on Monday, there were 18 chickens and 12 sheeps in a field. there were no other animals in the field. what was the ratio of chickens to sheep i the field on monday?


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Answer:

x could be -5, -4, -3, -2, -1

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The Boolean duality principle is a fundamental concept in Boolean algebra which states that any statement or expression in the algebra can be transformed into an equivalent form by interchanging the roles of AND and OR operators, as well as 0's and 1's.

The Boolean duality principle, also known as De Morgan's laws, is a fundamental concept in Boolean algebra that states that every Boolean expression remains valid if you perform the following steps:
1. Swap AND (⋅) operators with OR (+) operators and vice versa.
2. Replace all 1's with 0's and all 0's with 1's.
3. Complement (invert) all variables.
In other words, the Boolean duality principle allows us to derive a dual expression from an original Boolean expression by applying these transformations. This principle is useful in simplifying Boolean expressions and designing digital circuits.

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The probability of getting at least one head is 15/16.

What is probability?

The ratio of positive outcomes to all possible outcomes of an event is known as the probability.

Formula for probability = favourable outcomes/ total outcomes

Main body:

if 4 coins are tossed , total no. of outcomes = 2⁴ = 16

In a toss there are 2 outcomes T or H

so, Probability of getting Head = 1/2

The probability of getting at least 1 head = 1- probability of getting no heads

⇒1 - Probability of getting tail in 4 tosses

⇒ 1 - (1/2)⁴

⇒ 1 - 1/16

⇒ 15/16

So the probability of getting at least one head is 15/16.

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Answer:

We can split this into ∛8 * ∛n⁹. ∛8 = 2 and ∛n⁹ = n³ so the answer is 2n³.

Answer:

2n^3

Step-by-step explanation:

Answer:

tanA = 40/9

Step-by-step explanation:

Try to construct a right-angled triangle with it's adjacent side=9 and hypotenuse = 41,

By pyth. theorem, we can get the remaining side (opposite side)

= √(41^2 - 9^2)

= 40

tanA = oppside side/ adjacent side

tanA = 40/9

Answer:

\(Area_{kite}=736m^2\)

Step-by-step explanation:

There are a few methods to find the area of this figure:

1. kite area formula

2. 2 triangles (one top, one bottom)

3. 2 triangles (one left, one right)

4. 4 separate right triangles.

Recall the formula for area of a kite:  \(Area_{kite}=\frac{1}{2} d_{1}d_{2}\) where d1 and d2 are the lengths of the diagonals of the kite ("diagonals" are segments that connect non-adjacent vertices -- in a quadrilateral, vertices that are across from each other).

If you've forgotten why that is the formula for the area of a kite, observe the attached diagram: note that the kite (shaded in) is half of the area of the rectangle that surrounds the kite (visualize the 4 smaller rectangles, and observe that the shaded portion is half of each, and thus the area of the kite is half the area of the large rectangle).

The area of a rectangle is \(Area_{rectangle}=bh\), sometimes written as \(Area_{rectangle}=bh\), where w is the width, and h is the height of the rectangle.

In the diagram, notice that the width and height are each just the diagonals of the kite.  So, the Area of the kite is half of the area of that surrounding rectangle ... the rectangle with sides the lengths of the kite's diagonals.Hence, \(Area_{kite}=\frac{1}{2} d_{1}d_{2}\)

For our situation, each of the diagonals is already broken up into two parts from the intersection of the diagonals.  To find the full length of the diagonal, add each part together:

For the horizontal diagonal (which I'll call d1): \(d_{1}=40m+6m=46m\)

For the vertical diagonal (which I'll call d2): \(d_{2}=16m+16m=32m\)

Substituting back into the formula for the area of a kite:

\(Area_{kite}=\frac{1}{2} d_{1}d_{2}\\Area_{kite}=\frac{1}{2} (46m)(32m)\\Area_{kite}=736m^2\)

If one doesn't remember the formula for the area of a kite, and can't remember how to build it, the given shape could be visualized as 2 separate triangles, the given shape could be visualized as 2 separate triangles (one on top; one on bottom).

Visualizing it in this way produces two congruent triangles.  Since the upper and lower triangles are congruent, they have the same area, and thus the area of the kite is double the area of the upper triangle.

Recall the formula for area of a triangle:  \(Area_{triangle}=\frac{1}{2} bh\) where b is the base of a triangle, and h is the height of the triangle (length of a perpendicular line segment between a point on the line containing the base, and the non-colinear vertex).  Since all kites have diagonals that are perpendicular to each other (as already indicated in the diagram), the height is already given (16m).

The base of the upper triangle, is the sum of the two segments that compose it:  \(b=40m+6m=46m\)

Finding the Area of the upper triangle\(Area_{\text{upper }triangle}=\frac{1}{2} (46m)(16m) = 368m^2\)

Finding the Area of the kite

\(Area_{kite}=2*(368m^2)\)

\(Area_{kite}=736m^2\)

The given shape could be visualized as 2 separate triangles (one on the left; one on the right).  Each triangle has its own area, and the sum of both triangle areas is the area of the kite.

Note:  In this visualization, the two triangles are not congruent, so it is not possible to  double one of their areas to find the area of the kite.

The base of the left triangle is the vertical line segment the is the vertical diagonal of the kite.  We'll need to add together the two segments that compose it:  \(b=16m+16m=32m\).  This is also the base of the triangle on the right.

Finding the Area of left and right triangles

\(Area_{\text{left }triangle}=\frac{1}{2} (32m)(40m) = 640m^2\)

The base of the right triangle is the same length as the left triangle: \(Area_{\text{right }triangle}=\frac{1}{2} (32m)(6m) = 96m^2\)

Finding the Area of the kite

\(Area_{kite}=(640m^2)+(96m^2)\)

\(Area_{kite}=736m^2\)

If you don't happen to see those composite triangles from option 2 or 3 when you're working this out on a particular problem, the given shape could be visualized as 4 separate right triangles, and we're still given enough information in this problem to solve it this way.

Calculating the area of the 4 right triangles

\(Area_{\text{upper left }triangle}=\frac{1}{2} (40m)(16m) = 320m^2\)

\(Area_{\text{upper right }triangle}=\frac{1}{2} (6m)(16m) = 48m^2\)

\(Area_{\text{lower left }triangle}=\frac{1}{2} (40m)(16m) = 320m^2\)

\(Area_{\text{lower right }triangle}=\frac{1}{2} (6m)(16m) = 48m^2\)

Calculating the area of the kite

\(Area_{kite}=(320m^2)+(48m^2)+(320m^2)+(48m^2)\)

\(Area_{kite}=736m^2\)

Answer:

A. <3 and <5

is the answer.

Answer:

Step-by-step explanation:

Hello friend!!!

The first option is correct

<3 and <5 are the alternate interior angles

Hope this helps

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By applying dilatation and congruency theorem, it can be concluded that the distance between points R and R' is 3 units (option A).

Dilation is a transformation of a geometric shape, either becoming larger or smaller, without changing the original shape using a certain scale factor.

Two shapes are said to be congruent if a pair of corresponding sides have the same ratio and the corresponding angles have the same measure.

From the problem we obtained the following information:

QR is dilated to create Q'R' ⇒ QR // Q'R'

The dilatation factor is 1.5 ⇒ Q'R'/QR = 1.5

Now we look at the ΔTRQ and ΔTR'Q':

QR // Q'R'

∠TRQ = ∠TR'Q'

So ΔTRQ is congruent to ΔTR'Q' and TR'/TR = Q'R'/QR

Now we can calculate y using this equation:

   TR'/TR = Q'R'/QR

(6 + y) / 6 = 1.5

      6 + y = 9

            y = 3

Thus, the distance between points R and R' is 3 units.

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The solution of the inequality |x+3| < 2 is -5 < x < -1.

And the graph is given in the image below.

The correct option is C.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

To solve the inequality |x+3| < 2, we need to consider two cases:

Case 1: x+3 ≥ 0

In this case, the inequality simplifies to x+3 < 2, which gives us x < -1.

Case 2: x+3 < 0

In this case, the inequality simplifies to -(x+3) < 2, which gives us -x-3 < 2, or -x < 5, or x > -5.

Combining the results from both cases, we get the solution:

-5 < x < -1

To graph the solution, we draw an open circle at x=-3

(since the absolute value is less than 2, not less than or equal to), and shade the region between -5 and -1.

Therefore, the solution is -5 < x < -1.

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Answer:

\(y = \frac{5}{2} x^{2}\)

Step-by-step explanation:

When you scale a parabola vertically, you multiply the \(x^{2}\) by what you are scaling it vertically by.

For example, say you have  \(y = 8x^{2}\). That means that  \(y = x^{2}\) was scaled vertically by a factor of 8.

I hope this helps!

The matrix of a quadratic form is always a symmetric matrix.A quadratic form is a mathematical expression that consists of variables raised to the power of two, multiplied by coefficients, and added together.

It can be represented in matrix form as Q(x) = x^T A x, where x is a vector of variables and A is the matrix of coefficients. The matrix A is known as the matrix of the quadratic form.

To show that the matrix of a quadratic form is symmetric, let's consider the expression Q(x) = x^T A x. Using the properties of matrix transpose, we can rewrite this expression as Q(x) = (x^T A^T) x. Since the transpose of a matrix A is denoted as A^T, we can see that A^T is the same as A, as A is already a matrix.

Therefore, we have Q(x) = x^T A x = x^T A^T x. This implies that the matrix of the quadratic form A is symmetric, as A^T = A. In other words, the elements of the matrix A are symmetric with respect to the main diagonal. This property holds true for any quadratic form, regardless of its coefficients or variables, making the matrix of a quadratic form symmetric.

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To find next year's population in one step, the current population should be multiplied by 0.962. This value is obtained by subtracting 3.8% from 100% (1) and converting it to a decimal form (0.962).

1. Multiplying the current population by this factor accounts for the decrease of 3.8% and gives an estimate of the population for the next year.

2. To calculate next year's population in one step, we need to consider the decrease of 3.8% per year. When a population decreases by a certain percentage, we can express it as a decimal value by subtracting that percentage from 100%. In this case, subtracting 3.8% from 100% gives us 96.2%. To convert this to a decimal form, we divide it by 100, resulting in 0.962.

3.By multiplying the current population by 0.962, we take into account the decrease of 3.8% and estimate the population for the next year. This approach assumes a consistent decrease rate over time. For example, if the current population is 100, multiplying it by 0.962 would yield an estimated next year's population of 96.2.

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The solution of the double inequality is -5 <= x <= 1/3 and the  three solutions in the solutions are -5, -4 and -3

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

The inequality expression is given as

-2 <= (3x - 1)/8 <= 0

Multiply through the inequality expression by 8

So, we have the following inequality expression

-2 * 8 <= (3x - 1)/8 * 8 <= 0 * 8

Evaluate the products in the above inequality expressions

So, we have

-16 <= 3x - 1 <= 0

Add 1 to all sides of the inequality expression

So, we have

-15 <= 3x <= 1

Multiply all sides of the inequality expression by 1/3

So, we have

-5 <= x <= 1/3

The numbers in the above solution are -5, -4 and -3

Hence, the solution of the double inequality is -5 <= x <= 1/3 and the  three solutions in the solutions are -5, -4 and -3

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30 Balloons were filled per hour during the first 8 hours.

From the graph , its clearly visible that the line is not changing its path.  Slope of the graph is consistent at 2 , 4  ,6 ,8 hrs , hence we can say it is a straight line which means even distribution of balloons per hour.

The number of balloons filled in first 8 hours as given per graph is 240.

The number of balloons filled per hour = Total no. of balloons filled / Total time taken

= 240/8

=30

Hence, the number of balloons filled per hour during first 8 hours are 30.

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Answer:

Step-by-step explanation:

-8 + 8a = -12 + 4a

4a - 8 = -12

4a = -4

a = -1

Answer:

a = -1

Step-by-step explanation:

\(4(-2+2a) = -12 +4a\\-8+8a=-12+4a\\8a = -4 +4a\\4a=-4\\\frac{4a}{4} =\frac{-4}{4} \\a=-1\)

I hope that makes since... I tried to show my work the best I could.

Answer:

-6

Step-by-step explanation:

? - (-4) = -2

? + 4 = -2

-6 + 4 = -2

Your Answer will be -6

Hope that helps!

Answer:

-6

Step-by-step explanation:

because you are just doing basic math so just take 6-4 and you will get 2, except you put negitave signs so the answer is -6

The transformation rule used are the reflection over the y-axis, dilation and vertical and horizontal shift.

The translation rule for reflection of the coordinate point (x, y) across the y-axis is (-x, y)

The rule (x, y) → (0.5x, 0.5y) shows a dilation of the coordinate (x, y) by a factor of 0.5. It will reduce the size of the resulting figure since the factor is less than 1.

The rule  (x, y) → (x - 2, y + 2) shows that the figure then shifted horizontally by 2units to the right and up by 2units.

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The general solution to the given differential equation is:

y = (1/6) exp(-x³) (exp(3x²) + C"),

where C" is the combined constant of integration.

The given differential equation is,

y' + 3x²y = x²

This differential equation is a first-order linear ordinary differential equation.

To solve it, we'll use an integrating factor,

Which is a function that makes the left-hand side of the equation exact.

To find the integrating factor,

We multiply both sides of the equation by the exponential of the integral of the coefficient of y, which is 3x²:

⇒ exp(∫3x²dx) y' + 3x² exp(∫3x²dx) y = x² exp(∫3x²dx)

Now, we can recognize the left-hand side as the product rule of the product of the integrating factor and y:

⇒ [d/dx (exp(∫3x²dx) y)] = x² exp(∫3x²dx)

We can integrate both sides with respect to x to get:

⇒ exp(∫3x²dx) y = ∫x² exp(∫3x²dx) dx + C

where C is the constant of integration.

Now, we need to solve the integral on the right-hand side.

We can use u-substitution with u = 3x² and du/dx = 6x:

⇒ ∫x² exp(∫3x²dx) dx = (1/6) exp(∫u du) + C' = (1/6)  exp(3x²) + C'

where C' is another constant of integration.

Substituting this back into our previous equation, we get:

⇒ exp(∫3x²dx) y = (1/6) exp(3x²) + C'

To solve for y, we divide both sides by the integrating factor and simplify:

⇒ y = (1/6) exp(-∫3x²dx) (exp(3x²) + C")

where C" is the combined constant of integration.

Therefore, the general solution to the given differential equation is:

⇒ y = (1/6) exp(-x³) (exp(3x²) + C")

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The approximate probability that Maurice will obtain a sample proportion less than 0.06 is 0.2119, rounded to three decimal places.

The population proportion is p = 0.08 since we are aware that the actual percentage of students who have not declared a major is 0.08. We are asked to estimate the likelihood that Maurice will acquire a sample fraction smaller than 0.06 from a simple random sampling of n = 250 students.

The sample proportion p' is a random variable with a mean equal to the population proportion p and standard deviation σ = √(p(1-p)/n). In this case, we have:

p = 0.08

n = 250

σ = √(0.08×(1-0.08)/250)

  = 0.025

To find the probability that p' < 0.06, we can standardize the variable using the standard normal distribution:

z = (p' - p) / σ

z = (0.06 - 0.08) / 0.025

 = -0.8

Using a standard normal distribution table or a calculator, we find that the probability of getting a z-score less than -0.8 is approximately 0.2119.

Therefore, the approximate probability that Maurice will obtain a sample proportion less than 0.06 is 0.2119, rounded to three decimal places.

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Translating the new coordinate up by 2 units and 5 units to the left will given a final coordinate at X''''(10, 1), Y''''(-4, 15) and Z''''(4, 19)

This is a technique used to change the position or size of an object on the xy plane.

Given the coordinate points X(2, 4), Y(5,-3) and Z(-7, 1)'

If the coordinate points is rotated 90 degrees clockwise, then the resulting coordinate will be at X(4, -2), Y(-3,-5) and Z(1, 7)

If the resulting coordinate is dilated by by a scaling factor of 2, then the new coordinate points wil be at X''(8, 4), Y''(-6, -10) and (2, -14)

If the resulting coordinate is reflected over the x-axis, then the new coordinate points wil be at X'''(8, -4), Y''(-6, 10) and (2, 14)

Finally, translating the new coordinate up by 2 units and 5 units to the left will given a resulting coordinate at X''''(10, 1), Y''''(-4, 15) and Z''''(4, 19)

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Our quotient is 1482 R 4. We can also write this as 1482 and 4/5 or 1482.8.

To find the quotient of a division problem, we must divide the dividend by the divisor. In this case, our dividend is 7415 R 112 R 412 R 214 R 4 and our divisor is 5.

First, we divide 5 into 74 and get a quotient of 14 with a remainder of 4. We bring down the next digit, 1, and get a new dividend of 41. We divide 5 into 41 and get a quotient of 8 with a remainder of 1. We bring down the next digit, 2, and get a new dividend of 12.

We divide 5 into 12 and get a quotient of 2 with a remainder of 2. We bring down the next digit, 1, and get a new dividend of 21. We divide 5 into 21 and get a quotient of 4 with a remainder of 1.

Finally, we bring down the last digit, 4, and get a new dividend of 14. We divide 5 into 14 and get a quotient of 2 with a remainder of 4.

Therefore, our quotient is 1482 R 4. We can also write this as 1482 and 4/5 or 1482.8.

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Let's represent the area of the lawn with "x" (in square meters).

Maria charged $135 plus $9.55 per square meter, so her total earnings can be expressed as:

Total earnings = $135 + $9.55 x

We know that Maria was paid $1854, so we can set up an equation and solve for x:

$1854 = $135 + $9.55 x

Subtracting $135 from both sides:

$1719 = $9.55 x

Dividing both sides by $9.55:

x = 180

Therefore, the area of the lawn is 180 square meters.

The segment that is opposite ∠ E is C. UJ.

A segments that could be formed through connecting the endpoints of the adjacent segments are called the opposite segments. This can also create an intersection in certain types of lines or segment configurations, depending on their individual set ups.

When looking at angle ∠ E, we can see that the segment opposite it is Segment UJ. This is because it was formed by connecting the endpoints of the adjacent segments of UE and JE.

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Answer: 16

Step-by-step explanation:

Unless snap cube is a different term for something I'm unaware of, this is simple division.

64 (total snap cubes) / 4 (groups) = 16 snap cubes per group

Answer:

Step-by-step explanation:

True. The function appears to be f(x) = x/4.

Number 1 answer :

Cream cheese = 12    Sugar= 15    12 divided by 15 = 0.8

There are 0.8 ounces of cream cheese for every ounce of sugar.

Number 2 answer:

 Sugar= 15   Cream cheese = 12   15 divided by 12 = 1.25

There are 1.25 ounces of sugar for every ounce of cream cheese.

Answer: 12x - y = 16

Answer :

59+55+854+456+456+7894=9,774