Convert each of the following to a common fraction: in a sequence way. ​

6 people be lined up to get on the bus in 480 ways

A permutation is an act of arranging objects or numbers in order. Combinations are the way of selecting objects or numbers from a group of objects or collections, in such a way that the order of the objects does not matter.

For this, the easiest way is doing the complement. Calculate how many the 2 people are together and subtract from the total, so:

We can consider 2 people a block that will permutation, so, instead of 6 people we have 5 [a block of 2 people and 4 more):

5! = 5.4.3.2.1 = 120

The 2 people from the block will permutation as well:

2! = 2.1 = 2

Total: 5!.2! = 120.2 = 240.

For the case they are not following each other:

720 - 240 = 480

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The value of x in the system of equations is: x = 11.2.

The value of x can be found by solving the system of equations.

One method is to substitute the value of x from one equation into the other equation, solve for y, then use the value of y to find x.

Starting with the second equation: 5x + 2y = 48

Solve for y: y = (48 - 5x) / 2

Now substitute this expression for y into the first equation:

-5x - 12((48 - 5x) / 2) = -8

-5x - 6(48 - 5x) = -8

-5x - 288 + 30x = -8

25x - 288 = - 8

25x = -8 + 288

25x = 280

x = 280/25

x = 11.2

Finally, solving for x:

x = 11.2

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Answer:

-11.8

Step-by-step explanation:

To find the value of x in this system of equations, we can use substitution or elimination method.

Using substitution:

Solve for one of the variables in one of the equations and substitute it into the other equation. We can start by solving for y in the second equation:

[tex]\sf:\implies{5x + 2y = 48}[/tex]

[tex]\sf:\implies{2y = -5x + 48}[/tex]

[tex]\sf:\implies{y = (-5/2)x + 24}[/tex]

Now, substitute this expression for y into the first equation:

[tex]\sf:\implies{-5x - 12y = -8}[/tex]

[tex]\sf:\implies{-5x - 12((-5/2)x + 24) = -8}[/tex]

[tex]\sf:\implies{-5x + 30x + 288 = -8}[/tex]

[tex]\sf:\implies{25x = -296}[/tex]

[tex]\sf:\implies{x = -11.84}[/tex]

The value of x rounded to the nearest tenth is -11.8.

The function u(x, y) = x^(1/3) * y^(2/3) is a multivariable function.

We have the function u(x,y) = x1/3y2/3. The function u(x, y) = x^(1/3) * y^(2/3) is a multivariable function, where x and y are variables and x^(1/3) and y^(2/3) are exponents. It describes the relationship between the inputs x and y and the output u. To solve for u, you would need to substitute specific values for x and y and evaluate the expression.

However, it is not possible to solve this function in the traditional sense because it is not a linear equation with a single solution. Instead, it is a surface in a three-dimensional space, where x and y are the two axes and u is the height. The value of u at any given point on the surface can be found by evaluating the function with the corresponding x and y values.

Therefore, The function u(x, y) = x^(1/3) * y^(2/3) is a multivariable function

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The correct statements regarding the algebraic expression are given as follows:

In 2a, 2 is a coefficient, as it multiplies the letter that composes the expression.

(2a + 5) is a sum of two terms.

In (2a + 5), 5 is the constant.

4 and 1 are like terms, as they have the same variable part of x^0 = 1.

2a + 5 is a factor, not just 2a.

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The right solution is option C, which is Y'(1, -4) and Z'(-2, -1).

A triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same. A triangle is a three-sided polygon with three edges and three vertices in geometry. The total of a triangle's interior angles equals 180 degrees, which is its most essential feature. This is known as the angle sum property of a triangle.

Here,

To translate a triangle, you need to add the same value to each x-coordinate and each y-coordinate. In this case, the translation moves each point 2 units to the left and 3 units down, so the new coordinates of Y and Z would be:

Y'(3 - 2, -1 - 3) = Y'(1, -4)

Z'(0 - 2, 2 - 3) = Z'(-2, -1)

The correct answer is Y'(1, -4) and Z'(-2, -1) that is option C.

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Answer:

100

1,000

10,000

Step-by-step explanation:

10 times 10 is 100.

10 times 10 times 10 is 1,000

10 times 10 times 10 times 10 is 10,000.

To determine whether the sequence converges or diverges, we can use the Squeeze Theorem.

We can see that

4/ n+5n^2 < = An <= 4+3n^2/ n+5n^2

As n tends to infinity,  4/ n+5n^2  tends to 0 and 4+3n^2/ n+5n^2 tends to  4/5n^2 which also tends to 0.

So by the Squeeze Theorem, we can say that An tends to 0 as n tends to infinity. Hence the limit of the sequence is Lim n-> An = 0

We can also see that the numerator of An is a constant and the denominator is a polynomial with degree 2. Since the denominator's degree is greater than the numerator, the limit will be zero as n -> infinity.

Therefore, the sequence converges to 0.

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Answer: 240

Step-by-step explanation:

Answer: 240

Step-by-step explanation:

60 percent *400

= (60/100)*400

= (60*400)/100

= 24000/100 = 240

Now we have: 60 percent of 400 = 240

Question: What is 60 percent of 400?

We need to determine 60% of 400 now and the procedure explaining it as such

Step 1: In the given case Output Value is 400.

Step 2: Let us consider the unknown value as x.

Step 3: Consider the output value of 400 = 100%.

Step 4: In the Same way, x = 60%.

Step 5: On dividing the pair of simple equations we got the equation as under

400 = 100% (1).

x = 60% (2).

(400%)/(x%) = 100/60

Step 6: Reciprocal of both the sides results in the following equation

x%/400% = 60/100

Step 7: Simplifying the above obtained equation further will tell what is 60% of 400

x = 240%

Therefore, 60% of 400 is 240

Answer:86 yards

Step-by-step explanation:

We have the diameter, so the solution simply is:

D= 2 r= 2 x 43= 86 yards

P.S. I'm sorry if this isn't clear enough, but that's how i could explain.

The number of complete days that 4 packs of treats will last, we need to determine the total number of packs each day and divide it into the total number of packs Mrs. Mills has bought.

Let's call the number of days the treats will last "d".

Then, the number of packs Fluff eats in "d" days is d * (1/6 of a pack per day) = (1/6)d.

Similarly, the number of packs Tigger eats in "d" days is d * (1/5 of a pack per day) = (1/5)d.

The total number of packs they eat in "d" days is (1/6)d + (1/5)d = (11/30)d.

Since Mrs. Mills has bought 4 packs, we have 4 = (11/30)d.

Finally, solving for "d", we have d = (30/11) * 4 = 120/11 days.

Since "d" must be a whole number, we round down to get 10 complete days that the 4 packs of treats will last.

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The total number of packs they eat in "d" days is (1/6)d + (1/5)d = (11/30)d.

Since Mrs. Mills has bought 4 packs, we have 4 = (11/30)d.

Finally, solving for "d", we have d = (30/11) * 4 = 120/11 days.

Bar notation is used to show the decimal is repeating.

So,

"We use bar notation to show that a decimal is terminating" is an incorrect statement.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Bar notation is used in decimal numbers to show that the number is repeating.

Example:

1/3 = 0.33333333

This can be written as,

1/3 = 0.[tex]\over3[/tex]

Thus,

Bar notation is used to show the decimal is repeating.

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The ratio of the orbital radii of the planets is  4:1.

The ratio of their periods is 8:1.

What is orbital radius and periods in circular motion?

Planetary bodies circle the Sun according to Kepler's three laws. They explain how planets orbit the Sun in elliptical fashion, how they traverse the same amount of space in a given length of time regardless of where they are in their orbit, and how their orbital periods are related to the size of their orbits (its semi-major axis).

An object's orbital radius is the typical distance it travels around a bigger object. An illustration would be that the Sun and Earth are typically 150 million kilometres apart. The orbital radius is also this.

Let the mass of the planet be m and the mass of the star be M.

r = radius of ordit

v = speed

We know that

gravitational attraction = centripital force

GMm/[tex]r^{2}[/tex] = m[tex]v^{2}[/tex]/r

Hence

v  ∝ 1/

a) Here v₁/v₂ = v/2v =  

squaring both sides

1/4 = r2/r1

Thus r1/r2 = 4/1

Hence ratio of orbital radii is 4:1.

b) As per keplers law of planetary motion,

T^2 ∝ [tex]r^{3}[/tex]

Thus ratio of time periods is 8:1.

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Answer:

The coefficient a = -1, b = 4, c = -1 and d = 0. To solve for the coefficients, substitute the values from the table into the equation y = ax³ + bx² + cx+d. When x = 0 and y = 0, we get 0 = -1a + 4b + c + d, so d = 0. When x = 1 and y = -2, we get -2 = -1a + 4b + c, so c = -1. When x = 2 and y = -26, we get -26 = -1a + 4b, so b = 4. Finally, when x = 3 and y = -54, we get -54 = -1a, so a = -1.

Step-by-step explanation:

The total amount of deposits shown is, $713.29.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

The graph of a passbook is shown in figure.

Now, By figure,

The total amount of deposits is,

⇒ $310.58 + $402.71

⇒ $713.29.

Thus, The total amount of deposits shown is, $713.29.

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Using unitary method, turkey's temperature after 55 minutes is 120.815° Also, it will take approximately 68 minutes for the turkey to cool down to 105°.

Now, According to the question:

What is unitary method?

The formula of the unitary method is to find the value of a single unit and then multiply the value of a single unit to the number of units to get the necessary value.

Reduction in temperature after 30 minutes = 185° - 150° = 35°

Reduction in temperature after 1 minute = 35/30 = 1.167°

Reduction in temperature after 55 minutes = 55 × 1.167 = 64.185°

Temperature after 50 minutes = 185° - 64.185° = 120.815°

Decrease in temperature when the turkey has cooled down to 105° = 185° - 105° = 80°

Time taken by the turkey to cool down 80° = 80/1.167 = 68.55 minutes.

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A country's population in 1995 was 23 million. In 2001 it was 25 million, the population in 2013 using the exponential growth formula in 2013 will be around 30 million.

For this problem, we have the final population P, the starting population A, and the time passed t.

We still need to determine the value of the growth factor k.

This can be done using the information for the years 1995 and 2001.

In this case, A will be 23 million (the population in 1995), P will be 25 million (the population in 2001), and t will be 6 years (the number of years between 1995 and2001):

[tex]P=Ae^{kt}[/tex]

[tex]25=23e^{k 6}[/tex]

[tex]e^{6k} =\frac{25}{23}[/tex]

[tex]k = \frac{ln(25) - ln(23)}{6}[/tex]

k = 0.013897

Now, let's use this information to determine P in 2013.

A will still be 23 million, but t will be 18 years.

[tex]P= 23e^{0.013897*18} \\P= 23e^{0.250146} \\P=23 * 1.28421\\P=29.5368\\[/tex]

Therefore, the population in 2013 using the exponential growth formula in 2013 will be around 30 million.

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The relation is not a function, enter NONE in the Domain is possible x values from the graph i.e (-infinity,-2) U [2,infinity)

Range is all possible functional values i.e (-infinity,4] U (7,infinity)

A) vertical line test :

the vertical line through the point x = -2 cuts the graph at two points

the points on the graph are (-2,-1) and (-2,5)

that is x=-2 assigned to two values -1,5.

recollect that a relation represents a function when each element of x-coordinate associated with unique element of y-coordinate

therefore, this relation is not a function.

Domain is none and codomain is also none.

B) any vertical line through graph cuts the line at only one point.

that is each element of x coordinate associated with the unique element of y-coordinate. so, it represents a function.

Domain is possible x values from the graph i.e (-infinity,-2) U [2,infinity)

Range is all possible functional values i.e (-infinity,4] U (7,infinity)

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The second and third image will be congruent to the pre-image. The solution has been obtained by applying the concept of transformations.

What is transformation?

Any action that moves a polygon or other two-dimensional object on a plane or coordinate system is referred to as a transformation.

Pre-image or "inverse image" refers to the two-dimensional shape that exists before any change. The transformed shape is represented by the image.

1. This is not congruent because both the coordinates are dilated and after dilation the size of the image is not the same as of original figure.

2. This is congruent because there is only translation which means it is same as the original figure but the position is different.

3. This is congruent because only translation has taken place which means it is same as the original figure but the position is different.

4. This is not congruent because one coordinate i.e. x has been dilated and after dilation the size of the image is not the same as of original figure.

Hence, second and third are congruent to the pre-image.

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the linear correlation coefficient given to determine the coefficient of determination,  R² = 0.0784.

The strength of the linear link between two variables, x and y, is measured by the linear correlation coefficient, which is a number derived from the supplied data. The linear link between variables x and y is indicated by the sign of the linear correlation coefficient.

In order to examine the relationship between two quantitative variables, correlation and linear regression are the two methods that are most frequently utilised. As opposed to regression, which expresses the connection as an equation, correlation measures the strength of the linear relationship between two variables.

The linear correlation coefficient is given as:

r = -0.28

Calculation of coefficient of determination:

R² = r²

R² = (-0.28)²

or, R² = 0.0784

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Lucy divides 1.8 into 6 groups of 0.3.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

Based on the information, Lucy solves 1.8 ÷ 0.3. This will be:

= 1.8 / 0.3

= 6

In conclusion, Lucy divides 1.8 into 6 groups of 0.3.

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Lucy solves 1.8 ÷ 0.3 using the diagram shown.

Use the drop-down menus to explain her reasoning.

Lucy divides ______

into _______

groups ______

of

The student can only work a whole number of hours, the student should work 8 hours at the doctor's office each week. The student should then tutor for 12 hours each week in order to earn at least $375.

Let x represent the number of hours the student works at the doctor's office each week, and let y represent the number of hours the student tutors each week. The system of inequalities that represents the given constraints can be written as:

x + y ≤ 20

15x + 25y ≥ 375

To maximize the number of hours the student works at the doctor's office while still earning at least $375, we must solve this system of inequalities. To do this, we can subtract 15x from both sides of the second inequality to isolate y:

25y ≥ 375 - 15x

We can then divide both sides of this equation by 25 to solve for y:

y ≥ (375 - 15x) / 25

We can then substitute this expression for y in the first inequality to solve for x:

x + (375 - 15x) / 25 ≤ 20

We can then rearrange and solve this equation for x:

15x + 375 ≤ 500

15x ≤ 125

x ≤ 8.33.

Since the student can only work a whole number of hours, the student should work 8 hours at the doctor's office each week. The student should then tutor for 12 hours each week in order to earn at least $375.

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Approximately 84% of scores fall between the mean and z = -1 for normally distributed scores.

In a normal distribution, approximately 68% of the scores fall within one standard deviation of the mean, both above and below. Z-scores are used to describe the location of a score relative to the mean, in terms of standard deviations.

A z-score of -1 indicates that a score is 1 standard deviation below the mean. So, if we consider all the scores that are 1 standard deviation below the mean or closer to the mean, then we would have a total of 68% of the scores, which includes the mean.

And, if we consider only the scores that are between the mean and 1 standard deviation below the mean, then we would have 84% of the scores. Hence, approximately 84% of scores would fall between the mean and z = -1 for normally distributed scores.

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If the account earns 6.5% simple interest per year , Diego will give his granddaughter a sum of $1130

To calculate the simple interest earned on an initial amount of $500 at 6.5% for 18 years, you can use the formula:

$I = Prt$, where

$I$ = interest earned

$P$ = initial amount ($500)

$r$ = interest rate (6.5%)

$t$ = time in years (18)

So, $I = 500 * 6.5 * 18 / 100 = 630$.

Thus, on the granddaughter's 18th birthday, Diego will give her $500 + 630 = $1130.

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If time to complete a constructions project is normally distributed  , then the probability the project will be finished in 62 weeks or less is 0.6915 or 69.15% .

The required probability can be calculated using the Z-score.

The Z-score is defined as a measure of how many standard deviations a value is from mean.

The mean = 60 and standard deviation = 4 of the normal distribution, the Z-score can be calculated as follows:

⇒ Z = (x - mean) / standard deviation = (62 - 60) / 4 = 0.5

Using a standard normal table, the p value for z = 0.5  is approximately 0.6915.

Therefore, the probability that the project will be finished in 62 weeks or less is approximately 0.6915.

The given question is incomplete , the complete question is

The time to complete a constructions project is normally distributed with a mean of 60 weeks and a standard deviation of 4 weeks. What is the probability the project will be finished in 62 weeks or less ?

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The solution to this system of equations is x = -6, y = 9, and z = 5.

To solve this system of equations using row operations or elementary matrices, we can first start by subtracting 4x from both sides of the first equation. This leaves us with 3x - 3x = -6. Since the x terms cancel out, this equation is now true for any value of x. We can then use this equation to substitute -6 for the x terms in the other two equations. In the second equation, we have 5y - 2y - 6 = -16. We can then subtract 5y from both sides of the equation to get -2y - 6 = -16. Dividing both sides by -2 gives us y = 9. The third equation is now 3y - 3z - 4z - 4z = -6. We can then subtract 3y from both sides of the equation to get -3z - 4z = -15. We can then divide both sides of the equation by -3 to get z = 5. Therefore, the solution to this  system of equations  is x = -6, y = 9, and z = 5.

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The original points for the parent function of f(x) = -2|1/4(x-1)| +3 is (0, 0)

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

f(x) = -2|1/4(x-1)| + 3

The above function is an absoluute value function

The parent function of an absolute value function is represented as

y = |x|

When x = 0. we haeve

y = 0

This means that (0, 0) is the point on the parent function

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By applying standard equation of a circle concept, it can be concluded that the equation that defines the circle is  (x + 4)² + (y - 3)² = 50.

Circle is a collection of points on a plane line that are all the same distance (the radius) from a given point (the center).

Standard equation of a circle can be written as:

(x - h)² + (y - k)² = r²   , where:

(h,k) = center of the circle

r = radius

We know that the radius of the circle has endpoints (-4,3) and (1,-2), which means that one of these points is the center of the circle.

Since we know that its center is in the second quadrant, we can conclude that (-4,3) is the center.

Now we can substitute these values into the equation:

   (x - h)² + (y - k)² = r²

(1 - (-4))² + (-2 - 3)² = r²

              5² + (-5)² = r²

                25 + 25 = r²

                        50 = r²

As we know the r, now we can have the standard equation of the circle:

   (x - h)² + (y - k)² = r²

(x - (-4))² + (y - 3)² = 50

 (x + 4)² + (y - 3)² = 50

Thus the equation that defines the circle is  (x + 4)² + (y - 3)² = 50.

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Amount of loaves of bread to be placed on each platter= 12 /7

The Total loaves of bread equal to 12

The Total number of platters to 7

find the amount of loaves of bread to be placed on each platter ?

In order to find the amount of loaves of bread to be placed on each platter, we will divide total loaves of bread by total number of platters.

Thus, amount of bread in each platter can be given by:

amount of loaves of bread to be placed on each platter= Total loaves of bread  / Total number of platters

Amount of loaves of bread to be placed on each platter= 12 /7

Therefore option D is correct.

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The equation of line is given by y = 3x - 1 and the slope is m = 3

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Substituting the values in the equation , we get

y = 3x - 1   be equation (1)

And , equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

So , the slope of the line is m = 3

The y intercept of the line b = -1

Hence , the equation of line is y = 3x - 1 and the graph is plotted

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The required value of integration of given function is 82.

To evaluate the integral  we need to find the anti-derivative of F(x) and then evaluate it at the limits of integration.

Since F(x) = 8 for x < 8 and F(x) = x for x ≥ 8, we can split the integral into two parts, one from 0 to 8 and another from 8 to 10

According to question:

[tex]$$\begin{aligned}& \int_0^{ 10} \mathrm{~F}(\mathrm{x}) \mathrm{dx} \\& =\int_0^8 F(x) d x+\int_8^{10} F(x) d x\end{aligned}\\$$[/tex]

The anti-derivative of

[tex]F(x)=8$ is $F(x)=8 x$, so:$$[/tex]

[tex]$$\begin{aligned}& \int_8^{10} F(x) d x \\& =\left.\left(x^2 / 2\right)\right|_8 ^{10} \\& =\left(10^ 2 / 2\right)-\left(8^2 / 2\right) \\& =50-32 \\& =18\end{aligned}$$[/tex]

Putting it all together

[tex]$\int_0^10 \mathrm{~F}(\mathrm{x}) \mathrm{dx}=64+18=82$[/tex]

So, the value of the integral [tex]$\int_0^{10} F(x) d x$[/tex] is 82.

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Complete question: