Can 10 people be divided into two groups with a ratio of 1 : 2? Explain.

Consider the prime factorization of 20!.

[tex]20! = 20 \times 19 \times 18 \times \cdots \times 3 \times 2 \times 1[/tex]

The LCM of 1, 2, ..., 20 must contain all the primes less than 20 in its factorization, so

[tex]M = 2 \times 3 \times 5 \times 7 \times 11 \times 13 \times 17 \times 19 \times m[/tex]

where [tex]m[/tex] is some integer not divisible by any of these primes.

Compare the factorizations of the remaining divisors of 20!, and check off any whose factorizations are already contained in the product of primes above.

[tex]4 = 2^2[/tex] - missing a factor of 2

[tex]6 = 2\times3[/tex] - ✓

[tex]8 = 2^3[/tex] - missing a factor of 2²

[tex]9 = 3^2[/tex] - missing a factor of 3

[tex]10 = 2\times5[/tex] - ✓

[tex]12 = 2^2\times3[/tex] - missing a factor of 2

[tex]14 = 2\times7[/tex] - ✓

[tex]15 = 3\times5[/tex] - ✓

[tex]16 = 2^4[/tex] - missing a factor of 2³

[tex]18 = 2\times3^2[/tex] - missing a factor of 3

[tex]20 = 2^2\times5[/tex] - missing a factor of 2

From the divisors marked "missing", we add the necessary missing factors to the factorization of [tex]M[/tex], so that

[tex]M = 2 \times 3 \times 5 \times 7 \times 11 \times 13 \times 17 \times 19 \times 2^3 \times 3[/tex]

Then the LCM of 1, 2, 3, …, 20 is

[tex]M = 2^4 \times 3^2 \times 5 \times7 \times 11 \times 13 \times17 \times 19[/tex]

[tex]\implies \boxed{M = 232,792,560}[/tex]

Answer:

i got 12.2

Step-by-step explanation:   (5x-3) +73 =131 is the equation and from that x = 12.2

The mean of the distribution that follows the uniform probability distribution is 29.5 minutes.

The mean is the average or the most common value in a data set of numbers.

Since the distribution follows the uniform probability distribution, which is a type of probability distribution that gives all outcomes equal chances, it implies that the set of 18 values between 21 and 38 can result in a total value of 531 minutes.

The total value between 21 and 38 minutes = 531 minutes

The total number of values = 18

The average or mean = 29.5 (531/18)

Thus, the mean of the distribution that follows the uniform probability distribution is 29.5 minutes.

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Answer: ? = 72

Step-by-step explanation:

   We will set up a proportion to solve.

[tex]\displaystyle \frac{?}{56} =\frac{45}{35}[/tex]

   Now, we will cross-multiply.

? * 35 = 56 * 45

35? = 2,520

? = 72

The binomial with degree 2 is 3x + 3x²

A mathematical expression consisting of two terms connected by a plus sign or minus sign.

As, the binomial with degree 2 means the polynomial whose highest power of the coefficient is 2.

Also, binomial is polynomial having two terms.

Hence, the binomial with degree 2 is 3x + 3x².

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The area of the given trapezium ​is 1781 cm².

Area of the trapezium = ½(a + b) × h

Given;

AB = 60cm , AD = 26cm and DC = 77 cm

Area = ½(60 + 77) × 26

Area = ½(137)× 26

Area = 1781 cm²

Hence, the area of the given trapezium ​is 1781 cm².

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The value of the angle c will be 50°. Option C is correct.

An angle measure is the measurement of the angle created by two rays or arms at a shared vertex in geometry. A protractor is used to measure angles in degrees (°).

If the two line segment intersects at each other the angle formed by the intersecting lines will be the same.

From the given digrame,∠x =50°

Hence option C is correct.

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Using sampling concepts, it is found that the 100 students surveyed in this example would be the would be the sample.

It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.

Hence, in this problem:

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By using the perimeter formula for an orthogonally oriented rectangle set on a Cartesian plane, we find that the perimeter of the figure is 68/3 units.

In this question we have a rectangle oriented with respect to the two orthogonal axes of a Cartesian plane. In this case, the vertices of the figure are of the form:

A(x, y) = (a, b), B(x, y) = (c, b), C(x, y) = (a, d), D(x, y) = (c, d)

And the perimeter of this rectangle is equal to this:

p = 2 · |a - c| + 2 · |b - d|

If we know that a = - 5, b = 2, c = 2, d = - 7/3, then the perimeter of the rectangle is:

p = 2 · |- 5 - 2| + 2 · |2 - (- 7/3)|

p = 14 + 26/3

p = 68/3

By using the perimeter formula for an orthogonally oriented rectangle set on a Cartesian plane, we find that the perimeter of the figure is 68/3 units.

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The length of the 4th side on quadrilateral ABCD will be D. 8cm.

From the information given, we are told that the lengths of the three longest sides in quadrilateral ABCD are 24 feet, 16 feet, and 12 feet long.

In this case, the side will be:

24/16 = 12/x

x = (16 × 12)/24

x = 8

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Answer:

An outlier is something that is out of place compared to the rest of the group. For example, If you had the numbers 3,4,5,4,3,4, and 19, 19 would be the outlier.

Step-by-step explanation:

An outlier is a number that's far away from the rest of your data.

For example, if we look at the numbers 3, 2, 4, 5, 27, and 1, you can likely consider 27 to be an outlier because it's so far away from the rest of the data.

The specific definition of how far something has to be from the rest of the data to be an outlier depends entirely on the situation, but in general: if a number obviously sticks out from the rest, it's probably an outlier.

Answer:

8. 0

9. undefined

Step-by-step explanation:

8. 0

> because the y variable is the same for all x-values, this is a horizontal line. Horizontal lines have a slope of 0.

  > Thinking of slope as rise over run: we will always rise 0, and run __ from any two points--0 divided by any number is always 0

9. undefined

> because the x variable is always the same, no matter what y variable we graph, we will have the same outcome. So, this would look like a straight line, which have an undefined slope.

   > If you think of a slope as rise / run; if you go from any two points, there will be a 0 in the denominator--which is undefined

hope this helps!! have a lovely day :)

Answer: 4230.14

Step-by-step explanation:

The amount that the balance is multiplied by each month is

[tex]\frac{2448}{2040}=1.2[/tex].

So, after t months, the balance is [tex]1700(1.2)^{t-1}[/tex].

Substituting in t=6, we get the balance is

[tex]1700(1.2)^{6-1}=\boxed{4230.14}[/tex], to the nearest hundredth.

Answer:

10sqrt(7)

Step-by-step explanation:

[tex]4 \sqrt{7} + 3 \sqrt{28} \\ \\ 4 \sqrt{7} + 3(2 \sqrt{7} ) \\ \\ 4 \sqrt{7} + 6 \sqrt{7} = 10 \sqrt{7} [/tex]

Answer:

36 minutes

Step-by-step explanation:

 Speed = 60 km/hr

 time = 30 mins = 30/60 = 1/2 hour

 [tex]\sf \boxed{\bf Distance =speed * time}[/tex]

                   [tex]\sf = 60 * \dfrac{1}{2}\\\\ = 30 \ Km[/tex]

Distance = 30 km and speed = 50 km/hr

    [tex]\sf \boxed{\bf Time =\dfrac{Distance}{speed}}[/tex]

               [tex]\sf = \dfrac{30}{50}\\\\=\dfrac{3}{5} \ hour\\\\=\dfrac{3}{5}*60\\\\= 3*12\\\\= 36 \ minutes[/tex]

Answer:

0.6 hours

Step-by-step explanation:

• First calculate the distance travelled at 60km/h:

distance = speed x time

              = 60  x  0.5

              = 30 km

• Now calculate the time taken at 50 km/h:

time = distance/ speed

       = 30 / 50

       = 0.6 hours

       = 0.6 x 60 min

      = 36 minutes

The best approximation for the solution of the system of equations is (0.88,0.65).

