Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of $203. Ming sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220. Find the cost each of one small box of oranges and one large box of oranges.


help :((

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]

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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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:

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:

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 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 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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Model A shows the 3-D shape of the molecule, but model B does not. Then the correct option is C.

The compound can be represented in the form of 3-D shape and as well as chemical formula.

The particles are bound together, this becomes simpler to comprehend the precise structure or architecture of the compound when model A depicts the molecule in three dimensions.

Model A shows the 3-D shape of the molecule, but model B does not.

Then the correct option is C.

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Answer:

Step-by-step explanation:

According to the diagram MK is the angle bisector of  ∠LMJ in the triangle LMJ.

Use angle bisector theorem, which states:

Applied to the given triangle, the ratios are:

Use segment addition postulate and substitute known values to get:

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

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 answer is P(>204.3) = 0.5000

There are an infinite number of real numbers > 204.3, but an equally infinite number of real numbers < 204.3

The chance of randomly selecting a number >204.3 is 1/2 or 50%

or for 4 decimals: 50.0000%

The probability of an event can be calculated via chance formula with the aid of truly dividing the favorable range of effects by means of the whole number of feasible effects.

Opportunity = the wide variety of ways of achieving fulfillment. The whole range of viable effects. As instance, the possibility of flipping a coin and it being head is ½, because there is 1 way of having a head and the whole range of viable effects is two (a head or tail).

Chance is the department of mathematics that research the possible outcomes of given occasions together with the outcomes' relative likelihoods and distributions.

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Answer:

isn't that the midpoint formula??

Answer:

1 999 000

Step-by-step explanation:

Formula:

[tex]1+2+3+.\ .\ .+n=\frac{n\times \left( n+1\right) }{2}[/tex]

………………………………………

Then

[tex]1+2+3+....+1997+1998+1999=\frac{1999\times \left( 1999+1\right) }{2}[/tex]

[tex]1+2+3+....+1997+1998+1999=\frac{1999\times \left( 2000\right) }{2}[/tex]

[tex]1+2+3+....+1997+1998+1999=\frac{3998000 }{2}[/tex]

[tex]1+2+3+....+1997+1998+1999=1999000[/tex]

Answer:

a. x = total - $5

b. x = $6

c. x = $10

Step-by-step explanation:

a. pen + book = total

Let x = book

$5 + x = total

x = total - $5

b. pen + book = total

Total = 411

$5 + x = $11

x = $11 - $5

x = $6

c. pen + book = total

Total = $15

$5 + x = $15

x = $15 - $5

x = $10

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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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]

Answer:

72°

Step-by-step explanation:

Adjacent angles of a rhombus are supplementary, so

Since opposite angles of a parallelogram are congruent, angle BCD is congruent to angle BAD.

The measure of angle BAD is 3(22)+6 = 72°

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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The set that can represent an exponential function is the one in option c.

An exponential function is of the form:

[tex]f(x) = A*(b)^x[/tex]

So, as x increases by one unit, we multiply the previous number by b.

From the given options, the only one that can represent an exponential function is the third one:

(1, 1/2) , (2, 1/4) , (3, 1/8) ( 4, 1/16)

As you can see, as x increases, the value of y keeps being divided by 2.

This exponential function is:

[tex]f(x) = 1*(1/2)^x = (1/2)^x[/tex]

Evaluating it, we get:

[tex]f(1) = (1/2)^1 = 1/2\\\\f(2) = (1/2)^2 = 1/4\\\\f(3) = (1/2)^3 = 1/8\\\\etc...[/tex]

Then we conclude that the correct option is the third one.

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Answer:

-10+25m

Step-by-step explanation:

We can write the equation  as (-5)(2-5m)

Distribute: -5*2 = -10, -5m*-5 = 25m

Put the answers together: -10+25m

The reciprocal is determined by interchanging y with 2x to have y/2x. Hence the reciprocal of 2x/y is y/2x

The reciprocal is determined by changing the numerator for denominator

Given the expression

f(x, y) = 2x/y

The reciprocal is determined by interchanging y with 2x to have y/2x. Hence the reciprocal of 2x/y is y/2x

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The reciprocal of 2x / y is equals to y / 2x

Reciprocal is simply defined as the inverse of a value or a number.

For example If x is a real number, then its reciprocal will be 1/x.

Therefore, the reciprocal of 2x / y can be calculated as follows:

Reciprocal of 2x / y =

Hence,

[tex]\frac{1}{\frac{2x}{y} } = 1 X \frac{y}{2x}[/tex]

Therefore, the reciprocal of 2x / y = y / 2x

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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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Answer:

55 white

Step-by-step explanation:

So ratio 5:4 is essentially saying, for each 5 white marbles, there are 4 red ones. This can be represented in the equation: 5x+4x=99. We specifically want an integer solution. Because what is 1.2 of a marble? And what is -1 marbles? So as x increases by 1, the entire thing increases by 9. This gives you the equation: 9x=99 which gives you x=11. So there are 55 white and 44 red.

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]

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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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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The equation x² − 10x − 11 = 0 that is equivalent to (x – 5)² = 36. Then the correct option is A.

The equivalent is the expressions that are in different forms but are equal to the same value.

The equation is given below.

x² − 10x − 11 = 0

Then the equation can be written as

x² − 10x + 25 – 25 − 11 = 0

                        (x – 5)² = 36

Then the correct option is A.

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The proportional relationship is correctly graphed by graph vs.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

In this problem, the relationship that gives the montant M considering the number of items sold n is:

M = 3n.

Considering that the montant is the vertical axis, the graph is composed by points (n, 3n), that is, points (100, 300), (200, 600) and so on, hence the graph is graph vs.

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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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