prove that if five cards are chosen from an ordinary 52-card deck, at least two of the cards will be of the same suit. use the pigeonhole proof only.

Using probability the answer to all the subparts are shown:

(1) P (burgers | 9th grader): 6/13

(2) P (burgers / 10th grader): 3/8

(3) P (9th grader /pizza): 13/7

(4) There are 1200 pupils in the school, and 750 of them enjoy pizza, therefore being in the tenth grade is independent of liking pizza.

The probability is calculated by dividing the total number of outcomes by the total number of potential events.

Odds and probability are two different concepts.

Calculating odds involves dividing the probability of an event by the probability that it won't happen.

So that they are aware of the diversity of ways we describe odds, I constantly remind them that we can express probabilities as ratios, percentages, fractions, or decimals.

So, (1) P (burgers | 9th grader):

= P (burgers | 9th grader)

= 600 / 1300

= 6/13

(2) P (burgers / 10th grader):

= P (burgers / 10th grader)

= 450 / 1200

= 3/8

(3) P (9th grader /pizza):

= P (9th grader /pizza)

= 1300 / 700

= 13/7

(4) Yes, being a 10th-grade student is independent of preferring pizza as there are a total of 1200 students and out of which 750 prefer a pizza.

Therefore, using probability the answer to all the subparts are shown:

(1) P (burgers | 9th grader): 6/13

(2) P (burgers / 10th grader): 3/8

(3) P (9th grader /pizza): 13/7

(4) There are 1200 pupils in the school, and 750 of them enjoy pizza, therefore being in the tenth grade is independent of liking pizza.

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The sampling technique used in the given scenario is Systematic sampling technique.

Systematic sampling technique

Systematic sampling is a probability sampling technique in which researchers randomly choose individuals of a population at regular intervals. The sampling interval, or fixed periodic interval, is calculated by dividing the population size by the required sample size.

Types of Systematic sampling technique

A systematic sample can be generated in three ways:

Systematic random sampling: The most common type of systematic sampling in which the subject is chosen at a predefined interval.

Linear systematic sampling: Instead of picking the sample interval at random, a skip pattern is constructed by following a linear path.

Circular systematic sampling: It occurs when a sample begins from the same spot where it ends.

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Answer:

She has a 67% chance of getting anything other than a multiple of 3.

Step-by-step explanation:

8 to 4

If a storage facility charges $1 per cubic yard and the storage space is 32 ft. The storage charge is $1999.97.

What is mathematical conversions?

Mathematical conversions refer to the process of changing one unit of measurement to another unit of measurement that is equivalent in value.

First, we need to convert the dimensions from feet to yards, since the rate is given per cubic yard.

32 feet = 10.6667 yards (dividing by 3)

160 feet = 53.3333 yards (dividing by 3)

10 feet = 3.3333 yards (dividing by 3)

Next, we can calculate the volume of the storage space in cubic yards by multiplying the three dimensions:

Volume = 10.6667 yards x 53.3333 yards x 3.3333 yards

Volume = 1999.97 cubic yards (rounded to two decimal places)

Finally, we can calculate the storage charge by multiplying the volume by the rate:

Charge = 1999.97 cubic yards x $1/cubic yard

Charge = $1999.97

Therefore, the storage charge is $1999.97.

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An equation that will give you the costs at different times is y = \(1.048^{t}\).

The price of the dinner in 60 years will be $425.04.

An exponential function is usually in the form: \(ab^{x}\).

Where:

Rate of increase = (cost of the meal now / cost of the meal 60 years ago)^(1 / number of years)

(25.25 / $1.50) ^(1/60) = 4.8%

y = \(1.048^{t}\).

25.25 x 1.048^60 = $425.04

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The standard deviation is 16.54 if the population of customers ages is 45, 76, 30, 22, 51, 40, 63, 66, and 41.

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

\(\rm SD = \sqrt{\dfrac{ \sum (x_i-X)^2}{N}\)

SD is the standard deviation

xi is each value from the data set

X is the mean of the data set

N is the number of observations in the data set.

It is given that:

The data set:

45, 76, 30, 22, 51, 40, 63, 66, 41

From the formula:

∑(x(i) - X)² = 2463.55

N = 9

SD = √(2463.55/9)

SD = 16.54

Thus, the standard deviation is 16.54 if the population of customers ages is 45, 76, 30, 22, 51, 40, 63, 66, and 41.

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Answer:

The answers are as follows:

Step-by-step explanation:

Let us look at the statements one by one

1. The additive inverse of 10 is -10.

The additive inverse of a number is the opposite of a number with respect to sign.

The sum of a number and its additive inverse is zero.

\(10+(-10) = 10-10 = 0\)

This statement is true.

2. Zero is a positive number.

Zero is neither a positive number nor a negative number. It is only used as reference to decide whether a number is positive or negative.

This statement is false.

3. To divide two unlike signs, the quotient is always positive.

When two unlike signs are divided, the answer will be negative as division involves multiplication, and multiplication of two numbers with unlike signs will always be negative.

This statement is false.

4. Commutative Property states that:

a + (b + c ) = (a + b ) + c

Commutative property deals with two numbers or variables only. The property with three numbers or varibales is associative property. Hence,

This statement is false.

5. One is the identity element of for addition.

Additive identity is a number that when added to a number x, the result will always be x. Zero is additive identity.

Hence,

This statement is false.

The answers are as follows:

Tariq's goal in the online video game is to catch balls and increase his energy level.

Tariq's objective in the online video game is to catch balls dropped from above before they hit the ground. Each time he catches a ball, he moves up an energy level, and each time a ball hits the ground, he moves down a level. Tariq's goal is to reach energy level 10, as this will earn him bonus points in the game.

To achieve this objective, Tariq needs to carefully time his movements and react quickly to catch the falling balls. As he successfully catches more balls, his energy level increases, bringing him closer to the target of level 10.

However, Tariq also needs to be cautious because if he misses a ball and it hits the ground, he will lose energy and move down a level. This adds an element of challenge and risk to the game, as Tariq must balance his speed and accuracy to maintain or increase his energy level.

Tariq's strategy should involve focusing on his timing and coordination skills, anticipating the trajectory of the falling balls, and positioning himself to catch them. By practicing and improving his hand-eye coordination, he can increase his chances of successfully catching more balls and progressing through the energy levels.

As Tariq reaches higher energy levels, the game may become more difficult, with faster and more unpredictable ball drops. This increases the challenge and excitement for Tariq as he strives to reach energy level 10 and earn the bonus points.

In summary, Tariq's goal in the online video game is to catch balls and increase his energy level. By carefully timing his movements, improving his coordination, and avoiding missed catches, he can progress towards reaching energy level 10 and earning the bonus points.

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Answer:

A

Step-by-step explanation:

2 and 1/2 is can be written as 5/2

5/2 cups of soda for every 2/5 cup of pineapple juice

Unit rate means per 1 of something, in this case pineapple juice

5/2 per 2/5  or (5/2) / (2/5)

5/2 ÷ 2/5 = 25/4 or 6 and 1/4

Answer:

Step-by-step explanation:

\(y=x^2-2x-3\)

When \(y=1\),

\(x^2-2x-3=1\)

\(x^2-2x-4=0\)

Using quadratic equation,

\(x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}\)

\(x=\frac{-(-2)\pm\sqrt{(-2)^2-4\times1\times(-4)} }{2\times1}\)

   \(=\frac{2\pm\sqrt{4+16} }{2}\)

  \(=\frac{2\pm\sqrt{20} }{2}\)

  \(=\frac{2\pm2\sqrt{5} }{2}\)

  \(=1\pm\sqrt{5}\)

Solution: \(x=1+\sqrt{5} ,1-\sqrt{5}\)

a) The range is 14.

b) The sample variance is 20.78.

c) The sample standard deviation is 4.56.

a) Range

The range of a given set of data values is the difference between the maximum and minimum values in the set. In this case, the maximum value is 15 and the minimum value is 1. So, the range is:

Range = maximum value - minimum value

Range = 15 - 1

Range = 14

b) Sample variance

To calculate the sample variance, follow these steps:

1. Calculate the sample mean (X). To do this, add up all of the data values and divide by the total number of values:

n = 9

∑x = 7 + 4 + 6 + 12 + 8 + 15 + 1 + 9 + 13 = 75

X = ∑x/n = 75/9 = 8.33

2. Subtract the sample mean from each data value, square the result, and add up all of the squares:

(7 - 8.33)² + (4 - 8.33)² + (6 - 8.33)² + (12 - 8.33)² + (8 - 8.33)² + (15 - 8.33)² + (1 - 8.33)² + (9 - 8.33)² + (13 - 8.33)² = 166.23

3. Divide the sum of squares by one less than the total number of values to get the sample variance:

s² = ∑(x - X)²/(n - 1) = 166.23/8 = 20.78

Therefore, the sample variance is 20.78 (rounded to two decimal places).

c) Sample standard deviation

To calculate the sample standard deviation, take the square root of the sample variance:

s = √s² = √20.78 = 4.56

Therefore, the sample standard deviation is 4.56 (rounded to two decimal places).

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Subtract 3 from each side

In the equation:

\(w + 3 = - 4\)

Subtracting 3 from both sides of the equation. We have:

\(w + 3 - 3 = - 4 - 3 \\ w + 0 = - 7\)

Therefore: \(w = - 7\)

The simplest way to do this is by moving 3 to the other side of the equation, where it then changes to -3 due to the equality sign (=). this is what I mean:

\(w + 3 = - 4 \\ w = -4 - 3 \\ w = - 7\)

Given that a continuous random variable x has a normal distribution with a mean of 12.25 and the probability that x is less than 13 is 0.82, we can use the symmetry of the density function to find the probability that x is greater than 11.50.

Since the normal distribution is symmetric, the probability of x being less than 13 is equivalent to the probability of x being greater than the mean minus 13. Therefore, P(x < 13) = P(x > 12.25 - 13).

To find the probability that x is greater than 11.50, we can use the same reasoning. We know that the probability of x being less than 11.50 is equivalent to the probability of x being greater than the mean minus 11.50. Therefore, P(x < 11.50) = P(x > 12.25 - 11.50).

To illustrate the computation, we can sketch the density curve of the normal distribution with the relevant regions shaded. The mean, 12.25, is the center of the distribution. We shade the region to the left of 13, representing P(x < 13), and shade the region to the right of 11.50, representing P(x > 11.50). By using the symmetry of the density function, we can see that the shaded region to the right of 11.50 is equal to the shaded region to the left of 13.

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The effect of the mentoring program based on the regression output, you would need to look at the coefficient of the variable representing the mentoring program in the regression equation.

1. Identify the variable representing the mentoring program in the regression output. It could be labeled as "Mentoring" or something similar.

2. Look at the coefficient of the mentoring program variable. This coefficient represents the estimated effect of the mentoring program on the outcome variable.

3. Interpret the coefficient. If the coefficient is positive, it suggests that the mentoring program has a positive effect on the outcome variable. If the coefficient is negative, it suggests a negative effect. The magnitude of the coefficient indicates the strength of the effect.

4. Include any statistical measures of significance, such as p-values or confidence intervals, if available. These measures indicate the level of confidence in the estimated effect. A lower p-value or a narrower confidence interval indicates a higher level of significance.

In your report, you can say something like, "Based on the regression analysis, the mentoring program had a [positive/negative] effect on the outcome variable. The estimated effect was [coefficient value]. This effect was found to be [statistically significant/insignificant] with a p-value of [p-value] (or a [confidence level] confidence interval of [lower limit - upper limit])."

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Answer:

No

Step-by-step explanation:

Linear values will increase by a common difference. For example, a linear function might increase by 6 every time or -4. However, this table does not; each time it increases by a different factor. Since there is no common difference and it does not follow an arithmetic function it is not linear.

Answer:

Step-by-step explanation:

Not linear.

If the inputs were 1, 2, 3, 4 and we wanted a linear function, one such function would be 1, 2, 3, 4 or 10, 20, 30, 40, and so on.

The given table shows that y increases faster and faster as x increases.

From x = 1 to x = 2, y increases from 1 to 2 (an increase of 1).

From x = 2 to x = 3, y increases from 2 to 6 (an increase of 4).

From x = 3 to x = 4, y increases from 6 to 24 (an increase of 18)

No, the table does not represent a linear function.

According to the question, the four consecutive numbers can be written as :

First = \(x\); Second = \(x+2\);  Third = \(x+4\); Fourth = \(x+6\)

As per the question, the final expression is :

\(2((x+2)+(x+4)) = 3(x)+32\)

\(4x+12 = 3x+32\)

\(x = 20\)

Therefore, the four values can be calculated by substituting the above value:

\(x=20; x+2=22; x+4=24; x+6=26\)

The four consecutive numbers are: \(20,22,24,26\)

Substitute the calculated values in the final expression, to check whether the answer is correct or not.

\(2(22+24) = 3(20)+32\)

\(92=92\)

Therefore, the calculated values are correct.

What are consecutive terms?

Consecutive terms are those terms which follow one sequential order.

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An unreliable study can occur if the test administration is inconsistent

Consistency is the key to success in anything and it implies to the studies and surveys as well. If you want the results of the study to be reliable, then you must be consistent in test administration.

Inconsistency can lead to various issues like improper representation of the feedback which may alter the results. This can lead to various problems.

For example, test performed at certain time may have a different set of people and absence of periodic tests can accommodate feedback from irrelevant people.

Therefore, a proper set schedule must be followed for the tests with consistency.

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Answer:

The length of the base will be: 17 m

Step-by-step explanation:

Given the area of the triangle

\(A=102\:m^2\)

Using the formula of Area of a triangle:

\(A=\frac{1}{2}\left(b\times h\right)\)

Here,

As the base of a triangle is 7 less than twice its height.

so

\(b=2h-7\)

so the formula of Area of a triangle becomes

\(102=\frac{1}{2}\left(\left(2h-7\right)\times \:h\right)\)

\(204=h\left(2h-7\right)\)

\(2h^2-7h=204\)

\(2h^2-7h-204=0\)

\(\left(2h+17\right)\left(h-12\right)=0\)

\(2h+17=0\quad \mathrm{or}\quad \:h-12=0\)

\(h=-\frac{17}{2},\:h=12\)

As height can not be negative, so:

\(h=12\) m

Hence, the length of the base:

\(b=2h-7\)

   \(= 2(12)-7\)

    \(=24-7\)

     \(= 17\) m

Therefore, the length of the base will be: 17 m

Answer:

21x2(x-3)

Step-by-step explanation:

Answer: Its C- 3(7x^2+5)(x-3)

Step-by-step explanation:

took it on edge2022

Answer:

7.5 minutes

Step-by-step explanation:

Given

See attachment for complete question

Let

\(t \to time\)

\(y \to capacity\)

From the question, we have the following points

\((t_1,y_1) = (0,7)\) --- When he first sees it

\((t_2,y_2) = (3,5)\) --- 3 minutes later

First, we calculate the rate (m)

\(m = \frac{y_2 -y_1}{t_2 -t_1}\)

\(m = \frac{5 -7}{3 -0}\)

\(m = -\frac{2}{3}\)

The discharge rate is 2/3 gallons per minute

To calculate the additional minute, we simply consider the capacity of the tank at the later time. i.e. 5 gallons

To calculate time (t), we have:

\(Rate * Time = Capacity\)

\(\frac{2}{3} * t = 5\)

Solve for t

\(t = 5 *\frac{3}{2}\)

\(t = \frac{15}{2}\)

\(t = 7.5\)

Based on the following  observations, we can write the equation of the rational function as: f(x) = (x + 1)/(x - 1)

A rational function is a type of mathematical function that is defined as the ratio of two polynomial functions.

In other words, it is a function that can be expressed as f(x) = p(x)/q(x), where p(x) and q(x) are polynomials and q(x) is not the zero polynomial.

To find the equation of the rational function represented by the given graph, we need to analyze the behavior of the graph and identify its key features. given below are the steps:

Look at the behavior of graph as x approaches infinity and negative infinity. The graph appears to have horizontal asymptotes at y = -1 and y = 1. This suggests that the function has a degree of 1 in both the numerator and denominator.

Identify any vertical asymptotes. The graph have vertical asymptote at x = 1. This suggests that the denominator of the function has a factor of (x - 1).

Look for any x-intercepts or y-intercepts.The graph's x-intercept and y-intercept are both at x = -1 and 1, respectively. This suggests that the numerator of the function has a factor of (x + 1) and that the function has a constant term of 1 in the numerator.

This function has a degree of 1 in both the numerator and denominator, a vertical asymptote at x = 1, and horizontal asymptotes at y = -1 and y = 1. It also has an x-intercept at x = -1 and a y-intercept at y = 1, which match the features of the graph given.

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The statement "Quadrilaterals A and B are both squares" does not provide enough information to determine whether A and B are scale copies of one another.

To determine if two quadrilaterals are scale copies of each other, we need to compare their corresponding sides and angles. If the corresponding sides of two quadrilaterals are proportional and their corresponding angles are congruent, then they are scale copies of each other.

In this case, since both A and B are squares, we know that all of their angles are right angles (90 degrees). However, we do not have any information about the lengths of their sides. Without knowing the lengths of the sides of A and B, we cannot determine if they are scale copies of each other.

Therefore, the statement cannot be determined as true or false based on the given information.

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The addition of the expression \((-8-\frac{1}{4}p )+(\frac{5}{8}p-7 )\) is \(-15+\frac{3}{8}p\)

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Therefore, let's add the given linear expression as follows:

Hence,

\((-8-\frac{1}{4}p )+(\frac{5}{8}p-7 )\)

Hence, let's open the brackets of the expression as follows

\(-8-\frac{1}{4}p +\frac{5}{8}p-7\)

Combine like terms as follows;

\(-8-7-\frac{1}{4}p +\frac{5}{8}p\)

\(-15+\frac{-2p+5p}{8}\)

\(-15+\frac{3}{8}p\)

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Answer: y = 18000(0.89)^x, where x represents the number of years in the future.

Step-by-step explanation:

Answer:

Y= 18,000 X (0.11x)

Step-by-step explanation:

x being years y being car

The number of choices the coach is 969. From Selecting Groups of Basketball Players If there are ten players on a basketball team.

"Number of choices" refers to the total number of different ways that something can be selected or arranged. It is a mathematical concept used in counting and combinatorics. The number of choices the coach has in selecting each of the following are:

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The expression representing the width of the garden is given as follows:

6w + 2.

An equivalent expression is given as follows:

2(3w + 1).

The width of the rectangle is represented as follows:

w.

Six times the width of the rectangle is represented as follows:

6w.

Two feet plus six times the width of the rectangle is represented as follows:

6w + 2.

6 = 2 x 3, hence the simplified expression can be given as follows:

2(3w + 1).

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Answer:

B) $1.25/ 4

Step-by-step explanation:

if Anna had $5.00 to start with and after buying 4 pencils she had $3.75 left that would mean each pencil was around $1.25.

$5.00 subtract $3.75 equals $1.25

hope this helps :D

The vector v with initial point (9, 2, 3) and terminal point (-7, -4, -1) has the component form v = <-16, -6, -4>, and its magnitude is sqrt(308). A unit vector in the direction of v is u = <-8/ sqrt(77), -3/ sqrt(77), -2/ sqrt(77)>.

Explanation:

To find the component form of the vector v, we subtract the coordinates of the initial point from the coordinates of the terminal point. We get:

v = <-7 - 9, -4 - 2, -1 - 3> = <-16, -6, -4>

Therefore, the component form of v is <-16, -6, -4>.

To find the magnitude of v, we use the formula:

|v| = sqrt(x^2 + y^2 + z^2)

where x, y, and z are the components of v. We get:

|v| = sqrt((-16)^2 + (-6)^2 + (-4)^2) = sqrt(308)

Therefore, the magnitude of v is sqrt(308).

To find a unit vector in the direction of v, we divide v by its magnitude:

u = v / |v| = <-16/sqrt(308), -6/sqrt(308), -4/sqrt(308)>

We simplify by rationalizing the denominator:

u = <-16/sqrt(308) * sqrt(77)/sqrt(77), -6/sqrt(308) * sqrt(77)/sqrt(77), -4/sqrt(308) * sqrt(77)/sqrt(77)>

u = <-8/ sqrt(77), -3/ sqrt(77), -2/ sqrt(77)>

Therefore, a unit vector in the direction of v is u = <-8/ sqrt(77), -3/ sqrt(77), -2/ sqrt(77)>.

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EXPLANATION:

1.The first thing we must do is use a suitable method that allows us to find the value of y for the two equations of the line

2. The correct and most appropriate method is the matching method.

The exercise is as follows: