3. Solve the equation (x + 3)² = 49

(a) The probability that at least one individual with a reservation cannot be accommodated on the trip is 0.4202.

(b) The expected number of available places when the limousine departs is 0.338.

Let the random variable Y represent the number of passenger reserving the trip shows up.

The probability of the random variable Y is, p = 0.70.

Success in this case an be defined as the number of passengers who show up for the trip.

The random variable Y follows a Binomial distribution with probability of success as 0.70.

(a)

It is provided that n = 6 reservations are made.

Compute the probability that at least one individual with a reservation cannot be accommodated on the trip as follows:

P (At least one individual cannot be accommodated) = P (X = 5) + P (X = 6)

= 0.4202

Thus, the probability that at least one individual with a reservation cannot be accommodated on the trip is 0.4202.

The expected number of available places when the limousine departs is 0.338.

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The equation is 967.50 = 450 + 28.75p which models the situation. The team could bring 18 players to the tournament.

Setting up an equation based on the given information.

Let p be the number of players on the team.

Then the total amount of money spent on meals will be 28.75p.

The total amount of money spent on the bus and meals will be 450 + 28.75p.

Since they spent all the money they raised, the equation models the situation as follows:

967.50 = 450 + 28.75p

To solve for p, subtract 450 from both sides:

517.50 = 28.75p

Then divide both sides by 28.75:

p = 18

Therefore, the team could bring 18 players to the tournament.

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The complete question is as follows:

Members of a baseball team raise $967.50 to go to a tournament. They rented a bus for $450.00 and budgeted $28.75 per player for meals. They will spend all the money they raised.

Write and solve an equation that models the situation and could be used to determine the number of players, p, the team could bring to the tournament.

Non of the lines is perpendicular rather they are parallel to each other

Perpendicular lines are straight lines that make an angle of 90° with each other

But Parallel lines are coplanar lines on a plane that do not intersect and are always the same distance apart. In two dimensions, parallel lines have the same slope and can be written as an equation if we know a point on the line and an equation of the given line.

The given equations are

1. Line a: y = −4x + 7

Line b: x = 4y + 2

Line c: -4y + x = 3

Solving each of them

line 1: y = −4x + 7

making y the subject

y = −4x + 7

Line 2:  x = 4y + 2

making y the subject

4y = x -2

y = (x-2)/4

line 3:  -4y + x = 3

making y the subject of the relation

-4y = -x + 3

y =( x - 3)/4

From the answers the lines are not perpendicular as their values are not the same

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Answer:

y = 9

Step-by-step explanation:

When a line crosses the y-axis, it crosses at point (0,y).

Substitute x = 0 in to the line equation we get:

y + 4 = 0 + 13

So y = 13 - 4 = 9

The line crosses the y-axis at point (0,9)

The multiplication of decimals are wrong in he solution

The equations are false because the student is carrying out the wrong multiplication of decimal points

The correct multiplication should be:

Pattern A

3.675 • 10 = 36.75

3.675 • 100 = 367.5

3.675 • 1,000 = 3,675

Pattern B

3.675 • 0.1 = 0.3675

3.675 • 0.01 = 0.03675

3.675 • 0.001 = 0.003675

Hence the student has to solve this correctly because the previous values are wrong

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Answer:

Below

Step-by-step explanation:

There is an image uploaded below of the stem-and-leaf plot of the video game scores!

The names possible for the shape are

Quadrilateral -  this means a four sided figure

Parallelogram - Opposite sides are parallel to each other

Rhombus - The vertex angles are not all equal to each other

A polygon with four sides and angles is known as a quadrilateral. This two-dimensional plane shape features straight borders that connect at its four vertices, also referred to as corners.

A rhombus is a parallelogram because the opposites sides are parallel to each other

Geometrically speaking, a rhombus denotes a specific kind of quadrilateral encompassing four equal-lengthed border lines.

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We have the formula for the surface area of a cylinder:

SA = 2πrh + 2πr^2

Given that the surface area is 378π cm^2 and the radius is 7 cm, we can plug in these values and solve for the height:

378π = 2π(7)(h) + 2π(7)^2

378π = 14πh + 98π

280π = 14πh

h = 20 cm

Therefore, the height of the cylinder is 20 cm.

Answer:

The probability of getting heads on a single coin flip is 1/2. The probability of getting heads on two coin flips in a row is (1/2) * (1/2) = 1/4. Therefore, if George performs this experiment 100 times, we can expect that he will get both flips landing on heads about 25 times

Step-by-step explanation:

Common difference between jumping jacks is 50

The slope of line that connects 3 rd and 4th point is 50

The slope is constant.

The common difference between jumping jacks is 50

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

m=100-500/2-1=50

The slope of line that connects 3 rd and 4th point

Slope = 200-150/4-3=50

The slope of line that connects 1 st and 4th point

slope = 200-50/4-1

=150/3=50

The slope is constant

jumping jacks completed after a given period of time in minutes is linear so it is constant

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The equation for translation of the graph given is y = |x/2-2| + 4

Given is a function y = |x/2-2| + 3, it is translated one unit up, we need to find the translated function.

We know that, f(x) + k moves f(x) by k units up.

So, y = |x/2-2| + 3 → y = |x/2-2| + 3 + 1

y = |x/2-2| + 4

Hence, the equation for translation of the graph given is y = |x/2-2| + 4

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The probability that a randomly selected tire will have a life of at most 47,500 miles is 0.9332, or 93.32%.

To find the probability that a randomly selected tire will have a life of at most 47,500 miles, we need to calculate the z-score and use a standard normal distribution table.

The formula for the z-score is:

z = (x - μ) / σ

where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

Plugging in the values given in the problem, we get:

z = (47,500 - 40,000) / 5,000
z = 1.5

Using a standard normal distribution table, we can find that the probability of a z-score being less than or equal to 1.5 is 0.9332.

Therefore, the probability that a randomly selected tire will have a life of at most 47,500 miles is 0.9332 (or 93.32%) to four decimal places.

To answer your question, we will use the normal distribution, mean, standard deviation, and Z-score. Given that the life expectancy of the tire is normally distributed with a mean of 40,000 miles and a standard deviation of 5,000 miles, we will find the probability of a tire having a life of at most 47,500 miles.

First, we calculate the Z-score using the formula: Z = (X - μ) / σ, where X is the value we're interested in (47,500 miles), μ is the mean (40,000 miles), and σ is the standard deviation (5,000 miles).

Z = (47,500 - 40,000) / 5,000 = 7,500 / 5,000 = 1.5

Now, we look up the Z-score of 1.5 in a standard normal distribution table or use a calculator with a cumulative distribution function (CDF). The CDF value for a Z-score of 1.5 is approximately 0.9332.

So, the probability that a randomly selected tire will have a life of at most 47,500 miles is 0.9332, or 93.32%.

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The cube root of a number is a special value that when cubed gives the original number.

We can simplify the given expression as follows:

(3^(5/6)) / (3^(1/6)) = 3^((5/6) - (1/6)) = 3^(4/6) = 3^(2/3)

Next, we can simplify the expression cube root of 6 * cube root of 9 as follows:

cube root of 6 * cube root of 9 = cube root of (6 * 9) = cube root of 54

We can simplify the expression square root of 9 * square root of 27 as follows:

square root of 9 * square root of 27 = square root of (9 * 27) = square root of 243

Since 243 can be factored as 3^5, we have:

square root of 243 = square root of (3^5) = 3^(5/2)

Therefore, the final expression becomes:

(3^(2/3)) / cube root of 54 * 3^(5/2)

We can simplify the denominator as:

cube root of 54 * 3^(5/2) = cube root of (54 * 3^3) = cube root of (2^3 * 3^6) = 6 * 3^2 = 54

Thus, the final expression simplifies to:

(3^(2/3)) / 54

which cannot be further simplified.

Therefore, the final answer is:

(3^(2/3)) / 54

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The probability that the Yankees would score fewer than 5 runs when they lose the game is 0.45.

Let A be the event that the Yankees win a game, B be the event that they score 5 or more runs, and C be the event that they lose and score fewer than 5 runs.

Using the total probability rule, we can find the probability of losing and scoring fewer than 5 runs:

P(C) = P(Lose and Score fewer than 5 runs) = P(Lose and not Score 5 or more runs) = P(not A and not B) = 1 - P(A) - P(B) + P(A and B)

P(C) = 1 - 0.55 - 0.56 + P(A and B)

To find P(A and B), we can use the fact that P(A and B) = P(B|A) * P(A), where P(B|A) is the conditional probability of scoring 5 or more runs given that they win.

We are not given this conditional probability directly, but we can find it using Bayes' theorem:

P(B|A) = P(A and B) / P(A) = (0.55 * 0.56) / 0.55 = 0.56

Substituting this value into the equation for P(C), we get:

P(C) = 1 - 0.55 - 0.56 + 0.56

P(C) = 0.45

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Answer: about 25 km2 to 35 km2

Step-by-step explanation:

hope this helps ;)

Answer: About 40 to 50 km^2

Step-by-step explanation:

So basically area is length x width so you want to count the squares for the length then multiply by the number of squares for the width which is 8 x 5 which equals 40

The surface area of the given pyramid is 76 cm². Option B is correct.

We can start by finding the area of each triangular face of the pyramid. The area of a triangle can be calculated using the formula:

Area = 0.5 * base * height

where the base is the length of one side of the triangle (which is equal to the base length of the pyramid in this case), and the height is the slant height of the triangle (which is given as 5 for one face and 5.5 for the other face).

Area of the first triangular face = 0.5 * 6 * 5 = 15

Area of the second triangular face = 0.5 * 4 * 5.5 = 11

To find the surface area of the pyramid, we need to add the area of the base to the sum of the areas of the triangular faces. The area of the base is simply the area of a rectangle, which can be calculated using the formula:

Area = length * width

where length and width are the dimensions of the base of the pyramid.

Area of the base = 6 * 4 = 24

Therefore, the total surface area of the pyramid is:

Total surface area = Area of base + Sum of areas of triangular faces

Total surface area = 24 + 2*15 + 2*11

Total surface area = 76 cm²

Hence, the surface area of the given pyramid is 76 cm².

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To arrange the 7 men and 7 women alternately around a table, we can first place the men in a circular manner. Since there are 7 men, there will be 6! ways to arrange them (considering that rotations are identical). Next, we can place the women in the 7 available spaces between the men.

A) In how many ways can 7 men and 7 women sit around a table so that men and women alternate? Assume that all rotations of a configuration are identical and hence counted as just one.

First, we can choose the position of the men around the table in 7! ways. Then, we can place the women in the remaining positions in 7! ways as well. However, we need to account for the fact that men and women must alternate. We can do this by fixing the position of one gender (say, men) and arranging the other gender (women) in the spaces in between. We have 7 spaces in between the men, so we can arrange the women in these spaces in 7! ways. However, we must also account for the fact that we could have started with women and arranged men in the spaces in between. Therefore, the total number of ways to arrange 7 men and 7 women around a table so that men and women alternate is:

2 * 7! * 7! * 7! = 20,160,000

B) In how many ways can 8 distinguishable rooks be placed on a 8 x 8 chessboard so that none can capture any other, namely no row and no column contains more than one rook?

First, we can place the first rook in any of the 64 squares on the board. Then, we must place the second rook in a square that is not in the same row or column as the first rook. There are 14 squares in the same row or column as the first rook, so there are 50 squares remaining for the second rook to be placed in. We continue in this manner, placing each subsequent rook in a square that is not in the same row or column as any of the previously placed rooks. Therefore, the total number of ways to place 8 distinguishable rooks on an 8 x 8 chessboard so that none can capture any other is:

64 * 50 * 36 * 25 * 20 * 15 * 10 * 5 = 3,416,748,800

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The answer is  3x+3 = ±5 when the square roots of both sides of the equation  (3x+3)² = 25 are taken. Both x = 2/3 and x = -8/3 are possible answers to the "x" equation.

The squared term on one side of the equation must first be isolated in order to solve  (3x+3)²= 25 by calculating the square roots of both sides we get:

(3x+3)²= 25

The result of taking the square root of both sides will:

3x+3 = ±5

Two potential equations result from simplifying the right side:

3x+3 = 5 or 3x+3 = -5

The right side can be simplified into one of two equations:

3x = 2

x = 2/3

Solving for x in the second equation, we get:

3x = -8

x = -8/3

Therefore, the answer to the equation (3x+3)² = 25 are x = 2/3 and x = -8/3.

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The rate of population growth is proportional to the logarithm of the ratio of the carrying capacity to the current population.

The Gompertz function is a solution of the differential equation:

dP/dt = c ln(K/P) P

where P(t) is the population at time t, c is a constant, and K is the carrying capacity, i.e., the maximum population that can be sustained by the available resources.

To solve this differential equation, we can use separation of variables:

dP/P ln(K/P) = c dt

Integrating both sides, we get:

∫ dP/P ln(K/P) = ∫ c dt

Integrating the left-hand side requires a substitution. Let u = ln(K/P), then du/dP = -1/P and the integral becomes:

-∫ du/u = -ln|u| = -ln|ln(K/P)|

The right-hand side is just:

c t + C

where C is an arbitrary constant of integration.

Putting these together, we get:

-ln|ln(K/P)| = ct + C

Taking the exponential of both sides, we get:

|ln(K/P)| = e^(-ct-C)

Using the absolute value is unnecessary, since ln(K/P) is always positive, so we can drop the absolute value and write:

ln(K/P) = e^(-ct-C)

Solving for P, we get:

P = K e^(-e^(-ct-C))

This is the Gompertz function, which gives the population as a function of time, under the assumption that the rate of population growth is proportional to the logarithm of the ratio of the carrying capacity to the current population.

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The type of random variable in this scenario is a geometric random variable. Its parameter is the probability of failure for each integrated circuit being tested.

The type of random variable you're dealing with in this scenario, where you are testing integrated circuits in sequence until you find the first failure, is called a Geometric Random Variable. This type of random variable represents the number of trials needed for the first success (or failure, in this case) in a series of independent Bernoulli trials with the same probability of failure. The parameter for a Geometric Random Variable is the probability of failure, denoted as p. In summary, the type of random variable in this problem is a Geometric Random Variable, and its parameter is the probability of failure (p).

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We know that n^2 is a multiple of both 24 and 108, which means it must be a multiple of their least common multiple (LCM). The LCM of 24 and 108 is 216.

So, n^2 must be a multiple of 216. This means that n must be a multiple of the square root of 216, which is 6√6.

Therefore, every integer n in s must be of form 6√6 * k, where k is a positive integer.

To find the divisors of every integer n in s, we need to find the common factors of all such expressions.

We can express 6√6 as 2√6 * 3. So, every integer n in s can be written as 2√6 * 3 * k.

The divisors of every integer n in s must be factors of 2√6 and 3.

The factors of 2√6 are 1, 2, √6, and 2√6.

The factors of 3 are 1 and 3.

Therefore, the integers that are divisors of every integer n in s are 2 and 3, which are both positive integers.

So, the correct answer is none of the given options (a, b, c, d).

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Step-by-step explanation:

by using Pythagoras theorem you can find the answer

[tex] {a}^{2} + {b }^{2} = {c}^{2} \\ {9 }^{2} + {x}^{2} = {24 }^{2} \\ 81 + {x}^{2} = 576 \\ {x }^{2} = 576 - 81 \\ {x }^{2} = 495 \\ \sqrt{ {x}^{2} } = \sqrt{495 } \\ x = 22.2485954613[/tex]

Answer:

3√55

Step-by-step explanation:

Because this is a right triangle we can use Pythagorean theorem to find the missing side length. Pythagorean theorem states the a^2 + b^2 = c^2 where c is the hypotenuse and a and b are the other two sides. In this case 24 is the hypotenuse

x^2 + 9^2 = 24^2

x^2 + 81 = 576

Subtract 81 from both sides to isolate the x

x^2 = 495

Find the square root of both sides

√x^2 =√495

Now factor √495 to simplify

x = √3· 3 · 5 · 11

There is a pair of 3's so we move them to the outside of the radical

x = 3√5·11

x = 3√55

Because the equation of the asymptote is given as y = -4, the points on the function y = (1/2)ˣ  -4 are:

Vertical Aymptote : x = 0

y-intercept: (0,3)

x-intercept: (-2.32, 0). See the attached graph.

As x approaches zero and the base of the exponent in y = ((1/2)ˣ - 4 becomes increasingly small, the function value approaches infinity from the right side while simultaneously  approaching zero from the left side.

This phenomenon is known as a vertical asymptote at x=0.

Note that the in the function:

y = (1/2)ˣ  -4 , where x = 0

y = y(1/2)^0 - 4
y = 1 - 3

y = -3

Hence the y intercept is -3


To dertive the x-intercept,

we set y to zero.

0 = (1/2)^x -4
(1/2)^x = 4

Using Log we can solve x to be = -2.32

Thus, it is correct to state that the points are:

Vertical Asymptote : x = 0

y-intercept: (0,3)

x-intercept: (-2.32, 0).

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To formulate this problem as a linear programming problem, we need to identify the decision variables, objective functions, and constraints.

Decision Variables:
Let x be the number of model A printers manufactured per month, and y be the number of model B printers manufactured per month.

Objective Function:
The objective is to maximize monthly profits, which can be expressed as P = 25x + 40y.

Constraints:
1. The total number of printers demanded per month cannot exceed 3000, so we have the constraint x + y ≤ 3000.
2. The company has earmarked not more than $600,000/month for manufacturing costs, so the cost constraint is 120x + 140y ≤ 600,000.
3. The number of printers manufactured must be non-negative, so x ≥ 0 and y ≥ 0.

Therefore, the linear programming problem is:
Maximize P = 25x + 40y
Subject to:
x + y ≤ 3000
120x + 140y ≤ 600,000
x ≥ 0, y ≥ 0

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If Ash can dig 5 holes in 2 hours, and Bruce can dig 9 holes in 5 hours. The number of holes they can dig is:  64.5 holes .

Ash rate:

5 holes / 2 hours

= 2.5 holes per hour

Bruce rate

9 holes / 5 hours

= 1.8 holes per hour

Number of holes they can dig together in one hour

2.5 holes per hour + 1.8 holes per hour

= 4.3 holes per hour

Now let find the number of holes they can dig in 15 hours,

4.3 holes per hour x 15 hours

= 64.5 holes

Therefore, Ash and Bruce can dig 64.5 holes.

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Answer: To determine if any of these data values are outliers, you would first need to calculate the median and interquartile range (IQR) of the data set. You can then use the following rule to identify potential outliers:

- Any data value that is less than Q1 - 1.5(IQR) or greater than Q3 + 1.5(IQR) is a potential outlier.

Assuming the data set is in order, the median is 451.5 and the first and third quartiles are 389 and 495, respectively. The IQR is therefore 495 - 389 = 106. Using the rule above, we can check each data value to see if it is a potential outlier:

- 451 is not a potential outlier.

- 501 is not a potential outlier.

- 388 is not a potential outlier.

- 428 is not a potential outlier.

- 510 is not a potential outlier.

- 480 is not a potential outlier.

- 390 is not a potential outlier.

Therefore, there are no outliers in this data set.

Step-by-step explanation:

To combine two divisions, we got to have a common denominator. In this case, ready to utilize the distributive property to induce a common denominator of (1+x) for both divisions:

1/(1x) + 2/(1+x) = 1/(1x*(1+x)) + 2x/(x(1+x))

Directly able to combine the two divisions by counting their numerators and composing them over the common denominator:

1/(1x(1+x)) + 2x/(x(1+x)) = (1+2x)/(x(1+x))

In this way, the given expression as a single division is:

(1+2x)/(x(1+x))

Writing 1/(1 + x) + 2/(1 + x) as a single fraction , we get 3​/(1 + x)

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

1/1_x+2/1+x​

Express the fractions properly

So, we have

1/(1 + x) + 2/(1 + x)

Take the LCM of the fractions

So, we have

(1 + 2)/(1 + x)

Evaluate the sum of like terms

3​/(1 + x)

Hence, the solution is 3​/(1 + x)

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