Please help I don't understand

The inductive hypothesis of the inductive step of an inductive proof for k≥4, if 2k≥3k, then 2^k+1≥3(k+1) is used in Step 4 of the proof.

The following is the solution to the problem.2^k+1≥2⋅2^k (Step 1)≥2⋅3k (Step 2)≥3k+3k (Step 3)≥3k+3 (Step 4)≥3(k+1) (Step 5)Therefore, the inductive hypothesis is used in step 4 of the proof. Step 4 demonstrates that the statement is correct for k+1.

Learn more about hypothesis

https://brainly.com/question/32562440

#SPJ11

Weighted sum approach is a mathematical technique used to combine two or more values into a single, overall score.

It is used to assign weights to the different values to reflect their relative importance and then add the weighted values together to get the overall score.

The formula for weighted sum approach is: Overall Score = \((Weight1*Value1) + (Weight2*Value2) +…+(Weightn*Valuen)\). The weights should always add up to 1.

For example, if two criteria, A and B, were to be evaluated with weights of 0.6 and 0.4, respectively, the overall score could be calculated as: Overall Score =\((0.6*Value of A) + (0.4*Value of B).\)

Weighted sum approach is a useful tool for making decisions in situations where multiple criteria need to be taken into account. It can be used to compare different options and determine which one is the best overall.

Learn more about weighted sum here:

https://brainly.com/question/28471551

#SPJ4

Answer:

See answers below:

Step-by-step explanation:

Using corresponding angles properties, angles opposed by the vertex, and supplementary angle properties, we get:

<1 = 75 degrees

<2 = 105 degrees

<3 = 44 degrees

<4 = 136 degrees

<5 = 44 degrees

<6 = 90 degrees

<7 = 46 degrees

<8 = 75 degrees

<9 = 105 degrees

<10 = 75 degrees

<11 = 59 degrees

<12 = 46 degrees

<13 = 75 degrees

<14 = 105 degrees

<15 = 44 degrees

<16 = 136 degrees

<17 = 44 degrees

<18 = 136 degrees

Answer:

2.2

Step-by-step explanation:

To find a, you use a formula called the law of cosines:

The law of cosines tells us:

a^2 = b^2 + c^2 - 2bc cosA

So lets plug in the values:

a^2 =  4^2 + 3^2 -2(4)(3)cos(32)

a^2 = 25-24cos32

a^2 is roughly equal to 4.97

therefore a roughly equal to 2.2

Answer: The answer is A. 2.2. Hoped this helps! :)

Step-by-step explanation:

The clerk actually spent approximately 15.71% of his time on messenger work during the week.

The clerk spent 1/5 of his time sorting mail, which is equal to 7 hours (1/5 x 35 hours). He also spent 1/2 of his time filing letters, which is equal to 17.5 hours (1/2 x 35 hours). Additionally, he spent 1/7 of his time in reception work, which is equal to 5 hours (1/7 x 35 hours).

To find the amount of time he spent on messenger work, we can subtract the total time spent on sorting mail, filing letters, and reception work from the total 35-hour workweek:

35 hours - 7 hours - 17.5 hours - 5 hours = 5.5 hours

Thus, the clerk spent 5.5 hours on messenger work during the week. To find the percentage of time he spent on messenger work, we can divide this amount by the total number of hours worked and multiply by 100:

(5.5 hours / 35 hours) x 100% ≈ 15.71%

To learn more about time click on,

https://brainly.com/question/28987291

#SPJ4

To determine the distance between two points in a rectangular coordinate system, we can use the distance formula. Given the coordinates of the points (4.8, 2.5) and (-3.2, 5.0), we can calculate the distance as follows:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the values, we get:

Distance = √((-3.2 - 4.8)^2 + (5.0 - 2.5)^2)

Simplifying further:

Distance = √((-8)^2 + (2.5)^2)

Distance = √(64 + 6.25)

Distance = √70.25

Distance ≈ 8.38 centimeters

Therefore, the distance between the points (4.8, 2.5) and (-3.2, 5.0) is approximately 8.38 centimeters.

Learn more about coordinate system here: brainly.com/question/11004434

#SPJ11

Answer:

4

Step-by-step explanation:

(9 - 1) / (3 - 1) = 8/2 = 4

Answer:

4

Step-by-step explanation:

To find the slope using two points

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

   = (9-1)/(3-1)

   = 8/2

   = 4

Answer:

\(f^{-1} (x) = x - 3\)

Step-by-step explanation:

Step-by-step explanation:

Heyy friends here you come

vnn-nuhg-vib

n=4 is the degree maclurins polynomial is required so that the error in the approximation is less than 0.001.

Given that,

The expression is

e⁰⁵=1+0.5+0.5²/2!+0.5³/3!+.....

We have to find what degree maclurins polynomial is required so that the error in the approximation is less than 0.001.

We know that,

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

√e=1.64872

Pₙ( x)= e⁰⁵=1+0.5+0.5²/2!+0.5³/3!+.....

P₂=1+0.5+0.5²/2!=1.625

P₃= P₂+0.5³/3!=1.6458

P₄= P₃+0.5⁴/4!=1.648404

√e - P₄ = -0.0003158

Therefore, n=4 is the degree maclurins polynomial is required so that the error in the approximation is less than 0.001.

To learn more about approximation visit: https://brainly.com/question/15696262

#SPJ4

Answer:

w = 39°

Step-by-step explanation:

108° and y° are suplementary angles

111° 69°and x° are suplemantary angles

then:

108 + y = 180

y = 180 - 108

y = 72°

111 + x = 180

x = 180 - 111

x = 69°

Internal angles of a triangle sum 180°

then:

x + y + w = 180

69 + 72 + w = 180

141 + w = 180

w = 180 - 141

w = 39°

Answer:

I DON'T KNOW WHO so what is yours

The percentage discount on the object is 33.3%

Percent discount is the amount of money discounted from the sales price of a product.

Given the following

Cost price = Rs 150

Selling Price = Rs 100

%discount = CP - SP/CP * 100
%discount = 150-100/150 * 100

%discount 50/150 * 100

%discount = 33.3%

Hence the percentage discount on the object is 33.3%

Learn more on discount here; https://brainly.com/question/24304697

#SPJ1

The simple linear regression equation for miles per gallon as the response variable and weight as the predictor variable is

M = \(\beta\)0 + \(\beta\)1W + ε

The car rental company can use this model to determine the effect of weight (of the car) on miles per gallon.

Given: To write a simple linear regression equation with Miles per gallon as the response variable and weight as the predictor variable.

What is simple linear regression?

Simple linear regression is used to estimate the relationship between two quantitative variables.

Let's say "Miles per gallon" is represented as M and

"Weight" be represented as W

The simple linear regression equation is :

M = \(\beta\)0 + \(\beta\)1W + ε

where,

How might the car rental company use this model?

The car rental company might use the regression model to determine the

Know more about "simple linear regression" here: https://brainly.com/question/14313391

#SPJ4

Answer:

1. x = 3

2. p = -3

3. a = 4

4. n = -2

5. g = 2

6. k = -18

7. s = 18

8. c = -8

9. a = -6

10 v = 9

The limits of the function \(f(x) = -x^6 + x^5 + x^4 + x^3 - 2x^2 - 2x + 2\) as x approaches positive and negative infinity are both -∞.

To evaluate the limits of the function \(f(x) = -x^6 + x^5 + x^4 + x^3 - 2x^2 - 2x\) + 2 as x approaches positive and negative infinity, we examine the leading term of the function as x becomes very large or very small.

lim(x→∞) f(x):

As x approaches positive infinity, the term with the highest power dominates the function. In this case, the term is \(-x^6\). As x becomes very large, \(-x^6\) approaches negative infinity. Therefore, the limit of f(x) as x approaches positive infinity is:

lim(x→∞) f(x) = lim(x→∞) \((-x^6 + x^5 + x^4 + x^3 - 2x^2 - 2x + 2)\) = -∞

lim(x→-∞) f(x):

Similarly, as x approaches negative infinity, the term with the highest power dominates the function. In this case, the term is \(-x^6\). As x becomes very small (large negative),\(-x^6\) approaches negative infinity. Therefore, the limit of f(x) as x approaches negative infinity is:

lim(x→-∞) f(x) = lim(x→-∞) \((-x^6 + x^5 + x^4 + x^3 - 2x^2 - 2x + 2)\) = -∞

To know more about function,

https://brainly.com/question/31221086

#SPJ11

Answer:

Partition means to separate or to divide. A line segment can be partitioned into smaller segments which are then compared as ratios.

Step-by-step explanation:

Answer:

Step-by-step explanation:

o.10

Answer:

14.2 km.

Step-by-step explanation:

That's a standard application of Al-Kashi law of cosines (or Carnot theorem, depends on how your book presents it)

Let's call x the distance between the group, and a and b the distance from each group from the Treasure.

\(x^2=a^2+b^2-2ab\cdot cos57 =\\12.3^2 + 16.4^2 -2(12.3)(16.4)(0.544) \approx 200.52\\x= \sqrt {200.52} \approx14.2 km\)

Obviously it's a distance so we take the positive value of the square root.

Answer:

\(5 \times ( - 1)3 + 2 \\ \\ 5 - 3 + 2 \\ \\ = 4\)

Step-by-step explanation:

\(5 {x}^{3} + 2 \\ x = - 1 \\ 5 \times {( - 1)}^{3} + 2 \\ = - 5 + 2 \\ = - 3 \\ or \: 5x3 + 2 \\ = 5 \times - 1 \times 3 + 2 \\ = - 1 5 + 2 \\ = - 13 \\ thank \: you\)

The two numbers are 68 and 47 for the sum of two numbers is 115 and the difference is 21 and the correct mathematical expressions are x + y = 115; y-x=21 

Given: Sum of the two numbers is 115

x + y = 115

Difference between two numbers is 21

y - x = 21  

We have two equations:

x + y = 115

y - x = 21

We can solve the equations using elimination-method to find the values of x and y.

We can add the two equations to eliminate x:

x + y + y - x = 115 + 21  

2y = 136

y = 68.

Now, we can find the value of x:

x + 68 = 115

x = 115 - 68

x = 47.

Therefore, the two numbers are 68 and 47.

To know more about mathematical-expression visit:

https://brainly.com/question/30350742

#SPJ11

The area of the region enclosed by the curve r = 9cos(3θ) is (27/2)π.

What is integration?

In mathematics, and notably in calculus, integration is a fundamental notion. It is a mathematical process that seeks to determine a function's integral. The accumulation or total of all infinitesimally small changes in a quantity is represented by the integral.

To find the area of the region enclosed by the curve r = 9cos(3θ), we can set up a double integral in polar coordinates.

In polar coordinates, the area element is given by dA = r dr dθ. To determine the limits of integration, we need to find the values of θ where the curve intersects itself and encloses a region.

The polar curve r = 9cos(3θ) completes one loop for every 2π/3 radians, so we can integrate over the range 0 ≤ θ ≤ 2π/3. The corresponding limits for r can be determined by setting r = 0 and solving for θ.

At r = 0, we have:

0 = 9cos(3θ)

cos(3θ) = 0

The equation cos(3θ) = 0 has solutions at θ = π/6, π/2, 5π/6. These values divide the interval [0, 2π/3] into three subintervals.

Now we can set up the double integral:

Area = ∬R dA

Using polar coordinates, we have:

dA = r dr dθ

The limits of integration are:

0 ≤ r ≤ 9cos(3θ)

0 ≤ θ ≤ 2π/3

Thus, the double integral becomes:

Area = ∫[0 to 2π/3] ∫[0 to 9cos(3θ)] r dr dθ

Now we can evaluate this double integral:

Area = ∫[0 to 2π/3] (1/2)r² ∣[0 to 9cos(3θ)] dθ

Area = (1/2) ∫[0 to 2π/3] (81cos²(3θ)) dθ

Using the trigonometric identity cos²(3θ) = (1 + cos(6θ))/2, we can simplify further:

Area = (1/2) ∫[0 to 2π/3] (81/2)(1 + cos(6θ)) dθ

Area = (81/4) ∫[0 to 2π/3] (1 + cos(6θ)) dθ

Now we can integrate term by term:

Area = (81/4) [(θ + (1/6)sin(6θ)) ∣[0 to 2π/3]]

Area = (81/4) [(2π/3 + (1/6)sin(4π) - (1/6)sin(0))]

Simplifying further:

Area = (81/4) [(2π/3 + 0 - 0)]

Area = (81/4) (2π/3)

Area = (27/2)π

Therefore, the area of the region enclosed by the curve r = 9cos(3θ) is (27/2)π.

To know more about integration follow the given link:

https://brainly.com/question/30094386

#SPJ4

The mean, median and mode of the data sets are 0.23, 0.19 and 0.12 respectively.

Mean, median and mode are measure of central tendency.

The mean is the average of the numbers.

The median is the middle number in a sorted, ascending or descending list of numbers.

The mode is the number that occurs the highest number of times.

Therefore, let's arrange the data in ascending order.

$0.12,  $0.12, $0.15, $0.17 , $0.18, $0.20, $0.24, $0.28, $0.29, $0.55

Hence,

mean = sum of the numbers / 10

mean = 0.12 + 0.12 + 0.15 + 0.17 + 0.18 + 0.20 + 0.24 + 0.28 + 0.29 + 0.55 / 10

mean = 2.3 / 10

mean = 0.23

median = 0.18 + 0.20 / 2

median = 0.38 / 2

median = 0.19

mode = 0.12

learn more on mean, median and mode here: https://brainly.com/question/12749269

#SPJ1

Answer:

Step-by-step explanation:

Mean is 0.23, since you add all the numbers up, then divide by all the numbers there are.

For example, there are 10 numbers, and if you add all of the numbers together, you get 2.3.

2.3 divided by 10 is 0.23

I will get the median and modes later.

Answer:

1 kg of mushrooms costs £2.7.

Step-by-step explanation:

Step 1: Write equations.

Let a be the cost of apples per kg and m the cost of mushrooms per kg.

First equation: Ibrar buys 3 kg of apples. He also buys 0.4 kg of mushrooms. The total cost is £6.93.

\(3a + 0.4m = 6.93\)

Second equation: 1 kg of apples cost £1.95.

\(a = 1.95\)

Step 2: Solve the system of equations.

1) \(3a + 0.4m = 6.93\)

2) \(a = 1.95\)

Substitute a in the first equation with a from second.

\(3a + 0.4m = 6.93\\3(1.95) + 0.4m = 6.93\)

Solve for m.

\(5.85 + 0.4m = 6.93\\0.4m = 6.93 - 5.85 \\0.4m = 1.08\\m = \frac{1.08}{0.4}\\m = \text{\£}2.7\)

The cost of 1 kg of mushrooms is £2.7.

Two or more expressions with an Equal sign is called as Equation.

Given that Ibrar buys 3kg of apples

Ibrar buys 0.4kg of mushrooms.

The total cost is £6.93

3x+0.4y=6.93...(*)

1kg of apples cost is £1.95

x=1.95

Substitute the value of x in *

3(1.95)+0.4y=6.93

5.85+0.4y=6.93

Subtract 5.85 on both sides

0.4y=6.93-5.85

0.4y=1.08

Divide both sides by 0.4

y=2.7

Hence, the cost of 1 kg of mushrooms is £2.7.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ2

Answer:

200 Photos

Step-by-step explanation:

20-4 = 16

16/0.08 = 200

For the function y = 4x^2, it is possible to find the maximum or minimum. the value of y at the maxima/minima of the function y = -3x^2 + 6x is 3.

The function represents a quadratic equation with a positive coefficient (4) in front of the x^2 term. This indicates that the parabola opens upward, which means it has a minimum point.

For the function y = 3x, it is not possible to find the maximum or minimum because it represents a linear equation. Linear equations do not have maxima or minima since they have a constant slope and continue indefinitely.

For the function y = -3x^2 + 6x, we can find the maxima or minima by finding the vertex of the parabola. The vertex can be found using the formula x = -b/(2a), where a and b are coefficients of the quadratic equation.

In this case, the coefficient of x^2 is -3, and the coefficient of x is 6. Plugging these values into the formula, we have:

x = -6 / (2 * -3) = 1

To find the value of y at the vertex, we substitute x = 1 into the equation:

y = -3(1)^2 + 6(1) = -3 + 6 = 3

Therefore, the value of y at the maxima/minima of the function y = -3x^2 + 6x is 3.

Learn more about maxima/minima

https://brainly.com/question/32055972

#SPJ11

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

2 3/10 ÷ 2 2/9

Step 02:

division:

the number of distinct seating arrangements when two seatings are considered the same when everyone has the same two  without neighbors regard to whether they are right or left neighbors is:5!6⋅2=10.6⋅25! = 10

There are $(6-1)! = 5! = 120$ ways to seat six people around a circular table if the seatings are considered distinct. However, we must divide this number by $6$ to account for the fact that rotations of the same seating arrangement are considered the same. We also must divide by $2$ to account for the fact that reflections (i.e., reversing the order of people) of the same seating arrangement are also considered the same.

Therefore, the number of distinct seating arrangements when two seatings are considered the same when everyone has the same two neighbors without regard to whether they are right or left neighbors is:

5!6⋅2=10.6⋅25! = 10

learn more about number here

https://brainly.com/question/10547079

#SPJ4

It will take Firefighter Corrigan 45 minutes to complete the job alone.

Let's assume the amount of work required to paint the fence is represented by "1 job" or "1 unit of work."

We can use the concept of work rate to solve this problem. The work rate is the amount of work done per unit of time.

Let's denote the work rate of Firefighter Ginley as G (in jobs per minute) and the work rate of Firefighter Corrigan as C (in jobs per minute).

According to the given information:

Firefighter Ginley can complete the job alone in 30 minutes, so his work rate is 1 job / 30 minutes = 1/30 jobs per minute.

Firefighter Ginley and Firefighter Corrigan together can complete the job in 18 minutes, so their combined work rate is 1 job / 18 minutes = 1/18 jobs per minute.

Now, let's express the work rates in terms of time taken by Firefighter Corrigan alone:

Work rate of Firefighter Ginley + Work rate of Firefighter Corrigan = Combined work rate

1/30 + C = 1/18

To find the work rate of Firefighter Corrigan, we subtract the work rate of Firefighter Ginley from the combined work rate:

C = 1/18 - 1/30

C = (5/90) - (3/90)

C = 2/90

Simplifying, we get:

C = 1/45

This means that Firefighter Corrigan can complete 1/45 of the job per minute.

To find out how long it will take Firefighter Corrigan to complete the job alone, we can invert the work rate:

Time taken by Firefighter Corrigan = 1 / Work rate of Firefighter Corrigan

Time taken by Firefighter Corrigan = 1 / (1/45)

Time taken by Firefighter Corrigan = 45 minutes

Therefore, it will take Firefighter Corrigan 45 minutes to complete the job alone.

Learn more about work rate at https://brainly.com/question/14305692

#SPJ11