In this exercise, we consider finding the first five coefficients in the series solution of the first-order linear initial value problem (x²+2)y′′ − 6y = 0 subject to the initial condition y(0) = 1, y′(0) = 2. Since the equation has an ordinary point at x=0 and it has a power series solution in the form y = Lim(n=0→[infinity])Σ cₙxⁿ.(1) Insert the formal power series into the differential equation and derive the recurrence relation: cn= __________cₙ₋₂ for n=2,3,⋯ The solution to this initial value problem can be written in the form y(x)= c₀y₁(x)+c₁y₂(x) where c₀ and c₁ are determined from the initial conditions. The function y₁(x) is an even function and y₂(x) is an odd function. For this example, from the initial conditions, we have c₀ = ______ and c₁ = ______. The function y₁(x) is an infinite series y₁(x) = 1+ Lim(n=1→[infinity])Σ aₙx²ⁿNote that the constant c₀ has been factored out. (2) Use the recurrence relation to find the first few coefficients of the infinite series: a₂ = _______, a₄ = _______, a₆ = _______, a₈ = _______.Note that the constant c₀ has been factored out. Finally the polynomial y₂(x)= _______NOTE: The function y₂(x) is an odd degree polynomial with first term x. In other words, note that the constant c₁ has been factored out.

Final answer:

45 students need to make it to the boat to be rescued.

Explanation:

The question asks us to calculate how many students attended a field trip, given that 15% of the 300 students at a middle school attended.

Therefore, 45 students need to make it to the boat to be rescued.

Answer:

bib

peep

ewe

kayak

racecar

level

noon

Answer:

15.50=25.25

Step-by-step explanation:

15+0.50=15.50

25+0.25=25.25

So 15+0.50=25.25 = 9.75 because you subract 25.25-15.50=9.75

Hope this helps

Answer:

-1/2

Step-by-step explanation:

Note the slope intercept form:

y = mx + b

y = (x , y)

m = slope

x = (x , y)

b = y-intercept.

In this case, the number that replaces the m (slope) is -1/2, which is your answer.

~

Answer:

m= -1/2

Step-by-step explanation:

This equation is in slope intercept form:

y=mx+b

where m is the slope and b is the y intercept

We have the equation:

y= -1/2x -3

If we compare the 2 equations:

y=-1/2x -3

y=mx+b

The slope must be -1/2, since x is being multiplied by -1/2

Answer:

The size of the sample should be at least 1037.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error of the interval is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].

A level of confidence of 99% will be used and an error of no more than .04 is desired. There is no knowledge as to what the population proportion will be. The size of sample should be at least

We need a sample size of at least n.

n is found when [tex]M = 0.04[/tex]

We don't know the proportion of the population, so we use [tex]\pi = 0.5[/tex]

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.04 = 2.575\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.04\sqrt{n} = 2.575*0.5[/tex]

[tex]\sqrt{n} = \frac{2.575*0.5}{0.04}[/tex]

[tex](\sqrt{n})^{2} = (\frac{2.575*0.5}{0.04})^{2}[/tex]

[tex]n = 1036.03[/tex]

Rounding up

The size of the sample should be at least 1037.

Answer:

90

Step-by-step explanation:

2*30= 60

3*30= 90

Answer:

Number of families that should be surveyed if one wants to be 90% sure of being able to estimate the true mean PSLT within 0.5 is at least 43.

Step-by-step explanation:

We are given that one wants to estimate the mean PSLT for the population of all families in New York City with gross incomes in the range $35.000 to $40.000.

If sigma equals 2.0, we have to find that how many families should be surveyed if one wants to be 90% sure of being able to estimate the true mean PSLT within 0.5.

Here, we will use the concept of Margin of error as the statement "true mean PSLT within 0.5" represents the margin of error we want.

SO, Margin of error formula is given by;

       Margin of error =  [tex]Z_(_\frac{\alpha}{2}_ ) \times \frac{\sigma}{\sqrt{n} }[/tex]

where, [tex]\alpha[/tex] = significance level = 10%

            [tex]\sigma[/tex] = standard deviation = 2.0

            n = number of families

Now, in the z table the critical value of x at 5% ( [tex]\frac{0.10}{2} = 0.05[/tex] ) level of significance is 1.645.

