how many ways are there to arrange 7 elves and 5 goblins in a row in such a way that no goblins stand next to each other

The value of the equation is x = 348

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

x ÷ 4 = 87   be equation (1)

On simplifying the equation , we get

x/4 = 87

Multiply by 4 on both sides of the equation , we get

x = 87 ( 4 )

x = 348

Therefore , the value of x is 348

Hence , the equation is x = 348

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Answer:

5%

Step-by-step explanation:

Decreased amount = 40 - 38

                                 = £ 2

[tex]\sf \boxed{decreased \ percentage = \dfrac{decreased \ amount}{oringinal price}*100 }[/tex]

                                  [tex]= \dfrac{2}{40}*100\\\\= 5 \%[/tex]

The cylinder container has a radius of 1.63 centimeters.

The volume of a cylinder is equal to the product of the area of the circular base and the height of a cylinder.

V = πr²h

where 'r' is the radius of the base (circle) of the cylinder

'h' is the height of the cylinder

Given that cylinder container has a height of 15 centimeters and a volume of 125.6 cubic centimeters.

Substitute the known values in the formula, and solve for radius:

125.6  = π(r)² × 15

(r)² = 125.6/π × 15

(r)² = 2.66

r = √2.66

r = 1.63 cm

Thus, the radius of the cylinder is 1.63 centimeters.

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So the total amount received by Sohail is 100 * y². To get the precise amount, we must first determine the value of x.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.

Let's call the number of days Sohail was in town and cleaned the house "y". Then we can write:

y = x - 8 (since he was out of town for 8 days)

And the amount he was promised per day is 10, so the total amount promised is:

10 * y = 10 * (x - 8)

At the end of the break, his mother decided to square the amount due to him, so the final amount he received is:

(10 * y)² = (10 * (x - 8))²

Expanding the square and simplifying, we get:

100 * y²= 100 * (x - 8)²

So the final amount Sohail received is 100 * y². To find the exact value, we need to know the value of x.

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Answer:

[tex]{ \sf{ \frac{17}{25} }} \\ [/tex]

Step-by-step explanation:

• For 5/16;

[tex]{ \tt{ \frac{5}{16} = 0.3125 }} \\ \\ { \tt{ |0.5 - 0.3125| = 0.1875 }}[/tex]

• For 17/25;

[tex]{ \tt{ \frac{17}{25} = 0.68 }} \\ \\ |{ \tt{0.5 - 0.68}}| = { \tt{0.18}}[/tex]

By observation, we should get a lesser value of the two values of 0.1875 and 0.18

[tex]{ \tt{0.18 < 0.1872}}[/tex]

The farmer requests that the pen's length be 20 feet longer than its breadth. If we use the symbol w to indicate width. The length would then equal w + 20.

You play the part of a middle schooler who is attempting to make your family's farm profitable in Farmer Math.

The challenge first asks us to determine the longest length given that the fencing will not exceed 100 feet.

We are aware that a rectangular area's perimeter is 2l + 2w (where l is the length and w the width)

Therefore, 2l + 2w 100 would be required for the fencing.

In order to solve for w, we will use the values for l and w that we mentioned in the beginning:

2l + 2w ≤ 100

2(w+20) +2w ≤ 100

2w + 40 +2w ≤ 100

4w ≤ 100 - 40

4w ≤60

w ≤ 15

The breadth must therefore be less than or equal to 15.

The longest length is achieved when the width is at its greatest value because the length is 20 feet greater than the width.

This makes the length at w = 15 the longest it can possibly be, at 35.

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The effect of eliminating a redundant constraint from a linear programming model depends on the specifics of the model and the constraint in question. It is important to analyze the model carefully to determine the effect that eliminating a constraint would have on the optimal solution.

No effect: If the constraint was indeed redundant, meaning that it did not affect the optimal solution, then eliminating it would have no effect on the optimal solution.

Improved solution: If the constraint was affecting the optimal solution, then eliminating it might result in a better solution. For example, if the constraint was limiting the feasible region of the solution, then eliminating it might expand the feasible region and result in a better solution.

Different solution: If the constraint was affecting the optimal solution, then eliminating it might result in a different solution. For example, if the constraint was forcing the optimal solution to go through a particular point, then eliminating it might result in a different solution.

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Answer:

34.8 pounds

Step-by-step explanation:

The cat weighs 10.4. Which is 24.4 pounds less that the dog. So find the weight of the dog, we need to make an equation. This equation would be:

[tex]dog[/tex][tex]-24.4=10.4[/tex]

Solve:

[tex]dog-24.4=10.4[/tex]

      [tex]+24.4[/tex]     [tex]+24.4[/tex]

[tex]dog=34.8[/tex]

Hope this helped!
Stay safe and have a great day/night! (:

1 1/4 divided into three parts you mean? You can simply take 1 1/4 or 1.25 and divide that by 3.

By fraction, you would want to convert the mixed number into an improper fraction, that way, it's easier. 1 1/4 to an improper fraction is 5/4.

5/4 divided by 3

Now whenever you're dividing fractions, remember this tip: keep, change, flip. Keep the first fraction, change the division sign to a multiplication sign, and flip the second fraction.

So 3, or 3/1 is now 1/3 and the sign is now multiplication.

5/4 x 1/3 = 5/12

That's your answer!

Hope this helped!

Reason:

Focus on Q(0, 5) and Q′(9, 5)

More specifically, focus on the x coordinates. We go from x = 0 to x = 9, which means "shift 9 units to the right" since we added 9 to the old x coordinate to get the new x coordinate. The y coordinates stay the same.

The translation rule is [tex](\text{x},\text{y}) \to (\text{x}+9, \text{y})[/tex]

The container having same volume and greater surface area than Amanda's container is -

Option 3: Container with dimensions 6 ft × 2 ft × 2 ft.

What is volume?

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

The measurements of the box filled by Amanada is -

Length = 3 feet, Width = 2 feet and height = 4 feet

The formula for volume of a cuboid is -

Volume = l×w×h

Substitute the values in the equation -

Volume = 3 × 2 × 4

Volume = 24 ft³

The formula for surface area of a cuboid is -

Total Surface Area = 2(lw + wh + lh)

Substitute the values in the equation -

Total Surface Area = 2[(3 × 2) + (2 × 4) + (3 × 4)]

Total Surface Area = 2(6 + 8 + 12)

Total Surface Area = 2(26)

Total Surface Area = 52 ft²

Amanada wants a container with greater surface area and same volume.

The first and fourth containers are cubes and not cuboids so they are not considered.

The second container has same measurements as that Amanda filled, so they will have same volume and surface area.

Consider the third container with measurements -

Length = 6 feet, Width = 2 feet and height = 2 feet

The formula for volume of a cuboid is -

Volume = l×w×h

Substitute the values in the equation -

Volume = 6 × 2 × 2

Volume = 24 ft³

The formula for surface area of a cuboid is -

Total Surface Area = 2(lw + wh + lh)

Substitute the values in the equation -

Total Surface Area = 2[(6 × 2) + (2 × 2) + (6 × 2)]

Total Surface Area = 2(12 + 4 + 12)

Total Surface Area = 2(28)

Total Surface Area = 56 ft²

Therefore, the third container is the right choice.

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Answer:

There are 44 jackets and 12 coats.

Step-by-step explanation:

hope this helps

Answer:  Cars rate in kilometers is 112kmph. I did this by multiplying 70 by 1.6 which got me 112. Then the distance in kilometers traveled after 5 hours is 560 kilometers since 112x5 is 560

Step-by-step explanation:

The solution of the operation is -0.814 approximately.

Therefore the answer is E. None of the above.

The expression being evaluated in this problem is the result of performing several mathematical operations in a specific order. First, the expression inside the parentheses is evaluated:

(-2.6 + 56 - 16)

= 56 - 2.6 - 16

= 37.4

(-87 × 0.35) = -30.45

Next, the expression outside the parentheses is evaluated:

(−87 × 0.35) ÷ (−2.6 + 56 - 16)

= -30.45 ÷ 37.4

≈ -0.814

So, the solution to the expression is -0.814.

--The question is not in English, the question in English is--

"What is the solution of the operation, (−87 × 0.35) ÷ (−2.6 + 56 - 16)?

A. -629

B. -196

C. 629

D. 296

E. None of the above"

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The probability that the mean contents of the bottles in a six-pack is less than 295 ml is approximately 0.1587, or 15.87%.

To solve this, use the standard normal distribution and the cumulative distribution function (CDF) of the normal distribution.

Standardize the value of 295 ml by subtracting the mean of the distribution (298 ml) and dividing by the standard deviation (3 ml):

Z = (295 - 298) / 3 = -1

The CDF of the standard normal distribution gives us the probability that a random variable from a standard normal distribution is less than or equal to a certain value. Using a standard normal table or a calculator with normal distribution functions, we find that the probability that a standard normal random variable is less than or equal to -1 is approximately 0.1587.

Since the contents of the bottles are normally distributed with mean 298 ml and standard deviation 3 ml, we can use the standard normal distribution and the standard score Z to approximate the probability of observing a mean contents of less than 295 ml in a six-pack of bottles. This probability is approximately 0.1587, or 15.87%.

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During the times the Sun is facing the equator, the length of day and night is nearly equal (12 hours each) at the equator because the sun's rays are hitting the earth at a 90-degree angle.

The Equator is an imaginary line that circles the Earth, equidistant from the North and South Poles and dividing the Earth into the Northern and Southern Hemispheres.

It is important because it serves as a reference for determining the latitude of a location, as well as its climatic and ecological zones. The Equator also plays a crucial role in the distribution of sunlight, affecting weather patterns and ocean currents, and is a key factor in the Earth's climate and ecosystems.

The Equator, as should be noted is used as a reference for navigation, mapping, and astronomical observations.

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Full Question:

Short answer questions:

The Sun faces the Equator twice in a year. How is the length of the day and night during that time and why?

The equation for A, in terms of x, represents the amount of money remaining on the card after buying x cups of coffee is $10 - $2x = A.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

The equation will be written as below,

$10 - $2x = A.

A is the amount of money remaining on the card.

x is cups of coffee.

Therefore, the equation for A, in terms of x, represents the amount of money remaining on the card after buying x cups of coffee is $10 - $2x = A.

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The probability of an event for rolling a die P(E) is 1/2.

What is the probability of an event?

The probability of an event is a number (always positive) that expresses the likelihood that the event will occur. The likelihood that an event will occur falls between zero and one. A certain occurrence has a probability of one while an impossible event has a chance of zero. As implied by its name, probability deals with uncertainty.

Given, E be the event defined as {3,4,6}

So, the total number of an event E, n(E) = 3

For a die, total events are {1,2,3,4,5,6}

So, the total number of rolls of a die event, n(T) = 6

Then,

P(E) = [tex]\frac{n(E)}{n(T)} = \frac{3}{6} = \frac{1}{2}[/tex]

So, the required value of P(E) is 1/2.

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The formula h = 63.2 + 2.31f ,relates the length of someone's femur (f) to their expected height (h) within a certain population. When f = 39, height(h) is 153.29 cm.

The constant term, 63.2, is the y-intercept of the line that represents the relationship between femur length and height. It represents the expected height of someone with a femur length of 0 cm.

The constant 2.31 represents the slope of the line. It represents the expected change in height for a 1 cm change in femur length. So, for every additional centimeter of femur length, the expected height increases by 2.31 cm.

When f = 39, we can substitute this value into the formula to find the expected height:

h = 63.2 + 2.31 * 39

h = 63.2 + 90.09

h = 153.29 cm

So, when the length of someone's femur is 39 cm, their expected height is 153.29 cm.

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Answer:

The answer is in the attachment

Step-by-step explanation:

The expression that will not be equivalent to the number given -(-20) is -20 (option D).

A number is said to be equivalent not only if the number is equal in value, for example, 15 = 10 + 5, but also if the negative or positive sign is equal, for example, 5 is not equal to -5.

The original expression is -(-20), this expression can be simplified as 20 or +20 considering that minus plus minus is equivalent to +. Based on this, the expression that is not equivalent is -20.

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Therefore , the solution of the given problem of equation comes out to be (2/3)x + 7 = 2x .

In arithmetic equations, the identical figure (=) is used to denote the equivalence of two assertions. It is demonstrated that mathematical methods, which have acted as manifestations of reality, can be used to assess a variety of numerical factors. The equal sign actually splits the number 12 into two separate pieces, despite the fact that the result is y + 6 = 12. Calculations can be made to determine how many protagonists are also present at either end of a particular character. Conflicting sign interpretations are frequent.

Here,

Let's call the number we're looking for "x".

According to the problem, "two-thirds of a number" can be expressed as (2/3)x, and "is added 7" can be expressed as +7. Finally, "the result is twice the same number" can be expressed as 2x.

Putting it all together, we can write the equation:

(2/3)x + 7 = 2x

This equation represents the information given in the problem.

Therefore , the solution of the given problem of equation comes out to be (2/3)x + 7 = 2x .

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The type of probability situation being used depends on the type of situation being analyzed.

Single event: A single event refers to a single outcome of a random process. For example, the outcome of a coin flip (heads or tails) is a single event.

Two mutually exclusive events: Two events are said to be mutually exclusive if they cannot occur at the same time. For example, the events "rolling a 4 on a die" and "rolling a 6 on a die" are mutually exclusive, because a die cannot show both 4 and 6 at the same time.

Multiple independent events: Multiple independent events are events that do not influence each other. For example, the outcome of rolling two dice is made up of two independent events (the outcome of each individual die roll).

Multiple dependent events: Multiple dependent events are events that are influenced by each other. For example, if you draw two cards from a deck, the outcome of the second draw depends on the outcome of the first draw (since there are fewer cards left in the deck).

Conditional: A conditional probability is the probability of an event occurring given that another event has already occurred. For example, the probability of getting heads on a coin flip given that the first flip was tails is still 50%, because the outcome of the first flip does not change the probability of the second flip.

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Answer: B

Step-by-step explanation:

This question finds congruent triangles. A similarity statement relating the 3 triangles is ABC-DAC-DBA.

From the triangle ABC-DAC-DBA, it has conditions that can be said to be congruent, because it has side lengths with patterned comparisons if the magnitudes are not the same.

The conditions for two congruent plane shapes, namely:

The above conditions also apply to congruent triangles.

Two triangles are congruent if they have:

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