Which fraction is in simplest form? ​3/12​ ​5/10​ ​2/3​ ​4/6

interest + interest      = total interest

0.08*x   + 0.09*(9000-x) = 750    dollars

0.08x + 810 - 0.09x = 750

-0.01x = 750 - 810 = -60  ====>  x = \(\frac{-60}{-0.01}\) = 6,000

Answer.  $6000 was invested at 8%.  The rest   9000-6000 = 3000 dollars were invested at 9%.

Check.   0.08*6000 + 0.09*3000 = 480 + 270 = 750 dollars.  

Using linear approximation, the expression √125.2 can be approximated as approximately 10.02.

To find the equation of the tangent line to the function f(x) = √x at x = 125, determine the slope (m) and the y-intercept (b) of the tangent line.

First, find the slope (m) using the derivative of the function f(x) = √x:

f'(x) = 1 / (2√x)

Evaluate the derivative at x = 125:

f'(125) = 1 / (2√125) = 1 / (2 × 5) = 1/10

Now, find the y-coordinate of the point on the function f(x) at x = 125:

f(125) = √125 = 5

So, the tangent line at x = 125 passes through the point (125, 5) and has a slope of 1/10.

Using the point-slope form of a linear equation, the equation of the tangent line can be written as:

y - 5 = (1/10)(x - 125)

To simplify, multiply through by 10:

10y - 50 = x - 125

Rearranging the equation, express it in the form y = mx + b:

y = (1/10)x - 75/10 + 5

Simplifying further:

y = (1/10)x - 75/10 + 50/10

Combining the terms:

y = (1/10)x - 25/10

Therefore, the equation of the tangent line to f(x) = √x at x = 125 is y = (1/10)x - 25/10.

Now, use this tangent line to approximate the value of √125.2:

Substitute x = 125.2 into the equation:

y = (1/10)(125.2) - 25/10

y = 12.52 - 2.5

y ≈ 10.02

So, using linear approximation, approximate √125.2 as approximately 10.02.

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\( \: \: \: \: \large\bf\implies \: 4.32\)

\( \longrightarrow \bf \: 1.42 - ( - 2.9) \\ \longrightarrow \bf \: 1.42 + 2.9 \\ \longrightarrow \bf \: 4.32\)

First of all we know that to do this type of question that is ↓

Answer:

8/25 , 38%, 0.41

Step-by-step explanation:

This should be the correct answer. Hope this helps!

Answer:

This graph is not a function.

The domain is -3<x<3.

The range is 1<y<3.

Answer:

n=-17

Step-by-step explanation:

8(2n-5)=3(6n-2)

1) Distributive property

16x-40=18x-6

16x−40=18x−6

2) Subtract 16x16x from both sides.

-40=18x-6-16x

−40=18x−6−16x

3) Simplify 18x-6-16x18x−6−16x to 2x-62x−6.

-40=2x-6

−40=2x−6

4) Add 66 to both sides.

-40+6=2x

−40+6=2x

5) Simplify -40+6−40+6 to -34−34.

-34=2x

−34=2x

6) Divide both sides by 22.

-\frac{34}{2}=x

−

2

34

=x

7) Simplify \frac{34}{2}

2

34

to 17

−17=x

8) Switch sides.

x=−17

Answer: ALL OF THE ABOVE

Step-by-step explanation:

a translation doesn't change any of the above, they all remain the same. it's a trick question :P

The potential of an organization to generate growth and development is decided by its capacity. So, the option is correct.

Capacity is the correct option.

We know that

while generating an organization we do measure it by the growth and capacity and these two terms are called as capacity

whereas

The option B. Flexibility in an organization underlines the readiness and capability to change. Hence, the option is incorrect.

The option C. Organizational volatility is a degree of how uncertain a change might be. So, the option is not correct.

The option D. Sustainability in an organization can be achieved when the activities, processes, elements, resources, and other components do not harm or negatively affect the environment. Hence, the option is not correct.

The option E. The level of variation among diverse components of the organization is termed complexity. So, the option is incorrect.

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The height of a nearby tree is 15ft

What is Application of trigonometry ?

Trigonometry is the study of lengths, heights, and angles through computations involving triangles. There are many applications for trigonometry and its functions in daily life. For instance, it is employed in astronomy to gauge the distances between nearby stars, in geography to gauge the separations between landmarks, and in the satellite navigation system.

According to question

let

The height of tree = h

Angle elevation = α

Given

Length of shadow of tree = 20 ft

height of man = 6 ft

Length of shadow of man = 8 ft

We know that

tanθ = Perpendicular/Base

therefore:

tanα = 6/8 = h/20

⇒ 6*20 = 8h

⇒ 120 = 8h

⇒ h = 120/8

⇒ h = 15

hence, the height of a nearby tree is 15 ft.

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The value of the variable 'w' for the given equation 7 ( w + 7 )³ = 7(6³)  is equal to w = -1.

As given in the question,

Given equation is equal to :

7 ( w + 7 )³ = 7(6³)

Divide both the side of the equation by 7 we get,

⇒ 7 ( w + 7 )³ / 7 = 7(6³) /7

⇒( w + 7 )³ = (6³)  

Take cube root both the side of the equation we get,

⇒∛( w + 7 )³ = ∛(6³)  

⇒ w + 7 = 6

Now subtract 7 from both the side of the equation we get,

⇒w + 7 - 7 = 6 - 7

⇒ w = -1

Therefore, the value of the variable 'w' for the given equation is equal to w = -1.

The complete question is:

Solve this equation:

7 ( w + 7 )³ = 7(6³)

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Answer:

A.

Step-by-step explanation:

Answer:

hmm length x breadth... I'd simple formula

Answer:

A:The Reqd. No. of Permutations=3360

Step-by-step explanation:

I couldn’t find the answer to B..sorry

Answer:

24

Step-by-step explanation:

\(\sqrt{25^2-7^2}\\\\=\sqrt{(25-7)(25+7)}\\\\=\sqrt{18(32)}\\\\=\sqrt{9*2*2^5}\\\\=\sqrt{3^2\cdot 2^6}\\\\=\sqrt{(3\cdot2^3)^2}\\\\=3\cdot2^3\\\\=3\cdot8\\\\=24\)

Answer:

24

Step-by-step explanation:

First we compute the number under the radical.

We have 25² = 625 and 7² = 49, so 25² - 7² = 625 - 49 = 576.

Thus, √25² - 7² = √576 = √24², which is 24.

Answer:

4,5

Step-by-step explanation:

Answer:

y = (x - 4)² + 2 , x ≥ 4.

Step-by-step explanation:

Finding the inverse of

f(x) = 4 + √(x - 2)

Begin by swapping the x and y variables in the equation:

x = 4 + √(y - 2)

Subtract 4 from both sides:

x - 4 = √(y - 2)

Square both sides:

(x - 4)² = y - 2

Add 2 to both sides to get your equation:

y = (x - 4)² + 2

However, the domain restriction also needs to be included since the question involves finding the inverse of a square root function. In this case, the domain restriction would be x ≥ 4.

The pair of fractions 1/4 and 1/3 when evaluated is; 7/12.

From the task content;

On this note, it follows that the common factor between the two fractions is used in evaluation.

This therefore follows that the pair of fractions is; 7/12.

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Answer:

The 3rd set

Step-by-step explanation:

The first set has a range of 6, not 5

The second set has a range of 5, but not a mean of 5

The third set has both a mean and a range of 5

Answer:

Add each side of the rectangle together to get the perimeter.

Step-by-step explanation:

Subscribe to Clutch Gam3r on YT

Answer:

Measuring it with a ruler and jotting down the length.

Step-by-step explanation:

If you are copying a line segment, the best way to copy it perfectly is to take the measure of the original line segment and copy down the measurement and then construct the other line segment to the exact measure.

Answer:

Brianlliest!

Step-by-step explanation:

you must measure the current line segment and copy it with the same length and make a new one

The correct total weight of the bags of granola is 8 1/4 pounds.

One thing that can be done to improve Roberto's reasoning is to ensure the accuracy of the calculations.

In his conclusion, Roberto added the weights of the bags of granola (2 1/2, 2 3/4, and 3) and claimed that the total weight was 8 1/4 pounds. However, the sum of these weights does not equal 8 1/4 pounds.

To address this, Roberto should recheck his calculations. Adding mixed numbers involves adding the whole numbers separately and then adding the fractions separately. In this case, 2 1/2 + 2 3/4 + 3 can be calculated as follows:

2 + 2 + 3 = 7 (sum of whole numbers)

1/2 + 3/4 = 2/4 + 3/4 = 5/4 = 1 1/4 (sum of fractions)

Thus, the correct sum is 7 + 1 1/4 = 8 1/4 pounds.

By double-checking the calculations and providing the accurate sum, Roberto's reasoning would be more precise, reliable, and free from errors.

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The probable question may be:

Roberto made a line plot to show the weight in pounds of the bags of granola in his store he concluded that the total weight of the granola was 2 1/2+2 3/4+3=8 1/4 pounds.

what is one thing that you could do to Roberto's Reasoning

Answer:

0.388

Step-by-step explanation:

7/9 x 1/2 = 0.388

Complete the  following Division

Quotient of 96, 55, 84 and 63 is 12, 11, 14 and 21 respectively

What is Division?

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.

1) 96

Divisor = 8

96 / 8

= 12

Quotient = 12

2) 55

Divisor = 5

55 / 5

= 11

Quotient = 11

3) 84

Divisor = 6

84 / 6

= 14

Quotient = 14

4) 63

Divisor = 3

63 / 3

= 21

Quotient = 21

Hence , Quotient of 96, 55, 84 and 63 is 12, 11, 14 and 21 respectively

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Answer:

24 students are in class

Step-by-step explanation:

1/5 of 15 is 3

15 - 3 = 12

12 boys + 12 girls = 24 students

The equation of the line that is parallel and perpendicular to y = -8x + 6 and passes through the point (7, 5) are y = -8x + 61 and  \(y = \frac{1}{8}x + \frac{33}{8}\) respectively.

The slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given the equation of the original line:

y = -8x + 6

Using the slope intercept:

Slope m = -8

Since the desired line is parallel, it will have the same slope.

Therefore, the slope of the parallel line is also -8.

Plug in the slope m = -8 and the poin (7,5) into the point-slope form:

( y - y₁ ) = m( x - x₁ )

( y - 5) = -8( x - 7 )

Simplify

y - 5 = -8x + 56

y = -8x + 56 + 5

y = -8x + 61

The equation of the parallel line is y = -8x + 61.

For the perpendicular line:

The slope of the perpendicular line will be the negative reciprocal of -8, which is 1/8.

Hence, plug slope m = 1/8 and point (7,5) into the point-slope form:

( y - y₁ ) = m( x - x₁ )

\(y - 5 = \frac{1}{8} ( x + 7 )\\\\y - 5 = \frac{1}{8}x + \frac{7}{8} \\\\y = \frac{1}{8}x + \frac{7}{8} + 5\\\\y = \frac{1}{8}x + \frac{33}{8}\)

Therefore, the perpendicular line is \(y = \frac{1}{8}x + \frac{33}{8}\).

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\(\\ \sf\Rrightarrow \left(\dfrac{1}{2}x-\dfrac{1}{3}\right)+5x^2-2x+6\)

\(\\ \sf\Rrightarrow \left(\dfrac{x}{2}-\dfrac{1}{3}\right)+5x^2-2x+6\)

\(\\ \sf\Rrightarrow \dfrac{3x-2}{6}+5x^2-2x+6\)

\(\\ \sf\Rrightarrow \dfrac{3x-2+30x^2-12x+36}{6}\)

\(\\ \sf\Rrightarrow \dfrac{30x^2+3x-12x-2+36}{6}\)

\(\\ \sf\Rrightarrow \dfrac{30x^2-9x+34}{6}\)

Answer:

7

Step-by-step explanation:

77777777777 and then you multiply