SO,        Margin of error =  [tex]Z_(_\frac{\alpha}{2}_ ) \times \frac{\sigma}{\sqrt{n} }[/tex]

                          0.5   =  [tex]1.645 \times \frac{2}{\sqrt{n} }[/tex]

                         [tex]\sqrt{n} =\frac{2\times 1.645 }{0.5}[/tex]

                         [tex]\sqrt{n} =6.58[/tex]

                           n  =  [tex]6.58^{2}[/tex]

                               = 43.3 ≈ 43

Therefore, number of families that should be surveyed if one wants to be 90% sure of being able to estimate the true mean PSLT within 0.5 is at least 43.

Answer:

9 boards

Step-by-step explanation:

2/3 of the porch= 6 boards

so to figure out how much one third of the porch needs you find half of what it takes to fill in 2/3 of the porch and you get 3.

so 3=1/3 of the porch

then you simply do 3times 3 or 3+3+3 and you get 9

so it takes 9 boards to fill the whole porch

Answer:

5

Step-by-step explanation:

[tex]\sqrt{(2-(-2))^{2} + (6-(-3))^2}[/tex]

=[tex]\sqrt{4^{2} + 3^{2} } \\[/tex]

=[tex]\sqrt{25}[/tex]

=5

Answer:

A number line going from negative 7 to negative 1. A closed circle is at negative 5. Everything to the right of the circle is shaded.

Step-by-step explanation:

-4.4 ≥ 1.6 x - 3.6

Solving for the value of x,

1.6 x ≤ -4.4 + 3.6

 1.6 x ≤ - 0.8

Dividing 1.6 from both sides to know value of x

x ≤ - 0.5

Answer:

the answer is a

Step-by-step explanation:

Edenuity

To determine the number of adult Americans needed for the distribution of the sample proportion to be approximately normal, we can use the formula n = (Z/E)^2 * p * (1-p).

To determine the number of adult Americans needed for the distribution of the sample proportion to be approximately normal, we need to calculate the minimum sample size n required. We can use the formula:

n = (Z₃/E)^2 * p * (1-p)

Where Z₃ is the critical value, E is the maximum error tolerance (which is half the width of the confidence interval), and p is the estimated proportion of adult Americans who support the changes.

For part (a), where 20% of all adult Americans support the changes, the estimated proportion p is 0.20. Plugging in the values for Z₃ and E, we can solve for n. Similarly, for part (b), where 25% of all adult Americans support the changes, the estimated proportion p is 0.25. Plugging in the values for Z₃ and E, we can solve for n.

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(a) The researcher needs to sample 15 more adult Americans if 20% support the changes.

(b) The researcher needs to sample 5 more adult Americans if 25% support the changes.

To determine how many more adult Americans the researcher needs to sample for the distribution of the sample proportion to be approximately normal, we need to use the Central Limit Theorem (CLT).

According to the CLT, the sampling distribution of the sample proportion [tex]\(\hat{p}\)[/tex] is approximately normal if both [tex]\(n \hat{p} \geq 10\)[/tex] and [tex]\(n (1 - \hat{p}) \geq 10\)[/tex], where n is the sample size and [tex]\(\hat{p}\)[/tex] is the sample proportion.

Let's find the required sample size for both cases:

Case (a): 20% of all adult Americans support the changes

Given [tex]\(\hat{p} = 0.20\),[/tex]

To ensure normality:

[tex]\[n \hat{p} \geq 10 \quad \text{and} \quad n (1 - \hat{p}) \geq 10\][/tex]

1. [tex]\( n \hat{p} \geq 10 \)[/tex]

  [tex]\[ n \times 0.20 \geq 10 \implies n \geq \frac{10}{0.20} = 50 \][/tex]

2. [tex]\( n (1 - \hat{p}) \geq 10 \)[/tex]

  [tex]\[ n \times 0.80 \geq 10 \implies n \geq \frac{10}{0.80} = 12.5 \][/tex]

The stricter condition is [tex]\( n \geq 50 \).[/tex]

Since the researcher already has a sample size of 35, the additional number of adults needed is:

[tex]\[50 - 35 = 15\][/tex]

Case (b): 25% of all adult Americans support the changes

Given [tex]\(\hat{p} = 0.25\),[/tex]

To ensure normality:

[tex]\[n \hat{p} \geq 10 \quad \text{and} \quad n (1 - \hat{p}) \geq 10\][/tex]

1. [tex]\( n \hat{p} \geq 10 \)[/tex]

  [tex]\[ n \times 0.25 \geq 10 \implies n \geq \frac{10}{0.25} = 40 \][/tex]

2. [tex]\( n (1 - \hat{p}) \geq 10 \)[/tex]

  [tex]\[ n \times 0.75 \geq 10 \implies n \geq \frac{10}{0.75} = 13.33 \][/tex]

The stricter condition is [tex]\( n \geq 40 \).[/tex]

Since the researcher already has a sample size of 35, the additional number of adults needed is:

[tex]\[40 - 35 = 5\][/tex]

Answer:

I mean I guess sure

Step-by-step explanation:

Anyway hope you have a good day!!

ig..

Answer:

  0.80

Step-by-step explanation:

The z-score is found from the formula ...

  Z = (X -μ)/σ

  Z = (77 -73)/5 = 4/5 = 0.80

Jennifer's Z-score was 0.80.

Answer:

The null and alternative hypothesis are:

[tex]H_0: \mu=110\\\\H_a:\mu\neq 110[/tex]

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the average room price in Atlanta is significantly different from $110 (P-value=0.317) .

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the average room price in Atlanta is significantly different from $110.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=110\\\\H_a:\mu\neq 110[/tex]

The significance level is 0.05.

The sample has a size n=64.

The sample mean is M=112.

The standard deviation of the population is known and has a value of σ=16.

We can calculate the standard error as:

[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{16}{\sqrt{64}}=2[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{112-110}{2}=\dfrac{2}{2}=1[/tex]

This test is a two-tailed test, so the P-value for this test is calculated as:

[tex]P-value=2\cdot P(z>1)=0.317[/tex]

As the P-value (0.317) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the average room price in Atlanta is significantly different from $110.

Answer:

28.27 cm^2 (2 decimal places)

Step-by-step explanation:

side of box = 24/4 = 6

diameter of coin would be 6 too

area of coin = pi x (6/2)^2 = 28.2743

Answer:

b) x > - 5

Step-by-step explanation:

x  >  - 5

x ∈ (- 5 ; + oo)

Answer:

B

Step-by-step explanation:

Edge2022

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image below to see the step by step explanation to the question above.

Answer:

D

Step-by-step explanation:

Because their slopes are equal. Rest of the step-by-step explanation is in the attached file!!

Answer:

335 = 50 + 6p

Step-by-step explanation:

50 +6p=335

subtract from both sides

-50      -50

6p=285

/6p   /6p

divide both sides

p=47.5

Answer:

C

Step-by-step explanation:

Option D is correct, There are two clusters, at 10 and 11, and at 13, 14, and 15.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Data is a collection of discrete values that convey information, describing quantity, quality, fact, statistics, other basic units of meaning

Clustering is the task of dividing the population or data points into a number of groups such that data points in the same groups are more similar to other data points in the same group than those in other groups.

There are two clusters, at 10 and 11, and at 13, 14, and 15 is  best describes the clusters in the data set

Hence, Option D is correct, There are two clusters, at 10 and 11, and at 13, 14, and 15.

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answer:

the first one and the last one

The correlation coefficient helps us to know how strong is the relation between two variables. The situations in which there exists a negative relationship are A and E.

The correlation coefficient helps us to know how strong is the relation between two variables. Its value is always between +1 to -1, where, the numerical value shows how strong is the relation between them and, the '+' or '-' sign shows whether the relationship is positive or negative.

A negative correlation is a relation in which as one variable increases the other decreases, therefore, there exists an inverse relationship between the two varibles.

A.) The number of calories consumed and the amount of weight lost by a person

It is known that if a person consumes more calories then he will gain more weight, therefore, the number of calories consumed and the amount of weight lost by a person have a negative correlation.

B.) The temperature outside and the number of pool guests.

If the temperature outside is more, more people will come to visit the pool. Thus, there exists a positive correlation.

C.) The number of children assigned to a class and the number of desks

The more the number of students, the more desk will be needed for them. Thus, there exists a positive correlation.

D.) The price of rice and the number of penguins at the South Pole.

The price of rice and the number of penguins at the south pole are two completely independent variables, therefore, there exists zero correlation.

E.)The thickness of the ice on a lake and the likelihood of falling through the ice.

If the thickness of the ice on a lake is more, there will be less likelihood of falling through the ice. Therefore, there exists a negative correlation.

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Answer:

-5/4; -4/3

Step-by-step explanation:

12x^2 + 31x + 20 =

(4x + 5)(3x + 4) -->

x = -5/4 OR -4/3

Answer:

It will take 36.1 years for her money to reach $105,000.

Step-by-step explanation:

The amount of money earned after t years in continuous interest is given by:

[tex]P(t) = P(0)e^{rt}[/tex]

In which P(0) is the initial investment and r is the interest rate, as a decimal.

Anna invests $7,000 in an account that compounds interest continuously and earns 7.5%.

This means that [tex]P(0) = 7000, r = 0.075[/tex]

How long will it take for her money to reach $105,000?

This is t for which P(t) = 105000.

[tex]P(t) = P(0)e^{rt}[/tex]

[tex]105000 = 7000e^{0.075t}[/tex]

[tex]e^{0.075t} = \frac{105000}{7000}[/tex]

[tex]e^{0.075t} = 15[/tex]

[tex]\ln{e^{0.075t}} = \ln{15}[/tex]

[tex]0.075t = \ln{15}[/tex]

[tex]t = \frac{\ln{15}}{0.075}[/tex]

[tex]t = 36.1[/tex]

It will take 36.1 years for her money to reach $105,000.

Answer:

size=13.80966

Step-by-step explanation:

Missing information:

size=13.80966

Since p-value of FP is less than 0.05 so it is significant to the model.

If all other things remain constant then a fire place add approximately $6476 to the selling price of the average house. So statement "A fireplace adds around $6476 to the selling price of the average house." is supported by the model.

It is impossible to definitively determine the correct statement without the actual regression output. While we can make educated guesses about the significance of the 'Fireplace' variable and its impact on the house's selling price, further information like t-values, p-values, and standard errors is required to make a detailed and accurate estimate.

With the information provided, it is impossible to definitively determine which of the four options are correct without the actual regression output. However, if it were provided and the p-value for the Fireplace's coefficient is higher than 0.05, we could say at α = .05, FP is not a significant predictor in a two-tailed test. If the regression coefficient for the Fireplace is $6,476 and it is significant, then a fireplace adds around $6476 to the selling price of the average house is correct. However, declaring that FP is a more significant predictor than Size or that a large house with no fireplace will sell for more than a small house with a fireplace, would require further information that goes beyond the coefficients themselves, including the standard errors, t-values, and p-values associated with each coefficient.

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Answer:

140

Step-by-step explanation:

The volume of a triangular prism with a base of 5 cm and height of 8cm and the height of the prism as 7cm is 140 cm³

volume of triangular prism = 1 / 2 bhl

where

Therefore,

base = b = 5 cm

height = h = 8 cm

l  = 7cm

Hence,

volume of the triangular prism = 1 / 2 × 5 × 8 × 7

volume of the triangular prism = 280 / 2

volume of the triangular prism = 140 cm³

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Answer:

Option A  is correct.

Step-by-step explanation:  

The linear function that has the steepest slope is,

Explanation:

Slope intercept form: The general formula is,  where m is the slope and b is the y-intercept.

Option A:

According to slope intercept form:

Slope is -8

Similarly, for

Option B :

Slope is -2

Option C:

Slope is 7

Option D :

Slope is 6

Steepest slope defined as that is closest to being vertical.

This could be a line that is positive or negative slope respectively.

Therefore, the linear function that has the steepest slope is, option A

The steepest slope is in Option 4 with a slope of -4. Therefore, Option 4 has the steepest slope.

To determine which linear function has the steepest slope, we need to compare the slopes of the given options.

The slope of a linear function can be calculated using the formula:

[tex]\[ \text{Slope} = \frac{\text{change in } y}{\text{change in } x} \][/tex]

We will calculate the slopes for each option and compare them.

Option 1:

[tex]\[ \text{Slope} = \frac{-2 - 4}{1 - (-1)} = \frac{-6}{2} = -3 \][/tex]

Option 2:

[tex]\[ \text{Slope} = \frac{13 - 10}{6 - 3} = \frac{3}{3} = 1 \][/tex]

[tex]\[ \text{Slope} = \frac{16 - 10}{9 - 3} = \frac{6}{6} = 1 \][/tex]

[tex]\[ \text{Slope} = \frac{19 - 13}{12 - 9} = \frac{6}{3} = 2 \][/tex]

Option 3:

[tex]\[ \text{Slope} = \frac{-4 - 2}{-1 - 2} = \frac{-6}{-3} = 2 \][/tex]

Option 4:

[tex]\[ \text{Slope} = \frac{-12 - (-4)}{4 - 2} = \frac{-8}{2} = -4 \][/tex]

[tex]\[ \text{Slope} = \frac{-20 - (-12)}{6 - 4} = \frac{-8}{2} = -4 \][/tex]

[tex]\[ \text{Slope} = \frac{-28 - (-20)}{8 - 6} = \frac{-8}{2} = -4 \][/tex]

Comparing the slopes:

- Option 1: Slope = -3

- Option 2: Slopes = 1, 1, 2

- Option 3: Slope = 2

- Option 4: Slopes = -4, -4, -4

The steepest slope is the largest magnitude of slope, regardless of whether it's positive or negative. In this case, the steepest slope is in Option 4 with a slope of -4. Therefore, Option 4 has the steepest slope.

Answer:

42 inches

By regulation it may be no more than 2.75 inches (7.0 cm) in diameter at the thickest part and no more than 42 inches (1.067 m) in length.

Step-by-step explanation:

baseball bat - is a smooth wooden or metal club used in the sport of baseball to hit the ball after it is thrown by the pitcher.

length- a measure of distance.

Answer:

30 inches

Step-by-step explanation:

Answer:

(a) The percentage of people having an IQ score between 67 and 133 is 99.73%.

(b) The percentage of people having an IQ score less than 89 or greater than 111 is 31.73%.

(c) The percentage of people having an IQ greater than 111 is 15.87%.

Step-by-step explanation:

The random variable X can be defined as the scores of an IQ test.

The random variable X is normally distributed with parameters μ = 100 and σ = 11.

(a)

Compute the probability of people who has an IQ score between 67 and 133 as follows:

[tex]P(67<X<133)=P(\frac{67-100}{11}<\frac{X-\mu}{\sigma}<\frac{133-100}{11})\\\\=P(-3<Z<3)\\\\=P(Z<3)-P(Z<-3)\\\\=0.99865-0.00135\\\\=0.9973[/tex]

The percentage is, 0.9973 × 100 = 99.73%.

Thus, the percentage of people having an IQ score between 67 and 133 is 99.73%.

(b)

Compute the probability of people having an IQ score less than 89 or greater than 111​ as follows:

[tex]P(X<89\ \cup\ X>111)=1-P(89<X<111)\\\\=1-P(\frac{89-100}{11}<\frac{X-\mu}{\sigma}<\frac{111-100}{11})\\\\=1-P(-1<Z<1)\\\\=1-[P(Z<1)-P(Z<-1)]\\\\=1-[0.84134-0.15866]\\\\=0.31732\\\\\approx 0.3173[/tex]

The percentage is, 0.3173 × 100 = 31.73%.

Thus, the percentage of people having an IQ score less than 89 or greater than 111 is 31.73%.

(c)

Compute the probability of people having an IQ score greater than 111​ as follows:

[tex]P(X>111)=P(\frac{X-\mu}{\sigma}>\frac{111-100}{11})\\\\=P(Z>1)\\\\=1-P(Z<1)\\\\=1-0.84134\\\\=0.15866\\\\\approx 0.1587[/tex]

The percentage is, 0.1587 × 100 = 15.87%.

Thus, the percentage of people having an IQ greater than 111 is 15.87%.

The % of people having an IQ score between the 67 and the 133 is 99.73%. The % of people having an IQ score less than the 89 or greater than 111 is 31.73%. The % of people having an IQ greater than 111 is 15.87%.

As per the IQ test which is done to check the intelligent quotient of  a score that s derived from a standard sets of tests. They are made to test human intelligence. The IQ score falls in a bell-shaped curve with the distortion of 100 and  SD of 11.

The percentage of the people having a score between the 67 and 133 was 099.7% and those between the 89 of more 111 is 31.7% and those having a greater IQ of 111 are 15.8 % that is declining to the top.

Find out more information about the IQ test.

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