Write the explicit and recursive rules for a geometric sequence given a table of values.

Answer:

Below

Step-by-step explanation:

The bisector divides the base into lengths proportionate to the two sides (Angle Bisector theorem)

x+ 2 = 15/(15+20) * 14

x = 4 units

The inverse of the expression represented as 12/(x-1) is (12/x) + 1

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

12/(x - 1)

The given parameter is an expression

Also, we can see that the above expression is a quotient expression

So, we start by expressing it as an equation

This is represented as

y = 12/(x - 1)

Swap/Switch the positions of the variables x and y

So, we have the following representation

x = 12(y - 1)

This gives

y - 1 = 12/x

Make y the subject

y = (12/x) + 1

Hence, the inverse is (12/x) + 1

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Answer:

8% increase

Step-by-step explanation:

Difference between the two populations:  110160 - 102000 = 8160

Difference ÷ Initial population:  8160 ÷ 102000 = 0.08

The equivalent form of the compound inequality is -9>-x≥-10.

A sentence having two inequality statements connected by the words "or" or "and" is referred to as a compound inequality. The conjunction "and" denotes the simultaneous truth of both statements in the compound sentence. It is when the solution sets for the various statements cross over or intersect. The conjunction "or" means that the entire compound sentence is true as long as either of the two statements is true. It consists of the union or combination of the solution sets for the various statements. A conjunction is a compound inequality that contains the word "and." Even though "and" and "or" are considered to be conjunctions of speech, their meanings in mathematics are distinct from their grammatical counterparts. The conjunction (part of speech) "or"—when used to demonstrate this point—is whenever used in a compound inequality, it creates a disjunction, as the name suggests. Simply keep in mind that "con" stands for "with another" and "dis" for "one OR the other."

Given -33>-3x-6≥-36.

Dividing everything by 3 we get -11>-x-2≥-12.

Now adding to every side we get compound inequality as -9>-x≥-10.

The equivalent form of the compound inequality is -9>-x≥-10.

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The income of the man is 24000.

Step-by-step explanation:

income of man =24000

Let the income of man be x

According to the question,

20%*x = 4800

0.2x=4800

As a result, x =24000

(4800*10= 48000/2= 24000)

So the income of a man is 24000.

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Man's income is, 24000 rupees.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given, 20% of an income of a man is Rs 4,800.

To find the income:

Use percentage formula,

let m be the man's income.

So, m x 20 / 100 = 4800

Rearranging,

m = 4800 x 100 / 20

m = 24000

Therefore, the income is, 24000 Rs.

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The equation of the line that passes through the point ((0, 3) & (3, 0) is y = -1x - 3.

What is the system of linear equations?

A system of linear equations is a group of one or more linear equations that can be solved by using a simultaneous equation or elimination method. Therefore, by using the substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).

To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope of the line (m) and the y-intercept (b).

To find the slope of the line, we can use the slope formula:

m = (y2 - y1)/(x2 - x1)

We have given the line passes through the points(0, 3) & (3, 0),

so, m = (0-3)/(3-0)

= -3/3

m = -1

The y-intercept is the point where the line intersects the y-axis. This point is (0, b), where b is the y-intercept.

Since the given line passes through the point (3, 0), we can substitute these values into the slope-intercept form of the equation to find the y-intercept:

y = mx + b

0 = -1 * 3 + b

b = -3

Solving for b gives us:

b = -3

Therefore, the equation of the line that passes through the point ((0, 3) & (3, 0) is y = -1x - 3.

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Answer: 21 students

Step-by-step explanation:

A number being 30% smaller means that it has reduced to 70% of its original size.

This means we can multiply the original value by its new percentage, 30x0.7=21 students.

Answer:

multiplication

Step-by-step explanation:

you multiply. I know this because I am in pre algebra right now and we learned about this again. If you are doing division then it’s the opposite same for subtraction as well as addition.

Answer: $5,250

Step-by-step explanation:

1) Half of 5000 is 2500. But that's 50%.
2) Divide the remaining value by 10. You now have 250, which is 5%.

It's a given rule in math that if you're working with the Powers of 10, by either multiplying or dividing them, all you need to do is add or remove some zeros.

Answer:

to much money to buy a car I try to work it down to 10k

Answer:

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

We need to find the remainder when -5x³ + 2x + 3  is divided by x + 2.

According to the remainder theorem, the remainder is the value of the polynomial when x = - 2:

The matching choice is B.

Answer:

B.  39

Step-by-step explanation:

Divide the polynomials using long division:

[tex]\large \begin{array}{r}-5x^2+10x-18\phantom{)}\\x+2{\overline{\smash{\big)}\,-5x^3\;\;\;\;\;\;\;\;\;\;\;+2x+3\phantom{)}}}\\{-~\phantom{(}\underline{(-5x^3-10x^2)\phantom{-b)))))))}}\\10x^2+2x+3\phantom{)}\\-~\phantom{()}\underline{(10x^2+20x)\phantom{)))}}\\-18x+3\phantom{)}\\-~\phantom{()}\underline{(-18x-36)\phantom{}}\\39\phantom{)}\\\end{array}[/tex]

The solution is the quotient plus the remainder divided by the divisor.

Solution

[tex]-5x^2+10x-18+\dfrac{39}{x+2}[/tex]

The ratio of Marcus's point to Scott's point will be = 1 : 2

According to the table given attached below,

We can find the ratio of the squares,

First, let us know about the definition of Ratio and Proportion.

The ratio is defined as the comparison between the two similar quantities

The fraction can also be represented as a ratio using the ' : ' sign

For example, let us consider two numbers a and b

In fraction, we could write it as = [tex]\frac{a}{b}[/tex]

Writing it as a ratio = a : b

According to the table given below,

Marcus's points = 7

Scott's points = 14

The ratio of Marcus's points to Scott's points = [tex]\frac{Marcus}{Scott}[/tex]

14 / 7

2 / 1

2 : 1

Therefore, The ratio of Marcus's point to Scott's point will be = 1 : 2

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The points that make both equations true are, (0,3) and (-3,3).

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The graph of the equations is attached with the answer below. The points are (0,3) and (-3,3).

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Answer:x=$7.31

Step-by-step explanation:6lbs  

$12.90 x

6lbs x=($12.90 )(3.4 lbs)

6lbs x=43.86$lbs

6lbs x/6lbs=43.86$lbs/6lbs

Answer: Mattie has 16 stamps and Arnav has 4 :)

Step-by-step explanation:

the system of equations used to solve it is

m=4a

m-8=2a

Martie have 48 stamps and Arnav have 12 stamps.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

Let Matie has x stamps and Arnav has y stamps.

Given that,

Matie has 4 times as stamps as Arnav

Implies that,

x = 4y            (1)

Also, If Matie gives 8 stamps to Arnav will have twice stamps to Arnav.

Implies that,

x - 8 = 2(y+8)

x - 8 = 2y + 16

x = 2y + 24      (2)

From equation (1) and (2),

y = 12

and x = 48

Matie and Arnav each have 48 and 12 stamps respectively.

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The distance traveled by train would be 300 miles.

What is the relation between speed, distance, and time?

You can use the equivalent formula d = rt which means distance equals rate times time. To solve for speed or rate use the formula for speed, s = d/t which means speed equals distance divided by time. To solve for time use the formula for time, t = d/s which means time equals distance divided by speed.

A train travels for 3.75 hours at 80 miles per hour.

The distance traveled = speed * time

                                     = 3.75 * 80

                                     = 300 miles.

Hence, the distance traveled by train would be 300 miles.

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Answer:

4 6 8 10

Are the ans

Step-by-step explanation:

Plus 2 each time

Answer: There are several statements that could be false if f(x) is continuous on [a, b] and differentiable on (a, b):

1 The function f(x) has a maximum or minimum value at some point in the interval [a, b].

2 The function f(x) is monotonic (either increasing or decreasing) on the interval [a, b].

3 The function f(x) has an inflection point (a point where the concavity of the function changes) in the interval [a, b].

4 The function f(x) has an asymptote (a line that the function approaches but never touches) in the interval [a, b].

5 Note that these statements are not necessarily false, but they could be false depending on the specific function f(x).

The value of x = 9 (back)

The value of x = 12 (orange)

The value of x = 8 (purple)

The value of x = 12.75 (green).

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

We have,

10 and 2x - 8 are parallel lines.

10 = 2x - 8

10 + 8 = 2x

18 = 2x

x = 9 (black)

7 and -17 + 2x are the two parts of a line separated by a midpoint.

7 = -17 + 2x

7 + 17 = 2x

2x = 24

x = 12 (orange)

7 and x + 15 are two parts of a line separated by a midpoint.

7 = x + 15

7 - 15 = x

x = 8 (purple)

m∠2 = 4x + 8

one angle = 45°

Other angle = 180 - 104 = 76°

The sum of the triangles is 180.

45 + 4x + 8 + 76 = 180

4x = 180 - 129

4x = 52

x = 12.75 (green)

Thus,

The value of x = 9 (back)

The value of x = 12 (orange)

The value of x = 8 (purple)

The value of x = 12.75 (green).

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Answer:

a) {A,E,I}

b) {red, orange, yellow, green, blue, violet, indigo}

c) {9,18,27,36,45}

d) {12,14,16,18,20,22}

Lol I'm not sure if I did all of these correct :]

(Also what is this for? Like the coding class or something? (Just curious))

The area of the paper that remains is 375.04cm².

What is an area?

The measurement that expresses the size of a region on a plane or curved surface is called an area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Here,

We take it that the semicircles cover the full width of the paper.

So the radius is 16/2 = 8 cm

Since there are two of them, the area is full circle.

First, we find the area of the rectangle before the cuts were made.

Area = L * W

L = 36

W = 16

Area = 36×16 = 576 cm²

Now, we find the area of the circle cutouts.

r = 8

Area = pi * r²

Area = 3.14 * 8²

Area = 3.14 * 64

Area = 200.96cm²

Now, we find the total area left

Total Area Left = rectangle - circle

Total Area Left = 576 - 200.96

Total Area left = 375.04cm².

Hence,  the area of the paper that remains is 375.04cm².

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The value of (f . g) (3) is 594 and  (f + g) (3) is 42 when function is f(x) =  4x² - 3 and g(x) = 2x + 3.

i) (f . g) (3)

(f . g) (x) = f(x) . g(x)

(f . g) (3) = f(3) . g(3)

= 4(3)² - 3 * 2(3) + 3

= 36 - 3 * 6 + 3

= 33 * 18

(f . g) (3) = 594

The value of (f . g) (3) is 594 when function is f(x) =  4x² - 3 and g(x) = 2x + 3

ii) ( f +​ g )( ​3 )

( f + g )( x ) = f ( x ) + g ( x )

​( f +​ g )( ​3 ) = f (3 ) + g ( 3 )

= 4(3)² - 3 + 2(3) + 3

= 4(9) + 6

= 36 + 6

​( f +​ g )( ​3 ) = 42

The value of (f + g) (3) is 42 when function is f(x) =  4x² - 3 and g(x) = 2x + 3.

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As per binomial distribution the probability of the following conditions are as follow:

a. probability for out of 5 none is concerned is 0.09924.

b. probability for out of 5 all are concerned is 0.02825

c. probability for out of 5 three are concerned is 0.4669.

As given in the question,

Percent of adults are concerned = 37%

p = 0.37

Percent of adults are not concerned = (100 -37)%

                                                         = 63%

1 - p = 0.63

Total number of adults 'n' = 5

Probability using binomial distribution

= ⁿCₓ pˣ ( 1- p)ⁿ⁻ˣ

a. Out of 5 none is concerned

here x = 0

⁵C₀( 0.37)⁰(0.63)⁵⁻⁰

= 0.09924

b. Out of 5 all are concerned

here x = 5

⁵C₅( 0.37)⁵(0.63)⁵⁻⁵

= 0.02825

c.  Out of 5 three are concerned

here x = 3

⁵C₃( 0.37)³(0.63)⁵⁻³

= 0.4669

Therefore , using binomial distribution the probability of the given percent of adult data is equal to as follow:

a. probability for out of 5 none is concerned is 0.09924.

b. probability for out of 5 all are concerned is 0.02825

c. probability for out of 5 three are concerned is 0.4669.

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Confidence interval for given data is (82.156,88.843)

The confidence interval is the range of values that, if you repeated your experiment or resampled the population in the same manner, you would anticipate your estimate to fall within a specific proportion of the time.

The alpha value determines the confidence level, which is the proportion of times you anticipate being able to recreate an estimate between the top and lower boundaries of the confidence interval.

general form of a confidence interval is: 

                              point estimate + Z SE (point estimate)

    Formula for confidence interval is given by

                                          [tex]X[/tex] ±  [tex]Z\frac{s}{\sqrt{n} }[/tex]

Where:

   X is the mean

   Z is the chosen Z-value from the table above

   s is the standard deviation

   n is the number of observations

In given ques

X = 85.5, Z=1.960, s =+ 12.3, n= 52

confidence interval = 85.5± (1.960×12.3/√52)

(82.156,88.843)

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If  hose fills a hot tub at a rate of 3.49 gallons per minute. Then 1.64 hours will it take to fill a 343​-gallon hot​ tub

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given,

A hose fills a hot tub at a rate of 3.49 gallons per minute.

We need to find how many  hours will it take to fill a 343​-gallon hot​ tub

3.49/1=343/x

Apply cross multiplication

x=343/3.49

x=98.28 minutes

1 hr=60 minutes

So divide 98.28/60

1.64

Hence, it takes 1.64 hours to fill the hot tub.

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The  first digit in the quotient of 1, 592 64 should be placed in the; Hundredths place.

When we carry out long division, it is pertinent to note that the first digit of the quotient usually appears over the least significant digit of the very first portion of the dividend that is now greater than or equal to the divisor.

In this question, when we perform long division, we compare;

64 vs 1 . . . no quotient digit

64 vs 15 . . . no quotient digit

64 vs 159 . . . the first quotient digit appears with the same place value as the 9 in 1.59. That is, the first quotient digit will be 0.02, with 2 being in the hundredths place.

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Answer: y = 3/2x +-9

Step-by-step explanation:

      The equation in slope-intercept form, y = mx + b, is the equation y = 3/2x +-9.

      See attached for more information on slope-intercept form.

The mean and standard deviation of the sample data in the table is 182 and 508 respectively.

To calculate the mean and standard deviation,

mean= E(x)

=  ∑x*f(x)

= 1(2) + 2(13) + 3(15)+4(11) + 5(13)

=2+26+45+44+65

=182

Standard deviation = E(x²)

=  ∑x²*f(x)) - E(x)

=1(2) + 4(13) + 9(15)+16(11) +25(13)  - E(x)

= 2 +52+135+176+325  - E(x)

=690 - 182   - E(x)

=508

The mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally.

The three most frequently employed measures of central tendency are the mean, median, and mode.

The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean. 

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Dude I am so sorry that I do not know this answer

Solving for y, the linear equation is: y = -4/5x - 2/5.

The table showing the corresponding y-value for each x-value is:

x |  -8  -3   2   7

y |   6   2  -2  -6

The graph is in the attachment.

To graph the linear equation of 4x + 5y = -2, rewrite in slope-intercept form by solving for y.

4x + 5y = -2

5y = -4x - 2

y = -4/5x - 2/5

Complete the table given by plugging each value of x into the linear equation, y = -4/5x - 2/5.

For x = -8:

y = -4/5(-8) - 2/5

y = 6

For x = -3:

y = -4/5(-3) - 2/5

y = 2

For x = 2:

y = -4/5(2) - 2/5

y = -2

For x = 7:

y = -4/5(7) - 2/5

y = -6

The complete table is:

x |  -8  -3   2   7

y |   6   2  -2  -6

See the graph below.

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