A) A sequence is defined using this term-to-term rule.

Un+1 = 2un+ 20

If uy = 8, find u2

b) Another sequence is defined using this term-to-term rule,

unty = ku,+r

where k and rare constants.

Given that u, = 37, uz = 188 and ug = 943, find the value of k and

the value of r.

Answer:

just ask your teacher for clarification, then you will actually learn...

Answer:

The function that correctly depicts the scenario is:

cost(n) = 18.50 * 1.06^n

This function takes the number of years n as input and returns the cost of eating at the all-you-can-eat buffet after n years.

The cost of eating at the all-you-can-eat buffet 10 years from now can be calculated as follows:

cost(10) = 18.50 * 1.06^10 ≈ $30.59

The cost of eating at the all-you-can-eat buffet 15 years ago can be calculated as follows:

cost(-15) = 18.50 * 1.06^(-15) ≈ $8.01

Step-by-step explanation:

The p-value of the test statistic is p-value = 0.006. The null hypothesis will be rejected at 5% level of significance.

A two-tailed test in statistics determines if a sample is more than or less than a specific range of values by using a two-sided critical area of a distribution. It is employed in testing the null hypothesis and determining statistical significance. The alternative hypothesis is accepted in place of the null hypothesis if either of the critical areas apply to the sample under test.

A two-tailed test in statistics determines if a sample is greater or less than a range of values by using a two-sided critical area of a distribution.

It is employed in testing the null hypothesis and determining statistical significance.

The alternative hypothesis is accepted in place of the null hypothesis if either of the crucial areas apply to the sample under test.

Conventionally, two-tailed tests with a 2.5% cutoff on each side of the distribution are employed to evaluate significance at the 5% level.

How to calculate the p-value?

Determine the level of relevance, sometimes referred to as the level, in step one. Assume 0.05 if it isn't specified. Step 2: Evaluate the level of significance in relation to the p-value. Make the conclusion that supports the possible change and reject the null hypothesis if the p-value is lower.

To know more about  Two-Tailed Test refer to:

brainly.com/question/4621112

#SPJ4

The solution of x in the given linear equation (x - 13 + 155 = 180) is equal to 38.

To solve the equation (x - 13 + 155 = 180), we need to pursue the following steps.

Step 1. Move all terms to the left:

⇒(x - 13 + 155 - (180)) = 0

Step 2. Add all the numbers jointly, and all the variables

⇒(x - 38) = 0

Step 3. Get rid of parentheses

⇒x - 38 = 0

Step 4. Transfer all terms including x to the left, and all other terms to the right

⇒x = 38

Hence, the required solution of x in the given linear equation (x - 13 + 155 = 180) is 38.

To know more about linear equation, here

https://brainly.com/question/19770987

#SPJ4

The value of a perfect square is either a positive number or zero. They cannot be neutral.

Perfect squares are generated when you square an integer. For instance, the number 81 is a perfect square since it can be derived by squaring 9: 99=81. 144 is a perfect square since 12 is squared to produce it. 169 is a perfect square since 13 may be squared to obtain it. Mathematical language Informally: When an integer (a "whole") number, whether positive, negative, or zero, is multiplied by itself, the outcome is referred to as a square number, a perfect square, or simply "a square." Therefore, all square numbers are 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on.

given

The value of a perfect square is either a positive number or zero. They cannot be neutral.

Square differences can be positive, negative, or zero depending on the order in which the numbers are obtained.

One squared term will be added to the difference of squares, and another squared term will be subtracted.

To know more about perfect square visit :-

brainly.com/question/385286

#SPJ4

A is the variable and X is the coefficient term in the supplied  X2 expression. An algebraic expression is used to solve a particular mathematical problem .

In mathematics, a variable is an alphabet or phrase that denotes an unknowable quantity, unknowable value, or unknowable number. In the case of algebraic expressions or algebra, the variables are employed specifically. The two primary categories of variables are categorical and numeric. Then, for categorical and numerical variables, respectively, nominal or ordinal and discrete or continuous subcategories are created for each category. This section provides a quick overview of these types.

given

The coefficient term is denoted as X2, and the variable is A.

An algebraic expression is used to solve a particular mathematical problem by combining words and numbers.

