Find each unit rate. Show your work

45.5 meters in 13 seconds

The time required for one cycle is 1 second.T o find the maximum displacement, we can look at the amplitude of the simple harmonic motion.

In this case, the amplitude is the coefficient of the cosine function, which is 9. Therefore, the maximum displacement is 9 inches.

The frequency of the motion can be determined by looking at the coefficient in front of the variable t in the cosine function. In this case, there is no coefficient, which means it is implicitly 1. Therefore, the frequency is 1 cycle per second.

To find the time required for one cycle, we need to determine the period of the motion. The period is the time it takes for the motion to complete one full cycle. In this case, the period can be found by using the formula T = 2π / ω, where T is the period and ω is the angular frequency.

Since the frequency is 1 cycle per second, the angular frequency ω is equal to 2π times the frequency, which is 2π * 1 = 2π rad/s.

Plugging this value into the formula for the period, we have T = 2π / (2π) = 1 second.

Therefore, the time required for one cycle is 1 second.

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Answer:

Step-by-step explanation:

20y

Meaning 20xy

Y=1

So 20 is 20

For the given rectangle RSTW, the condition satisfies the criteria of rectangles is equal to m ∠SRZ = 40°.

As given in the question,

In the given figure of rectangle RSTW,

Conditions satisfies the criteria of the rectangles are as follow:

a. m ∠SRZ = 40°

Line segment SR is parallel to TW. TR is the transversal.

m ∠SRT = m ∠WTR ( Alternate interior angles)

T -Z - R

m ∠SRZ = m ∠WTZ = 40°

Given criteria is satisfies the criteria of rectangles.

b. m ∠STZ = 40°

All the interior angles of rectangle are of measure 90°

m ∠STW = 90°

m ∠WTZ = 40° (given)

m ∠STZ + m ∠WTZ = 90°

⇒ m ∠STZ = 50°

Given option does not satisfies the criteria of rectangles.

c. m ∠SRW = 80°

All the interior angles of rectangle are of measure 90°

Given option does not satisfies the criteria of rectangles.

d. m ∠TWR = 80°

All the interior angles of rectangle are of measure 90°

Given option does not satisfies the criteria of rectangles.

Therefore, for the given rectangle RSTW, the condition satisfies the criteria of rectangles is equal to  m ∠SRZ = 40°.

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Answer:

The answer is 1/6

Step-by-step explanation:

So Think of a half and then divide it into 3 parts for a half it will be 1/3 but for a meter it will be 1/6 because there is 2 half's in 1 whole

Hope this helps!! :D

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Answer:

  14400 cm³/s

Step-by-step explanation:

Find the rate of change of volume in terms of edge length, and evaluate the expression for the given conditions.

  V = s³ . . . . volume in terms of edge length (s)

  dV/dt = 3s²·ds/dt . . . . . . derivative of volume with respect to time

For the given values of s and ds/dt, this is ...

  dV/dt = 3(40 cm)²(3 cm/s) = 14400 cm³/s

If the target behavior is recorded whenever it occurs at any point within the scoring interval, the measurement procedure used is called continuous recording or event recording. This method involves observing and recording each instance of the behavior without considering its duration or intensity.

Continuous recording is typically used when the target behavior is discrete and occurs relatively infrequently or has a short duration. With this measurement procedure, each occurrence of the behavior is recorded as a separate event, regardless of when it starts or ends within the scoring interval. Examples of behaviors that can be measured using continuous recording include vocalizations, hand clapping, or instances of aggression.

Continuous recording provides a comprehensive account of the frequency or rate at which the behavior occurs, allowing for a detailed analysis of its occurrence patterns. This method is particularly useful when a precise count of behavior instances is needed and when the duration or intensity of the behavior is not a focus of measurement.

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Answer:

725

Step-by-step explanation:

The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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ANSWER and EXPLANATION

We are given that m<8 = 23 degrees.

First, let us find m<7.

m<7 and m<8 are angles on a straight line. Angles lying on a straight line sum up to 180 degrees.

This means that:

23 + m<7 = 180

m<7 = 180 - 23

m<7 = 157 degrees

Since m<8 and m<5 also lie on a straight line, we have that:

m<5 = 157 degrees

m<8 and m<6 are vertically opposite angles. Vertically opposite angles are equal, therefore:

m<6 = 23 degrees

m<8 and m<4 are corresponding angles, based on their positions. Corresponding angles are equal, therefore:

m<4 = 23 degrees

m<4 and m<2 are vertically opposite angles, therefore:

m<2 = 23 degrees

m<5 and m<1 are corresponding angles, therefore:

m<1 = 157 degrees

m<1 and m<3 are vertically opposite angles, therefore:

m<3 = 157 degrees

The percentage of values between 488 and 524 for an Apex brand battery, assuming a normal distribution with a mean of 500 days and a standard deviation of 12 days, is approximately 81.61%.

We can use the standard normal distribution table to find the percentage of values between 488 and 524 for a normal distribution with a mean of 500 and a standard deviation of 12.

We need to convert the values of 488 and 524 to z-scores using the formula:z = (x - μ) / σwhere x is the value, μ is the mean, and σ is the standard deviation.

Using this formula, we get:z1 = (488 - 500) / 12 = -1z2 = (524 - 500) / 12 = 2Therefore, we want to find the area under the standard normal distribution curve between -1 and 2.

Using the standard normal distribution table or a calculator, we find that this area is approximately 0.8161, or 81.61%.

Therefore, the percentage of values between 488 and 524 for an Apex brand battery, assuming a normal distribution with a mean of 500 days and a standard deviation of 12 days, is approximately 81.61%.

Summary:The percentage of values between 488 and 524 for an Apex brand battery, assuming a normal distribution with a mean of 500 days and a standard deviation of 12 days, is approximately 81.61%.

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The set of integers for which p(k) is true is all even integers for which p(k) is proved true if we also prove that p(k)^p(k 2)=> p(k-2).

Considering that p(- 2) and p(0) are valid and expecting that p(k)^p(k+2) => p(k-2), we can decide the arrangement of numbers k for which p(k) is valid by acceptance. In particular, we can show that p(k) is valid for all even numbers k by enlistment, as follows.

To begin with, since p(- 2) and p(0) are valid, the base instance of k = - 2 is valid.

Then, expect that p(k) is valid for some even number k. Then, at that point, utilizing the given ramifications, we have p(k+2) is valid.

At long last, utilizing a similar ramifications once more, we have that p(k-2) is valid. Accordingly, by acceptance, we have shown that p(k) is valid for all even numbers k.

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Answer:

the answer is 1649

Step-by-step explanation:

Find the number in the whole number place 8 and look one place to the right for the rounding digit on the right side of the decimal point 5.Round up if this number is greater than or equal to 5 and round down if it is less than 5.

1649

hope i helped and have a wonderful day

64854755555557427382675

The side with length 5 cm is the hypotenuse.

The given lengths of the sides are 3 cm,4 cm and 5 cm

3²=3×3=9;

4² =4×4=16;

5² =5×5=25;

We found that

9+16=25

3²+4²+5²

Therefore, the triangle is a right-angled triangle.

Note : In any right-angled, triangle the hypotenuse happens to be the longest side.

In this example the side with length 5 cm is the hypotenuse.

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Answer:

4/11

Step-by-step explanation:

there are 4 green out of 11 total

Answer:

4/11 is the probability you will get a green marble

Step-by-step explanation:

First you must determine the denominator by adding 4 and 7 to make the total number of marbles

4 + 7 = 11.

Next, you have 4 green marbles so you make it 4/11

Lastly, have a great day!

For a 3×3 matrix A, with the real eigenvalue is 2 and two complex conjugate eigenvalues, the complex conjugate eigenvalues of matrix A are equal to 1 ± i.

Eigenvalues are defined as a special set of scalar points that is associated with set of linear equations and matrix equations. We have a matrix A of order 3×3. It has real and complex eigenvalues. As we know number of eigenvalues for 3×3 matrix are 3. The real eigenvalue, λ

= 2

Number of complex eigenvalues= 2

Also, the determinant of matrix A, det(A) = 50

Trace of matrix A, tr(A) = 8

We have to determine the complex eigenvalues.

The characteristic polynomial for 3×3 is written as below, f( λ )= det(A − λI3 )= −λ³ + 4λ² - 6 λ + 4.

For eigenvalues, −λ³ + 4λ² - 6 λ + 4 = 0

Now, one of eigenvalue of matrix is 2, λ = 2. Using the synthesis division, for calculating the remaining, follow the steps present in above figure. In the last step of division we get a quadratic equation, -λ² + 2λ - 2 = 0, solve it by quadratic formula, \(λ = \frac{-2 ± \sqrt{ 2² - 4 (-2)(-1)}}{2(-1)}\)

\(= \frac{-2 ± \sqrt{4 - 8 }}{-2}\)

=> λ = 1 ± i

Hence, required values are 1 ± i.

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The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

The statement that is true is: d. All of these are true.Explanation:A study may have various sources of variability, including participant selection, the setting in which the study is conducted, and the measure used. The following options are as follows:a. The study may be affected by a situational variable.b. The construction noise may contribute to variability in test scores.c. The study has a confounding variable. The groups differ in the time they are to report to the testing room.d. All of these are true.Therefore, all of these options are true. For example, the study may be affected by a situational variable if a natural disaster or other unforeseen event happens that causes the study to be disrupted. In this case, the study was disrupted by a noisy construction crew, which may have contributed to variability in test scores. The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

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The system of linear equations are;

a + b = 5.30

a + b = 7

Expressing the information as a system of linear equations:

Consider that apples = a, oranges = b

If $5.30 is charged for one apple and one orange, then we get the equation as

a + b = 5.30 - - - (1)

If $14 is charged for 2 apples and 2 oranges,  then we get the equation as ;

2a + 2b = 14 - - - - (2)

a + b = 7

Since both equations give varying combined cost for an equal amount of fruit, so a unique cost cannot be obtained for each fruit from the systems of equation using a simultaneous equation process.

From (1)

a = 5.30 - b

Put a, b in (2)

2(5.30 - b) + 2b = 14

10.6 - 2b + 2b = 14

10.6 = 14

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Let's say Dali's walking speed is x and his running speed is 3x.

In the morning, let's say the total distance is d. Therefore, Dali walks d/2 with speed x and runs d/2 with speed 3x. The time it takes for him to complete this distance is given by:

d/2x + d/2(3x) = 24

Simplifying this equation, we get:

d = 3x(8)

d = 24x

So, the total distance Dali covers in the morning is 24x.

After school, let's say the distance from school to home is d'. Therefore, Dali walks d'/2 with speed x and runs d'/2 with speed 3x. The time it takes for him to complete this distance is given by:

d'/2x + d'/2(3x) = ?

We don't know how much time it takes Dali to get home, so we'll leave the right-hand side of the equation blank for now.

Now, let's look at the ratios of Dali's walking and running speeds:

Walking speed : Running speed = x : 3x = 1 : 3

This means that for every 4 parts of the distance Dali covers, he walks one part and runs three parts. So, we can write:

d' = 4y, where y is the distance Dali walks

This also means that Dali spends one-fourth of the total time walking and three-fourths running. So, we can write:

d'/2x + d'/2(3x) = (1/4)t + (3/4)t, where t is the total time it takes Dali to get home

Simplifying this equation, we get:

2d' = 2t(x + 3x)

4y = 8tx

y = 2tx

Substituting this value of y in the equation d' = 4y, we get:

d' = 8tx

So, the total distance Dali covers in the afternoon is 8tx.

Now, we have two equations:

d = 24x

d' = 8tx

We need to simplify these equations further to find the value of t (the total time it takes Dali to get home).

From the first equation, we get:

x = d/24

Substituting this value of x in the second equation, we get:

d' = 8t(d/24)

d' = (1/3)dt

So, the total distance Dali covers in the afternoon is (1/3)dt.

Now, we can equate the two expressions we have for d':

d' = 8tx = (1/3)dt

Simplifying this equation, we get:

24x = t

Therefore, it takes Dali 24 minutes to get home.

The correct option is C as it consists exact domain and range that we need.

What is domain and range?

The domain of a function f(x) is that the set of all values that the function is outlined, and also the range of the operate is that the set of all values that f takes.

The set of all attainable values that qualify as inputs to a operate is thought because the domain of the operate, or it also can be outlined because the entire set of values attainable for freelance variables. .

Main body:

the given function :

{(2,3), (7,9), (4,-7), (6,2), (3,-5)}

domain = (2,7,4,6,3)

range = (3,9,-7,2,-5)

Hence the correct option is C.

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The value of f[g(x)] is - 64x³ - 336x² - 588x - 340 and the value of g[f(x)] is -4x³ + 19

The functions are as follows; f(x) = -x³ +3 and g(x) = 4x+7

The value of f[g(x)] is obtained by replacing every x in f(x) with the value of g(x) as given below

f[g(x)] = f(4x + 7) = - (4x + 7)³ + 3

When we expand (4x + 7)³, it gives us 64x³ + 336x² + 588x + 343

Then

f[g(x)] = - 64x³ - 336x² - 588x - 340

Similarly, g[f(x)] is obtained by replacing every x in g(x) with the value of f(x) as shown below;

g[f(x)] = g(-x³ + 3) = 4(-x³ + 3) + 7g

[f(x)] = -4x³ + 19

Therefore,

f[g(x)] = - 64x³ - 336x² - 588x - 340

g[f(x)] = -4x³ + 19

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In general, to evaluate the function f(x) at a specific value of x, we substitute that value into the expression for f(x) and simplify.

In mathematics, a function is a relation between two sets, where for every element in the first set (called the domain), there is exactly one element in the second set (called the range) that the function maps to. In simpler terms, a function is a rule that assigns each input value from the domain to exactly one output value in the range. Functions are usually represented by a formula or equation that describes the relationship between the input and output values. For example, the function f(x) = 2x + 1 maps every input value of x to an output value that is twice the input value plus 1.

Here,

To evaluate the function f(x) = 4x - 6, we substitute the given values of the independent variable into the expression for f(x) and simplify.

For example:

f(0) = 4(0) - 6 = -6

f(1) = 4(1) - 6 = -2

f(2) = 4(2) - 6 = 2

f(-1) = 4(-1) - 6 = -10

f(3a) = 4(3a) - 6 = 12a - 6

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Answer:

80√3c+12√5c⁴

Step-by-step explanation:

You gave 2√10c (4√30 + 3√2c³) so...

1.) Distribute
You will then get 8√300c+6√20c⁴

2.) Simplify the radical expression and you will get
8x10√3c+6x2√5c⁴

3.) Calculate
80√3c+12√5c⁴

And that is your answer

Answer:

80√3c+12√5c⁴

Step-by-step explanation:

2√10c (4√30 + 3√2c³) so first things first:

1.) Distribute

You will then get 8√300c+6√20c⁴

2.) Simplify the radical expression and you will get

8x10√3c+6x2√5c⁴

3.) Calculate

80√3c+12√5c⁴

Answer:

121 π

Step-by-step explanation:

A= π * r^2

r^2 = 121 * π

The derivative of the function is 5/(cos^8(1)). Since there is no answer choice that matches this expression, the correct answer is "None of the other answers".

Let's begin by using the chain rule to find the derivative of the function:

ds/dt = 5(tan'(1) - sec^2(1) * d/dt(1))^4

We know that the derivative of tan(x) is sec^2(x), so:

ds/dt = 5(sec^2(1) - sec^2(1) * 0)^4

ds/dt = 5(sec^2(1))^4

ds/dt = 5(1/cos^2(1))^4

ds/dt = 5(cos^2(1))^(-4)

Now we can simplify using the trigonometric identity cos^2(x) + sin^2(x) = 1:

ds/dt = 5/(cos^8(1))

Therefore, the derivative of the function is 5/(cos^8(1)). Since there is no answer choice that matches this expression, the correct answer is "None of the other answers".

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Answer:

9.1 meters or 910 centimeters

Step-by-step explanation:

10.5 meters = 1050 centimeters

1050 - 140 = 910 centimeters

x = - 3 / 4Y

y = - 117 + 4Y / 9

The volume of the hexagonal prism is approximately 198.25 cubic centimeters.

To find the volume of a hexagonal prism, we need to know the area of the base and the height of the prism. In this case, we are given that the base has an area of 30.5 square centimeters and the height is 6.5 centimeters.

First, let's find the perimeter of the base. Since a hexagon has six sides, the perimeter will be six times the length of one side. To find the length of one side, we can use the formula for the area of a regular hexagon, which is:

Area = (3√3 / 2) × s²

where s is the length of one side.

30.5 = (3√3 / 2) × s²

s² = 30.5 × 2 / (3√3)

s² ≈ 11.13

s ≈ 3.34

So the perimeter of the base is 6 × 3.34 ≈ 20.04 centimeters.

Now we can use the formula for the volume of a prism, which is:

Volume = Base area × Height

Volume = 30.5 × 6.5 ≈ 198.25 cubic centimeters

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Answer:

-12i - 64j

Step-by-step explanation: