QUESTION IS ON A PICTURE ​

The simplified form of the expression is ∛5/3x

Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given is an expression, \(\sqrt[3]{\frac{10x^{5} }{54x^{8} } }\)

Simplifying, we get,

\(\sqrt[3]{\frac{10x^{5} }{54x^{8} } }\\= \sqrt[3]{\frac{10x^{3+2} }{2*27x^{3+3+2} } }\\= \frac{x}{3x^{2} } \sqrt[3]{\frac{10x^{2} }{2x^{2} } }\\= \frac{\sqrt[3]{5} }{3x}\)

Hence, the expression is ∛5/3x

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The given statement "Both triangles are isosceles triangles in which one angle measures 15" is false because there can be multiple isosceles triangles where one angle measures 15 degrees.

An isosceles triangle has two equal sides and two equal angles. If one of the angles measures 15 degrees, the other two angles must add up to 165 degrees (180 - 15 = 165). However, there can be multiple isosceles triangles that satisfy this condition, such as a triangle with angles measuring 15, 75, and 90 degrees or a triangle with angles measuring 15, 75, and 90 degrees.

Therefore, it is incorrect to assume that both triangles are the same just because they are both isosceles triangles with one angle measuring 15 degrees.

The statement is false because there can be multiple isosceles triangles with one angle measuring 15 degrees. An isosceles triangle has two equal sides and two equal angles, so if one angle measures 15 degrees, the other two angles must add up to 165 degrees.

However, there can be multiple combinations of angles that satisfy this condition, so it is incorrect to assume that both triangles are the same just because they are both isosceles triangles with one angle measuring 15 degrees.

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Answer:

The minus sign between the two fractions was not distributed correctly.

Step-by-step explanation:

The error made in this solution of rational fractions' subtraction is that the minus sign between the two terms will change the signs of numerator of second fraction so the numerator in the answer will be 3.

The correct solution is:

\(\frac{1}{x-2} - \frac{1}{x+1}\\=\frac{x+1}{(x-2)(x+1)} - \frac{x-2}{(x-2)(x+1)}\\=\frac{x+1-(x-2)}{(x+1)(x-2)}\\=\frac{x+1-x+2}{(x+1)(x-2)}\\=\frac{3}{(x+1)(x-2)}\)

Hence,

The error was in the last step of subtraction.

Answer:

You must subtract all terms of the numerator being subtracted out, not just the first term.

The negative 2 should have been subtracted out to get a numerator of x+1 - x+2

The simplified numerator of the difference should be 3, not –1.

Step-by-step explanation:

got it right on edge 2020

The value of y when x is 9 and the constant of proportionality(k) is 4 is 36.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, x and y vary directly and y is 44 when x is 11.

Let, y ∝ x.

y = kx.

44 = 11k.

k = 44/11.

k = 4.

Now x = 9.

y = 4×9.

y = 36.

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Answer:

positive assosiation

Step-by-step explanation:

here is a screenshot of them plotted on a graph on

the velocity field is given by: \(u = Ax - 3Bxy^2, v = By^3\)

the pressure gradient is given by: ∇P = \((\rho By^3, -\rho Ax + 3\rho Bx*y^2)\)

What is velocity?

Velocity is a vector quantity that describes the rate at which an object changes its position with respect to time.

To find the velocity field and the pressure gradient from the given stream function, we can make use of the relationships between stream function, velocity components, and pressure gradient in two-dimensional flow.

The stream function (ψ) is related to the velocity components (u, v) as follows:

u = ∂ψ/∂y

v = -∂ψ/∂x

And the pressure gradient (∇P) is related to the stream function as follows:

∇P = -ρ (∂ψ/∂x, ∂ψ/∂y)

where ρ is the fluid density.

Given the stream function as \(y = Ax* - Bxy^3\), we can calculate the velocity components and the pressure gradient.

Velocity components (u, v):

Differentiating the stream function with respect to y:

∂ψ/∂y = \(Ax - 3Bx*y^2\)

Differentiating the stream function with respect to x:

∂ψ/∂x = \(0 - B*y^3\)

Now we can substitute these derivatives into the expressions for the velocity components:

u = ∂ψ/∂y = \(Ax - 3Bxy^2\)

v = -∂ψ/∂x = \(By^3\)

So, the velocity field is given by:

u = \(Ax - 3Bxy^2\)

v = \(By^3\)

Pressure gradient (∇P):

Using the relationship between pressure gradient and the stream function, we have:

∇P = -ρ (∂ψ/∂x, ∂ψ/∂y)

Substituting the derivatives of the stream function:

∇P = \(-\rho (-By^3, Ax - 3Bxy^2)\)

Simplifying, we get:

∇P = \(\rho(By^3, -Ax + 3Bxy^2)\)

So, the pressure gradient is given by:

∇P = \((\rho By^3, -\rho Ax + 3\rho Bx*y^2)\)

where ρ is the fluid density.

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The statement given " With large sample sizes, even small differences between the null value and the true value of the parameter, a difference often called the effect size, will be identified as statistically significant." is true because with a large sample size, the standard error of the mean decreases, making it easier to detect even small differences between the null value and the true value of the parameter.

With a large sample size, the standard error of the mean decreases. This means that the sample mean becomes a more accurate estimate of the true population mean. As a result, it becomes easier to detect even small differences between the null value and the true value of the parameter, which is often referred to as the effect size. The statistical significance of an effect is based on the probability that the observed effect could have occurred by chance alone, and with a large sample size, the likelihood of obtaining a statistically significant result increases.

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Answer: D.

Step-by-step explanation:

You can start out with the form AX = B and solve for matrix X that would yield the answer

Then X = (A^-1)(B)

A = [1    -1]

      [1     1]

A^-1 = (1/(1 - (1)(-1)))*[1    1]

                             [-1   1]

which can be written as (1/2) * [1    1]

                                                  [-1   1]

B = [26]

     [6]

(A^-1)(B) = (1/2)*[1    1] [6]

                        [-1   1] [26]

= (1/2)*[32]

          [20]

= [16]

  [10]

The probability P(GH) is 0%.

Since we know that,

Probability denotes the likelihood of something happening. It is a mathematical discipline that deals with the occurrence of a random event. The value ranges from zero to one.

Probability has been introduced in mathematics to predict the likelihood of occurrences occurring. Probability is defined as the degree to which something is likely to occur.

This is the fundamental probability theory, which is also utilized in probability distribution, in which you will learn about the possible results of a random experiment.

To determine the likelihood of a particular event occurring, we must first determine the total number of alternative possibilities.

Now to find the probability of GH,

We can see that there is no any poit G and H are showing in the given number line,

Therefore,

Favorable outcomes = 0

Since we know that,

Probability = number of favorable outcomes/total number of outcomes

Thus,

⇒ P(GH) = 0/total number of outcomes

Hence,

⇒ P(GH) = 0%

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Answer:

Option C

Step-by-step explanation:

2 pentagons and 5 rectangles are needed to build this pentagonal prism!

The two-dimensional shapes needed to build the pentagonal prism are 2 pentagons and 5 rectangles.

It has 2 congruent cross-sections that are pentagons, the other 5 faces are rectangles.

Value of function f(x, y, z) = xz + yz + xy, g(t) = (et, cos(t), sin(t)) is e^t sint + e^t cost + cos²t - sin²t + e^t cost - e^t sint.

The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain. Let's investigate the universe of mathematical functions.

Given

Composition function

f(x, y, z) = xz + yz + xy, g(t) = (et, cos(t), sin(t))

= f/x i + f/y j + f/x k

= ( z + y)i +(z +x)j + (x + y)k

g(t) = e^t , cos(t) , sin(t) )

g(t) = e^t + cos(t) i + sin(t) k

g'(t) = d g'(t)/dt

g'(t) = e^t i + (- sint) j + cos(t) k

f(e^t, cost , sint)

e^t sint + cos t × sin t + e^t cos t

(f 0 g ) (t)

d(f 0 g ) (t)

d/ dt (e^t sin t + cost sint + e^t cost

e^t sint + e^t cost + cos²t - sin²t + e^t cost - e^t sint

Value of function f(x, y, z) = xz + yz + xy, g(t) = (et, cos(t), sin(t)) is e^t sint + e^t cost + cos²t - sin²t + e^t cost - e^t sint.

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P( X≥23.5) = 0.5 + A(0.277)

P( X≥23.5) = 0.5 + A(1.388)

Given that the mean of the Population = 26 weeks

The Standard deviation of the Population = 9 weeks

Let 'X' be a Normal distribution

Z = \(\frac{x-mean}{standard deviation}\)

Z = \(\frac{23.5-26}{9}\)

Z = -2.5/9

Z = -0.277

The probability that a single randomly selected value is greater than 23.5

P( X≥23.5) = P(Z≥-0.277)

P( X≥23.5) = 0.5 + A(-0.277)

P( X≥23.5) = 0.5 + A(0.277)              

Let 'X' be a Normal distribution

Z = \(\frac{x-mean}{\frac{standard deviation}{\sqrt{n} } }\)

Z = \(\frac{23.5-26}{\frac{9}{\sqrt{25} } }\)

Z = -2.5/9/5

Z = -2.5/1.8

Z = -1.388

The probability that a  sample of size randomly selected value is greater mean greater than 23.5

P( X≥23.5) = P(Z≥-1.388)

P( X≥23.5) = 0.5 + A(-1.388)

P( X≥23.5) = 0.5 + A(1.388)

Therefore,

P( X≥23.5) = 0.5 + A(0.277)

P( X≥23.5) = 0.5 + A(1.388)

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Answer:

0.6275

Explanation:

We were given the following informationL

Flounder = 278

Red Drum = 382

Black Drum = 194

Bluefish = 348

Sea Trout = 159

Total = 278 + 382 +194 + 348 + 159 = 1,361

The probability that the next fish caught is a drum or a flounder is given by:

Therefore, the probability of the next fish being a Drum or Flounder is: 0.6275

Answer:

a - 1/50 is the ans

1/5 divided by 10 = 0.02

1/50 is also 0.02

Answer:

33

Step-by-step explanation:

f(4) = 4(4) - 3 = 16 - 3  =  13

g(-5) = -2(-5) + 10  =  10 + 10  =  20

13 + 20 = 33

At the end of the year, Achley Company's owner's equity is $4,685,000 and can be calculated by starting with the beginning owner's equity, adding the revenues, subtracting the expenses, and subtracting the owner's withdrawals.

To calculate Achley Company's owner's equity at the end of the year, we start with the beginning owner's equity of $5,175,000. We then add the revenues of $225,000 and subtract the expenses of $165,000. This gives us the net income, which is the difference between revenues and expenses, and represents the increase in owner's equity.

So, net income = revenues - expenses = $225,000 - $165,000 = $60,000. Next, we subtract the owner's withdrawals of $550,000 from the net income. Owner's withdrawals are personal expenses or cash withdrawals made by the owner and reduce the owner's equity.

Owner's equity at the end of the year = Beginning owner's equity + Net income - Owner's withdrawals.Owner's equity at the end of the year = $5,175,000 + $60,000 - $550,000. Calculating the above expression, we find that Achley Company's owner's equity at the end of the year is $4,685,000.

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The direction of the induced emf in this scenario would be from terminal b to terminal a.

The direction of the induced electromotive force (emf) in a coil depends on the change in magnetic flux through the coil. According to Faraday's law of electromagnetic induction, when there is a change in magnetic flux through a coil, an emf is induced that opposes the change causing it. This is known as Lenz's Law.

In your scenario, if the current is directed from terminal a to terminal b of the coil, it implies that there is a current flowing in the coil in that direction. This current creates a magnetic field around the coil.

When the magnetic field changes, such as when the current in the coil changes or when the external magnetic field passing through the coil changes, the magnetic flux through the coil also changes. As a result, an induced emf is generated in the coil.

According to Lenz's Law, the induced emf will be in a direction that opposes the change in magnetic flux. In this case, since the current is flowing from terminal a to terminal b, the induced emf will be in the opposite direction, i.e., from terminal b to terminal a. The induced emf will try to create a magnetic field that opposes the change in the original magnetic field or the change in the current flow in the coil.

Therefore, the direction of the induced emf in this scenario would be from terminal b to terminal a.

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The quotient of 405/27 fraction using division is 15.

It should be noted that the information is simply to divide the numbers.

In this case, the numerator is 405 and the denominator is 27

Therefore, the quotient based on the information illustrated will be:

= 405 / 27

= 15

Therefore, the quotient is 15.

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Answer:

Red Car Gas mileage:

= Distance travelled/ Gas used

= 300/12

= 25 mpg

Blue Car gas mileage:

= 330/15

= 22 mpg

The car with the better mileage is the one that goes further per gallon of gas which is the Red Car.

Answer:

-4/5

Step-by-step explanation:

1. C is the center

2. EF is a secant line

3. AD is the diameter

4. CD is the radius

5. FD is the arc

6. The region bounded by AC, BC and arc AB is a segment

7. The region bounded by FE and arc FE is a sector

8. EF is the chord

9. GF is the tangent line

To match the statements, we need to know the following;

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Answer: 52.73

Explain: 56.40 - 3.67 = 52.73

Answer:

$134217728

Step-by-step explanation:

Day 1: $1

Day 2: $2

Day 3: $4

Day 4: $8

Day 5: $16

Day 6: $32

Day 7: $64

Day 8: $128

Day 9: $256

Day 10: $512

Day 11: $1024

Day 12: $2048

Day 13: $4096

Day 14: $8192

Day 15: $16384

Day 16: $32768

Day 17: $65536

Day 18: $131072

Day 19: $262144

Day 20: $524288

Day 21: $1048576

Day 22: $2097152

Day 23: $4194304

Day 24: $8388608

Day 25: $16777216

Day 26: $33554432

Day 27: $67108864

Day 28: $134217728

Parker should build the playhouse with a height of 1.59 meters, which is equivalent to 159 centimeters.

Parker is planning to build a playhouse for his sister. The scaled model below gives the reduced measures for width and height. The width of the playhouse is 22 centimeters and the height is 10 centimeters. Not drawn to scale The yard space is large enough to have a playhouse that has a width of 3.5 meters.

If Parker wants to keep the playhouse in proportion to the model, he should use the following cross multiplication of the proportion to find the height: `3.5/22 = 3.5x/h`.

First, the given proportions should be simplified. We will cross-multiply the given proportions:`22h = 3.5 × 10``22h = 35

`Divide both sides by 22 to solve for h:`h = 35/22

`The final answer is `h = 1.59 meters`. Parker should build the playhouse with a height of 1.59 meters, which is equivalent to 159 centimeters.

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Answer:

f(2) = 0 and g(-2) = 0

Step-by-step explanation:

0.8 is the slope of the line M'N'.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

So, the coordinates of M' are (0.82, 0.84) = (1.6, 3.2), and the coordinates of N' are (0.83, 0.85) = (2.4, 4).

Now, we can find the slope of line M'N' using the slope formula:

slope of M'N' = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) = (1.6, 3.2) and (x2, y2) = (2.4, 4).

slope of M'N' = (4 - 3.2) / (2.4 - 1.6)

the slope of M'N' = 0.8

Therefore, the slope of line M'N' is 0.8.

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Answer:

72 words per minute

Step-by-step explanation:

\(\frac{1}{y}= \frac{42}{3024}\)

42 × y = 1 × 3024

42y = 3024

42y ÷ 42 = 3024 ÷ 42

y = 72

To determine Bob's expected utility for each option, we calculate the utility for each outcome and weigh them by their respective probabilities.

Option A:

Expected utility = 0.5v(316 - 30) + 0.5v(4 - 0)

= 0.5v(48) + 0.5v(4) = 0.548 + 0.54 = 26.

Option B: Expected utility = v(8) = 8.  

Bob would choose Option A as it has a higher expected utility.

ii. Option A: Expected utility = 0.5v(-16) + 0.5v(-4) = 0.5*(-32) + 0.5*(-8)

= -20.

Option B: Expected utility = v(-12) = -24. Bob would choose Option B as it has a higher expected utility.

iii. Option A: Expected utility = 0.5v(8) + 0.5v(-4) = 0.58 + 0.5(-8) = 0. Option B: Expected utility = v(1) = 1.  Bob would choose Option B as it has a higher expected utility.

 (b) If Bob buys the hammer for $2, his utility would be v(-2) = -4. If he does not buy the hammer, his utility would be v(0) = 0. Bob would prefer not to buy the hammer since the utility is higher at 0.

(c) If Bob sells the hammer for $2, his utility would be v(2) = 2. If he does not sell the hammer, his utility would be v(0) = 0. Bob would prefer to sell the hammer since the utility is higher at 2. (d) Bob's buying price is not the same as his selling price.

This concept is known as loss aversion, where individuals tend to value losses more than equivalent gains. One study that demonstrates a similar concept is the "Prospect Theory" by Daniel Kahneman and Amos Tversky, which shows how people's decision-making is influenced by the potential for gains and losses and how they weigh them differently.

The study revealed that individuals are generally more averse to losses and are willing to take greater risks to avoid losses compared to the risks they are willing to take for potential gains of equal value.

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Answer:

The perimeter of Elie's vegetable garden is 34 meters.

Step-by-step explanation:

The formula for area is: a=w*l.

A = area

W = width

L = length

If the length is 9 meters, then we know two of the values, the area, and the length. Substitute.

72=w*9

You can divide both sides by 9 to get the width, which is 8 meters.

To find perimeter, we add l+w+l+w, or 2l+2w. Substitute for our values:

2(9)+2(8)=34

The perimeter of Elie's vegetable garden is 34 meters.