In 2005 the gdp per capita of a country was 955 and it increases by about 1.35% per year. write a function that represents the gdp per person of the country years since 2005

Answer:

V≈904.78

Step-by-step explanation:

You have to multiply

6*3.14

Answer:

288π

Step-by-step explanation:

Answer:18

Step-by-step explanation:

a straight line is equal to 180

you already have part of the angle (162)

so then you subtract the two angles

180-162=18

The value of the integral of ∫[1,3] (x² + 2x - 4) dx is 8/3. The final answer is 8/3.

To evaluate the integral of ∫[1,3] (x² + 2x - 4) dx, we can first rewrite the integral by distributing it over the expression:

∫[1,3] (x² + 2x - 4) dx = ∫[1,3] x² dx + ∫[1,3] 2x dx - ∫[1,3] 4 dx

Next, we integrate each term of the expression using the power rule of integration:

∫[1,3] x² dx = [x³/3]₁³ = (3³/3) - (1³/3) = 9/3 - 1/3 = 8/3

∫[1,3] 2x dx = [x²]₁³ = (3²) - (1²) = 9 - 1 = 8

∫[1,3] 4 dx = [4x]₁³ = 4(3) - 4(1) = 12 - 4 = 8

Combining the results, we have:

∫[1,3] (x² + 2x - 4) dx = ∫[1,3] x² dx + ∫[1,3] 2x dx - ∫[1,3] 4 dx

= 8/3 + 8 - 8

= 8/3

Therefore, the value of the integral of ∫[1,3] (x² + 2x - 4) dx is 8/3. The final answer is 8/3.

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Answer:

$0.56, or 56¢.

Step-by-step explanation:

According to the picture, there are two dimes, two nickels, a penny, and a quarter.

A penny is worth $0.01.

A nickel is worth $0.05.

A dime is worth $0.10.

A quarter is worth $0.25.

2(0.1) + 2(0.05) + (0.01) + (0.25) = 0.2 + 0.1 + 0.01 + 0.25 = 0.3 + 0.26 = 0.56.

So, Vivian is using $0.56, or 56¢, to buy a toy. That's a cheap one!

Hope this helps!

Answer:

a = 6

Step-by-step explanation:

Answer:

ur doing exams

Step-by-step explanation:

hahhaha ur doing exams

We can see here that matching the letters to the correct terms, we have:

C - 3. y-intercept.

D - 2. vertex

A - 1. axis of symmetry

B - 4. x-intercept

A vertex is a location where two or more lines, curves, or edges cross in mathematics. In computer science, graph theory, and geometry, the word "vertex" is frequently used to refer to an object's corners or points.

When two or more line segments, rays, or lines come together to make an angle, they form a vertex in geometry. Each of the three spots where the three sides of a triangle intersect is known as a vertex. In a similar way, each of a cube's eight corners is a vertex.

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Answer:

Answer in the attached image.

Answer:

you divide 11 by 25 and then round to the nearest hundredth

Step-by-step explanation:

11÷25= 0.44

The Values of (a+b)ab are undefined.

Given that, a = 3an and db = -2We need to find the values of (a+b)

Now, we have a = 3an... equation (1)Also, we have db = -2... equation (2)From equation (1), we get: n = 1/3... equation (3)Putting equation (3) in equation (1), we get: a = a/3a = 3... equation (4)Now, putting equation (4) in equation (1), we get: a = 3an... 3 = 3(1/3)n = 1

From equation (2), we have: db = -2=> d = -2/b... equation (5)Multiplying equation (1) and equation (2), we get: a*db = 3an * -2=> ab = -6n... equation (6)Putting values of n and a in equation (6), we get: ab = -6*1=> ab = -6... equation (7)Now, we need to find the value of (a+b).For this, we add equations (1) and (5),

we get a + d = 3an - 2/b=> a + (-2/b) = 3a(1) - 2/b=> a - 3a + 2/b = -2/b=> -2a + 2/b = -2/b=> -2a = 0=> a = 0From equation (1), we have a = 3an=> 0 = 3(1/3)n=> n = 0

Therefore, from equation (5), we have:d = -2/b=> 0 = -2/b=> b = ∞Now, we know that (a+b)ab = (0+∞)(0*∞) = undefined

Therefore, the values of (a+b)ab are undefined.

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A sample size of at the least 103 batteries should be randomly decided on and examined from the manufacturing run to make sure that the hypothesis test has a level of significance of 0.02 and that the possibility of erroneously accepting a batch with an average use life of much less than 400 hours isn't any more than 10%.

To determine the specified sample size for the hypothesis test, we want to apply the formulation for the sample size required for checking out a population mean, given by:

\(n = (zα/2 * σ / E)^2\)

in which:

In this example, the margin of error E may be calculated with the aid of subtracting the required minimum mean use life of 400 hours from the actual mean use existence of 384 hours, and taking the absolute value  

E = |384 - 400| = 16

The critical value zα/2 may be determined the usage of a standard normal distribution table or calculator, with a level of significance of 0.02:

zα/2 = 2.33

Substituting those values into the sample size method, we get:

\(n = (2.33 * 35 / 16)^2 = 72.43\)

Rounding up to the closest whole range, we get a recommended sample size of 73.

But, the production manager additionally needs a sampling procedure that only 10% of the time might show erroneously that the batch is suitable.

This requirement corresponds to the possibility of type I errors, or α, that's identical to 0.10. To make certain that the probability of kind I error is no more than 0.02, we need to modify the extent of significance and the critical price consequently:

zα/2 = 2.58 (from standard ordinary distribution table with α = 0.02)

Substituting this elements into the sample size formulation, we get:

\(n = (2.58 * 35 / 16)^2 = 102.07\)

Rounding as much as the closest entire number, we get a encouraged sample length of 103.

Thus, 103 sample size is recommended for the hypothesis test.

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So normally, the way i am doing so is by moving from each place of the array comparing each other with two for cycles, the second cycle will count the iterate numbers, some people use Math.max imported function.

int birthdayCakeCandles(vector<int> candles) {

   int count = 0;

   int max = 0;

for(size_t i = 0; i < candles.size() ; i++)

   {

       int num = candles[i];

       if (num > max)

       {

           max = num.

           count = 1.

       } else if (max == num)

       {

           count++.

       }

   }

   return count.

}

This should be much clear, iterate through the array find max if max already exists again increase count, if some other element greater than max set it to max and reset count to 1.

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Answer:

Step-by-step explanation:

First Pair.

If you divide the top equation by 3 you get

x + 2y = 12

x + y = 7          From that I get that y = 5

Second pair

Do the same thing to the top equation only this time divide by 6

x + 2y = 4                

x + y = 7

If you subtract again you get y = - 3

There is only one child in the park who does not like to play either cricket or football or soccer.

Additionally, you should ignore any typos or irrelevant parts of the question .Here's how you can solve the given problem :Given that ,In a park, 25 children play every day in the evening.

12 children like to play cricket.8 children like to play football.4 children like to play soccer.Total children who like to play either of these three sports = \(12 + 8 + 4 = 24.\)

Therefore, the number of children who do not like to play any of these sports = Total number of children - Number of children who like to play any of these sports= \(25 - 24= 1\).

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The vertex form of the equation is y = (x - 3)² - 4, which corresponds to option OD.

To convert the given equation from standard form to vertex form, we need to complete the square.

The vertex form of a parabola's equation is y = a(x-h)² + k, where (h, k) represents the vertex of the parabola.

Given equation: y = x² - 6x + 14

Move the constant term to the right side:

y - 14 = x² - 6x

Complete the square by adding and subtracting the square of half the coefficient of x:

y - 14 + 9 = x² - 6x + 9 - 9

Group the terms and factor the quadratic:

(y - 5) = (x² - 6x + 9) - 9

Rewrite the quadratic as a perfect square:

(y - 5) = (x - 3)² - 9

Simplify the equation:

y - 5 = (x - 3)² - 9

Move the constant term to the right side:

y = (x - 3)² - 9 + 5

Combine the constants:

y = (x - 3)² - 4

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Answer: Find the the height and length of the triangle. I'm not sure what it would be but then use a1  + a2 to find the area

Answer:

Formula of triangle: A = 1/2 x b x h

Step-by-step explanation:

Solve the base of the triangle by solving the distance between points (-2,0) and (f, -5) in units, and then do the same for height: find distance between points (-2, 6) and (-2, 0). Once you find the distance, input value of base and height into the formula and solve to get the area!

Answer:

The scale factor is 1.5

Step-by-step explanation:

Given

\(AB = 12\)

\(DE = 8\)

Required

Determine the scale factor

From the question, we have that:

1. DEF is the original triangle and ABC is only its scale factor

2. AB and DE are the longest sides in both triangles

(2) implies that, AB is a translation of DE

The scale factor is calculated as follows

\(AB = DE * k\)

Where k is the scale factor;

Substitute values for AB and De

\(12 = 8 * k\)

\(12 =8k\)

\(k = \frac{12}{8}\)

\(k = 1.5\)

Hence:

The scale factor is 1.5

Answer:

19/35

Step-by-step explanation:

6/7 - 11/35

19/35

Using proportions, the costs are given as follows:

a) Total Labor Cost: $2,505,600.

b) Total Product Cost: $1,950,000.

c) Total Cost = $4,455,600.

d) Cost per home = $461.77.

e) Cost per week = $99,013.33.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

For item a, the labor cost is found using the earnings of the workers, as follows:

45 weeks x 5 days x 8 hours x 58 per hour x (12 + 8 + 4 workers)

Hence:

Total Labor Cost = 45 x 5 x 8 x 58 x 24 = $2,505,600.

For item b, the product cost is the cost of the boards, hence:

(175 + 150 + 50 boards) x 5,200

Total Product Cost = 375 x 5,200 = $1,950,000.

For item c, the total cost is the sum of the product cost and the labor cost, hence:

Total Cost = 2,505,600 + 1,950,000 = $4,455,600.

For item d, the cost per home is found dividing the total cost by the 9,649 homes, hence:

Cost per home = 4455600/9649 = $461.77.

For item e, the cost per week is found dividing the total cost by the 45 weeks, hence:

Cost per week = 4455600/45 = $99,013.33.

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The correct statement about the study is: "The result of the study is not reliable because there is no randomization and the confounding variables are not controlled."

Although the study found greater weight loss in the vegetarian group, we cannot confidently conclude that a vegetarian diet helps people lose more weight based on the given information. There are several reasons for this:

1. Lack of randomization: Randomization is a crucial aspect of experimental studies to ensure that participants are assigned to groups (vegetarian vs. control) in a random and unbiased manner. Without randomization, there is a risk of selection bias, as individuals may have chosen their diet based on personal preferences or other factors that could influence weight loss.

2. Confounding variables: Confounding variables are factors that may affect the outcome but are not controlled or accounted for in the study design. In this case, there could be various confounding variables that contribute to the difference in weight loss between the vegetarian and control groups. For instance, differences in calorie intake, exercise levels, or individual motivations could influence the results.

3. Sample size: While sample size plays a role in the statistical power and precision of a study, it alone does not determine the reliability of the results. Even with a large sample size, if the study design lacks proper control and randomization, the findings may still be compromised.

4. Lack of control group: The absence of a proper control group makes it difficult to establish a causal relationship between the vegetarian diet and weight loss. A control group is essential to compare the effects of the intervention (vegetarian diet) against a baseline or standard treatment (low-calorie diet with meat).

Therefore, the study described does not provide sufficient evidence to support the conclusion that a vegetarian diet helps people lose more weight. Further research with a randomized controlled design and careful control of confounding variables is necessary to draw reliable conclusions about the effectiveness of a vegetarian diet for weight loss.

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Answer:

16

Step-by-step explanation:

48 divided by 3 is 16, so each of his friends will get 16 cookies.

Answer:

3 days

Step-by-step explanation:

20/6 is 3.333

Answer:

3 days

Step-by-step explanation:

cuz after three days you will have two pounds left so you cant go another day

Using implicit differentiation dz/dt = -34

Differentiation is the process of finding the derivative of a function.

Since x² + y² + z² = 9, dx/dt = 8, and dy/dt = 9, we need to find dz/dt when (x, y, z) = (2, 2, 1).

So, differentiating implicitly and also applying the chain rule, we have that

x² + y² + z² = 9

d(x² + y² + z²)/dt = d9/dt

dx²/dx × dx/dt  + dy²/dy × dy/dt + dz²/dz × dz/dt = d9/dt

2xdx/dt  + 2ydy/dt + 2zdz/dt = 0

xdx/dt  + ydy/dt + zdz/dt = 0

Making dz/dt subject of the formula, we have that

zdz/dt = -(xdx/dt  + ydy/dt)

dz/dt =  -(xdx/dt  + ydy/dt)/z

Given that

Substituting the values of the variables into the equation, we have that

dz/dt =  -(xdx/dt  + ydy/dt)/z

dz/dt =  -(2 × 8  + 2 × 9)/1

= -(16 + 18)/1

= - 34

So, dz/dt = -34

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The question is incomplete. Here is the complete question

If  x² + y² + z²  = 9, dx/dt = 5, and dy/dt = 4, find dz/dt when (x, y, z) = (2, 2, 1).

The solution to the system of equations is x = 1.

To solve the system of equations y = x/(3x - 1) and y = 1/(x + 1) and find the value of x, we can substitute the expression for y from one equation into the other and solve for x.

Let's start by substituting the expression for y from the second equation into the first equation:

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

Now, we can cross-multiply to eliminate the denominators:

x(x + 1) = 3x - 1

Expanding the left side:

x^2 + x = 3x - 1

Next, we rearrange the equation by moving all the terms to one side:

x^2 + x - 3x + 1 = 0

Combining like terms:

x^2 - 2x + 1 = 0

Now, we have a quadratic equation in standard form. We can solve this equation by factoring, completing the square, or using the quadratic formula. In this case, the equation can be factored as:

(x - 1)^2 = 0

Taking the square root of both sides:

x - 1 = 0

x = 1

Therefore, the solution to the system of equations is x = 1.

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The change from Fahrenheit to Celsius temperature data will have no effect on the correlation coefficient. The correlation coefficient, denoted as r, measures the strength and direction of the linear relationship between two variables. In this case, the correlation coefficient is calculated as r = -0.1198.(option c)

Changing the temperature data from degrees Fahrenheit to degrees Celsius involves a linear transformation of the data. Specifically, the formula for converting temperature from Fahrenheit to Celsius is C = (F - 32) * (5/9), where C is the temperature in Celsius and F is the temperature in Fahrenheit.

Linear transformations of data do not affect the correlation coefficient. The correlation coefficient measures the strength and direction of a linear relationship between two variables, and this relationship remains unchanged under linear transformations of either variable. Therefore, converting the temperature data from degrees Fahrenheit to degrees Celsius will have no effect on the correlation coefficient, and it will remain at r = -0.1198.

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52 tiles are there in the 25th figure in this pattern.

A pattern is described as a series of recurring symbols, figures, or numbers. Any form of event or object can be related to a pattern.

A pattern has a rule that specifies which items fall within the pattern's umbrella and which do not.

A pattern in mathematics is a recurring arrangement of numbers, forms, colors, and other elements.

Any kind of event or object can be connected to the Pattern.

A pattern is referred to as a rule or a way in which a group of numbers is related to one another.

Sometimes a pattern is also referred to as a sequence.

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Hi there! Assume that this is your question.

\( \large{ \int \limits^a_b ( {x}^{2} + 2x)dx}\)

Before we get to Integral, you have to know Differentiation first. If you know how to differentiate a polynomial function then we are good to go in Integral!

We call the function that we are going to integrate as Integrand. Integrand is a function that's differentiated. In Integral, Integrating requires you to turn the function from differentiated to an original function.

For Ex. If the Integrand is x² then the original function is (1/3)x³ because when we differentiate (1/3)x³, we get x²

\( \large{f(x) = \frac{1}{3} {x}^{3} \longrightarrow f'(x) = {x}^{2} } \\ \large{f'(x) = 3( \frac{1}{3} ) {x}^{3 - 1} } \\ \large{f'(x) = {x}^{2} }\)

So when we Integrate, make sure to convert Integrand as in original function. From the question, our Integrand is x²+2x. The function is in differentiated form. We know that x² is from (1/3)x³ and 2x comes from x²

\( \large{ f(x) = {x}^{2} \longrightarrow f'(x) = 2x} \\ \large{f'(x) = 2 {x}^{2 - 1} } \\ \large{f'(x) = 2x}\)

Thus,

\( \large{ \int \limits^a_b ( {x}^{2} + 2x)dx} \\ \large{\int \limits^a_b ( \frac{1}{3} {x}^{3} + {x}^{2}) }\)

Normally, if it's an indefinite Integral then we'd just put + C after (1/3)x³+x² but since we have a and b, it's a definite Integral.

\( \large{ \int \limits^b_a f(x)dx = F(b) - F(a)}\)

Define F(x) as our anti-diff

From our problem, substitute x = a in then subtract with the one that substitute x = b

\( \large{ (\frac{1}{3}{a}^{3} + {a}^{2} ) - ( \frac{1}{3} {b}^{3} + {b}^{2}) }\)

Simplify as we get:

\( \large \boxed{ \frac{1}{3}{a}^{3} + {a}^{2} - \frac{1}{3} {b}^{3} - {b}^{2}}\)

Answer:

6 1/2 minutes per miles

2/13 miles per minutes

Step-by-step explanation:

Distance travelled = 2 1/2 miles

Time taken = 16 1/4 minutes

Average: minutes per mile

= 16 1/4 minutes / 2 1/2 miles

= 65/4 ÷ 5/2

= 65/4 × 2/5

= 13/2

= 6 1/2

Average time per mile in minutes

= 6 1/2 minutes per mile

Average (miles per minutes)

= 2 1/2 ÷ 16 1/4

= 5/2 ÷ 65/4

= 5/2 × 4/65

= 20 / 130

= 2/13 miles per minutes

Sample 1: Mean=10.01, Standard deviation=13.90 Sample 2: Mean

=11.43, Standard deviation

=14.10

Sample size of 1st year = n1

= 1012Mean of 1st year sample

= X1 = 10.01Standard deviation of 1st year sample

= s1

= 13.90Sample size of 2nd year

= n2

= 1012Mean of 2nd year sample

= X2

= 11.43

Standard deviation of 2nd year sample = s2

= 14.10 Let us assume a significance level of α = 0.05, which implies that the critical region consists of 2.5% in both tails (since it is a two-tailed test).

Therefore, we do not have sufficient evidence to conclude that the mean number of hours per week spent on the Internet differs between 2010 and another year.

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