All of the following are rational numbers except
-16
1.33
2/3
3.14159...

[tex] \frac{13}{(x + 2)} = \frac{8}{(x - 1)} [/tex]

By cross - multiplication

[tex] \implies13 \times (x - 1) = 8 \times (x + 2)[/tex]

[tex] \implies13x - 13 = 8x + 16[/tex]

[tex] \implies13x - 8x = 16 + 13[/tex]

[tex] \implies5x = 29[/tex]

[tex] \implies \: x = \frac{29}{5} [/tex]

[tex] \implies \: x = 5.8[/tex]

Answer:

941

Step-by-step explanation:

= 1, 2, 3...900 is the number of parents that are going to attend the ceremony.

we are given a random number of parents (0 1 2)

each of these random numbers have a probability of 1/3

so we multiply the numbers by their probability

E(X) = 0*1/3 + 1*1/3 +2*1/3

= 1

E(X²) = 0²*1/3 + 1²*1/3 + 2²*1/3

= 5/3

we calculate the variance

= E(X²)-[E(X)²

= 5/3 - 1²

= 2/3( got this by taking the lcm)

∑Xi with n = 900 will have  to be the number of parents attending this ceremony for all seniors

E|S| = 900 * 1

= 900

var |S| = 900*2/3

=600

we are usng normal distribution to solve this

μ = E(S) = 900

σ² = var(S) = 600

for a seating area wth 900 seats now we are to find the probability that all the parents present will have seats

s-μ/√σ

900 -900/√600

= 0

p(z≤0)

= 0.5

for a seating area wth 925 seats we are to fnd probability that all parents will be seated

= s-μ/√σ

= 925-900/√600

= p(z≤1.0208)

= 0.84623

going to the table of standard normal distribution we have

p(z≤1.644845)= 0.95

s-μ/σ≤1.644845 = 0.95

we cross multply

s-μ≤1.644845σ

we make s subject of the formula

s ≤ μ+1.644845σ = 0.95

we now μ = 900 and

σ = √600

900+1.644845*√600

=900 +40.388

=940.388

= 941

we have that the minimum number of seat requred for all parents n attendance to be seat is 941 at a probability of 0.95

We have the minimum number of seats required for all parents' attendance to be seat is 941 at a probability of 0.95.

It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.

1, 2, 3, .....900 is the number of parents that are going to attend the ceremony.

A random number of parents (0, 1, 2)

The probability is 1/3.

[tex]\rm E(X) = 0 * \dfrac{1}{3} + 1*\dfrac{1}{3}+2*\dfrac{1}{3} = 1\\\\\\E(X^2) = 0^2*\dfrac{1}{3}+1^2*\dfrac{1}{3}+2^2*\dfrac{1}{3}= \dfrac{5}{3}[/tex]

Then the variance will be

[tex]\rm Var = E(X^2) -[E(X)]^2\\\\Var = \dfrac{5}{3} -1 \\\\Var = \dfrac{2}{3}[/tex]

∑Xi with n = 900 will have to be the number of parents attending this ceremony for all seniors

[tex]\rm E \left| S \right| = 900* 1 \\\\E \left| S \right| = 900[/tex]

And

[tex]\rm Var \left| S \right| = 900 * \dfrac{2}{3} \\\\Var \left| S \right| = 600[/tex]

Then by the normal distribution, we have

[tex]\rm \mu = E(S) = 900\\\\\sigma ^2 = Var (S) = 600[/tex]

For a seating area with 900 seats then the probability of the parents present will have seats.

[tex]\rightarrow \dfrac{S - \mu }{\sqrt{\sigma}}\\\\\\\rightarrow \dfrac{900-900}{\sqrt{600}}\\\\\\\rightarrow 0[/tex]

For a seating area with 925 seats then the probability of the parents present will have seats.

[tex]\rm \rightarrow \dfrac{S - \mu }{\sqrt{\sigma}}\\\\\\\rightarrow \dfrac{925-900}{\sqrt{600}}\\\\\\\rightarrow P(z \leq 1.0208) \\\\\rightarrow 0.84623[/tex]

From the standard normal distribution table, we have

[tex]\rm p(z\leq 1.644845) = 0.95\\\\\dfrac{S-\mu}{\sqrt{\sigma }} \leq 1.644845= 0.95\\\\S \leq \mu + 1.644845 \sqrt{\sigma }= 0.95\\\\S=900 + 1.644845*\sqrt{600}\\\\S= 941[/tex]

We have the minimum number of seats required for all parents' attendance to be seat is 941 at a probability of 0.95.

More about the normal distribution link is given below.

https://brainly.com/question/12421652

Answer:

3/4, 0.78, 0.8

Step-by-step explanation:

3/4= 0.75.

0.78 is greater and 0.8 is greater again.

Answer:

7.5/2 = 3.75

3.75/5 = .75

he gets .75 pounds of candy

Answer:

x * (x+1)^2 = x(x+1)(x+1) = x(x^2 + 2x + 1) = x^3 + 2x^2 + x

Step-by-step explanation:

Is the "$" supposed to be there?

(x+1)^2 = (x+1)(x+1) = x^2 + 2x + 1

That's all I CAN do...I'm not that old yet... =\

Answer:x^(2)+2x^(2)+x hoped i helped

Step-by-step explanation:

Answer:

15 = 9 + 5j

Step-by-step explanation:

When you want to make words become an equation, the word is usually means = and more usually means +.

In this case, we have 15 is 9 more than 5j.

We can rewrite this as 15 = 9 + 5j.

Answer:

see below

Step-by-step explanation:

14. We can represent 1 as √1 and 2 as √4 and because 1 < 3 < 4, we know that √3 is in between 1 and 2. However, 3 is closer to 4 than it is to 1 so √3 is about 2.

15. Again, 3 is √9 and 4 is √16. 9 < 10 < 16 so √10 is in between 3 and 4, however, since 10 is closer to 9 as it is to 16, we know that √10 is about 3.

16. -4 = -√16 and -5 = -√25, since 16 < 22 < 25, we know that -√22 is in between -4 and -5 but 22 is closer to 25 so the answer is -5.

17. -10 = -√100 and -11 = -√121 so -√120 is in between -10 and -11. Since 120 is closer to 121, the answer is -11.

Answer:

the answers are below

Step-by-step explanation:

1. the populaton of ths study are the college students that are beng tested on the effect of alcohol on their emotions. college students are the main focus of this experiment.

2. The sample for this study is the 120 students from the University. the sample of a study is actually the number of participants in that study. this queston says that they are 120

3. the null hyothesis:

 h₀ : alcohol has no effect on college students emotions

4. the alternate hypothesis:

 h₁: there is effect of alcohol on college students emotions

5. The researcher would have to use a t test which is an inferential statistical test. A t test is used to test for the existence of statistical difference between two means that may have similar features

Answer:

9

Step-by-step explanation:

The absolute value of -3 is |-3|, which in turn is 3.  Thus we have

3(3), or 9.  The fourth answer choice is the correct one.

Answer:

Step-by-step explanation:

Answer:

54

Step-by-step explanation:

4x+7=18

subtracting 7 from both side of the equation

4x+7- 7=18 - 7

4x = 11

to find value of x , we divide both side of the equation by 4

4x/4 = 11/4 = 2.75

x = 2.75

now we plug in the found value of x = 2.75 in place of x in equation 12x+21

12*2.75 + 21 = 33 + 21 = 54

Thus, answer is 54

Answer:

rotation of 270°

Step-by-step explanation:

Consider the coordinates of of preimage and image of ABC

A(1, 0 ) → A'*0, - 1 )

B(6, - 7 ) → B'(- 7, - 6 )

C(0, - 4 ) C'(- 4, 0 )

What we note is the x- coordinate of the image is the y- coordinate of the preimage and the y- coordinate of the image is the negative of the x- coordinate of the preimage, that is

(x, y ) → (y, - x )

This is equivalent to a counterclockwise rotation about the origin of 270°

This question is incomplete, the complete question is;

The Millennium Falcon is chased by the Imperial Forces. The ship is moving at a speed of 0.525 c. Han Solo is shooting at the imperial fighters with his newly installed proton cannon purchased at the MSU Surplus Store for $20.00 plus 6.00% TAX. The cannon emits protons at a speed of 0.741 c with respect to the ship.

What is the velocity of the protons in the resting frame of the movie audience in terms of the speed of the light when the cannon is shot in the forward direction?  0.911 ANS .

What is the velocity of the protons in the resting frame when the cannon is shot in the backward direction?

(Use positive sign for the forward direction, and negative for the backward direction.)

Answer:

A)

the velocity of the protons in the resting frame of the movie audience in terms of the speed of the light when the cannon is shot in the forward direction is 0.911c

B)

the velocity of the protons in the resting frame when the cannon is shot in the backward direction -0.3535c.

The negative sign indicates that the proton is moving in the opposite direction of the ship. (backward)

Step-by-step explanation:

Given that;

speed of ship u = 0.525C

speed of proton emission v = 0.741C

Now When Cannon is shot in Forward Direction

Relativistic speed S is Calculated as;

S = (u+v) / ((1 + (uv))/c²)

we substitute (0.525 + 0.741 )C / ((1 + (0.525 × 0.741) C)/c²)

the C² cancel each other

so we have

S = 1.266 / 1.389925

S = 0.9108 ≈ 0.911c

Therefore the velocity of the protons in the resting frame of the movie audience in terms of the speed of the light when the cannon is shot in the forward direction is 0.911c

When Cannon is shot in Backward  Direction

Relativistic speed S is Calculated as;

S = ( u – v ) / ( 1 – uv / c ²)

S =  (0.525 - 0.741) C / ((1 - (0.525 × 0.741) C)/c²)

the C² cancel each other

so S = -0.216 / 0.610975

S = -0.3535c

The negative sign indicates that the proton is moving in the opposite direction of the ship. (backward)

Therefore the velocity of the protons in the resting frame when the cannon is shot in the backward direction -0.3535c.

Answer:

C) e²+(w-x)²=b²

Step-by-step explanation:

C) e²+(w-x)²=b²

B is the hypotenuse and takes the place of c in the Pythagorean Theorem.  The second answer (x²+e²=b²) is also true, but isn’t what the question is asking for.

Answer:

(6,-4)

Step-by-step explanation:

That’s where they intersect

Just write it in the order it first was in for instance. Firstly she put flour in the bowl. Secondly she added water. And finally she put the sugar in. Like that.

Answer:

Firstly she put flour in the bowl. Secondly she added water. And finally she put the sugar in.

Answer:

60.96 cm

Step-by-step explanation:

1 feet = 12 inches

2 feet = x inches

Cross Multiply

x inches = 2 feet × 12 inches/1 feet

= 24 inches

From the question, we are told:

1 inch = 2.54cm

24 inches = y cm

Cross Multiply

y cm = 24 inches × 2.54cm/1 inch

y cm = 60.96 cm

Therefore, 2 feet is equivalent or equal to 60.96 cm

By the chain rule,

[tex]\dfrac{\partial w}{\partial r}=\dfrac{\partial w}{\partial x}\dfrac{\partial x}{\partial r}+\dfrac{\partial w}{\partial y}\dfrac{\partial y}{\partial r}+\dfrac{\partial w}{\partial z}\dfrac{\partial z}{\partial r}[/tex]

and similarly, [tex]\frac{\partial w}{\partial\theta}[/tex] is the same with [tex]r[/tex] replaced with [tex]\theta[/tex].

We have

[tex]\dfrac{\partial w}{\partial x}=y+z[/tex]

[tex]\dfrac{\partial w}{\partial y}=x+z[/tex]

[tex]\dfrac{\partial w}{\partial z}=x+y[/tex]

[tex]\dfrac{\partial x}{\partial r}=\cos\theta[/tex]

[tex]\dfrac{\partial y}{\partial r}=\sin\theta[/tex]

[tex]\dfrac{\partial z}{\partial r}=\theta[/tex]

Putting everything together, we get

[tex]\dfrac{\partial w}{\partial r}=(y+z)\cos\theta+(x+z)\sin\theta+(x+y)\theta[/tex]

Replace [tex]x,y,z[/tex] with their equivalent expressions in terms of [tex]r,\theta[/tex]:

[tex]\dfrac{\partial w}{\partial r}=r(\sin\theta+\theta)\cos\theta+r(\cos\theta+\theta)\sin\theta+r(\cos\theta+\sin\theta)\theta[/tex]

[tex]\dfrac{\partial w}{\partial r}=2r\theta\sin\theta+2r\theta\cos\theta+r\sin(2\theta)[/tex]

When [tex]r=4[/tex] and [tex]\theta=\frac\pi2[/tex], the derivative has a value of

[tex]\dfrac{\partial w}{\partial r}\left(4,\dfrac\pi2\right)=\boxed{4\pi}[/tex]

The same process will yield

[tex]\dfrac{\partial w}{\partial\theta}\left(4,\dfrac\pi2\right)=\boxed{-8\pi}[/tex]

The value of partial derivative are,

                    [tex]\frac{\partial w }{\partial r}(4,\frac{\pi}{2} )=4\pi[/tex]     and  [tex]\frac{\partial w }{\partial \theta}(4,\frac{\pi}{2} )=-8\pi[/tex]

It is given that,

                  [tex]w = xy + yz + zx, x = r cos(\theta), y = r sin(\theta), z = r\theta[/tex]

We have to find partial derivative.

            [tex]\frac{\partial w }{\partial r}=\frac{\partial w }{\partial x}*\frac{\partial x }{\partial r}+\frac{\partial w }{\partial y}*\frac{\partial y }{\partial r}+\frac{\partial w }{\partial z}*\frac{\partial z }{\partial z}\\\\\frac{\partial w }{\partial r}=(y+z)cos\theta+(x+z)sin\theta+(x+y)\theta\\\\\frac{\partial w }{\partial r}=2r\thetasin\theta+2r\thetacos\theta+rsin(2\theta)[/tex]

When [tex]r=4,\theta=\frac{\pi}{2}[/tex]

      [tex]\frac{\partial w }{\partial r}(4,\frac{\pi}{2} )=4\pi[/tex]

Similarly,

      [tex]\frac{\partial w }{\partial \theta}(4,\frac{\pi}{2} )=-8\pi[/tex]

Learn more about the chain rule of derivative here:

https://brainly.com/question/11549233

Answer:

-7/2

Step-by-step explanation:

2/3(6x - 18) = -26

divide by 2/3 or multiply by 3/2 (same thing)

6x - 18 = -39

add 18 to both sides

6x = -21

divide by 6

x = -21/6

simplify

x = -7/2

Answer: 9.46 grams

Step-by-step explanation:

Given: Number of muffins made in one batch = 1 dozen =12 ]

[ as 1 dozen = 12]

Also, in one batch the quantity of sugar = [tex]\dfrac14[/tex] pound

As there are 454 grams of sugar in a pound.

So,  in one batch the quantity of sugar = [tex]\dfrac14\times454=113.5\ grams[/tex]

i.e. in 12 muffins , there is 113.5 grams of sugar.

Then, in one muffin the quantity of sugar = (113.5 grams) ÷ 12

≈9.46 grams

Hence, there are 9.46 grams of sugar in 1 muffin.

Answer:

w ≥ 14

Step-by-step explanation:

Step 1: Solve

11 ≤ w - 3

11 + 3 ≤ w

14 ≤ w

Therefore w is bigger or equal to 14

Answer:

Step-by-step explanation:

[tex]11 \leqslant w - 3 \\ 11 + 3 \leqslant w \\ 14 \leqslant w[/tex]

Step 1 : Collect like terms and simplify

Answer =

w≤14

Answer:  see image below

Step-by-step explanation:

Draw a line and label it L

Plot three points on the line and label them, M, N, and Q.

I am using o to represent each point.

<---------o-------------o---------------o-----------> L

           M              N                 Q

Answer:

9.2 =x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp/ adj

tan 57 = x/6

6 tan 57 = x

9.239189783 = x

9.2 =x

Answer:

x = 9.2

Step-by-step explanation:

Step 1: Find out what primary trigonometry ratio is needed

The give us the adjacent and the angle.  We need to find the opposite value so we will use tangent

Step 2: Plug in information and solve

[tex]tan(57)=\frac{x}{6} \\x=6tan(57)\\x=9.239[/tex]

Therefore x= 9.2

Answer:

£107,714  > £107,674

Step-by-step explanation:

Given

£107,714  and £107,674

Required

Determine the relationship between them using > or <

From the given parameters, we understand that

£107,714  is greater than £107,674

The keyword greater than is represented mathematically with  >

Hence:

£107,714  is greater than £107,674

becomes

£107,714  > £107,674

Step-by-step explanation:

[tex] \frac{3}{4} = \frac{w}{28}[/tex]

[tex] \frac{3}{4} = \frac{w}{4 \times 7} [/tex]

[tex]3 = \frac{w}{7} [/tex]

[tex]w = 21[/tex]

Answer:

Hey there!

Are there any more options, because the probability is 7/12.

Also, this is a mutually inclusive event.

Let me  know if this helps :)

Step-by-step explanation:

A rational number is any number that can be divided (written as a fraction) by.

Examples: 1/2, 3, 5/9

*Irrational numbers: cannot be divided

Examples: π, 3.53465374765768957965...

Answer: A rational number is a number that can be expressed as the quotient (i.e. ratio or fraction) of two integers.

Step-by-step explanation: Integers are rational since any integer, n ,can be written as n/1 )Rational numbers are numbers that can be expressed as fractions whereas irrational numbers cannot be expressed as fractions A rational number is a number that terminates or ends. As in a perfect square like: 144; 36; 625 etc.More specifically, a rational number is a number that can be expressed as the ratio of two integers, where the denominator is not zero. 1.37, for instance, is rational because it can be expressed as 137 / 100.It is any whole number even if it's a negative number Any number that can be expressed as a fraction is a rational number whereas irrational numbers can't be expressed as a fractions.In mathematics, a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, p and q, with the denominator q not equal to zero. Since q may be equal to 1, every integer is a rational number.

Answer:

Table 1 and 2 represent a function

Step-by-step explanation:

Given

Table 1

x 5 10 11

y 3 9 15

Table 2

x 5 10 11

y 3 9 9

Table 3

x 5 10 10

y 3 9 15

Required

Determine which of the tables represent that y is a function of x

For a relation to be a function; the x values must be unique.

In other words, each x value must not be repeated;

Having said that;

Analyzing Table 1

Table 1

x 5 10 11

y 3 9 15

Note that the x rows are unique as no value were repeated;

Hence, Table 1 is a function

Table 2

x 5 10 11

y 3 9 9

Note that the x rows are unique as no value were repeated;

Hence, Table 2 is a function

Table 3

x 5 10 10

y 3 9 15

Note that the x rows are not unique because 10 was repeated twice;

Hence, Table 3 is not a function

Answer:

D. x= 10/3

Step-by-step explanation:

|x+3| = 4x -7

1. x+3 > 0 or  x> -3

Since 10/3 is greater than -3, it is accepted correct

2. x+3 < 0 or  x < -3

Here we have 4/5 > - 3, it is contradicting with x< -3 so this is not correct

So there is one solution:

Answer:

Mean=80

Median=120

Mode=61

Step-by-step explanation:

Mean= sum of the data ÷ number of the data

= 720÷9

= 80

Median= the middle number

= 120

Mode= the number which is repeated

= 61

Hope it helps you :)