find the values of p for which the series is convergent. [infinity] 3 n(ln(n)) p n = 2

Answer:

(- 2, 4 )

Step-by-step explanation:

A translation of 5 units left means subtract 5 from the original x- coordinate.

A translation of 6 units up means add 6 to the original y- coordinate.

Thus

(3, - 2 ) → (3- 5, - 2 + 6 ) → (- 2, 4 )

The coordinates of the point (3,-2), translated 5 units left and 6

units up are (-2, 4) option (D) (-2, 4) is correct.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

It is given that:

The point (3,-2), translated 5 units left and 6 units up.

A 5-unit left translation entails taking 5 away from the initial x-coordinate.

A translation of six units upwards entails multiplying the initial y-coordinate by six.

After applying the translation:

(3, -2) → (3- 5, - 2 + 6) → (-2, 4)

Thus, the coordinates of the point (3,-2), translated 5 units left and 6

units up are (-2, 4) option (D) (-2, 4) is correct.

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Answer:

(-6,0.5)

Step-by-step explanation:

(-9 + -3)÷2= -6

(-4 + 5)÷2=0.5

(-6,0.5)

Answer:

100° and 40°

Step-by-step explanation:

In an isosceles, 2 interior angles are equal.

If one angle is 40°, another one of its angles must be also 40°.

Fact of a triangle

Sum of interior angles of a triangle is 180°.

Let the unknown angle be x.

x + 40° + 40° = 180°

x + 80° = 180°

x = (180 - 80)°

x = 100°

So, the other angle is 100°

Hence,

100° and 40° are the possible measures for the other two triangles.

For the following  equation, L.H.S = R.H.S is proved by solving the left-hand side and equating with it with the right-hand side equation :

\(\frac{tan x}{1-cot x} + \frac{cot x }{1-tan x} = 1+ tan x+ cot x\)

L.H.S =  \(\frac{tan x}{1- cot x} + \frac{cot x }{1 - tan x}\)

\(\frac{- tan^{2}x }{1- tan x} + \frac{cot x }{1 - tan x}\)

\(\frac{-tan^{2} x + cot x}{1 - tan x}\)

Multiply \(\frac{tan x}{tan x}\) we get,

\(\frac{1- tan^{3} x}{tan x (1- tan x)}\)

\(\frac{(1 - tan x ) (1 + tan x + tan ^{2}x) }{tan x (1 - tan x )}\)

\(\frac{( 1- tan x + tan^{2}x) }{tan x}\)

Divide each term separately,

\(\frac{1}{tan x} + \frac{tan x}{tan x} + \frac{tan^{2}x }{tan x}\)

cot x + 1 + tan x

therefore, 1+ tan x + cot x = R.H.S

L.H.S = R.H.S, hence the theory is proved.

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The dominant strategy for each player in this three-player game is R.

In game theory, a dominant strategy is a strategy that yields the best outcome for a player regardless of the strategies chosen by the other players. To identify the dominant strategy for each player in this game, we can consider the payoffs for each strategy combination.

Starting with Player 1, we can see that choosing strategy L results in a payoff of 2 when Player 2 plays U or D, and a payoff of 0 when Player 2 plays L. On the other hand, choosing strategy R results in a payoff of 2 when Player 2 plays U or D, and a payoff of 5 when Player 2 plays L. Since 5 > 2, Player 1's dominant strategy is R.

Similarly, for Player 2, we can see that choosing strategy L results in a payoff of 2 when Player 3 plays L or R, and a payoff of 0 when Player 3 plays U or D. On the other hand, choosing strategy R results in a payoff of 2 when Player 3 plays L or R, and a payoff of 1 when Player 3 plays U or D. Since 2 > 1, Player 2's dominant strategy is also R.

Finally, for Player 3, we can see that choosing strategy L results in a payoff of 2 when both Player 1 and Player 2 play L or R, and a payoff of 0 when either Player 1 or Player 2 plays U or D. On the other hand, choosing strategy R results in a payoff of 2 when both Player 1 and Player 2 play L or R, and a payoff of 1 when either Player 1 or Player 2 plays U or D. Since 2 > 1, Player 3's dominant strategy is also R.

Therefore, the dominant strategy for each player in this three-player game is R. It's worth noting that, unlike in other games, there is no Nash equilibrium in this game where all players are playing their dominant strategies simultaneously. Instead, any combination of R and L could be a Nash equilibrium, depending on the choices made by the other players.

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Answer:

You are going to spend $3.48 in total.

Step-by-step explanation:

You need to add the two numbers together.

1.49+1.99=$3.48

You are going to spend $3.48 in total. (I'm assuming we aren't supposed to include tax)

the derivative of a(x) = 2 - 9x is -9, indicating that the slope of the function remains constant at -9 for all values of x.

The derivative of a function represents its rate of change or slope at any given point. To find the derivative of a function, we apply the power rule and constant rule of differentiation. In this case, the function a(x) = 2 - 9x is a linear function with a constant slope of -9.

The power rule states that the derivative of x^n is nx^(n-1), where n is a constant. In this function, the derivative of 2 is 0, and the derivative of -9x is -9. Since there are no other terms or variables involved, the derivative simplifies to -9.

Therefore, the derivative of a(x) = 2 - 9x is -9, indicating that the slope of the function remains constant at -9 for all values of x.

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Answer:

C

Step-by-step explanation:

f(x) = x-8 when x>3, f(7)=7-8=-1

The rate of change is 961.37 gallons/hour. This means that the water level decreases by 961.37 gallons every hour.

In mathematics, comparing two related quantities stated in different units is known as a rate. A rate is the ratio of two distinct values that are gauged in various ways. It is not the same as a unit rate to compare a certain number of units of the first quantity to one unit of the second. In general, the rate can be expressed as the ratio of two quantities with distinct units. With the help of rate, we can create a connection between two otherwise unconnected components. By doing this, we can gain a deeper understanding of a scenario.

Given,

The total amount of water the pool can hold =  9613.7 gallons

The time taken to drain the pool completely = 10 hours

We are asked to find the change in water level per hour of the pool.

This can be called the rate of change.

Rate of change = Total amount of water/ Time taken to drain

                       = 9613.7 / 10 = 961.37 gallons / hour

Therefore the rate of change is 961.37 gallons/hour. This means that the water level decreases by 961.37 gallons every hour.

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Answer:

-16r^2 - 10r

Step-by-step explanation:

all you got to do is distribute

110ft²

Area of figure=(10×8)+(1/2×6×8)

=80+24

=112 ft²

=110 ft² (to nearest tenth)

Answer:

9(y-4)

Step-by-step explanation:

Gave in your previous question!

Answer:

Where is the formula

Step-by-step explanation:

Answer:

I = $ 0.74

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 4%/100 = 0.04 per year,

putting time into years for simplicity,

6 months ÷ 12 months/year = 0.5 years,

then, solving our equation

I = 37 × 0.04 × 0.5 = 0.74

I = $ 0.74

The simple interest accumulated

on a principal of $ 37.00

at a rate of 4% per year

for 0.5 years (6 months) is $ 0.74.

BRAINLIEST PLEASE

Answer with explanation:

Part A:

One solution.

The number of points of intersection represents the number of solutions. Since the two lines only intersect at one point, there is only one solution.

Part B:

(3, 4)

The point(s) of intersection marks the solution(s) to the lines. Since lines A and B intersect at the point (3, 4), the solution to the equation of their lines is (3, 4), or \(x=3, y=4\), as coordinates are written as (x, y).

Answer:

680 candy bars must be sold

Step-by-step explanation:

2.5 times 680 equals 1700 that minus 200 is 1500.

since r is so widely used, it is appropriate to calculate r for nonlinear data: False.

The calculation of r (Pearson's correlation coefficient) is based on the assumption that the relationship between the two variables is linear. Therefore, it is not appropriate to calculate r for nonlinear data as it may give misleading results.

In summary, it is not appropriate to calculate r for nonlinear data as it assumes a linear relationship between the variables. Other methods such as Spearman's rank correlation or Kendall's tau may be used for nonlinear data.


n: The correlation coefficient 'r' is specifically designed to measure the strength and direction of a linear relationship between two variables. While it is widely used, calculating 'r' for nonlinear data is not appropriate, as it will not accurately capture the true nature of the relationship between the variables.

When dealing with nonlinear data, it is better to use other statistical methods designed for such data, rather than relying on the correlation coefficient 'r'.

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Answer: 8

Step-by-step explanation:

From the question, we are informed that a 2-mile walking trail has a distance marker every 1\4 mile. Hl

The number of markers that are along the trail will be calculated as:

= Length of walking trail / interval of distance marker

= 2 ÷ 1/4

= 2 × 4

= 8

There are 8 markers along the trail.

The distance between the two points is √2 units

The length along a line or line segment between two points on the line or line segment.

Distance=√(x₂-x₁)²+(y₂-y₁)²

From the graph the two points are at (2, 4) and (3,3)

We have to find the distance between two points.

The formula for distance is Distance=√(x₂-x₁)²+(y₂-y₁)²

=√(3-2)²+(3-4)²

=√1+1

=√2 units

Hence, the distance between the two points is √2 units

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Given:

The parent function is

\(f(x)=x^2\)

The graphs of f(x) and g(x) are given.

To find:

The function g(x).

Solution:

From the given graph it is clear that the graph of f(x) is reflected over the x-axis and shifted 3 units down to get the graph of g(x).

The translation is defined as

\(g(x)=kf(x+a)+b\)                .... (1)

Where, k is stretch factor, a is horizontal shift and b is vertical shift.

If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k. If k<0, then the graph of f(x) reflected over the x-axis.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

From the given graph it is clear that the graph of f(x) is reflected over the x-axis and shifted 3 units down to get the graph of g(x). So, k=-1, a=0 and b=-3.

\(g(x)=(-1)f(x+0)+(-3)\)

\(g(x)=-f(x)-3\)

\(g(x)=-x^2-3\)          \([\because f(x)=x^2]\)

Therefore, the required function is \(g(x)=-x^2-3\). So, the correct option is B.

The name of the figure with equal opposite sides and equal diagonals is rectangle.

option A.

The distance between the coordinate points is calculated by applying the formula for distance between points as follows;

Distance between (-10, 8) and (-7, 13)

A = √ (-7 + 10)² + (13 - 8)²

A = 5.83

Distance between (3, 7) and (0, 2)

B = √ (0 - 3)² + (2 - 7)²

B = 5.83

Distance between (-10, 8) and (3, 7)

C = √ (3 + 10)² + (7 - 8)²

C = 13.04

Distance between (-7, 13) and (0, 2)

D = √ (0 + 7)² + (2 - 13)²

D = 13.04

Distance between (-10, 8) and (0, 2)

E = √ (0 + 10)² + (2 - 8)²

E = 11.66

Distance between (-7, 13) and (3, 7)

F = √ (3 + 7)² + (7 - 13)²

F = 11.66

Thus, the name of the figure with equal opposite sides and equal diagonals is rectangle.

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Answer:

\(\frac{x-5}{x-7}\)

Step-by-step explanation:

Given

\(\frac{x^2-2x-15}{x^2-4x-21}\) ← factor numerator and denominator

= \(\frac{(x-5)(x+3)}{(x-7)(x+3)}\) ← cancel (x + 3) on numerator and denominator

= \(\frac{x-5}{x-7}\)

Answer:

\(\frac{x-5}{x-7}\) is the answer

Step-by-step explanation:

\(\frac{x^{2}-2x -15 }{ x^{2}-4x-21}\)

Factorising,

\(\frac{x^{2}-5x+3x-15}{x^{2}-7x+3x-21 }\)

\(\frac{x(x-5)+3(x-5)}{x(x-7)+3(x-7)}\)

\(\frac{(x+3)(x-5)}{(x+3)(x-7)}\)

\(\frac{x-5}{x-7}\)

Therefore , the solution of the given problem of percentage comes out to be 38 years old is the median age.

In statistics, a "a%" is a figure or statistic that is expressed as a percentage of 100. The words "pct," "pct," but instead "pc" are also not frequently used. However, the sign "%" is frequently used to represent it. The percentage sum is flat; there are no dimensions. Percentages are truly integers because their numerator almost always equals 100. Either the % symbol (%) or the additional term "fraction" must come before a number to denote that it is a percentage.

Here,

The following algorithm must be used to determine the mean age:

=> mean = (all years added together) / (total number of persons)

The representative age for each age group is the age that falls in the middle of the range. With this approach, we can determine the total age as follows:

=>18(9) + 23(28) + 28(33) + 33(90) + 38(122) + 56(48) + 48(24) + 76(20) + 1089(0.25)

=> 162 + 644 + 924 + 2970 + 4636 + 2688 + 1152 + 1520 + 272.25

=>18(9) + 23(28) + 28(33) + 33(90) + 38(122) + 56(48) + 48(24) + 76(20) + 1089(0.25)

According to the information provided, there are 460 people in total.

=> mean = 17745.25 / 460

=> mean = 17745.25 / 460

As a result, the average lifespan is roughly 38.552 years.

The age category in this instance with the highest frequency has a midpoint of 38 and a frequency of 122. As a result, 38 years old is the median age.

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Answer:

Most Unlikely:  Less than 5

Likely:  2-digit number

Unlikely:  Multiple of 3

Equally Likely:  Odd

Most Likely:  Greater than 10

Step-by-step explanation:

there are 6x5, or 30 outcomes

Less than 5 has 1 outcome - spinner and dice both are one

Odd has 15 outcomes

Multiple of 3 has 8 outcomes:  1+5, 2+1, 2+7, 2+12, 3+12, 4+5, 5+7, 5+10

Two-digits has 12 outcomes

Greater than ten has 16 outcomes

Answer:

Most Unlikely:  Less than 5

Likely:  2-digit number

Unlikely:  Multiple of 3

Equally Likely:  Odd

Most Likely:  Greater than 10

--

To implement the function f(w1,w2,w3) = Σ m(0, 2, 4, 5, 7) using a 3 to 8 binary decoder and an OR gate, we can connect the input lines w1, w2, and w3 to the A, B, and C inputs of the decoder, respectively.

To implement the given function f(w1,w2,w3) = Σ m(0, 2, 4, 5, 7), we first need to convert it into a truth table as follows:

w1    w2    w3    f

0       0       0     0

0       0        1      1

0        1       0      0

0        1       1       1

1        0       0      0

1        0       1       0

1        1        0       1

1        1       1         1

Here, the binary values of w1, w2, and w3 are listed in the first three columns, and the corresponding value of f is listed in the fourth column. The expression Σ m(0, 2, 4, 5, 7) indicates that the function f should be equal to 1 for the minterms 0, 2, 4, 5, and 7.

We can use a 3 to 8 binary decoder to implement this function as follows:

The input lines of the decoder are w1, w2, and w3.

The outputs of the decoder are eight lines labeled Y0, Y1, Y2, Y3, Y4, Y5, Y6, and Y7, each corresponding to one of the possible input combinations of w1, w2, and w3.

The output line corresponding to each minterm that evaluates to 1 is connected to the input of an OR gate.

The output of the OR gate is the output of the function f.

Specifically, we can connect the input lines w1, w2, and w3 to the decoder as follows:

w1 is connected to the A input of the decoder.

w2 is connected to the B input of the decoder.

w3 is connected to the C input of the decoder.

The eight outputs of the decoder are connected to the inputs of an OR gate as follows:

Y0 is not connected to the OR gate since it corresponds to the input combination 000, which is not a minterm in the function.

Y1 is connected to one input of the OR gate since it corresponds to the input combination 001, which is a minterm in the function.

Y2 is not connected to the OR gate since it corresponds to the input combination 010, which is not a minterm in the function.

Y3 is connected to one input of the OR gate since it corresponds to the input combination 011, which is a minterm in the function.

Y4 is connected to one input of the OR gate since it corresponds to the input combination 100, which is a minterm in the function.

Y5 is connected to one input of the OR gate since it corresponds to the input combination 101, which is a minterm in the function.

Y6 is not connected to the OR gate since it corresponds to the input combination 110, which is not a minterm in the function.

Y7 is connected to one input of the OR gate since it corresponds to the input combination 111, which is a minterm in the function.

The other input of the OR gate is connected to ground (or logic 0).

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The number of snacks they can buy to split among them is 3.

Rachel, Adam, Michelle, Hannah, and James are going to the movies. They have $65 to spend on tickets and snacks. Each movie ticket costs $9.5, and each snack item costs $4.5. We need to calculate the number of snacks they can buy.

Let the number of snacks they can buy be represented by the variable "n". The total money is $65. The amount of money left after buying movie tickets for all the people is calculated below.

C = 65 - 5*9.5

C = 65 - 47.5

C = 17.5

Hence, they have $17.5 to spend on snacks. The number of snacks they can buy is determined by the ratio of the money left to the price of each snack.

n = 17.5/4.5

n = 3.89

They can buy the snacks in whole numbers. Hence, the number of snacks they can buy is 3.

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Answer:

Reflection across x = -5

Answer: Let's start by assuming that Matilde started out with some amount of money, which we will call "x" (in euros).

According to the problem, she spent two-thirds of her money in the first shop. This means that she had one-third of her money left after leaving the first shop:

Money left after first shop = x - (2/3)x = (1/3)x

Matilde then spent two-thirds of this remaining money in the second shop. This means that she had one-third of her original money left after leaving the second shop:

Money left after second shop = (1/3)x - (2/3)(1/3)x = (1/9)x

We are told that she had €18 left at this point so that we can set up an equation:

Money left after second shop = (1/9)x = 18

Solving for x, we get:

x = 162

Therefore, Matilde started out with €162.

Step-by-step explanation: