What is the average rate of change of the function y = 3 sin(2x) on the interval [0,π4] ?

Answer:

Alternative Hypothesis

Answer:

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Complete the square as follows:

The probability that at least one person receives his/her own hat is 1 - (1/n)^n, using the inclusion-exclusion principle.

The inclusion-exclusion principle states that the probability of event A or B occurring is equal to the probability of event A plus the probability of event B minus the probability of event A and B occurring. In this case, the probability of at least one person receiving his/her own hat is the probability of one person receiving his/her own hat plus the probability of two people receiving their own hats minus the probability of three people receiving their own hats, and so on. This can be expressed mathematically as 1 - (1/n)^n, where n is the number of guests. This formula can be applied to any situation where a random event is being repeated multiple times with the same set of outcomes.1 - (1/10)^10 = 0.99.

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Store D provides the best value, with the lowest price per donut at $0.24.

To determine which store has the best deal, you should compare the price per donut at each store.

At Store A, the BOGO offer means that you can buy one dozen donuts for the regular price of $6.35 and get a second dozen for free. This means that you are paying $6.35 for 2 dozen donuts, or $0.27 per donut.

At Store B, a dozen donuts cost $3.35, or $0.28 per donut.

At Store C, a dozen and a half donuts cost $6.50, or $0.26 per donut.

At Store D, if you buy 2 dozen donuts at $3.70 each and receive a 25% discount, you will pay $3.70 × 2 × (1 - 0.25) = $5.77 for 2 dozen donuts, or $0.24 per donut.

Thus, based on these prices, Store D is the best deal, as it has the lowest price per donut at $0.24.

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Answer:

The perimeter of Elie's vegetable garden is 34 meters.

Step-by-step explanation:

The formula for area is: a=w*l.

A = area

W = width

L = length

If the length is 9 meters, then we know two of the values, the area, and the length. Substitute.

72=w*9

You can divide both sides by 9 to get the width, which is 8 meters.

To find perimeter, we add l+w+l+w, or 2l+2w. Substitute for our values:

2(9)+2(8)=34

The perimeter of Elie's vegetable garden is 34 meters.

Answer:

There is one unique solution, (−6, 5).

Step-by-step explanation:

2x + 4y = 8

2x + 6y = 18

2x + 4y = 8  ==> solve for 2x

2x + 4y - 4y = 8 - 4y

2x = 8 - 4y

2x + 6y = 18  ==> solve for 2x

2x + 6y - 6y = 18 - 6y

2x = 18 - 6y

8 - 4y = 18 - 6y  ==> 2x = 8 - 4y   and   2x = 18 - 6y

8 - 4y + 6y = 18 - 6y + 6y  ==> solve for y by first adding 6y on both sides to

                                                remove negative y

8 + 2y = 18  ==> simplify

8 - 8 + 2y = 18 - 8  ==> isolate y

2y = 10

y = 5

2x + 4(5) = 8  ==> substitute 5 for y in 2x + 4y = 8

2x + 20 = 8

2x - 20 + 20 = 8 - 20  ==> subtract 20 on both sides to isolate 2x

2x = -12

x = -6

x = -6, y = 5  ==> (6, 5)

Answer: There is one unique solution, (−6, 5).

Answer:

The value of the car at the end of 3 years will be $13707.

Step-by-step explanation:

If the original value of the car is $20000, then after the first year, the value of the car will be $20000 - (12/100)*$20000 = $17600.

After the second year, the value of the car will be $17600 - (12/100)*$17600 = $15552.

After the third year, the value of the car will be $15552 - (12/100)*$15552 = $13707.

Therefore, the value of the car at the end of 3 years will be $13707.

The graphs in this problem that show continuous data are given as follows:

Continuous and discrete graphs have different formats to show the data, which are presented as follows:

For a continuous data, the data shown is all the real numbers in an interval, hence a continuous graph is represented by solid lines. This means that the second and third graphs in this problem, that is, the top right and the bottom left graphs represent continuous data.

For discrete data, only certain values are represented in an interval, hence the graph of discrete data is composed only by dots, which is the case for the first and last graphs in this problem, that is, the top left graph and the bottom right graph.

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Different x values must be taken into account in order to graph h (x). So the graph of the h(x) is given below.

In the given question, we use the graphs of f and g to graph h(x) = (f + g)(x).

A diagram that compares the fluctuation of one variable to that of one or more other variables, such as a collection of points, lines, line segments, curves, or regions.

The graph is given below:

h (x) = (f + g) (x)

The function h(x) can be written as

h (x) = f (x) + g (x)

Different x values must be taken into account in order to graph h (x).

h (0) = f (0) + g (0) = 2 - 1 = 1

h (1) = f (1) + g (1) = 3 + 0 = 3

h (2) = f (2) + g (2) = 1 + 0.5 = 1.5

h (3) = f (3) + g (3) = 2 + 0 = 2

So the graph of the h(x) is given below:

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The water level is rising at a rate of 0.0764 cm per second.

Using implicit differentiation, it is found that the water level is rising at a rate of 0.0764 cm per second.

The volume of a cone of radius r and height h is given by:

V = πr²h/3

Applying implicit differentiation, the rate of change is given by:

dV/dt = 2πr/3 dr/dt + πr²/3 dh/dt

In this problem:

The radius is constant, thus dr/dt = 0

Height of 5 cm and radius of 3 cm, thus h = 5, r=3.

Water poured at a rate of 2 cm³/s, thus dV/dt = 2

Then

dV/dt = 2πr/3 dr/dt + πr²/3 dh/dt

2 = 25π/3 dh/dt

dh/dt = 6/25π

dh/dt = 0.0764

The water level is rising at a rate of 0.0764 cm per second.

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Answer:

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

Given:

Divide the number of inches by the time to get the rate of snowfall:

3 15/8 = 39/8 = 4 7/8

2 13/6 = 25/6 = 4 1/6

1.shade 3 full 8/8 circles 2. Shade 15 little slices in the rest 3. You done with the first one 1. Shade 2 full 6/6 circles 2. Shade 13 more little slices in the rest 3. TADAAA you done

Step-by-step explanation:

Answer:

Use this site, it will help you in the long run.

Answer: y = 14.50x + 2.99

Step-by-step explanation:

The equation is y = mx + b

y is the total cost and x is the number of shirt

We know each shirt is $14.50, and she bought x shirts, so 14.50 is the slope

The 2.99 shipping fee is the y-intercept

So our equation is

y = 14.50x + 2.99

Answer:

[tex]y=-\frac{2}{3}x+1[/tex]

Step-by-step explanation:

Parallel means same slope.

[tex]y=-\frac{2}{3}x+b[/tex]

[tex]5=-\frac{2}{3} (-6)+b[/tex]

5 = 4 + b

b = 1

[tex]y=-\frac{2}{3}x+1[/tex]

Answer:

x = 25

Step-by-step explanation:

The two interior angles equal the exterior angle.

6x - 12 = 3x + 2x + 13  Combine like terms

6x - 12 = 5x + 13  Subtract 5x from both sides of the equation

6x -5x - 12= 5x - 5x + 13

x - 12 = 13  Add 12 to both sides of the equation

x - 12 + 12 = 13 + 12

x = 25

If new automobile prices are roughly regularly distributed, with a mean of $17,000 and a standard deviation of $500, then it means that the majority of the prices paid for the car will fall within a certain range.

Specifically, approximately 68% of the prices paid will be within one standard deviation of the mean, which in this case would be between $16,500 and $17,500.

Approximately 95% of the prices paid will be within two standard deviations of the mean, which would be between $16,000 and $18,000. And approximately 99.7% of the prices paid will be within three standard deviations of the mean, which would be between $15,500 and $18,500. This demonstrates that the prices paid for the cars are generally consistent, with only a tiny percentage deviating from the mean and standard deviation-defined range.

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Moussa's age if the product of their ages is 24 is 4 years.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Moussa is younger than Sophia. Their ages are consecutive even integers.

Let the ages be x and x + 2.

This will be illustrated as:

x(x + 2) = 24

x² + 2x = 24

x² + 2x - 24 = 0

x² + 6x - 4x - 24 = 0

x(x + 6) -4(x + 6) = 0

x - 4 = 0

x = 4

x + 2 = 4 + 2 = 6

The ages are 4 and 6 years.

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If the product of Sophia age and Moussa age is 24, the age of Moussa is 4 years.

Moussa is younger than Sophia.  Their ages are consecutive even integers.

The product of there ages is 24. Moussa's age can be found as follows:

Even numbers are those numbers that can be divided into two equal groups or pairs and are exactly divisible by 2.

Hence,

Let

x = age of Moussa

x + 2 = age of Sophia

Hence, the product of their age will be as follows:

x(x + 2) = 24

x² + 2x = 24

x² + 2x - 24 = 0

lets factorise the quadratic equation. The numbers one can multiply to get -24 and add to get 2 are -4 and 6. Therefore,

x² - 4x + 6x - 24 = 0

x(x - 4) + 6(x - 4) = 0

(x + 6)(x - 4) = 0

Therefore,

x = - 6 and x = 4

We can only use positive numbers.

Therefore, the age of Moussa is 4 years

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Answer:

here is the answer with proper steps.

sample consists of 87 subjects, with 71 successes.the test statistic, rounded to 2 decimal places ,Test statistic = (71/87) = 0.81

To calculate the test statistic, you need to divide the number of successes by the total number of subjects in the sample.

In this case, the number of successes is 71 and the total number of subjects is 87.

Therefore, the test statistic is calculated a

s 71/87 = 0.81

which can be rounded to two decimal places. The result of the calculation is that the test statistic is 0.81.

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=(2x2 −2xz+z ^2 )(2x−z)(z)

if it is not possible to obtain a list of all elements in a population, this is a; group of answer choices  finite population statistic

It is also known as the group of the study, that targets the population, which helps to find the survey, which is the sampled population. It is measured by an ideal world, which will be the same, and they're always unique.  

Its sampling distribution of the "x bar" should also be naturally independent of the random sample, that is usually distributed.

We consider the population as endless if the sampling size is at least 20 times greater than the sample size.

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Answer:

<E=180-60=120

t=60 degrees

u=8

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I would like to construct a 95% confidence interval with a 4% margin of error. We don't have an estimate for the percentage, so we use a conservative estimate.

This is the minimum sample size, so we need to round up to 601. The larger the sample, the more confident the responses truly represent the population.

This shows that for a given confidence level, the confidence interval gets smaller as the sample size increases. At least 1450 samples from each group are required.

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Answer:

40mins

Step-by-step explanation:

4hrsx60

=240mins

240mins/6 lessons

=40mins per lesson

Answer:

y – 5 = m(x – 6)

Step-by-step explanation:

using y =mx +c as our guide line

Step 1 : identification of coordinates

(6,5) ;x1= 6,y1 = 5

step 2 : applying the formula

y – y1 = m(x – x1)

y – 5 = m(x – 6)

The distance traveled by light in 1 minute = 18 million kilometers and the distance traveled by light in 1 second = 0.3 million kilometers.

We are given that -

The distance traveled by light in 10 minutes = 180 million km.

Now we have to find the distance traveled by light in 1 minute.

Using the unitary method, we get -

Distance traveled by light in 1 min = 180000000 / 10

Distance traveled by light in 1 min = 18 million kilometers

Now we have to find the distance traveled by light in 1 second.

We know that 1 minute= 60 seconds,

Thus, In 60 seconds light travels a distance of = 18 million kilometers. (from above)

therefore, in 1 second light would travel a distance of = 18 million / 60

                                                                                         = 0.3 million km

Hence, the distance traveled by light in 1 second = 0.3 million kilometers.

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The complete question is -

Light travels about 180 million kilometers in 10 minutes. How far does it travel in one minute? How far does it travel in one second?

The value of first quartile of the given data set is 2.5

The lower quartile, or first quartile (Q1), is the value under which 25% of data points are found when they are arranged in increasing order.

Given is a data set,

According to the data,

The lower quartile is between 0 and 2.5, which under 25% of the data.

Hence, The value of first quartile of the given data set is 2.5

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