How to list rational numbers from least to greatest on a number line?

Answer:

Hence, the correlation coefficient is:

               r=1.0

Step-by-step explanation:

We know that the correlation coefficient ''r'' is calculated by the formula:

[tex]r=\dfrac{\sum{XY}}{\sqrt{\sum{X^2}\sum{Y^2}}}--------------(1)[/tex]

Let x denote the data point (Number of days since purchase)

Let y denote the data point (Mileage Displayed on odometer)

x         y        X=x-x'       Y=y-y'        XY         X²          Y²

15      67       -20            -95           1900     400      9025

25     122      -10            -40            400       100       1600

35     164        0               2               0           0            4

45     210       10             48             480       100       2304

55     247      20             85           1700       400      7225

x' be the mean of the data of the x-values.

[tex]x'=\dfrac{15+25+35+45+55}{5}\\\\\\x'=\dfrac{175}{5}\\\\\\x'=35[/tex]

Also let y' denote the mean of the y-values.

[tex]y'=\dfrac{67+122+164+210+247}{5}\\\\\\y'=\dfrac{810}{5}\\\\\\y'=162[/tex]

Now we have:

∑ XY=4480

∑ X²=1000

∑ Y²=20158

Hence, we put all the  values in the formula (1) to obtain:

r=0.997 which is close to 1.0

Also from the scatter plot we could observe that the relationship is linear and also strong positive relationship.

Hence, the correlation coefficient is 1.0

Answer:

The slope represents the cost for each hour it takes to repair the machine.

Step-by-step explanation:

We are given that  the cost of a service call to fix  a washing machine can be expressed by the linear function

[tex]y=45x+35[/tex]

Where

y=Total cost of  a service to fix  the machine.

x=Number of hours takes to fix the machine

We have to find that slope in this function what represents.

General equation of line is given by

[tex]y=mx+c[/tex]

Where m=Slope of line

c=y- intercept

Comparing the general equation with the given function

We get m=45,c=35

m=45 represents the cost for each hour it takes to repair the machine because when number of hours multiplied by 45 then we get total cost of x hours.

Hence, the slope represents the cost for each hour it takes to repair the machine.

The point marked A is the point where the birth rate is higher than the death rate.

The term birth rate refers to the rate at which new organims are introduced into the population and the death rate refers to the rate at which individuals exit in the population.

In this case, when we observe the graph, we can see that the point marked A is the point where the birth rate is higher than the death rate.

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This is a problem of calculus where the product and quotient rules are used to find the derivatives of functions u and v at x=1. The values need to be taken from the provided graph.

This is a calculus question related to the product rule and the quotient rule of derivatives. First, let's explore the definitions: the product rule states that the derivative of the product of two functions is the derivative of the first times the second plus the first times the derivative of the second. The quotient rule states that the derivative of the quotient of two functions is the bottom times the derivative of the top minus the top times the derivative of the bottom, all over the bottom squared. From the graph, we have to find out the values of f(1), g(1), f'(1), and g'(1).

Then, we can calculate u'(1) by using the product rule: u'(1) = f'(1)g(1) + f(1)g'(1). In the same way, we can calculate v'(1) by using the quotient rule: v'(1) = [g(1)f'(1) - f(1)g'(1)] / [g(1)]^2. The specific values need to be derived from the provided graph

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(u’(1) = 5)

[tex](v’(1) = \frac{-13}{4})[/tex]

We have two functions:

(u(x) = f(x)g(x))

[tex](v(x) = \frac{f(x)}{g(x)})[/tex]

We need to find the derivatives of both (u(x)) and (v(x)) at (x = 1).

1. Derivative of (u(x)):

Using the product rule, we have:

[ u’(x) = [tex]v \cdot \frac{du}{dx} + u \cdot \frac{dv}{dx} ][/tex]

Where:

(v = g(x))

[tex](\frac{du}{dx})[/tex] is the derivative of (f(x))

[tex](\frac{dv}{dx})[/tex] is the derivative of (g(x))

From the graph:

At (x = 1), we have (f(1) = 3) and an estimated slope of the tangent line for (f’(1)[tex]\approx -2).[/tex]

Similarly, at (x = 1), we have (g(1) = 2) and an estimated slope of the tangent line for [tex](g’(1) \approx 3).[/tex]

Now let’s calculate (u’(1)):

[ u’(1) = [tex]g(1) \cdot f’(1) + f(1) \cdot g’(1)[/tex] = (2)(-2) + (3)(3) = 5 ]

2. Derivative of (v(x)):

Using the quotient rule, we have:

[ v’(x) = [tex]\frac{v \cdot \frac{du}{dx} - u \cdot \frac{dv}{dx}}{v^2} ][/tex]

Substitute the values we found earlier:

(v = g(x) = 2)

[tex](\frac{du}{dx}[/tex] = f’(x) = -2)

[tex](\frac{dv}{dx} = g’(x) = 3)[/tex]

Now let’s calculate (v’(1)):

[tex][ v’(1) = \frac{(2)(-2) - (3)(3)}{2^2} = \frac{-13}{4} ][/tex]

Therefore:

(u’(1) = 5)

[tex](v’(1) = \frac{-13}{4})[/tex]

Answer:

true

Step-by-step explanation:

The statement 'The graph of y = 6cos(x - 2) - 3 is obtained by shifting the graph of y = 6cos x - 3 horizontally 2 units to the right.' is True.

"It is a set of points that satisfy given function."

"It means that the curve representing the graph either 'moves to left / right/ up/ down' or 'it expands or compresses' or 'it reflects'."

"A shift of the graph of a  function up, down, left, or right, without changing the shape, size, or dimensions of the graph."

For given question,

We have been given a function y = 6cos x - 3

Also we have been given a transformed function y = 6cos(x - 2) - 3

We know that when function f(x) is transformed to f(x - k) then the graph of f(x) is translated 'k' units right.

So, the graph of y = 6cos(x - 2) - 3 is obtained by shifting the graph of y = 6cos x - 3 horizontally 2 units to the right.

Therefore, the statement 'The graph of y = 6cos(x - 2) - 3 is obtained by shifting the graph of y = 6cos x - 3 horizontally 2 units to the right.' is True.

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Answer:

The rule is [tex]\\ f(x) = 6^{x}[/tex]

Step-by-step explanation:

The resulting values are powers of 6:

[tex]\\ 6^{1} = 1[/tex]

[tex]\\ 6^{2} = 36[/tex]

[tex]\\ 6^{3} = 216[/tex]

[tex]\\ 6^{4} = 1296[/tex]

[tex]\\ 6^{5} = 7776[/tex]

One factor that is not defined in the question is whether the domain (the set of values for which a function is defined [WolframAlpha, 2019]) of the function [tex]\\ f(x) = 6^{x}[/tex]  is only for x = {1, 2, 3, 4, 5} or defined for all possible values this function can take, that is, x = (-∞;∞) or all real numbers.

As you can see from the graph attached:

In the last case, we have to redefine the function as:

[tex]\\ f(x) = 6^{x}[/tex] for [tex] x = \{1, 2, 3, 4, 5\}[/tex].

Answer:

If a parallelogram does not have four right angles, then it is not a rectangle.

Step-by-step explanation:

"If a parallelogram has four right angles, then it is a rectangle."

To get the inverse of the conditional statement, we take the negation of both the hypothesis and the conclusion.

So, the inverse of the given statement will be :

If a parallelogram does not have four right angles, then it is not a rectangle.

A hair dryer converts electrical energy mainly into thermal energy to heat the air, but it also produces mechanical energy to power a fan and creates sound energy during operation.

A hair dryer converts electrical energy into three main forms of energy: thermal energy, mechanical energy, and sound energy. When a hair dryer is turned on, the electrical energy is primarily converted into thermal energy to heat the air. This is achieved by passing the electric current through resistive heating coils, which transfer energy to the surrounding air as heat. Furthermore, some of the electrical energy is transformed into mechanical energy to power a fan that blows the hot air out of the dryer. Lastly, the operation of the hair dryer also produces sound energy due to the movement of the fan and the rushing air.

Answer:

Length of the rectangle = 13 ft

Step-by-step explanation:

Let l be the length and w be the width of this rectangle.

Two less than three times the width of a rectangle is equal to the length, that is

          3w - 2 = l---------------------------eqn 1

The area of the rectangle is 65 square ft

          l x w = 65  

Substituting eqn 1

           (3w - 2) x w = 65

            3w² - 2w -65 = 0

Solving quadratic eqn

            [tex]w=\frac{-(-2)\pm \sqrt{(-2)^2-4\times 3\times (-65)}}{2\times 3}=\frac{2\pm \sqrt{4+780}}{6}\\\\w=\frac{2\pm \sqrt{784}}{6}\\\\w=\frac{2\pm 28}{6}\\\\w=\frac{2+28}{6}\texttt{ or }w=\frac{2-28}{6}\\\\w=5\texttt{ or }w=-4[/tex]

w cannot be negative

Hence width, w = 5 ft

Substituting in eqn 1

              3 x 5 - 2 = l

             l = 13 ft

Length = 13 ft

Length of the rectangle = 13 ft

Answer- The Answer is -12

Step-by-step explanation:

I took the test

It take 6.434 month  or  6 month and 13 days you to accumulate a balance of $1000 in your account.

Word problem is a mathematical problem totally described in language that is frequently used as an educational tool.

Your current account balance is $215.

Your per month income is $444.

Your per month expense is $322.

Hence, your per month savings is = $444 - $322 = $122.

Let, it take x month you to accumulate a balance of $1000 in your account.

Then mathematically,

215 + 122 x = 1000

Rearrange the equation can be written that:

122 x = 1000 -215

After the subtraction, the result will be:

122 x = 785

Rearrange the equation can be written that:

x = 785/122

After the division, the result will be:

x = 6.434 = 6 month and 13 days.

Hence,  it take 6.434 month  or  6 month and 13 days you to accumulate a balance of $1000 in your account.

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Answer:

The answer is C, 0.5(90 - x) -18

Step-by-step explanation: