Consider the following. (2 + x^2)y'' - xy' + 4y = 0, x_0 = 0 Seek power series solutions of the given differential equation about the given point x_0. y_1: a_2k + 2 = y_2:a_2k + 3 = Find the recurrence relation. a_n + 2 =, n = 0, 1, 2, ... Find the first four terms in each of two solutions y_1 and y_2 (unless the series terminates sooner). y_1(x) = +... y_2(x) = +... By evaluating the Wronskian W(y_1, y_2)(x_0), show that y_1 and y_2 form a fundamental set of solutions. Since x_0 = 0, we find W(y_1, y_2)(0) =. Therefore, y_1 and y_2 form a fundamental set of solutions. If possible, find the general term in the solution.

Answer:

f(8)=-161

Step-by-step explanation:

f(x) = -3x^2 + 3x + 7

f(x) = -3x2 + 3x + 7

f(8)= -3(8)^(2) + 3(8) + 7= -192+24+7=-161

Answer:

f(8) = -161

Step-by-step explanation:

The question is asking us to evaluate the function.

In this problem, the function is:

\(\large{\textsf{$ f(x) = -3x^2 + 3x + 7 $}\)

Plug in 8 for x:

\(\large\text{$ f(8) = -3(8)^2 + 3(8) + 7 $}\)

Simplify.

\(\large\text{$ f(8) = -3 * 64 + 24 + 7 $}\)

\(\large\text{$f(8) = -192 + 31 $}\)

\(\large\text{ f(8) = -161}\)

Therefore, f(8) = -161.

The required  the probability that accidents occur no more than 2 days in 8 days is 0.144.

Probability is tied in with assessing or computing how likely or 'plausible' something is to occur. The opportunity of an occasion happening can be depicted in words, for instance 'certain', 'unimaginable' or 'logical'. In math, probabilities are constantly composed as portions , decimals or rates with values somewhere in the range of 0 and 1.

We have,

Probability(p) of lost-time accidents occur in a company at a mean rate of 0.5 per day.

Then, the Probability(q) of accident is not occur is 1 - 0.5 = 0.5.

The likelihood that a mishap doesn't happen (q) is then determined utilizing the accompanying supplement rule.

p =0.5 , q = 0.5

Each probability is calculated using:

P = ⁿCₐpᵃqⁿ⁻ᵃ

The probability that accidents occur no more than 2 days in 8 days is

P(x≤2) = P(0) + P(1) + P(2)

P(x≤2) = ⁸C₀p₀p⁰q⁸⁻⁰ + ⁸C₁p¹q⁸⁻¹ + ⁸C₂p²q⁸⁻²

P(x≤2) = (0.5)^8 + 8(0.5)(0.5)^7 + 28(0.5)^2(0.5)^6

P(x≤2) = 37(0.5)^8

P(x≤2) = 37(0.00390625) = 0.144

Hence, the probability that accidents occur no more than 2 days in 8 days is 0.144.

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Answer:

The watermelon candies taste $0.13 more.

Step-by-step explanation:

First, in order to find out how much each candy costs per ounce, you have to take the cost and divide it by the number of ounces. 3.48 divided by 12 is 0.29, so the watermelon candies cost $0.29 per ounce. 1.38 divided by 8 is 0.16, so the chewy chocolates cost $0.16 per ounce. In order to find how much more the watermelon candies cost, we have to subtract the cost of the watermelon candies by the cost of the chocolate candies. 0.29-0.16=0.13, so the watermelon candies cost $0.13 more than the chocolate candies.

Answer: she earns $62 in two weeks

Step-by-step explanation:

Lisa gets 31 dollars a week for 2 weeks so all you have to do is multiply 31 x 2. If you did all of those correctly you would get $62 for your answer.

Answer:

1.5

Step-by-step explanation:

Answer:

(3, -2)

Step-by-step explanation:

2+4 = 6

3-7 = -4

6/2 = 3

-4/2 = -2

Answer:

x = 5

Step-by-step explanation:

A quadratic equation:

f(x) = y = a*x^2 + b*x + c

Has a vertex in a point:

(h, k) such that:

h = -b/2a

and:

k = f(-b/2a)

And the axis of symmetry (this is the line that cuts the graph in two halves) is:

x = h.

In this case, the vertex is (5, -6)

Then the axis of symmetry is:

x = 5.

Answer: 105

Step-by-step explanation: If the car is going 63/30 is 2.1 which is the miles/minute, then to get to 50 miles you’d have to multiply 2.1 x 50 = 105 miles in 50 minutes.

Answer:

$528

Step-by-step explanation:

I'm assuming you mean up 32%?

Last week Bob was paid total of $480 for the items that he produced that week and this week Bob produced 2 items more than last week and was paid a total of $510 for the items that he produced this week.

Let's start with the simplest case:

he produced 36 or less items this week.

In this case he produced less than 36 items last week too.

So he was paid the same amount of dollar per item. Using assumptions (1) and (2), we have:

$480 + 2X = $510

⇒2X=510-480$

⇒2X=$30

⇒2X=$30/2

⇒X=$15

He was paid $15 per item.

Last week he received his $480.

480/15= 32 items.

This week he received his $510.

510/15=34 items. Other cases have no solution.

seems your question is incomplete., but most probably the complete question was

If Bob produces 36 or fewer items in a week, he is paid X dollars per item. If Bob produces more than 36 items in a week, he is paid X dollars per item for the first 36 items and 3/2 times that amount for each additional item. How many items did Bob produce last week?(1) Last week Bob was paid total of $480 for the items that he produced that week.(2) This week Bob produced 2 items more than last week and was paid a total of $510 for the items that he produced this week.

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Answer:

£35

Step-by-step explanation:

20/4=5 (1 ratio)

7*5=35

Answer:

0 (undefined)

Step-by-step explanation:

distribute on the left side first:

-4(3k-6)-4k

so -12k+24-4k

combine like terms

-16k+24

now the right side

-8k+24-4k

combine like terms

-12k+24

so it'll look like this

-16k+24=-12k+24

add -12k to the left

-4k+24=24

so then subtract 24

that'll leave you with 0

Answer:

\(y = \frac{7}{4}x +14\)

Step-by-step explanation:

Given

\(y = \frac{7}{4}x + 4\)

Required

Determine the equation of line that passes through (-8,0) and parallel to \(y = \frac{7}{4}x + 4\)

Parallel lines have the same slope.

In \(y = \frac{7}{4}x + 4\)

The slope, m is

\(m = \frac{7}{4}\)

because the general form of a linear equation is:

\(y = mx + b\)

Where

\(m = slope\)

So, by comparison:

\(m = \frac{7}{4}\)

Next, is to determine the equation of line through (-8,0)

This is calculated using:

\(y - y_1 = m(x - x_1)\)

Where

\(m = \frac{7}{4}\)

\((x_1,y_1) = (-8,0)\)

So, we have:

\(y - 0 = \frac{7}{4}(x -(-8))\)

\(y - 0 = \frac{7}{4}(x +8)\)

\(y - 0 = \frac{7}{4}x +\frac{7}{4}*8\)

\(y - 0 = \frac{7}{4}x +7*2\)

\(y - 0 = \frac{7}{4}x +14\)

\(y = \frac{7}{4}x +14\)

the answer is a || b, or the first option

Answer:

x=  

6

43

​

Step-by-step explanation:

pasos  

4

3

​

x−5=  

8

3

Agrega 5 a ambos lados.

4

3

​

x=  

8

3

​

+5

Convertir 5 a la fracción  

8

40

​

.

4

3

​

x=  

8

3

​

+  

8

40

​

Como  

8

3

​

 y  

8

40

​

 tienen el mismo denominador, sume sus numeradores para sumarlos.

4

3

​

x=  

8

3+40

​

Suma 3 y 40 para obtener 43.

4

3

​

x=  

8

43

​

Multiplica los dos lados por  

3

4

​

, el recíproco de  

4

3

​

.

x=  

8

43

​

×(  

3

4

​

)

Multiplica  

8

43

​

 por  

3

4

​

 (para hacerlo, multiplica el numerador por el numerador y el denominador por el denominador).

x=  

8×3

43×4

​

Realiza las multiplicaciones en la fracción  

8×3

43×4

​

.

x=  

24

172

​

Reduzca la fracción  

24

172

​

 a su mínima expresión extrayendo y anulando 4.

x=  

6

43

​

Where the above are given,

10. The nurse should give 2.45ml of the liquid medication.

11. The nurse can give 24ml of meperidine in 24 hours.

12. The patient should take 42 tablets of the antibiotic.

13. The IV rate is 100ml/hr at 1500gtt/min with a 15gtt/ml drip factor.

14. Each dose of codeine contains 15000mg.

15. The patient should be given 2.67oz (approximately) of the cough syrup.

10. To determine how much   of the liquid should be given, we can set up a  proportion

1g/3.5ml = 700mg/x

Cross-multiplying,

1g * x = 700mg * 3.5ml

x = (700mg * 3.5ml) / 1g

x = 2450mg*ml/g

Therefore, the amount of liquid to be given is 2.45ml.

11. The order states meperidine 75mg IM every 6 hours PRN pain, and the pharmacy sends a vial that contains 25mg/2ml. To calculate how many ml can be given in 24 hours, we need to consider the frequency and duration.

In 24 hours, there are 24/6 = 4 doses to be given. Each dose contains 75mg of meperidine.

To find the volume (ml) of each dose, we can set up a proportion  -

25mg/2ml = 75mg/x

25mg * x = 75mg * 2ml

x = (75mg * 2ml) / 25mg

x = 6ml

12.  To calculate the number of tablets the patient should take, we need to consider the dosage and the duration.

Each tablet contains 250mg of the antibiotic.

To find the number of tablets for the total dosage, we can set up a proportion  -

250mg/1 tab = 0.75g/x

250mg * x = 0.75g * 1 tab

x = (0.75g * 1 tab) / 250mg

x = 0.003 tab

Since we cannot take a fraction of a tablet, the patient should take 1 tablet every 4 hours for 7 days, resulting in a total of 1 * 6 * 7

= 42 tablets.

13.  To determine the IV rate, we need to calculate the number of drops per minute.

The formula to calculate the IV rate in drops per minute (gtt/min) is -

IV rate (ml/hr) = Total volume (ml) / Total time (hr)

IV rate (gtt/min) = IV rate (ml/hr) * Drop factor (gtt/ml)

IV rate (ml/hr) = 1000ml / 10hr = 100ml/hr

IV rate (gtt/min) = 100ml/hr * 15gtt/ml =

1500gtt/min

Therefore, the IV rate is 100ml/hr at 1500gtt/min.

14. To determine the   amount of milligrams of  codeine in each dose, we need to convert grams to milligrams.

1  gram (g) = 1000   milligrams (mg)

15 grams (gr) = 15 * 1000mg = 15000mg

Therefore, each dose contains 15000mg of codeine.

15. To calculate how much cough syrup should be given in ml's, we can set up a proportion -

225mg/1oz = x ml/600mg

225mg * x = 1oz * 600mg

x = (1oz * 600mg) / 225mg

x = 2.67oz

Therefore, 2.67oz of cough syrup should be given in ml's.

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The function f(x) = (3)x-2 represents a linear equation with a slope of 3 and a y-intercept of -2. So, the correct graph that represents the function f(x) = (3)x-2 is the one that is a straight line that passes through the points (0, -2) and (1, 1).

The slope of the line determines how much the value of y increases or decreases for each unit increase in x. In this case, the slope is positive, which means that the line slopes upwards from left to right. To graph this equation, we need to plot the y-intercept, which is -2 on the y-axis, and then use the slope to find another point on the line. One way to do this is to use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.

We can substitute the values of m and b into this equation to get y = 3x - 2. Now, we can choose any value of x and use the equation to find the corresponding value of y. For example, if we choose x = 0, we get y = -2. This gives us one point on the line, which is (0, -2). Next, we can use the slope of 3 to find another point on the line. The slope tells us that for each unit increase in x, y increases by 3. So if we increase x by 1, we get y = (3)(1) - 2 = 1. This gives us another point on the line, which is (1, 1).

We can continue this process to find more points on the line, or we can simply connect the two points we have found to draw the line.

The graph that represents the function f(x) = (3)x-2 is a straight line that passes through the points (0, -2) and (1, 1).

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the rate is 60 minutes per day bo will practice the piano.

what is proportional relationship?

When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the term used to describe that constant.

Given x and y will have a proportional relationship if the ratio of x to y will be equal for all given values.

the equation m = 60d

The rate is m/d = 60d/d = 60 minutes per day.

Hence, the rate is 60 minutes per day bo will practices the piano.

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Answer:

(x−5)^2+(y+6)^2=9

Step-by-step explanation:

Answer:

I'm not sure if this is right but I'm gonna say no, the tip of each triangle seems off by just a bit

Given:

The given polynomial is:

\(8x^2+2x^1-3\)

To find:

The name of the polynomial based on its degree and number of terms.

Solution:

Consider the given polynomial:

\(8x^2+2x^1-3\)

Here the highest power of x is 2. It means the degree of the polynomial is 2.

We know that, the second degree polynomial is called quadratic polynomial.

The terms in the given polynomial are \(8x^2,2x^1,-3\). The number of terms in the given polynomial is 3.

We know that, the polynomial that contains three terms is called trinomial.

Therefore, the name of the polynomial based on its degree is quadratic polynomial and based on the number of terms is trinomial.

To separate the middle 24% from the tails in the standard normal distribution, the z-scores are approximately -0.877 and +0.877.

 To find the z-scores that separate the middle 24% of the distribution from the area in the tails of the standard normal distribution, we can follow these steps:

1. Determine the area in the tails: Since the middle 24% is being separated from the tails, we need to find the area in the tails. Since the standard normal distribution is symmetric, each tail will have an area of (100% - 24%) / 2 = 38% / 2 = 19%.

2. Convert the tail area to a z-score: We can use a standard normal distribution table or a calculator to find the z-score corresponding to an area of 19%. This z-score represents the cutoff point between the middle 24% and the tails.

Using a standard normal distribution table or calculator, the z-score that corresponds to an area of 19% in the tail is approximately -0.877.Therefore, the z-scores that separate the middle 24% of the distribution from the area in the tails of the standard normal distribution are approximately -0.877 and +0.877.

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Answer:

x = 5

Step-by-step explanation:

Translate the word problem into an equation and solve for x

4x - 25 = -x

Add 25 to both sides

4x = -x + 25

Add x to both sides

5x = 25

Divide both sides by 5

x = 5

Answer:

10:4, 35:14, 55:22

Step-by-step explanation: