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The simplest radical form of the expression is [tex]\mathbf{40 ^{2/3}x^{{10}/{3}}y^2}[/tex].

When we have indices in the form [tex]\mathbf{ax^{2/3}}[/tex], we are going to find the cube root of the (ax)². This can be mathematically expressed as:

[tex]\mathbf{=(\sqrt[3]{ax})^2 }[/tex]

From the given information:

[tex]\mathbf{=(8x^55y^3)^{2/3}}[/tex]

[tex]\mathbf{=(\sqrt[3]{8x^55y^3} } )^2[/tex]

[tex]\mathbf{=(\sqrt[3]{40x^5y^3} } )^2[/tex]

[tex]= (\sqrt[3]{40x^5} \times \sqrt[3]{y}^3)^2[/tex]

[tex]\mathbf{= 40 ^{2/3}x^{{5*2}/{3}}y^2}[/tex]

[tex]\mathbf{= 40 ^{2/3}x^{{10}/{3}}y^2}[/tex]

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Answer:

squares: 204

rectangle: 1,296

Step-by-step explanation:

Board Size: 8 x 8

The total number of squares is thus:

[tex]1^{2} + 2^{2} + ... + n^{2}[/tex]

sum = [tex]\frac{n(n + 1)(2n + 1)}{6}[/tex]

For a chess board, with n = 8,

sum = [tex]\frac{(8)((8) + 1)(2(8) + 1)}{6}[/tex]

sum = 204

the number of rectangles on a chess board,

to make a rectangle you need to pick any two of the vertical lines, and any two of the horizontal lines. There are 36 distinct pairs and the same number of vertical pairs, so the answer is 36 × 36 = 1,296.

Step-by-step explanation:

a complicated way to say "the probability to roll a number that is less or equal to 5".

and that is

5 desired cases over 6 total cases, and that means

5/6 = 0.833333333...

Answer:

B

Step-by-step explanation:

millimeter means one-thousandth of a meter meaning the number of millimeters will be larger by a factor of 1000.

Answer:

B

Step-by-step explanation:

Millimetres is A LOT smaller than meters, meaning the individual number of millimetres is larger than the individual number of meters.

Usando el teorema fundamental de conteo, se encuentra que 132 maneras diferentes de otorgar las medallas.

Es un teorema que establece que si hay n cosas, cada una con [tex]n_1, n_2, \cdots, n_n[/tex] formas de hacer, cada cosa independiente de la otra, el número de formas en que se pueden hacer es:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

En este problema:

Así, el número de maneras diferentes en que se pueden otorgar las medallas es dado por:

[tex]N = n_1 \times n_2 = 12 \times 11 = 132[/tex]

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An equivalent expression is given by  (2 / x ^ 3) * sqrt (2)

We have the following expression

8 / x ^ 6

Rewriting we have

sqrt (8 / x ^ 6)

The expression consists of numbers and arithmetic operators. It does not contain equality or inequality symbols.

sqrt (2 * 4 / ((x ^ 2) * (x ^ 2) * (x ^ 2)))

(2 / (x * x * x)) sqrt (2)

(2 / x ^ 3) * sqrt (2)

An equivalent expression is given by

(2 / x ^ 3) * sqrt (2)

Therefore an equivalent expression is given by  (2 / x ^ 3) * sqrt (2).

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The probability that a student is a female or major in civil engineering is 62%

Let A represent Female and B represents civil engineering.

So, we have:

P(A) = 49%

P(B) = 21%

P(A and B) = 8%

The required probability is calculated as:

P(A or B) = P(A) + P(B) - P(A and B)

This gives

P(A or B) = 49% + 21% - 8%

Evaluate

P(A or B) = 62%

Hence, the probability that a student is a female or major in civil engineering is 62%

At a certain college, 49% of the students are female, and 21% of the students major in civil engineering. Furthermore, 8% of the students both are female and major in civil engineering. What is the probability that a randomly selected female student majors in civil engineering?

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Answer:

1200

Step-by-step explanation:

I'm not 100% sure but that seems like the most reasonable answer

Answer:

288 grams

Step-by-step explanation:

Chelsea

12 × 3 = 36

48 × 4 = 192

Pierre

8 × 3 = 24

24 × 4 = 96

together

192 + 96 = 288 grams

Th amount of money that Diana is left with is $8,430.23.

The first step is to determine the interest earned in the first year and the total amount that was made in the 2 years.

The formula used to determine the future value with monthly compounding is:

P(1 + r)^( n x m)

Where:

Total amount made in 2 years = $8000 x ( 1 + 5% / 12)^(12 x 2) = 8839.53

Interest earned in the first year = [ $8000 x ( 1 + 5% / 12)^(12) ] - 8000 = $409.29

Amount she is left with =  8839.53 - $409.29 = $8430.23

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Answer:

  x/5

Step-by-step explanation:

The revenue from sales is the product of the selling price of the ticket and the number of tickets sold.

__

If n represents the number of tickets sold, then the revenue from selling tickets for £5 each will be ...

  (n)(£5) = £x

Dividing by the coefficient of n will given the number of tickets sold:

  n = £x/(£5) = x/5

The number of tickets sold is x/5.

Answer: [tex]a_{n}=64\left(\frac{1}{4} \right)^{n-1}[/tex]

Step-by-step explanation:

The common ratio is 16/64 = 1/4, so substituting into the formula, we get that [tex]a_{n}=64\left(\frac{1}{4} \right)^{n-1}[/tex]

Answer:

The airplane reaches its maximum height of 74 feet in 14 seconds.

Step-by-step explanation:

The easiest thing to do here is to plug in the two numbers given in the answer choices. Finding the height at 14 seconds and the height after 74 seconds is straightforward from here.

h (14) = -(14-14)²+ 74

h (14) = 0 + 74

h (14) = 74

h (74) = -(74-14)² + 74

h (74) = -(60)² + 74

h (74) = -3600 + 74

h (74) = -3,526

Now, we know that a height of an airplane won't be negative, as the height below the ground cannot be reached.

because our equation includes -(t-14)², any number greater than 14 will be a larger negative than 0--setting the height to an impossible number.

{However, we add +74 feet, so our t-14 could be any number that is less than 74 when squared (after first subtracting 14 from the number). Numbers like 15, (resulting in subtracting 1 from 74), 16 (resulting in -4 from 74), 17 (74-9), 18 (74-16), 19 (74-25), 20 (74-36), 21 (74-49), 22 (74-64) are still above the minimum input}

{So, our t could be up to 22, and any number above this maximum limit, such as 23, result in a height of 0}

for example: -(23-14)²  + 74

-(9)² = -81

-81 + 74 = -7

All numbers below 14, which would end in an eventual negative outcome  [ -(x)² = negative if x < 0 ]

are greater than a t of 14.

-(13-14)² = -1

; showing that t = 14 is our maximum height

(remember that if you have -(x)² you get the negative version of x² [pemdas. the negative outside of the parenthesis is equivalent to multiplying the parenthesis by -1. (E)xponents comes before (M)ultiplication].)

The answers to the given question are as follows:-

1.  Cos(∠mA)  =  [tex]\dfrac{3}{5}[/tex]

2. Sin(∠mA)   = [tex]\dfrac{\sqrt{20}}{\sqrt{35}}[/tex]

3. Tan(∠mB)  =  [tex]\dfrac{b}{a}[/tex]

Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.

The angles will be calculated by using trigonometric identities.

1. For the first triangle:-

Cos∠mA = [tex]\rm \dfrac{Base}{Hypotenuse}[/tex]

We can see in the first triangle base is 3 and the hypotenuse is 5.

Cos∠mA =  [tex]\dfrac{3}{5}[/tex]

2. For the second triangle:-

Sin∠mA = [tex]\rm \dfrac{Perpendicualr }{Hypotenuse}[/tex]

We can see in the first triangle Perpendicular is √20 and the hypotenuse is √35.

Sin∠mA =  [tex]\dfrac{\sqrt{20}}{\sqrt{35}}[/tex]

3. For the third triangle:-

Tan∠mB = [tex]\rm \dfrac{Perpendicualr }{Base}[/tex]

We can see in the first triangle Perpendicular is b and the Base is a.

Tan∠mA =  [tex]\dfrac{b}{a}[/tex]

Therefore  answers to the given question are as follows:-1. Cos(∠mA)  =  [tex]\dfrac{3}{5}[/tex]2. Sin(∠mA)   = [tex]\dfrac{\sqrt{20}}{\sqrt{35}}[/tex] and 3. Tan(∠mB)  =  [tex]\dfrac{b}{a}[/tex]

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Sum of two interiors=Exterior

[tex]\\ \rm\Rrightarrow 39+6x+11=11x-10[/tex]

[tex]\\ \rm\Rrightarrow 6x+50=11x-10[/tex]

[tex]\\ \rm\Rrightarrow 60=5x[/tex]

[tex]\\ \rm\Rrightarrow x=12[/tex]

Answer:

5 faces

Step-by-step explanation:

V – E + F = 2

We know that V = 5 and E = 8

Substitute these into the equation

5 -8+F = 2

-3+F =2

Add 3 to each side

-3+F+3 = 2+3

F=5

Kyles's monthly repayment on the television based on hire purchase agreement is R229

The monthly repayment is the amount paid monthly with interest on a particular loan or to recover from debt.

From the given information:

Thus

principal amount left to be repaid = 5600 - 840 = 4760

Using the formula:

[tex]\mathbf{M=\dfrac{P( \dfrac{r}{12}) (1+\dfrac{r}{12})^n }{(1+\dfrac{r}{12})^n - 1}}[/tex]

[tex]\mathbf{M=\dfrac{4760( \dfrac{0.14}{12}) (1+\dfrac{0.14}{12})^{24} }{(1+\dfrac{0.14}{12})^{24} - 1}}[/tex]

M = R228.54

M ≅ R229

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Answer:

A graph shows zeros to be ±3. Factoring those out leaves the quadratic

 (x-2)² +1

which has complex roots 2±i.

The function has roots -3, 3, 2-i, 2+i.

Step-by-step explanation:

Answer:

See below ~

Step-by-step explanation:

The function is :

f(x) = x⁴ - 4x² - 5

=============================================================

Plotting on a graph :

⇒ Once plotted on graph, check where the line of the function intersects the x-axis

⇒ Those will be the zeros of the function

===========================================================

Solution :

⇒ x = -2.236

⇒ x = 2.236

The region is C is the correct option because intersection region is on the region C after drawing on the coordinate plane.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

The question is incomplete:

The complete question is:

Which region represents the solution to the given system of inequalities?

y < -1/2x and y ≥ 2x+3 and the missing figure is shown in the picture please refer to the picture.

We have two inequalities:

y < -1/2x

y ≥ 2x+3

After drawing the inequalities on the coordinate plane we see that the intersection region is on the region C.

Thus, the region is C is the correct option because intersection region is on the region C after drawing on the coordinate plane.

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The total length of the ribbon is 52 m.

Aleena initially cuts 3/8 of the ribbon, i.e. a length of (3/8)x.

1 - (3/8)x = (5/8)x.

i.e. (4/5) * (5/8)x = (20/40)x = (1/2)x

(3/8)x + (1/2)x = (3/8)x + (4/8)x = (7/8)x

That means  1 - (7/8)x = (1/8)x remains, and that is a length of 6.5 m.

1/8 of what number is 6.5?

Let y = the unknown number.

(1/8)y = 6.5

Multiply both sides of the equation by 8 to clear the fraction.

y = 52 m

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Answer:

1 matter

2 atoms

3 molecules

4 matter and energy

5 solid liquid and gas
6 mass

i dont know the rest to be honest

Step-by-step explanation:

kung 5ft and a width of 9ft and the area of prism is 174 the answer is 5ft

Answer:

Both plans cost the same when 50 texts are sent

Step-by-step explanation:

Both the plans cost the same amount $22.5 when 50 texts are sent:

[tex]20+0.05*50 = 10+0.25*50[/tex]✔️

Have a nice day! :)

Answer:

  (a)  This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour.

Step-by-step explanation:

The equation of direct variation is ...

  y = kx

for some constant k. Here, we have x in hours and y in dollars. We can see if k is constant for the values given in the table.

__

Solving the direct variation formula for k, we have ...

  k = y/x

Using the table values, we can see if this is constant:

  k = dollars/hour = 10/2 = 20/4 = 30/6 = 40/8 = 5

The "rate of change" is constant at $5 per hour.

The function represents direct variation because it passes through the origin and has a constant rate of change of $5 per hour.

The distribution of the sample means when the samples of size n = 60 are randomly selected from the population is normal (approximately).

Calculating the sample mean is as simple as adding up the number of items in a sample set and then dividing that sum by the number of items in the sample set.

Here, the distribution of the sample means when the samples of size n = 60 are randomly selected from the population is normal (approximately).

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Answer:

3y-15

Step-by-step explanation:

(y-7)3=3y-21

3y-21+6=3y-15

Answer:

[tex] - \infty < x < \infty [/tex]

Step-by-step explanation:

Answer:

6 cups

Step-by-step explanation:

Answer:

That would be 6 cups I believe