The total cost of a catered meal for the Armstrong family reunion was to be split equally by the 20 people who came. Before the meal started, five more Armstrong's unexpectedly appeared. The total cost was shared equally among the 25 people, and so each person in the original group owed $4 less. What was the total cost of the catered meal?

To test the given hypothesis, where the null hypothesis (H_ọ) states that the population mean (µ) is equal to 190, and the alternative hypothesis (H_A) states that µ is greater than 190, a one-tailed test should be performed.

Given that the sample mean (X) is 186, the sample standard deviation (s) is 22, and the sample size (n) is 14, we can use the t-test for a single sample to test the hypothesis.

Calculate the test statistic:

t = (X - µ) / (s / √n)

t = (186 - 190) / (22 / √14)

t ≈ -0.8182

Determine the critical value for the given significance level and degrees of freedom.

Since the alternative hypothesis is one-tailed (µ > 190), we need to find the critical value corresponding to the desired significance level (α). Let's assume a significance level of α = 0.05 and degrees of freedom (df) = n - 1 = 14 - 1 = 13. Using a t-distribution table or calculator, the critical value for a one-tailed test at α = 0.05 and df = 13 is approximately 1.771.

Compare the test statistic to the critical value:

If the test statistic is greater than the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

Since -0.8182 is less than 1.771, we fail to reject the null hypothesis.

Therefore, based on the given sample, assuming a normal population, and performing a one-tailed test at α = 0.05, we fail to reject the null hypothesis (H_ọ: µ = 190) in favor of the alternative hypothesis (H_A: μ > 190).

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[tex]c_0 = 9, c_1 = 2(9^2), c_2 = 3(9^3), c_3 = 4(9^4)[/tex]and [tex]c_4 = 5(9^5)[/tex]. The radius of convergence R is infinity.

To find the coefficients of the power series representation of the function f(x) = 5/(1 - 9x)², we can expand the function using the geometric series formula. The formula states that for |x| < 1, we have:

1/(1 - 9x) = 1 + 9x + (9x)² + (9x)³ + ...

Now, let's differentiate both sides of the equation with respect to x:

d/dx [1/(1 - 9x)] = d/dx [1 + 9x + (9x)² + (9x)³ + ...]

To differentiate the left side, we can use the power rule:

d/dx [1/(1 - 9x)] = (1 - 9x)⁻²

To differentiate the right side, we differentiate each term individually. Since the derivative of x^n with respect to x is nxⁿ⁻¹, the terms with powers of x become:

d/dx [1 + 9x + (9x)² + (9x)³ + ...] = 0 + 9 + 2(9²)x + 3(9³)x² + ...

Equating the derivatives, we have:

(1 - 9x)⁻² = 9 + 2(9²)x + 3(9³)x² + ...

To obtain the coefficients of the power series representation, we compare the terms on both sides of the equation. Since the expression on the right side is already in the desired form, we can read off the coefficients as follows:

[tex]c_0 = 9\\c_1 = 2(9^2)\\c_2 = 3(9^3)\\c_3 = 4(9^4)\\c_4 = 5(9^5)[/tex]

Now, let's find the radius of convergence R of the series. The radius of convergence can be determined using the ratio test. The ratio test states that if the limit of |[tex]c_{n+1} / c_n[/tex]| as n approaches infinity is L, then the series converges if L < 1 and diverges if L > 1.

Applying the ratio test to our series, we have:

|[tex]c_{n+1} / c_n[/tex]| = |[(n+1)(9ⁿ⁺¹)] / [n(9ⁿ)]| = 9((n+1)/n)

Taking the limit as n approaches infinity, we get:

lim(n->∞) |[tex]c_{n+1}/ c_n[/tex]| = lim(n->∞) 9((n+1)/n) = 9

Since the limit is 9, which is less than 1, the series converges for all values of x within a radius of convergence R. Therefore, the radius of convergence R is infinity (R = ∞).

Therefore,[tex]c_0 = 9, c_1 = 2(9^2), c_2 = 3(9^3), c_3 = 4(9^4)[/tex]and [tex]c_4 = 5(9^5)[/tex]. The radius of convergence R is infinity.

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Answer:100.53mm

Step-by-step explanation:

The solution an for the recurrence relation is given by the formula,an = (25/19)*(10)^n + (102/19)*(-9)^n for n > 1.

Given the recurrence relation,ao = 7, a1 = 8 and for n > 2 an = -20 x an-1-90 x an 2.

To find the solution, an, of the recurrence relation we need to follow the below steps.

Step 1:Find the general formula for the recurrence relation. We have an = -20 x an-1-90 x an 2. This is a second-order recurrence relation.

To solve a recurrence relation of this order, we assume the solution of the form an = r^n.Then substituting this value of an in the given relation we have r^n = -20r^(n-1) - 90r^(n-2).

Dividing both sides by r^(n-2), we have the characteristic equation r^2 = -20r - 90.On simplifying the above equation we get, r = 10 and r = -9.

Now, the general solution for an is given by, an = c1 * (10)^n + c2 * (-9)^n.

Step 2:Find the value of constants c1 and c2. We have a0 = 7 and a1 = 8.

Substituting n = 0 in the above general formula for an, we get c1 + c2 = 7.

 Substituting n = 1 in the above general formula for an, we get 10c1 - 9c2 = 8.

On solving the above two equations we get, c1 = (25)/19 and c2 = (102)/19.

Hence, the solution to the given recurrence relation is,an = (25/19)*(10)^n + (102/19)*(-9)^n.

The solution is valid for n > 1.

Therefore, the solution an for the recurrence relation is given by the formula,an = (25/19)*(10)^n + (102/19)*(-9)^n for n > 1. This is the required answer.

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Answer:

C=3e

Step-by-step explanation:

Slope=

Answer:

100/π cm

Step-by-step explanation:

Volume of a cylinder = πr²h

Volume = 10,000cm³

Radius = 10cm

The formula for the height of a cylinder is obtained as:

V = πr²h

h = V/ πr²

h = 10000 /π × 10²

h = 10000 /π × 100

h = 100/π cm

The height of the cylinder in terms of π = 100/π cm

Answer:

6.

m1 : 61

m2 : 61

m3 : 29

7.

m1 : 87

m2 : 45

m3 : 45

m4 : 52

Answer:

v = 340 cm³

Step-by-step explanation:

base area = 12 x 10 x 0.5 = 60 cm²

v = 60 x 17 x 1/3 = 340 cm³

Answer: The other team is extra information. 150 – 60 = 90

He got 90 yards running.

Step-by-step explanation:

Answer:

7:42

Step-by-step explanation:

First off you add the ratio together-

6+1=7

Then you divide-

49÷7= 7

7 is equal to 1 in this ratio.

To write out the ratio you need to multiplicate-

7×1=7

and

6×7= 42

Leaving the as-

7:42

Answer:

7:42  

Step-by-step explanation:

First, add up the two numbers in the ratio to get 49.

Next, divide the total amount by 49, i.e. divide £16 by 8 to get £5. £5 is the amount of each 'unit' in the ratio.

Then you need to divide the total amount using that number i.e. 49/16 = 7/42.

To work out how much each person gets, you then multiply their share by the ratios. Therefore, the answer is 7 yd and 42 yds.

Answer:

D) 2,4

Step-by-step explanation:

The only answer with positive numbers

Answer:

D) 2,4

Step-by-step explanation:

Among the pairs of events A&B, A&C, A&D, B&C, B&D, and C&D, the pairs A&C and B&D satisfy the condition P(A∩B) = P(A) × P(B), indicating that they are independent events.

To determine if two events are independent, we compare the product of their individual probabilities to the probability of their intersection. If the product of the individual probabilities is equal to the probability of the intersection, then the events are independent.

Let's examine each pair of events:

A&B: Rolling a double and getting a sum of even scores are not independent events. The occurrence of one event does not guarantee the occurrence of the other.

A&C: Rolling a double and having the score on the blue die greater than the score on the red die are independent events. The probability of rolling a double is solely dependent on the outcome of the dice roll, while the probability of the blue die having a greater score than the red die is independent of the outcome of rolling a double.

A&D: Rolling a double and getting a 6 on the red die are not independent events. The occurrence of rolling a double does not affect the probability of getting a 6 on the red die.

B&C: Getting a sum of even scores and having the score on the blue die greater than the score on the red die are not independent events. The occurrence of one event does not guarantee the occurrence of the other.

B&D: Getting a sum of even scores and getting a 6 on the red die are independent events. The probability of getting a sum of even scores is solely dependent on the outcome of the dice roll, while the probability of getting a 6 on the red die is independent of the sum of the scores.

C&D: Having the score on the blue die greater than the score on the red die and getting a 6 on the red die are not independent events. The occurrence of one event does not guarantee the occurrence of the other.

In summary, the pairs of events A&C and B&D are the only pairs that satisfy the condition P(A∩B) = P(A) × P(B), indicating that they are independent events.

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Answer:

[tex]73[/tex]

Step-by-step explanation:

[tex]73=\sqrt{55^{2} +48^{2} }[/tex]

ok so lets say that you have a pizza cutted out in 5 sections and want to pick up only a certain piece, let's say pepperoni. If you took a piece at random, the chances of getting that certain piece of pepperoni in 60 spins is:    12 / 60

Answer:

Step-by-step explanation:

You can't receive money if you withdraw in the midst of a year.

So 4000 * 1/25 * 2 = $4320

Answer: 1.56 kilometers

Step-by-step explanation:

you multiply 520 by 3 because she ran for three days

so she ran 1560 meters

1000 meters= 1 kilometer

that makes it 1.56 kilometers

Answer:

180

Step-by-step explanation:

From basic rules of a triangle we know that the interior angles of a triangle have to add up to equal 180°

But here is a formula for future references for finding the sum of the interior angles

interior angle sum = (n-2)180

where n = number of sides

and here is an example:

a triangle has 3 sides so we plug in 3 for n

(3-2)180

3-2=1

1*180 = 180

so the interior angles add up to equal 180

Answer:

the transfer of energy from one organism to another

Step-by-step explanation:

Answer:

x = - 8, y = 2

Step-by-step explanation:

[tex]x = - 4y......(1) \\ x + 5y = 2....(2) \\ plug \: x = - 4y \: in \: equation \: (2) \\ - 4y + 5y = 2 \\ y = 2 \\ plug \: y = 2 \: in \: equation \: (1) \\ x = - 4(2) \\ x = - 8\\[/tex]

Phase portrait as a function of the control parameter μ and the classification of bifurcations that occur as μ varies in the following questions are:

1. θ = μ sin θ - sin 2θA) μ<0, stable equilibrium at θ = nπ, where n is an odd integerB) μ>0, stable equilibrium at θ = 0, unstable equilibrium at θ = nπ, where n is a non-zero even integer. Hence, we have homoclinic bifurcation at μ = 0.

2. θ = sin θ/ μ+cos θA) μ<1, stable equilibrium at θ = nπ, where n is an integerB) μ>1, stable equilibrium at θ = sin−1 (μ) + nπ, where n is an integer. Hence, we have a pitchfork bifurcation at μ = 1.

3. θ = sin θ / μ + sin θA) μ<−1, stable equilibrium at θ = nπ, where n is an integerB) μ>−1, stable equilibrium at θ = 0, unstable equilibrium at θ = nπ, where n is a non-zero integer. Hence, we have homoclinic bifurcation at μ = −1.

4. θ = μ + cos θ + cos 2θA) μ>−1, stable equilibrium at θ = nπ, where n is an even integerB) μ<−1, no equilibrium point exists. Hence, we have fold bifurcation at μ = −1.

5. θ = μ sin θ + cos 2θA) μ>0, stable equilibrium at θ = sin−1 (−μ) + 2nπ, where n is an integerB) μ<0, stable equilibrium at θ = sin−1 (−μ) + (2n+1)π, where n is an integer. Hence, we have pitchfork bifurcation at μ = 0.

6. θ = sin 2θ/ 1 + μ sin θA) μ<−1, unstable equilibrium at θ = nπ/2, where n is an odd integerB) μ>−1, unstable equilibrium at θ = 0, stable equilibrium at θ = π. Hence, we have pitchfork bifurcation at μ = −1.

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Step-by-step explanation:

12. n^2+2n

if you insert 1 for k and then work up by inserting 2 for k and adding those together and stoping at n.

13. 8-2(2^n)

if you insert 3 for k and then work up by inserting 4 for k and adding those together and keep on going but stopping at n.

Hope that helps :)

After considering the given data and analysing the information carefully we conclude that the lowest species richness observed is Forest A with only 18 species.

Let us get into the explanation part by first keeping in mind that to determine this, we need to evaluate the total number of species in each forest.

From the given data set, we clearly see that Forest A has 18 species, Forest B has 28 species, and Forest C has 25 species.

Hence, Forest A has the lowest species richness with only 18 species then Forest A has the lowest species richness among the three forests.

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The exponential distribution applies to the lifetimes of a certain component. Its failure rate is unknown. The probability that the component will survive the past 5 years assumes:

(a) lambda=.5

Pr= 0.082

(b) lambda=0.9

Pr= 0.082

(c) lambda=1.1

Pr= 0.036

In the exponential distribution, the failure rate is a degree of the way fast the factor is expected to fail. It is regularly denoted through the parameter lambda (λ).

The opportunity that a thing will continue to exist beyond a positive time may be calculated using the exponential survival function, which is given by:

[tex]Pr(X > t) = e^(-λt)[/tex]

where X represents the random variable denoting the life of the thing, t is the specific time, and e is the bottom of the herbal logarithm.

Now let's calculate the possibilities for each case:

(a) lambda = 0.5, t = 5

Pr(X > 5) = [tex]e^(-0.5 * 5)[/tex] ≈ 0.082

In this example, with a lambda of 0.5, the element has a notably low failure price. The opportunity of the thing surviving beyond 5 years is about 0.082, or 8.2%.

(b) lambda = 0.9, t =5

Pr(X > 5) = [tex]e^(-0.9 * 5)[/tex] ≈ 0.082

With a lambda of 0.9, the issue has a slightly higher failure rate as compared to the previous case. The probability of the aspect surviving beyond 5 years stays at about 0.082, or 8.2%.

(c) lambda = 1.1, t = 5

Pr(X > five) = [tex]e^(-1.1 * 5)[/tex]≈ 0.036

In this situation, with a lambda of one.1, the factor has a better failure fee. The possibility of the element surviving beyond 5 years decreases to approximately 0.036, or 3.6%.

In precis, the possibility of a component surviving the past five years in an exponential distribution relies upon the failure price parameter lambda.

A lower failure price ends in a higher chance of survival, at the same time as a higher failure price decreases the opportunity of survival. It is essential to don't forget these chances when assessing the reliability and toughness of additives in diverse packages.

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Answer:

175 dollars

Step-by-step explanation:

from that word problem the equation that i was able to get out of it was

1225/ 7

^ the travel allowance and how much days they are going to be there

i dont know if you are allowed to use a calculator in your class but puting 1225/ 7 does give you a answer of a positive number of 175 dollars

meaning that they can only use 175 dollars a day so they dont go over the allowance

i hope this helps you! please stay safe and have a good day :)

Answer:

Um, the answer for that is 175.

Step-by-step explanation:

all you need to do is divide $1,225 by 7 which is 175.

Answer:

$5.41

Step-by-step explanation:

654 divided by 120.99=5.405... therefore the answer is $5.41

Answer:

Step-by-step explanation:

Pi*r^2 = Area

20.5^2 * Pi = 1320.25