what is the side length of a cube with a volume of 314 ft^3

The general solution to the differential equation y'' + 16y = 0 is y(x) = (c₁ + c₂) * cos(4x)

To solve the differential equation y'' + 16y = 0 using reduction of order, we'll assume a second solution of the form y₂(x) = u(x) * y₁(x), where y₁(x) is a known solution and u(x) is an unknown function.

Given y₁(x) = cos(4x), we'll differentiate it to find y₁'(x) and y₁''(x):

y₁'(x) = -4sin(4x)

y₁''(x) = -16cos(4x)

Now we substitute y₂(x) = u(x) * y₁(x) into the original differential equation:

y'' + 16y = 0

(-16cos(4x)) + 16(u(x) * cos(4x)) = 0

Simplifying the equation:

-16cos(4x) + 16u(x) * cos(4x) = 0

cos(4x)(-16 + 16u(x)) = 0

For this equation to hold for all values of x, we must have (-16 + 16u(x)) = 0.

Solving for u(x):

-16 + 16u(x) = 0

16u(x) = 16

u(x) = 1

Now we have the second solution:

y₂(x) = u(x) * y₁(x)

y₂(x) = 1 * cos(4x)

y₂(x) = cos(4x)

Therefore, the general solution to the differential equation y'' + 16y = 0 is:

y(x) = c₁ * y₁(x) + c₂ * y₂(x)

y(x) = c₁ * cos(4x) + c₂ * cos(4x)

y(x) = (c₁ + c₂) * cos(4x)

Where c₁ and c₂ are arbitrary constants.

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Answer: All four answer choices would create congruent shapes.

===================================================

Explanation:

Reflections, rotations, and translations are considered rigid transformations. What this means is that they keep the same shape, but the shape has been moved in some fashion. As such, the "before" (preimage) and "after" (image) are congruent figures.

Imagine you drew a triangle on a clear piece of glass. If you took a picture of it from one side, then took another picture from the opposite side, then you'd get reflected versions of the triangle. Notice how the triangle has not moved at all. The camera has. Therefore, this proves that reflections keep the same exact shape. The only thing different is the orientation has swapped.

Now imagine you drew a triangle etched in stone. Grab your camera to take a picture of it. Then rotate the camera to get another picture. The two triangles are rotated copies of each other. They're the same exact triangle since the figure etched in stone hasn't changed. Only the camera has. This thought exercise proves rotations are a rigid transformation, aka an isometry.

Lastly, we'll go back to the triangle etched in stone to work with translations. A translation is any shifting. Take a picture of the triangle etched in stone. Then move the camera around to pan to another location (panning is when you keep your aim at the subject but move side to side, or up and down). Imagine the camera is stuck on a train track and can only aim one direction. The camera will take two pictures of the same triangle, of course the only difference is that they have shifted in the frame. Therefore, translations are the third final type of rigid transformation.

-----------------

Dilations are not rigid transformations, but only if the scale factor was something else than 1.

If the scale factor is less than 1, then the image shrinks.

If the scale factor is greater than 1, then the image enlarges.

If the scale factor is exactly 1, then the image doesn't change at all. This is because we multiplied all sides by 1. Multiplying by 1 doesn't change the number.

So because choice (2) mentions the scale factor is 1, this places it in the "rigid transformation" category and it's one of the four answers. Change the scale factor to anything else, and it wouldn't be an answer.

Answer:

Step-by-step explanation:

A surface analysis chart is a type of weather map that displays information about the current pressure and wind patterns over a particular region. The chart provides a snapshot of the weather conditions at a specific point in time and helps meteorologists to identify and track the location, movement, and development of high- and low-pressure systems, fronts, and other weather features.

The surface analysis chart typically shows a map of the Earth's surface with various meteorological symbols and information, including isobars (lines of equal pressure), fronts (boundaries between different air masses), and wind direction and speed. The chart may also include information about temperature, precipitation, and cloud cover.

Surface analysis charts are used in weather forecasting, air traffic control, and other applications where an understanding of current weather conditions is important. They provide important information for short-term weather forecasting, such as predicting the location of fronts and the development of thunderstorms, and for long-term weather planning, such as determining the most suitable routes for shipping or aviation.

The p-value of the given hypothesis is; 0.9999

The formula for the z-score of proportions is;

z = (p^ - p)/√(p(1 - p)/n)

where;

p^ is sample proportion

p is population proportion

n is sample size

We are given;

p^ = 15% = 0.15

p = 20% = 0.2

n = 5000

Thus;

z = (0.15 - 0.2)/√(0.2(1 - 0.2)/5000)

z = -8.8388

From p-value from z-score calculator, we have;

P(Z < -8.8388) = 1 - 0.0001 = 0.9999

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The correct sampling method described in the question is a stratified random sample among the simple random sample,  stratified random sample, cluster random sample and  Voluntary random sample

The sampling method described in the question is a stratified random sample.

In a stratified random sample, the population is divided into subgroups or strata based on certain characteristics or criteria. Then, a random sample is selected from each stratum. The key idea behind this method is to ensure that each subgroup is represented in the sample proportionally to its size or importance in the population. This helps to provide a more accurate representation of the entire population.

In the given sampling method, the population is divided into subgroups, and a fixed number of units is taken from each group. This aligns with the process of a stratified random sample. The sample selection is random within each subgroup, but the number of units taken from each group is fixed.

Other sampling methods mentioned in the question are:

Simple random sample: In a simple random sample, each unit in the population has an equal chance of being selected. This method does not involve dividing the population into subgroups.

Cluster random sample: In a cluster random sample, the population is divided into clusters or groups, and a random selection of clusters is included in the sample. Within the selected clusters, all units are included in the sample.

Voluntary random sample: In a voluntary random sample, individuals self-select to participate in the sample. This method can introduce bias as those who choose to participate may have different characteristics than those who do not.

Therefore, the correct sampling method described in the question is a stratified random sample.

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Answer:

\(y = 2x - - 3\)

That's the answer. Hope this helps

Please could you give me brainliest

Answer: No if you said that the ratio is the same like 1=1 but yes if you mean that the ratio is the same as before

Step-by-step explanation:

If you said that the ratio must be the same than is a no cause since 21 and 35 is not equal with each other so if you add an same number up it remain the same

If you mean that the ratio is the same as if it was not added 5 to both side than is a yes, you add both side an equal number and it would stay the same

Answer:yeah

Step-by-step explanation:

yeah

Answer:

True

Step-by-step explanation:

for every X there can be on Y

that doesn't necessarily go the other way around, but that's not what the problem is asking, so whatever.

Answer:

-300

Step-by-step explanation:

Step 1:  Find the amount Elmer's funds decreased after purchasing the rabbits:

Let x represent Elmer's funds.

Since Elmer bought five rabbits for $10 each, he lost $10 5 times.

x - (10 * 5)

x - 50

Thus, Elmer lost (spent) $50 for the 5 rabbits.

Step 2:  Find the amount Elmer's funds decreased after purchasing the  cupboards:

Since Elmer bought four cupboards for $70 each, he lost $70 4 times:

x - (50 + (70 * 4))

x - (50 + 280)

x - 330

Thus, after purchasing the rabbits and cupboards, Elmer lost $330.

Step 3:  Find the amount Elmer's funds increased after finding the twenty-dollar bill:

Since Elmer found a twenty-dollar bill, he gained $20

x - (330 + 20)

x - 310

Step 4:  Find the amount Elmer's funds increased after returning one rabbit:

Since Elmer returned one rabbit, he gained $10:

x - (310 + 10)

x - 300

Thus, Elmer's funds changed totally by -$300.

Putting all the information together, we have:

x - 10 - 10 - 10 - 10 - 10 - 70 - 70 - 70 - 70 + 20 + 10

x - 50 - 280 + 30

x - 330 + 30

x - $300

819 is the answer because thats how many visitors he got

Answer:

216 elements

Step-by-step explanation:

the total number of elements of a dice is :

6^n

6 stand for the 6 faces of the dice

n stands for the number trial

then total number of elements in 3 trials of rolling a 6-sided die is 6^3=216 elements

The five-number summary is:

Minimum: 9

First Quartile: 16.5

Median: 25.5

Third Quartile: 39

Maximum: 51

3. Range = 42

4. Interquartile range = 22.5

Given the data for the lengths as, 36, 15, 9, 22, 36, 14, 42, 45, 51, 29, 18, 20, to find the five-number summary of the data set, we would follow the steps below:

1. The numbers in ordered from the smallest to the largest would be:

9, 14, 15, 18, 20, 22, 29, 36, 36, 42, 45, 51

2. The five-number summary for the lengths in minutes would be:

3. Range of the data = max - min = 51 - 9 = 42

4. The interquartile range for the data set = Q3 - Q1 = 39 - 16.5

Interquartile range for the data set = 22.5

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Answer:

ZQLR

Step-by-step explanation:

Hope this helps!

9514 1404 393

Answer:

  x ≈ 32.4

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relation between angle, adjacent side, and hypotenuse:

  Cos = Adjacent/Hypotenuse

  cos(72°) = 10/x

  x = 10/cos(72°)

  x ≈ 32.4

The scale factor is 2.5

for B = 10/4 = 2.5

for C = 15/6 = 2.5

Answer:

The constant of proportionality is 1/4.

Step-by-step explanation:

Keep in mind that the constant of proportionality can always be found by dividing any y value by any x value, as long as the values are in the same row. For example, in this table, the constant of proportionality would be 1/4, as, in the first row, the y value is 2 and the x value is 8, and 2/8 equals 1/4.

Hope this helps! Comment any questions <3

The probability that at most two customers purchase the investment is 0.1875 or 18.75%.

To calculate the probability that at most two customers purchase the investment,  to calculate the probabilities for each possible outcome: 0, 1, and 2 customers purchasing the investment, and then sum them up.

Let's consider the customers as A, B, C, and D, with D being the fourth customer.

Probability of 0 customers purchasing:

P(0 customers) = (1 - probability of sale)²number of customers

= (1 - 0.5)²4

= 0.0625

Probability of 1 customer purchasing:

P(1 customer) = (probability of sale)²1 ×(1 - probability of sale)²3 (since 3 customers won't purchase)

= 0.5²1 ×0.5²3

= 0.5 × 0.125

= 0.0625

Probability of 2 customers purchasing:

P(2 customers) = (probability of sale)²2 × (1 - probability of sale)²2 (since 2 customers will purchase)

= 0.5²2 ×0.5²2

= 0.25 × 0.25

= 0.0625

Now  sum up these probabilities to find the probability that at most two customers purchase the investment:

P(at most 2 customers) = P(0 customers) + P(1 customer) + P(2 customers)

= 0.0625 + 0.0625 + 0.0625

= 0.1875

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Answer:

Im pretty sure the answer that is on the picture is right (25.87)

Step-by-step explanation:

Answer:

x = 6; XZ = 27cm

Step-by-step explanation:

Since 4x + 3 is the whole line and the other two equations equal the full line, I will set up the equation as 4x + 3 = the sum of the other two lines since they are equal to each other.

4x + 3 = 8 + 2x + 7

4x + 3 = 15 + 2x

Isolate the variable

Subtract 2x from both sides

2x + 3 = 15

Subtract 3 from both sides

2x = 12

Divide 2 from both sides

x = 6

To solve for the full line, plug in 6 for x for the equation that represents the full line

4(6) + 3

24 + 3

27

Answer:

7^5 (7 to the fifth power)

Step-by-step explanation:

those sevens can be represented by 7^5 because there are five sevens to multiply together

you can check the answer by doing 7 x 7 x 7 x 7 x 7=16807

and making sure that 7^5 is also equal to 16807, which it is.

Hope this helps! :)

Answer: Ok so what i'v got for this one is that i averaged up all three numbers and i got an average of about 85%. Now you have to put in a fourth number which will actually be another 80% i believe

Step-by-step explanation: add up all 3 divide them all by the numbers then once your done with that plug in the 80% and see what your answer will be.

Answer:

$7.80

Step-by-step explanation:

Multiply 0.4 (that is 40%) by 13

It would be 5.2

So subtract 5.2 from $13.00

7.8

So the CD price would be $7.80 with a 40% discount

Hope this helps you :)

Answer:

$5.20

Step-by-step explanation:

First you needed to multiply 0.40 and 13 so that would give you 5.2 so because you are dealing with money you need to add a two after the 2 in 5.2 to make it $5.20. I hope this helped!

The utility’s percent change from 2010 to 2020 is a decrease of 4.07%

How many years are between 2010 and 2020?

There are 10 years in between 2010 and the year 2020, which means that the total decline over a period of 10 years is the annual decrease multiplied by 10.

Total decrease in 10 years=2.6*10

Total decrease in 10 years=26.0

Utility industry jobs in 2020=639.5-26.0

Utility industry jobs in 2020=613.5

The percentage change 2010-2020=(2020 jobs/2010 jobs)-1

The percentage change 2010-2020=(613.5/639.5)-1

The percentage change 2010-2020=-4.07%

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Use this to answer

Using two of the points on the line, you can find the slope of the line by finding the rise and the run. The vertical change between two points is called the rise, and the horizontal change is called the run. The slope equals the rise divided by the run

Answer:

0,1

2,2

4,3

6,4

Step-by-step explanation:

Some Examples

4 = 1/2 (6) + 1

4 = 3 + 1

4=4

----------

2 = 1/2 (2) + 1

2 = 1 + 1

2 = 2

h

0

2

4

6

...................

Consider the given expression,

First of all, convert the mixed fraction into standard form,

Now, resolve the parenthesis,

Now, simplify the last fraction,

Thus, the simplified fraction of the given expression is 52/15.

If one angle in an isosceles triangle is 90 degrees then the measure of each angle of an isosceles triangle will be 45 degrees

What is an isosceles triangle ?

A triangle with two equal sides is said to be isosceles. Also equal are the two angles that face the two equal sides. In other terms, an isosceles triangle is a triangle with two sides that have the same length.

If the sides AB and AC of a triangle ABC are equal, then the triangle ABC is an isosceles triangle with B = C. "If the two sides of a triangle are congruent, then the angle opposite to them is likewise congruent," states the theorem that characterizes the isosceles triangle.

Since this triangle's two sides are equal, the base of the triangle is the side that is not equal.

As we know that in an isosceles triangle set of two angles are equal

And

we also know that sum of all the angles of a triangle is 180 degrees

So, According to the question

90 degrees + other angles =180 degrees

other angles = 90 degrees

one angle = 90/2

one angle = 45 degree  

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The quotient of (2x4 – 3x3 – 3x2 7x – 3) ÷ (x2 – 2x 1) is 2x² + x – 3.

A quotient is a quantity produced by the division of two numbers.

The quotient is most frequently encountered as two numbers, or two variables, divided by a horizontal line. The words "dividend" and "divisor" refer to each individual part, while the word "quotient" refers to the whole.

For example when 8 is divided by 2, the result obtained is 3. Thus, the quotient is 4.

To determine the quotient when (2x4 – 3x3 – 3x2 + 7x - 3) is divided by (x2 - 2x + 1), we'll apply the long division method as shown below:

              2x² + x – 3

x² - 2x + 1|2x⁴ – 3x² – 3x² + 7x - 3

              –(2x⁴ – 2x³ + 2x²)

                 x³ – 5x² + 7x – 3

              –(x³ – 2x² + x)

             –3x² + 6x – 3

            –(3x² + 6x – 3)

                    0

Thus, the quotient is 2x² + x – 3.

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Answer:

(9,1), Z(5,1)

Step-by-step explanation: