Which expression is equivalent to

The expression that results from applying the law of indices and expression is 5x^(-7/3).

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression. An expression, also known as a mathematical expression, is a finite combination of symbols that are well-formed in accordance with context-dependent rules.

Here,

The resulted expression will be,

(125x)^(7/3)^(-1/3)

125=5^3

(a^n)^m = a^mn

(5x)^3^7/3^-1/3

(5x)^7*-1/3

5x^(-7/3)

The resulted expression will be 5x^(-7/3) using the law of indices and expression.

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The terms through degree four of the Maclaurin series is \(f(x)=x+x^{2} +\frac{5x^{3} }{6} +\frac{5x^{4} }{6} +.....\).

In this question,

The function is f(x) = \(\frac{sin(x)}{1-x}\)

The general form of Maclaurin series is

\(\sum \limits^\infty_{k:0} \frac{f^{k}(0) }{k!}(x-0)^{k} = f(0)+\frac{f'(0)}{1!}x+\frac{f''(0)}{2!}x^{2} +\frac{f'''(0)}{3!}x^{3}+......\)

To find the Maclaurin series, let us split the terms as

\(f(x)=sin(x)(\frac{1}{1-x} )\) ------- (1)

Now, consider f(x) =  sin(x)

Then, the derivatives of f(x) with respect to x, we get

f'(x) = cos(x), f'(0) = 1

f''(x) = -sin(x), f'(0) = 0

f'''(x) = -cos(x), f'(0) = -1

\(f^{iv}(x)\) = cos(x), f'(0) = 0

Maclaurin series for sin(x) becomes,

\(f(x) = 0 +\frac{1}{1!}x +0+(-\frac{1}{3!} )x^{3} +....\)

⇒ \(f(x)=x-\frac{x^{3} }{3!} +\frac{x^{5} }{5!}+.....\)

Now, consider \(f(x) = (1-x)^{-1}\)

Then, the derivatives of f(x) with respect to x, we get

\(f'(x) = (1-x)^{-2}, f'(0) = 1\)

\(f''(x) = 2(1-x)^{-3}, f''(0) = 2\)

\(f'''(x) = 6(1-x)^{-4}, f'''(0) = 6\)

\(f^{iv} (x) = 24(1-x)^{-5}, f^{iv}(0) = 24\)

Maclaurin series for (1-x)^-1 becomes,

\(f(x) = 1 +\frac{1}{1!}x +\frac{2}{2!}x^{2} +(\frac{6}{3!} )x^{3} +....\)

⇒ \(f(x)=1+x+x^{2} +x^{3} +......\)

Thus the Maclaurin series for \(f(x)=sin(x)(\frac{1}{1-x} )\) is

⇒ \(f(x)=(x-\frac{x^{3} }{3!} +\frac{x^{5} }{5!}+..... )(1+x+x^{2} +x^{3} +......)\)

⇒ \(f(x)=x+x^{2} +x^{3} - \frac{x^{3} }{6} +x^{4}-\frac{x^{4} }{6} +.....\)

⇒ \(f(x)=x+x^{2} +\frac{5x^{3} }{6} +\frac{5x^{4} }{6} +.....\)

Hence we can conclude that the terms through degree four of the Maclaurin series is \(f(x)=x+x^{2} +\frac{5x^{3} }{6} +\frac{5x^{4} }{6} +.....\).

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Answer:

5, 3

Step-by-step explanation:

correct on edge2020

Answer:

(5, 3)

Step-by-step explanation:

late but still lol

Given that \(\(T(n)\) = \(10n^2-3n\)\) if (\(\(n=1\)\)), you have to prove it by induction. So, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if ( n= 1). The given statement is true for all positive integers n

Let's do it below: The base case (n=1) is given as follows: \(T(1)\) =\(10\cdot 1^2-3\cdot 1\\&\)=\(7\end{aligned}$$\). This implies that \(\(T(1)\)\) holds true for the base case.

Now, let's assume that \(\(T(k)=10k^2-3k\)\) holds true for some arbitrary \(\(k\geq 1\).\)

Thus, for n=k+1, T(k+1) = \(10(k+1)^2-3(k+1)\\&\) = \(10(k^2+2k+1)-3k-3\\&\)=\(10k^2+20k+7k+7\\&\) = \(10k^2-3k+20k+7k+7\\&\) = \(T(k)+23k+7\\&\) = \((10k^2-3k)+23k+7\\&\) =  \(10(k+1)^2-3(k+1)\).

Therefore, we have proved that the statement holds true for n=k+1 as well. Hence, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if (n=1). Therefore, the given statement is true for all positive integers n.

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(a) i. (T – R)(2) = 3, ii. 2T(3) – 4R(1) = -14, iii. (T/R)(3) = Undefined, iv. T(R(3)) = 5.

(b) Vertical intercept of T(x): (0, 5).

(c) Horizontal intercept of R(x): (3, 0).

(d) \([T(R(2))]^{-1} + R^{-1}(2) = 1/3\).

(a) Find the value of each of the following expressions:

i. (T – R)(2):

To find the value of (T – R)(2), we subtract the corresponding values of R(x) from T(x) at x = 2:

(T – R)(2) = T(2) - R(2) = 2 - (-1) = 3.

ii. 2T(3) – 4R(1):

To find the value of 2T(3) – 4R(1), we substitute the values of T(3) and R(1) into the expression:

2T(3) – 4R(1) = 2(1) – 4(4) = 2 - 16 = -14.

iii. (T/R)(3):

To find the value of (T/R)(3), we divide the value of T(3) by R(3):

(T/R)(3) = T(3) / R(3) = 1 / 0 (Since R(3) = 0) = Undefined.

iv. T(R(3)):

To find the value of T(R(3)), we substitute the value of R(3) into T(x):

T(R(3)) = T(0) = 5.

(b) Find the vertical intercept of T(x):

The vertical intercept of a function occurs when x = 0. From the given table, we can see that T(0) = 5. Therefore, the vertical intercept of T(x) is (0, 5).

(c) Find a horizontal intercept of R(x):

The horizontal intercept of a function occurs when the function's output is zero. From the given table, we can see that R(x) = 0 when x = 3. Therefore, the horizontal intercept of R(x) is (3, 0).

(d) Evaluate \([T(R(2))]^{-1} + R^{-1}(2)\):

To evaluate \([T(R(2))]^{-1} + R^{-1}(2)\), we need to find the compositions T(R(2)) and \(R^{-1}(2)\) separately and then add them.

T(R(2)) = T(1) = 3.

To find \(R^{-1}(2)\), we need to determine the input value that results in R(x) = 2. Looking at the given table, we can see that R(x) = 2 when x = 0. Therefore, \(R^{-1}(2) = 0\).

Thus, \([T(R(2))]^{-1} + R^{-1}(2) = (3)^{-1} + 0 = 1/3 + 0 = 1/3.\)

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Step-by-step explanation:

remember the original trigonometric triangle inside the norm circle (radius = 1).

sine is the up/down distance from the triangle baseline or corresponding circle diameter.

cosine is the left/right distance from the center of the circle (and the point of the angle).

for larger triangles and circles all these function results need to be multiplied by the actual radius (which we skipped for the norm circle, as a multiplication by 1 is not changing anything).

when you look at the triangle with K representing the angle, we have 10 a the cosine value, 24 as the sine value and 26 as the radius.

so,

10 = cos(K) × 26

cos(K) = 10/26 = 5/13

The total differential of w = x^3yz^4 + sin(yz) is given by dw = (3x^2yz^4)dx + (x^3z^4cos(yz))dy + (x^3y^4cos(yz)). This is the required answer to the question.

In mathematics, the total differential is defined as the derivative of a multivariable function. The total differential of the given function w = x^3yz^4 + sin(yz) can be obtained by differentiating the function with respect to each independent variable while keeping all other independent variables constant, then adding the results. This can be represented as:

dw = ∂w/∂x dx + ∂w/∂y dy + ∂w/∂z dz

where ∂w/∂x is the partial derivative of w with respect to x, ∂w/∂y is the partial derivative of w with respect to y, and ∂w/∂z is the partial derivative of w with respect to z.

Now, let's calculate each partial derivative of the given function with respect to x, y, and z.

∂w/∂x = 3x^2yz^4

∂w/∂y = x^3z^4cos(yz)

∂w/∂z = x^3y^4cos(yz)

Using these partial derivatives, we can calculate the total differential as follows:

dw = (3x^2yz^4)dx + (x^3z^4cos(yz))dy + (x^3y^4cos(yz))dz

Therefore, the total differential of w = x^3yz^4 + sin(yz) is given by dw = (3x^2yz^4)dx + (x^3z^4cos(yz))dy + (x^3y^4cos(yz)). This is the required answer to the question.

The total differential is a multivariable differential calculus concept, sometimes known as the full derivative. It provides a linear approximation of the change in a function due to changes in all its variables, in contrast to the partial derivative, which only estimates the change in the function resulting from changes in one variable while keeping the others fixed.

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Answer:

The Perimeter figure is: 21.42 mm

Step-by-step explanation:

The given figure consists of two parts:

1) Semicircle

2) Square

Determining the Perimeter of the Semicircle:

Given

Diameter d = 6 mm

Radius r = d/2 = 6/2 = 3 mm

In a semi-circle, the perimeter is made up of half the circumference (arc) of the circle and the diameter of the circle.

Perimeter = 1/2 × ( circumference of the circle ) + d

                = 1/2 × (2πr) + d

                = πr + d

                = 3.14(3) + 6

                = 9.42 + 6

                = 15.42 mm

Thus, the Perimeter of the semi-circle is: 15.42 mm

Determining the Perimeter of the Square:

Given

Length of a side = a = 2mm

Perimeter of square = 4a = 4(2) = 8mm

Thus, the Perimeter of the Square is: 8mm

Now, in order to determine the Perimeter of a complete figure, we need to add the Perimeter of the square and the perimeter of the semicircle and subtract 2 mm.

The reason why we need to subtract 2mm because one side of the square (2mm) is overlapped along the diameter of the semicircle.

Now,

Figure Perimeter = Perimeter of square + Perimeter of Semicircle -  2

                             = 8 + 15.42 - 2

                             = 21.42 mm

Therefore, the Perimeter figure is: 21.42 mm

Note: It seems you may have missed adding the correct choice there.

Answer:

He does not have enough money, as 10 < 10.50.

Step-by-step explanation:

The first step to solve this question is finding the cost of 7 packs of gum.

1 pack costs $1.50.

So 7 packs will cost 7*1.50 = $10.50.

Pablo has 10 dollars, which is less than $10.50(10 dollars and 50 cents). So he does not have enough money.

Withholding food and fluids before surgery is done to ensure that the patient's stomach is empty. This helps to minimize the risk of aspiration, which occurs when stomach contents enter the lungs. Aspiration can lead to respiratory complications such as pneumonia, which can be dangerous for the patient.

The appropriate response by the nurse is d) It prevents aspiration and respiratory complications. Withholding food and fluid before surgery is important to prevent aspiration, which occurs when stomach contents enter the lungs during surgery, and can cause respiratory complications. It also helps ensure a clear surgical field. However, the patient will still receive necessary fluids and medications through an IV during surgery to prevent dehydration and maintain blood pressure. It is important to follow the healthcare provider's instructions on pre-operative fasting to ensure the safest surgical experience.
d) It prevents aspiration and respiratory complications.
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The p-value(s) at which you would reject the null hypothesis for a two-sided test at the 90% confidence level are D) 1100, E) 0.0900, F) 0.0500 and G) 0.0250

A thesis test is a formal statistical test we use to reject or fail to reject some thesis.

Null thesis: There's no effect or difference between the new system and the old system, a p- value indicates how credible the null thesis is, given the sample data and specifically, assuming the null thesis is true, the p- value tells us the probability of carrying an effect at least as large as the bone we actually observed in the sample data and if the p- value of a thesis test is sufficiently low, we can reject the null thesis and specifically, when we conduct a thesis test, we must choose a significance position at the onset, common choices for significance situations are 0.01,0.05, and 0.10, also if the p- values is lower than our significance position, also we can reject the null thesis but if the p- value is equal to or lesser than our significance position, also we fail to reject the null thesis.

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The focus of a parabola can be found by adding p to the y-coordinate k if the parabola opens up or down. (h, k + p) exist (2, 0).

Given: \($y=\frac{1}{8} (x^{2} -4x-12)\)

\($y=\frac{x^{2}}{8}-\frac{x}{2}-\frac{3}{2}$$\)

Use the form \($a x^{2}+b x+c$\) to find the values of a, b, and c.

\($a=\frac{1}{8}$\), \($b=-\frac{1}{2}$\) and \($c=-\frac{3}{2}$\)

Consider the vertex form of a parabola \($a(x+d)^{2}+e$\)

To estimate the value of d using the formula \($d=\frac{b}{2 a}$\).

Substitute the values of a and b into the formula

\($d=\frac{-\frac{1}{2}}{2\left(\frac{1}{8}\right)}$$\)

\($d=-\frac{1}{2} \cdot \frac{1}{\frac{2}{8}}$$\)

Cancel the common factor 2 and 8.

\($d=-\frac{1}{2} \cdot \frac{1}{\frac{1}{4}}$$\)

\($d=-\frac{1}{2}(1 \cdot 4)$$\)

Multiply the numerator by the reciprocal of the denominator.

\($d=-\frac{1}{2} \cdot \frac{1}{2\left(\frac{1}{8}\right)}$$\)

\($d=-\frac{1}{2} \cdot \frac{1}{\frac{2}{8}}$$\)

equating, we get

\($d=-\frac{1}{2}(1 \cdot 4)$$\)

\($d=-\frac{1}{2} \cdot 4$$\)

The value of \($d=-2$\)

Find the value of e using the formula \($e=c-\frac{b^{2}}{4 a}$\).

Substitute the values of c, b and a into the above formula, and we get

\($e=-\frac{3}{2}-\frac{\left(-\frac{1}{2}\right)^{2}}{4\left(\frac{1}{8}\right)}$$\)

simplifying the equation, we get

\($e=-\frac{3}{2}-\frac{(-1)^{2}\left(\frac{1}{2}\right)^{2}}{4\left(\frac{1}{8}\right)}$\)

Apply the product rule to \($\frac{1}{2}$\).

\($e=-\frac{3}{2}-\frac{1\left(\frac{1}{4}\right)}{4\left(\frac{1}{8}\right)}$$\)

\($e=-\frac{3}{2}-\frac{\frac{1}{4}}{4\left(\frac{1}{8}\right)}$$\)

\($e=-\frac{3}{2}-\frac{\frac{1}{4}}{\frac{4(1)}{8}}$$\)

simplifying the above equation, we get

\($e=-\frac{3}{2}-\frac{\frac{1}{4}}{\frac{4 \cdot 1}{4 \cdot 2}}$$\)

\($e=-\frac{3}{2}-\frac{\frac{1}{4}}{\frac{4 \cdot 1}{4 / 2}}$$\)

\($e=-\frac{3}{2}-\frac{\frac{1}{4}}{\frac{1}{2}}$$\)

Multiply the numerator by the reciprocal of the denominator.

\($e=-\frac{3}{2}-\left(\frac{1}{4} \cdot 2\right)$$\)

\($e=\frac{-3-1}{2}$$\)

\($e=\frac{-4}{2}=2$\)

Substitute the values of \($a, d_{t}$\) and e into the vertex form \($\frac{1}{8}(x-2)^{2}-2$\).

Set y equal to the new right side.

\($y=\frac{1}{8} \cdot(x-2)^{2}-2$\)

Use the vertex form, \($y=a(x-h)^{2}+k$\), to determine the values of a, h, and k.

\($a=\frac{1}{8}$\)

\($h=2$\)

\($k=-2$\)

Find the vertex \($(h, k)$\)

\($(2,-2)$\)

Find \($\boldsymbol{p}$\), the distance from the vertex to the focus.

To estimate the distance from the vertex to a focus of the parabola \($\frac{1}{4 a}$\)

Substitute the value of a into the formula

\($\frac{1}{4 \cdot \frac{1}{8}}=\frac{1}{\frac{4(1)}{8}}$\)

\($\frac{1}{\frac{4 \cdot 1}{4-2}}=\frac{1}{\frac{4 \cdot 1}{4 \cdot 2}}$\)

\($\frac{1}{\frac{1}{2}}=2$\)

The focus of a parabola can be found by adding p to the y-coordinate k if the parabola opens up or down. (h, k + p)

Substitute the known values of h, p, and k into the formula, we get

(2,0).

Therefore, the correct answer is (2,0).

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Answer:

Step-by-step explanation:

boody boody

Answer:

x 3

Step-by-step explanation

Answer:

c, 1  more than the independent variable.

Step-by-step explanation:

c, 1 more than the independent variable b/c when x is 1, y is 2, it only has a difference of 1

Answer:

72 Sayfa

Step-by-step explanation:

50% = (50/100) = 0.50

30% = (30/100) = 0.30

0.3 x 360 = 108

0.5 x 360 = 180

180 - 108 = 72

Answer: the original price was $60! <3

Step-by-step explanation:

Answer:

There are 3 ways

Step-by-step explanation:

The formula for a sector's area is:

1. A = (sector angle / 360 ) * (pi *r2)

2. A = (sector angle / (2*pi)) * (pi * r2)

3. A = (fraction of the circle) * (pi * r2)

The measurement of the remaining two sides of the triangle be 4cm and 6cm.

Given :- Perimeter of triangle = 18m.

Area of triangle = √135m².

One side of triangle = 8m.

Triangle  is a plane figure with three straight sides and three angles.

Let the equation be Area of ∆ = 1/2bh

= 1/2 ab sin C = 1/2 bc sin A = 1/2 ca sin B

= √( s(s-a)(s-b)(s-c) ) [ where s = (a + b + c)/2 ]

By using Heron's formula to get the Area of triangle,

s = (Perimeter /2) = (18/2) = 9m.

Putting values now we get :-

√(s(s-a)(s-b)(s-c) ) = √135

substitute the values in the above equation, we get

√[9(9-8)(9-b)(9-c)] = √135

Squaring Both sides we get,

9 × 1 × (9-b)(9-c) = (√135)² = 135

Dividing both sides by 9, we get,

(9-b)(9-c) = 15

81 - 9c - 9b + bc = 15

simplifying the above equation, we get

81 - 9(b + c) + bc = 15

9(b + c) - bc = 81 - 15

9(b + c) - bc = 66 -------- (1).

Also, if Rest two sides are b and c, we get,

→ 8 + b + c = 18

→ (b + c) = 18 - 8 = 10 cm. ------ (2).

Putting value of (2) in (1) , we get,

→ 9 × 10 - bc = 66

simplifying the above equation, we get

→ bc = 90 - 66

→ bc = 24 ------------ (3).

We do Factors of (3), we just have to check now, which satisfy Equation (2) also . (sum of Factors will be 10).

24 = ( 1, 24) , (24, 1), ( 2,12), (12,2) , (3,8) ,(8,3) , (4,6),(6,4)

We can see (4,6) or (6,4) Satisfy the (2).

Therefore, the measurement of the remaining two sides of the triangle be 4cm and 6cm.

The complete question is:

the perimeter of a triangular garden is 18 m. if its area is under root 135 m^2 and one of the tree sides is 8 m, find the remaining two sides

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This is an example of an isosceles triangle. An isosceles triangle is a triangle with two equal sides and two equal angles.

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Answer:

5n + 60

Step-by-step explanation:

5 × (n + 12) = 5 × n + 5 × 12 = 5n + 60

Answer:

~ 1017.4

Step-by-step explanation:

volume of a cone  1/3 pi r^2 h

1/3 pi * 9^2 * 12 = 1017.8

Answer:

26

Step-by-step explanation:

Answer:

18.84cm

Step-by-step explanation:

Formula for circumference= 2πr

2x3.14x(12/2)

2x3.14x6

37.68

Circumference of half circle= 37.68/2

=18.84cm

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

a = 4, b = -21, c = -18

to keep from getting "mixed up", evaluate the discriminant first ...

b² - 4ac = (-21)² - 4(4)(-18) = 729

sqrt(729) = 27

x = (21 +/- 27)/8

x = -3/4, x = 6

since the discriminant is a perfect square, the original quadratic will factor ...

4x² - 21x - 18 = 0

(4x + 3)(x - 6) = 0

x = -3/4, x = 6

Answer:729

Step-by-step explanation: Use the values of a, b and c to find the discriminant. Which is 729

The value of the probability density function (pdf) at 0 for a uniform random variable between 5 and 15 is 0, because the pdf for a uniform distribution is constant between its minimum and maximum values, and is 0 elsewhere.

To explain further, a uniform distribution is a continuous probability distribution where every value within a certain range has an equal chance of being selected. In this case, the range is between 5 and 15. The pdf for a uniform distribution is constant within the range of the distribution and is 0 outside of it.

Since 0 is not within the range of the uniform distribution, the pdf at 0 is 0. This means that the probability of selecting a value of 0 from this uniform distribution is 0. The area under the pdf curve between 5 and 15 is equal to 1, which means that the probability of selecting a value within this range is 1.

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Answer:

5

Step-by-step explanation:

The total cost of the laptop with sales tax included is approximately $638.10.

To find the total cost of the laptop with sales tax included, you need to calculate the sales tax amount and then add it to the listed price.

First, calculate the sales tax amount by multiplying the listed price by the sales tax rate:

Sales tax amount = 594.98 * 0.0725

Sales tax amount = 43.11965 (rounded to two decimal places)

Next, add the sales tax amount to the listed price:

Total cost = Listed price + Sales tax amount

Total cost = 594.98 + 43.11965

Total cost = 638.09965 (rounded to two decimal places)

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