A Cap is discounted at 25% off. The original price is $60.
What is the sales price?
O $40
O $50
O $45
O $30

Based on the given information, it is explicitly mentioned whether the sample was randomly selected. This means that, based on the sample data, we can estimate the range within which the true proportion of interested participants is likely to fall with 95% confidence.

In statistics, a sample refers to a subset of a population that is selected for analysis or study in order to make inferences about the entire population. It is often not feasible or practical to collect data from an entire population, so a sample is used as a representative subset to gather information and draw conclusions about the larger population.

Here,

(a) The parameter that the confidence interval will estimate is the proportion of people in the area who are interested in participating in the LARPing event.

(b) The conditions that must be met to use a confidence interval procedure for a proportion are:

Random Sample: The survey respondents must be randomly sampled from the population of interest. This ensures that the sample is representative of the population.

Large Sample Size: The sample size must be sufficiently large, typically with at least 10 successes and 10 failures in the sample. This ensures that the sampling distribution of the sample proportion is approximately normal.

Independence: The responses of the survey respondents must be independent of each other. This means that one respondent's answer should not influence the answer of another respondent.

Based on the given information, it is not explicitly mentioned whether the sample was randomly selected or whether the sample size is large enough, and whether the responses are independent. This information would need to be provided or assumed in order to determine if the conditions for using a confidence interval procedure for a proportion have been met.

(c) The appropriate critical value can be found using a table or calculator. For a 95% confidence interval, the critical value is 1.96. The standard error of the sample proportion can be found using the formula:

SE = √(p(1-p)/n)

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

SE = √(0.288(1-0.288)/1500)

= 0.020

(d) The 95% confidence interval can be calculated using the formula:

sample proportion ± (critical value) x (standard error)

Plugging in the values from the problem, we get:

0.288 ± 1.96 x 0.020

= 0.288 ± 0.0392

The 95% confidence interval is (0.2488, 0.3272).

(e) The interpretation of the confidence interval constructed in part (d) would be: We are 95% confident that the true proportion of people in the area who are interested in participating in the LARPing event lies between the lower and upper bounds of the confidence interval. The larger the confidence interval, the less precise our estimate, but the higher our level of confidence in the range.

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The sampling soldiers until her margin of error for a 82% confidence interval is less than 0.004, soldiers should Haley sample is 12,724 soldiers.

The degree of inaccuracy in survey findings from random sampling is known as the margin of error in statistics. A wider margin of error in statistics denotes a reduced chance of relying on a survey's or poll's findings, meaning that there will be less trust in the results' ability to accurately reflect a community. It is a very important tool for market research since it shows the degree of assurance that should be placed in survey data by the researchers.

A confidence interval is a measure of how unpredictable a given statistic is. It is typically used in conjunction with the margin of error to indicate how confidently a statistician feels that the findings of an online survey or online poll are worthy of being considered representative of the total population.

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi (1-\pi)}{n} }[/tex]

In which, z is the z-score that has a p-value of 1+∝/2.

The margin of error is of:

[tex]M=z\sqrt{\frac{\pi (1-\pi)}{n} }[/tex]

Estimate of the proportion of 64%, hence π = 0.64.

94% confidence level

So , ∝ = 0.94 z is the value of Z that has a p-value of , so z = 1.88

Margin of error of less than 0.008 is wanted, hence, we have to find n when M = 0.008.

[tex]M=z\sqrt{\frac{\pi (1-\pi)}{n} }\\0.008 =1.88\sqrt{\frac{0.64(0.36)}{n} } \\0.008\sqrt{n} = 1.88\sqrt{0.64(0.36)} \\n = 12723.84\\[/tex]

Therefore, Haley should sample 12,724 soldiers.

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The final price of the pen is $1.76 after adding the markup percentages by both the wholesaler and the retailer.

The final price is the total amount of money that a customer pays to purchase a product or service. It includes the cost of the product or service plus any additional fees or charges, such as taxes or shipping costs.

The final price of the pen can be found by adding the markup percentages to the original price of $0.50.

Markup by the wholesaler = 60% of $0.50 = $0.30

Price after markup by wholesaler = $0.50 + $0.30 = $0.80

Markup by the retailer = 120% of $0.80 = $0.96

Final price of the pen = $0.80 + $0.96 = $1.76

Therefore, the final price of the pen is $1.76 after adding the markup percentages by both the wholesaler and the retailer.

For example, if a product costs $50 and there is a 10% sales tax, the final price would be $55 (50 + 5). Similarly, if a service costs $100 and there is a $10 delivery fee, the final price would be $110 (100 + 10).

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Step-by-step explanation:

There are several methods to solve a quadratic equation, but the most common ones are:

Factoring:

This method involves factoring the quadratic expression into two linear expressions and setting each factor equal to zero. For example, to solve the equation x^2 + 5x + 6 = 0, you can factor it as (x + 2)(x + 3) = 0, and then set each factor equal to zero to get x = -2 or x = -3.

Using the square roots:

If the quadratic expression can be written in the form of x^2 = a, where a is a constant, then the solutions can be found by taking the square root of both sides. For example, to solve the equation x^2 = 16, you can take the square root of both sides to get x = ±4.

Completing the square and the quadratic formula:

This method involves completing the square on the quadratic expression to obtain an equivalent expression in the form of (x + b)^2 = c, where b and c are constants. The solutions can then be found by taking the square root of both sides and solving for x. Alternatively, you can use the quadratic formula, which is a general formula that gives the solutions of any quadratic equation in the form of ax^2 + bx + c = 0. The quadratic formula is given by x = (-b ± sqrt(b^2 - 4ac)) / 2a, where a, b, and c are the coefficients of the quadratic expression.

Answer:

see below :)

Step-by-step explanation:

The three common methods for solving quadratic equations are:

Factoring Method:

In this method, the quadratic equation is factored into two binomials, and then the values of x that make each binomial equal to zero are found. This method works only if the quadratic equation can be factored. The factored form of the quadratic equation is:

ax^2 + bx + c = 0

The factors of the quadratic equation are (mx + p) and (nx + q), where m, n, p and q are constants. The factored form of the quadratic equation can be written as:

(mx + p)(nx + q) = 0

The values of x that satisfy this equation are:

x = -p/m or x = -q/n

Using the Square Roots Method:

This method is used when the quadratic equation is in the form of:

x^2 = a

The solutions to this equation can be found by taking the square root of both sides:

x = ± √a

Completing the Square and the Quadratic Formula Method:

This method is used to solve any quadratic equation, even if it cannot be factored. The steps involved in this method are:

Step 1: Rewrite the quadratic equation in the form of:

ax^2 + bx + c = 0

Step 2: Complete the square by adding and subtracting a constant term to the quadratic equation:

ax^2 + bx + c + (b/2a)^2 - (b/2a)^2 = 0

Step 3: Simplify the equation by grouping the first three terms and factoring the perfect square trinomial:

a(x + b/2a)^2 + (c - b^2/4a) = 0

Step 4: Solve for x by taking the square root of both sides and using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

This formula gives two solutions for x, one with the plus sign and one with the minus sign.

Check the picture below.

so the surface area of the pyramid is really just the area of four triangles with a base of 7 and a height of "h" and a 7x7 square, and we also know that that is 210 yd²

[tex]\stackrel{ \textit{\LARGE Areas} }{\stackrel{ \textit{four triangles} }{4\left[\cfrac{1}{2}(\underset{b}{7})(h) \right]}~~ + ~~\stackrel{ square }{(7)(7)}}~~ = ~~210\implies 14h+49=210 \\\\\\ 14h=161\implies h=\cfrac{161}{14}\implies h=11.5[/tex]

Answer:

the square pyramid's slope height is roughly 5.75 yards.

Step-by-step explanation:

The square pyramid's slope height should be "l."

A square pyramid's surface size is determined by:

Surface area equals base area plus (1/2) * base radius plus slope height.

Given that the base's length is 7 yards and the surface size is 210 yards. The base's size is thus:

Base area equals side times side, or 7 times 7 square yards.

As a result, we have:

210 = 49 + (1/2) * 4 * 7 * l

When we simplify the previous solution, we get:

210 - 49 = 28l

161 = 28l

l = 161/28

Consequently, the square pyramid's slope height is roughly 5.75 yards. (rounded to two decimal places).

Hence, 96 kilometers separate the two tourism destinations in reality as it is a proportion to determine the real distance (in kilometers).

The actual distance is the measurement in feet between the blast site and the closest residence, public structure, school, church, or other commercial or institutional structure that is not owned or leased by the perpetrator of the blast.

Given :

To find the actual distance between the two tourist attractions, we need to use the scale given in the problem.

The scale of the map is 3 inches: 2 km.

We can use this scale to convert the distance on the map (5-5-144 inches) to the actual distance.

First, we need to convert the distance on the map from inches to km. To do this, we divide the distance on the map by the number of inches per km:

1 km = 1,000,000 microns

1 inch = 25,400 microns

1 km = 39.37 inches

So, 5-5-144 inches = (5 x 39.37) + (5 x 39.37) + 144 = 314.96 + 314.96 + 144 = 774.92 inches

Next, we can use the scale to convert the distance on the map from inches to km:

3 inches: 2 km

774.92 inches : x km

where x is the actual distance we are trying to find.

We can solve for x by cross-multiplying and simplifying:

3x = (774.92 x 2) / 2.54

3x = 60929.92 / 2.54

3x = 24000

x = 8000 km

Therefore, the actual distance between the two tourist attractions is 8000 km.

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The probability that exactly 5 of the next 7 patients survive the operation is approximately 0.123, or 12.3%.

To find the probability that exactly 5 out of the next 7 patients survive the operation, we can use the binomial probability formula, which is:
[tex]P(X=k) = C(n, k) * p^k * (1-p)^(n-k)[/tex]
where:
- P(X=k) represents the probability of exactly k successes (survivals) in n trials (operations)
- C(n, k) is the number of combinations of n items taken k at a time
- n is the number of trials (in this case, 7 patients)
- k is the number of successful outcomes (5 patients surviving)
- p is the probability of a successful outcome (0.9 for a patient surviving the operation)
Applying the formula, we have:
[tex]P(X=5) = C(7, 5) * 0.9^5 * (1-0.9)^(7-5)[/tex]
First, let's calculate the number of combinations C(7, 5):
C(7, 5) = 7! / (5! * (7-5)!)
C(7, 5) = 7! / (5! * 2!)
C(7, 5) = (7 * 6 * 5 * 4 * 3 * 2 * 1) / (5 * 4 * 3 * 2 * 1 * 2 * 1)
C(7, 5) = 21
Now, we can plug this into the binomial probability formula:
[tex]P(X=5) = 21 * 0.9^5 * 0.1^2[/tex]
P(X=5) = 21 * 0.59049 * 0.01
P(X=5) ≈ 0.1232019.

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Answer:

3

Step-by-step explanation:

And also,PLEASE DONT YELL AT ME/US!!

Answer:

a.  a = 144, b = 67

Step-by-step explanation:

a + 36 = 180  they are consecutive interior angles, so they add up to 180

a = 180 - 36 = 144

b + 113 = 180  they are consecutive interior angles, so they add up to 180

b = 180 - 113 = 67

For supplementary angles 13x + 14 = A, 11x + 28= B​ and A is parallel B, A=B

Therefore x=7

A and B's corresponding angles are congruent if A and B are parallel. As a result, we may equalize the formulas for the respective angles and find x:

13x + 14 = 11x + 28

2x = 14

x = 7

Consequently, we must fix x equal to 7 in order to make A and B parallel. When we insert this value into the formulas for A and B, we obtain:

A = 13(7) + 14 = 105

B = 11(7) + 28 = 105

The corresponding angles of A and B are now congruent, and A and B are equal and parallel.

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The price of a ticket to a baseball game this year is $40.80.

This year's ticket price is 0.85 times last year's ticket price of $48. We can calculate this by multiplying 0.85 by 48:

Using the above as a guide, we have the following:

Total cost = 0.85 × 48

Evaluate

Total cost = 40.80

Therefore, the price of a ticket to a baseball game this year is $40.80.

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Answer: The length of an arc of a circle is given by the formula:

L = rθ

where L is the length of the arc, r is the radius of the circle, and θ is the central angle in radians.

To find the length of the bottom arc, we have:

L1 = r1θ1

where r1 = 5 inches and θ1 = 135° = (135/180)π radians.

L1 = 5(135/180)π = 16.88 inches (rounded to two decimal places)

To find the length of the top arc, we have:

L2 = r2θ2

where r2 = 23 inches and θ2 = 135° = (135/180)π radians.

L2 = 23(135/180)π = 29.07 inches (rounded to two decimal places)

The difference in length between the top arc and the bottom arc is:

L2 - L1 = 29.07 - 16.88 ≈ 12

Therefore, to the nearest inch, the top arc is 12 inches longer than the bottom arc.

Step-by-step explanation:

The missing frequency in the given table is 24.

What is frequency?

To find the missing frequency, we need to use the information given in the histogram and the frequency table.

We can see from the histogram that the missing class interval is 26-28.

The total frequency for all class intervals is the sum of the frequencies in the table:

110 + 36 + 180 + f = 326 + f

We also know that the total frequency is the number of phones recorded by the manufacturer, so we can assume that the total frequency is a whole number.

Since the sum of the frequencies in the table is 326, the missing frequency must be:

f = total frequency - sum of the other frequencies

f = 350 - 326

f = 24

Therefore, the missing frequency is 24.

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For two populations for which μ₁ = 31,σ₁ = 2, μ₂ = 27, and σ₂ = 4. The shape of the distribution is approximately normal. So, the correct choice for answer is option (b). The mean of normal distribution is equals to 4.

In statistics, the collected data distribution shape sometimes normal and sometimes non-normal. In testing of hypothesis, to use the test statistics we have to check whether data is normally or not. Here we have, two populations. In first population : mean μ₁ = 31,

standard deviations,σ₁ = 2,

sample size, n₁ = 49

In case of second sample, mean, μ₂ = 27,

standard deviations, σ₂ = 4.

Sample size, n₂ = 59

Since, population standard deviation are known and sample sizes are greater than 30, therefore the shape of the sampling distribution of the difference of sample means is approximately normal. The shape of the distribution is approximately normal. Mean of the sampling distribution of [tex] \bar x_1 - \bar x_2[/tex] are

[tex]\mu_{ \bar x_1 - \bar x_2} = \mu_1 - \mu_2 [/tex]

= 31 - 27 = 4

Hence, Mean of the distribution is 4.

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Complete question:

Consider two populations for which μ₁ = 31,σ₁ = 2, μ₂ = 27, and σ₂ = 4. Suppose that two independent random samples of sizes n₁ = 49 and n₂ = 59 are selected. Describe the approximate sampling distribution of x₁ bar - x₂ bar (center, spread, and shape). What is the shape of the distribution?

a) The distribution would be non-normal.

b) The distribution is approximately normal.

c) The shape cannot be determined.

What is the mean of the distribution?

Answer:

1.5 × 4.5 × 6 = 40.5 cubic meters

Answer:

A = 3 1/4 + 2 1/4 = 5 2/4 = 5 1/2

B = 2 1/4 + 1 1/2 = 2 1/4 + 1 2/4 = 3 3/4

C = A + B = 5 1/2 + 3 3/4 = 5 2/4 + 3 3/4 =

8 5/4 = 9 1/4

The patient will reach a level of Ibuprofen of only 10 mg between the 6th and 7th hour after taking the 200 mg dose.

A logarithm is a mathematical function that measures the relationship between two quantities, by expressing one quantity in terms of another. More specifically, a logarithm is the power to which a base must be raised to produce a given number.

To model the decay of Ibuprofen in the patient's system, we can use the equation:

A = A0 * [tex]e^(-kt)[/tex]

where A is the amount of Ibuprofen in the patient's system after t hours, A0 is the initial amount of Ibuprofen (200 mg in this case), and k is the decay constant.

To find k, we can use the fact that after one hour, the amount of Ibuprofen in the patient's system has decayed to 136 mg:

136 = 200 * [tex]e^(-k)[/tex]

Solving for k, we get k = ln(5/7) ≈ -0.3365.

Now we can use the equation A = 10 mg and solve for t:

10 = 200 * [tex]e^(-0.3365t)[/tex]

Dividing both sides by 200 and taking the natural logarithm of both sides, we get:

ln(0.05) = -0.3365t

Solving for t, we get t ≈ 6.8 hours.

Therefore, the patient will reach a level of Ibuprofen of only 10 mg between the 6th and 7th hour after taking the 200 mg dose. Answer: C.

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Answer:

STAN BTS

Step-by-step explanation:

1. The perimeter is approximately 24.16 units.

2. Determining the height of this triangle was different from the previous activities because we had to first find the length of one side of the triangle and then find the corresponding height that intersects that side at a right angle. In previous activities, the height was either given or easily determined from the given information.

The probability that a rental car delivered to the firm needs a tune-up is 0.0000308, or approximately 0.0031%. The probability that a car comes from agency 2 needs a tune-up is 0.0234, or approximately 2.34%.

The probability that an event will occur or a claim will be true is measured by probability theory, a branch of mathematics. The probability of an occurrence is a number from 0 as well as 1, where around 0 represents how likely the occurrence would be to occur while 1 represents certainty. A probability is just a numeric illustration of the possibility that a specific occurrence will take place. Probabilities can also be expressed as percentages ranging between 0% to 100% or even from 0 to 1. the ratio of the number of outcomes to the proportion of occurrence in a whole set of equally probable options that lead to a specific occurrence.

given,

(a) Let's denote the event that a car comes from agency i as Ai and the event that a car needs a tune-up as T. We want to find the probability that a rental car delivered to the firm will need a tune-up, which can be written as P(T).

P(T) = P(T|A1)P(A1) + P(T|A2)P(A2) + P(T|A3)P(A3)

Substituting the given probabilities, we get:

P(T) = 0.05% * 0.36% + 0.02% * 0.06% + 0.02% * 0.58%

P(T) = 0.000018 + 0.0000012 + 0.0000116

P(T) = 0.0000308

Therefore, the probability that a rental car delivered to the firm will need a tune-up is 0.0000308, or approximately 0.0031%.

(b) Let's denote the event that a car comes from agency 2 as A2. We want to find the probability that a car comes from agency 2 given that it needs a tune-up, which can be written as P(A2|T).

P(A2|T) = P(T|A2)P(A2) / P(T)

Substituting the given probabilities, we get:

P(A2|T) = 0.02% * 0.06% / 0.0000308

P(A2|T) = 0.00000072 / 0.0000308

P(A2|T) = 0.0234

Therefore, the probability that a rental car delivered to the firm needs a tune-up and came from agency 2 is 0.0234, or approximately 2.34%.

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the adult population in millions in 2015 was 197.37 million

The student question is asking about the adult population in millions, given that the Bureau of Labor Statistics announced that 141.13 million were employed, 16.59 million were unemployed, and 39.65 million were not in the labor force in 2015.

To find the adult population, we need to add the number of employed, unemployed, and not in the labor force adults. This can be done as follows:

Adult population = Employed + Unemployed + Not in the labor force

= 141.13 million + 16.59 million + 39.65 million= 197.37 million

Therefore, the adult population in millions in 2015 was 197.37 million (rounded to two decimal places).

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Answer:

[tex]x = 4 \frac{1}{2} [/tex]

Approximately 58.33% of the workers in the group are making over $25 an hour. The percentage was obtained by finding the area under the uniform distribution curve above the value of $25.

Since the hourly wages of the workers are uniformly distributed on the interval [20, 32], the probability density function is constant on this interval. The area under the probability density function between any two points a and b gives the probability that a randomly chosen worker's wage will be between a and b. Therefore, the probability that a worker's wage is above $25 is given by the area under the probability density function from 25 to 32, which is (32-25)/(32-20) = 7/12 or approximately 58.33%. Thus, approximately 58.33% of the workers are making over $25 an hour.

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The special two-item character sequence that represents special characters like \n is known as an Escape Sequence. So the option B is correct.

An escape sequence is a sequence of characters that does not represent itself when used inside a character or string literal, but is translated into another character or a sequence of characters. It is used to signal an alternative interpretation of a series of characters. Common examples are the escape sequences used in C/C++ and other programming languages, such as "\n" for newline, "\t" for tab, and "\\" for a backslash. So the option B is correct.

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The complete question is:

The special two-item character sequence that represents special characters like \n is known as a(n) ?

a. backslash code

b. escape sequence

c. Unicode spec

d. literal character

The statistical test to run in this scenario is a paired t-test.

A paired t-test is appropriate in this situation because it is used to compare the means of two related groups. In this case, the related groups are the same patients measured at two different time points (2 weeks and 6 months after being prescribed a new medication). The paired t-test assumes that the differences between the two time points are normally distributed.

To conduct the test, we would calculate the mean difference between the two time points and the standard deviation of the differences. We would then calculate the t-statistic and compare it to the critical value from the t-distribution with n-1 degrees of freedom. If the calculated t-value exceeds the critical value, we would reject the null hypothesis that there is no difference between the two time points.

Therefore, a paired t-test is the appropriate statistical test to determine whether there is a significant difference in medication adherence between the two time points

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The measure of ZL in parallelogram JKLM is 14x - 5.

A parallelogram is a quadrilateral with two pairs of parallel sides. That is, opposite sides are parallel and congruent. Parallelograms have several properties that make them useful in geometry and other fields.

In a parallelogram, opposite sides are parallel and congruent. Therefore, we can set up an equation that relates the measures of the opposite sides of parallelogram JKLM:

KL = MJ

We can use this equation to solve for x, and then find the measure of ZL.

Starting with KL, we have:

KL = 15x - 12

Now, for MJ, we need to notice that MJKL is a rectangle because it has a right angle at K. In a rectangle, opposite sides are congruent. Therefore, we have:

MJ = KL = 15x - 12

Now we can use the given expression for MJ to set up an equation for JL in terms of x:

JL = 14x - 5

We can use the fact that JKLM is a parallelogram to set up another equation that relates JL and ZL:

JL = ZL

Putting the two equations together, we get:

JL = JL

14x - 5 = JL = ZL

Therefore, ZL = 14x - 5.

We can substitute the expression we found earlier for JL into this equation to get:

ZL = 14x - 5 = JL = 14x - 5

Simplifying, we get:

ZL = 14x - 5

Therefore, the measure of ZL in parallelogram JKLM is 14x - 5.

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An equation that models the relationship of the variables for Ethan's job and its days of paid vacation is y(x) = 10 + 3x.

The number of paid vacation days that Ethan has had in the eight years since work began is 30 paid vacation days.

We are given that Ethan starts with 10 paid vacation days and earns an additional 6 days for every two years, up to a maximum of 6 work weeks (30 days). To find an equation that models this relationship, we can set up a piecewise function as follows:

y(x) = 10 + 3x

To find out how many paid vacation days Ethan has earned after 8 years, we can plug in x = 8 into the piecewise function:

Since 8 > 6, we use the second part of the piecewise function:

y(8) = 30

So, Ethan has earned 30 paid vacation days after working for 8 years at the company.

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70% of the population prefers coca-cola over pepsi, the probability that both prefer coca-cola is 0.49.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means.

Probability is a way to gauge how likely something is to happen. Several things are difficult to forecast with absolute confidence. With it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty. For pupils in Class 10, probability is a crucial subject since it teaches all the fundamental ideas of the subject. One is the probability of every event in a sample space.

70% of the population prefers Coca-Cola over Pepsi,

that is 0.7

The probability of the Pepsi is 30% = 0.3

The probability that both prefers coca cola is 0.7 x 0.7 = 0.49.

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part B:  In student A's verification the two trigonometric identities are

                             i)  sin²x+cos²x=1 [ Pythagorean trigonometric identity]

                             ii) cot x= cos x/ sin x  [ Ratio trigonometric identities]

                                 tan x= sin x/ cos x

And the identities appeared in step 3 and 6.

What is trigonometric identities?

Trigonometric Identities are being needed whenever trigonometric functions are involved in an expression.  Geometrically, these identities involve  trigonometric functions for example sine, cosine, tangent, cotangent of one or more angles.

Here first trigonometric identity showed in step 3

1 is replaced by sin²x+cos²x.

Based on Pythagorean trigonometric identities if Ф is an acute angle of a right angled triangle then sin²Ф+ cos²Ф = 1.

Another trigonometric identity used in step 6

cot x= cos x/ sin x  

tan x= sin x/ cos x

These are called ratio trigonometric identities.

Hence, In student A's verification the two trigonometric identities are

                             i)  sin²x+cos²x=1 [ Pythagorean trigonometric identity]

                             ii) cot x= cos x/ sin x  [ Ratio trigonometric identities]

                                 tan x= sin x/ cos x

And the identities appeared in step 3 and 6.

To know more about trigonometric identities

https://brainly.com/question/24496175    from the link.

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Step-by-step explanation:

In a right triangle such as this   cos R  will equal the other angle' s Sin

  so cos R = sin S

= 24/51