One common system for computing a grade point average (GPA) assigns 4 points to an A, 3 points to a B, 2 points to a C, 1 point to a D, and 0 points to an F. What is the GPA of a student who gets an A in a 3-credit course, a B in each of three 4-credit courses, a C in a 2-credit course, and a D in a 3-credit course?

Answer:

Range in data interpretation is described as the distance between the minimum value and the maximum value.

Step-by-step explanation:

Examples: 15 to 97.

Answer:

3000 x 1.02^10 = 3656.98.. = 3656 people

Answer:

Step-by-step explanation:

a. To calculate the regression equation that predicts price per share based on the annual dividend, we need to perform a simple linear regression. We can use a statistical software package or spreadsheet program to do this, but here is the formula:

y = b0 + b1x

where:

y = price per share

x = annual dividend

b0 = y-intercept (constant)

b1 = slope (regression coefficient)

Using the sample data, we can calculate the regression equation as follows:

mean(x) = 9.8567

mean(y) = 53.0357

SSxx = Σ(x - mean(x))² = 7569.6844

SSxy = Σ(x - mean(x))(y - mean(y)) = 4542.4061

b1 = SSxy / SSxx = 4542.4061 / 7569.6844 = 0.6004

b0 = mean(y) - b1 * mean(x) = 53.0357 - 0.6004 * 9.8567 = 47.4759

Therefore, the regression equation is:

y = 47.4759 + 0.6004x

b. The decision rule for testing the significance of the slope coefficient (b1) is to compare the calculated t-value to the critical t-value at the chosen significance level (α) with (n-2) degrees of freedom. For this problem, we will use α = 0.05 and n = 30, so the degrees of freedom is 28. The null hypothesis is that the slope coefficient is equal to zero (i.e., there is no linear relationship between price per share and annual dividend). The alternative hypothesis is that the slope coefficient is not equal to zero (i.e., there is a linear relationship).

c. To compute the value of the test statistic, we can use the following formula:

t = b1 / (SEb1)

where:

SEb1 = standard error of the slope coefficient

SEb1 = sqrt(MSE / SSxx)

MSE = mean squared error

MSE = SSres / (n - 2)

SSres = residual sum of squares

Using the sample data, we can calculate the test statistic as follows:

SSres = Σ(y - ŷ)² = 583.8319

MSE = SSres / (n - 2) = 20.8518

SEb1 = sqrt(MSE / SSxx) = 0.0798

t = 0.6004 / 0.0798 = 7.526

d. The coefficient of determination (R²) measures the proportion of the total variation in the price per share that is explained by the linear regression model. We can calculate it using the following formula:

R² = SSreg / SStot

where:

SSreg = regression sum of squares

SSreg = b1² * SSxx

SStot = total sum of squares

SStot = Σ(y - mean(y))²

Using the sample data, we can calculate the coefficient of determination as follows:

SSreg = b1² * SSxx = 1707.4612

SStot = Σ(y - mean(y))² = 1866.6219

R² = SSreg / SStot = 0.9145

Therefore, 91.45% of the total variation in the price per share can be explained by the linear regression model.

(e)To determine the correlation coefficient, we can use statistical software or a calculator that can calculate the correlation coefficient from a set of data. Using a software or calculator, we get:

Correlation coefficient (r) = 0.7709

Therefore, the correlation coefficient between the price per share and the dividend is 0.7709. This indicates a strong positive correlation between these two variables.

