Match the base to the corresponding height.

Answer:

K(8, 4)

Step-by-step explanation:

Given:

M(2, 1), P(12, 6)

MK:KP = 3:2

Required:

Coordinates of K

SOLUTION:

Coordinates of K can be determined using the formula below:

[tex] x = \frac{mx_2 + nx_1}{m + n} [/tex]

[tex] y = \frac{my_2 + ny_1}{m + n} [/tex]

Where,

[tex] M(2, 1) = (x_1, y_1) [/tex]

[tex] P(12, 6) = (x_2, y_2) [/tex]

[tex] m = 3, n = 2 [/tex]

Plug in the necessary values to find the coordinates of K:

[tex] x = \frac{mx_2 + nx_1}{m + n} [/tex]

[tex] x = \frac{3(12) + 2(2)}{3 + 2} [/tex]

[tex] x = \frac{36 + 4}{5} [/tex]

[tex] x = \frac{40}{5} [/tex]

[tex] x = 8 [/tex]

[tex] y = \frac{my_2 + ny_1}{m + n} [/tex]

[tex] y = \frac{3(6) + 2(1)}{3 + 2} [/tex]

[tex] y = \frac{18 + 2}{5} [/tex]

[tex] y = \frac{20}{5} [/tex]

[tex] y = 4 [/tex]

The coordinates of K = (8, 4)

Answer:

x = 6

Step-by-step explanation:

Area of rectangle = length * width

                              = 10 * (x +2)

                              = 10*x + 10*2

                              = 10x + 20 square units

Area of triangle = [tex]\frac{1}{2}*bh[/tex]

                          [tex]=\frac{1}{2}*2*(x + 4)\\\\\\=1 * (x +4)\\\\\\[/tex]

                          = (x + 4) square units

Area of rectangle = 8* area of triangle

10x + 20 = 8 *( x+ 4)

10x + 20 = 8x + 32

Subtract 20 form both sides.

10x  = 8x + 32 - 20

10x = 8x + 12

Subtract 8x form both sides

10x - 8x = 12

2x = 12

Divide both sides by 2

2x/2 = 12/2

x = 6

Answer:

9.

Step-by-step explanation:

I am assuming that the two numbers are positive.

Let the numbers be 3x and 7x.

Then 3x * 7x = 19

21x^2 = 189

x^2 = 9

x = 3.

So the smaller of these numbers is 3*3 = 9.

Answer:

9 if that does not work try - 21

Step-by-step explanation:

Let the two numbers be x and y

x/y = 3/7               which means that x is the smaller number.

x*y = 189

Cross multiply the top equation

7x = 3y      

Divide by 7

x = 3/7 ^ y

x*y = 189

(3/7  y) * y = 189

Multiply by 7

3y^2 = 189*7

3y^2 = 1323

Divide by 3

y^2 = 441

Take the square root of both sides

y = 21

The question is a bit ambiguous. You could use - 9 and - 21 in which case the smallest number is -21. I think they intend 9 however.

x = 3/7 * 21

x = 3*3

x = 9

Check

x*y = 9 * 21 = 189

Answer:

p = T - a - b

Step-by-step explanation:

Hope that helps, not sure if it is correct though.

Answer:

Your answer is absolutely correct

Step-by-step explanation:

The work would be as follows:

[tex]\int _0^{\sqrt{\pi }}4x^3\cos \left(x^2\right)dx,\\\\\mathrm{Take\:the\:constant\:out}:\quad \int a\cdot f\left(x\right)dx=a\cdot \int f\left(x\right)dx\\=> 4\cdot \int _0^{\sqrt{\pi }}x^3\cos \left(x^2\right)dx\\\\\mathrm{Apply\:u-substitution:}\:u=x^2\\=> 4\cdot \int _0^{\pi }\frac{u\cos \left(u\right)}{2}du\\\\\mathrm{Apply\:Integration\:By\:Parts:}\:u=u,\:v'=\cos \left(u\right)\\=> 4\cdot \frac{1}{2}\left[u\sin \left(u\right)-\int \sin \left(u\right)du\right]^{\pi }_0\\\\[/tex]

[tex]\int \sin \left(u\right)du=-\cos \left(u\right)\\=> 4\cdot \frac{1}{2}\left[u\sin \left(u\right)-\left(-\cos \left(u\right)\right)\right]^{\pi }_0\\\\\mathrm{Simplify\:}4\cdot \frac{1}{2}\left[u\sin \left(u\right)-\left(-\cos \left(u\right)\right)\right]^{\pi }_0:\quad 2\left[u\sin \left(u\right)+\cos \left(u\right)\right]^{\pi }_0\\\\\mathrm{Compute\:the\:boundaries}:\quad \left[u\sin \left(u\right)+\cos \left(u\right)\right]^{\pi }_0=-2\\=> 2(-2) = - 4[/tex]

Hence proved that your solution is accurate.

Answer:

[tex]\int\limits^{\sqrt{\pi}}_0 {4x^3\cos(x^2)} \, dx=-4[/tex]

Step-by-step explanation:

So we have the integral:

[tex]\int\limits^{\sqrt{\pi}}_0 {4x^3\cos(x^2)} \, dx[/tex]

As told, let's use u-substitution first and then use integration by parts.

For the u-substitution, we can let u to be equal to x². So:

[tex]u=x^2[/tex]

Differentiate:

[tex]du=2x\, dx[/tex]

We can rewrite our integral as:

[tex]\int\limits^{\sqrt{\pi}}_0 {2x(2x^2)\cos(x^2)} \, dx[/tex]

Therefore, by making our u-substitution, our integral is now:

[tex]\int\limits {2u\cos(u)} \, du[/tex]

We also need to change our bounds. Substitute them into u. So:

[tex]u=\sqrt{\pi}^2=\pi\\u=(0)^2=0[/tex]

Therefore, our integral with our new bounds is:

[tex]\int\limits^{\pi}_{0} {2u\cos(u)} \, du[/tex]

Now, let's use integration by parts. Integration by parts is given by:

[tex]\int\limits {v}\, dy=vy-\int y\, dv[/tex]

(I changed the standard u to y because we are already using u).

Let's let v be 2u and let's let dy be cos(u). Thus:

[tex]v=2u\\dv=2\,du[/tex]

And:

[tex]dy=\cos(u)\\y=\sin(u)[/tex]

So, do integration by parts:

[tex]=2u\sin(u)-\int \sin(u)2\,du[/tex]

Simplify:

[tex]=2u\sin(u)-2\int \sin(u)\,du[/tex]

Evaluate the integral:

[tex]=2u\sin(u)+2\cos(u)[/tex]

Now, use the bounds. So:

[tex](2(\pi)\sin(\pi)+2\cos(\pi))-(2(0)\sin(0)+2\cos(0))[/tex]

Evaluate:

[tex]=(2\pi(0)+2(-1))-(0(0)+2(1))[/tex]

Simplify:

[tex]=(-2)-(2)[/tex]

Subtract:

[tex]=-4[/tex]

And we're done!

Answer:

A. x+2+x+2

B. 2(x)

C. x+2+x+2=p

2(x)= a

Answer:

7/24

Step-by-step explanation:

Answer:

2.999 millions hours ago

Step-by-step explanation: :)

Answer:

If we defelt 4 cards from 52 cards

Step-by-step explanation:

P(b) favorable outcome /total number of outcomes

48/52

The probability that all 4 cards are picture cards is  0.00183

A standard 52-card deck comprises 13 ranks in each of the four French suits: clubs (♣), diamonds (♦), hearts (♥) and spades (♠). Each suit includes three court cards (face cards), King, Queen and Jack, with reversible (double-headed) images.

as, we know

A face card is any of the twelve cards in a deck which has a picture of a face. The face cards are kings, queens, and jacks.

So, the possibilities to get a picture card is are 3*4=12.

Now, he probability that all 4 cards are picture cards

=(12/52) * (11/51) * (10/50) * (9/49)

=( 11880 / 6497400 )

= ( 0.0018284237 )

= 0.00183

Learn more about deck of cards here:

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Answer:

1/5 = 2/10 = 3/15 = 4/20

= 5/25 = 6/30 = 7/35 = 8/40

= 9/45 = 10/50 = 11/55 = 12/60

= 13/65 = 14/70 = 15/75 = 16/80

= 17/85 = 18/90 = 19/95 = 20/100

= 21/105 = 22/110 = 23/115 = 24/120

= 25/125 = 26/130 = 27/135 = 28/140

= 29/145 = 30/150 = 31/155 = 32/160

= 33/165 = 34/170 = 35/175 = 36/180

= 37/185 = 38/190 = 39/195 = 40/200

= 41/205 = 42/210 = 43/215 = 44/220

= 45/225 = 46/230 = 47/235 = 48/240

= 49/245 = 50/250 = 51/255 = 52/260

= 53/265 = 54/270 = 55/275 = 56/280

= 57/285 = 58/290 = 59/295 = 60/300

= 61/305 = 62/310 = 63/315 = 64/320

= 65/325 = 66/330 = 67/335 = 68/340

= 69/345 = 70/350 = 71/355 = 72/360

= 73/365 = 74/370 = 75/375 = 76/380

= 77/385 = 78/390 = 79/395 = 80/400

= 81/405 = 82/410 = 83/415 = 84/420

= 85/425 = 86/430 = 87/435 = 88/440

= 89/445 = 90/450 = 91/455 = 92/460

= 93/465 = 94/470 = 95/475 = 96/480

= 97/485 = 98/490 = 99/495 = 100/500

Step-by-step explanation:

all of these are equivalent

Answer: 36/11  Or 3 3/11

Step-by-step explanation:

Answer:

y=4

y=8

y=12

y=16

2)4=19

5=22

addition of 3 to each value

3)17

4)3a^2

5)a^4

6)1

7)An arithmetic sequence is such that the difference between any term and the one immediately preceeding it is constant.

8)A geometric sequence is such in which each term is a constant multiple of its preceeding.

9)1.25

10)B.

Answer:

y=4

y=8

y=12

y=16

2)4=19

5=22

addition of 3 to each value

3)17

4)3a^2

5)a^4

6)1

7)An arithmetic sequence is such that the difference between any term and the one immediately proceeding it is constant.

8)A geometric sequence is such in which each term is a constant multiple of its proceeding.

9)1.25

10)B.

Step-by-step explanation:

Answer:

n=2

Step-by-step explanation:

(6n-7)+(8n+2)=23

14n-5=23

14n=28

n=2

Answer:

-2n + 8/9

Step-by-step explanation:

Try that tell me I it don't work

Answer:

$20,736

Step-by-step explanation:

When these kind of advertisements are displayed,, it means the EMI cost per month shall be $288.

Since it provides the time period, that is 72 months,

Total cost of car in this case shall be $288 [tex]\times[/tex] 72 months = $20,736

Also, these include an interest factor, but overall it is = $20,736 only,

If one down payment for full price of the car is made the cost shall reduce by the interest amount, but since no interest rate is provided it shall be ignored.

Answer: the integers are closed under addition, multiplication, and subtraction, but NOT division.

Step-by-step explanation:

Answer:

x≤2

Step-by-step explanation:

Answer:

x ≤ 2

Step-by-step explanation:

well, -6 x 4 = -24

-6 x X = -6x

so far, we have -24 -6x ≤-4(x+1)

-4 x X = -4x

and -4 x 1 = -4 , so we now have -24 -6x ≤ -4x + -4

now we subtract x on one side, and to the other side as well, and you do the same for the numbers!

Answer: D

Step-by-step explanation:

Since we know that the area of the square is 900 in², we can use that to find the length of each side.

900=x²                 [square root both sides]

x=30

Now that we know each side is 30 in, we know that the diameter of the circle is also 30 in. To find the radius, divide the diameter by 2.

2r=30                    [divide both sides by 2]

r=15

With the radius, we can find the area of the circle.

A=π(15)²               [exponent]

A=225π

Since the problem said to leave in terms of π, the area is A=225π in².

Answer:

= -2

-7(5+3)+216/4

-7(8)+216/4

-56+54

= -2

Answer:

y = 40

Step-by-step explanation:

The sum of the angles of a triangle are 180 degrees

y+10 + 2y +50 = 180

3y+60 = 180

Subtract 60 from each side

3y+60-60 = 180-60

3y = 120

Divide each side by 3

3y/3 = 120/3

y = 40

Answer:

Image result for State the domain and range in set notation​

The domain is the set of all first elements of ordered pairs (x-coordinates). The range is the set of all second elements of ordered pairs (y-coordinates). Only the elements "used" by the relation or function constitute the range. Domain: all x-values that are to be used (independent values).

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

The last option is not complete, but since the first three options are incorrect, the last option is correct

Answer:

The confidence interval will decrease

Step-by-step explanation:

Generally the confidence interval is mathematically represented as

[tex]\= x \pm z_c * \frac{s}{\sqrt{n} }[/tex]

Here [tex]z_c[/tex] is called the critical value of [tex]\frac{level \ of \ significance }{2}[/tex] obtained from the normal distribution table , s is the standard deviation , n is the sample size (number of measurements )

Now looking at the formula we that if the increase the sample size that the confidence level would decrease

So if the n is increased to 10  

   The  confidence interval would decrease

This image should help with that.                                                

Answer:

F(-6, 3) --> F'(-6,3)

G(-4,3) --> G'(-8,3)

H(-2,4) --> H'(-10,4)

Answer:

F(-6,3)

G(-8,3)

H(-10,4)

Step-by-step explanation:

If your reflecting over the red line then all I do is first try to recreate the shape on the other side of the red line. (Like a reflection) And then look at the points it landed on. And that's your answer

Answer:  1) 1/3,654     2) 3/406     3) 72,684,900,288,000      4) 120

Step-by-step explanation:

1)         First       and        Second         and         Third

  [tex]\dfrac{3\ total\ prizes}{29\ total\ people}\times \dfrac{2\ remaining\ prizes}{28\ remaining\ people}\times \dfrac{1\ remaining\ prize}{27\ remaining\ people}=\dfrac{6}{21,924}\\\\\\.\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad =\large\boxed{\dfrac{1}{3,654}}[/tex]

2)         First       and          Second

   [tex]\dfrac{3\ total\ prizes}{29\ total\ people}\times \dfrac{2\ remaining\ prizes}{28\ remaining\ people}=\dfrac{6}{812}=\large\boxed{\dfrac{13}{406}}[/tex]

[tex]3)\quad \dfrac{29!}{(29-10)!}=\large\boxed{72,684,900,288,000}[/tex]

[tex]4)\quad _{10}C_3=\dfrac{10!}{3!(10-3)!}=\large\boxed{120}[/tex]

To determine the number of seconds it would take Dariya to download  7 songs at the same rate, we first find the unit rate and multiply it by 7.

Hence, option 4. By finding the unit rate and multiplying it by 7 is the right option.

Unit Rate = 7second/song.

Time to download 7 songs = 49 seconds.

A unit rate is a quantity taken for a unit of another quantity.

We are given that it takes Dariya 35 seconds to download 5 songs from the Internet. We are asked about the time it will take Dariya to download y songs at the same rate.

We will first determine the unit rate of the time taken for downloading a song.

5 songs take 35 seconds.

∴ 1 song takes 35/5 = 7 seconds.

∴ Unit rate is 7seconds/song.

Now to determine the time for downloading 7 songs, we multiply the unit rate by 7.

∴ Time taken to download 7 songs = 7 songs * unit rate

or, Time taken to download 7 songs = 7 songs * 7 second/song

or, Time taken to download 7 songs = 49 seconds.

∴ To determine the number of seconds it would take Dariya to download  7 songs at the same rate, we first find the unit rate and multiply it by 7.

Hence, option 4. By finding the unit rate and multiplying it by 7 is the right option.

Learn more about the unit rate at

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2.

The domain of this function is 3≤x≤5 in interval notation that is [3,5]

The range is -3≤y≤3. In interval notation that is [-3,3]

4.

The domain of this function is -5≤x≤-1 in interval notation that is [-5,-1]

The range is 1≤y≤5. In interval notation that is [1,5]

:)

Answer:

22/5

Step-by-step explanation:

6x-24=x-2

6x-x=-2+24

5x=22

x=22/5

Answer:

The probability is 0.357

Step-by-step explanation:

Given that,

The system has at least one type of defect,

Suppose, A certain system can experience three different types of defects.

Let [tex]A_{i}[/tex] (i = 1,2,3) denote the event that the system has a defect of type i.

Suppose that the following probabilities are,

[tex]P(A_{1})=0.11[/tex]

[tex]P(A_{2})=0.08[/tex]

[tex]P(A_{3})=0.05[/tex]

[tex]P(A_{1}\cup A_{2})=0.13[/tex]

[tex]P(A_{1}\cup A_{3})=0.13[/tex]

[tex]P(A_{2}\cup A_{3})=0.11[/tex]

[tex]P(A_{1}\cap A_{2}\cap A_{3})=0.01[/tex]

[tex]P(A_{1}\cap A_{2})=0.06[/tex]

[tex]P(A_{1}\cap A_{3})=0.03[/tex]

[tex]P(A_{2}\cap A_{3})=0.02[/tex]

[tex]P(A_{1}\cup A_{2}\cup A_{3})=0.14[/tex]

We need to calculate the probability that it has exactly one type of defect

Using given data

[tex]P=\dfrac{P(A_{1}\cap A_{2}'\cap A_{3}')}{P(A_{1}\cup A_{2}\cup A_{3})}+\dfrac{P(A_{1}'\cap A_{2}\cap A_{3}')}{P(A_{1}\cup A_{2}\cup A_{3})}+\dfrac{P(A_{1}'\cap A_{2}'\cap A_{3})}{P(A_{1}\cup A_{2}\cup A_{3})}[/tex]

[tex]P=\dfrac{P(A_{1})-P(A_{1}\cap A_{2})-P(A_{1}\cap A_{3})+P(A_{1}\cap A_{2}\cap A_{3})}{P(A_{1}\cup A_{2}\cup A_{3})}[/tex] + [tex]\dfrac{P(A_{2})-P(A_{1}\cap A_{2})-P(A_{2}\cap A_{3})+P(A_{1}\cap A_{2}\cap A_{3})}{P(A_{1}\cup A_{2}\cup A_{3})}[/tex]+ [tex]\dfrac{P(A_{3})-P(A_{1}\cap A_{3})-P(A_{2}\cap A_{3})+P(A_{1}\cap A_{2}\cap A_{3})}{P(A_{1}\cup A_{2}\cup A_{3})}[/tex]

P = [tex]\dfrac{P(A_{1})+P(A_{2})+P(A_{3})-2P(A_{1}\cap A_{2})-2P(A_{1}\cap A_{3})-2P(A_{2}\cap A_{3})+3P(A_{1}\cap A_{2}\cap A_{3})}{P(A_{1}\cup A_{2}\cup A_{3})}[/tex]

Put the value into the formula

[tex]P=\dfrac{0.11+0.08+0.05-2(0.06)-2(0.03)-2(0.02)+3(0.01)}{0.14}[/tex]

[tex]P=0.357[/tex]

Hence, The probability is 0.357