately 0.1446. Similarly, for case (b) with λ = 12 and k = 11, and for case (c) with λ = 8 and k = 6, we can apply the same formula to find the respective Poisson probabilities.

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Answer:

1942.5435 dollars

Step-by-step explanation:

1500(1.09)^t  (t=3)

1500(1.09)^3= 1942.5435 dollars

With the help of binomial distribution we can conclude our answer.

acc to our question-

The confidence interval can be found out using,

Hence, the confidence interval for the mean load required to pull the wood apart is (29,485.192 , 32,114.8).

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Answer:

a) See attachment

b) P has coordinates of (5,7)

Step-by-step explanation:

Step-by-step explanation:

It doesn't have neither the greater than or equal to or less than or equal to signs so

take the natural logarithm of both sides:

Divide both sides by ln(12):

Answer:

Amy is (21.6 - 14.4) 7.2 km/hr faster than Bill.

Distance = speed / time

Amy's speed

40 minutes = 40/60 = 2/3 hours

14.4 = speed / 2/3

Speed = 14.4 * 3/2 = 21.6 km/ hr

Bill speed

60 minutes = 1 hour

Speed = 14.4 km / hr.

Answer: (0,-1)

Step-by-step explanation:

Let's start with the first inequality, \(y < -x^{2}+x\). To check which points satisfy this inequality, we can substitute the x- and y-coordinates and see if they satisfy the inequality.

Once again, we can repeat this for the second inequality (but this time, we only need to check the points that satisfy the first inequality).

Therefore, the answer is (A) (0, -1).

Answer:

There are 3024 different ways the artist can arrange 4 paintings side-by-side on the wall and there are 126 different groups of 4 paintings the artist could choose to display.

Step-by-step explanation:

(a) To find the number of ways the artist can arrange 4 paintings side-by-side on the wall, we will use the permutation formula.

In this case, n = 9 (total works of art) and r = 4 (number of paintings to display).

Permutations (nPr) = n! / (n-r)! = 9! / (9-4)! = 9! / 5! = 362880 / 120 = 3024

So, there are 3024 different ways the artist can arrange 4 paintings side-by-side on the wall.

(b) To find the number of different groups of 4 paintings the artist could choose to display, we will use the combination formula.

In this case, n = 9 and r = 4.

Combinations (nCr) = n! / [r! * (n-r)!] = 9! / (4! * (9-4)!) = 9! / (4! * 5!) = 362880 / (24 * 120) = 362880 / 2880 = 126
So, there are 126 different groups of 4 paintings the artist could choose to display.

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The curl of vector field F is -i - j and the divergence of the vector field F is 0.

We have to follow the below steps:

Step 1: Find curl.

Step 2: Find divergence.

Curl :

Curl is the vector operator that defines the cross product of two vectors. It is applied to a vector field to generate another vector field.

Step 1:

Find the curl of vector field

Curl of the vector field F is defined as ,F = (P, Q, R)

Curl F = (Ry - Qz)i + (Pz - Rx)j + (Qx - Py)k

Where, Ry denotes the partial derivative of R with respect to y. Qz denotes the partial derivative of Q with respect to z, Pz denotes the partial derivative of P with respect to z .Rx denotes the partial derivative of R with respect to x, Qx denotes the partial derivative of Q with respect to x. Py denotes the partial derivative of P with respect to y.

Here,P = -x, Q = y, and R = -2.Then

Ry = 0, Qz = 0, Pz = 0, Rx = 0, Qx = 0, and Py = 0

Therefore, the curl of F = (Ry - Qz)i + (Pz - Rx)j + (Qx - Py)k= -i - j + 0k= -i - j

Then, the curl of vector field F is -i - j.

Divergence:

Divergence is a vector operator that operates on a vector field to produce a scalar value. It measures the magnitude of the outward flux of the vector field from an infinitesimal region around a particular point. Divergence is given by,

Divergence of the vector field F = (P, Q, R)div F = ∂P/∂x + ∂Q/∂y + ∂R/∂z

Here, P = -x, Q = y, and R = -2.Then, ∂P/∂x = -1, ∂Q/∂y = 1, and ∂R/∂z = 0

Therefore, the divergence of the vector field F is

div F = ∂P/∂x + ∂Q/∂y + ∂R/∂z= -1 + 1 + 0= 0

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Answer:

A

Step-by-step explanation:

its the most logical one to me

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

2y = -10x - 2

y = -5x - 1

y - 12 = -5(x - 0)

y - 12 = -5x + 0

y = -5x + 12

(a) According to Neyman-Pearson's lemma, the rejection region of the type I error rate (α) for testing H0: θ = θ0 against HA: θ = θA, where θ0 < θA, is given by:

{X: f(x; θA) / f(x; θ0) > k}

where f(x; θ) is the probability mass function (PMF) of the distribution of the data, given the parameter θ, and k is chosen such that the type I error rate is α.

For this problem, we have H0: p = 0 and HA: p > 0.4, with α = 0.05. Therefore, we need to find the value of k such that P(X ∈ R | H0) = α, where R is the rejection region.

Using the fact that X follows a binomial distribution with n trials and success probability p, we have:

f(x; p) = (n choose x) * p^x * (1-p)^(n-x)

Then, the likelihood ratio is:

L(x) = f(x; pA) / f(x; p0) = (pA / p0)^x * (1-pA / 1-p0)^(n-x)

We want to find k such that:

P(X ∈ R | p = p0) = P(L(X) > k | p = p0) = α

Using the distribution of L(X) under H0, we have:

P(L(X) > k | p = p0) = P(X > k') = 1 - Φ(k')

where Φ is the cumulative distribution function (CDF) of a standard normal distribution, and k' is the value of k that satisfies:

(1 - pA / 1 - p0)^(n-x) = k'

k' can be found using the fact that X ~ Bin(n, p0) and P(X > k') = α, which yields:

k' = qbinom(α, n, 1-pA/1-p0)

Therefore, the rejection region R is given by:

R = {X: X > qbinom(α, n, 1-pA/1-p0)}

(b) We have n = 20, p0 = 0.45, pA = 0.65, and X = 11. Using the rejection region R defined in part (a), we have:

R = {X: X > qbinom(0.05, 20, 1-0.65/1-0.45)} = {X: X > 12}

Since X = 11 is not in R, we fail to reject H0 at the 5% level of significance.

(c) The p-value is the probability of observing a test statistic as extreme as the one computed from the data, assuming H0 is true. For this problem, the test statistic is X = 11, and we want to find the probability of observing a value as extreme or more extreme than 11, under the null hypothesis H0: p = 0. Using the binomial distribution with p = 0.45, we have:

p-value = P(X >= 11 | p = 0) = 1 - P(X <= 10 | p = 0)

= 1 - pbinom(10, 20, 0.45)

= 0.151

Therefore, the p-value is 0.151, which is greater than the level of significance α = 0.05, so we fail to reject H0.

Answer:

50%

Step-by-step explanation:

10x5=50

10 is the Percentage.

5 is the Time.

Answer:

7 1/10 inch

Step-by-step explanation:

Events, of randomly drawing a King OR a card with an even number describe by a) Mutually Exclusive.

The events of randomly drawing a King and drawing a card with an even number are mutually exclusive. This means that the two events cannot occur at the same time.

In a standard deck of 52 playing cards, there are no Kings that have an even number.

Therefore, if you draw a King, you cannot draw a card with an even number, and vice versa.

The occurrence of one event excludes the possibility of the other event happening.

It is important to note that mutually exclusive events cannot be both independent and conditional. If two events are mutually exclusive, they cannot occur together, making them dependent on each other in terms of their outcomes.

The correct option is (a) Mutually Exclusive.

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Answer:

the answer should be y=35 and x=27.8

The way you get this is you look at how angle D and A are the same for both triangles. given this, they are equal to each other. So you'd do 2y-5=65. You will get 35. 35=y, so substitute that in for your other equation. You will get 2x+35=90.6. solve that and you will get 27.8=x

(a) Without more information, we cannot determine the initial number of insects. (b) The differential equation satisfied by P(t) is: dP/dt = kP, where k is the growth rate of the insect population.

(c) To find the time it takes for the population to double, we can use the formula:

2P(0) = P(0)e^(kt)

where P(0) is the initial population size. Solving for t, we get:

t = ln(2)/k

(d) Without more information, we cannot determine the time at which the population will equal a certain value.
Hi! To answer your question, I need the specific function P(t). However, I can provide you with a general framework to answer each part of your question once you have the function.

(a) To find the initial number of insects, evaluate P(t) at t=0:
P(0) = [Insert the function with t=0]

(b) To find the differential equation satisfied by P(t), differentiate P(t) with respect to t:
dP(t)/dt = [Insert the derivative of the function]

(c) To find the time at which the population doubles, first determine the initial population, P(0), then solve for t when P(t) is twice that value:
2*P(0) = P(t)
Solve for t: [Insert the solution for t]

(d) To find the time at which the population equals a specific value (let's call it N), set P(t) equal to N and solve for t:
N = P(t)
Solve for t: [Insert the solution for t]

Once you have the specific function P(t), you can follow these steps to find the answers to each part of your question.

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Answer:

\(m=-3\)

Step-by-step explanation:

Slope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)

Simply plug in the 2 coordinates into the slope formula to find slope m:

\(m=\frac{5-(-1)}{-5-(-3)}\)

\(m=\frac{5+1}{-5+3}\)

\(m=\frac{6}{-2}\)

\(m=-3\)

In the picture there are 2 problems. The similarity is they two have to find 2 question. The difference is given question are different.

Given that,

In the picture there are 2 problems.

We have to find the difference and similarities of question in the picture.

The similarities are they 2 are word problems.

Another similarity is they two have to find 2 question.

1. How much money for 10 days and How many days to collect the money $1.05?

2.How much gallon of water need for 50 minutes and How much time take to fill the pool?

Another similarity is they two have to justified the answer in a mathematical model.

Now,

The difference is,

First question has given sisters and money problem where as the second has given pool and gallon water problem.

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Answer: \(\frac{5}{9}\ m\)

Step-by-step explanation:

Given

Area of the rectangular piece of paper is \(A=\frac{1}{3}\ m^2\)

Length of the paper is \(l=\frac{3}{5}\ m\)

Suppose width of the paper is \(w\)

Area is the multiplication of length and width

\(\therefore A=lw\\\\\Rightarrow \dfrac{1}{3}=\dfrac{3}{5}\times w\\\\\Rightarrow w=\dfrac{5}{9}\ m\)

Thus, the width of the paper is \(\frac{5}{9}\ m\)

Answer:

150 ft

Explanation:

The number of feet of fencing needed should cover the entire perimeter of the rectangular garden.

Now the perimeter of the rectangle is

Hence, the 150 ft of fencing is required to enclose the rectangular garden,

Answer:

Lines 2 and 4 are perpendicular

Step-by-step explanation:

Line 2: 4y=3x-4

y=3/4x - 1

Line 4: 4x+3y=-6

3y=-6-4x

y=-2 - 4/3x

The two lines are perpendicular since -4/3= - (inverse of 3/4)

Two lines 2 and 4 are perpendicular to each other. The correct option is C.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

For two lines to be perpendicular the slope should be negative reciprocal. For two lines to be parallel the slope of the lines should be equal.

The equation of lines 2 and 4 is,

y = (3/4)x -1

y =(-4/3)x - 2

Here the slope of the two lines is reciprocal as well as negative.

Therefore, two lines 2 and 4 are perpendicular to each other. The correct option is C.

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Answer:

D

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ ADE is an exterior angle of the triangle , then

80° + ? = 100° ( subtract 80° from both sides )

? = 20° → D

The distribution would exhibit a negative skew.

A type of distribution in which more values are concentrated on the right side(tail) of the distribution graph while the left tail of the distribution graph is longer is called negatively skewed distribution.  Or a distribution is said to be negatively skewed or skewed to the left if the scores of the distribution falls mainly to the right of the graph and less to the left i.e. the lower scores are very few as compared to the high scores.

Here we are given that the three students who scored below 140 were dropped that means the some of the low scores are now dropped from the graph. Therefore, if 3 of the students who scored below 140 decide to drop the class, the shape of the distribution will be negative skewed or the distribution would exhibit a negative skew.

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Answer:

-5(-16)

=5x16

=80

Answer:

-43t - 22s - 3

Step-by-step explanation:

(–45t + 53s)+(–3 – 75s + 2t)

-45t + 53s - 3 - 75s + 2t

-45t + 2t +53s -75s -3

-43t - 22s - 3