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The required value for the lamina of uniform density [tex]\bar x\\[/tex] and  [tex]\bar y[/tex] are written below,

[tex]\bar x = \dfrac{5}{8}\\[/tex]

[tex]\bar y = \dfrac{5}{14}[/tex]

Given that:

Calculus's core idea of integration entails determining a function's integral. It is a reverse process of differentiation that enables us to compute cumulative numbers, find the area under a curve, solve differential equations, and more.

The function can be written as,

[tex]m = \rho\int_0^1x^{\frac{2}{3}}dx\\= \rho\left[\dfrac{x^{\frac{5}{3}}}{\frac{5}{3}}}\right]\\=\dfrac{3}{5}\rho[/tex]

The value of Mx can be calculated as,

[tex]M_x = \rho\int_0^1\dfrac{x^{\frac{2}{3}}}{2}}\times x^{\frac{2}{3}}dx\\=\dfrac{\rho}{2}\left[\dfrac{x^{(\frac{2}{7})}}{\frac{7}{3}}\right]_0^1\\=\dfrac{3}{14}\rho[/tex]

Calculate the value of My,

[tex]M_y =\rho \int_0^1 x\times x^{\frac{2}{3}}dx\\=\rho \left[\frac{x^\frac{8}{3}}{\dfrac{8}{3}}\right]\\=\dfrac{3}{8}{\rho[/tex]

The value of [tex]\bar x\\[/tex] will be calculated as,

[tex]\bar x = \dfrac{M_x }{m}\\=\dfrac{ \dfrac{3}{8}\rho}{\dfrac{3}{5}\rho}\\=\dfrac{5}{8}[/tex]

The value of [tex]\bar y\\[/tex] is calculated as,

[tex]\bar y= \dfrac{M_y }{m}\\=\dfrac{ \dfrac{3}{14}\rho}{\dfrac{3}{5}\rho}\\=\dfrac{5}{14}[/tex]

Therefore, the required values are [tex]\bar x = \dfrac{5}{8}\\[/tex] and  [tex]\bar y = \dfrac{5}{14}[/tex].

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Answer:

[tex]\huge\boxed{-3\overrightarrow{a}+5\overrightarrow{b}=\left<-21;\ 2\right>}[/tex]

Step-by-step explanation:

[tex]\overrightarrow{a}=\left<2;\ 6\right>\\\\\overrightarrow{b}=\left<-3;\ 4\right>\\\\-3\overrightarrow{a}+5\overrightarrow{b}=-3\left<2;\ 6\right>+5\left<-3;\ 4\right>=\left<-3\cdot2;\ -3\cdot6\right>+\left<5\cdot(-3);\ 5\cdot4\right>\\\\=\left<-6;\ -18\right>+\left<-15;\ 20\right>=\left<-6+(-15);\ -18+20\right>=\left<-21;\ 2\right>[/tex]

Answer:

2

Step-by-step explanation:

2

Answer:

0.6 in

Step-by-step explanation:

Scale of drawing = ½ inch to 15 ft (½ in : 15 ft)

That is, ratio of the width on paper to actual width.

Given an actual width of 18 ft, the width of the stage on paper can be calculated as shown below:

½ in : 15 ft = x in : 18 ft

[tex] \frac{\frac{1}{2}}{15} = \frac{x}{18} [/tex]

[tex] \frac{1}{2}*\frac{1}{15} = \frac{x}{18} [/tex]

[tex] \frac{1*1}{2*15} = \frac{x}{18} [/tex]

[tex] \frac{1}{30} = \frac{x}{18} [/tex]

Cross multiply

[tex] 30*x = 18*1 [/tex]

[tex] 30x = 18 [/tex]

Divide both sides by 30

[tex] \frac{30x}{30} = \frac{18}{30} [/tex]

[tex] x = \frac{18}{30} = \frac{6}{10} [/tex]

[tex] x = 0.6 [/tex]

Width of the stage in scale drawing = 0.6 in

Answer:

Step-by-step explanation:

1/6

The probability of getting 3 is 1/6.

Probability is defined as the possibility of an event to be happened which is the ratio of no. of favorable outcomes and total no. of outcomes.

Probability of an event = P(E) = No. of favorable outcomes/Total No. of outcomes

Here given that the dice are fair and six-sided is rolled.

Total no. of outcomes by rolling the dice = 6 i.e. {1,2,3,4,5,6}

The event is to get the number 3 by rolling the dice.

The favorable outcome is = {3}

Number of favourable outcomes= 1 i.e. {3}

As the dice is the set of equally likely outcomes.

Probability of getting 3 = P(getting 3)= No. of favorable outcomes/Total No. of outcomes= 1/6

Therefore the probability of getting 3 is 1/6.

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Answer:

2.5

Step-by-step explanation:

Use the formula y2-y1 divided by x2-x1

Plug in the values: (7-2)/(6-4)

5/2

=2.5

Answer:

A. Commutative property

B. Associative and distributive properties.

C. Associative property.

Step-by-step explanation:

We proceed to present which reason are utilized by supporting procedure:

1) [tex](4\cdot 3) \cdot i +(2\cdot 4)\cdot i[/tex] Given

2) [tex](4\cdot 3)\cdot i +(4\cdot 2)\cdot i[/tex] A. Commutative property

3) [tex]4\cdot (3\cdot i+2\cdot i)[/tex] B. Associative and distributive properties.

4) [tex]4\cdot (5\cdot i)[/tex] Addition.

5) [tex](4\cdot 5)\cdot i[/tex] C. Associative property.

6) [tex]20\cdot i[/tex] Multiplication/Result.

The possible third side to a triangle is 12.

Given that,

Based on the above information, the calculation is as follows:

Here we use the pythagoras theorem.

[tex]= \sqrt{13^2 - 4^2} \\\\= \sqrt{169-16} \\\\= \sqrt{153}[/tex]

= 12.37

= 12

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Answer:

b

Step-by-step explanation:

The amount of money Janet earns per hour is given by the slope of the line m = $ 7.50

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 4 , 30 )

Let the second point be Q ( 8 , 60 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = amount of money Janet earns per hour

So , slope m = ( 60 - 30 ) / ( 8 - 4 )

On simplifying , we get

The amount of money Janet earns per hour = 30/4

The amount of money Janet earns per hour = $ 7.50

Hence , the amount of money Janet earns = slope = $ 7.50

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2 tenths + 11 hundredths is greater than 0.14.

2 tenths +11 hundredths is 3 tenths and 1 hundredth, or 0.31

Answer:

The ratio 19/25 is the same as 76/100, or 0.76.

Multiplying this by 100%, we get 76%, the percentage of questions answered correctly.

Subtracting 76% from 100% results in 24%, which is the percentage of questions not answered correctly.

Step-by-step explanation:

Answer:

A composite number

Step-by-step explanation:

because it is possible to express it as a product of prime factors. In other words, 33 can be divided by 1, by itself and at least by 3 and 11. So, 33 is a 'composite number'.

Answer:

I believe that your answer is C and Moon.

Answer: Shannon sold the silver plated frame because 45 divided by 2.5 = $18, which is the wood frame rate.

Step-by-step explanation:

I know this because 45 divided by 2.5 = $18 And that’s the silver plated frame.

Answer:

109 sq in

Step-by-step explanation:

By adding up all the areas in the net, we get 112 sq in. We then use that number to subtract from the area of the cardboard which is 221 sq in. We then get 109 sq in from that. Hope this helps.

AnsweI'm nauseous, I'm dyin'

(She ripped my heart right out)

Can't find her, someone to

(My eyes are all cried out)

Lost it, riots

Gunfire inside my head, I've

Lost it, riots

Gunfire inside my headr:

Step-by-step explanation:

Answer:

x = 2/7

Step-by-step explanation:

Step 1: Write equation

20x + x - 2 = 4

Step 2: Solve for x

Step 3: Check

Plug in x to verify it's a solution.

20(2/7) + 2/7 - 2 = 4

40/7 + 2/7 - 2 = 4

42/7 - 2 = 4

6 - 2 = 4

4 = 4

Answer:

x = 2/7

Step-by-step explanation:

Collect like terms:

20x + x = 21x ----> 21x - 2= 4

Move the constant to the right hand side and change the sign of the constant:

21x = 4 + 2

Calculate:

21x = 4 + 2 ---> 21x = 6

Divide both sides by 21:

21/21 and 6/21 = 2/7

Solution:

x = 2/7 or x= 0.285714

Answer:

11.4

Step-by-step explanation:

10% of 57 is 5.7

5.7 in 1 min

5.7*2 for 2 min

you get 11.4

Hooray! You solved the problem!

Answer:

It's 11.4 Feet

Step-by-step explanation:

If it takes the sub 1 minute to go down 10% of 57 feet, then another minute will be another 10%. So 10% = 5.7 feet, and 10% + 10% = 11.4 feet.

Answer:

Drawing an ace of spades and then drawing another ace of spades without replacement from a standard deck of cards.

Step-by-step explanation:

Given four pair of events:

1. Drawing an ace of spades and then drawing another ace of spades without replacement from a standard deck of cards

2. Drawing a 2 and drawing a 4 with replacement from a standard deck of cards

3. Drawing a heart and then drawing a spade without replacement from a standard deck of cards

4. Drawing a jack and then drawing a 7 without replacement from a standard deck of cards

To find:

Which of the pairs is mutually exclusive?

Solution:

First of all, let us have a look at the definition of mutually exclusive events.

Mutually exclusive events do not have any case in common.

In other words, two events are known as mutually exclusive when both the events can not occur at the same time.

Now, let us have a look at the given options one by one:

1. Drawing an ace of spades and then drawing another ace of spades without replacement from a standard deck of cards.

We know that there is only one ace of spades in a standard deck.

Therefore, the two events can not occur one after the other, so these are mutually exclusive events.

2. Drawing a 2 and drawing a 4 with replacement from a standard deck of cards.

The two events can occur one after the other, so these are not mutually exclusive.

3. Drawing a heart and then drawing a spade without replacement from a standard deck of cards.

Separate cards are drawn one after the other, so not mutually exclusive.

4. Drawing a jack and then drawing a 7 without replacement from a standard deck of cards.

Separate cards are drawn one after the other, so not mutually exclusive.

Answer:

If there are N students, the total cost will be:

C(N) = $500 + $5*N.

And we want the amount that each student pays to be equal or less than $15.

then:

C(N)/N ≤ $15.

Then the inequality that represents this situation is:

($500 + $5*N)/N ≤ $15.

Now, let's solve this:

($500 + $5*N) ≤ $15*N

$500 ≤ $15*N - $5*N

$500 ≤ $10*N

$500/$10 ≤ N

50 ≤ N

So the minimum number of students needed is 50.

Answer:

decreasing, then increasing. the parabola decreases as it approaches the vertex, then increases afterward

Answer:

First one (5x=320-70)

Step-by-step explanation:

If she paid 70$ for parts, then you have to subtract it from 320$ because that is the total. Therefore, 5x will be equal to 320-70 or 5x=320-70 :)

Answer:

30000000000000000.. ....

Answer:

36 minutes

Step-by-step explanation:

If x is the flow rate of each faucet, then 8x is the flow of eight faucets, and the volume of the tank is:

V = (8x) (27)

V = 216x

When there are six faucets, the time is:

216x = (6x) t

t = 36

Answer:

48 & 68

Step-by-step explanation:

if you multiply the numbers you will see that you get 48 & 68 multiple times

Answer:

Angle 9 and Angle 8 they are the same

Step-by-step explanation:

Answer:

1,2,5

Step-by-step explanation: