a designer builds a model of a canoe. the finished model is exactly the same shape as the original, but smaller. the scale factor is . (a) find the ratio of the surface area of the model to the surface area of the original. (b) find the ratio of the height of the model to the height of the original. (c) find the ratio of the volume of the model to the volume of the original.

Answer:

FGHI is a Parallelogram

Answer:

It is C

Step-by-step explanation:

Answer:

x=1990

Step-by-step explanation:

x+10=2000

x=2000-10

x=1990

Answer:

therefore x = 1990

Step-by-step explanation:

x+10 = 2000

= x = 2000-10

= x = 1990

So, we need to find A and B that divide (-∞, 2)U(7, ∞) into three intervals

Given that the function is

\(f(x) = √-x² + 9x 14\)

The domain of a function is the set of all the possible values of x for which the function is defined, thus exists.

Denominator of the function is

\((-x²+9x-14)=-(x²-9x+14)=-(x-2)(x-7)\)

Thus, the domain of f(x) is the set of all real numbers except for the values of x which make the denominator zero.

So, the domain of the function is (-∞, 2)U(7, ∞).

Therefore, the domain consists of two intervals and we are given three intervals.

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The operation that Amjed should perform to determine the relative frequency of a person over 30 years old who prefers to ride a mountain bike is given as follows:

2) Divide 25 by 462.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of people is given as follows:

58 + 164 + 215 + 25 = 462.

Out of these people, 25 prefer mountain bike, hence the relative frequency is given as follows:

25/462.

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Total number of games for 9 teams so that each team will play 12 games in the baseball league will be 432

Total number of teams in the baseball league is 9

Total number of games that each team will play is 12

Since, each team will have option of 8 teams to play with since no team can play with itself

Therefore, number of games that each team will play after playing 12 games will be 8 x 12 = 96

Since there are 9 teams, therefore total number of games that two teams will play = 96 x 9 = 864

Now, as it takes two teams to play a game therefore the required number of games for the 9 teams = 864/2 = 432

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Answer:

x=35.44

Step-by-step explanation:

x=ky^3 and√z

x=k(y^3)(√z)

Find k when

x=7

y=2

z=4

7=k(2^3)(√4)

7=k(8)(2)

7=k(16)

7=16k

k=7/16

Find x when y=3, z=9

x=k(y^3)(√z)

x=(7/16)(3^3)(√9)

x=(7/16)(27)(3)

=7/16(81)

=567/16

x=35.4375

Approximate to 2 decimal places

x=35.44

\(\int(cos(x) - 1)/x dx = -ln|x| + (1/2) * x^3/3! - (1/4!) * x^5/5! + (1/6!) * x^7/7! - ...\)

This series expansion represents the indefinite integral of the given function.

What is integral?

In mathematics, the integral is a fundamental concept in calculus that represents the accumulation or total of a quantity over a given interval.

To evaluate the indefinite integral ∫(cos(x) - 1)/x as an infinite series, we can expand the integrand using the Maclaurin series representation of cosine and integrate each term individually.

The Maclaurin series expansion of cos(x) is given by:

\(cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + ...\)

Substituting this expansion into the integral, we have:

\(\int (cos(x) - 1)/x dx = \int [(1 - x^2/2! + x^4/4! - x^6/6! + ...) - 1]/x dx\)

Simplifying, we get:

\(\int (cos(x) - 1)/x dx = \int[-x^2/2! + x^4/4! - x^6/6! + ...]/x dx\)

Next, we can integrate each term of the series individually. Since the constant term -1 does not depend on x, it integrates to -x:

∫-1/x dx = -ln|x|

For the other terms, we can integrate them using the power rule:

\(\int x^{(2n)}/(n!)x dx = (1/(n+1)) * x^{(2n+1)}/(n!)\)

Therefore, the integral of each term becomes:

\(\int x^2/2! dx = (1/2) * x^3/3!\\\\\int x^4/4! dx = (1/4!) * x^5/5!\\\\\int x^6/6! dx = (1/6!) * x^7/7!\)

Putting it all together, the indefinite integral as an infinite series is:

\(\int(cos(x) - 1)/x dx = -ln|x| + (1/2) * x^3/3! - (1/4!) * x^5/5! + (1/6!) * x^7/7! - ...\)

This series expansion represents the indefinite integral of the given function.

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Answer:

15x + 20y

Step-by-step explanation:

First, we need to combine like terms,

10x + 20y + 5x

15x + 20y

Since x and y are different variables, we cannot combine them, meaning that the answer is,

15x + 20y

Answer:

The function is not one-to-one

Step-by-step explanation:

Required

Determine if \(f(x) = round(x)\)  is one-to-one

To answer this question, we need to make use of illustrating values of x.

Take x = 6.7

This implies that:

\(f(6.7) = round(6.7)\)

\(f(6.7) = 7\)

Also, Take x = 6.8

\(f(6.8) = round(6.8)\)

\(f(6.8) = 7\)

Notice that the above values of x give the same resulting value of f(x).

If you also take x = 7.4

\(f(7.4) = round(7.4)\)

\(f(7.4) = 7\)

This also gives the same value as the (2) illustration previously used

With these illustrations, we've seen that f(x) has the tendency to have more than one values for different values of x.

Hence:

The function is not one-to-one

Answer:

The ratio of cars to airplanes is 12:8 or 3:2.

To find the ratio, we need to compare the number of cars to the number of airplanes.

We can do this by stating the number of cars first, followed by a colon and then the number of airplanes.

12:8 is the ratio of cars to airplanes.

Alternatively, we can simplify the ratio by dividing both numbers by the greatest common factor. In this case, the GCF of 12 and 8 is 4, so we divide 12 by 4 and 8 by 4 to get 3:2.

The ratio of cars to airplanes is 12:8 or 3:2.

Step-by-step explanation:

Answer:

\(y=5/6\approx0.83\)

Step-by-step explanation:

So we have the equation:

\(5(2y+1)=4y+10\)

First, let's distribute the left side of our equation:

\(5(2y)+5(1)=4y+10\)

Multiply:

\(10y+5=4y+10\)

Now, let's isolate the y-variable. Subtract 4y from both sides:

\((10y+5)-4y=(4y+10)-4y\)

The right side cancels. Subtract on the left. So:

\(6y+5=10\)

Now, subtract 5 from both sides:

\((6y+5)-5=(10)-5\)

The left side cancels. Subtract on the right:

\(6y=5\)

Now, divide both sides by 6. So:

\(\frac{6y}{6}=\frac{5}{6}\)

The left will cancel. Therefore:

\(y=5/6\approx0.83\)

And we're done!

Answer:

if you meant she left a 15% tip then the tip was $9.60

Step-by-step explanation:

Using the sine function:

Using Trigonometric ratios, Tan(20 ) = -24/7 and cos(20) = 7/25

The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

It can be simpler to use a calculator when necessary. (See under)

The reference angle will be less than 45° since the magnitude of the tangent is less than 1. If the angle is less than 90 degrees when doubled, it will remain in the fourth quadrant, where the tangent is negative and the cosine is positive.

Additionally, you can use the identities.

cos(2) is equal to (1 - tan()2)/(1 + tan()2).

cos(2θ) = (1 -(-3/4)²)/(1 +(-3/4)²) = ((16-9)/16)/((16+9)/16)

cos(2θ) = 7/25

Tan(2)=2tan()/(1 -tan(2)2) = 2(-3/4)/((16-9/16) = (-6/4)(16/7)

tan(2θ) = -24/7

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Answer:

52.24 km

Step-by-step explanation:

Given that,

The distance needed to stop a car, d, varies directly as the square of the speed, s, at which it is travelling.

d = ks²

Where

k is constant

When s₁ = 70 km/hr, d₁ = 40 m, s₂ = 80 km/hr, d₂ = ?

So,

\(\dfrac{d_1}{d_2}=\dfrac{s_1^2}{s_2^2}\\\\d_2=\dfrac{d_1s_2^2}{s_1^2}\\\\d_2=\dfrac{40\times 80^2}{70^2}\\\\d_2=52.24\ km\)

So, the new distance is 52.24 km.

Zahra can knit (D) 5 scarves and 10 hats to meet her goal.

Given information:

System of inequalities:

To find the number of scarves and hats that Zahra can knit to meet her goal:

(A) 10 scarves and 5 hats -

(B) 7 scarves and 7 hats -

(C) 6 scarves and 11 hats -

(D) 5 scarves and 10 hats -

This option fulfills both conditions of inequality:

Therefore, Zahra can knit (D) 5 scarves and 10 hats to meet her goal.

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The complete question is given below:

Zahra is knitting items to sell at a craft fair. she has a total of 2,640 yards of yarn. a scarf uses 200 yards of yarn, and a hat uses 150 yards. she wants to knit a minimum of 15 items. this system of inequalities represents this situation, where x is the number of scarves and y is the number of hats. 200x 150y ≤ 2,640 x y ≥ 15 how many scarves and hats can Zahra knit to meet her goal?
A. 10 scarves and 5 hats

B. 7 scarves and 7 hats

C. 6 scarves and 11 hats

D. 5 scarves and 10 hats

The circle centered at C(-5,4) intersects the line y = 3x + 2 at the point Q, with coordinates (-1/10, 17/10). This point Q serves as the tangent point between the line and the circle.

To find the coordinates of the point Q where the line y = 3x + 2 is tangent to the circle with center C(-5,4), we can use the concept of the slope of a tangent line.

First, we need to find the slope of the tangent line. The slope of the line y = 3x + 2 is 3. For a tangent line to a circle, the radius drawn from the center of the circle to the point of tangency is perpendicular to the tangent line. Since the slope of the radius is the negative reciprocal of the tangent line's slope, the slope of the radius is -1/3.

Next, we find the equation of the radius line passing through the center C(-5,4) with a slope of -1/3. Using the point-slope form, we have:

y - 4 = (-1/3)(x + 5)

To find the point of tangency, we solve the system of equations formed by the line y = 3x + 2 and the radius line:

y = 3x + 2

y - 4 = (-1/3)(x + 5)

Substituting the value of y from the first equation into the second equation:

3x + 2 - 4 = (-1/3)(x + 5)

3x - 2 = (-1/3)x - 5/3

3x + (1/3)x = 5/3 - 2

(10/3)x = -1/3

x = -1/10

Substituting this value of x back into the first equation:

y = 3(-1/10) + 2

y = -3/10 + 20/10

y = 17/10

Therefore, the coordinates of the point Q, where the line y = 3x + 2 is tangent to the circle with center C(-5,4), are (-1/10, 17/10)

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The main point of Thoreau's idea is the government must end its unjust actions to earn the right to collect taxes from its citizens

The major idea behind Thoreau is to live simply, independently, and wisely. And then he suggests that people try to live free and uncommitted, away from things that overcomplicate life such as exchange economy and modern labor.

And in addition to his focus on ethics in an existential spirit, he also states that unique contributions to ontology, and the philosophy of science, and radical political thought.

He will tell that as long as the government commits unjust actions, then he will continued to make conscientious individuals must choose whether to pay their taxes or to refuse to pay them and defy the government.

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The true statement is: "Lou will lose 1/5 of his points in the next crash." This is supported by the equation y = 100 * (4/5), where Lou's score after crashes is determined by multiplying his previous score by 4/5, indicating a loss of 1/5 or 20% of his current score. Option B.

The equation y = 100 * (4/5) represents Lou's score after crashes. To determine which of the given statements is true, let's analyze the equation and the given options:

y = 100 * (4/5)

From the equation, we can see that Lou's score after crashes is obtained by multiplying his previous score by 4/5. This means that each time Lou crashes, he loses 1/5 (or 20%) of his current score.

Now let's evaluate the given options:

Lou will lose x more points in his next crash than he lost in his last crash.

Since the equation does not involve any variable 'x' and the formula is fixed at losing 1/5 of the current score, this statement is not true.

Lou will lose 1/5 of his points in the next crash.

This statement is true since the equation explicitly states that Lou's score after crashes is equal to 100 * (4/5), which means he loses 1/5 (or 20%) of his points.

Lou will lose 5 more points in his next crash than he lost in his last crash.

Based on the equation, Lou loses a percentage of his current score, not a fixed number of points. Therefore, this statement is not true.

Lou will lose x times as many points in his next crash as he lost in his last crash.

Similar to the first statement, since there is no mention or involvement of any variable 'x' in the equation, this statement is not true. Option B is correct.

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The correct option is D) 48. As the correlation coefficient ranges from -1 to +1, if the value of eta result is close to 1 or -1, it indicates strong correlation between the two variables. Therefore, the eta result 48 indicates strong relationship between dependent and independent variable.

In order to determine a strong relationship between dependent and independent variable, the correlation coefficient is computed.

It ranges between -1 and +1. Correlation coefficient ranges from -1 to +1 where -1 indicates perfect negative correlation and +1 indicates perfect positive correlation. On the other hand, 0 indicates no correlation.

Therefore, higher the value of correlation coefficient stronger the correlation or relationship between the two variables. The following eta results indicate strong relationship between dependent and independent variable: Option D) 48

As the correlation coefficient ranges from -1 to +1, if the value of eta result is close to 1 or -1, it indicates strong correlation between the two variables. Therefore, the eta result 48 indicates strong relationship between dependent and independent variable.

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The system of linear equations which has the rank of coefficient matrix equal to augmented matrix and equal to the number of unknowns, has only one solution called the unique solution.

Two types of system of equations exist- consistent and inconsistent.

Inconsistent means that it has no solution , i.e. the solution does not exist , here

Rank of augmented matrix is not equal to that of coefficient matrix.

Consistent system means a solution of the equation exists i.e.

rank of augmented matrix = rank of coefficient matrix.

Now, a consistent system can be of two types again - It may have a unique solution ,i.e.

rank of augmented matrix = rank of coefficient matrix = no. of unknowns

or an infinite number of solutions, where

rank of augmented matrix = rank of coefficient matrix < no. of unknowns   (here we need to assign an arbitrary value to a free variable to find its solutions).

For e.g. let us consider the system -

x + y+ z = 0

2x + 3y + 4z = 1

Since , (0,0,0) is obviously satisfying the equation and so is a solution to this system , the given system is a consistent system .

Also, for a system to be consistent , either a unique solution exists or an infinite number of solutions exist. There is no particular number of solutions.

Here, we see that (-1,1,0) is also a solution other than the zero solution.

We can clearly see that the number of unknown variables , x,y,z is 3 and the number of equations is 2.

Thus, The system if there are fewer equations than variables has infinite solutions, equal number of equations as the unknowns has the unique solution.

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residual = 3.48

The line of best fit underpredicts the temperature change.

============================================================

Explanation:

If s = 1.3, then ŷ is...

ŷ = -2.6s + 1.1

ŷ = -2.6*1.3 + 1.1

ŷ = -2.28

This is the estimated or predicted y value based on the input s = 1.3

Let's now compute the residual

e = residual error

e = (observed y value) - (predicted y value)

e = y - ŷ

e = 1.2 - (-2.28)

e = 1.2 + 2.28

e = 3.48 is the residual

A positive residual means that the predicted y value, aka ŷ, is an underestimate compared to the true observed value. In other words, the observed y value is higher than the ŷ value. Therefore, the line of best fit under-predicts the temperature change.

the best model in multiple linear regression is typically determined by selecting the appropriate subset of predictor variables that minimizes the sum of squared residuals while considering statistical significance, model fit criteria and avoiding issues like multicollinearity.

The best model for multiple linear regression is typically determined by minimizing the sum of the squared residuals. This is achieved by finding the combination of predictor variables that provides the smallest difference between the observed values and the predicted values of the dependent variable.

In multiple linear regression, multiple predictor variables are used to estimate the relationship with the dependent variable. The goal is to find the subset of predictor variables that collectively yield the most accurate predictions. This is done by selecting variables that contribute significantly to explaining the variation in the dependent variable while avoiding overfitting the model.

Using as many predictor variables as you can think of is not necessarily the best approach because it can lead to overfitting and a less generalizable model. Including irrelevant or redundant variables may introduce noise and decrease the model's performance.

Therefore, the best model in multiple linear regression is typically determined by selecting the appropriate subset of predictor variables that minimizes the sum of squared residuals while considering statistical significance, model fit criteria (such as adjusted R-squared), and avoiding issues like multicollinearity.

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The probability represents the combination consists only of even numbers as per given condition is equal to 0.020.

Total numbers in combination lock = 38

Numbers from 0 to 37.

To find the probability that the combination consists only of even numbers,

Determine the total number of combinations that can be formed using only even numbers

And divide it by the total number of possible combinations.

Total number of even numbers in the lock

= 19 (since there are 19 even numbers from 0 to 37)

Calculate the total number of combinations using only even numbers,

Use the concept of combinations (nCr).

Since there are 19 even numbers to choose from,

Choose 4 numbers without repetition, the number of combinations is,

Number of combinations

= ¹⁹C₄

= 19! / (4!(19-4)!)

= (19 × 18 × 17 × 16) / (4 × 3 × 2 × 1)

= 3876

Now, calculate the total number of possible combinations without any restrictions.

Since we have 38 numbers to choose from,

and  choose 4 numbers without repetition, the number of combinations is,

Number of total combinations

= ³⁸C₄

= 38! / (4!(38-4)!)

= (38 × 37 × 36 × 35) / (4 × 3 × 2 × 1)

= 194,580

Finally, find the probability by dividing the number of combinations using only even numbers by the total number of combinations,

Probability

= Number of combinations using only even numbers / Total number of combinations

= 3876 / 194580

≈ 0.0199

≈ 0.020 Rounded to three decimal places.

Therefore, the probability that the combination consists only of even numbers is approximately 0.020.

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C

Step-by-step explanation:

hope this helps

As a result, the function's absolute maximum and minimum values are 5 and -45, respectively, at x = -5 and x = 2, respectively.

Every element in a set (referred to as the domain) in mathematics is connected by a rule known as a function to exactly one component in some other set (called the range or codomain). In other terms, a role is a connection among 2 sets where every element in the domain matches exactly one member in the range. Using a formula or equation with a variable input, function notation is a common way to represent functions. As an illustration, the formula f(x) = 2x + 1 gives each true figure x the value 2x + 1.

given

We can apply the second derivative test to determine whether this critical point is a maximum or minimum. By taking f'(xderivative, )'s we arrive at:

f''(x) = -4

The critical point at x = 0 is a local maximum since f"(0) = -4 is a negative value.

Secondly, we must determine whether the interval's endpoints of -5 x 2 provide values that are higher or lower than the crucial point. By entering x = -5 and x = 2, we obtain:

\(f(-5) = 5-2(-5) (-5)^2 = 5 – 50 = -45\)

\(f(2) = 5 - 2(2) (2)^2 = -3\)

As a result, the function's absolute maximum and minimum values are 5 and -45, respectively, at x = -5 and x = 2, respectively.

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