Given a system of equations is y=-(2/5)x+1 and y=3x-2.

A system of linear equations consists of two or more equations, and one attempts to solve the equations together.

To find the best approximation solution solve the system of equations.

The given system of equations are

y=-(2/5)x+1     .......(1)

y=3x-2           .......(2)

Firstly, substitute the value of y into equation (1) to find the value of x, we get

3x-2=-(2/5)x+1

Now, we will add (2/5)x in both sides, we get

3x-2+(2/5)x=-(2/5)x+1+(2/5)x

3x-2+(2/5)x=1

Further, we will add 2 on both sides, we get

3x-2+(2/5)x+2=1+2

3x+(2/5)x=3

17x/5=3

Furthermore, we will multiply both sides with 5, we get

5×(17x/5)=3×5

17x=15

Now, divide both sides with 17, we get

17x/17=15/17

x=0.88

Further, we will find the value of y by substituting the value of x in equation (2), we get

y=3(0.88)-2

y=2.65-2

y=0.65

Hence, the best approximation for the solution of the system of equations y=-(2/5)x+1 and y=3x-2 is (0.88,0.65).

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Harper goes on a tour where the ticket price is $10.50 along with 29 people according to the given expression. Solving the given expression for 'n' results in the required number.

Solving an expression algebraically involves basic operations like addition, subtraction, multiplication, and division.

Given that,

A tour company charges a given price per ticket based on the number 'n' of people who take the tour.

The maximum number of people who are allowed to take the tour is 35. I.e., n ≤ 35.

The price per ticket is $20 for n < 10 people and the price per ticket is given by the expression 20-(n-10)/2 for n > 10 people.

Harper goes on a tour where the ticket price is $10.50.

Since the price is less than $20, so the number of people who went on this tour is known by the expression 20-(n-10)/2 for n > 10 people.

So, solving the given expression:

20-(n-10)/2 = $10.50

-(n-10)/2 = 10.50 - 20

-(n-10)/2 = -9.5

(n-10) = 9.5 × 2

n -10 = 19

∴ n = 19 + 10 = 29

Therefore, 29 people went on this tour for a ticket price of $10.50.

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Answer:

the answer is 1.1

Step-by-step explanation:

log13 =1.113

which is approximately 1.1

The value of given logarithmic expression is 1.1. Therefore, option C is the correct answer.

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.

The given logarithmic expression is log13.

The result can be shown in multiple forms.

Exact Form:

log(13)

Decimal Form:

1.11394335....

≈ 1.1

Therefore, option C is the correct answer.

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The 0.375 terminating decimals are equivalent to 3/8 option second is correct.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

The fraction is:

= 3/8

After dividing with 8

= 0.375

Thus, the 0.375 terminating decimals are equivalent to 3/8 option second is correct.

The complete question is:

Which of the following terminating decimals is equivalent to 3/8?

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Answer:

Option 2:    (0,-2) and (1,0)

Step-by-step explanation:

Solutions to graphed systems of equations are the places where the graphs overlap/intersect.

For this system of equations, the red and blue graphs overlap at two points.

Since all of the answers are given as ordered pairs, it is important to know what an ordered pair means.

An ordered pair, (x,y), is a pair of numbers, written in parentheses, with a comma between them, that represent the coordinates of a point when graphed on a coordinate system.  Each coordinate measures the distance in a certain direction from the origin.  The origin is the special point at the intersection of the axes.  The axes are the dark horizontal and vertical lines with numbers next to them, representing the value at that distance along the axis.

The first coordinate of an ordered pair is the x-coordinate, and measures the horizontal distance from the origin.  Points to the right of the origin are defined to have a positive x-coordinate, and points to the left of the origin are defined to have a negative x-coordinate.

The second coordinate of an ordered pair is the y-coordinate, and measures the vertical distance from the origin.  Points above the origin are defined to have a positive y-coordinate, and below the origin are defined to have a negative x-coordinate.

Looking directly below the origin, the blue curve and the red line intersect.  Since they intersect directly below the origin, the ordered pair there must have an x-coordinate of zero because no left/right movement was required to get to this point.  Only a vertical movement was necessary.  The number on the vertical axis tells us that this point has a height of "-2", so the ordered pair for this point is (0,-2).

Looking directly to the right from the origin, the blue curve and the red line intersect again.  Since they intersect directly to the right of the origin, the ordered pair there must have a y-coordinate of zero because no up/down movement was required to get to this point.  Only a horizontal movement was necessary.  The number on the horizontal axis tells us that this point has a horizontal value of "1", so the ordered pair for this point is (1,0).

Since the two points of intersection are (0,-2) and (1,0), the correct answer would be the second choice.

Answer:

[tex]f(x) = {2x}^{2} - 4x - 6 \\ {2x}^{2} - 4x + 3x - 6 \\ = 2x(x - 2) + 3(x - 2) \\ g(x) = {x}^{2} - 4 \\ (x + 2)(x - 2) \\ \frac{f(x)}{g(x)} = \frac{(2x + 3)(x - 2)}{(x + 2)(x - 2)} = \frac{2x + 3}{x + 2} [/tex]

[tex]\underline{\underline{\boxed{ \pink\star \: C.) \: \sf{\frac{2x +3}{x + 2}}}}}[/tex]

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Here,

[tex]\sf{f(x) = 2x^2 - x - 6}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\longrightarrow\sf{2x^2 - 4x + 3x - 6}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\longrightarrow\sf{2x(x-2)+3(x-2)}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\longrightarrow\sf{(2x+3)(x-2)}[/tex]

---------------------------------------------------

[tex]\sf{g(x) = x^2 - 4}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\longrightarrow\sf{x^2 - 2^2}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\longrightarrow\sf{(x+2)(x-2)}[/tex]

Therefore,

[tex]\huge\sf{ \frac{f(x)}{g(x)} = \frac{(2x+3)(x-2)}{(x+2)(x-2)}}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\longrightarrow \huge\sf{ \frac{2x + 3}{x + 2}}[/tex]

[tex]\boxed{\underline{\color{hotpink}{ \red \star \: ᖇEᒪᗩ᙭GᖇOᗯ \: \: }}}[/tex]

The first four terms of the sequence are -1, 6, -22, 90

A sequence is an order in which numbers occur in  a given group of numbers.

It is also numbers arranged based on a certain rule.

Analysis:

a1 = -1

for n ≥ 2

a2 = -4a1 +2

a2 = -4(-1) + 2 = 4+2 = 6

a3 = -4a2 + 2

a3 = -4(6) + 2 = -24 + 2 = -22

a4 = -4a3 +2

a4 = -4(-22) + 2 = 88 + 2 = 90

In conclusion, the first four terms of the sequence are -1, 6, -22, 90

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Answer:

135 units = x  

Step-by-step explanation:

81 is to x     as   x is to (81 + 144)

81/x = x / 225    cross multiply to get

18225 = x^2

x = 135

Answer:

b)

c=140°

a= 40°

b=40°

c)

p= 60°

q= 60°

r= 120°

d)

a=  65 °

b= 65°

c= 65°

d= 115°

e=65°

Step-by-step explanation:

Hope it helps

Answer:

B

Step-by-step explanation:

To find the length of the longest side of the triangle, first sketch the triangle. A graph paper is not needed here.

In this case we have a right-angled triangle, since the ends of the adjacent side has the same y-coordinate of 1 and the opposite side has the same y-coordinate of 5.

In a right-angled triangle, the hypotenuse side is the longest. The length of the hypotenuse side can be found using 2 methods.

1) Pythagoras' Theorem

a² +b²= c²

(adjacent)² +(opposite)²= (hypotenuse)²

Length of adjacent

= 5 -(-2)

= 7 units

Length of opposite side

= 4 -1

= 3 units

(hypotenuse)²

= 7² +3²

= 58

hypotenuse= [tex] \sqrt{58} [/tex]

2) Distance formula

Since we know that the hypotenuse side is the longest, we can simply find the length of the hypotenuse side instead of calculating the length of each side.

[tex]\boxed{{\text{Distance between 2 points}= \sqrt{(y_1 - y_2)^{2} + (x_1 - x_2)^{2} } }}[/tex]

Length of longest side

= distance between (5, 4) and (-2, 1)

[tex] = \sqrt{(4 - 1) {}^{2} + (5 - ( - 2)) {}^{2} } [/tex]

[tex] = \sqrt{3 {}^{2} + {7}^{2} } [/tex]

[tex] = \sqrt{58} [/tex]

Thus, the length of the longest side is [tex] \sqrt{58} [/tex] units.

Answer:

it is the third one

Step-by-step explanation:

third one

Answer:

x = - 3.5

Step-by-step explanation:

32 - 6x = 53 ( subtract 32 from both sides )

- 6x = 21 ( divide both sides by - 6 )

x = [tex]\frac{21}{-6}[/tex] = - [tex]\frac{7}{2}[/tex] = - 3.5

[tex]\large\boxed{x=-\frac{7}{2}}[/tex]

To solve for [tex]x[/tex], we need to isolate it on one side of the equation.

The most important part of this is knowing that whatever we do to one side of the equation, we must also do to the other.

Subtract 32 from both sides of the equation.

[tex]\begin{aligned}32-32-6x&=53-32\\-6x&=21\end{aligned}[/tex]

Divide both sides of the equation by [tex]-6[/tex].

[tex]\begin{aligned}\frac{-6x}{-6}&=\frac{21}{-6}\\x&=\boxed{-\frac{7}{2}}\end{aligned}[/tex]

The renaming of the fractions 1/10 and 1/4 using the least common denominator gives us; 2/20 and 5/20

To find the least common denominator here, we will just the least term that can divide both denominators. In this case, the least term will be 20. Thus;

1/10 = (1 * 2)/(2 * 10) = 2/20

1/4 = (1 * 5)/(4 * 5) = 5/20

Therefore renaming the fractions 1/10 and 1/4 using the least common denominator gives us; 2/20 and 5/20

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hope this helps, Plato

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation: }[/tex]

[tex]\mathbf{-8y = 7y - 5}[/tex]

[tex]\huge\textbf{Solving for the equation:}[/tex]

[tex]\mathbf{-8y = 7y - 5}[/tex]

[tex]\mathbf{7y - 5 = -8y}[/tex]

[tex]\huge\textbf{SUBTRACT 7y to BOTH SIDES}[/tex]

[tex]\mathbf{-8y - 7y = 7y - 5 - 7y}[/tex]

[tex]\huge\textbf{SIMPLIFY IT!}[/tex]

[tex]\mathbf{-15y = -5}[/tex]

[tex]\huge\textbf{DIVIDE -15 to BOTH SIDES}[/tex]

[tex]\mathbf{\dfrac{-15y}{-15} = \dfrac{-5}{-15}}[/tex]

[tex]\huge\textbf{SIMPLIFY IT!}[/tex]

[tex]\mathbf{y = \dfrac{-5}{-15}}[/tex]

[tex]\mathbf{y = \dfrac{-5\div-5}{-15\div-5}}[/tex]

[tex]\mathbf{y = \dfrac{1}{3}}[/tex]

[tex]\huge\textbf{Met your answer:}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{y = \dfrac{1}{3}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Finding the vertex of the quadratic functions, the correct statement is:

Function 1 has the larger maximum at (4, 1).

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The vertex is given by:

[tex](x_v, y_v)[/tex]

In which:

Considering the coefficient a, we have that:

For function 1, we have that:

f(x) = -x² + 8x - 15.

Hence the coefficients are a = -1, b = 8, c = -15, and the vertex is:

For function 2, we have that:

f(x) = -x² + 2x - 3.

Hence the coefficients are a = -1, b = 2, c = -3, and the vertex is:

1 > -2, hence the correct statement is:

Function 1 has the larger maximum at (4, 1).

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