which number is greater -4 or -2 explain why

Applying the properties of a rhombus and the Pythagorean Theorem, the length of one side of the rhombus is: 14.9

Recall:

Thus, given:

Find the length of one side using Pythagorean theorem as shown below:

\(HG = \sqrt{(\frac{1}{2}EG)^2 + (\frac{1}{2}FH)^2 } \\\\\)

\(HG = \sqrt{(\frac{1}{2} \times 22)^2 + (\frac{1}{2} \times 20)^2 } \\\\HG = \sqrt{11^2 + 10^2} \\\\\mathbf{HG = 14.9}\)

Therefore, applying the properties of a rhombus and the Pythagorean Theorem, the length of one side of the rhombus is: 14.9

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The fourth ordered pair using the two

sequences is ( 7/3 ,106) .

The first sequence is constructed by first multiplying the terms by 2 and then adding one-third starting from zero. So, sequence starts from 0.

First term of first sequence, a₁ = 0

a₂ = (2x0) + 1/3 = 1/3

a₃ = (2x1/3) + 1/3 = 2/3 + 1/3 = 1

a₄ = (2x1) + 1/3 = 2 + 1/3 = 7/3

Hence, the sequence is 0, 1/3, 1, 7/3, ...

The second sequence is constructed by first adding one half in terms and then multiplying by 4. The sequence starts from 1 ,

a₁ = 1

a₂ = (1 +1/2) × 4 = (3/2)4 = 6

a₃ = (6+1/2) x 4 = 13/2 x 4 = 26

a₄ = (26 + 1/2)× 4 = 53/2 x 4 = 106

Hence, the sequence is 1, 6, 26, se106, ...

Therefore, the fourth terms of the two sequences are the following, 7/3 and 106.

So, required ordered pairs is ( 7/3, 106).

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כ

Total possibilities is 350. It can be said that 350 ways are there to order a meal consisting of 1 appetizer, no entrees, and 3 different desserts.

Combinations: A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order. Combinations can be confused with permutations.

The fundamental guideline for combinations is that,

If you have n things and you have to select r things, the number of selections is represented by ⁿCr and

ⁿCr=n!/(n−r)!(r!)

All I have to do in your question is to select.

one appetizer out of seven and no main dish out of ten main courses and three dessert out of five.

What must be done now is take each individual choice from the three situations, then multiply them.

One thing to keep in mind is that and signifies "multiply" and or "add." (For instance, we would have provided the choices if you had requested to chose either one main meal or one dessert.)

For 1, the choices are:

⁷C₁= 35

Selections = 2 for 2.

¹⁰C₀= 1

For 3., the choices are:

⁵C₃= 10

Potentials in total =⁷C₁×¹⁰C₀×⁵C₃= 35×1×10=350.It can be said that 350 ways are there to order a meal consisting of 1 appetizer, no entrees, and 3 different desserts.

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The number of ways prizes can be distributed is 30240. The probability of getting a all four green balls is 0.0038

a. Seven prizes are distributed to a group of 9 people. So the total number of combinations will be

ₙCr = n!/ r!(n-r)!

₉C₇ =9!/ 7! (9-7)1 = 36

Total permutations between the chosen 7. Each will get either first, second, third or fourth. So the total permutation can be

nPr = n!/(n-r)!

₇P₄ = 7!/(7-4)! = 840

So the total ways the prize can be distributed = 36× 840 = 30240

b. Number of white balls = 5

Number of red balls = 10

Number of green balls = 6

Total number of balls = 5+10+6 =19

The combination of choosing 4 balls from 19 = ₁₉C₄ = 3876

The combination for all four balls to be green = ₆C₄ = 15.

Probability = number of likely events/ Total number of events = 15/3876 = 0.0038

So the answer for question a is 30240 and for b is 0.0038.

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The answer is that the maximum amount of lead allowed in drinking water is 0.015 mg/kg and the maximum amount of copper allowed is 1.3 mg/kg.

To express these values in parts per million (ppm), we need to convert the mass of the substance to the mass of the water.

To convert mg/kg to ppm, we need to multiply by 1,000,000 (1 million) and divide by the density of the water. The density of water is 1 gram per milliliter (g/mL), which is equivalent to 1,000,000 mg/L.

For lead:
0.015 mg/kg x 1,000,000 / 1,000,000 mg/L = 15 ppb (parts per billion)

For copper:
1.3 mg/kg x 1,000,000 / 1,000,000 mg/L = 1,300 ppb

Therefore, the maximum allowed levels of lead and copper in drinking water are 15 ppb and 1,300 ppb, respectively.
The maximum amounts of lead and copper allowed in drinking water, when expressed in parts per million (ppm), are 15 ppm for lead and 1,300 ppm for copper.

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The symmetric pure-strategy Bayesian Nash Equilibrium is given by p1=p2=5, b1=b2=2. The beliefs of both firms are such that b=2 with probability 1. Both firms believe that the other firm's type is b=2 with probability 1.

1. The action spaces are denoted as {p1} and {p2} for the two firms respectively.

2. The type spaces for both firms is {b1=1, b1=2} and {b2=1, b2=2} respectively.

3. The beliefs for Firm 1 are:

Beliefs when p2 > 3: F2 will play any price between 3 and 8, but not 2 or 9. If b2=1, p2=3.5, otherwise if b2=2, p2=6.5.

Beliefs when p2 = 3: F2 will play 2 or 3, with 50% probability each. If b2=1, F2 will play 3.

Beliefs when p2 < 3: F2 will play any price between 2 and 7 but not 3 or 8. If b2=1, p2=2.5, otherwise if b2=2, p2=5.5.

The beliefs of Firm 2 are as follows:

Beliefs when p1 > 3: F1 will play any price between 3 and 8, but not 2 or 9. If b1=1, p1=3.5, otherwise if b1=2, p1=6.5.

Beliefs when p1 = 3: F1 will play 2 or 3, with 50% probability each. If b1=1, F1 will play 3.

Beliefs when p1 < 3: F1 will play any price between 2 and 7 but not 3 or 8. If b1=1, p1=2.5, otherwise if b1=2, p1=5.5.

4. The payoff functions for both firms is given by

Πi(p1,p2,b1,b2)=(10−p1+2b2)(p1−c)+(10−p2+2b1)(p2−c)

Where c is a constant cost of production.

5. The symmetric pure-strategy Bayesian Nash Equilibrium is given by p1=p2=5, b1=b2=2. The beliefs of both firms are such that b=2 with probability 1. Both firms believe that the other firm's type is b=2 with probability 1.

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The answer is A

23/4 = 5.75

square root of 30= 5.47

5.44

16/3 = 5.33

The answer is A. Winter.

As the pattern is : F, W, Sp, Su, F... (letters used for convenience), then the next word in the pattern will be Winter, because that was shown in the previous sequence.

Step-by-step explanation:

3^-5= 1/3^5

9^-3=1/9^3

3^-4=1/3^4

Answer:

Step-by-step explanation:

3^-5 = 1/ 3 ^5 = 1/243

9^-3 = 1/9^3    = 1 /729

3^-4 = 1/3^4

For any number which has a negative power there will be a 1 as the numerator and the number with its power as the denominator

Answer:

x² + 9x + 14 can be factored as (x+2)(x+7)

Step-by-step explanation:

The general form is ax² + bx + c. If a=1, then you can start looking for two numbers that multiplied give c and added give b.

14 = 2*7

and

9 = 2+7

hence the easy factorization

(x+2)(x+7)

Keep in mind that it only works if a=1.

Answer:

( + 2 ) (x+7 )

Step-by-step explanation:

Use the sum-product pattern   2 + 9 + 1 4 2 + 7 + 2 + 1 4 2

Common factor from the two pairs   2 + 7 + 2 + 1 4 ( + 7 ) + 2 ( + 7 ) 3

Rewrite in factored form   ( + 7 ) + 2 ( + 7 ) ( + 2 ) ( + 7 )

Answer:

1. +12x and 15

2. 14x

3. 2

Step-by-step explanation:

Step 1: Distribute -3

To distribute -3, you would multiply both -4x and -5 by -3, changing them to 12x and 15

Step 2: Combine 12x and 2x

Then you would combine like terms, meaning that you would add 12x and 2x, creating 14x.

Step 3: Combine 15 and -13

You would finish combining like terms by adding 15 to -13, creating 2

Answer:

-1

Step-by-step explanation:

lim x tends to 4 (x^2-9x+20)/(x-4). (x^2-9x+20)(x-4)=x-5.

So the limit is 4-5=-1

To determine if a matrix is a linear combination of other matrices, we need to check if it can be written as a weighted sum of those matrices where the weights are scalar values (numbers).

If a matrix can be expressed in this way, it is said to be a linear combination of the other matrices.

For example if we have matrices: A, B & C and we can write matrix D as follows:

Then D is a linear combination of matrices A, B and C. This concept is important in linear algebra as it allows us to express one matrix in terms of others. Making it easier to manipulate & analyze the matrices. A matrix is a linear combination of other matrices if it can be expressed as a weighted sum of those matrices where the weights are scalar values.

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The solutions of the system of equations are (-1, 2) and (3, -5)

Here we have a graph of a system of equations. The solutions are all the points where the graphs of the two equations intersect.

Here we can see two intersection points, thus, we have two solutions. We can see that the first intersection is at (-1, 2) and the second intersection is at (3, -5)

So these two are the solutions of the system of equations.

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The correct answer is option c. Cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the opposite side in a right triangle.

In a right triangle, the hypotenuse is the side opposite the right angle, the opposite side is the side opposite the angle of interest, and the adjacent side is the side adjacent (next to) the angle of interest.

To understand why cosine is defined as adjacent/ opposite, let's consider a right triangle:

In the triangle above, the angle of interest is θ (theta). The adjacent side is the side adjacent to θ, and the opposite side is the side opposite to θ. The hypotenuse is the side opposite the right angle.

The cosine of θ is defined as the ratio of the length of the adjacent side to the length of the opposite side:

cos(θ) = adjacent / opposite

This definition stems from the trigonometric ratios in right triangles. By dividing the adjacent side by the opposite side, we can determine the cosine of an angle, which represents the ratio of the lengths of these two sides.

Therefore, option c, "Adjacent / opposite," correctly represents the definition of cosine in the context of a right triangle.

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Answer:

3w

Step-by-step explanation:

\(w=\frac{a}{3} \\3w=a\\\)

Answer: A

Step-by-step explanation: The distance from A to C and C to D is equal

The prime factorization of the number 22 is 22 = 2×11.

The given number is 22.

Prime factorization is a way of expressing a number as a product of its prime factors. A prime number is a number that has exactly two factors, 1 and the number itself.

Here, prime factors of the number 22 are as follows

22 = 2×11

Therefore, the prime factorization of the number 22 is 22 = 2×11.

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Answer:

259 cm will be the answer, if i am wrong im very sorry about getting it wrong

Step-by-step explanation:

i tried my best.

The radius of the cone, when the volume is 36 units^3 and the height is 12 units, is approximately 1.6939 units.

To find the radius of a right circular cone when the volume and height are given, we can use the formula for the volume of a cone and solve for the radius. Let's proceed with the calculation.

The formula for the volume of a cone is:

V = (1/3) * π * r^2 * h

Where:

V is the volume of the cone,

π is the mathematical constant pi (approximately 3.14159),

r is the radius of the cone, and

h is the height of the cone.

In this case, we are given that the volume of the cone is 36 units^3 and the height is 12 units. We can substitute these values into the formula and solve for the radius.

36 = (1/3) * π * r^2 * 12

To isolate the radius, we can divide both sides of the equation by (1/3) * π * 12:

36 / [(1/3) * π * 12] = r^2

Simplifying the right side:

36 / (4π) = r^2

Taking the square root of both sides:

√(36 / (4π)) = r

Simplifying further:

√(9 / π) = r

Therefore, the radius of the cone is √(9 / π) units.

To obtain an approximate value for the radius, we can substitute the value of π (approximately 3.14159) into the equation:

r ≈ √(9 / 3.14159)

Calculating this expression gives us the approximate value of the radius.

r ≈ √(2.8654) ≈ 1.6939

Hence, the radius of the cone, when the volume is 36 units^3 and the height is 12 units, is approximately 1.6939 units.

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To solve the inequalities -2x + 4 < 8 and 3x + 4 ≤ -5, we will solve them individually and then represent the solutions on a number line.

For the first inequality, -2x + 4 < 8, we will isolate x:

-2x + 4 - 4 < 8 - 4

-2x < 4

Dividing both sides by -2 (remembering to reverse the inequality when multiplying/dividing by a negative number):

x > -2

For the second inequality, 3x + 4 ≤ -5, we isolate x:

3x + 4 - 4 ≤ -5 - 4

3x ≤ -9

Dividing both sides by 3:

x ≤ -3

Now we represent the solutions on a number line. We mark -2 with an open circle (since x > -2), and -3 with a closed circle (since x can be equal to -3). Then we shade the region to the right of -2 and include -3 to represent the solutions.

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Answer:

9/11

Step-by-step explanation:

Using the method KCF (keep, change, flip), and converting the fractions into improper fractions (before using the method), we get the answer 9/11.

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6.75\% of 9.99}}{\left( \cfrac{6.75}{100} \right)9.99} ~~ \approx ~~ 0.67~\hfill~\underset{ total~cost }{\stackrel{ 9.99~~ + ~~0.67 }{\approx\text{\LARGE 10.66}}}\)

The length of the shorter leg of the triangle ABC is approximately 24.49 units. Let's denote the right triangle ABC, where C is the right angle.

Let D be the midpoint of AB, and E be the foot of the altitude from C to AB. Then we have:

CD = 1/2 AB (definition of median)

CE = 12 (given altitude to the hypotenuse)

Let x be the length of the shorter leg of the triangle ABC. Then we have:

AE = x (definition of altitude)

EB = AB - x (definition of complementary leg)

By the Pythagorean theorem, we have:

AC^2 = AB^2 + BC^2

(2CD)^2 = AB^2 + x^2

AB^2 = 4CD^2 - x^2

By the similarity of triangles AEC and ABC, we have:

CE/AC = AE/AB

12 / (AB + BC) = x / AB

AB = x / (12/x + 1)

Substituting AB into the previous equation, we get:

4CD^2 - x^2 = x^2 / (12/x + 1)^2

Simplifying and solving for x, we get:

x^4 - 576x^2 - 14400 = 0

This is a quadratic equation in x^2, so we can solve for it using the quadratic formula:

x^2 = [576 ± sqrt(576^2 + 4*14400)] / 2

x^2 = [576 ± 624] / 2

Since x is a length, we take the positive square root:

x^2 = 600

x ≈ 24.49

Therefore, the length of the shorter leg of the triangle ABC is approximately 24.49 units.

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The Fundamental Theorem for line integrals can be used to evaluate the line integral because the function is conservative on its domain and has a potential function. The line integral can be evaluated using this theorem.

The Fundamental Theorem for line integrals states that if a function is conservative on its domain, the line integral over a closed curve depends solely on the endpoints of the curve. It can be computed by finding a potential function corresponding to the given function. In this particular scenario, we need to determine if the function is conservative and possesses a potential function in order to apply the Fundamental Theorem for line integrals.

To evaluate the line integral, we must identify the potential function F(x, y) = (1/2) * x^2 * sin(y) for the function f(x, y) = x * sin(y). By obtaining the antiderivative of f(x, y) with respect to x, we find \(F(x, y) = (1/2) * x^2 * sin(y)\).

Utilizing the Fundamental Theorem for line integrals, we can compute the line integral along the path from (0, 0) to (ln(7), y). Employing the potential function F(x, y), the line integral is evaluated as F(ln(7), y) - F(0, 0). After simplification, the final answer becomes \((1/2) * (ln(7))^2 * sin(y)\).

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Answer:

Rudy answered 2 questions more than Camilo.

Step-by-step explanation:

The value of m so that the condition satisfies is -2, the correct option is A.

We are given that;

y=f(x) is continuous

Now,

To find the numbers c that satisfy the conclusion of the Mean Value Theorem, we need to solve the equation:

f’© = [f(2) - f(0)] / (2 - 0)

f’(x) = 8x - 2

f(2) = 4(2)^2 - 2(2) + 3 = 23

f(0) = 4(0)^2 - 2(0) + 3 = 3

f’© = (23 - 3) / (2 - 0)

f’© = 10

8m - 2 = 10

8m = 12

m = 12/8

m = -2

Therefore, by the given function the answer will be -2.

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