Write 796.384 in expanded form

x=0.295 this is the correct answer

The equation will be if x = 3g + 2 after transformation g as subject g = x / 3 - 2 / 3.

An assertion that two mathematical expressions have equal values is known as an equation. An equation simply states that two things are equal. The equal to sign, or "=," is used to indicate it.

Given:

x = 3g + 2

Rearrange the terms as shown below

x - 2 = 3g (Here the constant term is brought to the left)

x - 2 / 3  = g  (Take the term 3 to the left side as shown)

x / 3 - 2 / 3 = g

g = x / 3 - 2 / 3

Thus, the equation will be g = x / 3 - 2 / 3.

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The g subject of the equation x = 3g + 2 is g = (x - 2) / 3.

To make g the subject of the equation x = 3g + 2, you need to isolate g on one side of the equation. Here is a step-by-step guide:

Subtract 2 from both sides of the equation to get x - 2 = 3g.

Divide both sides of the equation by 3 to isolate g, resulting in g = (x - 2) / 3.

Now, g is the subject of the equation, and it can be expressed as g = (x - 2) / 3.

False, because the IQR of 9 observations is 17 and the IQR of 10 observations is 13.

The given observations are 145, 139, 126, 122, 125, 113, 96, 110, 118, 118.

The Interquartile Range (IQR) formula is a measure of the middle 50% of a data set. The smallest of all the measures of dispersion in statistics is called the Interquartile Range. The difference between the upper and lower quartile is known as the interquartile range.

Interquartile range = Upper Quartile - Lower Quartile

Q2=Q3 - Q1

Ascending order of the given observation is

96, 110, 113, 118, 118, 122, 125, 126, 139, 145

Here, Q1 (median of lower quartile) =113 and

Q3 (median of upper quartile) =126

Q2= 126-113

= 13

The value 96 were removed from the data set, so

110, 113, 118, 118, 122, 125, 126, 139, 145

Q1 =(113+118)/2 =115.5

Q3 =(126+139)/2

= 132.5

Q2 =132.5-115.5

= 17

False, because the IQR of 9 observations is 17 and the IQR of 10 observations is 13.

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Answer:

Option A) 20 ... ... ... ✔

Step-by-step explanation:

[tex] \underline{\tt{❖ \: Given \: \: ❖}}[/tex]

[tex] \underline{\tt{❖ \: Solution \: ❖}}[/tex]

We know that interior sum of all angle is 180°

[tex]\; \;\dashrightarrow \;\pmb {2x+3x+4x=180°}[/tex]

[tex]\; \;\dashrightarrow \;\pmb {9x=180°}[/tex]

[tex]\; \;\dashrightarrow \;\pmb {x = \dfrac{180}{9} }[/tex]

[tex] \; \;\dashrightarrow\; \; {\pmb{\underline{\boxed{\red{\frak { x = 20 }}}}}} \; \green\bigstar[/tex]

The answer is E)4/3

That is because tangent X = a/b

Since this is a rectangle, the parallel sides are equal.

In this case, a=4, B=3, and C=5.

So, tanX = 4/3

Hope this helps!

Answer:

1. 2.4x=1.2x+15

2. 13

Step-by-step explanation:

Final answer:

To find the value of x, multiply the original average of 6 by the original number of scores (8) to find the initial total. Then, use the new average of 7 to find the new total when the two scores (15 and x) are added. Solve for x to find that it equals 7.

Explanation:

The question asks to find the value of x such that when two new scores, 15 and x, are added to a set of eight scores with an average of six, the new average for all ten scores is seven.

To solve this, first calculate the total sum of the original scores by multiplying the average by the number of scores: 6 × 8 = 48. Adding the two new scores, the equation to find the new total sum is 48 + 15 + x = 7 × 10 (since there are now ten scores). Simplify this to get 63 + x = 70, therefore x equals 7.

Answer:

Decrease in area would be 26.67%

Step-by-step explanation:

By decreasing each side of a rectangle by 1 unit area of the rectangle decreases from 60 square feet to 44 square feet.

So decrease in area = 60 - 44 = 16 square feet.

Percentage decrease in the area will be = [tex]\frac{\text{Decrease in area}}{\text{Area before decrease}}\times 100[/tex]

                                             = [tex]\frac{16}{60}\times 100[/tex]

                                            = [tex]\frac{160}{6}[/tex]

                                            = 26.67%

Decrease in area would be 26.67%

The perfect decrease in area of the rectangle when each side is decreased by 1 unit, resulting in a decrease from 60 square feet to 44 square feet, is 16 square feet.

The question asks to calculate the perfect decrease in area of a rectangle when each side is decreased by 1 unit, resulting in a change in area from 60 square feet to 44 square feet. To solve for this, let's assign variables to the original dimensions of the rectangle. Let the length be L and the width be W.

The original area A1 is given by L imes W = 60. After reducing each dimension by 1, the new length and width are L - 1 and W - 1, respectively, so the new area A2 is (L - 1)  imes (W - 1) = 44. The perfect decrease in area is the difference between the original and new areas, which is 60 - 44 = 16 square feet.

The probability a two-digit number to be divisible by 5 from 10 to 99 inclusive and chosen at random is 1/5 or 0.2.

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.

As the probability of an event can not be more than the number 1. Thus he probability of failure of a event is equal to the difference of the 1 to the success of the event.

A two-digit number from 10 to 99, inclusive, is chosen at random. The probability that this number is divisible by 5 has to be find out.

The number of two-digit numbers which is divisible b 5 from 10 to 99 are 18.

[tex](10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95)[/tex]

There are total number from 10 to 99 are 90. Thus, the probability that the chosen number is divisible by 5

[tex]P=\dfrac{18}{90}\\P=\dfrac{1}{5}\\P=0.2[/tex]

Hence, the probability a two-digit number to be divisible by 5 from 10 to 99 inclusive and chosen at random is 1/5 or 0.2.

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Final answer:

The probability that a randomly chosen two-digit number from 10 to 99 is divisible by 5 is 1/5 or 20%.

Explanation:

To find the probability that a randomly chosen two-digit number from 10 to 99 is divisible by 5, we first establish the total number of two-digit numbers, which is 99 - 10 + 1 = 90. Numbers divisible by 5 end in either 0 or 5, so we can count how many of these there are within our range. Starting from 10, the first such number, we have 10, 15, 20, ..., 95. We clearly have two of such numbers per every 10 numbers, resulting in a total of 90/10 * 2 = 18 numbers divisible by 5 between 10 and 99. Hence, the probability is the number of favorable outcomes (numbers divisible by 5), divided by the total number of possible outcomes (two-digit numbers), which gives us a probability of 18/90 = 1/5 or 20%.

Final answer:

The best step to eliminate the x variable from the given system of equations is to multiply the first equation by –2 and the second by 3, facilitating the cancellation of the x terms and allowing for straightforward calculation of y.

Explanation:

To select the best possible first step to solving the system by first eliminating the x variable from the given equations 3x – 9y = 6 and 2x – 11y = 6, we need to make the coefficients of x in both equations equal in magnitude but opposite in sign. This way, when we add the equations together, the x terms will cancel out, leaving us with an equation in terms of y only. Here are the options analyzed:

Multiply the first equation by –2 and multiply the second equation by 3, resulting in –6x + 18y = –12 and 6x - 33y = 18. Adding these together will eliminate the x variable, which is the desired outcome.

Multiplying the first equation by –2 and the second equation by –3 does not effectively eliminate x because it gives us –6x + 18y = –12 and –6x + 33y = –18, which does not help in eliminating x when added or subtracted.

Multiplying the first equation by 2 and the second equation by 3 does not suit our needs for elimination as it results in 6x – 18y = 12 and 6x – 33y = 18, where adding or subtracting does not eliminate x.

Therefore, the correct first step is to multiply the first equation by –2 and multiply the second equation by 3. This approach aligns with standard algebraic methods for solving systems of equations by elimination, providing a clear and effective strategy to simplify the problem by removing one variable, allowing for the straightforward solution of the other.

F'(2) = 3

[tex]\int\limits^x_0 {\sqrt{t^3+1}} \, dt[/tex]

Using Fundamental Theorem of Calculus:

Since x = 2, you now have:

[tex]\int\limits^2_0 {\sqrt{t^3+1} } \, dt[/tex]

so F'(x) = [tex]\sqrt{t^3+1}[/tex]

--> F'(2) = [tex]\sqrt{2^3+1}[/tex] = [tex]\sqrt{9}[/tex] = 3

so F'(2) = 3

F'(2) is the square root of [tex](2^3+1)[/tex], which simplifies to 3.

If F(x) is defined as the integral of [tex]\sqrt(t^3+1)[/tex] dt from 0 to x, then F'(x) represents the derivative of F with respect to x. According to the Fundamental Theorem of Calculus, the derivative of an integral function of this form is simply the value of the function inside the integral evaluated at x. Therefore, F'(2) is the square root of (2^3+1), which simplifies to sqrt(9), or 3.

Final answer:

Absolute extrema refer to the highest or lowest points on the entire domain of a function, while relative extrema are high or low points within a specific region. Calculus techniques such as finding derivatives are used to identify these points.

Explanation:

The concepts of absolute extrema and relative extrema are important in the context of mathematics, specifically in calculus and the study of functions. An absolute extrema (or global extrema) refers to the highest or lowest point over the entire domain of a function. Relative extrema (or local extrema), on the other hand, are points where the function takes on a maximum or minimum value within a particular region or interval, but not necessarily the highest or lowest over the entire function. More formally, an absolute maximum is the largest function value and an absolute minimum is the smallest function value in the entire domain; relative maximums and minimums may not be the absolute highest or lowest, but are higher or lower than points immediately around them. To find extrema, calculus students typically use techniques involving derivatives to identify where function values change from increasing to decreasing or vice versa.

For example, let's consider the function f(x) = x^2 on the interval [-1,1]. The absolute extrema of this function would be the global maximum and minimum values, which occur at x = -1 and x = 1, respectively. The relative extrema of this function would be the local maximum and minimum values, which occur at x = 0.

Final answer:

The system of equations given has no solution because substitution leads to a contradiction, indicating that the lines are parallel and do not intersect.

Explanation:

To solve the given system using the substitution method, we start with the two equations:

From the second equation, we can express y in terms of x by dividing by 2:

y = 2x

Now, we substitute this expression for y into the first equation:

2x − 2x = 816

This simplifies to:

0 = 816

This is a contradiction since 0 cannot equal 816. Therefore, there is no solution to the system of equations. This means that the two lines represented by these equations are parallel and never intersect.

To find the vertex of the quadratic function using the completing-the-square method, rearrange the equation in vertex form, complete the square, and simplify. The vertex of the given function is located at (1, 1) and represents a maximum point.

To find the vertex of the function f(x) = -3x^2 + 6x - 2 using the completing-the-square method, follow these steps:

The vertex of the function is at the point (1, 1). Since the coefficient of x^2 is negative, the vertex represents a maximum point. Therefore, the vertex is a maximum point located at (1, 1).

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