the length of the path described by the parametric equations x=cos3t and y=sin3t , for 0≤t≤π2 is given by

The correct expression is 1 Over 5 x Superscript minus 8 Baseline y Superscript minus 13 Baseline endFraction.

Given expression [tex](3x)^-6*y^-3/ 15x^2*y^10[/tex]

Lets simplify the equation:

[tex]= > (3x)^-6*y^-3/ 15x^2*y^10\\=1/5 x^-8*y^-13[/tex]

Expression:

An expression is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/Variable, Math Operator, Number/Variable)

Hence the correct expression is 1 Over 5 x Superscript minus 8 Baseline y Superscript minus 13 Baseline EndFraction.

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See below for the solution to each expression

Expression 1

The expression is given as:

(x-y)(y-z)(x+z)/(2x^2+4yz+6)

Expand the numerator

(x^2 - y^2 -xz + yz)(x + z)/(2x^2+4yz+6)

Further, expand the numerator

(x^3 - xy^2 - x^2z + xyz + x^2z - y^2z - xz^2 + yz^2)/(2x^2+4yz+6)

Evaluate the like terms

(x^3 - xy^2  + xyz - y^2z - xz^2 + yz^2)/(2x^2+4yz+6)

Hence, the equivalent expression of (x-y)(y-z)(x+z)/(2x^2+4yz+6) is (x^3 - xy^2  + xyz - y^2z - xz^2 + yz^2)/(2x^2+4yz+6)

Expression 2

The expression is given as:

4(x+y)(x-y)(y-x)

Apply the difference of two squares

4(x^2 - y^2)(y - x)

Expand the expressions in the brackets

4(x^2y - x^3 - y^3 + xy^2)

Open the bracket

4x^2y - 4x^3 - 4y^3 + 4xy^2

Hence, the equivalent expression of 4(x+y)(x-y)(y-x) is 4x^2y - 4x^3 - 4y^3 + 4xy^2

Expression 3

The expression is given as:

(√25+√9/2) + √21675

Take the square roots of 25, 9 and 21675

(5 +3/2) + 5√867

Evaluate the sum

13/2 + 5√867

Hence, the equivalent expression of (√25+√9/2) + √21675 is 13/2 + 5√867

Expression 4

The expression is given as:

(9x^2+3x+27)(3+6y)(4+6y) /1+2a+38+4c+2000z

Factor out 3 and 2 from the numerator

3(3x^2 +x + 9) * 3(1 + 2y) * 2(2 + 3y)/1+2a+38+4c+2000z

This gives

18(3x^2 +x + 9)(1 + 2y)(2 + 3y)/1+2a+38+4c+2000z

The expression cannot be further simplified.

Hence, the equivalent expression of (9x^2+3x+27)(3+6y)(4+6y) /1+2a+38+4c+2000z is 18(3x^2 +x + 9)(1 + 2y)(2 + 3y)/1+2a+38+4c+2000z

Expression 5

The expression is given as:

(x^2+6x+5)/(x+2)(x+6)

Factorize the numerator

(x + 1)(x + 5)/(x + 2)(x + 6)

Hence, the equivalent expression of (x^2+6x+5)/(x+2)(x+6) is (x + 1)(x + 5)/(x + 2)(x + 6)

Expression 6

6) (xy/m) + (xm/y) - (m/x) = 63

Factor out x

x(y/m + m/y) - m/x = 63

Evaluate the sum

x(y^2 + m^2)/y - m/x = 63

Multiply through by xy

x^2(y^2 + m^2) - my = 63xy

Add my to both sides

x^2(y^2 + m^2)  = 63xy + my

The above implies that the variable x cannot be isolated from the equation

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Answer:927652832

Step-by-step explanation:

using long multiplication step by step multiply.

Answer:

Step-by-step explanation:

x times 8 +12

8x+x=9x-12

Answer = 9x-12

the probability that the sample mean will be smaller than m = 22 is 0.02275.

For the given question,

A z-score measures exactly how many standard deviations a data point is above or below the mean. It allows us to calculate the probability of a score occurring within our normal distribution and enables us to compare two scores that are from different normal distributions.

Here sample size, n = 4

mean, μ = 30

standard deviation, σ = 8

The probability that the sample mean will be smaller than m = 22 is

z = [tex]\frac{m-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]

⇒ z =[tex]\frac{22-30}{\frac{8}{\sqrt{4} } }[/tex]

⇒ z = [tex]\frac{22-30}{\frac{8}{2} }[/tex]

⇒ z = [tex]-\frac{8}{4}[/tex]

⇒ z = -2

Refer the Z table for p value,

Thus for P(z < -2) is 0.02275.

Hence we can conclude that the probability that the sample mean will be smaller than m = 22 is 0.02275.

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Answer:

Yes

Step-by-step explanation:

As the Average speed increases, the amount of distance covered will increase. As the average speed decreases, the amount of distance traveled will decrease as well over a certain period.

Answer:

There is only one way to assign the athletes to the team by giving 5 athletes to each team

If the radius of sector is 12 centimeters and angle of 65 degrees then the arc's length is 13.6 cm.

Given a sector has a radius of 12 cm and an angle 65 degrees.

We have to calculate arc's length.

We know that arc's length is equal to Θr where Θ is in radians.

We have been given angle in degrees ,so we have to convert degrees in radians.

Angle=65*π/180=13π/36

length of arc =Θr

Putting the values in the formula above :

length =13π/36*12

=13*3.14/3

=40.82/3

=13.6

Hence if the radius of sphere is 12 cm and angle 65 degrees then the length of arc of sphere is 13.6 cm.

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Answer: (8,10)

Step-by-step explanation:

To go from A to C, we go right 2 units and up 6 units.

So, if we let the fourth vertex be D, then to go from B to D, we must also go right 2 units and up 6 units from B.

Therefore, the answer is (8, 10).

Answer:

[tex]16x^2-26x+20[/tex]

Step-by-step explanation:

Since it represents the sum of interior angles, the angle is essentially: [tex]angle + angle + angle + angle + angle[/tex], and there are 5 angles since a pentagon has 5 interior angles. To find what one interior angle is, we simply divide the polynomial by 5, to do this we can just divide each coefficient by 5 (distributing the division): [tex]\frac{40x^2-65x+50}{5} = \frac{40x^2}{5} - \frac{65x}{5} + \frac{50}{5}[/tex] this simplifies to: [tex]8x^2-13x+10[/tex]. This represents what one of the interior angles is. Since we want an expression measuring two of the angles, we simply multiply this polynomial by 2, to do this we just multiply each coefficient by 2 (distributing the 2): [tex]2(8x^2-13x+10) = 16x^2-26x+20[/tex] which is the solution

Jake travel to the coffee shop by bike with speed of [tex]8mph[/tex] is  [tex]56mile[/tex] and when bike got a flat so Jake walked [tex]4mile[/tex]

How to find the speed by biking and walking ?

let [tex]b[/tex] = time spent biking

then   [tex]8-b[/tex] =time spent walking

Write distance equation

[tex]dist=speed *time[/tex]

So bike distance [tex]+[/tex] walk distance [tex]=60mile[/tex]

[tex]8b+4(8-b)=60\\8b+32-4b=60\\4b=60-32\\b=28/4\\\\b=7hrs[/tex]

Then [tex]8-7=1 hrs[/tex] spent walking.

For cross check the answer find that actual distance for each

[tex]8(7)=56mi\\4(1)=4mi\\-------\\total distance=60mile[/tex]

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Answer:

? = 120°

Step-by-step explanation:

the central angle is the same as the arc that subtends it , that is

? = 120°

The  C is perpendicular to AB

When using paper, the paper perpendicular te construct to is folded so that AB is divided equally and the two sides of. line AB will lie exactly on top of each other.

When using a reflective device to construct a live perpendicular to line AB, set One end of the device to coincide with point C, and then swing the other end of the device so that the reflection of line AB coincides with the midpoint of AB

The question is incomplete hence the complete question is shown here

Select the correct answer from the drop-down menu. Compare the steps for constructing a perpendicular line to line  through point  using a reflective device and using paper. , When using paper to construct the perpendicular line, the paper is folded so that and the two sides of line  will lie exactly on top of each other. When using a reflective dewice to construct a line perpendicular to line  , set one end of the device to coincide with , and then swing the other end of the device so the reflection of line  coincides with.

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Answer:

I toke the test, I think the first one is A and  B coincide

Step-by-step explanation:

D. not continuous at X=0

if you trace the function you'll find a jump in the graph. To be continuous the line can't have any breaks in it. In this example, it's discontinuous when X=0

Answer:

Please see the picture below.

Step-by-step explanation:

Answer:

  x^4 +2 +x^-4

Step-by-step explanation:

The square of a binomial is a form worthy of memorization.

  (a +b)² = a² +2ab +b²

Here, you have a binomial with a=x² and b=1/x². Using these values in the pattern, we have ...

  [tex]\left(x^2+\dfrac{1}{x^2}\right)^2=(x^2)^2+2(x^2)\dfrac{1}{x^2}+\left(\dfrac{1}{x^2}\right)^2\\\\=\boxed{x^4+2+\dfrac{1}{x^4}}[/tex]

$662.18 needs to be saved per month.

$90,000 now at 3% inflation will become 90000*1.03^30 after 30 years.

i.e.  $218,454 is required in retirement years (for 20 years)

Calculating the PV of these payments at 7% is calculated as below.

FV = 0

1/y = 7%

n=20; PMT = 218454; calculate PV = $2,314,305

Now we want to get $2,314,305 at the start of retirement by saving per year. Enter the following in the financial calculator to get the per month amount.

FV = 2314305; PV = 0; n= 12*30; 1/y = 12%/12; calculate PMT  = $662.18

So $662.18 needs to be saved per month.

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#1

#b

#c

#f

#i

Answer:

a) 3₁₀

b) 6₁₀

c) 7₁₀

f) 19₁₀

i) 181₁₀

Step-by-step explanation:

Binary to Decimal Conversion (Positional Notation Method)

For a binary number with 'n' digits:

For example, to convert the binary number 111001₂ into a decimal:

[tex]\begin{array}{ c c c c c c}1 & 1 & 1 & 0 & 0 & 1\\\downarrow & \downarrow & \downarrow & \downarrow & \downarrow & \downarrow \\2^5 & 2^4 & 2^3 & 2^2 & 2^1 & 2^0\\\end{array}[/tex]

Multiply each digit by the base (2) raised to the power as indicated above and sum them:

[tex]=(1 \times 2^5)+(1 \times 2^4)+(1 \times 2^3)+(0 \times 2^2)+(0 \times 2^1)+(1 \times 2^0)[/tex]

[tex]= 32+16+8+0+0+1[/tex]

[tex]= 57[/tex]

Finally, express as a decimal number ⇒ 111001₂ = 57₁₀

Question (a)

[tex]\begin{aligned}\implies 11_2 & = (1 \times 2^1)+(1 \times 2^0)\\& = 2+1\\& = 3\end{aligned}[/tex]

Therefore, 11₂ = 3₁₀

Question (b)

[tex]\begin{aligned}\implies 110_2 & = (1 \times 2^2)+(1 \times 2^1)+(0 \times 2^0)\\& = 4+2+0\\& = 6\end{aligned}[/tex]

Therefore, 110₂ = 6₁₀

Question (c)

[tex]\begin{aligned}\implies 111_2 & = (1 \times 2^2) +(1 \times 2^1)+(1 \times 2^0)\\& =4+2+1\\& = 7\end{aligned}[/tex]

Therefore, 111₂ = 7₁₀

Question (f)

[tex]\begin{aligned}\implies 10011_2 & =(1 \times 2^4)+(0 \times 2^3)+ (0 \times 2^2) +(1 \times 2^1)+(1 \times 2^0)\\& =16+0+0+2+1\\& = 19\end{aligned}[/tex]

Therefore, 10011₂ = 19₁₀

Question (i)

[tex]\phantom{)))}10110101_2 \\\\=(1 \times 2^7)+(0 \times 2^6)+(1 \times 2^5)+(1 \times 2^4)+(0 \times 2^3)+ (1 \times 2^2) +(0 \times 2^1)+(1 \times 2^0)\\\\=128+0+32+16+0+4+0+1\\\\= 181[/tex]

Therefore, 10110101₂ = 181₁₀

Answer:

7. a) slope = 5

7. b) slope = 1/2

8. slope = 1

Step-by-step explanation:

slope = rise/run

rise is the vertical change, run is the horizontal change

7. a)

Pick any two points on your line. (0,0) and (1,5) are easy to work with.

The vertical change between the two points is 5

The horizontal change between those points is 1

so slope = 5/1 = 5

7. b)

Again, you can use (0,0) as one of your points. The point (2,4) is good as the second.

slope = 4/2 = 1/2

8. We don't have a graph, but we are given two points to work with, (1,4) and (5,8). Use the formula given...

m = slope = (y2-y1) / (x2-x1)

= (8 - 4) / (5 - 1)

= 4/4

= 1

I hope that helped!

Answer:

None of the answers

Step-by-step explanation:

There are 60 minutes in one hour so to find the number of minutes in two hrs we multiply 2 by 60: 2*60 = 120 minutes

We then add the extra 20 minutes: 120+20 = 140 minutes

None of the answers include 140 minutes.

the polar coordinates are:

(√130, 285.3°)

For rectangular coordinates (x, y), the polar coordinates are:

[tex]R = \sqrt{x^2 + y^2}[/tex]

For the angle θ we need to notice that if both coordinates are negative, like in this case, we would be on the fourth quadrant, then:

θ = arctan(y/x) + 270°

In this case, we have:

x = -11

y = -3

Then:

[tex]R = \sqrt{(-11)^2 + (-3)^2} = \sqrt{130} \\\\\theta = arctan(-3/-11) + 270\° = 285.3\°[/tex]

Then the polar coordinates are:

(√130, 285.3°)

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Answer:

The class and exam medians are almost the same.

Step-by-step explanation:

The median of a box-and-whisker plot is the line inside the box.

• As we can see, the medians of  class and median are very similar, both around 85. This is why the first option is correct.

•The second option is incorrect because the exam median is not much higher than the class median; the difference is very small.

• The third option is incorrect because exam does not have the lowest median. In fact, exam median is slightly higher than class median.

• The fourth option is incorrect because outliers do not affect the median.

Answer:

statement 1(one)

Step-by-step explanation:

Answer:

H. 15 ft by 15 ft

Step-by-step explanation:

area of square = side²

225 ft² = side²

side = √(225 ft²)

side = 15 ft

Answer: H. 15 ft by 15 ft

Using division, the 8 cupcakes are there in 28 ounce package if one cupcake weighs 3 1/2.

According to the question,

One cupcake weighs 3 1/2 ounces. In order to find the number of cupcakes are there in 28 ounce package.

1 cupcake = 7/2 ounces

x cupcakes = 28 ounces

28 = 7/2 * x [cross multiplication]

x = (28*2)/7     [Using division]

x = 8

Hence, using division, the 8 cupcakes are there in 28 ounce package if one cupcake weighs 3 1/2.

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Answer:

The answer is B) b

Step-by-step explanation:

According to the Trapezoid area formula, the area of the trapezoid is [(2d+a+b) × c] ÷ 2, however the area also equals (d+b) × c.

So d+(a+b)/2=d+b

(a+b)/2=b

a+b=2b

a=b

hope this helps <3

Answer:

Step-by-step explanation:

For the frequency distribution, count the numbers that satisfy each category.

79 to 83: 4 (81, 82, 83, 81)

84 to 88: 3 (87, 88, 86)

89 to 93: 7 (92, 93, 93, 93, 90, 90, 91)

94 to 98: 1 (97)

For the historagram, raise the bars at the bottom of the histogram to the numbers above (4, 3, 7, 1; in this order)

Answer:

398.2 cm^2

Step-by-step explanation:

[tex]\frac{270}{360}[/tex] * [tex]169\pi[/tex] ≈398.2 cm^2