which expression is equivalent to c^2 - 4 / c + 3 /

Answer:

Since we know the dot product of unit vectors, we can simplify the dot product formula to a⋅b=a1b1+a2b2+a3b3. we can use the same formula, but with a3=b3=0, a⋅b=a1b1+a2b2.

Step-by-step explanation:

Answer:

The probability tree is;

                            0.95        [tex](+)[/tex]

                   [tex](S)[/tex]

          0.1              0.05        [tex](-)[/tex]

[  P  ]

          0.9             0.15          [tex](+)[/tex]                                                        

                  [tex](S_{no})[/tex]    

                             0.85         [tex](-)[/tex]        

Step-by-step explanation:

Given the data in the question;

10% of the rugby team members use steroids

so Probability of using steroid; P( use steroid ) = 10% = 0.10

Probability of not using steroid; P( no steroid use ) = 1 - 0.10 = 0.90

Since the test show positive for an athlete who uses steroids, 95% of the time.

Probability of using steroids and testing positive = 95% = 0.95

Probability of using steroids and testing Negative = 1 - 0.95 = 0.05

Also from the test, 15% of all steroid-free individuals also test positive.

so

Probability of not using steroids and testing positive = 15% = 0.15

Probability of not using steroids and testing negative = 1 - 0.15 = 0.85

To set up the probability tree, Let;

[tex](S)[/tex] represent steroid use

[tex](S_{no})[/tex] represent no steroid use

[tex](+)[/tex] represent test positive

[tex](-)[/tex] represent test negative

so we have;

                            0.95        [tex](+)[/tex]

                   [tex](S)[/tex]

          0.1              0.05        [tex](-)[/tex]

[  P  ]

          0.9             0.15          [tex](+)[/tex]                                                        

                  [tex](S_{no})[/tex]    

                             0.85         [tex](-)[/tex]        

Answer:

52.25 - 1.50 = 50.75

Step-by-step explanation:

I'd recommend using a calculator or pencil and paper

53.25

-  1.50

--------

50.75

Answer:

7x is monomial according to question.

Answer:

There are 32 nickels and 23 dimes.

Step-by-step explanation:

Lets say x is nickels and y is dimes

The first equation would be 55 = x + y

The second equation would be .05x + .10y = 3.90

The Solving Part:

Move y to the other side: x = 55 - y

Substitute x in the second equation: .05(55-y) + .10y = 3.90

Distribute, rearrange, and combine like terms: .05y = 1.15

Solve for y: Y = 23

Plug in 23 for y and solve: 55 - y = x ; 55 - 23 = x ; 55 - 23 = 32

x = 32

y = 23

32 nickels and 23 dimes

Answer:

There are 32 nickels and 23 dimes.

Step-by-step explanation:

Yay :) we solved the problem together :)))))

Given:

If x, y, and z are positive integers, then

[tex]2^x\times 3^y\times 5^z=54000[/tex]

To find:

The value of [tex]x+y+z[/tex].

Solution:

First we need to find the prime factors of 54000.

[tex]54000=2\times 2\times 2\times 2\times 3\times 3\times 3\times 5\times 5\times 5[/tex]

[tex]54000=2^4\times 3^3\times 5^3[/tex]        ...(i)

We have,

[tex]54000=2^x\times 3^y\times 5^z[/tex]        ...(ii)

On comparing (i) and (ii), we get [tex]x=4,y=3,z=3[/tex].

The sum of [tex]x,y,z[/tex] is:

[tex]x+y+z=4+3+3[/tex]

[tex]x+y+z=10[/tex]

Therefore, the value of [tex]x+y+z[/tex] is 10.

Answer:

D. [tex]3x\sqrt{2x}[/tex]

Step-by-step explanation:

The problem gives on the following equation:

[tex]\sqrt{32x^3}+-\sqrt{16x^3}+4\sqrt{x^3}-2\sqrt{x^3}[/tex]

Alongside the information that ([tex]x\geq0[/tex]).

One must bear in mind that the operation ([tex]\sqrt[/tex]) indicates that one has to find the number that when multiplied by itself will yield the number underneath the radical. The easiest way to find such a number is to factor the term underneath the radical. Rewrite the terms under the radical as the product of prime numbers,

[tex]\sqrt{2*2*2*2*2*x*x*x}-\sqrt{2*2*2*2*x*x*x}+4\sqrt{x*x*x}-\sqrt{2*x*x*x}[/tex]

Now remove the duplicate factors from underneath the radical,

[tex]2*2*x\sqrt{2x}-2*2*x\sqrt{x}+4x\sqrt{x}-2x\sqrt{x}[/tex]

Simplify,

[tex]4x\sqrt{2x}-4x\sqrt{x}+4x\sqrt{x}-x\sqrt{2x}[/tex]

[tex]3x\sqrt{2x}[/tex]

Answer:

-1.683

Step-by-step explanation:

Given :

Group 1 :

x1 = 667 ; n1 = 10 ; s1 = 20

Group 2 :

x2 = 679 ; n2 = 14 ; s2 = 15

The test statistic assuming equal variance :

x1 - x2 / √[Sp² * (1/n1 + 1/n2)]

sp² = [(n1 - 1)*s1² + (n2 - 1)*s2²] ÷ (n1 + n2 - 2)

Sp² = [(10 - 1)*20² + (14 - 1)*15²] = 296.59

Test statistic =

(667 - 679)/ √[296.59 * (1/10 + 1/14)]

-12 / 7.1304978

Test statistic = - 1.682

hope it helps

please mark Brainliest

Let it be x

Using basic proportionality theorem

[tex]\\ \sf\longmapsto \dfrac{x}{10}=\dfrac{14}{7}[/tex]

[tex]\\ \sf\longmapsto \dfrac{x}{10}=2[/tex]

[tex]\\ \sf\longmapsto x=10(2)[/tex]

[tex]\\ \sf\longmapsto x=20[/tex]

Answer:

Quadrant 2

Step-by-step explanation:

Given

[tex]\theta = 115^o[/tex]

Required

The quadrant

We have:

[tex]0^o < \theta < 90^o[/tex] --- quadrant 1

[tex]90^o < \theta < 180^o[/tex] --- quadrant 2

[tex]180^o < \theta < 270^o[/tex] --- quadrant 3

[tex]270^o < \theta < 360^o[/tex] --- quadrant 4

So, by comparison; we have:

[tex]90^o < \theta < 180^o[/tex]

Substitute 115 for [tex]\theta[/tex]

[tex]90^o < 115 < 180^o[/tex]

The above is true for quadrant 2

Answer:

Mr. Rowley=16:14

=8:7

Ms.Rivera= 64:60

=16:15

Answer:

75.03

Step-by-step explanation:

14×11×sin(77)

= 75.02649499..

≈ 75.03 (rounded to nearest hundredth)

Answered by GAUTHMATH

Answer:

B half the circumference or pi r

Step-by-step explanation:

The base of the parallelogram is pi r

To form the parallelogram the triangles are  removed from the bottom half of the circle and moved to flip the gaps in the top half.

Answer:

y = -3 (you have to draw an horizontal line that passes for the point (0,-3)

Step-by-step explanation:

We have to find the middle points of the segments that unite the corrispettive points.

We are lucky because the images of the points have the same x coordinate of the original ones, so we have just to find the y coordinates.

Segment CC‘

(y1 + y2)/2 = (-1-5)/2 = -3

Segment AA’

(0-6)/2 = -3

Segmet BB’

(1-7)/2 = -3

Segment DD’

(1-7)/2 = -3

In conclusion we can say that the points of the reflection have all the y coordinate equal to -3.

the line is horizontal and its equation is : y = -3

Answer:

Step-by-step explanation:

Need the diagram for reference in order to answer...........

Answer:C

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

common ratio is

9÷27=1/3

3÷9=1/3

1÷3=1/3

therefore common ratio is 1/3

Answer: 1/3

Step-by-step explanation:

Let us confirm that this is a geometric sequence. 9/27 = 1/3 and 3/9 = 1/3. Thus, the common ratio is 1/3.

Answer:

[tex][1, -4 ,5][/tex]

Step-by-step explanation:

In this question we are multiplying together two matrices. When we multiply a (1 x 3) matrix with a (3 x 3) matrix, we get a (1 x 3) matrix.

To compute each value, all you need to do is take the each value in each row in the first matrix, and multiply it by each value in each column of the second matrix and add up the result. So let's do that.

[tex]a = (2 * 1) + (1 * -1) + (0 * 0) = 2 - 1 + 0 = 1[/tex]

[tex]b = (2 * -1) + (1 * -2) + (0 * 1) = -2 -2 = -4[/tex]

[tex]c = (2 * 2) + (1 * 1) + (0 * 1) = 4 + 1 + 0 = 5[/tex]

Answer:

13

Step-by-step explanation:

since n is 4 substitute it where there's n in the equation

3(4)+1

12+1

13

I hope this helps

Answer:

13

Step-by-step explanation:

so you start with the equation 3n+1

since you know n=4 then u put it in place of n making the equation 3*4+1

then you multiply and it's 12+1 which equals 13

Answer: use photo. math

Step-by-step explanation:

boom

Firstly , before solving the equation , we should know about the chain rule and its formula.

Formula For the Chain rule-

$\rightarrow$ $\sf\dfrac\pink{dy}\pink{dx}$=$\sf\dfrac\pink{dy}\pink{du}$ $\times$ $\sf\dfrac\pink{du}\pink{dx}$ $\leftarrow$

_____________________________

$\sf\huge\underline{\underline{Question:}}$

$\sf\small{Differentiate\: x\: the \:function: (3x² - 9x + 5²)}$

$\sf\huge\underline{\underline{Solution:}}$

$\sf{Let\:y = (3x^2 - 9x + 5)^9}$

$\space$

☆ Differentiating both the sides w.r.t.x using chain rule-

$\mapsto$ [tex]\sf\dfrac{dy}{dx}=[/tex][tex]\sf\dfrac{d}{dx}[/tex][tex]\sf{(3x^2 - 9x + 5)^9}[/tex]

$\space$

$\space$

$\mapsto$ [tex]\sf\dfrac{dy}{dx}[/tex]=[tex]\sf{9(3x^2-9x+5)^8}[/tex] [tex]\times[/tex] [tex]\sf\dfrac{d}{dx}[/tex]$\sf\small{(3x^2-9+5)}$

$\space$

$\space$

$\mapsto$ [tex]\sf\dfrac{dy}{dx}[/tex]=[tex]\sf{9(3x^2-9x+5)^8}[/tex] [tex]\times[/tex][tex]\sf(6x-9)[/tex]

$\space$

$\space$

$\mapsto$ [tex]\sf\dfrac{dy}{dx}[/tex]=[tex]\sf{9(3x^2-9x+5)^8}[/tex] $\times$ [tex]\sf{3(2x-3)}[/tex]

$\space$

$\space$

$\mapsto$ [tex]\sf\dfrac{dy}{dx}[/tex]=[tex]\sf{27(3x^2-9x+5)^8(2x-3)}[/tex]

$\space$

$\space$

$\sf\underline\bold\green{❍ dy:dx=27(3x^2-9x+5)^8(2x-3)}$

______________________________

The first three terms of the Arithmetic Progression are 12, 17 and 22.

For an ARITHMETIC PROGRESSION, AP ;

First term = a

Second term = a + d

Third term = a + 2d

Where, d = common difference ;

If third term exceeds smallest by 10 ;

Third term - first term

a + 2d - a = 10

2d = 10

d = 10/2

d = 5

Sum of the three terms :

a + (a + d) + a + 2d = 51

3a + 3d = 51

d = 5

3a + 3(5) = 51

3a + 15 = 51

3a = 51 - 15

3a = 36

a = 12

The AP would be:

First term, a = 12

Second term, a + d = 12 + 5 = 17

Third term = a + 2(d) = 12 + 10 = 22

Therefore , the first three terms of the AP are :

12, 17 and 22

Learn more about ARITHMETIC PROGRESSION :

https://brainly.com/question/12006170

Answer:

k=4

Step-by-step explanation:

remove x:

10x.(-3) + ky.(-3)=-8.(-3)         (1)

-15x.2 - 6y.2 = 12.2               (2)

(1) - (2)  => -3ky+12y = 0

<=> (12-3k)y = 0

so that y has infinitely many solutions then

12-3k = 0 => k=4

Answer:

When time is short and you just want a rough estimate of the standard deviation, turn to the range rule to quickly estimate the standard deviation value. The standard deviation is approximately equal to the range of the data divided by 4. That's it, simple.

Answer:

C

Step-by-step explanation:

Just trust

Answer:

C

Step-by-step explanation:

I did the assignment in edge and got it right.

Proof:

Answer:

A majority of the data will lie between 38 and 46.

Step-by-step explanation:

It can be said that a majority of the data of a distribution lies within 1 standard deviation of the mean.

In this question:

Mean of 42, standard deviation of 4.

42 - 4 = 38

42 + 4 = 46

A majority of the data will lie between 38 and 46.

Answer:

[tex]-8-6i[/tex]

Step-by-step explanation:

[tex]\frac{2-36i}{2+3i} * \frac{2-3 i}{2-3i}[/tex]

-104-78i /13

-8-6i

The square root of (2-36i)/(2+3i)​ is √(112-66i)/13.

The given expression is [tex]\frac{2-36i}{2+3i}[/tex].

The square root of a number is the inverse operation of squaring a number. The square of a number is the value that is obtained when we multiply the number by itself, while the square root of a number is obtained by finding a number that when squared gives the original number.

Multiply both numerator and denominator by 2-3i.

Now, [tex]\frac{2-36i}{2+3i}\times\frac{2-3i}{2-3i}[/tex]

= [tex]\frac{(2-36i)(2-3i)}{(2+3i)(2-3i)}[/tex]

= [tex]\frac{(4-72i+6i-108i^2)}{4-9i^2}[/tex]

= [tex]\frac{(4-66i+108)}{4+9}[/tex]

= [tex]\frac{(112-66i)}{13}[/tex]

Now square root is √(112-66i)/13

Therefore, the square root of (2-36i)/(2+3i)​ is √(112-66i)/13.

To learn more about the square root of a number visit:

https://brainly.com/question/8971086.

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Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

Factors of 45: 1, 3, 5, 9, 15, 45

The common factors between the two numbers are 1, 3, 5, 15.

Hope this helps!