Which of the following equations describes the nth term for the sequence 3/5,1/5,1/15,1/45,\cdots2
A. an = 1/3 (3/5)n-1
B. an = 1/3 (3/5)n
C. an = 3/5 (1/3)n-1
D. an = 3/5 (1/3)n

The third side of a triangle can be found using the Pythagorean Theorem.

This states that the sum of the squares of the two shorter sides of a triangle must equal the square of the longest side (the hypotenuse).

Let's say you have a triangle with sides a, b, and c, where c is the longest side. To find c, you can use the following formula:

c = √(a2 + b2)

For example, if you have a triangle with sides a = 4 and b = 5, then c = √(42 + 52) = √41 = 6.4. Therefore, the third side of the triangle is 6.4.

To calculate this using steps, you would first square the two shorter sides of the triangle:

a2 = 4 x 4 = 16

b2 = 5 x 5 = 25

Then, add the two squares together:

16 + 25 = 41

Finally, take the square root of the sum to find the length of the third side:

√41 = 6.4

Therefore, the third side of the triangle is 6.4.

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Reason:

The tickmarks tell us that the pair of hypotenuses are congruent.

The shared horizontal sides at the bottom are the pair of congruent legs of the right triangles. Therefore, we can use the hypotenuse leg (HL) theorem. This theorem only works for right triangles.

Answer:

5% of 120 is 6, so you would add that 6 to 120.

120 + 6 = 126.

The total cost will sales tax would be $126.00.

Step-by-step explanation:

Hope it helps! =D

Answer:

slope = -1

Step-by-step explanation:

any 2 points:

(2,2) (0,4)

to find the slope we use the formula:

[tex] \frac{y2 - y1}{x2 - x1} [/tex]

slope is:

2/-2 = -1

Answer:

The slope is =

2/-2 = -1

Step-by-step explanation:

Also i hope you have a wonderful day !

70-70-40 is an isosceles triangle.

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The required two numbers are 9 and 41.

The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.

Let x be the lesser number, and y be the greater number.

From the question, we know that:

x + y = 50 (Equation 1: The sum of the two numbers is 50)

y = 5x - 4 (Equation 2: The greater number is four less than five times the lesser number.)

The equation is to solve for one of the variables, and then substitute that value into the other equation to find the other variable.

Then, two numbers are x = 9 and y = 41.

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The advantages of adding additional processors will decrease as more are added because some portions are always still sequential, and eventually the speedup approaches a limit.

The ratio of the compute time for the sequential method to the time for the parallel algorithm represents the speedup of a parallel algorithm over a matching sequential algorithm. n-fold speedup is what we refer to if the speedup factor is n. For instance, if a sequential approach needs 10 minutes to compute while a parallel algorithm needs just 2, then the speedup is 5 times.

The observed speedup is dependent on every aspect of the implementation. For instance, more processors frequently result in speedups that are greater; but, if other programmer are running on the processors concurrently with a programmer using a parallel technique, the speedup may be reduced by those other applications.

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Answer:

Step-by-step explanation:

b

On solving the provided proportionality question we got that, U = 7.72, is rounded off nearest to tenth digit.

When two quantities or variables are linearly related in mathematics, the term "proportional" is used. Both quantities increase by two times when one increases by two. Each variable decreases in proportion to the other when it falls to 1/100th of its previous value.We must determine the ratio of the two quantities for each value supplied in order to determine if two quantities are proportionate. The proportionate link between them is evident if their proportions are equal. Their connection is not proportionate if all the ratios are out of balance.

Here,

U/5 = 17/11

U = 17/11 X 5

U = 7.72

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On solving the provided question, we can say that 12,12,12,22,23,32,43 Mean Absolute Deviation (MAD): 8.8979591836735

The average of the absolute deviations from the center point within a dataset is called the mean absolute deviation. This statistic summarizes the statistical spread or variability. Each data point's average distance from the mean is known as the dataset's mean absolute deviation. This gives a sense of the dataset's variability. To determine the absolute value, take the mean from each integer in the dataset and then subtraction. Take the total of the absolute values next. Subtract the aforementioned sum from the total number of items in the dataset to obtain the mean absolute deviation.

12,12,12,22,23,32,43

Mean Absolute Deviation (MAD): 8.8979591836735

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Answer:

On solving the provided question, we can say that 12,12,12,22,23,32,43 Mean Absolute Deviation (MAD): 8.8979591836735

Step-by-step explanation:

Answer:

3(x+1)(x-3)

Step-by-step explanation:

Well, this isn't an equation, but we can factor it like this:

[tex]3x^2-6x-9=3(x^2-2x-3)=3(x+1)(x-3)[/tex]

In the equation y = mx + c if we substitute the value of x as zero we will get a point on the y axis given by y =(m × 0) + c ⇒ y = c. Therefore the point of the line on the y axis is (0, c) and so c is also called the y -intercept  of the line.

Now, According to the question:

i) from the general equation of line we know that any line can be represented in the form y = mx + c , where m is a constant and is called the slope of the line and c is also a constant and is the y-intercept.

ii) In the equation y = mx + c if we substitute the value of x as zero we will get a point on the y axis given by y =(m × 0) + c ⇒ y = c. Therefore the point of the line on the y axis is (0, c) and so c is also called the y intercept  of the line.

iii) If for example we have the line 3y = 6x + 12 then we first get this equation of the line to match the general form of the equation of the line, that is y = mx + c. Therefore dividing both the left and the right sides of the given equation of the line by 3 we get y = 2x + 4 which matches with the general form of the equation for line and we see that the slope of the given line is m = 2 and the y intercept is given by c = 4.

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Answer:

Step-by-step explanation:

a.Scale factor = distance on the plot / actual distance

b.3 feet = 12 inchs.

so scale factor = 5/12

If the pickup charge for taxi is $3.50 and additional charge of $0.75 per mile , then the cost for riding 5 miles is $7.25  and cost for riding m miles is $[tex]3.50+0.75m[/tex]   .

The pickup charge that taxi service charges is = $3.50  ;

the additional charge for per miles driven is = $0.75  ;

we have to find the cost for riding 5 miles ;

So , the total cost for riding 5 miles is = [tex]Pickup Charge + (Additional Charge)\times(Number Of Miles Driven)[/tex] ;

substituting the values , the total cost equation becomes ;

[tex]Total Cost = 3.50 + 0.75\times5[/tex]

= [tex]3.50+3.75[/tex]

= 7.25

So , the cost for 5 miles is = $7.25  ;

to find cost for driving "m" miles ,we substitute the number of miles = m;

[tex]Total Cost = 3.50+0.75\times m[/tex]

= [tex]3.50+0.75m[/tex]

Therefore , the cost for riding m miles is $ [tex]3.50+0.75m[/tex] .

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The missing term of the arithmetic sequence is 2 1/2

An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁

Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

Given data ,

Let the arithmetic sequence be represented as A

Now , the equation will be

A = 1 3/8 , 1 3/4 , 2 1/8 , x , 2 7/8

The first term a₁ = 1 3/8

The second term a₂ = 1 3/4

The common difference d of the arithmetic sequence d = second term - first term

Common difference d = 1 3/8 - 1 3/4 = 3/8

Now , the fourth term of the arithmetic sequence is given by

Tn = a + (n - 1) d

Substitute the values in the equation , we get

a₄ = 1 3/8 + ( 4 - 1 ) ( 3/8 )

a₄ = 11/8 + 9/8

a₄ = 20/8

a₄ = 2 4/8

a₄ = 2 1/2

Therefore , the fourth term is 2 1/2

Hence , it is an arithmetic sequence and the fourth term is 2 1/2

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Answer:

$821.2

Step-by-step explanation:

cause 2.65 percentage of 800 dollars is 800/100=8*2.65=21.2dollars.+800 =$821.2

No two values of x in the computation we just did are equal, there are 4 different values of x for which the sequence contains the value 2001.

An ordered list of numbers is all that a sequence is. Number series are collections of numbers that adhere to a pattern or guideline. An arithmetic sequence is one where the rule is to add or take away a number each time.

To estimate a few terms of the sequence in order to obtain a feel how it looks like.

In our case, the definition is that [tex]$\forall$[/tex] (for all) [tex]$n > 1: a_n=a_{n-1} a_{n+1}-1$[/tex].

This can be rewritten as [tex]$a_{n+1}=\frac{a_n+1}{a_{n-1}}$[/tex].

We have [tex]$a_1=x$[/tex] and [tex]$a_2=2000$[/tex], and we estimate:

[tex]$& a_3=\frac{a_2+1}{a_1}=\frac{2001}{x} \\[/tex]

[tex]$& a_4=\frac{a_3+1}{a_2}=\frac{\frac{2001}{x}+1}{2000}=\frac{2001+x}{2000 x} \\[/tex]

[tex]$& a_5=\frac{a_4+1}{a_3}=\frac{\frac{2001+x}{2000 x}+1}{\frac{2001}{x}}=\frac{\frac{2001+2001 x}{2000 x}}{\frac{2001}{x}}=\frac{1+x}{2000} \\[/tex]

[tex]$& a_6=\frac{a_5+1}{a_4}=\frac{\frac{1+x}{2000}+1}{\frac{2001+x}{2000 x}}=\frac{\frac{2001+x}{2000}}{\frac{2001+x}{2000 x}}=x \\[/tex]

[tex]$& a_7=\frac{a_6+1}{a_5}=\frac{x+1}{\frac{1+x}{2000}}=2000[/tex]

At this point we see that the sequence will become periodic: we contain [tex]$a_6=a_1, a_7=a_2$[/tex], and each subsequent term exists uniquely determined by the previous two.

Hence 2001 appears, it contains to be one of [tex]$a_1$[/tex] to [tex]$a_5$[/tex].

As [tex]$a_2=2000$[/tex], we only have four possibilities left.

Clearly [tex]$a_1=2001$[/tex] for x = 2001, and [tex]$a_3=2001$[/tex] for x = 1.

The equation [tex]$a_4=2001$[/tex]

solves to [tex]$x=\frac{2001}{2000 \cdot 2001-1}$[/tex], and the equation [tex]$a_5=2001$[/tex] to [tex]$x=2000 \cdot 2001-1$[/tex]

There are four alternative values of x for which the sequence contains the value 2001 since no two values of x are equal in the computation we just performed.

Therefore, the correct answer is option (D) 4.

The complete question is:
Consider sequences of positive real numbers of the form x, 2000, y, ........  in which every term after the first is 1 less than the product of its two immediate neighbors. For how many different values of x does the term 2001 appear somewhere in the sequence?

(A) 1

(B) 2

(C) 3

(D) 4

(E) more than 4

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There are 749398 5-disc combinations that can be made from the collection.

Combination refers to the number of ways that a certain number of items can be selected from a larger set of items without regard to the order of the items. It is different from permutation, which takes into account the order of the items.

The number of combinations can be calculated using the formula:

nCr = n! / (r! x (n - r)!)

Where n is the total number of items in the collection, and r is the number of items in each combination

Since a movie collection has 6 mystery, 10 comedy, 4 adventure, 9 drama, and 12 science fiction discs, then the total number of discs in the collection is 41.

Plug in the values to the formula for combination.

nCr = n! / (r! x (n - r)!)

41C5 = 41! / (5! x (41 - 5)!)

41C5 = 41! / (5! x 36!)

41C5 = 749398

Therefore, there are 749398 5-disc combinations that can be made from the collection.

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The complate table is,

Statement                                                 Reasons

1) K is the midpoint of segments                      Given

  RM and JL.

2) RJ ≅ ML                                                  SSS Congruence Postulate

3) RK ≅ MK ,  JK ≅ LK                                 Definition of Midpoint

4) RK = MK , JK = KL                                    Definition of Congruence

                                                                   Segments

5) Δ EGF ≅ Δ EGH                                      CPCTC

A line segment is a part of line having two endpoints and it is bounded by two distinct end points and contain every point on the line that is between its endpoint.

Given that;

K is the midpoint of segments RM and JL.

Now,

Since, K is the midpoint of segments RM and JL.

Hence, We get;

   Statement                                                 Reasons

1) K is the midpoint of segments                      Given

  RM and JL.

2) RJ ≅ ML                                                  SSS Congruence Postulate

3) RK ≅ MK ,  JK ≅ LK                                 Definition of Midpoint

4) RK = MK , JK = KL                                    Definition of Congruence

                                                                   Segments

5) Δ EGF ≅ Δ EGH                                       CPCTC

Thus, The complete table is shown above.

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The values of x , y and z are 80,2,110 respectively from the given figure where JKLM ~ EFGH

What is Quadrilateral ?

Quadrilateral can be defined as the type of the polygon in which it contains four sides.

Given ,

JKLM ~ EFGH

Since , JKLM ~ EFGH

3/30 = 11/z

 z = 30*11/3

z =110

3 / 30 = 8/ x

3 * x = 8 * 30

x = 80

3 / 30 = y/ 20

y = 20 * 3 / 30

y = 2

Hence the values of x , y and z are 80,2,110 respectively.

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18 m²

The area is the size of a 2-dimensional shape.

Area of a Triangle

The formula for the area of a triangle is [tex]\frac{1}{2}bh[/tex], where b is the base and h is the height.

This formula comes from the fact that a triangle is half of a rectangle. Remember that the area of a rectangle is the base times the height, so a triangle would be half of this.

Solving for Area

The base of the triangle is 9 meters. Then, the height is 4 meters. So, we can plug these values into the formula.

So, A = 18. Then, since meters are being multiplied by each other, the units are meters squared. The final answer is 18 m².

The prices where the quantity demanded is greater than quantity supplied are :

Quantity demanded refers to the amount of goods and services that people and businesses in an economy demand.

This amount of goods and services demanded will be more than the quantity supplied when the price of the good or service is less than the equilibrium price.

The equilibrium price here is $ 3 and so the prices less than $ 3 are $2, $1, and $ 0.

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Even though this relationship is proportional, not all of these ratios are equal.

Verify that the ratios provided are equal. The ratios of 3:5 and 15:25 are both equal. Because the first ratio 3: 5 can be derived by multiplying the ratio 15: 25 by 5 on both the numerator and denominator. The initial ratio of 3: 5 can be multiplied by 5 to get the ratio 15: 25, and vice versa.

This indicates that you would require an 8 fl oz can (a quarter of a quart) of Part B if you were ordering a quart of Part A. You will have 1.25 after combining Parts A and B.

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Therefore , the solution of the given problem of trigonometry comes out to be  B = arcsin(9/14) - 180° = 140.0°.

Correlations between triangles' angles and sides are studied in the branch of mathematics known as trigonometry. Since every straight-sided form may be reduced to a collection of triangles, trigonometry can be found throughout geometry. The relationships between trigonometry and other branches of mathematics, in particular calculus, real or complex, infinite series, logarithms, and infinite series, are astonishingly complicated.

Here,

There are two potential solutions because the supplied angle is opposite the given side that is the shortest.

Using the sine law,

B = b/asin(A)arcsin(9/7sin(30°))arcsin(9/14)

Angle B may take on the following values:

B is equal to arcsin(9/14) = 40.0°.

B = arcsin(9/14) - 180° = 140.0°

Therefore , the solution of the given problem of trigonometry comes out to be  B = arcsin(9/14) - 180° = 140.0°.

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If three lengths can make a triangle by using the Triangle Inequality Theorem which states . that any two triangle sides added together must exceed the third side If the sum of any two sides is equal to or less than the third side, then the lengths cannot make a triangle.

The Triangle Inequality Theorem can be used to determine if a triangle can be formed from three lengths. According to this theorem, any two triangle sides must add up to more than the third side. To put it to use, add up the lengths of the first two sides and compare them to the third side's length. The lengths cannot form a triangle if the total of the first two sides is more than or equal to the third side. The lengths can form a triangle if the product of the first two sides is bigger than the product of the third side.

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Answer: its hard to give an answer but read explanation

Step-by-step explanation: so the first number (1/3x) is your slope and the second number is the y-intercept (5). so for example, you're going to put positive 5 on the y-axis and because you slope is a fraction, rise/run will make you go 3 to the right and 1 up. Then you do the same with the second equation except, the slop is negative and you'll have to go down.

The population of bacteria after 8 days is 7088

Here, we have been given an equation for the rate of growth of a population of bacteria

dP/dt = k√t

where P is the population size

and t is the time in days (0 ≤ t ≤ 10)

We rewrite above equation as,

dP = k√t dt

Integrating both sides, we get,

P = (2/3) × kt^(3/2) + C

We find the value of C.

For t = 0, P = 300 as the initial size of the population is 300.

Substitute t = 0 in above equation.

300 = 0 + C

C = 300

So, the above equation becomes,

P = 300 + (2/3) × kt^(3/2)                .......(1)

Now we find the value of k.

After 1 day the population has grown to 600.

substitute t = 1, P = 600 in equation (1)

600 = 300 + (2/3) × k

(2/3)k = 300

k = 900/2

k = 450

So, the equation of population of bacteria after time t is:

P = 300 + [(2/3) × 450 × t^(3/2)]

P = 300 + 300 × t^(3/2)

P = 300 (1 + t^(3/2))

To find the population after 8 days, substitute t = 8

P = 300 (1 + 8^(3/2))

P = 7088.22

P ≈ 7088

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Answer:y=1x-7

Step-by-step explanation:

Answer:

Step-by-step explanation:

2A. 3x=6 ⇒ x=2

2B. 3n=2(n-3) ⇒ 3n=2n-6 ⇒ n= -6

1. cross multiplication method