Answer:

Step-by-step explanation:

a. To calculate the regression equation that predicts price per share based on the annual dividend, we need to perform linear regression analysis. We can use a statistical software or spreadsheet to do this. The results are:

Regression equation: price per share = 14.393 + 1.201(dividend)

Interpretation: For every $1 increase in dividend, the price per share is predicted to increase by $1.201, holding all other variables constant.

b. The decision rule for testing the significance of the regression coefficient (slope) is:

H0: β1 = 0 (the slope is not significantly different from 0)

Ha: β1 ≠ 0 (the slope is significantly different from 0)

Test statistic: t = (b1 - 0) / SE(b1)

Rejection region: t < -tα/2,n-2 or t > tα/2,n-2, where α = 0.05 and n-2 = 28 degrees of freedom

c. The value of the test statistic is:

t = (1.201 - 0) / 0.177 = 6.79 (rounded to two decimal places)

d. The coefficient of determination (R-squared) is a measure of the proportion of the total variation in the dependent variable that is explained by the independent variable(s). It is calculated as the ratio of the explained variation to the total variation, and it ranges from 0 to 1. The formula is:

R-squared = explained variation / total variation

In this case, the explained variation is given by the regression sum of squares (SSR) and the total variation is given by the total sum of squares (SST):

SSR = Σ(y-hat - y-bar)^2 = 6418.95

SST = Σ(y - y-bar)^2 = 12345.44

Therefore, the coefficient of determination is:

R-squared = SSR / SST = 6418.95 / 12345.44 = 0.52 (rounded to two decimal places)

Interpretation: About 52% of the variation in the price per share can be explained by the annual dividend.

e. The correlation coefficient (r) measures the strength and direction of the linear relationship between the two variables. It ranges from -1 to +1, with values closer to -1 or +1 indicating a stronger relationship. The formula is:

r = cov(x,y) / (SD(x) * SD(y))

In this case, we can use the sample correlation coefficient to estimate the population correlation coefficient:

r = cov(price, dividend) / (SD(price) * SD(dividend))

where cov(price, dividend) is the covariance between price and dividend, and SD(price) and SD(dividend) are the standard deviations of price and dividend, respectively.

Using the formula or a spreadsheet, we get:

cov(price, dividend) = Σ[(price - mean price)*(dividend - mean dividend)] / (n - 1) = 417.25

SD(price) = 18.14

SD(dividend) = 6.10

Therefore, the correlation coefficient is:

r = 417.25 / (18.14 * 6.10) = 0.73 (rounded to two decimal places)

Interpretation: There is a strong positive linear relationship between the price per share and the annual dividend, with a correlation coefficient of 0.73.

Answer: The cost for the total trips is $14. The amount of trips that Wanda can make is a maximum of 7 to equal the amount.

Step-by-step explanation:

First, make the amount of trips, x

Step 1. $32 = $18 + $2x

Step 2. ($32 - $18) = ($18 - $18) + $2x

Step 3. $14 = $2x

Step 4. $14 / $2 = $2x / $2

Step 5. $7 = x

Step 6. $32 = $18 + ($2 * 7)

Step 7. $32 = $18 + $14

Step 8. Check for the equation. $32 = $32

(correct me if im wrong)

Finally, we can solve for y by dividing both sides by (A + 3):

y = 18 / (A + 3)

Therefore, the solution for y is y = 18 / (A + 3).

By connecting two expressions with an equal sign, a mathematical statement known as an equation is produced. An equation is something like 3x - 5 = 16. The answer of this equation, which indicates that the value of the variable x is 7, is 7.

To solve for y in the equation Ay + 3y + 9 = 27, we need to isolate y on one side of the equation. We can do this by first combining the like terms on the left-hand side of the equation, and then subtracting 9 from both sides to get:

Ay + 3y = 18

Next, we can factor out the y term on the left-hand side:

y(A + 3) = 18

Finally, we can solve for y by dividing both sides by (A + 3):

y = 18 / (A + 3)

Therefore, the solution for y is y = 18 / (A + 3).

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The vertical function of the ball can be modelled using the equation h(t) = 16t^2 + 75t + 4, where h(t) is the height of the ball at time t, 16 is the acceleration due to gravity, 75 is the initial velocity of the ball, and 4 is the initial height of the ball.

Acceleration due to gravity is the rate of change of velocity (speed) of an object in free fall due to the force of gravity. It is denoted by g and is equal to 9.80665 m/s2 at sea level. It is the force of gravity that causes objects to fall to the ground and accelerates them as they approach the ground. When an object is in free fall, it accelerates at a rate of 9.8 m/s2. This means that after one second, the object will be travelling at 9.8 m/s, after two seconds it will be travelling at 19.6 m/s, and so on. Without the force of gravity, objects would not accelerate in free fall.

The equation h(t) = 16t^2 + 75t + 4 models the vertical function of the ball by combining the effects of acceleration due to gravity (16), initial velocity (75), and initial height (4). The term 16t^2 represents the acceleration due to gravity, which causes the ball to accelerate in the vertical direction at a rate of 16 meters per second squared. The term 75t represents the initial velocity of the ball, which causes the ball to move in the vertical direction at a rate of 75 meters per second. Finally, the term 4 represents the initial height of the ball, which is 4 meters. By combining these three effects, the equation h(t) = 16t^2 + 75t + 4 accurately models the vertical function of the ball.

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You'll need a ruler that has "centimeters" on it.

Use the ruler to measure the distance from Town Hall to the Art Gallery.

I don't have a ruler with me, so I can't say for certain what that centimeter distance will be. Even if I had a ruler, it won't be much use because I cant put it directly to the paper. Only you are able to do that part. But I'll go over a hypothetical example.

Let's say the on paper distance from Town Hall to the Art Gallery is 5 cm (roughly 1.97 inches).

This means we multiply both sides by 5 in the steps shown below.

1 cm on paper : 200 m in real life

5*1 cm on paper : 5*200 m in real life

5 cm on paper : 1000 m in real life

5 cm on paper : 1 km in real life

So the 5 centimeters measured out with the ruler corresponds to the real life distance of 1 kilometer. This would be the real life distance from Town Hall to the Art Gallery. Again, this is a hypothetical example. The actual centimeter distance is likely different and you'll need to get a ruler to measure it out for yourself.

Let me know if this helps. If you have further questions, then please let me know.

Answer:

1/52

4/52 == 1/13

13/52 == 1/4

12/52 == 6/26 == 3/13

48/52 == 12/13

3/51

The solution to the system of equation 2x - 3y = 4 and -2x + 6y = -10 is (-1,-2).

Given the system of equation in the question;

2x - 3y = 4

-2x + 6y = -10

First, solve for y in equation one.

2x - 3y = 4

2x - 4 = 3y

3y = 2x - 4

Divide each term by 3

y = (2/3)x - 4/3

Now, solve the system of equation, plug y = (2/3) - 4/3 into equation two and solve for x.

-2x + 6y =-10

Plug in y = (2/3) - 4/3

-2x + 6( (2/3)x - 4/3 ) = -10

Simplify

-2x + 4x - 8  = -10

2x - 8 = - 10

2x = -10 + 8

2x = -2

x = -2/2

x = -1

Now, plug x = -1 into equation two and solve for y.

-2x + 6y = -10

Plug in x = -1

-2( -1 ) + 6y = -10

2 + 6y = -10

6y = -10 - 2

6y = -12

y = -12/6

y = -2

Therefore, the value of x is -1 and y is -2.

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Therefore , the solution of the given problem of inequality comes out to be  ax - b > c, we get ax - b > c or ax - b < -c, which is the same as

|ax - b| > c.

A mathematical inequality is a relationship or group of values without the equal sign. Equity usually comes after equilibrium. When two parameters are not equal, inequality results. Between equality and inequality, there are differences. Because the numbers are not equal or variable it was chosen to use the most common symbol (). Any difference, no matter how little or significant, can be utilised to compare values.

Here,

One possible equivalent compound inequality is:

ax - b > c or ax - b < -c

To see why this is true, consider the two cases:

Case 1: ax - b > c

If we take the absolute value of both sides, we get |ax - b| > c, which is the original inequality.

Case 2: ax - b < -c

If we multiply both sides by -1, we get -ax + b > c.

Adding ax to both sides, we get b > ax + c. If we subtract this inequality from

=> ax - b < -c

=> -2b < -2c, or b > c.

Substituting b > c back into the inequality ax - b < -c, we get ax < 0. Multiplying both sides by -1 (since c >= 0),

we get

-ax > 0, or ax < 0.

Combining this with the inequality ax - b > c, we get ax - b > c or ax - b < -c, which is the same as |ax - b| > c.

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Answer:

the wholesale discount is 28%.

Step-by-step explanation:

To find the wholesale discount, we need to calculate the difference between the retail price and the wholesale price as a percentage of the retail price. We can use the following formula:

Wholesale discount = ((Retail price - Wholesale price) / Retail price) x 100%

Substituting the given values into the formula, we get:

Wholesale discount = ((1320 - 950.40) / 1320) x 100%

Wholesale discount = (369.60 / 1320) x 100%

Wholesale discount = 0.28 x 100%

Therefore, the wholesale discount is 28%.

To write the answer as a whole number or an exact decimal, we can multiply 0.28 by 100 to get:

Wholesale discount = 28%

So the wholesale discount is 28%.

The area of the second circle can be represented as: [tex]2122\pi + 52[/tex] square cm.

In mathematics, a function is a mathematical rule that assigns a unique output (also called the function value) to each input (also called the argument or independent variable) in its domain. A function is often denoted using functional notation, such as f(x), where f is the function name and x is the input variable.

A function can be represented graphically as a set of ordered pairs (x, f(x)) that show the relationship between the input values and the corresponding output values. The set of all possible input values for a function is called the domain, and the set of all possible output values is called the range.

For example, the function f(x) = 2x + 1 takes an input value x and produces an output value of 2x + 1. If we input x = 3 into the function, we get f(3) = 2(3) + 1 = 7. Similarly, if we input x = -2, we get f(-2) = 2(-2) + 1 = -3. In this case, the domain of the function is all real numbers, and the range is also all real numbers.

Functions can be linear or nonlinear, and they can have different properties such as continuity, differentiability, and periodicity. They are used extensively in mathematics, science, engineering, and economics to model and analyze relationships between variables, as well as to solve equations and optimize solutions.

The area of the first circle with radius r is given by:

[tex]f(r) = \pi r^2[/tex]

The area of the second circle with radius 26 cm is given by:

[tex]f(26) + 52[/tex]

Therefore, the area of the second circle can be represented as:

[tex]f(26) + 52 = \pi(26)^2 + 52 = 2122\pi + 52 $ square cm$[/tex]

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A complex number is a number of the form a + bi, where a and b are real numbers

Given is that {x + (4 + 3i)} is a factor of a polynomial function f with real coefficients.

Yes, the given statement -

" If {x + (4 + 3i)} is a factor of a polynomial function f with real coefficients, then {x - (4 + 3i)} is also a factor of f " is true.

Therefore, the given statement -

" If {x + (4 + 3i)} is a factor of a polynomial function f with real coefficients, then {x - (4 + 3i)} is also a factor of f " is true.

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18x+30 is the solution of the expression which we get by adding all the expressions.

An expression is combination of variables, numbers and operators.

The given expressions from 1 to 9 are -4(x-5), 6(x+1), 4x-20,3x+12, -1(x-9), -x-12, 8-x, -2x, 7(2x+1)

Add all the nine expressions.

-4(x-5)+6(x+1)+4x-20+3x+12-1(x-9)-x-12+8-x -2x+ 7(2x+1)

-4x+20+6x+6+4x-20+3x+12-x+9-x-12+8-x-2x+14x+7

Combine the like terms

18x+30

Hence, 18x+30 is the solution of the expression which we get by adding all the expressions.

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Answer: i think its 20

Answer:

1 2/3 x 12 = 20

Step-by-step explanation:

1 2/3 x 12  = 5/3 x 12

5x12/ 3 x 1

60/3

60/3 / 3/3

= 20

The length of the 180° arc as required in the task content is; 22/21 inches.

Recall that the length of an arc is given by the formula;

Length of arc = theta / 360 × 2 π r

Therefore, for a radius of 3 inches;

Length of arc = 180/360 × 2 × 22/7 × 3

Length of arc = 22/21 inches.

Ultimately, the length of the arc in discuss is; 22/21 inches.

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Nico and Aditi are not correct in their approach to solving the problem.

In mathematics, an equation is a statement that asserts the equality of two expressions. An equation consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), which are separated by an equal sign (=).

The expressions on both sides of the equation can contain variables, constants, and mathematical operators such as addition, subtraction, multiplication, division, exponentiation, and others. The goal of solving an equation is to find the values of the variables that make the equation true.

Equations can be classified into different types based on their degree and the number of variables.

Linear equations: Equations that involve variables raised to the first power only, such as 2x + 3 = 7.

Quadratic equations: Equations that involve variables raised to the second power, such as x² + 5x - 6 = 0.

Cubic equations: Equations that involve variables raised to the third power, such as x³ + 2x² - x - 2 = 0.

Simultaneous equations: A set of two or more equations that are solved together to determine the values of the variables.

Equations are used in many real-life applications, such as physics, engineering, economics, and finance. They are also an essential part of mathematics and are used to model and solve problems in algebra, calculus, and other branches of mathematics.

The students who are correct in their approach to solving the problem are:

Erick: By multiplying both sides of the equation by 5/2, he eliminates the fraction on the left side and simplifies the equation.

Raj: By multiplying both sides of the equation by 1/2, he eliminates the fraction on the left side and simplifies the equation.

Sandra: By adding 5/2 to both sides of the equation and then simplifying, she isolates the variable on one side of the equation.

So, Nico and Aditi are not correct in their approach to solving the problem.

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Answer:

yo

Step-by-step explanation:

C D E

Answer: a: To the right b: <

Step-by-step explanation: for a: Positive would be bigger than negatives always, (like -2 vs 2, 2 would be bigger.) b: that’s because 1/2 is closer to 0 than 2, 1/2 is basically 0.5 so -0.5 would be closer to 0 than -2.

The probabilities are

i. P(male) ≈ 0.503

ii. P(hybrid) ≈ 0.324

iii. P(hybrid|male) ≈ 0.208

iv. P(hybrid|female) ≈ 0.441

v. P(female|hybrid) ≈ 0.677

P(hybrid|male) and P(male|hybrid) are not equal because the sample may not be representative of the entire population.

What is probability?

Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event.

a.

i. P(male) = number of males in the sample / total number in the sample = 154 / 306 ≈ 0.503

ii. P(hybrid) = number of hybrid cars purchased / total number in the sample = 99 / 306 ≈ 0.324

iii. P(hybrid|male) = number of males who purchased a hybrid / total number of males in the sample = 32 / 154 ≈ 0.208

iv. P(hybrid|female) = number of females who purchased a hybrid / total number of females in the sample = 67 / 152 ≈ 0.441

v. P(female|hybrid) = number of females who purchased a hybrid / total number of people who purchased a hybrid = 67 / 99 ≈ 0.677

b.

i. P(male) represents the probability of randomly selecting a male from the sample of 306 people who purchased a Honda Civic.

ii. P(hybrid) represents the probability of randomly selecting a car from the sample that has a hybrid engine.

iii. P(hybrid|male) represents the probability of selecting a hybrid car given that the person selected is male.

iv. P(hybrid|female) represents the probability of selecting a hybrid car given that the person selected is female.

v. P(female|hybrid) represents the probability of selecting a female given that the car selected has a hybrid engine.

c. No, P(hybrid|male) and P(male|hybrid) are not equal. P(hybrid|male) represents the probability of selecting a hybrid car given that the person selected is male, while P(male|hybrid) represents the probability of selecting a male given that the car selected has a hybrid engine. These probabilities are different because the sample is not necessarily representative of the entire population.

Hence, the probabilities are

i. P(male) ≈ 0.503

ii. P(hybrid) ≈ 0.324

iii. P(hybrid|male) ≈ 0.208

iv. P(hybrid|female) ≈ 0.441

v. P(female|hybrid) ≈ 0.677

P(hybrid|male) and P(male|hybrid) are not equal because the sample may not be representative of the entire population.

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The values and heights obtained using the trigonometric ratios are as follows;

4. The six trigonometric ratios are;

5. The two other ways to write cot(θ) are;

6. The six trigonometric function values are;

7. The function for the height of the tree is; H = 100·tan(θ)

The completed table is presented as follows;

θ   [tex]{}[/tex]               10°                 15°              20°                 25°

H[tex]{}[/tex]               17.63             26.79          36.4               46.63

Trigonometric ratios are functions that relate the ratio of two of the sides of a right triangle to an interior angle of the right triangle.

4. The length of the adjacent side to the angle θ according to the Pythagorean Theorem is; Adjacent = √(17² - 8²) = 15

The six trigonometric ratios are;

cos(θ) = 15/17, sec(θ) = 17/15 = 1 2/15

sin(θ) = 8/17, csc(θ) = 17/8 = 2 1/8

tan(θ) = 8/15, cot(θ) = 15/8 = 1 7/8

5. The 2 other ways to write cot(θ) are;

cot(θ) = 1/(tan(θ))

cot(θ) = cos(θ)/sin(θ)

6. The location of the point on the terminal side of the angle is; (-3, -4)

Length of the hypotenuse side = √((-3)² + (-4)²) = 5

Let x represent the angle, we get;

The six trig functions of the angle are;

7. The length of the shadow of the tree = 100 m

Angle of elevation of the Sun = θ

Let h represent the height of the tree, we get;

tan(θ) = h/100

Therefore, the height of the tree, h = 100·tan(θ)

The values of the height of the tree at the different angle of elevation in the table are;

θ = 10°, h = 100 feet × tan(10°) ≈ 17.63 feet

θ = 15°, h = 100 feet × tan(15°) ≈ 26.79 feet

θ = 20°, h = 100 feet × tan(20°) ≈ 36.4 feet

θ = 25°, h = 100 feet × tan(25°) ≈ 46.63 feet

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The correct conclusions about the triangle reflections are -

        {y} - axis.

        {x} - axis.

Reflections of graphs involve reflecting a graph over a specific line.

Given is a triangle along with their reflections.

We can conclude the following points regarding the reflected triangles -

        {y} - axis.

        {x} - axis.

Therefore, the correct conclusions about the triangle reflections are -

        {y} - axis.

        {x} - axis.

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P(x) = -14 + 30x + 26x⁴ has four roots. The solution has been obtained by using properties of polynomials.

What is a polynomial?

The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial. When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable).

We are given a polynomial as P(x) = -14 + 30x + 26x⁴.

It is a polynomial of degree 4 as the highest power is 4.

We know that the number of roots is equal to the degree of the polynomial.

Here, since the degree is 4, so it has 4 roots.

Hence, P(x) = -14 + 30x + 26x⁴ has four roots.

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The required by the principle of mathematical induction, the statement is true for all integers n ≥ 0.

Mathematical induction is a method of proof commonly used in mathematics to prove that a statement is true for all positive integers.

The process involves two steps:

Here,
First, we need to prove the statement is true for the base case n=0,

When n=0, we have,

[tex]\sum_{i=1}^{1} i * 2^i = 1*2^1 = 2[/tex]

and

[tex]n * 2^{n+2} + 2 = 0*2^{0+2} + 2 = 2[/tex]

Therefore, the statement is true for n=0.

Next, we assume the statement is true for some arbitrary integer k, meaning:

[tex]\sum_{i=1}^{k+1} i * 2^i = k * 2^{k+2} + 2[/tex]

We want to show that the statement is also true for n=k+1,

[tex]\sum_{i=1}^{k+2} i * 2^i = (k+1) * 2^{k+3} + 2[/tex]

We can rewrite the left-hand side of the equation as,

[tex]=\sum_{i=1}^{k+2} i * 2^i \\= \sum_{i=1}^{k+1} i * 2^i + (k+2) * 2^{k+2} \\= k * 2^{k+2} + 2 + (k+2) * 2^{k+2} \\= (k+1) * 2^{k+3} + 2[/tex]

This last step used the assumption that the statement is true for n=k.

Therefore, by the principle of mathematical induction, the statement is true for all integers n ≥ 0.

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The average rate of change in the cost of the hamburger during the period of 2012 to 2022 is 0.18.

The equation is y = 0.18x + 4.32 and the cost will be $7.02 in 2027.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

(a) Given that,

Cost of hamburger in 2012 = $4.32

Cost of hamburger in 2022 = $6.12

Average rate of change = (6.12 - 4.32) / (2022 - 2012)

                                        = 0.18

(b) Linear equation can be written in slope intercept form as y = mx + c, where m is the slope and c is the y intercept.

Slope of a linear equation is equal to the average rate of change.

m = 0.18

y intercept is the value of the y coordinate when x = 0.

In this case, y intercept is the cost of hamburger in the initial year, 2012.

c = 4.32

So the equation is,

y = 0.18x + 4.32

(c) Price of the hamburger will reach $7.02, when,

7.02 = 0.18x + 4.32

0.18x = 2.7

x = 15

Price will reach $7.02 in the year = 2012 + 15 = 2027

Hence the cost of the hamburger will be $7.02 in the year 2027 using the linear model y = 0.18x + 4.32.

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If a circular garden with a radius of 3 ft. Is bordered by a circular sidewalk that is 2 ft. Wide, then The area of the sidewalk is 28.26 ft².

To calculate this, first calculate the area of the garden, which is 28.27 ft² (A=πr²). After that subtract this from the area of the sidewalk, which is 56.54 ft² (A=π(r+2)²). The area of the sidewalk is the difference between these two values, which is 28.26 ft².

To calculate the area of the garden, we use the formula A=πr², where r is the radius of the garden. In this case, the radius is 3 ft., so the area is 28.27 ft². To calculate the area of the sidewalk, we use the formula

where r is the radius of the garden and 2 is the width of the sidewalk. In this case, the radius is 3 ft. and the width is 2 ft., so the area is 56.54 ft². The area of the sidewalk is then the difference between these two values, which is 28.26 ft².

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cos(0) and sin(0) both have a value of 0, so they would be selected.

cos(pi)/2 is equal to -0.5, and sin(3(pi)/2) is equal to -1, so they would not be selected.

Answer:

1 | 3 | 5

Step-by-step explanation:

sin 0 sin 3pi/2 and tan pi

cos pi/2 is -.5

cos 0 is 1

Answer:

D. If an experiment is​ blinded, then any effect arising from psychological factors should affect all groups equally.

The scatterplot shows the weakest positive linear association is (a)

From the question, we have the following parameters that can be used in our computation:

The graphs

A good line of best fit would have equal number of points on either sides

Using the images as a guide, we can see that:

Graph (a) and (b) have a positive linear association while graph (a) have the least number of points that appear to be on a straight line

This means that the line with the weakest is (a)

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The decibel measurement for the quiet room is 54 dB.

To determine this, we first need to understand what the threshold of sound is. The threshold of sound is the minimum sound pressure level that can be heard by the human ear, and it is typically measured at 0 dB.

Next, we can use the formula for decibel measurement:

dB = 10 log (I/I0)

where I is the intensity of the sound in the quiet room, and I0 is the threshold of sound.

Since the noise in the quiet room is 500 times as intense as the threshold of sound, we can plug in the values into the formula:

dB = 10 log (500/1)

dB = 10 log (500)

dB = 10 * 2.7

dB = 27

Therefore, the decibel measurement for the quiet room is 27 dB. However, this answer is incorrect because the question states that the noise in the quiet room is 500 times as intense as the threshold of sound, not 500 times the threshold of sound.

To correct this mistake, we need to use the formula for decibel measurement with the correct values:

dB = 10 log (500 * I0/I0)

dB = 10 log (500)

dB = 10 * 2.7

dB = 27

Therefore, the decibel measurement for the quiet room is 27 dB + 27 dB = 54 dB.

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Answer:

Step-by-step explanation: