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\(\\ \sf\longmapsto \dfrac{\sqrt[4]{x^3}}{\sqrt[5]{x^2}}\)

\(\\ \sf\longmapsto \dfrac{x^{3\times \dfrac{1}{4}}}{x^{2\times \dfrac{1}{5}}}\)

\(\\ \sf\longmapsto \dfrac{x^{\dfrac{3}{4}}}{x^{\dfrac{2}{5}}}\)

\(\\ \sf\longmapsto x^{\dfrac{3}{4}-\dfrac{2}{5}}\)

\(\\ \sf\longmapsto x^{\dfrac{7}{20}}\)

\(\\ \sf\longmapsto \sqrt[20]{x^7}\)

Answer:

C) -3/4

Step-by-step explanation:

Since we know at least two points on a line, we can easily find the slope with the formula:

y2-y1 / x2-x1

basically we plug in the numbers and get

-5 - (-2) / 3 - (-1)

= -5+2 / 3+1

= -3/4

so the answer is C) -3/4

hope this helped !! <3

Answer:

A

Step-by-step explanation:

The range is your y values.

Your y values are : -8, -6, -2, 0, 3, 5

We are told that we are rising to these numbers, so we must be coming from negative infinity, but we are never going higher than 5.

Answer:

67.5

Step-by-step explanation:

Answer:

angle v

please take a look at the gif

Answer:

v

Step-by-step explanation:

Step-by-step explanation:

0c,02,4,6,8,10,12,14,16,18,20,22,24,26,28,30

The distribution (D) is negatively skewed because more values are concentrated on the right side (tail) of the distribution.

A statistic is a piece of data derived from a subset of a population. It's the inverse of a parameter — census data, which polls everyone.

Statistics is a method of comprehending data collected about us and the world.

Here, a negatively skewed (also known as left-skewed) distribution is a sort of distribution in which more values are concentrated on the right side (tail) of the distribution graph while the left tail of the distribution graph is longer.

Thus, the distribution (D) is negatively skewed

Hence, the correct answer is an option (D).

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If the Pascal's triangle row entries are 1,n,...,n,1 and the average is 2048 , then the value of n is  15  .

Let the number of entries in the row is = n + 1  .

Since the average of the entries is 2048,

So , the sum of the entries is = 2048 × (n + 1).

We know that the sum of the entries in a row of Pascal's Triangle is equal to 2ⁿ, so we have the equation as :

⇒ 2048 × (n + 1) = 2ⁿ ;

On simplifying ,

we get ;

⇒ n = -0.99975 and n = 15 .

Since the "n" cannot be in negative .So , n = 15   .

Therefore , the value of n is the  pascal's triangle is 15 .

The given question is incomplete , the complete question is

The entries in a certain row of Pascal's Triangle are 1,n,...,n,1 the average of the entries in this row is 2048. find  n  .

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Answer:

1. Yes, yes, no, yes

2. 224

3.182 R1

4. 65

5. ? (sorry)

8. 4692 divided by 23 = 204

Step-by-step explanation:

8. To sum up, 4692/23 = 204. It is a whole number with no fractional part. As division with the remainder the result of 4692 ÷ 23 = 204 R 0.

Sorry for not answering everything.

Answer:

$74.34

Step-by-step explanation:

Answer:

$74.34

Step-by-step explanation:

59×1.2=70.80

sales tax doesn't apply to tip so 59×0.06= 3.54

70.80+3.54= 74.34

Answer: <3, <6, <8

Step-by-step explanation:

Trust me

Answer:

46 bc 250 -20 =230 and 230÷5= 46

Answer:

\(-3x^2+6xy+4\)

Step-by-step explanation:

\((3x^2+2xy+7)-(6x^2-4xy+3)=\\\\3x^2-6x^2+2xy+4xy+7-3=\\\\-3x^2+6xy+4\)

Hope this helps!

Answer:

3x2-6xy

Step-by-step explanation:

I think i dont know

Answer:

The correct choice is option B.  3,429

Step-by-step explanation:

When rounded to the nearest hundred, 3429 becomes 3400.

Answer:

3,429 --- right answer

From the given options, the rational number that does not lie between 2/5 and 3/4 is option (d) 9/20.

We need to discover a number that is either smaller than 2/5 or greater than 3/4 in order to find a rational number that does not fall between these two numbers.

Let's contrast each choice with the range provided:

a. 17/20 does not fall between 2/5 and 3/4 because it is more than 3/4.

b. 13/20: This number falls inside the provided range and is not the solution we are seeking for because it is larger than 2/5 but smaller than 3/4.

c. 11/20: This number falls inside the provided range and is not the solution we are seeking for because it is larger than 2/5 but smaller than 3/4.

d. 9/20: Because this number is less than 2/5, it does not fall within the range.

From the given options, the rational number that does not lie between 2/5 and 3/4 is option (d) 9/20.

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Complete question =

Choose a rational number which does not lie between 2/5 and3/4.

a.17/20

b.13/20

c.11/20

d.9/20​

The solution to the equation 2 csc x = 3 csc θ − csc θ sin θ in the range 0 ≤ θ < 2π is:

θ = 7π/6

We can start by manipulating the given equation to express cscθ in terms of cscx:

2 csc x = 3 csc θ − csc θ sin θ

2/cscθ = 3 - sinθ

cscθ/2 = 1/(3 - sinθ)

cscθ = 2/(3 - sinθ)

Now we can use the identity sin²θ + cos²θ = 1 and substitute for cscθ in terms of sinθ:

1/cosθ = 2/(3 - sinθ)

cosθ = (3 - sinθ)/2

Next, we can use the identity sin²θ + cos²θ = 1 to solve for sinθ:

sin²θ + cos²θ = 1

sin²θ + [(3 - sinθ)/2]² = 1

Multiplying both sides by 4, we get:

4sin²θ + (3 - sinθ)² = 4

Expanding and simplifying, we get:

8sin²θ - 6sinθ - 8 = 0

Dividing both sides by 2, we get:

4sin²θ - 3sinθ - 4 = 0

Using the quadratic formula with a = 4, b = -3, and c = -4, we get:

sinθ = [3 ± √(3² - 4(4)(-4))]/(2(4))

sinθ = [3 ± √49]/8

sinθ = (3 ± 7)/8

Since 0 ≤ θ < 2π, we only need to consider the solution sinθ = (3 - 7)/8

= -1/2 corresponds to an angle of 7π/6 in the third quadrant.

To find cosθ, we can use the identity sin²θ + cos²θ = 1:

cosθ = ±√(1 - sin²θ)

Since we are in the third quadrant, we want the value of cosθ to be negative, so we take the negative square root:

cosθ = -√(1 - (-1/2)²)

cosθ = -√(3/4)

cosθ = -√3/2

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We evaluated the given iterated integral by first solving the inner integral with respect to y and then integrating the resulting expression with respect to x from 0 to 1. The final answer is 2.

To evaluate the iterated integral, we first need to solve the inner integral with respect to y and then integrate the resulting expression with respect to x from 0 to 1.

So, let's start with the inner integral:

∫1−x1 x(15x^2 - 6y)dy

Using the power rule of integration, we can integrate the expression inside the integral with respect to y:

[15x^2y - 3y^2] from y=1-x to y=1

Plugging in these values, we get:

[15x^2(1-x) - 3(1-x)^2] - [15x^2(1-(1-x)) - 3(1-(1-x))^2]

Simplifying the expression, we get:

12x^2 - 6x + 1

Now, we can integrate this expression with respect to x from 0 to 1:

∫01 (12x^2 - 6x + 1)dx

Using the power rule of integration again, we get:

[4x^3 - 3x^2 + x] from x=0 to x=1

Plugging in these values, we get:

4 - 3 + 1 = 2

Therefore, the value of the iterated integral is 2.

In summary, we evaluated the given iterated integral by first solving the inner integral with respect to y and then integrating the resulting expression with respect to x from 0 to 1. The final answer is 2.

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Answer:

- 1 and 7

Step-by-step explanation:

to find h(0) substitute x = 0 into h(x)

h(0) = 4(0) - 1 = 0 - 1 = - 1

to find h2) substitute x = 2 into h(x)

h(2) = 4(2) - 1 = 8 - 1 = 7

Answer:

\(y-x=3\)

Step-by-step explanation:

Subtract  y  from both sides of the equation.

\(x = 11-y\)

\(5x+3y=41\)

Replace all occurrences of x  in \(5x+3y=41\)  with  11 -y

\(x=11-y\)

\(5(11-y)+3y=41\)

simplify \(5(11-y)+3y=41\)

\(x=11-y\)

\(55-5y+3y=41\)

add -5y and 3y

\(x= 11-y\)

\(55- 2y=41\)

Solve for  y  in the second equation.

Move all terms not containing  y  to the right side of the equation.

\(x=11-y\)

\(-2y=-14\)

Divide each term by  − 2  and simplify.

\(x=11-y\)

\(y=7\)

Replace all occurrences of  y  in  x

\(x=11-(7)\)

\(y=7\)

simplify.

\(x=4\)

\(y=7\)

Replace the variable  x  with  4  in the expression.

\(y-(4)\)

Replace the variable  y  with  7  in the expression.

\((7) - (4)\)

Multiply  − 1  by  4 .

\(7-4\)

Subtract  4  from  7 .

\(3\)

Answer:y-x=3

Step-by-step explanation: substitution method

5x+3y=41........ equation 1

x+y=11 .........equation 2

Since we are given two different equations in terms of two different linear equations, let us try to solve them using the concept of method of substitution:

we find that y=11-x

we will substitue y into equation 1

5x+3(11-x) = 41

5x+33-3x=41

5x-3x=41-33

2x=8

2x/2=8/2

x=4

x+y=11

then you substitute

4+y=11

y=11-4

y=7

y-x

7-4=3

Answer:

40 cm²

Step-by-step explanation:

It asked the area of the shaded region and in my perspective the dark brown color is the shaded region it is talking about.

Area = length × height

Area = 8 cm × 5 cm

Area = 40 cm²

Hope this helps and tell me if I was right, thank you :)!!

Answer:

answer 240 cm2

Step-by-step explanation:

find the area of the shaded rectangle and then find the area of the one inside of it. next, subtract the small rectangle from the shaded.

280- 40=240

The remainder of the equation is \(\rm 28x+30\).

Given that,

When the equation \(\rm 3x^3-2x^2+4x-3\) is divided by \(\rm x^2+3x+3\).

We have to find,

The remainder of the equation?

According to the question,

The equation \(\rm 3x^3-2x^2+4x-3\) is divided by \(\rm x^2+3x+3\).

On the division of the polynomial, the remainder is,

\(\dfrac{\rm 3x^3-2x^2+4x-3}{\rm x^2+3x+3}\)

Factorize the equation to convert this into the simplest form,

\(\rm 3x^3-2x^2+4x-3\\\\3x^3-11x^2+9x^2+9x+28x-33x-33+30\\\\Taking \ the \ common \ terms \ and \ simplify\ the\ equation\\\\3x^3+9x^2+9x+11x^2+33x-33+28x+30\\\\3x(x^2+3x+3) - 11(x^2+3x+3) + 28x+30\\\\(3x+11) (x^2+3x+3) +28x +30\)

Now, the equation can be written as,

\(\rm = \dfrac{(3x+11) (x^2+3x+3) +28x +30}{ x^2+3x+3}\\\\= \dfrac{(3x+11) (x^2+3x+3) }{ x^2+3x+3} + \dfrac{28x +30}{ x^2+3x+3}\\\\= (3x+11) + \dfrac{28x +30}{ x^2+3x+3}\\\\\)

The relation between the divisor, remainder, and quotient is,

\(\rm = Quotient + \dfrac{Remainder}{Divisor}\)

On comparing with the equation,

The remainder becomes 28x +30.

Hence, The required remainder of the equation is \(\rm 28x+30\).

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Given that Owen has $1.05 in dimes and nickels. He has 3 more dimes than nickels. We are to find out how many coins of each type he has.Let us assume that Owen has x nickels.

he has x+3 dimes.Since the value of each nickel is $0.05, thus, the value of x nickels is 0.05x dollars.Since the value of each dime is $0.10, therefore, the value of (x+3) dimes is 0.10(x+3) dollars.Owen has a total of $1.05 which can be written as 105 cents.

The total number of coins is the sum of the number of nickels and the number of dimes.1. Therefore, the equation is

5x + 10(x+3) = 105.2.

Simplify the equation:5x + 10x + 30 = 10515x = 75x = 5O

wen has 5 nickels.3. Owen has x+3 dimes.

Since x = 5, then he has 5+3 = 8 dimes

.Owen has 5 nickels and 8 dimes.

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Answer:

The next three term in the arithmetic sequence is 32, 38, and 44

Step-by-step explanation:

The arithmetic sequence is add 6.

while the presence of only one spot on a TLC plate may suggest that the compound is pure, further analysis is needed to confirm the purity of the compound, such as melting point determination, NMR spectroscopy, or HPLC (high-performance liquid chromatography).

Using UV and seeing only one spot on a TLC (thin-layer chromatography) plate is not a definitive indicator of the purity of a product.

While it is true that a pure compound will only show one spot on a TLC plate, there are several reasons why a compound may still show only one spot even if it is not pure. For example:

The impurity may have a similar Rf (retention factor) value to the compound of interest and therefore co-migrate with it on the TLC plate, making it difficult to distinguish between the two.

The impurity may be present in such a small amount that it is not visible on the TLC plate.

The compound of interest may have multiple conformers or isomers that have the same Rf value and appear as a single spot.

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Answer:

$ 30

$ 20

Step-by-step explanation:

Sea el costo fijo xy el costo por km sea y suponiendo que es el mismo para ambos taxis.

De la pregunta obtenemos las dos ecuaciones

\(x+8y=190\quad ...(i)\)

\(x+5y=130\quad ...(ii)\)

Aplicando \((i)-(ii)\)

\(8y-5y=190-130\\\Rightarrow 3y=60\\\Rightarrow y=\dfrac{60}{3}\\\Rightarrow y=20\)

Sustituyendo en \((ii)\)

\(x+5y=130\\\Rightarrow x+5\times 20=130\\\Rightarrow x=130-100\\\Rightarrow x=30\)

Entonces, el costo fijo es de $ 30 y el costo por km es de $ 20.

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f(z)/g(z) → f'(zo)/g'(zo) as z → zo  of derivative to show that f(z) lim.

Let us use definition (3), Sec. 19, to give a direct proof that dw = 2z when w = z².

We know that dw/dz = 2z by the definition of derivative; thus, we can write that dw = 2z dz.

We are given w = z², which means we can write dw/dz = 2z.

The definition of derivative is given as follows:

If f(z) is defined on some open interval containing z₀, then f(z) is differentiable at z₀ if the limit:

lim_(z->z₀)[f(z) - f(z₀)]/[z - z₀]exists.

The derivative of f(z) at z₀ is defined as f'(z₀) = lim_(z->z₀)[f(z) - f(z₀)]/[z - z₀].

Let f(z) = g(z) = 0 at z = zo and f'(zo) and g'(zo) exist, where g'(zo) ≠ 0.

Using definition (1), Sec. 19, of the derivative, we need to show that f(z) lim ?

z~20 g(z) f'(zo) g'(zo).

By definition, we have:

f'(zo) = lim_(z->zo)[f(z) - f(zo)]/[z - zo]and g'(zo) =

lim_(z->zo)[g(z) - g(zo)]/[z - zo].

Since f(zo) = g(zo) = 0, we can write:

f'(zo) = lim_(z->zo)[f(z)]/[z - zo]and g'(zo) = lim_(z->zo)[g(z)]/[z - zo].

Therefore,f(z) = f'(zo)(z - zo) + ε(z)(z - zo) and g(z) = g'(zo)(z - zo) + δ(z)(z - zo),

where lim_(z->zo)ε(z) = 0 and lim_(z->zo)δ(z) = 0.

Thus,f(z)/g(z) = [f'(zo)(z - zo) + ε(z)(z - zo)]/[g'(zo)(z - zo) + δ(z)(z - zo)].

Multiplying and dividing by (z - zo), we get:

f(z)/g(z) = [f'(zo) + ε(z)]/[g'(zo) + δ(z)].

Taking the limit as z → zo on both sides, we get the desired result

:f(z)/g(z) → f'(zo)/g'(zo) as z → zo.

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Answer:

There are 4 possible scenarios where given relation could not be a function:

i)  \((-1, 4), (0,4), (2,5), (3,-6), (-1, 7)\)

ii) \((-1, 4), (0,4), (2,5), (3,-6), (0, 7)\)

iii) \((-1, 4), (0,4), (2,5), (3,-6), (2, 7)\)

iv) \((-1, 4), (0,4), (2,5), (3,-6), (3, 7)\)

Step-by-step explanation:

From Function Theory, we remember that a relation is not a function when at least one element from domain (x-coordinate) is related to one or more elements from range (y-coordinate). Hence, there are four possibilities of making the relation not a function:

i)  \((-1, 4), (0,4), (2,5), (3,-6), (-1, 7)\)

ii) \((-1, 4), (0,4), (2,5), (3,-6), (0, 7)\)

iii) \((-1, 4), (0,4), (2,5), (3,-6), (2, 7)\)

iv) \((-1, 4), (0,4), (2,5), (3,-6), (3, 7)\)

We know that it took 18 hours to drive 666 miles. If we divide the distance by the hours (666 miles)/(18 hours)

We find that 666/18= 37 miles per hour . which means we travel 37 miles each hour.

So, we can estimate that driving 37 miles it will take 1 hour (the distance to Chicago).

Answer:

666/18=37miles/hour

it would take 1 hour to drive 37 miles

When we roll three fair coins, there are two possible outcomes for each coin - either it lands heads up or tails up. There are 8 elementary events in the sample space of the experiment of rolling three fair coins.

The sample space of this experiment consists of all possible combinations of three outcomes, which can be calculated by multiplying the number of outcomes for each coin: 2 x 2 x 2 = 8.
Each of these combinations is called an elementary event, which means that there are 8 elementary events in the sample space of the experiment of rolling three fair coins. We can list them as follows:
1. HHH (all three coins land heads up)
2. HHT (two coins land heads up, one lands tails up)
3. HTH (two coins land heads up, one lands tails up)
4. THH (two coins land heads up, one lands tails up)
5. HTT (one coin lands heads up, two land tails up)
6. THT (one coin lands heads up, two land tails up)
7. TTH (one coin lands heads up, two land tails up)
8. TTT (all three coins land tails up)

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