For instance, the numerical coefficient in the equation 5x is 5, meaning that the variable x has been multiplied by 5 times.

To know more about variable visit :-

https://brainly.com/question/2466865

#SPJ4

Answer:Yes

Step-by-step explanation: It is a right triangle as if you imagine it, you can see that is half of a square, holding a right angle within it.

The vertex for the given equation [tex]y=x^2+5x-7 is (-2.5,-4.25)[/tex] and the solution  to the equation is x = -5,7/1. Similarly , the vertex for the given equation  [tex]y=-x^2+3x+8\ is\ (-3/2,1/4)[/tex] and the solution to the equation is [tex]x = -2,4[/tex].

The graph of a quadratic function is a symmetrical, U-shaped geometric form known as a parabola. It is the collection of all points that are equally spaced apart from a fixed point (referred to as the focus) and a fixed straight line (called the directrix).

A parabola's vertex is the location where its symmetry line and parabola intersect.

The vertex of a parabola is the highest or lowest point on the graph of the parabola. In the case of a parabola in the form of [tex]y = ax^2 + bx + c[/tex], the vertex is the point (h, k), where:

[tex]h = -b / 2a\\k = f(h) = a(h^2) + bh + c[/tex]

For the first equation: [tex]y = x^2 + 5x - 7[/tex]

The vertex would be:

[tex]h = -b/2a = -5/2 = -2.5\\k = f(h) = a(h^2) + bh + c = (1)((-2.5)^2) + (5)(-2.5) - 7 = 6.25 - 12.5 - 7 = -4.25[/tex]

So the vertex is [tex](-2.5,-4.25)[/tex]

For the second equation:[tex]y = -x^2 + 3x + 8[/tex]

The vertex would be:

[tex]h = -b/2a = -3/2(1) = -3/2\\k = f(h) = a(h^2) + bh + c = (-1)((-3/2)^2) + (3)(-3/2) + 8 = -9/4 + -9/2 + 8 = 1/4[/tex]

So the vertex is [tex](-3/2,1/4)[/tex]

To find the solutions or roots of the equation, you can set the equation equal to zero and solve for x.

[tex]y = x^2 + 5x - 7 = 0\\x^2 + 5x - 7 = 0\\x^2 + 5x - 7 + 7 = 0 + 7\\x^2 + 5x = 7\\x(x+5) = 7\\x = -5,7/1\\y = -x^2 + 3x + 8 = 0\\x^2 - 3x - 8 = 0\\(x-4)(x+2) = 0\\x = -2,4[/tex]

Solutions for first equation are x = -5 and x = 7/1 and for the second equation are x = -2 and x = 4

To learn more about parabolas visit:

brainly.com/question/21685473

#SPJ1

The sequences of transformations could be applied is

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

From the picture we have, g(x) = -3x - 1

Parent function: f(x) = x

1)  Reflect over the y-axis gives g(x) = -x

Vertically stretch by a factor of 3 gives g(x) = -3x

Shift down 1 unit gives g(x) = -3x - 1

2) Shift left 2 units: g(x) = x+2

Reflect over x-axis: g(x) = -x-2

Vertically stretch by a factor of 3 gives g(x) = -3x -6

3) Shift right 1 unit: g(x) = x-1

Reflect over the y-axis: g(x) = -x-1

Vertically stretch by a factor of 3: g(x) = -3x -3

4) Shift right 1 unit: g(x) = x-1

Reflect over the x-axis: g(x) = -x+1

Vertically stretch by a factor of 3: g(x) = -3x +3

5) Reflect over the x-axis: g(x) = -x

Vertically stretch by a factor of 3: g(x) = -3x

Shift down 1 unit: g(x) = -3x - 1

6) Shift down 1 unit: g(x) = x - 1

Reflect over the x-axis: g(x) = -x + 1

Vertically stretch by a factor of 3: g(x) = -3x + 3

Learn more about Transformation here:

https://brainly.com/question/11709244

#SPJ1

Reducing the object's size by dilation is a change. The items are enlarged or shrunk through dilation.

Resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation.

A diminution in the image occurs when the scale factor is between 0 and 1. An enlarged version of the image is shown if the scale factor is larger than 1.

An enlargement (imagine stretching) is a dilation that makes a larger image, whereas a reduction (think shrinking) is a dilation that creates a smaller image. A diminution in the image occurs when the scale factor is between 0 and 1. An enlarged version of the image is shown if the scale factor is larger than 1.

A transformation called a dilation (similarity transformation) alters the size of a figure. A center point and a scaling factor, k, are necessary. Which kind of dilation it is—an enlargement or a reduction—depends on the value of k. An enlargement results from a dilatation if |k|>1.

To learn more about dilation refer to:

https://brainly.com/question/3457976

#SPJ1

The equivalent expression of 5[tex]x^{3/2}[/tex] is  5√(x³). The correct option is last one.

Expressions that are equivalent to the same thing, even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

Given:

An expression,

5[tex]x^{3/2}[/tex]

To find the equivalent expression:

We have to simplify the expression,

5[tex]x^{3.1/2}[/tex]

= 5(x³)[tex]){1/2}[/tex]

= 5√(x³)

The above expression is an equivalent expression.

Therefore, 5√(x³) is an equivalent expression.

To learn more about the equivalent expression;

https://brainly.com/question/28170201

#SPJ1

Answer:

y = -x + 5

Step-by-step explanation:

The equation is y= mx + b

m = the slope or rise/run or (y2 - y1) / (x2 - x1)

b = y-intercept

The slope here is -1, and the y-intercept is 5, so our equation is

y = -x + 5

Answer: ≈ 100km/h

Step-by-step explanation:

62 : 0.62 = 100 km

Answer:

30.8% increase.

Step-by-step explanation:

17 - 13 |13| * 100% = 4 13 * 100 = 30.8%

I hope this helped you!

Answer: n=9

Step-by-step explanation:

I'm assuming you want to solve for n, as that's the only possible question I can think of.

To solve for n, we want to isolate n by using inverse operations.

2n+4=22            [subtract both sides by 4]

2n=18                 [divide both sides by 2]

n=9

Therefore, n=9 Is the answer.

The equivalent expressions of 10/9 + 2/9m − 4/9n are 2/9(5 + m - 2n) and -2/9(2n − m − 5)

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

109+ 29m − 49n

Express the expression properly

So, we have the following representation

10/9 + 2/9m − 4/9n

Factor out 2/9

So, we have

2/9(5 + m - 2n)

Factor out -1 from the expression

So, we have the following representation

-2/9(2n − m − 5)

Hence, the equivalent expression is -2/9(2n − m − 5)

Read more about equivalent expression at

https://brainly.com/question/2972832

#SPJ1

Total interest earned = 68

Total amount collected = 1268

Simple interest is a way to figure out how much interest will be paid on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the following year's principal to compute interest, the principal amount under simple interest remains constant.

Simple interest is a quick and simple approach to figure out how much money has accrued interest. Interest is always applied to the initial principle amount and is calculated at the same rate for each period of time. Any bank where we deposit money will pay us interest on that amount. Simple interest is one of several forms of interest that banks charge. Now, let's first clarify what a loan is before delving further into the idea of simple interest.

Since nothiong mentioned the interest is considered simple

Total amount = 1200 (principal)

Time = 1 year 5 month = [tex]1\frac{5}{12} = \frac{17}{12}[/tex]

rate = 4 %

Total interest earned = [tex]\frac{1200 * 4 * \frac{17}{12} }{100}[/tex] = 68

Total amount generated = 1200 + 68 = 1268.

To learn more about Simple interest refer to :

https://brainly.com/question/29709325

#SPJ4

Answer:

yes

Step-by-step explanation:

The word linear is used for a straight line. A linear function is a function of a straight line, which means that the degree of a linear function must be 0 or 1 . In this case, The degree of f(x)=2x−3 f ( x ) = 2 x - 3 is 1 , which makes the function a linear function.

∠BCE is drawn, line segment CA is drawn,  Ray CA is drawn, For Circle C is drawn, Ray BE is not drawn.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given that Circle C is inscribed with 5 lines

Point C is at the center of the circle

3 lines come out of point C and make points D, A, and B on the edge of the circle.

Another line comes out of point C and goes past the edge to point E.

For ∠ABC

The geometric figure is not drawn.

For ∠BCE

The geometric figure is drawn.

For line segment CA

The geometric figure is drawn.

For Ray CA

The geometric figure is drawn.

For Circle C

The geometric figure is drawn.

For Ray BE

The geometric figure is not drawn.

For Line segment AE

The geometric figure is not drawn.

Hence,  ∠BCE is drawn, line segment CA is drawn,  Ray CA is drawn, For Circle C is drawn, Ray BE is not drawn.

To learn more on Circles click:

https://brainly.com/question/11833983

#SPJ1

Answer:

To find out how many cups a single jug of water fills, you can divide the total number of cups filled by the number of jugs:

184 cups / 23 jugs = <<184/23=8>>8 cups/jug

This means that one jug of water fills 8 cups.

Step-by-step explanation:

Answer:

$42.00

Step-by-step explanation:

Interest = principle x rate x time

Interest = 300 x .07 x 2

Interest = 42

(x - 1) is thus a factor of f(x) = x3 - 2x2 - 5x + 6.

The factorization of x^3 2x^2 5x 6 is (x^2)(2x)(3) . This can be found by dividing x^3 2x^2 5x 6 by its prime factors.

You can also factor out x^2 from the expression x^3 2x^2 5x 6, which would leave you with x^2(x 2.5 6) or x^2(x 2.5 3)

Given that x3 - 2x2 - 5x + 6 = f(x),

We must determine the factored form of f in its entirety (x).

Consider (x - 1) as a factor (x).

Let's see if (x - 1) is a factor of f. (x).

f(1) = (1) (1)

3 - 2(1) (1)

2 - 5(1) + 6

= 1 - 2 - 5 + 6

= 6 - 6

= 0

f(1) = 0

(x - 1) is thus a factor of f(x) = x3 - 2x2 - 5x + 6.

Learn more about factors here: https://brainly.com/question/25829061

#SPJ4

An equation that combines with the given equation  x + 2y = 21 to form a system of equations with the solution x = 3 and y = 9 is 4x + y = 21.

The correct answer is an option (c)

As x = 3 and y = 9 are the solution of system of equations, the required equation must be true for x = 3 and y = 9.

Given equation is: x + 2y = 21

For x = 3 and y = 9 given equation is 3.

In order to find the required equation, we substitute the values of x and y in each equation and check whether the equation is true for x = 3 and y = 9.

a. For equation, 4x + 6y = 64

LHS = 4(3) + 6(9)

LHS = 12 + 54

LHS = 66

LHS ≠ RHS

So, this is not a required equation.

b. 2x + y = 36

LHS = 2(3) + 9

LHS = 6 + 9

LHS = 15

LHS ≠ RHS

So, this is not a required equation.

c. 4x + y = 21

LHS = 4(3) + 9

LHS = 12 + 9

LHS = 21

LHS = RHS

this is the required equation.

d. -3x + 4y = 33

LHS = -3(3) + 4(9)

LHS = -9 + 36

LHS = 27

LHS ≠ RHS

So, this is not a required equation.

e. 3x + 2y = 28

LHS = 3(3) + 2(9)

LHS = 9 + 18

LHS = 27

LHS ≠ RHS

So, this is not a required equation.

Therefore, the reuired equation is 4x + y = 21

Learn more about an equation here:

https://brainly.com/question/649785

#SPJ4

The perimeter of the possible larger triangle with possible side lengths of 24, 32 and 40 is 96 units

The perimeter of a figure is the length of the boundary surrounding the figure.

Two triangles that have proportional dimensions are similar triangles

The dimensions (arranged in the order of corresponding sides) of the possible similar right triangles in the question, obtained from a related question, having two similar right triangles, posted online are;

The similarity of the triangles (proportional corresponding sides, indicates that we get;

[tex]\dfrac{24}{9} = \dfrac{32}{12} = \dfrac{x}{15}[/tex]

Therefore, by cross multiplication, we get;

32 × 15 = 12 × x

x = 32 × 15 ÷ 12 = 40

The perimeter of the larger triangle is; 24 + 32 + 40 = 96

Please find attached the possible diagram of proportional right triangles, created with MS Word, obtained from a question with regards to proportional right triangles online.

Learn more about similar triangles here: https://brainly.com/question/29782809

#SPJ1

x     y   is the two-step function table of the given linear equation

0    -4

1     0

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

given an equation y  = 4x -4

Use the slope-intercept form to find the slope and y-intercept.

y = mx + c

m =4

c = -4

Slope = 4

The slope of the line is the value of m, and the y-intercept is the value of b.

y-intercept  : (0, -4)

x-intercept where y = 0 : (1, 0)

Therefore, the table of the two-step functions is Written below.

x     y  

0    -4

1     0

Learn more about linear equations here:

https://brainly.com/question/11897796

#SPJ1

Based on the two-way table, there seems to be a relationship between the type of books Julia's friends like best and the number of books they have read this month, A. Yes, because those who like fiction read one book at a rate four times that of those who read non-fiction books.

A two-way table, also called a contingency table, is a statistical table that shows the observed frequency for two variables.

The rows of a two-way table indicate one category and the columns indicate the other category.

For instance, based on the two-way table, one can observe that 80% of Julia's friends prefer fiction while 20% prefer non-fiction.

Among those who read 1 book this month, 80% read fiction against 20% who read non-fiction.  Similarly, among those who read 2 books this month, the same 80% read fiction against 20% who read non-fiction.

The number of students who prefer fiction = 60

The number of students who prefer non-fiction = 15

The number of fiction-preferring students who read 1 book this month = 40, which is 80% of the total (40/50 x 100).

The number of fiction-preferring students who read 2 books this month = 20, which is 80% of the total (20/25 x 100).

Thus, we can conclude that Option A is correct.

Learn more about the two-way table at https://brainly.com/question/16148316

#SPJ1

The Two-way Table:

                                       Read 1 book         Read 2 books     Total

Prefer fiction books               40                            20              60

Prefer non-fiction books        10                              5               15

Total                                       50                            25              75

x=12

L||M means L will be parallel to M.

Two lines are parallel if their corresponding angles are the same.

Corresponding angles are shown below.

As the two angles given are corresponding, L||M when x+5 = 2x-7.

x+5 = 2x-7

x = 12

Therefore, the value of x which makes L||M is 12.

Answer:

x = 12

Step-by-step explanation:

Now we have to,

→ find the required value of x.

Forming the equation,

→ x + 5 = 2x - 7

Then the value of x will be,

→ x + 5 = 2x - 7

→ x - 2x = -7 - 5

→ -x = -12

→ [ x = 12 ]

Hence, the value of x is 12.

Answer:

$68

Step-by-step explanation:

So, we will start off by putting our original price as a variable, x. Now, we will need an equation to show the relationship between the current price and three-fourths of the original price. The equation will look like this:

[tex]\frac{3}{4} x = 51[/tex]

Then, we will multiply both sides by 4 to get rid of the fraction, giving us:

3x = 204

Finally, we will divide by 3 to find the original price of the sneakers:

x = 68

So the pair of shoes originally cost $68.

Hope this helped!

40 percent price of the ring gone down due to a clearance sale

In mathematics, percent implies a relative value of any quantity. Generally, percent value expresses the hundredth parts of any given quantity. Sometimes, operator % is used to indicate a percent value.

From a given percent value we can determine the real value and percent value is calculated from the original data.

given, the original price of the emerald ring = $1730

after a clearance sale, the price of ring became = $1038

difference in price = $(1730-1038) = $ 692

hence, the price of the ring that gone down = $692

now, percent value of the price gone down = $692/$1730 × 100

                                                                          = 40%

hence, forty percent of the ring price gone down.

To know more about percent value visit:

https://brainly.com/question/8371652

#SPJ1

The necessary probabilities are 3/8, 1/3, 9/64, and 37/64.

The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.

Here,

S = { G1, G2, G3, Y1, Y2, Y3, Y4, Y5 }

G = { G1, G2, G3 }

P(G) = 3/8

E = { G2, Y2, Y4 }

P(G|E) = 1/3

P(G and E) = P(G)*P(E) = (3/8)*(3/8) = 9/64

P(G or E) = P(G) + P(E) - P(G and E) = (3/8) + (3/8) - (9/64) = (6/8) - (9/64) = (48/64) - (9/64) = 37/64

The required probability is 3/8, 1/3, 9/64 and 37/64.

To know more about probability,

https://brainly.com/question/30034780

#SPJ4