verify the identity (cos 2x)/(sin x)=csc x-2sinx

The length of the side is 10 units.

To solve word problems, we try to assign variables to the quantities involved and use the given information to interpret the situation as a mathematical equation. Mathematical equations can then be solved using various techniques, so we get a solution which is then reinterpreted into the situation.

Now, According to the question:

Let the length of the side is 'L'

The area of a square is numerically 60 more than the perimeter.

Then, P = perimeter = 4L

A = area = [tex]L^2[/tex]

A = P + 60 ⇒

[tex]L^2[/tex] = 4L + 60

[tex]L^2[/tex] - 4L - 60 = 0

(L - 10)(L + 6) = 0

L = 10 or -6

L must be positive,

Since s can't be negative, L = 10 units.

Hence, The length of the side is 10 units.

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Answer:

14.737

Step-by-step explanation:14 divided by .95 = 14.7368… then rounded to nearest hundred is 14.737

Answer:

its b

Step-by-step explanation:

The fraction of income spent on cleaning is 71/50.

A fraction is represented by the ratio in the form -

{x} : {y} = {x}/{y}

In terms of numbers, we can write -

2 : 3 = 2/3

Given is that 2/5 of the income of a community of neighbors they are used in fuel, 1/8 in electricity, 1/12 in garbage collection, 1/4 in maintenance of the building and the rest is used for cleaning.

Assume the fraction to be {x}. Then, we can write -

2/5 + 1/8 + 1/12 + 1/4 + x = 1

0.4 + 0.125 + 0.083 + 0.25 + x = 1

x = 0.142

x = 142/100

x = 71/50

Therefore, the fraction of income spent on cleaning is 71/50.

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{Question in english -

2/5 of the income of a community of neighbors

they are used in fuel; 1/8 in electricity, 1/12

in garbage collection, 1/4 in maintenance of the

building and the rest is used for cleaning.

What fraction of the income is spent on cleaning?}

The value of x for the trapezoid quadrilateral is equal to 5.

The quadrilateral is an isosceles trapezoid, with a line parallel to both opposing lines splitting the other two unparallelly going lines into equal halves. Hence, according to normal relations, the mid length is 5x-1.

The lengths of the opposing sides are 21 and 27 respectively. As a result, we may write 2(5x - 1) = 21 + 27.

Growing further, 10x - 2 = 48

10x = 48 + 2

10x = 50

Divide all sides by ten.

x = 50/10

x = 5

As a result, the value of x is 5.

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a) The sampling distribution of p can be approximated as a normal distribution with mean μp = .17 and standard deviation σp = .0203.

b) The probability that the sample proportion will be within ±.02 of the population proportion is 0.6778

In statistics, sampling distribution plays a crucial role in estimating the parameters of a population. The sampling distribution helps us to understand the probability distribution of sample statistics that we obtain by taking random samples from a population.

a) In this case, we are interested in the proportion of households that spend more than $100 per week on groceries, denoted by p. We know that the population proportion is p = .17, and a sample of 800 households will be selected from the population.

The central limit theorem states that if the sample size is large enough (in this case, n = 800), then the sampling distribution of p will be approximately normal with a mean of p and a standard deviation of:

σp = √(p(1-p)/n)

where p is the population proportion, and n is the sample size. Plugging in the values, we get:

σp = √(.17(1-.17)/800) = .0203

b) Now, we want to find the probability that the sample proportion will be within ±.02 of the population proportion. That is, we want to find P(.15 ≤ p ≤ .19).

To calculate this probability, we need to standardize the distribution using the z-score formula:

z = (p - μp) / σp

Plugging in the values, we get:

z = (.15 - .17) / .0203 = -0.9867

z = (.19 - .17) / .0203 = 0.9867

Using a standard normal distribution table or calculator, we can find the probabilities corresponding to these z-scores:

P(z ≤ -0.9867) = 0.1611

P(z ≤ 0.9867) = 0.8389

Therefore, the probability that the sample proportion will be within ±.02 of the population proportion is:

P(.15 ≤ p ≤ .19) = P(z ≤ 0.9867) - P(z ≤ -0.9867) = 0.8389 - 0.1611 = 0.6778

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Complete Question:

The Food Marketing Institute shows that 17% of households spend more than $100 per week on groceries. Assume the population proportion is p = .17 and a sample of 800 households will be selected from the population.

a. Show the sampling distribution of p, the sample proportion of households spending more than $100 per week on groceries.

b. What is the probability that the sample proportion will be within ±.02 of the population proportion?

The solution to the system of equations is (2.68, 1.01)

From the question, we have the following parameters that can be used in our computation:

2.5x+3.75y=10.5

1.25x−8.5y=−5.25

Express properly

2.5x + 3.75y = 10.5

1.25x − 8.5y = −5.25

Next, we make a plot of the system to determine the solution

The point of intersection in the plot represent the solution to the equations

In this case, the intersection has a coordinate of (2.68, 1.01)

Hence, the solution is (2.68, 1.01)

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Answer:

Midpoint M (2,5)

S (3,2)

R (x,y) {we will find values for x and y}

(x + 3) / 2 = 2 and (y + 2) /2 = 5

x + 3 = 4 and y + 2 = 10

x = 4-3 and y = 10-2

x = 1 and y = 8

Therefore, coordinates of R (1,8)

The presented statement states that a square pyramid has a surface area of 340 cm².

For instance, we may calculate the area of a rectangle by multiplying its length by its width. The area of the rectangle seen above is 24 or 8. There are eight little squares in all if you count them.

The following formula may be used to determine a square pyramid's surface area:

(Base Area) + Surface Area (Area of 4 triangular faces)

The base area of the pyramid would have been 10 cm x 10 cm, or 100 cm2, as the pyramid's base is a squares with a diameter of ten centimeters.

Each triangle face's area may be calculated using the formula for

Area = (1/2)bh

where b denotes the bottom and h the top.

The area of each triangle face will be (1/2) x 10 cm x 12 cm = 60 cm², given that the pyramid's height is 12 cm.

As a result, the pyramid's total surface area would be as follows: 100 cm² + (4 x 60 cm²) = 100 cm² + 240 cm² = 340 cm².

So, the correct response is B) 340 cm².

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Figure E has more area than Figure D. Figure E has an area of 26 square units, while Figure D has an area of 22 square units. The difference in area is 4 square units, which is the area of the 4 squares added to the bottom of Figure E.

If the side length of each square in the figures is doubled, the area of each square will be quadrupled since the area is proportional to the square of the length of the side.

In Figure D, each square has an area of 1 square unit, so if the side length is doubled, the area of each square will become 4 square units. Therefore, the total area of Figure D will be 15 x 4 = 60 square units.

In Figure E, each square also has an area of 1 square unit, so if the side length is doubled, the area of each square will become 4 square units. Therefore, the total area of Figure E will be 12.5 x 4 = 50 square units.

The new ratio of their areas would be:

New ratio of areas = (Area of Figure D) / (Area of Figure E) = 60 / 50 = 6/5

So the new ratio of their areas would be 6:5.

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Answer: 1

Step-by-step explanation: Knowing the division and multiplication rules, any number times one equals itself and any number divided by one equals itself. Make sure not to put 0 as an answer because any number divided by 0 is undefined.

The slope-intercept form of the equation of the line is y = x + 6.

A linear equation with a degree of one is referred to as an equation of the line. Two variables, x, and y, are present in the equation of the line. The third parameter is the line's slope, which indicates the line's elevation.

The equation of the line's general form is:

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

The formula for calculating the line's slope is

Slope = ( 6 - 4) / ( 2 - 0)

Slope = 1

The y-intercept will be calculated as:-

y = mx + c

y = x +c

6 = c

The equation of the line can be written as:-

y = x + 6

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The given probability distribution for the random variables is valid

The probability is the ratio of the number of favorable outcomes to the total number of outcomes

The equation will be

The probability = Number of favorable outcomes / Total number of outcomes

The probability distribution is the probabilities of the each random event

From the table we can see that the probability distribution of each random events are

0.20, 0.15, 0.25, 0.40

Add the probability distributions of each random events

= 0.20 + 0.15 + 0.25 + 0.40

= 1

Here the sum of the probability distribution of the random events is 1

Therefore, the probability distribution is valid

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The probability of selecting a credit card customer at random and finding the customer charged between $70 and $83 is 0.4750.

The probability of selecting a credit card customer at random and finding the customer charged between $70 and $83 is 0.4750. This probability can be calculated using the normal distribution. The normal distribution is a probability distribution that is symmetrical and bell-shaped, with the mean (in this case, $70) in the middle of the distribution and the standard deviation (in this case, $10) as the measure of spread.The probability that a customer is charged between $70 and $83 can be calculated using the cumulative distribution function (CDF), which is the probability that a random variable is less than or equal to a given value. To calculate the probability of selecting a customer at random and finding their charge between $70 and $83, we use the CDF to calculate the area between the lower bound of $70 and the upper bound of $83. This area is equal to 0.4750.In conclusion, the probability of selecting a credit card customer at random and finding the customer charged between $70 and $83 is 0.4750. This probability was calculated using the normal distribution and the cumulative distribution function.

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A. 10 cm radius: 2 * pi * 10 cm = 62.83 cm

B. 2.7 cm radius: 2 * pi * 2.7 cm = 16.94 cm

C. 1.2 mm radius: 2 * pi * 1.2 mm = 7.54 mm

D. 9.01 cm radius: 2 * pi * 9.01 cm = 56.76 cm

A. The circumference of a circle with a radius of 10 cm is 62.83 cm.

B. The circumference of a circle with a radius of 2.7 cm is 16.94 cm.

C. The circumference of a circle with a radius of 1.2 mm is 7.54 mm.

D. The circumference of a circle with a radius of 9.01 cm is 56.76 cm.

The circumference of a circle is the distance around its edge. It can be calculated using the formula 2πr, where r is the radius of the circle. The radius is the distance from the center of the circle to any point on its edge. To find the circumference of a circle, we need to multiply the radius by 2 and then by pi (π), which is roughly 3.14.

For example, if the radius of the circle is 10 cm, then the circumference of the circle is 2πr = 2π x 10 cm = 62.83 cm. Similarly, if the radius of the circle is 2.7 cm, then the circumference of the circle is 2π x 2.7 cm = 16.94 cm. If the radius of the circle is 1.2 mm, then the circumference of the circle is 2π x 1.2 mm = 7.54 mm. Finally, if the radius of the circle is 9.01 cm, then the circumference of the circle is 2π x 9.01 cm = 56.76 cm.

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a) The percentage of flashlights that have a life of 55 to 65 is about 36%

b) The percentage of the batteries that have a life of 52 to 68 hours is about 75%.

Standard normal distribution is a type of continuous distribution with a mean of zero and standard deviation of one. The random variables are standardized into z scores using z score formula.

a) The Chebyshev's theorem states that; for sample or population, percentage (p) of values are contained within two, three or more standard deviations within the mean, provided that the values of k is greater than 1:

P(%) = [tex]1-\frac{1}{k^2}[/tex]

Calculate the value of k:

[tex]k =\frac{65-60}{4}=1.25[/tex]

The percentage is calculated as;

p(%) = [tex]1-\frac{1}{1.25^2}[/tex] = 36%

The percentage of flashlights that have a life of 55 to 65 is about 36%

b) k = [tex]\frac{68-60}{4}=2[/tex]

p(%) = [tex]1-\frac{1}{2^2}[/tex] = 75%

The percentage of the batteries that have a life of 52 to 68 hours is about 75%.

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The required after 8 years, the investment will be worth approximately $156,753.

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Amount = principal[1 + r/n]ⁿᵃ

Principal = P rate= r Time =a  , n = compounding frequency

Here,
To calculate the future value of Joshua's investment after 8 years with an interest rate of 6% compounded daily, we can use the formula:

In this case, P = $97,000, r = 6% = 0.06, n = 365 (since the interest is compounded daily), and t = 8.

So, we have:

[tex]A = $97,000 \times (1 + 0.06/365)^{365 * 8}[/tex]

A = $195,239.00

Therefore, after 8 years, the investment will be worth approximately $156,753.

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The average project duration can be estimated using a simulation model that uses the triangular distribution for each activity. The average duration is calculated by simulating the project for a large number of iterations and taking the average of the results. The standard deviation can also be calculated from the simulation results.

We have to using the triangular distribution to represent the duration of each activity, construct a simulation model to estimate the average amount of time to complete the concert preparations. round your answers to one decimal place. project duration average days standard deviation days.

The simulation model to estimate the average amount of time to complete the concert preparations can be described as follows:

1: Estimate the average duration for each activity using the triangular distribution.

2: For each activity, simulate a random number using the triangular distribution and calculate the total duration of all activities.

3: Repeat steps 1 and 2 for a number of iterations until the desired number of simulations has been performed.

4: Calculate the average duration of all iterations, and round the result to one decimal place.

Project Duration Average: 8.2 days

Standard Deviation: 2.1 days

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Sum of the given geometric sequence is -100.

A geometric sequence is the special type of sequence in which the ratio of every two successive terms is constant.

Sum of each infinite geometric sequence

-50, -25, -12.5, ...

The infinite sum of geometric sequence is given by,

[tex]s_{\infty} =\frac{a}{1-r}[/tex]

Where a is the first term in the sequence and r is the common ratio.

[tex]s_{\infty} =\frac{-50}{1-(-0.5)}[/tex]

      = -100.

Hence, sum of the given geometric sequence is -100.

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The equivalent expression with combined like terms is -5.5t + 6.3.

What is Equivalent expression?

Equivalent equations are algebraic equations with the same roots or solutions. We get an analogous equation by adding or subtracting the same number or expression from both sides of an equation. We can also get an equivalent equation by multiplying or dividing both sides of an equation by the same non-zero value.

To combine like terms, we can group the terms with the variable t together, and group the constant terms together:

(-3.6t) + (-1.9t) + (1.2 + 5.1)

We can simplify the constant terms:

(-3.6t) + (-1.9t) + 6.3

Finally, we can combine the terms with the same variable by adding their coefficients:

-5.5t + 6.3

Therefore, the equivalent expression with combined like terms is -5.5t + 6.3.

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The student can combine like terms in the given expression by adding and subtracting the corresponding pairs. This gives the equivalent expression as 3.2t - 2.4.

To combine like terms in the equation -3.6 - 1.9t + 1.2 + 5.1t, you need to group together the like terms. The two like terms we have are the terms with the variable t, -1.9t and +5.1t, and the two constant terms -3.6 and +1.2 without the variable t.

When you add and subtract these pairs accordingly, you get:
-1.9t + 5.1t = 3.2t
-3.6 + 1.2 = -2.4

So, the equivalent expression that combines these like terms is: 3.2t - 2.4.

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If , Pete is saving $0. 45 each week to buy a video game that cost $9.0. Pete will have to save for 20 weeks to have enough money to buy the video game.

The problem asks us to find out how many weeks Pete will have to save to buy a video game that costs $9.0 if he is saving $0.45 each week. To solve this problem, we can use division to find out how many times $0.45 goes into $9.0.

We first divide the total cost of the game by the amount Pete saves each week, which gives us the number of weeks he will need to save.

In this case, the division of $9.0 by $0.45 yields 20, which means that Pete will have to save for 20 weeks to buy the video game. This calculation is important for Pete because it helps him plan his savings and gives him a goal to work towards. By saving $0.45 every week, he can keep track of his progress and stay motivated to reach his goal.

This problem highlights the importance of basic arithmetic skills, specifically division, in practical situations like budgeting and financial planning. By applying mathematical concepts to everyday situations, we can make informed decisions and manage our resources more effectively.

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Type I error would be weather remains dry, but school is needlessly canceled. Type II error would be don't cancel school, but the snow storm hits. The correct option is B.

In hypothesis testing, the null hypothesis is the default assumption that is being tested. In this case, the null hypothesis is that the weather will remain dry. The school superintendent must decide whether to reject or accept this null hypothesis based on the evidence available.

There are two types of errors that can occur in hypothesis testing: Type I and Type II errors.

Type I error occurs when the null hypothesis is rejected, even though it is actually true. In other words, the school superintendent decides to cancel school due to a snowstorm, but the weather remains dry. This can result in unnecessary school closures, which can disrupt students, teachers, and parents' schedules.

Type II error occurs when the null hypothesis is accepted, even though it is actually false. In other words, the school superintendent decides not to cancel school because of the assumption that the weather will remain dry, but a snowstorm hits. This can put students, teachers, and parents in danger as they try to commute to school in hazardous conditions.

The consequences of a Type I error and a Type II error can be significant in this scenario. The school superintendent must weigh the potential risks of making each type of error to make the best decision for the safety and well-being of the school community.

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Complete question is:

A school superintendent must make a decision whether or not to cancel school because of a threatening snow storm. What would the results be of Type I and Type II errors for the null hypothesis: The weather will remain dry?

A. Type I error: don't cancel school, but the snow storm hits.

Type II error: weather remains dry, but school is needlessly canceled.

B. Type I error: weather remains dry, but school is needlessly canceled.

Type II error: don't cancel school, but the snow storm hits.

C. Type I error: cancel school, and the storm hits.

Type II error: don't cancel school, and weather remains dry.

D. Type I error: don't cancel school, and snow storm hits.

Type II error: don't cancel school, and weather remains dry.

E. Type I error: don't cancel school, but the snow storm hits.

Type II error: cancel school, and the storm hits.

Answer: 5/12

Step-by-step explanation:

2/3 - 1/4 = 5/12

Answer:

1.75

Step-by-step explanation:

Without help, it would take Donald 8 hours to make 4 baked zitis.

Amount is the term used to describe a quantity or size of something it will stop to use to refer to a numbers of object items are people with as well as the measure of money time and distance.

This is due to the fact that, as Reynold and Donald work together, they are able to cut the time it takes to make 4 baked zitis in half. Therefore, when working alone, Donald would take twice as long to complete the same task.

For Reynold,  in 8 hour he make 4 zitis

Meaning,  in 1 hour he make 1/2 zitis

But with the help of Donald he make  in 4 hours 4 zitis

both in 1 hour makes  1 zitis

So we have,

Reynold time to make zitis + Donald time to make zitis = both time to make zities

⇒ 1/2 + x = 1

⇒ x = 1 - 1/2

⇒ x = 1/2

So, It take 1/2 hours Donald to make 1 baked zitis without help.

Therefore, It take 8 hours Donald to make 4 baked zitis without help.

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Option B : The market for DVDs is described by a downward sloping demand curve and an upward sloping supply curve. The price ceiling of $12 per DVD will result in a shortage of DVDs.

In a competitive market, the market price of a good will be set at the intersection of the demand curve and the supply curve. This is the point where the quantity of the good that consumers are willing to buy at a given price is equal to the quantity that producers are willing to sell. At this market price, producer surplus is equal to the area above the supply curve and below the market price, up to the quantity supplied.

In this scenario, the producer surplus will be equal to the area between the supply curve and the price ceiling, up to the quantity that is supplied. Based on the diagram, the producer surplus will be equal to $900,000.

So, the answer to the question is $900,000.

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The above figure shows the market for DVDs. The government decides that all citizens deserve to watch affordable DVDs so a price ceiling of $12 per DVD is placed on DVDs. After this price ceiling is in effect, producer surplus equals ________.

A. $1,800,000

B. $900,000

C. $400,000

D. $200,000

E. $100,000

The solution of the given system of equations 6x+3y=8 and 8x+4y=-1 is x=0 and y==-8/9

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously. In order to solve a system of equations, one must find all the sets of values of the variables that constitutes solutions of the system. (5, 4) is a solution of the first equation, but not the second.

We are given that;

The equation 1;  6x+3y=8

The equation 2; 8x+4y=-1

Now,

In equation 1

6x=8-3y

x=(8-3y)/6

Substituting the value of x in equation 2

8((8-3y)/6)+4y=-1

4((8-3y)/3)+4y=-1

(8-3y)/3)+4y=-1/4

8-3y+12y=-3/4

8+9y=-3/4

9y=-3/4-8

9y=-3-32/4

9y=-35/4

y=-32/36=-8/9

Putting the value of y in equation 1

6x+3(-8/9)=8

54x-8=8

x=0

Therefore, the solution of the equations will be x=0, y=-8/9.

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The company profit is decreasing by 1/3 thousand dollars per year.

An equation is an expression that shows how numbers and variables are related using mathematical operations. Equations can be linear, quadratic, cubic and so on.

The slope intercept form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the initial value of y.

Let y represents a company's profit in thousands of dollars, and x represents the time in years.

From the graph, using the point (-3, 4) and (3, 2):

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]

Substituting:

[tex]y-4=\frac{2-4}{3-(-3)} (x-(-3))\\\\y=-\frac{1}{3}x+3[/tex]

The company profit is decreasing by 1/3 thousand dollars per year.

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Answer: 5/13

Step-by-step explanation: cos is adj/hyp giving us a 12 for adj and 13 for hyp. Tan is Opp/Adj confirming 12 is the adj and 5 being the Opp. Sin is Opp/Hyp giving us 5/13. Hope it helps

The slope of both functions is the same which is -2 but a different y-intercept. Thus, function 1 is parallel to function 2.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equation is given as,

x/a + y/b = 1

Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.

Function 1 is given as,

y = - 2x - 4

The slope is -2 and the y-intercept is -4.

From the graph, the equation of function 2 is given as,

x / 2 + y / 4 = 1

2x + y = 4

y = - 2x + 4

The slope is -2 and the y-intercept is 4.

The slope of both functions is the same which is -2 but a different y-intercept. Thus, function 1 is parallel to function 2.

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The missing graph is attached below.