How many different selections of 4 books can be made from 10 different books, if (i) there is no restriction (ii) two particular books are always selected (iii) two particular books are never selected

The cost of 7 tickets will be $242.20.

In order to determine the cost of 7 tickets, the mathematical operation that would be used is multiplication. Multiplication is the process of determining the product of two or more numbers.

Multiplication is the process used to determine the result when a number is taken times. The sign used to represent multiplication is x. Other mathematical operations are addition, division and subtraction.

In order to determine the cost of 7 tickets, the cost of one ticket would be multiplied by 7.

Cost of 7 tickets = cost of one ticket x 7

$34.60 x 7 = $242.20

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Answer:

h(x) = 5x² - 35x + 60

Step-by-step explanation:

Given the zeros are 3 and 4 then the corresponding factors are

(x - 3) and (x - 4), then

h(x) = 5(x - 3)(x - 4) ← expand factors using FOIL

       = 5(x² - 7x + 12) ← distribute by 5

       = 5x² - 35x + 60 ← in standard form

The probability of the event "~ (a ∩ d)", or the probability that either "a" OR "d" does not occur, is 3/5.

The symbol "∩" represents the intersection of two events.

For example, "a ∩ d" means the event where both "a" and "d" occur together.

The symbol "~" means "not" or "complement." So, "~ (a ∩ d)" means the event where "a ∩ d" does NOT occur, or in other words, where "a" OR "d" does not occur.

Now, onto the question.

We are given that p(a ∩ d) = 2/5, which means that the probability of both events "a" and "d" occurring together is 2/5.

We want to find the probability of the event "~ (a ∩ d)", or the probability that either "a" OR "d" does not occur.

To find this probability, we need to use some basic probability rules.

One of these rules is that the probability of an event happening (let's call it "E") is equal to 1 minus the probability of the complement of that event not happening (~E).

In other words, p(E) = 1 - p(~E).

So, if we apply this rule to the event "~ (a ∩ d)", we get:
p(~ (a ∩ d)) = 1 - p(a ∩ d)

Now we can substitute in the value we were given for p(a ∩ d):
p(~ (a ∩ d)) = 1 - 2/5

Simplifying this gives:
p(~ (a ∩ d)) = 3/5

Therefore, the probability of the event "~ (a ∩ d)", or the probability that either "a" OR "d" does not occur, is 3/5.

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Answer: 0.6763 cm∧2

Step-by-step explanation: Variance is one of the measures of dispersion which is the the second central moment in probability. It is defined as a measure of by how much the values in a data set differs from the mean of the values. Thus it is the average of the squares of the deviations from the mean as this ensures that both the negative and positive deviations do not cancel each other out.

The sample variance would be calculated as follows:

Population size is 7 (5.6 4.9 6.0 5.1 5.5 5.1 7.5)

Mean: Sum of samples / population size ;

(5.6 4.9 6.0 5.1 5.5 5.1 7.5) / 7 = 5.67

Applying the formula for variance: [ Summation (x - mean) ] / population size =( |5.6 - 5.67| + |4.9 - 5.67| + |6.0 - 5.67| + (|5.1 - 5.67|) * 2 + | 5.5 - 5.67| + |7.5 - 5.67|) / 7 = 0.6763 cm^2

These standardization methods are crucial in chromatography to ensure accurate quantification and comparability of results.

In chromatography, standardization methods are used to ensure accurate and reliable results by establishing reference points or calibration standards. Here are three common methods of standardization in chromatography: External Standardization: In this method, a set of known standard samples with known concentrations or properties is prepared separately from the sample being analyzed. These standards are then analyzed using the same chromatographic conditions as the sample. By comparing the response of the sample to that of the standards, the concentration or properties of the sample can be determined. Internal Standardization: This method involves the addition of a known compound (internal standard) to both the standard solutions and the sample. The internal standard should ideally have similar properties to the analyte of interest but be different enough to be easily distinguished. The response of the internal standard is used as a reference to correct for variations in sample preparation, injection volume, and instrumental response. Internal standardization helps improve the accuracy and precision of the analysis. Standard Addition: This method is useful when the matrix of the sample interferes with the analysis or when the analyte concentration is unknown. It involves adding known amounts of the analyte of interest to different aliquots of the sample. The response of the analyte is then measured, and the concentration is determined by comparing the response with that of the standards. The difference in response between the sample and the standards allows for the determination of the analyte concentration in the original sample.

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The function graphed on the paper could be a quadratic function which has the two real roots equal to 3 and 9.

A parabola is a two dimensional figure on a plane which is U shaped and any point on the parabola is at an equal distance from a fixed point called focus and a fixed line called directrix.

The graph of a function is parabola when the function is quadratic.

Quadratic functions are of the form f(x) = ax² + b x + c.

Given that, the parabola touches the x-axis at 3 and 9.

This indicates that roots of the quadratic equation are 3 and 9.

That is, f(x) = 0, when x = 3 and x = 9.

It may be of the form f(x) = (x - 3)(x - 9) = x² - 3x - 9x + 27 = x² - 12x + 27.

So the function representing the graph on the paper is a quadratic function whose roots are 3 and 9 and the function could be of the form f(x) = x² - 12x + 27.

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A straight line represents constant opportunity costs, and a bowed out line represents increasing opportunity costs.

opportunity costs

Opportunity cost is the value of what you lose when choosing between two or more options. Every choice has trade-offs, and opportunity cost is the potential benefits you'll miss out on by choosing one direction over another.

The opportunity cost is time spent studying and that money to spend on something else.

Trade off

A trade-off usually refers to losing one quality or aspect of something in return for gaining another quality or aspect.

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Answer:

-3x-11x²+7

Step-by-step explanation:

Answer:

See Below

Step-by-step explanation:

a.) y-int = 1,000

The y-int represents the base (lowest) price of the antique at age 0

b.) 0 to 10 years = 500

30 to 40 years ≈ 2000

Domain: all real numbers

Range: y ≥ 1,000

Happy Birthday :)

Answer:

Part A —> y intercept is 1000

Y intercept represents the value in dollars

X intercept represents the age of antique

Part B

Domain —> (1000,+oo)

Range —> (1000,+00)

Explanation :

Domain is the set of x values (input)

Range is the set of y values (output)

Answer:

8x+5

Step-by-step explanation:

it would be 8x+5.

this is because 8x and 5 are not like terms so they cannot be collected which means that the answer is 8x+5

Answer:

71 degrees

Step-by-step explanation:

It is quite hard to see the question but I believe we are looking for the unknown angle E (correct me if I am wrong and I will revise my answer!)

The answer is A

Step-by-step explanation:

The length of the segment A'A is 18 units

The length of the segment B'B is 8 units

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

The similar triangle

Using the ratio of corresponding sides, we have

(AA' + 12)/20 = 12/8

So, we have

AA' + 12 = 20 * 12/8

AA' + 12 = 30

Evaluate

AA' = 18

Here, we have

(BB' + 6)/20 = 6/8

So, we have

BB' + 6 = 20 * 6/8

BB' + 6 = 15

Evaluate

BB' = 8

Hence, the length is 8 units

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Answer:

I hope this helps please rate my answer

Step-by-step explanation:

2/5×60

2×12=24

Answer:

Step-by-step explanation:

hearing, taste, touch,

Solving problems involving normal proportions requires careful attention to detail, as well as a good understanding of statistical concepts such as standardization and probability.

When solving a problem where you want to find normal proportions, you can follow the following steps:

Define the problem: Clearly define the problem you are trying to solve, including any relevant details such as the population, sample size, and the variable of interest.

Check assumptions: Check if the conditions for using normal distributions are met. The data should be continuous, the sample size should be large enough, and the distribution should be approximately normal.

Calculate the sample mean and standard deviation: If you are working with a sample, calculate the sample mean and standard deviation.

Standardize the data: Convert the data into standard normal distribution, by subtracting the mean from each observation and dividing by the standard deviation.

Determine the probability: Once the data has been standardized, you can use a standard normal distribution table or a calculator to determine the probability of the variable falling within a certain range or above/below a certain value.

Interpret the results: After determining the probability, interpret the results in the context of the problem. For example, you might conclude that there is a 95% chance that a randomly selected observation falls within a certain range, or that the variable of interest is higher than a certain value in 5% of cases.

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Answer:No

It won't fit

Step-by-step explanation:

This is due to the fact that 7.54545454545454... is larger than 7.5

No. The picture frame will not fit into a box that measures 7.5 inches on each side.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

Length of picture frame = 7 6/11 = 7.54 inches

Length of Box = 7.5 inches

So, From the above as we can see length of the box is smaller than the length of the picture frame.

Hence, it would not fit.

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Answer: infinite solutions

Explanation:

-1+5p ≥-1+5p

5p ≥5p

P ≥p

0 ≥p-p

0 ≥0 (therefore it is an infinite solution)

0.168 is the probability that exactly 1 of the 4 players has exactly one ace and one king.

The word "probability" derives from the Latin word "probitatem," which means "credibility, likelihood," from the noun probabilis in the 14th century (see probable). The phrase was first used in a mathematical meaning in 1718.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

a)

Given that,

each player gets 13 cards.

So, n = total no. of ways = ⁵²C₁₃ = 6.350× 10¹¹

As we know, there are 2 black aces and 4 kings in a deck of 52 cards. Since, one black ace out of 2 black aces can be chosen in ²C₁ ways, next one king out of 4 kings in ⁴C₁ ways and the remaining 11 cards from the remaining 46 cards in ⁴⁶C₁₁ ways.

So, m = ²C₁ × ⁴C₁ × ⁴⁶C₁₁

m = 1.067 × 10¹¹

Therefore, Required probability p =  m/n

p = (1.067 × 10¹¹) / (6.350× 10¹¹)

p = 0.168

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Answer:

isosceles triangle

Step-by-step explanation:

Answer:

Isosceles triangle

Step-by-step explanation:

A scalene triangle is a triangle with no lines of symmetry while an isosceles triangle has at least one line of symmetry and an equilateral triangle has three lines of symmetry.

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s183960

Don't forget to rate

Answer:

Takes her 2 hours

Step-by-step explanation:

The triangle with side lengths 11, 12, and 13 is not a right triangle

We can use the Pythagorean theorem to determine whether the given triangle is a right triangle.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

That is, for a right triangle with sides of lengths a, b, and c (where c is the hypotenuse), we have:

a^2 + b^2 = c^2

Let's apply this to the given triangle with side lengths 11, 12, and 13. We need to check whether 13 is the hypotenuse (the longest side) and whether 11 and 12 are the other two sides:

11^2 + 12^2 = 121 + 144 = 265

13^2 = 169

Since 169 is not equal to 265, we can see that the Pythagorean theorem does not hold for this triangle. Therefore, the given triangle is not a right triangle.

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To find the required sample size for a margin of error less than 3%, we can rearrange the formula for the margin of error:

\(n = (Z^2 * p * (1 - p)) / (E^2)\)

Here, Z represents the critical value, p is the estimated proportion (0.51), and E is the desired margin of error (0.03)

To determine the margin of error for the 95% confidence interval, we need to use the formula:

Margin of Error = Critical value * Standard error

The critical value for a 95% confidence level can be obtained from the standard normal distribution table, which corresponds to 1.96. The standard error can be calculated using the following formula:

Standard error = \(\sqrt{(p * (1 - p) / n)}\)

Given that the proportion of North Carolina residents planning to set off fireworks is estimated to be 51% (0.51) based on the survey, we can substitute the values into the formula. However, the sample size (n) is not provided in the question, so we need to determine it in the next part.

To find the required sample size for a margin of error less than 3%, we can rearrange the formula for the margin of error:

\(n = (Z^2 * p * (1 - p)) / (E^2)\)

Here, Z represents the critical value, p is the estimated proportion (0.51), and E is the desired margin of error (0.03). Substituting these values into the formula, we can solve for the required sample size.

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Answer:

Step-by-step explanation:

Answer:

Elimination

Step-by-step explanation:

Elimination is a process which involves complete removal of one of the variables in a given equation, so as to first determine the value of the other variable.

For example in solving a simultaneous equation, applying the elimination method is easily understood, straight forward and simple to use. Once the logic behind the process is well understood and followed, errors can easily be avoided.

Therefore my favorite way of solving an equation would be by applying the elimination method because it is easy and direct to apply.

Answer:

-6

Step-by-step explanation:

Natural numbers are any whole number that is 0+. So, we 100% know that -6 is an integer, as natural numbers are only positive.