rudy wanted to drive a car that uses less gasoline, so he bought a hybrid. there is a proportional relationship between the volume of gasoline rudy's car uses when driving on the highway (in gallons), x, and the distance he drives it on the highway (in miles), y. x (gallons) y (miles) 1 25 2 50 3 75 4 100 what is the constant of proportionality? write your answer as a whole number or decimal.

Answer:

3.7

Step-by-step explanation:

Absolute value is defined as the following:

\(\displaystyle{|x| = \left \{ {x \ \ \ \left(x > 0\right) \atop -x \ \left(x < 0\right)} \right. }\)

In simpler term - it means that for any real values inside of absolute sign, it'll always output as a positive value.

Such examples are |-2| = 2, |-2/3| = 2/3, etc.

The required Matlab code to find the greatest common divisor of a number using the Euclidean algorithm is shown.

To find the greatest common divisor (GCD) of two numbers using the Euclidean algorithm in MATLAB, you can use the following code:

% Replace '12345678' with your actual student number

studentNumber = '12345678';

% Extract the first 4 digits as the first number

firstNumber = str2double(studentNumber(1:4));

% Extract the last 3 digits as the second number

secondNumber = str2double(studentNumber(end-2:end));

% Find the GCD using the Euclidean algorithm

gcdValue = gcd(firstNumber, secondNumber);

% Display the result

disp(['The GCD of ' num2str(firstNumber) ' and ' num2str(secondNumber) ' is ' num2str(gcdValue) '.']);

Make sure to replace '12345678' with your actual student number. The code extracts the first 4 digits as the first number and the last 3 digits as the second number using string indexing. Then, the gcd function in MATLAB is used to calculate the GCD of the two numbers. Finally, the result is displayed using the disp function.

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Step-by-step explanation:

Number 1

\( log_{10}( {x}^{2} - 3x + 12 ) = 1 \\ log_{10}( {x}^{2} - 3x + 12 ) = log_{10}(10) \\ cancelling \: both \: logs \: we \: have \\ {x}^{2} - 3x + 12 = 10 \\ {x}^{2} - 3x + 12 - 10 = 0 \\ {x}^{2} - 3x + 2 = 0 \\ \)

\(solve \: \: by \: factorisation \: method \\ {x}^{2} - 2x - x + 2 \\ {x}(x - 2) \: - 1(x - 2) \\ (x - 2)(x - 1) \\ therefore \: x = 2 \: or \: x = 1\)

Number 2

Answer:

-29

Step-by-step explanation:

5x +30 +3x =2+8x+1

x= -29

The conversion of a fraction number with denominator 5 and numerator 2 , 2/5 in decimals is equals to the 0.4 value.

A decimal number can be defined as a number whose whole number part and fractional part are separated by a decimal point. Writing 2/5 as a decimal number by converting the denominator to powers of 10. We multiply the numerator and denominator by a number so that the denominator is a power of 10.

2/5 = (2 × 2) / (5 × 2) = 4/10

Now move the decimal point to the left as many places as there are zeros in the denominator, which is a power of 10.

The decimal moved one place to the left because the denominator was 10. Therefore, 4/10 = 0.4. Hence, required value is 0.4.

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Answer:

2√6

Step-by-step explanation:

find the hypotenuse of the triangle thats 3 and 7

pythagorean

3 squared + 7 squared

16 + 49 = 57

√57 is the hypotenuse

√57 is also the base of the triangle that has side thats 9

pythagorean theorem

x squared + √57 squared = 9 squared

x^2 + 57 = 81

x^2 = 81 - 57

x^2 = 24

x = √24

x = √4 * √6

x = 2√6

Substituting g(ln(x)) = 3e^(ln(x)) = 3x into f(x), we have:

(f∘g)(ln(x)) = f(3x)

To find (f∘g)(x), we need to substitute g(x) into f(x): Evaluate

(f∘g)(x) = f(g(x))

Substituting g(x) = 3e^x into f(x), we have:

function (f∘g)(x) = f(3e^x)

To find (f∘g)(ln(x)), we substitute ln(x) into g(x):

(f∘g)(ln(x)) = f(g(ln(x)))

Substituting g(ln(x)) = 3e^(ln(x)) = 3x into f(x), we have:

(f∘g)(ln(x)) = f(3x)

Now let's find (g∘f)(x), which is obtained by substituting f(x) into g(x):

(g∘f)(x) = g(f(x))

Substituting f(x) = x + 1 into g(x), we have:

(g∘f)(x) = g(x + 1)

Therefore:

(d) (f∘g)(x) = f(3e^x)

(e) (f∘g)(ln(x)) = f(3x)

(f) (g∘f)(x) = g(x + 1)

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Answer:

A function is strictly increasing in the interval where the derivate is positive.

Then we must look at the derivate of sin(x)

if f(x) = sin(x)

f'(x) = cos(x)

Then we must see which vales make cos(x) positive.

cos(0) = 1.

cos(90°) = 0

cos(-90°) = 0.

Then the cos(x) function is positive in the range (-90°, 90°) (notice that it is an open interval).

Then the function sin(x) will be strictly increasing in the interval (-90°, 90°)

And because these functions are periodic, where the period is 360°, we can actually write this interval as:

(-90° + n*360°, 90° + n*360°) where n is an integer number.

The volume of solid generated when region s is revolved about the horizontal line y is 93.04919.

We have to find the volume of the solid generated when region s is revolved about the horizontal line y.

As shaded region is revolved around y = -3.

Outer radius = f(x) + 3

Inner radius = g(x) + 3

Width = dx

Thus small volume "dv" formed when shaded region in above diagram is revolved around y = -3.

dv = π\((f(x) + 3)^3\)dx - π\((g(x) + 3)^2\)dx

dv = π(\(f^2\)(x) + 6f(x) + 9)dx - π(\(g^2\)(x) + 6g(x) + 9)dx

dv = π(\(f^2\)(x) + 6f(x))dx - π(\(g^2\)(x) + 6g(x))dx

Now integrating on both side:

\(\int dv=\pi\int^{3}_{0}9(1+x)\cos(\pi x/6) + 6\int^{3}_{0}f(x)dx-\pi\times 5.32021-6\times3.24125\)

Using the provided result or a scientific calculator, the entire definite integral was discovered.

v = π × 25.54298 + 6 × 8.16083 - π × 5.32021 - 6 × 3.24125

v = 93.04919

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The complete question is given below:

Answer:

6x+3x×12-30

9x×do 30-12

then multiple it and there is the ans

The volume of the right prism with a base area of 10 square feet and a height of 6 feet is 60 cubic feet.

A prism is a polyhedron that has a base and a top face that are the same in size and shape, with sides connecting them that are rectangles in a right prism.

A right prism is a prism in which all of the side faces are perpendicular to the base.

Therefore, the height of the right prism is perpendicular to the base as well.

A right prism has a volume equal to the product of the base area and the height.

This formula can be represented as:

V = Bh

Here, B represents the area of the base, and h represents the height.

The volume of the right prism can be found by multiplying the area of the base by the height of the prism, according to the formula:

V = Bh.

In this problem, the area of the base of the prism is given to be 10 square feet.

The height of the prism is 6 feet.

We can simply substitute these values into the formula to obtain the volume of the right prism as follows:

V = BhV

   = 10 × 6V

   = 60

Therefore, the volume of the right prism is 60 cubic feet.

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The product of (3 x 107) and (2 x 107) is 6.8694 x 10^4

To find the product of (3 x 107)and (2 x 107), we can use the distributive property of multiplication which states that the product of a number and a sum is equal to the sum of the products of the number and each term in the sum. In this case, we can multiply the numbers outside the parentheses first, and then multiply the result by the common factor of 107 to simplify the expression:

(3 x 107) x (2 x 107) = 6 x (107 x 107)

Next, we can calculate the product of 107 and 107, which is 11,449:

6 x 11,449 = 68,694

In scientific notation, this can be written as:

= 6.8694 x 10^4

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The system of equation represented in the grpah is y < x2 – 6x – 7; y > x – 3.

The system of equations can be   described as a set of inequalities. The first inequality, y < x² - 6x - 7, represents aquadratic function, while the second inequality, y > x - 3, represents a linear function.

The system represents the region where the values of y are less than the valuesof x² - 6x - 7, and greater than the values of x - 3.

The graph of the system of equations shows the shaded region where y is less than th parabolic curve represented by y = x² - 6x - 7, and greater than the line represented by y = x - 3.

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Answer:

(B) -6x + 4y = 11

Step-by-step explanation:

Two lines are parallel if they have the same slope

In the line equation, y = mx + b, m = slope

For y = 3/2*x - 7/4, slope = 3/2

(B) can be written as

4y = 6x +11

Dividing by 4 on both sides gives y = 6/4*x + 11/4 which is 3/2*x + 11/4 so the coefficient of x (the slope) is 3/2 which is the slope of the line in the question

Using same strategies for the other lines, you will see
(A) has slope -3/2

(C) has slope 1/2

(D) has slope -3/2

Answer:

Area= 8^2ft

:)

The sum of the lengths of the two bases of a trapezoid with a height of 6 feet and an area of 30 square feet must equal 5. Therefore, there are several possibilities for the lengths of the bases, as long as their sum is 5.

The area of a trapezoid is found using the formula Area = 1/2 × (base1 + base2) × height. Given that the area is 30 square feet and the height is 6 feet, you can use this formula to solve for the lengths of the bases. Setting up the equation gives 30 = 1/2 × (base1 + base2) × 6.

When you simplify this equation, you get 5 = base1 + base2. This means that the sum of the lengths of the two bases must be 5 feet. Therefore, there are several possible lengths for base1 and base2, as long as they add up to 5. For example, base1 could be 2 feet and base2 could be 3 feet, or base1 could be 1 foot and base2 could be 4 feet.

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Answer:

2 hours and 30 minutes to fill it up

Step-by-step explanation:

The Laplace transform of the given initial value problem is taken to solve for Y(s) to obtain the answer Y(s) = (-e^(-s)/s) / (s^2 + 6s + 19).

To find the Laplace transform of the initial value problem, we apply the Laplace transform to each term of the differential equation. Using the properties of the Laplace transform, we have:

s^2Y(s) - sy(0) - y'(0) + 6sY(s) - y(0) + 19Y(s) = L{T(t)}

Since T(t) is a periodic function, we can express its Laplace transform using the property of the Laplace transform of periodic functions:

L{T(t)} = T(s) = ∫[0 to 1] (1 - t)e^(-st) dt

Evaluating the integral, we have:

T(s) = ∫[0 to 1] (1 - t)e^(-st) dt

= [e^(-st)(1 - t)/(-s)] evaluated at t = 0 and t = 1

= [(1 - 1)e^(-s(1))/(-s)] - [(e^(-s(0))(1 - 0))/(-s)]

= -e^(-s)/s

Substituting T(s) into the Laplace transform equation, we get:

s^2Y(s) - y'(0)s + (6s + 19)Y(s) = -e^(-s)/s

Rearranging the equation and substituting the initial conditions y(0) = 0 and y'(0) = 0, we obtain:

(s^2 + 6s + 19)Y(s) = -e^(-s)/s

Finally, we solve for Y(s):

Y(s) = (-e^(-s)/s) / (s^2 + 6s + 19)

Therefore, Y(s) is the Laplace transform of y(t) for the given initial value problem.

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The possible value of QRP is 24^o.

A sine rule is a trigonometric rule which can be used to determine either the angle or length of side of a given triangle that is not a right angle.

sine rule states that;

a/Sin A = b/Sin B = c/Sin C

From the given question, let the measure of angle QRP be represented by R. So that;

9/ Sin 37 = 6/ Sin R

9 Sin R = 6 Sin 37

Sin R = 6 Sin 37/ 9

  = 3.611/ 9

  = 0.4012

R = Sin^-1 (0.4012)

  = 23.65

Thus, QRP is 24^o.

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The function f(x) that satisfies the given initial value problem is f(x) = -cos(x) + 3.

To find the function f(x) described by the given initial value problem, F'(x) = sin(x), and F(0) = 2, follow these steps:

1. Integrate F'(x) with respect to x to find f(x): ∫sin(x) dx = -cos(x) + C, where C is the constant of integration.
2. Use the initial condition F(0) = 2 to find the value of C: -cos(0) + C = 2 => C = 2 + cos(0) = 2 + 1 = 3.
3. Replace C with the found value in the function: f(x) = -cos(x) + 3.

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Answer:

-8xy^5-6xy^4

Step-by-step explanation:

-10xy^5+(2x^3)(y^2)-(6x^2)(y^2)

-10xy^5+2xy^5 -6xy^4

-8xy^5-6xy^4

This should be good but if your teacher requires it just put 0 with the exponent in descending order

Answer:

Answering on an Alt account to give brainliest :p

Step-by-step explanation:

One tax rate is specifically sampled in this case, but not every taxpayer in that bracket is included in the sample. Thus, a stratified sampling is required here. [RESPONSE, C]

The most prevalent term is "systematic," which most frequently refers to actions taken in accordance with a system or technique. a methodical strategy for learning that entails closely adhering to the program's instructions. What is systemic refers to or has an impact on a whole system.

Those that like to think individually tend to be deadline-driven, unwilling to participate in educational settings, and independent thinkers. Also, they frequently speak clearly and favor sharing facts and figures above personal beliefs. Also, they avoid small talk and favor talks with a clear agenda.

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Answer:

v = b

hope this helps

The volume of the prism will be reduced to 1/512 of its original size

The volume of a prism is given by the formula V = Bh, where B is the area of the base and h is the height of the prism. If the dimensions of a prism are multiplied by 1/8, then the new dimensions are 1/8 of the original dimensions. Therefore, the new base area is 1/64 of the original base area, and the new height is 1/8 of the original height.

Substituting these values into the formula for the volume of a prism, we get:

V' = (1/64)Bh(1/8)

Simplifying, we get:

V' = (1/512)Bh

Therefore, the new volume of the prism is 1/512 of the original volume of the prism.

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Answer:

Minimum < Q1 < Median < Q3< Maximum

Step-by-step explanation:

Given

Minimum, Median, Maximum, Q3 and Q1

See attachment for complete question

Required

Order from least to greatest

In a dataset, the range is:

\(Range = Maximum - Minimum\)

This implies that, the minimum is the least and the maximum is the highest of the dataset

So, we have:

Minimum <         <              <           < Maximum

The median is the middle item; So, the above becomes

Minimum <         < Median <           < Maximum

In a dataset, the IQR is:

\(IQR = Q_3 - Q_1\)

This implies that:

\(Q_3 > Q_1\)

So, we have:

Minimum < Q1 < Median < Q3< Maximum

The car loses all of its marketable value after 9 years, the x-intercepts represent the points at which the car has lost all of its value, so they are (9, 0) and (0, 22995).

The depreciation equation for the car can be represented as y = mx + b, where y is the value of the car at time x, m is the slope of the line, and b is the y-intercept.

To find the slope, we can use the information that the car loses all of its marketable value after 9 years. The market value of the car will be 0 after 9 years, so we can set y = 0 when x = 9:

0 = m * 9 + b

To find the y-intercept, we can use the information that Jason purchased the car for $22,995. This means that the value of the car at time 0 was $22,995, so we can set y = 22,995 and x = 0:

22,995 = m * 0 + b

Combining these two equations, we can solve for m and b:

0 = m * 9 + b

22,995 = m * 0 + b

b = 22,995

Now that we have found the y-intercept, we can use it to find the x-intercepts by setting y = 0 and solving for x:

0 = m * x + 22,995

0 - 22,995 = m * x

-22,995 = m * x

x = -22,995 / m

Since we don't know the value of m, we can't find the x-intercepts directly. However, since the car loses all of its marketable value after 9 years, the x-intercepts represent the points at which the car has lost all of its value, so they are (9, 0) and (0, 22995).

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1. The measure of AC = 8.4

2. The measure of AC' = 6

3. The measure of C'B' = 12.6

Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other.

Given:

Segment B'C' is parallel to segment BC.

A line splits a triangle's sides in the same proportion if it runs parallel to one side and crosses the other sides at two different spots.

Then,

10/4 = 6/x

x = 2.4

The measure of AC = 2.4

And,

14/8.4 = 21/y

y = 12.6

The measure of C'B' = 12.6

Therefore, all the required values are given above.

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Answer:  \(\frac{n-m}{n}\)

This is the same as writing (n-m)/n

Don't forget about the parenthesis if you go with the second option.

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

Explanation:

The probability that she wins is m/n, where m,n are placeholders for positive whole numbers.

For instance, m = 2 and n = 5 leads to m/n = 2/5. This would mean that out of n = 5 chances, she wins m = 2 times.

The probability of her not winning is 1 - (m/n). We subtract the probability of winning from 1 to get the probability of losing.

We could leave the answer like this, but your teacher says that the answer must be "in the form of a combined single fraction".

Doing a bit of algebra would have these steps

\(1 - \frac{m}{n}\\\\\frac{n}{n} - \frac{m}{n}\\\\\frac{n-m}{n}\\\\\)

and now the expression is one single fraction.

Can be cracked within eight hours by the average hacker.

With spaces included in the character count, 8 characters equals between 1 and 2 words. If spaces are excluded from the character count, 8 characters equals between 1 and 3 words.

There are 8-character passwords with capital letters, lowercase letters, and numerals that begin and end with the same symbol.A password of eight characters with just lowercase and capital letters offers 200 billion potential permutations.“1uppercase” is an example of an 8-character password. This password has one uppercase, one lowercase, one number, and one special character.

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