Farmer Fred was a quizzical man who loved to talk in circles. One day when a group of beginning farmers came to his farm, they asked him real nicely "farmer fred, how many chickens and rabbits do you have on your farm"? Being the quizzical guy that he was, he didn't dare give them a straight answer, but he reported "you know Im farmer Fren and what i`m all about, in this cage there are 24 heads and 36 feet use a system of equation to figure it out give 2 equations.

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

The negation of "p or q" is "not p and not q", which means that "p or q" is false if and only if both "p" and "q" are false.

To negate a disjunction, which is a statement of the form "p or q", we need to negate each of the component statements and change "or" to "and". The negation of "p or q" is "not p and not q", which means that "p or q" is false if and only if both "p" and "q" are false.

For example, if we have the statement "John will go to the beach or he will go to the park", we can negate it by saying "It is not the case that John will go to the beach or he will go to the park", which can be written symbolically as "not (John will go to the beach or he will go to the park)". Using the rule for negating a disjunction, we can rewrite this statement as "John will not go to the beach and he will not go to the park".

Note that this is different from the negation of a conjunction, which is a statement of the form "p and q". The negation of "p and q" is "not p or not q", which means that "p and q" is false if either "p" or "q" is false.

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The distribution of the data are symmetrical and left skewed, respectively

Stem and leaf plot 2

Here, we can see that the data increases uniformly till it gets to a peak, and then start decreasing till it gets to the initial level

This means that the plot is symmetrical

Hence, the distribution of the data is symmetrical

Stem and leaf plot 3

Here, we can see that the data has more points at the bottom that the upper part

This means that the plot is left skewed

Hence, the distribution of the data is left skewed

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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 margin of error is 9.8. The answer is (B).

Margin of error (ME) is the amount of random sampling error that is expected in a survey's results. It is the range of values above and below the sample statistic (such as the sample mean or proportion) within which the true population parameter (such as the population mean or proportion) is expected to lie with a certain degree of confidence.

The margin of error (ME) for a 95% confidence interval is given by:

ME = z*(σ/√n)

where z is the z-score for the desired level of confidence (in this case, 95%), σ is the population standard deviation, and n is the sample size.

We are given that σ = 50, n = 100, and the sample mean is 600. To find the z-score, we can use a standard normal distribution table or calculator. For a 95% confidence interval, the z-score is approximately 1.96.

Substituting the values into the formula, we get:

ME = 1.96*(50/√100) = 9.8

Therefore, the margin of error is 9.8. The answer is (B).

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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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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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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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The complex number can be represented as matrix as follow:

[tex]\left[\begin{array}{cc}2&-3\\3&2\end{array}\right][/tex] [tex]\left[\begin{array}{cc}1&-4\\4&1\end{array}\right][/tex] and the correct answer from the option is (B)

A complex number can be represented as a 2x2 matrix in the form:

[tex]\left[\begin{array}{cc}2&-3\\3&2\end{array}\right][/tex]

Addition and subtraction of complex numbers can be done by adding or subtracting the corresponding matrices.

Multiplication of two complex numbers can be done by multiplying the corresponding matrices and simplifying the result.

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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.

It is about the relationship between the magnitude of the cross product of two vectors and the product of their magnitudes. If u and v are in V3, then |u * v| ≤ |u||v|

Let's use the terms u, v, V3, and |u * v| in the answer.

In V3 (a 3-dimensional vector space), let u and v be two vectors. The magnitude of the cross product of u and v can be represented as |u * v|. According to the properties of the cross product, we have:

|u * v| ≤ |u||v|

This inequality means that the magnitude of the cross product of two vectors (|u * v|) is always less than or equal to the product of the magnitudes of the individual vectors (|u||v|). This result is known as the Cauchy-Schwarz inequality, which applies to vectors in any dimension, including V3.

In summary, if u and v are in V3, then |u * v| ≤ |u||v|.

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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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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:

Answer:

15

Step-by-step explanation:

1.4 x 15 equals 21 so if you round the question it equals 15 if not then 14.

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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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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Answer:

Step-by-step explanation:

2 would have a greater b value because its x.  Also the other answer is 2.

Answer:

Step-by-step explanation:

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

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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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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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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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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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)

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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The values of the angles and sides of the given right angle triangle are:

1) sin Q = 9/13

2) AB = 10

The common three trigonometric ratios in a right angle triangle are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

1) To find sin Q from the triangle, we have:

sin Q = pPR/PQ

sin Q = 9/15

2) Using Pythagoras theorem, we can find side AB as:

AB = √(6² + 8²)

AB = √100

AB = 10

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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.