Prove that 3 + 11 + + (8n 5) = 4n? _ n for all natural numbers n using the principle of mathematical induction.

Answer:

I'm not gonna answer

Step-by-step explanation:

but u have to multiply and divide your answer

The number of degrees of each turn made in the regular hexagonal pond is: 120°.

Altogether is 720°.

A hexagonal shape is a six (6) sided polygon that has 6 interior angles.

The sum of all interior angles of an x-sided polygon can be calculated as:

(n - 2)180.

To find the sum of all the interior angles of the hexagonal pond, substitute the n = 6 into (n - 2)180:

(6 - 2) × 180

= 4 × 180

= 720°

The measure of each interior angle of the hexagonal pond = 720/6 = 120°.

Therefore, it implies that, you made 120 degrees turn at each corner, and altogether, you made 720°.

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The slope of the main portion of the slide is equal to 0.65.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Note: 18 inches is equal to 1.5 feet.

Based on the information provided, we can logically deduce the following data points on the line:

Points on x-axis = (2, 12).

Points on y-axis = (1.5, 8).

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (8 - 1.5)/(12 - 2)

Slope (m) = 6.5/10

Slope (m) = 0.65.

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Answer:

750 meters

Step-by-step explanation:

120 meters/4 seconds = 30 meters per second

30 meters per second * 25 seconds = 750 meters

(you could calculate 3 * 25 first to get 75 and then add the zero at the end. It's the faster way.)

Answer:

x = 750 m

Step-by-step explanation:

Write and solve a equation of ratios:  

  120 m          4 sec

-------------  =  -------------

       x              25 sec

Inverting this equation yields

      x             25 sec

-------------- = -------------

  120 m          4 sec

Cross-multiplication yields (4 sec)x = (120 m)(25 sec).  This yields:

      3000 m-sec

x = --------------------  = 750 meters

           4 sec

Note that the same result can be obtained by multiplying (120 m) by (25/4).

Answer:

No, not a function.

Step-by-step explanation:

The graph touches the vertical line more than once.

Answer:

Not a Function

Step-by-step explanation:

It fails the vertical line test where each input has one output. Take x=0 for example. At x=0, y=4,-4. This input has two outputs so it is not a function.

Answer:

42.5

Step-by-step explanation:

those two dashes or lines on the sides of the tringle or between A and B or A and C mean that those line are the same length so I would guess your answer is the same as the other givin length which is 42.5

The volume of the given shape is  392.7hr² sq. units.

Given, the base of S is a circular disk with radius 5r.

Parallel cross-sections perpendicular to the base are isosceles triangles with height 5h and unequal side in the base.

we have to find the volume of the shape we are given,

As, Volume = area × height

Now, area = πr²

area = 3.14×(5r)²

area = 78.54r²

as, height = 5h

then, Volume = 78.54r²×5h

Volume = 392.7hr²

Hence, the volume of the given shape is  392.7hr² sq. units.

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17.85

so what i did is i took 20 divided by 3 = 7

than i did

2.55 x 7 = 17.85

answer:

____________________________________________________________17.85

Please mark brainlist if this helps!

The total cost of 20 toy cars is 17 dollars.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, at the toy store, 3 toy cars cost $2.55.

Here, cost of 1 toy car = 2.55/3

= 0.85

Cost of 20 cars = 20×0.85

= $17

Therefore, the cost of 20 toy cars is 17 dollars.

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Answer:

1,227

Step-by-step explanation:

3,000 divided by 3 is 1,000

600 divided by 3 is 200

80 divided by 3 is 26 r2

1 + r2 =3

and 3 divided by 3 is 1

1,000 + 200 + 26 + 1 = 1,227

Answer: Php. 3,300

Step-by-step explanation:

Assuming this is simple interest, the amount he would earn from Stacy after 2 years is:

= Amount loaned out * Interest rate * Number of years

= 7,500 * 10% * 2

= Php 1,500

Amount from Torrie:

= 7,500 * 12% * 2

= Php. 1,800

The total interest received is:

= 1,500 + 1,800

= Php. 3,300

The hash of the given message is 135.

In computing, a message digest is a fixed-sized string of bytes that represents the original data's cryptographic hash. This hash is used to authenticate a message, guaranteeing the integrity of the data in the message.

Here, it is given the message m = 23  

The formula to calculate hash is him) - (m*7;2 MOD 7793.

So, let's calculate the hash : him) - (m*7;2 MOD 7793(him) - (23*7;2 MOD 7793

⇒ (8*23) - (49 MOD 7793)

⇒ 184 - 49= 135.

So, the hash of the given message is 135.

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$24.20

Compound interest is the amount of interest paid on the principal and accumulated interest.

Interest Formula

The compound interest formula is \(A = P(1+\frac{r}{n} )^{nt}\). The variables for this formula are as follows:

To find the total amount in Karen's account after 2 years, we need to define our variables and plug them into the formula.

Solving Compound Interest

Firstly, let's identify the value of each of the variables. The original amount in the account is $20. So, P = 20. Additionally, the interest rate is 10%, which is equal to 0.1. So, r = 0.1. Since interest is compounded annually, it is compounded once a year. Thus, n = 1. Finally, we want to know the amount after 2 years, so t = 2.

Now, let's plug these values into the formula above.

This can be simplified to make the equation easier to solve.

Using this equation, we can say A = 24.20. Therefore, after 2 years, Karen will have $24.20 in her account.

Answer: n + 12 = -18              or  n + 12= -3(6)    

Step-by-step explanation:

12 more than a number means 12  is added to the number so the expression will be   n + 12  and the product of -3 and 6  is the same as  -3 times 6  which is -18 . n + 12 has to equal -18 .

n + 12 = -18    now subtract  12 from both sides

  -12        -12

n=  -30  

So the number  is -30

Answer:

True

Right angles measure 90° . So each vertical angle = 90° and hence they are equal

Step-by-step explanation:

You would expect to pay approximately $131.27 for the shipment. The correct option is: 1) 131.27

To calculate the expected cost of the shipment for a package weighing 33 ounces, we can use the given regression equation:

(cost of delivery) = 3.978 * (weight) + 2.207

Substituting the weight of the package as 33 ounces:

Expected cost of delivery = 3.978 * 33 + 2.207

Calculating:

Expected cost of delivery ≈ 131.27

Therefore, you would expect to pay approximately $131.27 for the shipment.

The correct option is:

1) 131.27

A regression equation is a mathematical formula that represents the relationship between two or more variables. It is used in statistical analysis to estimate the value of one variable based on the values of other variables.

In the context of linear regression, the regression equation takes the form:

Y = b0 + b1*X

where Y is the dependent variable, X is the independent variable, b0 is the y-intercept, and b1 is the slope of the regression line.

The regression equation is used to predict the value of the dependent variable (Y) for a given value of the independent variable (X), based on the estimated values of the coefficients (b0 and b1) obtained from the regression analysis.

It is important to note that the regression equation is specific to the dataset and variables used in the regression analysis. Different datasets and variables may have different regression equations.

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Answer:

y = -1/3x - 7/3

Step-by-step explanation:

To find the slope, you have to plug the values into the slope formula.

y2 - y1/ x2 - x1

-4 - (-2) / 5 - (-1)

-1/3

Now to find the y-intercept, plug in one of the coordinates into the equation.

y = -1/3x + b

-2 = -1/3(-1) +b

-2 = 1/3 + b

-7/3 = b

The equation is y = -1/3x - 7/3.  

The Solution is Y = - ( 1 / 3 )X - 7 / 3 where points are ( 5 , - 4) and ( - 1 , - 2) that passes through a straight line. Y = MX + C is the Formula for Straight line equation.

As per given problem, M is Slope

M = (Y2 - Y1) / (X2 - X1)

M = (- 4 - (- 2)) / ( 5 - (- 1))

M = - (1 / 3)

Now, Line becomes

- 2 = - ( 1 / 3) x (- 1)+ C

- 2 = 1 / 3 + C

C = - (7 / 3)

So, Solution:  Y = - (1 / 3)X - (7 / 3)

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Answer:

your answer is |||. hope that helps.

Answer:

16

Step-by-step explanation: -7 is the least number and 9 is the greatest. the range between -7 and 9 is 16

Answer:

5-0 =15 by using shuvam theorY

The probability that the sample mean will be within plus minus 2 of the population mean if the sample size is n = 100 between z-scores of 0 and 2.5 using a z-table.

The standard deviation of the sample distribution, commonly known as the standard error, can be computed using the formula given that the population mean is 100 and the standard deviation is 16:

Standard Error = Standard Deviation / sqrt(sample size)

Let's determine the likelihoods for sample sizes of n = 100 and n = 400:

For n = 100:

Standard Error = 16 / sqrt(100) = 16 / 10 = 1.6

We can determine the z-scores for the upper and lower boundaries to establish the likelihood that the sample mean will be within plus or minus 2 of the population mean:

Lower Bound z-score = (Sample Mean - Population Mean) / Standard Error

Lower Bound z-score = (100 - 100) / 1.6

Lower Bound z-score = 0

Upper Bound z-score = (Sample Mean - Population Mean) / Standard Error

Upper Bound z-score = (104 - 100) / 1.6

Upper Bound z-score = 4 / 1.6

Upper Bound z-score = 2.5

We can calculate the region under the normal distribution curve between z-scores of 0 and 2.5 using a z-table or statistical software. This shows the likelihood that the sample mean will be within +/- 2 standard deviations of the population mean.

For n = 400:

Standard Error = 16/√400

Standard Error = 16/20

Standard Error = 0.8

We determine the z-scores by following the same procedure as above:

Lower Bound z-score = (Sample Mean - Population Mean) / Standard Error

Lower Bound z-score = (100 - 100) / 0.8

Lower Bound z-score = 0

Upper Bound z-score = (Sample Mean - Population Mean) / Standard Error

Upper Bound z-score = (104 - 100) / 0.8

Upper Bound z-score = 4 / 0.8

Upper Bound z-score = 5

Once more, we may determine the region under the normal distribution curve between z-scores of 0 and 5 using a z-table or statistical software.

A larger sample size, like n = 400, has the benefit of a lower standard error. The sampling distribution of the sample mean will be more constrained and more closely resemble the population mean if the standard error is less.

As a result, there is a larger likelihood that the sample mean will be within +/- 2 of the population mean. In other words, the estimate of the population mean gets more accurate and dependable as the sample size grows.

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In a regression analysis, if SST = 4500 and SSE = 1575, then the coefficient of determination is 0.65.

The given data is as follows:

SST = 4500 ------ the total sum of squares

SSE = 1575 ---------the sum of squares error

In a regression model, the coefficient of determination is a statistical measurement that determines the proportion of variance for an independent variable.

The coefficient of determination (R²) is calculated using the following formula :

\(R^{2} = (\frac{SST - SSE}{SST} )\)

Substituting the values of SST and SSE in the coefficient of determination (R²) equation:

\(R^{2} = (\frac{4500-1575}{4500} )\)

\(R^{2} = \frac{2925}{4500}\)

R = 0.65

Therefore, we can conclude that  the coefficient of determination is 0.65

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We will see that the fourth statement:

"-0.3*|3 + 8x| = 0.9 has no solutions."

Is the true statement.

Here we need to see which statement regarding absolute value equations is true.

Here you can see that the fourth statement is:

-0.3*|3 + 8x| = 0.9   has no solutions.

Now, if you look at the left side of the above equation, the left side will always be negative, while the right side is positive, then the equation can't have a solution.

There is no value of x that makes that equation true, so it is true that the given equation has no solutions. This is the correct statement.

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A 95% confidence interval for percent of american adults who believe in aliens:  (0.6578, 0.7822)

In this question we have been given that in a survey conducted on an srs of 200 american adults, 72% of them said they believed in aliens

We need to find the 95% confidence interval for percent of american adults who believe in aliens.

95% confidence interval = (p ± z√[p(1 - p)/n])

Here, n = 200

p = 72%

p = 0.72

And the z-score for 95% confidence interval is 1.960

The upper limit of interval would be,

(p + z√[p(1 - p)/n])

= 0.72 + 1.960 √[0.72(1 - 0.72)/200]

= 0.72 + 1.960 √[(0.72 * 0.28)/200]

= 0.72 + 1.960 √0.001008

= 0.72 + 0.0622

= 0.7822

The lower limit of interval would be,

(p - z√[p(1 - p)/n])

= 0.72 - 1.960 √[0.72(1 - 0.72)/200]

= 0.72 - 1.960 √[(0.72 * 0.28)/200]

= 0.72 - 1.960 √0.001008

= 0.72 - 0.0622

= 0.6578

Therefore, a 95% confidence interval = (0.6578, 0.7822)

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The country is borrowing 1600 units of money on the world financial markets.

a. To determine the trade balance, we need to calculate the net exports (NX) using the given information. The formula for net exports is:

NX = Y - (C + I + G)

Given:

Y = 5000

C = 1000 + 0.5(Y - T) = 1000 + 0.5(5000 - 1000) = 1000 + 0.5(4000) = 1000 + 2000 = 3000

I = 2000

G = 1600

T = 1000

Plugging these values into the net exports equation:

NX = 5000 - (3000 + 2000 + 1600) = 5000 - 6600 = -1600

The trade balance is -1600. A negative trade balance indicates a trade deficit, which means that the country is importing more goods and services than it is exporting. In this case, the country is experiencing a trade deficit.

b. To determine whether the country is borrowing or lending money on the world financial markets, we need to examine the relationship between domestic investment (I) and national saving (S). If domestic investment exceeds national saving, the country is borrowing money. If national saving exceeds domestic investment, the country is lending money.

The formula for national saving (S) is:

S = Y - C - G

Plugging in the given values:

S = 5000 - 3000 - 1600 = 400

The national saving is 400.

Since investment (I) is 2000, which is greater than national saving (400), the country is borrowing money on the world financial markets. The amount being borrowed is the difference between investment and national saving:

Borrowing = I - S = 2000 - 400 = 1600

Therefore, the country is borrowing 1600 units of money on the world financial markets.

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The system of equations, (c) part

⇒ This system has infinitely many solutions,

The given equations:

We have to determine which system will produce infinitely many solutions:

A system of equation,

\(a_1x+b_1y=c_1, a_2x+b_2y=c_2\)

Then the system has infinitely many solution if,

\(\frac{a_1}{a_2}= \frac{b_1}{b_2}= \frac{c_1}{c_2}\)

(a) 2x + 5y = 24

2x + 5y = 42

\(\frac{2}{2}=\frac{5}{5}\neq \frac{24}{42}\)

⇒ This system does not have infinitely many solutions,

Now, For the system of equations,

(b) 3x - 2y = 15

6x + 5y = 11

\(\frac{3}{6}\neq \frac{-2}{5}\neq \frac{15}{11}\)

⇒ This system does not have infinitely many solutions,

Now, For the system of equations,

(c) 4x - 3y = 9

-8x + 6y = -18

\(\frac{4}{-8}=\frac{-3}{6}=\frac{9}{-18}=-2\)

⇒ This system has infinitely many solutions,

For the system of equations,

(d) 5x - 3y = 16

-2x + 3y = -7

\(\frac{5}{-2}\neq \frac{-3}{3}\neq \frac{16}{-7}\)

This system does not have infinitely many solutions,

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Answer:

\(b \approx 4.6\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Pre-Calculus

Step-by-step explanation:

Step 1: Define

A = 50°

B = 62°

a = 4

Step 2: Solve for b

The solution of the following equation using matlab is y₂ = x²+x+2

To solve the given second-order differential equation using MATLAB, we can use the built-in function dsolve. Here's how you can do it:

syms x y(x)

eqn = (1 - 2*x - x^2)*diff(y,x,2) + 2*(1 + x)*diff(y,x) - 2*y == 0;

ySol = dsolve(eqn, y(1) == 1);

ySol = simplify(ySol);

Let's break down the code:

We define symbolic variables x and y(x) using the syms function.

The given differential equation is assigned to the variable eqn.

We use the dsolve function to solve the differential equation, providing the equation eqn and the initial condition y(1) == 1.

Finally, we simplify the obtained solution using the simplify function.

After running the code, the variable ySol will store the symbolic solution of the differential equation. You can substitute specific values of x to evaluate the solution. Therefore , the final answer we get is y₂ = x²+x+2

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Using MATLAB, the second solution to the given second-order linear homogeneous differential equation is y₂ = x² + x + 2.

To solve the differential equation using MATLAB, we can utilize the built-in function dissolve. Here's the step-by-step explanation:

Step 1: Define the differential equation.

The given differential equation is (1 - 2x - x²)y" + 2(1 + x)y' - 2y = 0.

Step 2: Convert the differential equation into a symbolic expression.

We define the symbolic variables and convert the differential equation into a symbolic expression using the diff and syms functions:

syms x y(x)

eqn = (1 - 2*x - x^2)*diff(y, x, 2) + 2*(1 + x)*diff(y, x) - 2*y == 0;

Step 3: Solve the differential equation using dissolve.

We solve the differential equation using the dissolve function and specify the initial condition y₁ = x + 1:

ySol = dissolve(eqn, y(1) == 1, diff(y)(1) == 1);

Step 4: Extract the second solution.

The dissolve function returns a structure containing the solutions. We extract the second solution by accessing the second element of ySol:

y2 = ySol(2);

Step 5: Simplify the solution.

To simplify the solution, we use the simplify function:

y2 = simplify(y2);

The resulting simplified second solution is y₂ = x² + x + 2.

In summary, by using the dissolve function in MATLAB and specifying the given differential equation, we obtained the second solution as y₂ = x² + x + 2. This solution satisfies the given differential equation and the specified initial condition y₁ = x + 1.

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