is the square root of 5/8 rational or irrational

Answer:

Step-by-step explanation:

Area of a sector = [tex]\frac{\theta}{360} * \pi r^{2}\ where\ \pi r^{2} \ is\ the\ area\ of\ the\ circle[/tex]

theta is the sector's central angle

Area of the sector = [tex]\frac{\theta}{360} * \ area\ of\ a\ circle[/tex]

Given area of a circle = 18πin² and area of a sector = 6πin²

On substituting;

6π = [tex]\theta/360 * 18 \pi[/tex]

Dividing both sides by 18π we have;

1/3 = [tex]\theta/360[/tex]

[tex]3 \theta = 360\\\theta = 360/3\\\theta = 120^{0}[/tex]

The sector's central angle is 120°

Answer:

  On a graph, plot the line y = -x + 1, which has y-intercept = 1 and slope = -1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.

Step-by-step explanation:

Each equation is in slope-intercept form:

  y = mx + b . . . . . where m is the slope, and b is the y-intercept

The first equation is ...

  y = -x +1

so the slope is -1, and the y-intercept is +1.

__

The second equation is ...

  y = 2x +4

so the slope is 2, and the y-intercept is 4.

__

The slopes and intercepts are properly described in the last selection.

_______________________________

Hey!!

Answer:{2,4,5}

Explanation:

Let R be relation from A to B.The set of second components or the set of elements of B are called range.

Hope it helps..

_______________________________

Answer:

The answer is C

Step-by-step explanation:

did the quiz

Answer:

He is right it C just did the quiz let him have the brainly ;)

Step-by-step explanation:

Answer:

The value of the function f(x) at x=a can be determined by substituting a instead of x into the function expression.

1. When x=-1, then

f(-1) = 2 * (-1)^3 - 3 * (-1)^2 + 7 = -2 - 3 + 7 = 2.

2. When x=1, then

f(1) = 2 * 1^3 - 3 * 1^2 + 7 = 2 - 3 + 7 = 6.

3. When x=2, then

f(-1) = 2 * 2^3 - 3 * 2^2 + 7 = 16 - 12 + 7 = 11.

Step-by-step explanation:

Answer:

f(−1) =✔ 2

f(1) = ✔ 6

f(2) =✔ 11

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let x be the random variable representing the dollar value of unusual activity for a customer in a month. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = standard deviation

From the information given,

µ = 250

σ = √variance = √2400 = 48.99

a) the probability of $250 to $294 in unusual activity in a month is expressed as

P(250 ≤ x ≤ 294)

For x = 250,

z = (250 - 250)/48.99 = 0

Looking at the normal distribution table, the probability corresponding to the z score is 0.5

For x = 294

z = (294 - 250)/48.99 = 0.9

Looking at the normal distribution table, the probability corresponding to the z score is 0.8159

Therefore,

P(250 ≤ x ≤ 294) = 0.8159 - 0.5 = 0.3159

b) the probability of more than $294 in unusual activity in a month is expressed as

P(x > 294) = 1 - P(x < 294)

P(x > 294) = 1 - 0.8159 = 0.1841

c) since n = 10, the formula becomes

z = (x - µ)/(σ/n)

z = (294 - 250)/(48.99/√10) = 2.84

Looking at the normal distribution table, the probability is 0.9977

Therefore, the probability that at least one of these customers exceeds $294 in unusual activity in a month is

1 - 0.9977 = 0.0023

Answer: Jose should have the factory make 50 FS20 stereo tuners and 14 S100 stereo tuners each week to make the most profit

Step-by-step explanation:

Since each S100 takes 8 ounces of plastic and 4 ounces of metal. Each FS20 requires 4 ounces of plastic and 6 ounces of metal. And the factory has 312 ounces of plastic, 372 ounces of metal available, then,

For plastic

8 ounces + 4 ounces = 12 ounces

The number of stereo tuners it can produce will be

312/12 = 26 stereo tuners

For metal

4 ounces + 6 ounces = 10 ounces

The number of stereo tuners it can produce will be

372/10 = 37.2 = 37 approximately

Since FS20 generate more profit than S100, let assume that Jose produces 50 FS20 by consuming

4 × 50 = 200 ounces of plastic

6 × 50 = 300 ounces of metal

The remaining plastic will be

312 - 200 = 112

The remaining plastic will be

372 - 300 = 72

Divide 112 by 8 in order to make S100

112/8 = 14

Also 72/4 = 18.

Therefore, Jose should have the factory make 50 FS20 stereo tuners and 14 S100 stereo tuners each week to make the most profit

Answer:

17

Step-by-step explanation:

k(x)=-2x^2+10x+5

k(3)=-2(3)^2+10(3)+5

k(3)=-2(9)+30+5

k(3)=-18+35

     = 17

Answer:

71

Step-by-step explanation:

-2(3)^2+ 10(3)+5

So first you multiply the -2 by the 3

(-6)^2+10(3)+5

then you do the exponents

36+10(3)+5

then you multiply the 10 by 3

36+30+5

then you would add 36 and 30

66+5

then add the 5

71

Answer:

[tex]\frac{49}{15}[/tex]

Step-by-step explanation:

[tex]\frac{2}{5} \times \frac{7}{-6} \times -7[/tex]

[tex]\frac{2}{5} \times \frac{7}{-6} \times \frac{-7}{1}[/tex]

[tex]\frac{2 \times 7 \times -7}{5 \times -6 \times 1}[/tex]

[tex]\frac{-98}{-30}=\frac{98}{30}=\frac{49}{15}[/tex]

Answer:

-3.26 repeating

Step-by-step explanation:

2×7=14

5×(-6) = -30

14/30×(-7)= -3.26 repeating

Answer:

53

Step-by-step explanation:

8•7 is 56

56 - 3 is 53

Answer:

53

Step-by-step explanation:

z = 7

8z is the same as saying 8×z

8×7-3 (do multiplication first)

56-3 = 53

Answer:

M.

Step-by-step explanation:

Answer & Step-by-step explanation:

4(y + 2) - 2

Distribute 4 to (y + 2)

4y + 8 - 2

Combine like terms

4y + 6

So, your answer in the simplest form is 4y + 6

Answer:

True

True

Step-by-step explanation:

The unknown parameters are treated as variable and data serve as coefficients. The random variables are value whose outcome depends on some random event. The θ can exist when n ≥ 0. A sample mean is a sequence which has normal distribution and n ≥ 1. The sample average of X-n follows normal distribution for all integer and n is greater or equal to 1.

The given statement is True

The unknown parameters should be considered variable and data represent the coefficients. The random variables refers to the value where  outcome based on some random event. The θ could exist at the time when n ≥ 0. A sample mean represent the sequence that contains normal distribution and n ≥ 1.

Learn more about distribution here: https://brainly.com/question/24520301

Answer:

4

Step-by-step explanation:

The x-intercept occurs when y=0, if you think about it graphically.  Plug y=o into your equation:

10x - 5(0) = 40

10x = 40 (divide each side by 10)

x=4

Answer:

80 milk chocolates

Step-by-step explanation:

Probability of choosing a dark chocolate= number of dark

chocolate/number of total

chocolate

But the probability of choosing dark chocolate= 2/9

The number of dark chocolate= 24

Total chocolate= number of dark

chocolate/probability

of choosing dark

chocolate

Total chocolate= 24/(2/9)

Total chocolate=( 24*9)/2

Total chocolate= 108

Number of milk chocolate= total- dark

Number of milk chocolate

= 108-28

= 80

Answer:

[tex]cos=\frac{4}{5}[/tex]

Step-by-step explanation:

Cosine is the adjacent side over the hypotenuse (You can remember sin, cos, and tan by using sohcahtoa or sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite over adjacent). I think a picture would help, too.

I attached a picture of what I think the triangle would look like.

If the picture is right (we're assuming it is) and going with what we're given (the triangle was addressed as triangle XYZ, meaning that angle Y is in the middle and that's the one we'll use).

Looking at my picture then:

[tex]cos=\frac{64}{80} \\cos=\frac{8}{10} \\cos=\frac{4}{5}[/tex] .

Answer:

x = -7.33        OR         x = [tex]\frac{-22}{3}[/tex]

y = 13

Step-by-step explanation:

→You can use the substitution method. First, make y by itself in (-2 + 2y = 24):

-2 + 2y = 24

2y = 26

y = 13

→Then, plug in 13 for y into the other equation:

3x + 2y = 4

3x + 2(13) = 4

3x + 26 = 4

3x = -22

x = -7.33        OR         x = [tex]\frac{-22}{3}[/tex]

Answer:

They got £84 altogether.

Step-by-step explanation:

We can see that Richard get's 6 parts and Stephen gets 1 part. We can subtract these two to get 5 parts. We know that five parts equals £60, so we can divide by 5 to get 1 part equals £12. We are looking for the amount they got altogether, which is equal to 7 parts, 6 parts + 1 part. We multiply £12 by 7, leaving us with £84, which is our answer.

Answer:

1.75

Step-by-step explanation:

Divide the ounces by 16 to get the value.

Expectation is linear, meaning

E(a X + b Y) = E(a X) + E(b Y)

= a E(X) + b E(Y)

If X = 1 and Y = 0, we see that the expectation of a constant, E(a), is equal to the constant, a.

Use this property to compute the expectations:

E(X + 10) = E(X) + E(10) = $110

E(5Y) = 5 E(Y) = $450

E(X + Y) = E(X) + E(Y) = $190

Variance has a similar property:

V(a X + b Y) = V(a X) + V(b Y) + Cov(X, Y)

= a^2 V(X) + b^2 V(Y) + Cov(X, Y)

where "Cov" denotes covariance, defined by

E[(X - E(X))(Y - E(Y))] = E(X Y) - E(X) E(Y)

Without knowing the expectation of X Y, we can't determine the covariance and thus variance of the expression a X + b Y.

However, if X and Y are independent, then E(X Y) = E(X) E(Y), which makes the covariance vanish, so that

V(a X + b Y) = a^2 V(X) + b^2 V(Y)

and this is the assumption we have to make to find the standard deviations (which is the square root of the variance).

Also, variance is defined as

V(X) = E[(X - E(X))^2] = E(X^2) - E(X)^2

and it follows from this that, if X is a constant, say a, then

V(a) = E(a^2) - E(a)^2 = a^2 - a^2 = 0

Use this property, and the assumption of independence, to compute the variances, and hence the standard deviations:

V(X + 10) = V(X)  ==>  SD(X + 10) = SD(X) = $90

V(5Y) = 5^2 V(Y) = 25 V(Y)  ==>  SD(5Y) = 5 SD(Y) = $40

V(X + Y) = V(X) + V(Y)  ==>  SD(X + Y) = √[SD(X)^2 + SD(Y)^2] = √8164 ≈ $90.35

Answer:

y = -1/2x - 2

Step-by-step explanation:

If it's parallel, that means that the slope is the opposite of the one in the given equation, meaning that 2 would be flipped and turned negative into -1/2.

Then, fill in the x and y values to get the y-intercept.

1 = -1/2(-6) + b

1 = 3 + b

-2 = b

So your answer is y = -1/2x - 2

Answer:

225 I believe because if he has $90 that is 2/5 so add another 90 whitch is 2/5 as well and divide 90 by 2 and to get 45 which all adds up to 225

Answer:

The one with the better deal would be 30 ride tickets for $22.50 this is because you pay less money for more rides.

Step-by-step explanation:

First you divide 20 by 14. Doing this will give you the cost of a ride per ticket.

20/14 = 1.42

Then you do the same thing to 30 and 22.50.

30/22.50 = 1.30

Last you compare which deal has less money per ride.

1.42 > 1.30

Answer:

5x^3(to the power of 3)

Step-by-step explanation:

10x^5/2x^2

divide the 10/2 like normal to get 5

x^5/x^2 (subtract the powers 5-2 when dividing powers)

you would get 5x^3

Answer:

x = ±5

Step-by-step explanation:

x^2 – 9 = 16

Add 9 to each side

x^2 – 9+9 = 16+9

x^2 = 25

Take the square root of each side

sqrt(x^2) = ±sqrt(25)

x = ±5

Answer:

[tex]x = 5 \: \: \: or \: \: x = - 5[/tex]

Step-by-step explanation:

[tex] {x}^{2} - 9 = 16 \\ {x}^{2} = 16 + 9 \\ {x}^{2} = 25 \\ x = \sqrt{25} \\ x = 5 \\ x = - 5[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Complete Question

Let A be an n x n matrix, b be a nonzero vector, and x_0 be a solution vector of the system Ax = b. Show that x is a solution of the non-homogeneous system Ax = b if and only if y = x - x_0 is a solution of the homogeneous system Ay = 0.

Answer:

Step-by-step explanation:

From the question we are told that

    A is an  n × n matrix

   b is a zero vector

  [tex]x_o[/tex] us the solution vector of  [tex]Ax = b[/tex]

Which implies that  

     [tex]Ax_o = b[/tex]

So first we show that

  if [tex]x[/tex] is the solution matrix of [tex]Ax = b[/tex]

  and  [tex]y= x-x_o[/tex] is the solution of  [tex]Ay = 0[/tex]

Then

    [tex]A(x-x_o) = 0[/tex]

=>   [tex]Ax -Ax_o = 0[/tex]

=>   [tex]b-b = 0[/tex]

Secondly to show that

   if  [tex]y= x-x_o[/tex] is the solution of  [tex]Ay =0[/tex]

  then x is the solution of the non-homogeneous system

    [tex]Ax = b[/tex]

Now we know that [tex]y = x-x_o[/tex] is the solution of  [tex]Ay =0[/tex]

So

     [tex]Ay = 0[/tex]

=>  [tex]A(x- x_o) = 0[/tex]

=>   [tex]Ax - Ax_o = 0[/tex]

=>   [tex]Ax - b = 0[/tex]

=>    [tex]Ax = b[/tex]

Thus this has been proved

The volume of the solid (call it S) in Cartesian coordinates is

[tex]\displaystyle\iiint_S\mathrm dV=\int_{-1}^1\int_{-\sqrt{1-x^2}}^{\sqrt{1-x^2}}\int_{(x^2+y^2)^2-1}^{4-4(x^2+y^2)}\mathrm dz\,\mathrm dy\,\mathrm dx[/tex]

but I suspect converting to cylindrical coordinates would make the integral much more tractable.

Take

[tex]\begin{cases}x=r\cos\theta\\y=r\sin\theta\\z=z\end{cases}\implies\mathrm dV=r\,\mathrm dr\,\mathrm d\theta\,\mathrm dz[/tex]

Then

[tex]4-4(x^2+y^2)=4-4r^2=4(1-r^2)[/tex]

[tex](x^2+y^2)^2-1=(r^2)^2-1=r^4-1[/tex]

and the integral becomes

[tex]\displaystyle\iiint_S\mathrm dV=\int_0^{2\pi}\int_0^1\int_{r^4-1}^{4(1-r^2)}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta[/tex]

[tex]=\displaystyle2\pi\int_0^1r(4(1-r^2)-(r^4-1))\,\mathrm dr[/tex]

[tex]=\displaystyle2\pi\int_0^1r(5-4r^2-r^4)\,\mathrm dr[/tex]

[tex]=\displaystyle2\pi\int_0^15r-4r^3-r^5\,\mathrm dr[/tex]

[tex]=2\pi\left(\dfrac52-1-\dfrac16\right)=\boxed{\dfrac{8\pi}3}[/tex]

Answer:

112

Step-by-step explanation:

Difference between each 4,8,7,5,1

Add numbers next to each other in pairs = 12

So 12-1= 11 and

101+11=112

Answer:

given

3/4×1/7

=3×1/4×7

=3/28

thus the answer is 3/28

[tex]answer = \frac{3}{28} \\ solution \\ \frac{3}{4} \times \frac{1}{7} \\ = \frac{3 \times 1}{4 \times 7} \\ = \frac{3}{28} \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]

Answer:

There should be no pattern in the residual plot.

Step-by-step explanation

Remember a residual plot is calculating if a linear model is appropriate or not and since the engineer is trying to find a linear relationship with his air filters then he should be looking for no pattern.

Here, we are required to determine what should be apparent in the residual plot.

The residual plot will have a negative slope, i.e the residual plot descends from the top left to the bottom right.

According to the Engineer's believe, the thicker the air filter, the less pollution that gets through it.

By plotting each of the quantities on either of x and y axis on the residual plot, The residual plot therefore, has a negative slope.

Read more:

https://brainly.com/question/7412322