9.4 Board Game Sales
A small company is selling a new board game, and they need to know how many to
produce in the future.
After 12 months, they sold 4 thousand games; after 18 months, they sold 7 thousand
games; and after 36 months, they sold 15 thousand games.
1. Could this information be reasonably estimated using a single linear model?
2. If so, use the model to estimate the number of games sold after 48 months. If not,
explain your reasoning.

Answer:

4

Step-by-step explanation:

the nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex]r^{n-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = 2 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{4}{2}[/tex] = 2

then

a₂₈ = 2 [tex](2)^{27}[/tex]

a₂₆ = 2 [tex](2)^{25}[/tex]

using the rule of exponents

[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] , then

[tex]\frac{a_{28} }{a_{26} }[/tex]

= [tex]\frac{2(2)^{27} }{2(2)^{25} }[/tex] ( cancel 2 on numerator/ denominator )

= [tex]\frac{2^{27} }{2^{25} }[/tex]

= [tex]2^{(27-25)}[/tex]

= 2²

= 4

To prove <ABC is congruent to <ABD

congruent figures are those that match in terms of size and shape or are the same size and shape. The geometry of congruent angles

Congruent refers to something that is "exactly equal" in terms of size and shape. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, and stack them on top of one another.

According to the question

Both the triangles are right-angled

From RHS criterion

∠ABC ≅ ∠ABD

Definition of angle bisector segment addition property

The line or line segment that splits an angle into two equal pieces is known as the internal angle bisector (internal angle bisector)

definition of congruent angle transitive property

According to the transitive property of congruence, all shapes are congruent to one another if two shapes are congruent to a third shape.

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After Solving the provided question, the Michelle's point value after the third round is -4.5 by the third round

A value is computed using operands and a math operator as part of the mathematical "operation." In order to be applied to the provided operands or numbers, the math operator's symbol has predetermined rules.

Mathematical operations like addition (+), subtraction (-), multiplication (*), and division (**) take precedence over one another. Neither of the two operators can be used to solve an equation by itself. The brackets in any equation, whether arithmetic or algebraic, must be evaluated first, according to the order of operations principles, which we must abide by. The second place is where the order will be determined. After evaluating addition and subtraction, we'll analyze multiplication and division.

[tex]she starts off with a negative 2.3 of you add positive 4.5 = > (-2.3) + 4.5 = 2.2[/tex]

but after that, she lost another 6.7 points, leaving her with a negative score of 4.5.

[tex]= > 2.2 - 6.7 = ( -4.5 )[/tex]

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Hence, the equation is of the form [tex]2.5x+3.5y=52.50[/tex].

What is the system of equation?

A system of equations, also known as a set of simultaneous or an equation system, is a finite set of equations for which we sought the common solutions.

Here given that,

Nolan is going to a carnival that has games and rides. Each game costs $[tex]2.50[/tex] and each ride costs $[tex]3.50[/tex]. Nolan spent $[tex]52.50[/tex] altogether on [tex]17[/tex] games and rides.

So, let us assume that the number of games are [tex]x[/tex] and the number of rides are [tex]y[/tex].

So, the equation is of the form

[tex]2.5x+3.5y=52.50 ........(1)[/tex]

And Noaln spent altogether $[tex]52.50[/tex] on [tex]17[/tex] games and rides.

So,

[tex]x+y=17[/tex]

Then,

[tex]2.5x+2.5y=2.5(x+y)\\As,\\x+y=17\\So,\\=2.5(17)\\\\=42.5.....(2)[/tex]

Now, subtract equation [tex](2)[/tex] from equation [tex](1)[/tex], we get

[tex]x=52.5-42.5\\\\x=10[/tex]

[tex]y=17-10\\y=7[/tex]

So the equation is of the form

[tex]2.5(7)+3.5(10)=52.50\\17.5+35=52.50\\52.50=52.50[/tex]

Hence, the equation is of the form [tex]2.5x+3.5y=52.50[/tex].

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Answer:

Line down the middle

Step-by-step explanation:

There is only one line of symmetry in this shape because there is no rotational symmetry. Its a line down the middle.

5+2y=13, y-5=2(x-1), y/2 = x+7, x=-4 are linear equations.

An equation is said to be linear if the maximum power of the variable is consistently 1.

Another name for it is a one-degree equation.

A linear equation with one variable has the conventional form Ax + B = 0.

In this case, the variables x and A are variables, while B is a constant.

A linear equation with two variables has the conventional form Ax + By = C.

Here, the variables x and y, the coefficients A and B, and the constant C are all present.

As explained above about linear equation from given option we can verify that

5+2y = 13 can be written as 2y = 8 or 2y-8=0 which represents linear equation in one variable.

[tex]y = \frac{1}{2x^{2} +7}[/tex] cannot be written in any linear form and its highest degree is 2. So, it is not linear equation.

y-5= 2(x-1) can be written as 2x-y=-3 which is in the form of linear equation in two variables. So, it is linear equation in two variables.

x = -4 can be written as x + 4 = 0 which represents linear equation in one variable.

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The equation Vy = a sin(k(x - d)) + c is an equation for a sine wave. A sine wave is a periodic function that describes a periodic oscillation or vibration. It is commonly used to model periodic phenomena in many fields, such as sound, light, and electricity.

In this equation, Vy is the vertical position of the sine wave at a given point in time (x), a is the amplitude of the sine wave (the maximum distance from the midline), k is the wave number (the number of complete cycles per unit distance), x is the horizontal position (time or distance), d is the phase shift (the horizontal shift of the wave), and c is the vertical offset (the distance from the midline).

The equation y = a cos(k(x - d)) + c is similar to the equation for a sine wave, but it describes a cosine wave instead. A cosine wave is also a periodic function, but it is shifted by 90 degrees in phase compared to a sine wave.

Like a sine wave, a cosine wave can be used to model periodic phenomena and is commonly used in many fields. In this equation, y is the vertical position of the cosine wave at a given point in time (x), a is the amplitude of the cosine wave, k is the wave number, x is the horizontal position, d is the phase shift, and c is the vertical offset.

What is sin and cosine sum?

sin(x) + cos(x) = √2 * sin(x + 45°)

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Using square roots, we know that there are (A) 15 cubes in a row.

The value that a number produces when it is multiplied by itself is known as the square root of the number.

The square root is denoted by the radical sign. For instance, √16 = 4.

The root symbol or surds is another name for the radical symbol.

So, let x be the total number of cubes in a row.

The number of cubes in each row and column is equal because they are organized in a pattern with the same number of cubes in each.

Now,

Total cubes = x * x

Total cubes = x²

We know that the total number of cubes is 225.

So, we got:

x² = 225

Taking square roots:

x² = 225

x = √225

x = 15

Therefore, using square roots, we know that there are (A) 15 cubes in a row.

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Complete question:
A group of cubes is arranged in a pattern with the same number of cubes in each row and column. There are 225

cubes in the shape. How many cubes are in one row?

A) 15

B) 25

C) 56

D) 75

Answer:

(4,8)

Step-by-step explanation:

First, Let us see the midpoint formula:

m(x,x /2, y,y/2) (That probably looks really confusing online)

Let us label our cords

A: (1x,5y)

B: (7x,11y)

Now, Add the x's together

7x + 1 = 8

8÷2 = 4

Now, Add the y together

11 + 5 = 16

16÷2 = 8

(4,8)

Answer:

(5,0)

Step-by-step explanation:

When graphed the x-intercept meaning the line touching x

is 5 so then your answer is  (5,0) because the x-value comes first so then you'd put the 5 in front.

Answer:

Answer = 8 days

Step-by-step explanation:

Step 1: Find how long one machine takes to finish

    1. 6 ∙ 4 = 24 days

Step 2: Divide 24 by 3 to get the rate of speed of 3 machines

    2. 24 / 3 = 8 days

The equation of a polynomial that has zeros at x = 2i and x = 3 is given as follows:

x³ - 3x² + 4x - 12.

We are given the zeros of the polynomial, which then can be obtained using the Factor Theorem.

The zeros are given as follows:

Then the polynomial is obtained as the product of it's linear factors, due to the Factor Theorem, as follows:

(x - 2i)(x + 2i)(x - 3)

(x² + 4)(x - 3)

x³ - 3x² + 4x - 12.

(as the base complex number relation is i² = -1).

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Answer: 21

the hcf of 315 and 42 is 21.

Answer:

HCF of 315 and 42:

Your answer is 21 !

Let's call the smaller number "x" and the larger number "y." Since 7 is added to the larger number, y + 7 = 4x. Since 28 is added to the smaller number, x + 28 = 2y.

We can solve this system of equations by substituting the first equation into the second equation to eliminate one of the variables:

x + 28 = 2(y + 7)

x + 28 = 2y + 14

x - 2y = -14

Then, we can substitute the second equation into the first equation to eliminate the other variable:

y + 7 = 4(x + 28)

y + 7 = 4x + 112

y - 4x = -105

Now we have a system of two equations in two variables, which we can solve using methods such as substitution or elimination. Let's use substitution:

x - 2y = -14

y - 4x = -105

If we solve the second equation for y, we get y = 4x - 105. Substituting this expression into the first equation gives:

x - 2(4x - 105) = -14

x - 8x + 210 = -14

-7x = -224

x = 32

Substituting this value back into the expression for y gives us y = 4(32) - 105 = 107.

Therefore, the two numbers are x = 32 and y = 107. If 7 is added to the larger number, the value obtained is 107 + 7 = 114, which is four times the smaller number (32). If 28 is added to the smaller number, the value obtained is 32 + 28 = 60, which is twice the larger number (107).

Answer:

Step-by-step explanation:

68 Ounces B - 61.2

92.4 Ounces A - 60.06

70% of 160 = 112

A+B estimated 112

On solving the provided question, we got that - 0.8 > 0.3, 0.8 is greater as , it is more closer to 1 than 0.3.

The term "number line" refers to a horizontal line with numbers placed equally apart. Depending on the numbers present, you can choose how to respond to the numbers on the line. The corresponding question dictates how to use numbers. B. When arranging the points.

From the provided question,

we  have to compare between 0.3 and 0.8.

Here,

Obviously, 0.8 is greater than 0.3.

as on number 0.8 is closer to 1 than 0.3,

and 0.3 is more closer to 0 than 0.8.

Therefore,

0.8 > 0.3.

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375 hours  should be the warranty period so that only 1% of them fail before the warranty is over.

As per the details share in the above question are as follows,

A certain type of electric bulb is a random variable that is normally distributed with a mean of μ=500 hours

The standard deviation σ=20 hours

We have to determine what should be the warranty period so that only 1% of them fail before the warranty is over?

Now let us consider,

Probablity Z=(X-μ)/σ

Solving further we get,

P(Any bulb fail before 500 hours)

= P(z < (500 - 500)/20)

= P(z < 0) = 0.50

Thus,

P( Failed before 500 hours)

[tex]= (0.50)^3[/tex]

= 0.125

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The system of equation that represent situation is x + y = 25 and 0.50x + 0.25y = 10

Define System of Equation

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given,

Total money Anthony and Joan have to buy apples and oranges = $10

Total pieces of fruit the Anthony and Joan buy is = 25 pieces of fruit

Each Apple's cost = 50 cents

Each orange's cost = 25 cents

Let, x = be the apples

and, y = be the oranges

The equation applied for the number of pieces of fruit they will buy,

x + y = 25

And, the equation applied for cost is,

0.50x + 0.25y = 10.00     (Keep everything in same decimal places)

Hence, the system of equation that represent situation is x + y = 25 and 0.50x + 0.25y = 10

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The probability that a randomly selected student has a brother given they have a sister is 8/30.

We have provided that.

A class of 30 pupils has 13 brothers, 8 sisters, and 3 students who have both brothers and sisters.

The probability of an occurrence is calculated by dividing the total number of outcomes in the sample space by the proportion of favorable events.

Considering that there are 30 pupils overall and that 8 of them have both a brother and a sister,

The probability of a student having a brother given that they have a sister would then be 8/30 (8 out of the 30 students).

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Using the laws of cosines we know that to get the ball back to the pitcher, the outfielder must throw it 125 feet.

The square of a side of a plane triangle is equal to the sum of the squares of the other sides minus twice the product of those sides and the cosine of the angle between them, according to a trigonometry rule.

So, it is a given that the distance between the home plate and the pitcher's mound on a softball field is 43 feet.

27° east of the pitcher's mound is the angle at which a ball is struck.

Before an outfielder catches the ball, it travels 162 feet.

Using the law of cosines, we may now:

a² = b² + c² - 2bcosA

When b=43, c=162, and A=27° are entered, we get:

a² = 43² + 162² - 2(43)(162)cos27°

a² = 1849 + 26244 - 12413.4

a² = 15679.6

a = 125.21

a = 125ft

Therefore, using the laws of cosines we know that to get the ball back to the pitcher, the outfielder must throw it 125 feet.

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Complete question;
On a softball field, home plate is 43 feet from the pitcher’s mound. A ball is hit at an angle of 27° east of the pitcher’s mound. The ball travels 162 feet before it is caught by an outfielder. Law of cosines: a2 = b2 + c2 – 2bccos(A) Rounded to the nearest foot, the outfielder must throw the ball feet to return it to the pitcher.

Distance between (1,4) and (-2,8) is 5 units.

The separation between two points. The coordinates of two points in space are used in the formula.

In coordinate geometry, a two-dimensional or three-dimensional space can be used to calculate the distance between two points using the distance formula.

Let distance between two points ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2}[/tex],[tex]y_{2}[/tex]) be 'd' then,

d = [tex]\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]

We are given two points (1,4) and (-2,8)

So, using formula for distance we get,

d= [tex]\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]

=[tex]\sqrt{(-2-1)^{2} + (8-4)^{2} }[/tex]

d [tex]\sqrt{(-3)^{2} + 4^{2} } \\=\sqrt{25} \\=5[/tex]

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The  equation  for the length, h is h= ( 2V ) / ( πr² )

What is volume?

