Solve the initial-value problem by finding series solutions about x=0: xy'' – 3y = 0; y(0) = 1; y'(0) = 0 =

Answer:

1)speed=12.5 miles/hr

2)time=56.25hr or 0.36hr(i prefer this one..check explanation)

Step-by-step explanation:

speed=distance/time

s=3.75/0.3=12.5

speed is = 12.5 miles/hr

2nd part:

speed=distance/time

so time=speed*distance

: time=12.5*4.5=56.25hr(hard to believe the answer)

or

miles:hours

3.75:0.3

4.5:x

cross multiply

4.5*0.3/3.75=0.36

x=0.36hrs (answer is believeable)

Answer:

I think it's C or D

Step-by-step explanation:

All decimals are rational numbers and so are repeating ones

Answer:

Each repeating decimal number satisfies a linear equation with integer coefficients, and its unique solution is a rational number.

Step-by-step explanation:

Answer:

9:20

Step-by-step explanation:

one hour is 9:30, -10 minutes is 9:20

Answer:

9:20 is the time 50 minutes after 8:30

Answer:

21 gallons

Step-by-step explanation:

4 quarts = 1 gallon

16 quarts = 4 gallons

25 gallon - 4 gallons = 21 gallons

Answer:

Deon spent 60% of his money on lunch.

Step-by-step explanation:

Answer:

$102

Step-by-step explanation:

Reset Scarlet bought a coat originally priced at $120. She got a 15% discount. How much did she pay for the coat?

1. Convert the discount percentage to a decimal:

15/100 = 0.15

2. Multiply the original price by the decimal:

120*0.15 = $18

This is the discount they got.

3. Now, subtract the discounted value from the original price:

120 - 18 = $102

This means that they paid $102 for the coat.

Hope this helps!

Answer:

$102

Step-by-step explanation:

15% of 120

= 15/100×120

0.15×120=$18

therefore, 15% of 120 equal 18

discount= $18

Amount she paid= 120-18= $102

The measurements in millimeters of each folded leaflet are 210 mm by 99 mm.

millimetre (mm), also spelled millimetre, unit of length equal to 0.001 metre in the metric system and the equivalent of 0.03937 inch in the imperial system.

When an A4 sheet of paper is folded in thirds, it yields three equal sections with widths of 210/3 = 70 mm and heights of 297 mm. As a result, each folded leaflet will be 210 mm by 99 mm (since 297/3 = 99).

As a result, each folded leaflet measures 210 mm by 99 mm in millimetres.

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Answer:

38,300

Step-by-step explanation:

The hundredth number is the third number to the left from the right.

If we look to the number right of 2, there 7.

Since we are rounding: 5 or more...raise the score, 4 or less...let it rest.

Well 7 is greater than 5 so we round 2 up to 3

Hope this helps

Hi there!  

»»————-　★　————-««

I believe your answer is:  

38,273  ≈ 38,300

»»————-　★　————-««  

Here’s why:  

38,273

⸻⸻⸻⸻

38,273  ≈ 38,300

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

If a car is -0.67 standard deviations away from the mean speed of 50 miles per hour, it is traveling at approximately 43.3 miles per hour.

To find a particular value given the number of standard deviations away from the mean it falls, we can use the z-score equation:
z = (x - μ) / σ

where z is the number of standard deviations away from the mean, x is the value we want to find, μ is the mean, and σ is the standard deviation.

To rearrange this equation to find x, we can isolate it by multiplying both sides by σ and adding μ:
x = z * σ + μ

a. To find the value associated with a car that is 2.3 standard deviations above the z-score, we can use the above equation:
x = 2.3 * σ + μ

Since we don't have any specific values for μ and σ, we can't find an exact answer. However, we can make some generalizations based on the normal distribution.

For example, we know that about 2.3% of the area under the normal curve falls beyond 2.3 standard deviations above the mean.

So, if we assume that the data follows a normal distribution, we can say that the value associated with a car that is 2.3 standard deviations above the z-score is relatively rare and unlikely to occur.

b. To find how many miles per hour a car is traveling if it is -0.67 standard deviations away from the mean, we can use the same equation:

x = z * σ + μ

In this case, z = -0.67, and we don't have any specific values for μ and σ. Again, we can make some generalizations based on the normal distribution. For example, if we know that the mean speed of cars on a particular road is 50 miles per hour, and the standard deviation is 10 miles per hour, we can plug these values into the equation:

x = -0.67 * 10 + 50

x = 43.3 miles per hour

Therefore, if a car is -0.67 standard deviations away from the mean speed of 50 miles per hour, it is traveling at approximately 43.3 miles per hour.

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Answer:

Infinite Solutions

Step-by-step explanation:

\( \frac{2x + 6}{4} = \frac{1}{2} x + \frac{3}{2} \)

Get rid of the denominators by multiplying all whole equation by 4.

\(( \frac{2x + 6}{ 4} )4 = ( \frac{x}{2} )4 +( \frac{3}{2} )4 \\ 2x + 6 = 2x + 6\)

The interesting part is here. Both sides are same, meaning that if we continue to solve for the equation.

\(2x + 6 = 2x + 6 \\ 2x - 2x = 6 - 6 \\ 0 = 0\)

The equation is indeed true. Meaning that both graphs are the same and intercept both each others infinitely.

Therefore the answer is Infinite solution.

Answer:

x = 25

Step-by-step explanation:

From the picture attached,

ΔABC and ΔADE are the similar triangles.

Therefore, their corresponding sides will be in the same ratio.

\(\frac{\text{AB}}{\text{AD}}=\frac{\text{AC}}{\text{AE}}=\frac{\text{BC}}{\text{DE}}\)

\(\frac{\text{AB}}{\text{AD}}=\frac{\text{BC}}{\text{DE}}\)

And AB = AD + DB

             = 2(AD) [Since, AD = DB]

By substituting these values,

\(\frac{\text{2AD}}{\text{AD}}=\frac{\text{34}}{\text{(x-8)}}\)

2 = \(\frac{34}{x-8}\)

x - 8 = \(\frac{34}{2}\)

x - 8 = 17

x = 17 + 8

x = 25

What is the likelihood of rolling a 10 on a fair number cube numbered 1-6 is 0

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one

The sample space in the question is 1,2,3,4,5,6

The Probability of rolling a 10 is impossible  since 10 is not a possible outcome on a number cube numbered 1 to 6.

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There are 18 teams in the lacrosse league in the third year. It's important to note that percentages are a way of representing fractions out of 100.

In the first year, the lacrosse league has 20 teams.

In the second year, the number of teams increases by 20%, which is 20/100 x 20 = 4. Therefore, the number of teams in the second year is 20 + 4 = 24.

In the third year, the number of teams decreases by 25% from the second year, which is 25/100 x 24 = 6. Hence, the number of teams in the third year is 24 - 6 = 18.

Therefore, there are 18 teams in the lacrosse league in the third year.

It's important to note that percentages are a way of representing fractions out of 100. In the second year, the 20% increase can also be written as a multiplication factor of 1.2 (1 + 20/100). Similarly, the 25% decrease in the third year can be written as a multiplication factor of 0.75 (1 - 25/100). Using these multiplication factors can make it easier to calculate the number of teams in each year.

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The average rate of change and the secant line can provide valuable insights into the behavior of a function, but their exact values and equations depend on the specific function and interval in question.

To find the average rate of change of f(x) from a to b, we can use the formula:
average rate of change = (f(b) - f(a))/(b - a
Substituting the given values, we get:
average rate of change = (f( ) - f( ))/( - )
We need to know the function f(x) to find this value. Once we have that, we can use the formula above to calculate the average rate of change.
To find the equation of the secant line containing (a, f(a)) and (b, f(b)), we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where m is the slope of the line, and (x1, y1) is one of the given points.
The slope of the secant line is the same as the average rate of change, which we can find using the formula above. Once we have that, we can use either of the given points to find the equation of the line.
Unfortunately, without the function f(x), we cannot provide a specific answer to this question. The average rate of change is a measure of how much the output of a function changes over a given interval, and it can tell us how quickly the function is changing on average. The secant line, on the other hand, is a straight line that connects two points on a curve, and it can be used to estimate the slope of the curve at those points. In general, the average rate of change and the secant line can provide valuable insights into the behavior of a function, but their exact values and equations depend on the specific function and interval in question.

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Answer:

$1,131.56

Step-by-step explanation:

$1250 x (1-15%) = $1,062.50 Discounted Price

$1,062.50 x 6.5% = $69.06 Sales Tax

$1,062.50 + $69.06 = $1,131.56

Answer:

The correct option is;

D. 65% to 74%

Step-by-step explanation:

The accuracy of a forecast given based on a percentage or proportion or likelihood is determined by the based on the prevalence of the forecast in a similar proportion over the range of data points in which the forecast is made

Therefore, if it actually rained on 70% of those days for which the forecast was made, the forecast can be said to be very accurate.

Which is to say that the forecast of 70% chance of rain can be considered very accurate if it rained on 65 to 74% of those days which is in the range of the forecasted 70%.

Answer:

Step-by-step explanation:

C the probability that a customer buys a hat given that the customer has bought a sweater.

The speed of the ladybug as the disk spins is approximately 31 inches/second.

The ladybug is traveling at approximately 94 inches/second.

To determine the speed of the ladybug, we need to consider the linear velocity at the outer edge of the spinning disk. The linear velocity is the distance traveled per unit time.

First, we calculate the circumference of the disk using its diameter of 12 inches. The circumference of a circle is given by the formula C = π * d, where d is the diameter.

C = π * 12 inches = 12π inches.

Since the disk completes 50 revolutions per minute, we can calculate the number of rotations per second by dividing the number of revolutions by 60 seconds:

rotations per second = 50 revolutions/minute / 60 seconds/minute = 5/6 rotations/second.

Now, we can find the linear velocity by multiplying the circumference of the disk by the rotations per second:

linear velocity = (12π inches) * (5/6 rotations/second) ≈ 10π inches/second.

To approximate the value, we can use π ≈ 3.14:

linear velocity ≈ 10 * 3.14 inches/second ≈ 31.4 inches/second.

Rounding to the nearest integer, the ladybug is traveling at approximately 31 inches/second.

Therefore, the speed of the ladybug as the disk spins is approximately 31 inches/second.

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Answer:

2,0?

Step-by-step explanation:

To do this, find your first derivative and then find where it is equal to zero. Because we are only concerned about the interval from -5 to 0, we only need to test points on that interval. (i really don't know hot to explain)

The equilibrium point for the supply and demand equations p² + 4q = 253 and 183p² + 6q = 0 is (q, p) = (3, 10).

To find the equilibrium point, we need to solve the system of equations formed by the supply and demand equations. By substituting the value of q = 3 into the first equation, we get p² + 4(3) = 253, which simplifies to p² + 12 = 253.

Solving this equation gives us p = 10. Substituting the values of q = 3 and p = 10 into the second equation, we get 183(10)² + 6(3) = 0, which simplifies to 18300 + 18 = 0.

Since this equation holds true, we have found the equilibrium point to be (q, p) = (3, 10), where the equilibrium quantity is q = 3 and the equilibrium price is p = 10.

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a) The resulting change in area when the radius of a circle is increased from 4.00 to 4.08m is approximately 0.020106π square meters.

b) This change in area is approximately 1.25% of the circle's original area.

The formula for the area of a circle is A = πr^2, where A is the area and r is the radius. To estimate the change in area when the radius is increased from 4.00 to 4.08m, we can use the following equation

ΔA ≈ A2 - A1

ΔA ≈ π(r2^2 - r1^2)

ΔA ≈ π[(4.08)^2 - (4.00)^2]

ΔA ≈ π[0.0064]

ΔA ≈ 0.020106π square meters.

So the change in area is approximately 0.020106π square meters.

To express this change as a percentage of the circle's original area, we need to divide the change in area by the original area and multiply by 100

ΔA/A1 ≈ (0.020106π)/(π(4.00)^2)

ΔA/A1 ≈ 0.0125

Multiplying by 100, we get

ΔA/A1 ≈ 1.25%

So the resulting change in area is approximately 1.25% of the circle's original area.

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Answer:

-29

Step-by-step explanation:

5x +30 +3x =2+8x+1

x= -29

i believe the equation would be: \(3+\frac{1}{4} c=9\) and there would be 24 pieces of cake! <3

We would not be safe constructing the interval based on an SRS of size 24 from the population if the sample data exhibits a strong departure from normality.

Constructing a one-sample t interval assumes that the population distribution is approximately normal. However, if the sample data shows a significant departure from normality, it would be unsafe to rely on the t interval. In such cases, alternative approaches or non-parametric methods may be more appropriate for estimating the population mean.

When the sample size is large, the Central Limit Theorem allows for a certain degree of departure from normality. However, with a small sample size of 24, if the data is heavily skewed, exhibits strong outliers, or deviates significantly from a normal distribution, the assumptions underlying the t interval may not hold. In these situations, using the t interval would not provide reliable or valid inferences about the population mean.

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Answer:

150.72

Step-by-step explanation:

The volume of a cylinder is 2πrh. We have r = 3 and h = 8 so volume is 48π or 150.72.

Answer:

40 children tickets are sold while 20 adult tickets are sold

Step-by-step explanation:

Your system of equations are

11x+6y=460

x+y=60

we will use x+y=60 for the x to be eliminated

Multiply x+y=60 by 11 to get:

11x+11y=660

Then subtract:

11x+6y=460

-11x+11y=660

-5y=-200

Divide:

-5y=-200

-5     -5

y=40

The substitute y in one of the system of equations:

x+40=60

  -40  -40

x=20

And so 40 children tickets are sold while 20 adult tickets are sold

Hope It Helped :)

Answer:

divided both sides by the numeric factor on the left then solve x = 3

Step-by-step explanation:

Answer:

X= 7

Step-by-step explanation: