What is the common ratio for the geometric sequence below, written as a fraction?

768, 480, 300, 187.5,

Taking into account the definition of a system of linear equations, the movie theater sold 35 tickets for Movie A and 12 tickets for Movie B.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

On the other hand, you know:

So, the system of equations to be solved is

[tex]\left \{ {{xa + xb=47} \atop {4xa + 5xb=200}} \right.[/tex]

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable xa from the first equation, you obtain:

xa= 47 - xb

Substituting this expression in the second equation you get:

4×(47 -xb) + 5xb= 200

Solving:

4×47 - 4xb + 5xb= 200

188 - 4xb + 5xb= 200

- 4xb + 5xb= 200 - 188

xb= 12

Remembering that xa= 47 - xb. you get: xa=47 - 12 → xa= 35

Finally, the movie theater sold 35 tickets for Movie A and 12 tickets for Movie B.

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Answer:

Question have problem.

About 25 percent of the data are greater than 20.(option a)

About 50 percent of the data are less than 15. (option b)

20 is wrongly interpreted as the median. 20 is the third quartile. The data between 11 and 20 is 50%.

A box plot is used to study the distribution and level of a set of scores. The scores are distributed into 4 groups. Each group has a value of 25%

The box plot consists of two whiskers and a box. The first whisker represent the minimum value. The second whisker represents the maximum number.

On the box, the first line to the left represents the lower (first) quartile. 25% of the score represents the lower quartile. The next line on the box represents the median. 50% of the score represents the median. The third line on the box represents the upper (third) quartile. 75% of the scores represents the upper quartile.

20 is the third quartile. Score greater than 20 is 25% (100% - 75%)

15 is the median. Scores less than 15 is 50% (100 - 50%),

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The value of the x in the linear equation of the midpoint is a 3.85.

According to the statement

We have to find that the value of the x.

So, For this purpose, we know that the

Midpoint is the point on a line segment or an arc that is equidistant, when measured along the line or the arc, from both endpoints.

From the given information:

Given K is the midpoint of GH, GK = 5x - 3,and GH = 2x + 24

As the midpoint the both equation are equal to the each other.

Then

GK = GH

5x - 3 = 2x + 24

5x+2x = 24+3

7x = 27

x = 27/7

x = 3.85.

So, The value of the x in the linear equation of the midpoint is a 3.85.

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The minute hand has moved 25 times out of a possible 60 from the top of the clock as of 4:25. 150 degrees is 25 multiplied by 6 degrees. Simply subtracting those degrees from the above calculation, the angle from the minute hand to the hour hand is equal to 360 degrees. 342.5 degrees is 360 minus 17.5.

An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex. Using a protractor, angles are measured in degrees (°).

An angle is a figure in plane geometry that is created by two rays or lines that have a common endpoint. The Latin word "angulus," which means "corner," is the source of the English word "angle." The common endpoint of two rays is known as the vertex, and the two rays are referred to as sides of an angle. When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the word "angle" originates.

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Answer:

Step-by-step explanation:

The amount of fencing needed to enclose the secular pond is 72.22 feet

The perimeter of a shape is the sum of the side lengths of the shape

For all regular quadrilaterals, you add up the side lengths to determine the area

The given parameter is

Diameter, d = 23 feet

The radius is calculated as

r = d/2

So, we have

r = 23/2

This gives

r = 11.5 feet

The circumference of the circle is calculated as

C = 2pi r

So, we have

C = 2 * 3.14 * 11.5 feet

Evaluate the product

C = 72.22 feet

Hence, the amount of fencing needed to enclose the secular pond is 72.22 feet

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Answer:

Step-by-step explanation:

A mathematical model that gives the demand y in terms of the price x in dollars.

y = 1400/ x

This is further explained below.

Generally, The following formula would apply in the situation when there is an inverse link between y and x:

y = k/x

where k is constant.

In a relationship with an inverse connection, one variable will tend to decrease as the other variable grows.

y denotes the amount of demand.

x is equivalent to the cost.

400 = k/3.5

k = 400 * 3.5

k = 1,400

The following is the formula for the mathematical model that calculates the demand y based on the price x in dollars:

y = 1400/ x

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Answer:

5 5/8 pounds

Step-by-step explanation:

I added the fractions and got that

Answer: So that when we subtract the original number from the multiple, the repeating part cancels out. If we multiply by 10, we get 10x = 2.

Step-by-step explanation:

It should be noted a term is one of the two numbers that are in the ratio. An example is that in the "ratio of a to b" a is the first term and b is the second term.

It should be noted that it's important to understand ratio and use ratio language to describe the relationship between two quantities.

For example, it van be stated that the ratio of wings to beaks in the bird house at the zoo is 2:1, this implies that b for every 2 wings there is 1 beak.

Therefore, it should be noted a term is one of the two numbers that are in the ratio. An example is that in the "ratio of a to b" a is the first term and b is the second term.

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Answer:

[tex]\frac{1}{8}[/tex]

Step-by-step explanation:

Given : A scientist had [tex]\frac{3}{4}[/tex] of a bottle of a solution.

The part of the solution she used in the experiment :  [tex]\frac{1}{6}[/tex]

The part of bottle she used is given by :

[tex]\frac{1}{6} *\frac{3}{4}[/tex]

= [tex]\frac{1*3}{4*6}[/tex]

= [tex]\frac{3}{24}[/tex]

Simplify = [tex]\frac{1}{8}[/tex]

Hence, she used [tex]\frac{1}{8}[/tex] of the bottle .

If a > b then;

a + -b = a positive number

If b > a then;

a + -b = a negative number

If both addends are positive or if the positive addend has a greater absolute value than the negative addend, the sum will be positive. If both addends are negative or if the negative addend has a greater absolute value than the positive addend, the sum will be negative.

Answer:

C(x) = (1/9)x + 242/9

Step-by-step explanation:

Let x = number of pages.

Let y = cost.

We are given two ordered pairs, (x, y):

(100, 38) and (208, 50)

We must find the equation of the line that passes through these two points.

y = mx + b

m = (y_2 - y_1)/(x_2 - x_1) = (50 - 38)/(208 - 100) = 12/108 = 1/9

y = (1/9)x + b

Use point (100, 38) as x and y to find b.

38 = (1/9)(100) + b

38 × 9 = 100 + 9b

9b + 100 = 342

9b = 242

b = 242/9

The equation is:

y = (1/9)x + 242/9

Answer: C(x) = (1/9)x + 242/9

Answer:

Conditional Probability

Step-by-step explanation:

Conditional probability refers to the chances that some outcome occurs given that another event has also occurred. It is often stated as the probability of B given A and is written as P(B|A), where the probability of B depends on that of A happening

The quotient after the long division of 35/456 is 0.076.

So, after the long division:

Therefore, the quotient after the long division of 35/456 is 0.076.

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Answer:

[tex]c=\frac{bd}{ad+b}[/tex]

Step-by-step explanation:

By isolating the term c, we are trying to arrive at the equation c= ____.

[tex]a=b(\frac{1}{c}-\frac{1}{d} )[/tex]

Divide both sides by b:

[tex]\frac{a}{b}= \frac{1}{c}-\frac{1}{d}[/tex]

Add [tex]\bf{\frac{1}{d}[/tex] to both sides:

[tex]\frac{1}{c} =\frac{a}{b} +\frac{1}{d}[/tex]

Rewriting the right-hand side as a single fraction:

[tex]\frac{1}{c} =\frac{a(d)}{b(d)} +\frac{1(b)}{d(b)}[/tex]

[tex]\frac{1}{c} =\frac{ad+b}{bd}[/tex]

Find the expression of c:

[tex]1\div\frac{1}{c} =1\div\frac{ad+b}{bd}[/tex]

[tex]\bf{c=\frac{bd}{ad+b}[/tex]

Additional:

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Answer:

[tex]c=\dfrac{bd}{ad+b}[/tex]

Step-by-step explanation:

Given equation:

[tex]a=b\left(\dfrac{1}{c}-\dfrac{1}{d}\right)[/tex]

Divide both sides by b:

[tex]\implies \dfrac{a}{b}=\dfrac{b}{b}\left(\dfrac{1}{c}-\dfrac{1}{d}\right)[/tex]

[tex]\implies \dfrac{a}{b}=\dfrac{1}{c}-\dfrac{1}{d}[/tex]

Add 1/d to both sides:

[tex]\implies \dfrac{a}{b}+\dfrac{1}{d}=\dfrac{1}{c}-\dfrac{1}{d}+\dfrac{1}{d}[/tex]

[tex]\implies \dfrac{a}{b}+\dfrac{1}{d}=\dfrac{1}{c}[/tex]

[tex]\textsf{Simplify the left side by applying the fraction rule} \quad \dfrac{p}{q}+\dfrac{r}{s}=\dfrac{ps+qr}{qs}:[/tex]

[tex]\implies \dfrac{ad+b}{bd}=\dfrac{1}{c}[/tex]

Cross multiply:

[tex]\implies c(ad+b)=bd[/tex]

Divide both sides by (ad + b):

[tex]\implies \dfrac{c(ad+b)}{ad+b}=\dfrac{bd}{ad+b}[/tex]

[tex]\implies c=\dfrac{bd}{ad+b}[/tex]

The point that is 1/3rd of the distance from (-4.5,0) to (0,9) is (-3,3).We use a formula similar to the midpoint formula for finding the point.

We have been given two points (-4.5,0) and (0,9), we have to find the point is on the line formed by these two points and is 1/3rd away. We don't need to find the distance between these two points to find the asked point. We have to use a formula that is similar to finding the midpoint of a line. For two points (a,b) and (x,y) the midpoint is ([tex]\frac{a+x}{2} ,\frac{b+y}{2}[/tex]).We used equal parts of the two points to find the midpoint, for 1/3rd we will be using uneven parts of the two points.

[tex]x_{1} =\frac{2}{3} (-4.5)+\frac{1}{3} (0)=-3[/tex]

[tex]y_{1} =\frac{2}{3} (0)+\frac{1}{3} (9)=3[/tex]

Therefore the point that lies 1/3rd of the distance from (-4.5,0) and (0,9) is (-3,3).

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Step-by-step explanation:

use fog

3(1/3x-3)+9

=x

use gof

1/3(3x+9)-3

=x

we can see that both results give us x hence they are inverse

[tex]3 \cdot 3^2 + 8 : 2 - (4+3) =[/tex]

[tex]3 \cdot 3^2 + 4 - 7=[/tex]

[tex]3 \cdot 9 +4 -7=[/tex]

[tex]27 + 4 - 7 = 24[/tex]

==axel134==

The Area of the triangle with base 6 and height 4 is 12 square units.

Area of triangle with base "b" , and height "h" can be calculated using the formula

Area = 1/2*b*h  .

From the figure

It is given that height of triangle = 4

base of the triangle = 6

By using the formula for Area of the triangle we get ,

Area = 1/2*b*h

Substituting the value of base and height from above we get ,

Area= 1/2*6*4

=(6*4)/2

=24/2

=12

Therefore ,  the Area of the triangle with base 6 and height 4 is 12 Square units .

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Answer: use the 'grouping method' to get your answer (answer choice 'B')

Step-by-step explanation:

Take your first two terms, 2x^3 and 4x^2 and find a GCF. In this case, 2x^2 can go into both terms. Your first side should look like this 2x^2(x+2).

Take your last two terms (6x+12) and find a GCF. In this case, your GCF is 6 because both terms can fit into 6. Your second side should look like this 6(x+2).

We know we did this problem correctly because we can see that both parenthesis state the same thing, which is (x+2).

Your equation after finding a GCF in both sets should look something like this; 2x^2(x+2)+6(x+2).

Now, combine the 2x^2 and 6 together to get (2x^2+6) in one parenthesis set. Your second should include ONLY ONE of the '(x+2)'s.

Your final answer should look like this; (2x^2+6)(x+2). Therefore, your answer choice is 'B'.

Hope this helps, dawg.

The scale factor going from the first to the second triangle according to the task content is; 2.

The length of the longest side of.the triangle as required in the task content is; 24.

According to the task content, it follows that the two triangles are similar.

Therefore, the corresponding sides of such triangles must be in proportion.

Therefore the scale factor from the first to the second triangle as required is;

Scale factor = 12/6; since the shortest sides are corresponding sides.

Scale factor = 2.

Hence, since the length of the longest side in the first triangle is 14, the length of the longest side in the second triangle is;

L = 2 × 14

L = 28

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a. The distance around the park is 180 yards

b. QM = 18 yards

c. It takes 49 minutes  to travel the entire distance

a. The distance around the yard is given as;

PQ + QR + PQ

Where;

Total = 40 + 70 + 70 = 180 yards

b. To determine QM, we use the Pythagorean theorem;

PQ² = QM² + 1/2 PR²

40² = QM² + (35. 5)²

1600 = QM² + 1260. 25

Make 'QM' the subject

QM² = 1600 - 1260. 25

QM = √339. 75

QM = 18 yards

c. Average speed = 150 yards/ per minute

Total distance = 180 yards

Time = Average speed/ distance

Time = 150/ 180

Time = 0. 8 3 × 60

Time = 49 minutes

Thus, the distance around the park is 180 yards

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Answers in bold:

Problem 4) Shift 6 units left, 1 unit down

Problem 5) Shift 3 units right. Vertically stretch by a factor of 2.

The graphs are below.

==========================================================

Explanation:

In problem 4, the parent function is y = x^2

Replace every x with (x+6) and it will shift the parabola 6 units left. Why left instead of right? It's because the xy axis is moving 6 units to the right. Each old input x is now 6 units larger to get x+6. The xy axis moving 6 units right gives the illusion the curve shifts 6 units left. It's a bit backwards I know.

Luckily the -1 at the end is straight forward and it shifts everything down by 1 unit. This is because we subtract 1 from the y coordinate.

So that's how we get the "6 units left, 1 unit down" translation. No horizontal nor vertical dilations occur.

I recommend using GeoGebra or Desmos or similar to graph out the two equations, to see the comparison.

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

For problem 5, the parent function is y = |x|

Replacing every x with x-3 means that the xy grid moves 3 units left. That gives the illusion the V shaped curve is moving 3 units right.

The 2 out front will double each y coordinate. This visually stretches the graph by a factor of 2. It is now twice as tall as it was before. This is equivalent to doing a horizontal compression (since the graph is more skinny now).

Answer:

4.  Translated 6 units left and 1 unit down.

5.  Translated 3 units right and stretched vertically by a factor of 2.

Step-by-step explanation:

Transformations

[tex]\textsf{For $a > 0$}[/tex]

[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}[/tex]

[tex]a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}[/tex]

[tex]f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $\dfrac{1}{a}$}[/tex]

[tex]-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}[/tex]

[tex]f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}[/tex]

Parent function:

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

Translated 6 units left:

Add 6 to the x-variable of the function:

[tex]\implies f(x+6)=(x+6)^2[/tex]

Translated 1 unit down:

Subtract 1 from the function:

[tex]\implies f(x+6)-1=(x+6)^2-1[/tex]

Parent function:

[tex]f(x)=|x|[/tex]

Translated 3 units right:

Subtract 3 from the x-variable of the function:

[tex]\implies f(x-3)=|x-3|[/tex]

Stretched vertically by a factor of 2:

Multiply the function by 2:

[tex]\implies 2f(x-3)=2|x-3|[/tex]

Step-by-step explanation:

The formula for circumference when the diameter is given is C = π • d

C = circumference

π = pi

d = diameter

So to find the circumference plug in the number (18 - diameter).

C = π • 18

C = 56.5486677646

If needed to round to nearest ...

tenth = 56.5

hundredth = 56.55

However, if the directions say to use 3.14 for π (pi) then the answer would be different.

C = 3.14 • 18

C = 56.52

Hope this helps :)

The required possible side length of the tablecloth is 11ft x 11ft.

A square is for sided regular polygon, where the length of all sides is identical and the angle between the adjacent side is 90°.

Given the following parameters

Area of fabric =121 ft² of fabric.

She wants to make a square tablecloth for her dining room table.\

Area of the square = a²

121 = a²

a = √121

a = 11 ft

Thus, the required possible side length of the tablecloth is 11ft x 11ft.

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Here are the values of the expressions :

a. 3(4) = 12

b.  4 + 11 + (-4)  = 11

c. 3.2(2)  = 6.4

d. | (-2) + (-2) + (-2) | = 6

e. |2 (-7.5) |  = 15

f. 10 1/5(-5) = -51

a. 9(410)  = 3690

b. 6(592) = 3552

Take not of the following rules:

When a term is in bracket, it means that the values should be multiplied : 2 (3) = 2 x 3 = 6

When numbers are between this sings | |, it means that the answer should be an absolute value. e.g. | - 5 - 5 | = 10

When a negative sign is multiplied by a positive sign, the result would be a negative sign. -1 x + 1 = -1

a. 3(4) = 3 x 4 = 12

b.  4 + 11 + (-4)

= 4 + 11 - 4 = 11

c. 3.2(2)  = 3.2 x 2 = 6.4

d. | (-2) + (-2) + (-2) |

|- 2 - 2 - 2| = 6

e. |2 (-7.5) |

|2 x -7.5| = 15

f. 10 1/5(-5)

10 1/5 x - 5

51/5 x - 5 = -51

a. 9(410)

= (9 x 400) + (10 x 9)

3600 + 90 = 3690

b. 6(592)

= (6 x 500) + (92 x 6)

3000 + 552

3552

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