-2.73 as a mixed number

The solution is:

\(-7\leq x\leq -4\) or \(-2\leq x\leq 1\)

The coefficient of determination is approximately 0.544. This means that 54.4% of the total variation in the dependent variable can be explained by the independent variable(s) in the regression model.

The coefficient of determination, denoted as \(R^2\)measures the proportion of the total variation in the dependent variable that is explained by the independent variable(s). To calculate \(R^2\), we need the sum of squares due to regression (SSR) and the total sum of squares (SST). By dividing SSR by SST, we can find the coefficient of determination.

Given:

Sum of squares due to regression (SSR) = 46.9

Total sum of squares (SST) = 86.24

The coefficient of determination (R^2) is calculated as:

\(R^2\)= SSR / SST

Substituting the given values:

\(R^2\) = 46.9 / 86.24

Performing the division:

\(R^2\)≈ 0.544

The coefficient of determination is approximately 0.544, rounded to three decimal places. This means that approximately 54.4% of the total variation in the dependent variable can be explained by the independent variable(s) in the regression model.

The remaining 45.6% of the variation is unexplained and can be attributed to other factors or sources of variation.

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The derivatives of tan^2(x) and sec^2(x) are the same because they are related by the identity tan^2(x) = sec^2(x) - 1.

By using the chain rule, the derivative of tan^2(x) can be found by first finding the derivative of tan(x), then squaring it. The derivative of sec^2(x) can also be found using the chain rule, by first finding the derivative of sec(x), then squaring it.

Since tan^2(x) and sec^2(x) are related by a constant difference, their derivatives will be the same. This means that the rate of change of tan^2(x) with respect to x will be equal to the rate of change of sec^2(x) with respect to x. This is a useful relationship because it allows us to relate the derivatives of two important trigonometric functions, making it easier to integrate or differentiate expressions involving them.

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The slope of the equation c = 0.50t is 0.50. It represents the additional cost per minute of computer usage at the internet cafe.

In the given equation c = 0.50t, c represents the total cost of using the computer for t minutes. The coefficient 0.50 represents the price per minute of computer usage at the internet cafe.

The slope of the equation is equal to this coefficient, which is 0.50.

Interpretation: The slope of 0.50 indicates that for every additional minute of computer usage, the cost increases by $0.50. This means that the internet cafe charges $0.50 per minute for using the computer.

The slope provides a measure of the rate of change of the total cost with respect to the number of minutes used. In this context, it shows the additional cost incurred for each additional minute of computer usage at the cafe.

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The inequality that can be used to determine x, the maximum number of outfits Luis can purchase while staying within his budget is x ≤ 4

How is inequity resolved?

Luis has $420 to spend at a bicycle shop on new accessories and clothing.

He spends $209.67 on a brand-new bicycle.

He spends $6.04 apiece on two bicycle reflectors and $25.77 on a pair of cycling gloves.

He intends to use all or part of the remaining funds to purchase new riding clothing at $37.16 apiece.

Therefore,

x is the maximum amount of clothes Luis can buy on a tight budget.

In order to illustrate the scenario, the inequality that may be employed is as follows:

209.67 + 6.04(2) + 25.77 + 37.16x ≤ 420

235.44 + 12.08 + 37.16x ≤ 420

247.52 +  37.16x ≤ 420

37.16x ≤ 420 - 247.52

37.16x ≤ 172.48

divide both sides by 37.16

x ≤ 4.64155005382

x ≤ 4

Therefore, the inequality that can be used to determine x, the maximum number of outfits Luis can purchase while staying within his budget is x ≤ 4

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We have a value function of a machine at the end of the year t that is:

We know that C = 1038 and r = 0.28.

We have to calcula the value of the machine after 4 years (t = 4).

Then, we replace the parameters with their values and calculate V as:

Answer: the value is $278.95.

Distance between (2 , 3) (4 , -7)

\(d=\sqrt{(y_{2} -y_{1} )^{2} + (x_{2}-x_{1} )^{2}\)

\(d=\sqrt{(-7-3 )^{2} + (4-2 )^{2}\)

\(d=\sqrt{(-10 )^{2} + (2 )^{2}\)

\(d=\sqrt{100 + 4\)

\(d=\sqrt{104\)

\(d=10.198\) or \(2\sqrt{26}\)

Answer:

See below

Step-by-step explanation:

To find the distance between two points, we use the distance formula:

\(d = \sqrt{(x_{2}-x_1)^2 + (y_2-y_1)^2 }\)

Plug in what you know.

\(d = \sqrt{(4-2)^2 + (-7 - 3)^2 }\)

Simplify the parentheses.

\(d = \sqrt{(2)^2 + (-10)^2 }\)

Evaluate the exponents.

\(d = \sqrt{(4) + (100)}\)

Evaluate under the radical.

\(d = \sqrt{(104)}\)

Evaluate the square root.

\(d = 10.198\)

10.198 units

Plug in what you know.

\(d = \sqrt{(-3 -(-9))^2 + (6 - (-4))^2 }\)

Simplify the parentheses.

\(d = \sqrt{(-3 + 9)^2 + (6 + 4)^2 }\)

Simplify the parentheses.

\(d = \sqrt{(6)^2 + (10)^2 }\)

Evaluate the exponents.

\(d = \sqrt{(36) + (100) }\)

Evaluate under the radical.

\(d = \sqrt{(136)}\)

Evaluate the square root.

\(d = 11.662\)

11.662 units

Answer:

4.000

Step-by-step explanation:

The length of her fourth dive is -8.25 feet. The depth of her fifth dive is -9 feet. The depth of her sixth dive is -9.75 feet.

PART A:

To determine the length, in decimal form, of her fourth dive, we need to find an expression that represents the depth of the fourth dive. Since each subsequent dive is 0.75 feet deeper than the previous dives, we can write the expression as:

FOURTH DIVE = -7.5 ft - 0.75 ft

Evaluating the expression:

FOURTH DIVE = -8.25 ft

Therefore, the length of her fourth dive is -8.25 feet.

PART B:

To determine the depth, in decimal form, of her fifth dive, we can use a similar approach. The fifth dive is 0.75 feet deeper than the fourth dive. Thus, the expression for the fifth dive would be:

FIFTH DIVE = -8.25 ft - 0.75 ft

Evaluating the expression:

FIFTH DIVE = -9 ft

Therefore, the depth of her fifth dive is -9 feet.

PART C:

To determine the depth, in decimal form, of her sixth dive, we again consider that each subsequent dive is 0.75 feet deeper than the previous dive. So, the expression for the sixth dive is:

SIXTH DIVE = -9 ft - 0.75 ft

Evaluating the expression:

SIXTH DIVE = -9.75 ft

Therefore, the depth of her sixth dive is -9.75 feet.

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Answer:

Answer

4: 22 degrees

3: (9,2)

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

Use distributive property: a(b +c) =(a*b) + (a*c)

3(x + 6) = 27

3*x + 3*6 = 27

3x + 18  = 27 {Subtract 18 from both sides}

3x + 18 -18 = 27 - 18

         3x    = 9  {Divide both sides by 3}

        3x/3 = 9/3

x = 3

\(\huge\color{red}\underline \colorbox{yellow} {\color{gold}{scroll}}\)\(\blue{ \rule{99999pt}{99999999pt}}\)

\(\blue{ \rule{99999pt}{99999999pt}}\)

\(\blue{ \rule{99999pt}{99999999pt}}\)

\(\blue{ \rule{99999pt}{99999999pt}}\)

\(\blue{ \rule{99999pt}{99999999pt}}\)

\(\blue{ \rule{99999pt}{99999999pt}}\)

\(\blue{ \rule{99999pt}{99999999pt}}\)

\(\blue{ \rule{99999pt}{99999999pt}}\)

Answer:

2, 16, 18.

Step-by-step explanation:

The first number might be 4 , 9, 16 or 25.

The other 2 numbers are factors of 18 so could be:

2, 3, 6, 9 or 18.

If square no. = 4 then sum of other 2 = 32 but no 2 numbers will fit the required result.

If it is 9, the sum = 27 then 9 and 18 will fit but that makes 2 square numbers  so this is not the answer.

If square no. = 16, the sum of other 2 is 20. 2 and 18 will fit this.

Answer:

-1.3333333333333

Step-by-step explanation:

Answer:

2049.2

Step-by-step explanation:

512.3÷ 0.25​= 2049.2

You can use a calculator... (or long division.)

Answer:

2,049.2

Step-by-step explanation:

Hope this helped!

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The equation could be used to solve for charles' rate if it is represented by x is 2x=54.

In the given question wehave to find the equation could be used to solve for charles' rate if it is represented by x.

Bill riding a bicycle at an average rate of 9 mph.

Charles' rate is x.

So the relative rate = x−9 mph

Distance traveled by Bill in 4 hours = 9*4 =36 mph

Charles' overtook Bill in 2 hours. So

Relative Rate = Distance/Time

x−9=36/2

Multiply by 2 on both side. We get

2(x−9)=36

Simplifying

2x−18=36

Add 18 on both side, we get

2x=36+18

2x=54

Hence, the equation could be used to solve for charles' rate if it is represented by x is 2x=54.

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The length of the straw is 3.74 inches.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

In rectangular box,

Length (l) = 2 inches

Width (w) = 1 inches

Height (h) = 3 inches

Here, The straw is said to fit into the box diagonally from the bottom.

So, the length (s) of the straw is calculated as:

⇒ s = √ l² + w² + h²

⇒ s = √ 2² + 1² + 3²

⇒ s = √ 4 + 1 + 9

⇒ s = √ 14

⇒ s = 3.74 inches

Thus, The length of straw = 3.74 inches

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The length of the straw will be 3.7416  inches long in radical form.

If a cuboid has length = l units, breadth = b units, and height = h units, then we can evaluate the length of the diagonal of a cuboid using the formula : X²=l²+b²+h²

Here,

As per the question the length of the straw is equal to length of the diagonal of Rectangular box.

l= 3 inch , b= 2 inch , h= 1 inch

Let us consider the length of the straw be 'x'.

As, Diagonal of Cuboid is,

X²=14

X=√14

i.e. X=3.7416

We get, X= 3.7416 (in radical form)

Hence, the length of the straw will be  5.91607 inches.

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Studies have shown that each one met increase in cardiorespiratory endurance can lead to a decrease in the risk of a fatal heart attack by approximately 7-10%. So, improving your cardiorespiratory fitness through regular physical activity can significantly reduce your risk of heart disease and related health problems.
Hi! Based on the available research, each MET (Metabolic Equivalent of Task) increase in cardiorespiratory endurance is associated with a decrease in the risk of a fatal heart attack by approximately 10-15%. It's important to note that these percentages may vary depending on the study and population being examined. Improving cardiorespiratory endurance through regular exercise can significantly contribute to reducing the risk of heart-related issues.

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B. Square

There are numerous different types of squares in the world. A parallelogram with four congruent sides and four right angles is called a quadrilateral. There are two sets of parallel sides and four right angles in a square, so it is also a rectangle. Because the sides of a square are parallel, it is also a parallelogram.

D. I and IV

\(The\ statement\ is\ always\ true\ is\\ I\ All\ square\ is\ a\ rectanjile\ and\ IV\ Any\ two\ opposite\\ -sides\ of\ a\ perallelogran\ are\ parallel\)

\(So\ Chase\ D\)

{\({A\ souare\ is\ a\ special\ rectangle\)

B. 500 cm²

Calculate area of the rectangle:

\(\curvearrowleft\\ area=500\)

I hope this helps you

:)

Answer:

Step-by-step explanation:

a.Scale factor = distance on the plot / actual distance

b.3 feet = 12 inchs.

so scale factor = 5/12

Answer:

Step-by-step explanation:

The number which is absent in the first 31 digits of pi = 0

We know that a number pi is nothing but the ratio of the circumference of a circle to its diameter.

It is represented by a symbol 'π'

pi is an irrational number. This means that it is not equal to the ratio of any two whole numbers.

Its digits do not repeat.

An approximation 3.14 or 22/7 is often used for everyday calculations.

To 31 decimal places, the value of pi is 3.1415926535897932384626433832795

The numbers present in the first 31 digits of pi are:

1, 2, 3, 4, 5, 6, 7, 8, 9

Only '0' is not present.

Therefore, the number which is absent in the first 31 digits of pi = 0

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We have two right-angled triangles that share a common side, with side lengths 6 and 10. Let's label the sides of the triangles as follows:

Triangle 1:

Side adjacent to the right angle: 6 (let's call it 'a')

Side opposite to the right angle: x (let's call it 'b')

Triangle 2:

Side adjacent to the right angle: x (let's call it 'c')

Side opposite to the right angle: 10 (let's call it 'd')

Using the Pythagorean theorem, we can write the following equations for each triangle:

Triangle 1:\(a^2 + b^2 = 6^2\)

Triangle 2: \(c^2 + d^2 = 10^2\)

Since the triangles share a common side, we know that b = c. Therefore, we can rewrite the equations as:

\(a^2 + b^2 = 6^2\\b^2 + d^2 = 10^2\)

Substituting b = c, we get:

\(a^2 + c^2 = 6^2\\c^2 + d^2 = 10^2\)

Now, let's add these two equations together:

\(a^2 + c^2 + c^2 + d^2 = 6^2 + 10^2\\a^2 + 2c^2 + d^2 = 36 + 100\\a^2 + 2c^2 + d^2 = 136\)

Since a^2 + 2c^2 + d^2 is equal to 136, we can conclude that x (b or c) is between 11 and 12

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Answer:

0.625

Step-by-step explanation:

The value of expression 0.5 divided by 0.8 would be; 0.625

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get. Division can be interpreted as equally dividing the number that is being divided into total x parts, where x is the number of parts the given number is divided.

We need to find the expression of  0.5 divided by 0.8

A negative divided by a negative is positive, then we get;

0.5 / 0.8 = 0.625

Therefore, The value of expression 0.5 divided by 0.8 would be; 0.625

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Answer:

Whole numbers start from zero and include every single positive number that doesn't involve fractions or decimals. ... Therefore, all whole numbers will be an integer (as whole numbers are all the positive integers), but not all integers (since some are negative) will be whole numbers.

Answer: m is — 1

Step-by-step explanation:

Explanation is in the attached image

The output when the given pseudocode is executed with A = 5 and B = 3 will be "25, 16, 9, 4, 1".

The given pseudocode includes a loop that iterates as long as A is greater than or equal to B. In each iteration, the square of A is displayed, and A is decremented by 1. We are asked to determine the output when A is initially 5 and B is 3.

Step 1: Initialization

A is set to 5 and B is set to 3.

Step 2: Iteration 1

Since A (5) is greater than or equal to B (3), the loop executes.

The square of A (5²) is displayed, resulting in the output "25".

A is decremented by 1, so A becomes 4.

Step 3: Iteration 2

A (4) is still greater than or equal to B (3).

The square of A (4²) is displayed, resulting in the output "16".

A is decremented by 1, so A becomes 3.

Step 4: Iteration 3

A (3) is still greater than or equal to B (3).

The square of A (3²) is displayed, resulting in the output "9".

A is decremented by 1, so A becomes 2.

Step 5: Iteration 4

A (2) is still greater than or equal to B (3).

The square of A (2²) is displayed, resulting in the output "4".

A is decremented by 1, so A becomes 1.

Step 6: Iteration 5

A (1) is still greater than or equal to B (3).

The square of A (1²) is displayed, resulting in the output "1".

A is decremented by 1, so A becomes 0.

Step 7: Loop termination

Since A (0) is no longer greater than or equal to B (3), the loop terminates.

Therefore, The output generated by the code execution will be "25, 16, 9, 4, 1" as the squares of A (starting from 5 and decreasing by 1) are displayed in each iteration of the loop.

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Answer:

x=19

Step-by-step explanation:

The perimeter of the right triangle is

P=9+12+15 =36

The perimeter of the left triangle is

P =x-7+ x-7+ x-7 = 3x-21

Set them equal

36 = 3x-21

Add 21 to each side

36+21 = 3x-21+21

57 = 3x

Divide each side by 3

57/3 = 3x/3

19 =x

Answer:

\(x=19\)

Step-by-step explanation:

The perimeter of a shape is the sum of all of its side lengths. Therefore, the perimeter of the first triangle is \(x-7+x-7+x-7=3x-21\) and the perimeter of the second triangle is \(9+15+12=36\).

We are given that the perimeters of the triangles are equal, so \(3x-21\) equals \(36\). As an equation, that would be \(3x-21=36\). Solving for \(x\), we get:

\(3x-21=36\)

\(3x=57\) (Add \(21\) to both sides of the equation to isolate \(x\))

\(x=19\) (Divide both sides of the equation by \(3\) to get rid of \(x\)'s coefficient)

Hope this helps!

The dollar gains depreciated relative to the pound when the price of pounds in dollars increases, for instance, from $1 = 1 pound to $2 = 1 pound.

Devaluation of a currency can take place in both absolute and relative terms. When the value of one currency declines in relation to the values of other currencies, this is referred to as a relative devaluation. For instance, the British pound sterling may be worth more today than it did yesterday in terms of US dollars.

A currency's value declines when compared to other currencies, which is known as currency depreciation. Political unrest, interest rate differences, weak economic fundamentals, and investor risk aversion are a few examples of the causes of currency devaluation.

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