In three-dimensional space, volume is the area occupied by an object within its borders. Another name for it is an object's capacity.

The sphere, cube, cone, and cylinder, as well as the polyhedra more broadly, are some of the most basic solids.

Volume of a half-cylinder:

V= (1/2)πr²h

Move 2 to the left

=> 2V= πr²h

Solve for h

=> 2V/πr² = h

=> h= ( 2V ) / ( πr² )

Thus, the  equation  for h is h= ( 2V ) / ( πr² )

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The value of the correlation coefficient is 0.9866.

By the end of 2014, the number of movie tickets sold would be equal to 1,600,000,000 movie tickets.

In order to determine value of the correlation coefficient and line of best fit that models the data points contained in the table, we would use a graphing calculator (scatterplot).

In this scenario, the year would be plotted on the x-axis of the scatterplot while the number of tickets sold (in millions) would be plotted on the y-axis of the scatterplot.

On the Excel worksheet, you should right click on any data point on the scatterplot, select format trend line, and then tick the box to display an equation and correlation coefficient for the trend line (line of best fit) on the scatterplot.

From the scatterplot (see attachment) which models the relationship between the data points in the table, a linear equation for the line of best fit (trend line) is given by:

y = 20.012x - 38704

Correlation coefficient, R² = 0.9757.

By the end of 2014, the number of movie tickets sold is given by:

y = 20.012x - 38704

y = 20.012(2014) - 38704

y = 40,304.168 - 38704

y = 1,600.168 × 1,000,000 ≈ 1,600,000,000 movie tickets.

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Point= (1, -1)

Hence, this is not the solution of the desired answer.

inequality is defined as declaration of the relation of greater, greater than or equal to, smaller, or less than or equal to between two numbers or the algebraic expressions. Either queries or the declarations of fact in the form of theorems can be used to formulate and solve inequality problems.

Shaded Region represents y<2x-3

Given Point= (1, -1)

Hence, this is not the solution of the desired answer,

As it not defines the equality part.

As for example (2,-2) is the solution of the desired inequality and it satisfies the condition y<2x-3.

And given point (1, -1) is not the solution of the desired equation as it does not satisfy the inequality portion.

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supposed to questions

Step-by-step explanation:

people say the climate is changing

Answer: 3

Step-by-step explanation:

The triangles are similar using the angle-angle similarity theorem.

Using the fact that similar triangles have proportional side lengths yields:

[tex]\frac{5x-7}{4}=\frac{18}{9}\\\\\frac{5x-7}{4}=2\\\\5x-7=8\\\\5x=15\\\\x=3[/tex]

There are at least two restaurants with varying mean delivery times. The required hypothesis are ,

H0: The mean delivery time for all restaurants is the same.

H1: The average delivery time varies between at least two restaurants.

If the data are put through an ANOVA, a different mean delivery time for at least two of the restaurants would be the alternative hypothesis.

According to the alternative hypothesis (Ha), there is a significant statistical association between two variables. As opposed to the null hypothesis, which claims that there is no statistical connection between the two variables.

The analysis of variance procedure, or ANOVA, includes examining the validity of mean hypotheses in light of variances. The equality mean, or H0. All means are equal, is used as the null hypothesis in an ANOVA. Alternative hypothesis, however, includes at least two means that are not equal.

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Ms. Caraballo saw 17 lions, 13 tigers, and 10 bears at the zoo.

What is the system of linear equations?

A system of linear equations is a collection of two or more linear equations, and a solution to a system of linear equations consists of values of each of the unknown variables in the system that satisfies all of its equations or makes them true.

Let L be the number of lions, T be the number of tigers, and B be the number of bears. We can set up the following system of equations to represent the given information:

L + T + B = 40

L = T + 4

B = T - 3

We can solve this system of equations using substitution. Starting with the second equation, we can solve for T:

T = L - 4

Substituting this expression for T into the third equation, we get:

B = L - 4 - 3

B = L - 7

Substituting this expression for B into the first equation, we get:

L + L - 4 + L - 7 = 40

3L - 11 = 40

3L = 51

L = 17

Now that we know the number of lions, we can substitute this value back into the equation T = L - 4 to find the number of tigers:

T = 17 - 4

T = 13

Finally, we can substitute these values for L and T into the equation B = L - 7 to find the number of bears:

B = 17 - 7

B = 10

Hence, Ms. Caraballo saw 17 lions, 13 tigers, and 10 bears at the zoo.

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