Brainliest to fastest answer

Answer:

\( \frac{1}{12} \)

Step-by-step explanation:

\( \frac{2}{9} \div \frac{8}{3} \\ = \: \frac{1}{12}\)

So, if you divide 2/9 by 1/12, you'll get 8/3

Answered by GAUTHMATH

Answer:

2.98

Step-by-step explanation:

First find 3% of 16.05 which is 0.48.

Then add 0.48 to 16.05 which is 16.53.

Then multiply .18 by 16.53 which gets you 2.98

Hope it helps

Answer:

To find the amount of the sales tax, we need to multiply the bill amount by the tax rate of 3% or 0.03:

Sales tax = 0.03 x $16.05 = $0.48

To find the total amount of the bill after the sales tax was added, we need to add the bill amount to the sales tax:

Total bill = $16.05 + $0.48 = $16.53

To find the amount of the tip, we need to calculate 18% of the total bill after the sales tax was added:

Tip = 0.18 x $16.53 = $2.98

Rounding to the nearest cent, Penelope left a tip of $2.98.

Step-by-step explanation:

4) 2a²+a -11

1) If C = 2a²-5 and D = 3-a, then C -2D =?

2) D = 3-a

a=3-D Writing that for a

C -2D Plugging into C and D

2a² -5 - 2(3-a) Applying distributive property

2a²-5 -6 +a Combining like terms

2a² -11 +a

2a²+a -11

Answer:

We can start by using the second equation to eliminate x:

2x + 5y - 2z = 3

2x = -5y + 2z + 3

x = (-5/2)y + z + 3/2

Now we can substitute this expression for x into the first and third equations:

x + y + z = 4

(-5/2)y + z + 3/2 + y + z = 4

(-5/2)y + 2z = 5/2

x + 7y - 7z = 5

(-5/2)y + z + 3/2 + 7y - 7z = 5

(9/2)y - 6z = 7/2

Now we have a system of two equations with two variables, (-5/2)y + 2z = 5/2 and (9/2)y - 6z = 7/2. We can use any method to solve for y and z, such as substitution or elimination. However, we will find that the system is inconsistent, meaning there is no solution that satisfies both equations.

Multiplying the first equation by 9 and the second equation by 5 and adding them, we get:

(-45/2)y + 18z = 45/2

(45/2)y - 30z = 35/2

Adding these two equations, we get:

-12z = 40/2

-12z = 20

z = -5/3

Substituting z = -5/3 into (-5/2)y + 2z = 5/2, we get:

(-5/2)y + 2(-5/3) = 5/2

(-5/2)y - 10/3 = 5/2

(-5/2)y = 25/6

y = -5/12

Substituting y = -5/12 and z = -5/3 into any of the original equations, we get:

x + y + z = 4

x - 5/12 - 5/3 = 4

x = 29/12

Therefore, the solution is (x, y, z) = (29/12, -5/12, -5/3). However, if we substitute these values into any of the original equations, we will find that it does not satisfy the equation. For example:

2x + 5y - 2z = 3

2(29/12) + 5(-5/12) - 2(-5/3) = 3

29/6 - 5/2 + 5/3 ≠ 3

Since there is no solution that satisfies all three equations, the system is inconsistent.

Step-by-step explanation:

Answer:

See below for proof.

Step-by-step explanation:

A system of equations is not consistent when there is no solution or no set of values that satisfies all the equations simultaneously. In other words, the equations are contradictory or incompatible with each other.

Given system of equations:

\(\begin{cases}x+y+z = 4\\2x+5y-2z =3\\x+7y-7z =5\end{cases}\)

Rearrange the first equation to isolate x:

\(x=4-y-z\)

Substitute this into the second equation to eliminate the term in x:

\(\begin{aligned}2x+5y-2z&=3\\2(4-y-z)+5y-2z&=3\\8-2y-2z+5y-2z&=3\\-2y-2z+5y-2z&=-5\\5y-2y-2z-2z&=-5\\3y-4z&=-5\end{aligned}\)

Subtract the first equation from the third equation to eliminate x:

\(\begin{array}{cccrcrcl}&x&+&7y&-&7z&=&5\\\vphantom{\dfrac12}-&(x&+&y&+&z&=&4)\\\cline{2-8}\vphantom{\dfrac12}&&&6y&-&8z&=&1\end{aligned}\)

Now we have two equations in terms of the variables y and z:

\(\begin{cases}3y-4z=-5\\6y-8z=1\end{cases}\)

Multiply the first equation by 2 so that the coefficients of the variables of both equations are the same:

\(\begin{cases}6y-8z=-10\\6y-8z=1\end{cases}\)

Comparing the two equations, we can see that the coefficients of the y and z variables are the same, but the numbers they equate to is different. This means that there is no way to add or subtract the equations to eliminate one of the variables.

For example, if we subtract the second equation from the first equation we get:

\(\begin{array}{crcrcl}&6y&-&8z&=&-10\\\vphantom{\dfrac12}-&(6y&-&8z&=&\:\:\;\;\:1)\\\cline{2-6}\vphantom{\dfrac12}&&&0&=&-11\end{aligned}\)

Zero does not equal negative 11.

Since we cannot eliminate the variable y or z, we cannot find a unique solution that satisfies all three equations simultaneously. Therefore, the system of equations is inconsistent.

Answer:

BRO, u dont need to be a god :D, This is simple math and you just need to use your brains

Step-by-step explanation:

Given is a polynomial, and the values of the variables in it are given by showing what set are they an element of, right? It just gets easier from here

They tell us that 'z' is an element of set C, which stands for Complex Numbers.

And they also tell us that 'a' is an element of set Z, which stands for Integers, which are just numbers with a sign :).

They have also given us a root (solution) to the polynomial, which is also a complex number.

The two statements given are just there for us to verify that we are on the right track to the solution.

We can see that (z = 3 + i) which of course is a complex number, due to the presence of 'i', and 'a' is an integer for when we find its value.

Put it all together and we will get the answer.

Like this,

take the given value of 'z' and place it into the polynomial given, now keep your eyes open here. They said the value of z is as such when the polynomial is an equation which equals 0, so hence we get this:

P(z) = a(3+i)³ - 37(3+i)² + 66(3+i) - 10 = 0,

now just go on simplifying,

=> a(3³+i³+3×3²i+3×3i²) - 37(3²+2×3×i+i²) + 66×3 + 66×i - 10 = 0

=> a(27-i+27i-9i) - 37(9+6i-1) + 198 + 66i - 10 = 0

=> a(27+17i) - 37(8+6i) + 188 + 66i = 0

=>  a(27+17i) = 296 + 222i - 188 - 66i

=> a(27+17i) = 108 + 156i

=> a = (108+156i) / (27+17i)

=> a = (108+156i)(27-17i) / (27)² - (17i)²

=> a = (5568 + 2376i) / (699 + 289)

=> a = 5568 + 2376i / 1488

DONNEEE....yayyyy....lol

The rate at which the volume of the cylinder is changing is 600 mm^3/min, and the rate at which the surface area is changing is 240π mm^2/min.

To find the rate at which the volume and surface area of the cylinder are changing, we can use the given formulas for volume and surface area and differentiate them with respect to time. Let's calculate the rates at the moment when the radius of the base is 10 mm.

Given:

Radius rate of change: dr/dt = 3 mm/min

Height: h = 20 mm

Radius: r = 10 mm

Volume of the cylinder (V) = \(r^2h\)

Differentiating with respect to time (t), we have:

dV/dt = 2rh(dr/dt) + \(r^2\)(dh/dt)

Since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dV/dt = 2(10)(20)(3) + (10^2)(0)

dV/dt = 600 + 0

dV/dt = 600 mm^3/min

Therefore, the rate at which the volume of the cylinder is changing at the given moment is 600 mm^3/min.

Surface area of the cylinder (SA) = 2πrh + 2π\(r^2\)

Differentiating with respect to time (t), we have:

dSA/dt = 2πr(dh/dt) + 2πh(dr/dt) + 4πr(dr/dt)

Again, since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dSA/dt = 2π(10)(0) + 2π(20)(3) + 4π(10)(3)

dSA/dt = 0 + 120π + 120π

dSA/dt = 240π mm^2/min

Therefore, the rate at which the surface area of the cylinder is changing at the given moment is 240π mm^2/min.

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You have the following expression:

4 2/6 - 5/6

consider that 5/6 = 2/6 + 3/6, then:

4 2/6 - 5/6 = 4 2/6 - (2/6 + 3/6) = 4 2/6 - 2/6 - 3/6 = 4 3/6 = 4 1/2

Hence, the result is 4 1/2

Answer:

HCF: 1

LCM: 84

Step-by-step explanation:

7 is a  prime number. Nothing but 1 and 7 divide into which means that twelve and 7 have no highest common factor but 1.

The lowest common multiply (because 12 and 7 are prime to each other ) is 12 * 7 = 84

Answer:

LCM = 84 GCF = 1

Step-by-step explanation:

LCM of 7 and 12 is 84.

GCF(7,12) = 1

LCM(7,12) = ( 7 × 12) / 1

LCM(7,12) = 84 / 1

LCM(7,12) = 84

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).

GCF of 7 and 12 is 1. Now calculate the prime factors of 7 and 12, then find the greatest common factor (greatest common divisor) of the numbers.

To find the GCF of two numbers: List the prime factors of each number. Multiply those factors both numbers have in common. If there are no common prime factors, the GCF is 1.

Step-by-step explanation:

Guess "This afternoon l,he has the same number of annuals and perennials left to plant will take more time to plant.

Answer:

it'd be $1.06 rounded to the nearest thousendth or $1.06400

Step-by-step explanation:

13.30*8/100=Your Answer

Answer:

He used 5 47 cent stamps and 8 7 cent stamps

subtract 0.47 from 2.91 until you get 0.56 then you begin to subtract 0.07 to get 0.

Step-by-step explanation:

simple interest formula is I = p × r × t / 100

$32 = p × 8 × 3 / 100

$32 = 24p / 100

32 × 100 = 24p

3200 / 24 = $133.33

The differentiation of \(e\x^{x}\) is \(e\x^{x}\) proved using the first law of differentiation or limit law.

A technique for determining a function's derivative is differentiation. Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of change based on one of its variables. The most typical illustration is velocity, which is the rate at which a distance changes in relation to time.

Differentiation is the ratio of a slight change in one quantity to a little change in another that depends on the first quantity. Calculus' major emphasis on the differentiation of a function makes it one of the subject's key ideas. Differentiation is the process of determining the maximum or lowest value of a function, the speed and acceleration of moving objects, and the tangent of a curve. If y = f(x) and f(x) is differentiable, then f'(x) or dy/dx is used to indicate the differentiation.

\(\frac{d}{dx}e\x^{x}\) using first order or limits to differentiate we get

for \(\lim_{h \to0} \frac{f(x+h) - f(x)}{h} = \frac{d}{dx}f(x)\)

therefore,

\(\lim_{h \to 0} \frac{e\x^{(x +h)}- e\x^{x} }{h} \\\) = \(\lim_{h \to 0} \frac{e\x^{x}(e\x^{h}-1 ) }{h}\) = \(\lim_{h \to 0} \frac{e\x^{x}*e\x^{h} }{1} \\\) ( using L-Hospital)

\(\lim_{h \to 0} e\x^{x} * e\x^{h} = e\x^{x} (proved)\)

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Answer:

1. 33%

2. 28

3. 62.5

Step-by-step explanation:

Based on the data recorded by Anna on Saturday, we can estimate the number of people expected to visit The Youth Wing on Sunday.

Let's calculate the proportion of visitors to The Youth Wing compared to the total number of visitors on Saturday:

\(\displaystyle \text{Proportion} = \frac{\text{Visitors to The Youth Wing on Saturday}}{\text{Total visitors on Saturday}} = \frac{382}{382 + 461 + 355}\)

Next, we'll apply this proportion to the total number of visitors on Sunday to estimate the number of people expected to go to The Youth Wing:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \text{Proportion} \times \text{Total visitors on Sunday}\)

Now, let's substitute the values into the equation and calculate the estimated number of visitors to The Youth Wing on Sunday:

\(\displaystyle \text{Proportion} = \frac{382}{382 + 461 + 355}\)

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \text{Proportion} \times 800\)

Calculating the proportion:

\(\displaystyle \text{Proportion} = \frac{382}{382 + 461 + 355} = \frac{382}{1198}\)

Calculating the estimated number of visitors to The Youth Wing on Sunday:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \frac{382}{1198} \times 800\)

Simplifying the equation:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} \approx \frac{382 \times 800}{1198}\)

Now, let's calculate the approximate number of visitors to The Youth Wing on Sunday:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} \approx 254\)

Therefore, based on the data recorded on Saturday, we can estimate that around 254 people should be expected to go to The Youth Wing on Sunday.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

the area of the shape is 48m

Step-by-step explanation:

10*4=40

2*4=8

40+8=48

brake it up into two triangles. one is a triangle that is 10m tall and 8m wide at the top. you can solve that by doing 4*10=40. the other triangle is 4m wide at the bottom and 2m tall. you can solve that by doing 2*4=8. and 40+8=48.

Answer:

\(2\sqrt{x+1}-3\\domain:[-1, \infty)\)

Step-by-step explanation:

\(g(h(x)) = 2(\sqrt{x+1})-3\\g(h(x)) = 2\sqrt{x+1} - 3\\\)

the function is only defined when (x+1) >= 0 (since square root) so the domain is when x >= -1

Step-by-step explanation:

angles 1 and 3 are supplementary angles (together they have 180°), because together they make sure that line f is a straight line, and there are no segments of the line angling "off". a straight line can be always seen as prolonged diameter of a circle. each side represents a half-circle with 180°.

a line intersecting 2 parallel lines has the same intersection angles with both lines, as parallel lines perfectly copy each other's behavior and attributes except for the y-intercept.

the angles of intersecting lines are the same in both sides of any of the 2 lines, they are just left-right mirrored.

therefore,

angle 1 = 82° = angle 2

angle 3 = 180 - angle 1 = 180 - 82 = 98° = angle 4

Answer:

  ∠1 = 82°

  ∠3 = 98°

Step-by-step explanation:

You want the measures of angles 1 and 3 where a transversal crosses parallel lines and one of the angles is marked as 82°.

The "alternate interior angles theorem" tells you that the alternate interior angles created by a transversal crossing parallel lines are congruent. Hence angle 1 is congruent to the one marked 82°.

  ∠1 = 82°

The angles of a linear pair are supplementary. Angles 1 and 3 form a linear pair, so ...

  ∠3 = 180° -∠1 = 180° -82°

  ∠3 = 98°

__

Additional comment

"Interior" angles are between the parallel lines. "Exterior" angles are outside the parallel lines. "Alternate" angles are on opposite sides of the transversal. "Consecutive" or "same-side" angles are on the same side of the transversal. (Angles 2 and 4 are "consecutive".)

"Corresponding" angles are in the same direction from the point of intersection of the transversal with the parallel lines. In this figure, angle 2 and the one marked 82° are corresponding. Corresponding angles are congruent. If you remember that, and that vertical angles are congruent, and linear pairs are supplementary, you can figure out all of the other relationships.

In the end, when the lines are parallel, all of the acute angles are congruent, and all of the obtuse angles are congruent. The acute and obtuse angles are supplementary. The angle relations themselves are pretty simple; the rest is a lot of vocabulary.

Answer:

x= -1/2

Step-by-step explanation:

BECAUSE IT JUST DOES!!!!

Answer:

it is £16490.36

Step-by-step explanation:

since £156.78 is 100%, £16470.45 by 3.5 is £16490.36

Answer:

it's 17,046.92

Step-by-step explanation:

that's what my calculations said

Answer:

Step-by-step explanation:

diameter  = 12 cm

r = 12/2 = 6 cm

\(Area \ of \ semicircle = \dfrac{1}{2}\pi r^{2}\\\\\\=\dfrac{1}{2}* 3.14*6*6\\\\\\= 56.52 \ cm^{2}\)

The asnwer is C

for finding domain look at just x-axis from left to right , because there are arrows , so domain is all real numbers or from negative infinity to positive infinity

Please give brainliest

Answer:

1:27

2:54

3:81

4:108

5:135

Step-by-step explanation:

If this answer helped you then please consider liking this and marking it as brainliest :)

Answer:

the son age is 13band Evans age is 52 years old at present day

Dan is 12 years old.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let the Age of Dan is x years

Mr. Evans Age = 4x

If Mr. Evans was 46 years old 2 years ago

The, Present age of Mr. Evans = 48 years

So, Dan's Age = 48/4

                        = 12 years.

Hence, Dan is 12 years old.

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Answer's:

27. vertex: (-4, -5) and x-intercept: (√5 - 4, 0) and (-√5 - 4, 0)

28. vertex: (-5, -11) and x-intercept: (√11 - 5, 0) and (-√11 - 5, 0)

29. vertex: (1, 16) and x-intercept: (-3, 0) and (5, 0)

To find vertex, the quadratic function should be in f(x) = a(x - h)² + k form.

where:

27.

g(x) = x² + 8x + 11

completing square:

g(x) = (x² + 8x) + 11

g(x) = (x + 4)² + 11 - (4)²

g(x) = (x + 4)² - 5

g(x) = (x - (-4))² - 5

To find x-intercept: set y = 0

\(\sf (x + 4)^2 - 5 = 0\)

\(\sf (x + 4)^2 = 5\)

\(\sf x + 4 = \pm \sqrt{5}\)

\(\sf x= \sqrt{5}-4, \ - \sqrt{5}-4\)

Hence, the vertex is (-4, -5) and x intercepts (√5 - 4, 0) and (-√5 - 4, 0).

28.

f(x) = x² + 10x + 14

completing square:

f(x) = (x² + 10x) + 14

f(x) = (x + 5)² + 14 - (5)²

f(x) = (x + 5)² - 11

Find x intercept, so y = 0:

\(\sf (x + 5)^2 - 11 = 0\)

\(\sf (x + 5)^2 = 11\)

\(\sf x + 5 = \pm\sqrt{11}\)

\(\sf x = \sqrt{11} -5, \ -\sqrt{11} -5\)

Hence, the vertex is (-5, -11) and x intercepts (√11 - 5, 0) and (-√11 - 5, 0).

29.

f(x) = -(x² - 2x - 15)

f(x) = -((x² - 2x)) + 15

f(x) = -(x - 1)² + 15 + (-1)²

f(x) = -(x - 1)² + 16

Find the x-intercept's:

\(\sf -(x - 1)^2 + 16 = 0\)

\(\sf -(x - 1)^2 = -16\)

\(\sf (x - 1)^2 = 16\)

\(\sf x - 1 = \pm\sqrt{16}\)

\(\sf x - 1 = \pm4\)

\(\sf x = -3, \ 5\)

Hence, the vertex is (1, 16) and x intercepts (-3, 0) and (5, 0).

Answer:

\(\textsf{27.} \quad \textsf{Vertex}:(-4,-5) \quad \textsf{$x$-intercepts}: x=-4+\sqrt{5}, \:\:x=-4-\sqrt{5}\)

\(\textsf{28.} \quad \textsf{Vertex}:(-5,-11) \quad \textsf{$x$-intercepts}: x = -5+\sqrt{11}, \:\:x=-5-\sqrt{11}\)

\(\textsf{29.} \quad \textsf{Vertex}:(1,16) \quad \textsf{$x$-intercepts}: x = 5, \:\:x=-3\)

Step-by-step explanation:

Vertex form of a quadratic function:

\(\boxed{y=a(x-h)^2+k}\)

where:

Given function:

\(g(x)=x^2+8x+11\)

Change to vertex form by completing the square.

Add and subtract the square of half the coefficient of x:

\(\implies g(x)=x^2+8x+11 +\left(\dfrac{8}{2}\right)^2-\left(\dfrac{8}{2}\right)^2\)

\(\implies g(x)=x^2+8x+11 +16-16\)

\(\implies g(x)=x^2+8x+16+11-16\)

\(\implies g(x)=x^2+8x+16-5\)

Factor the perfect trinomial:

\(\implies g(x)=(x+4)^2-5\)

Therefore, the vertex is (-4, -5).

To find the x-intercepts, set the function to zero and solve for x:

\(\begin{aligned}g(x) & = 0\\\implies (x+4)^2 -5 & = 0\\(x+4)^2 & = 5\\\sqrt{(x+4)^2} & = \sqrt{5}\\x+4&=\pm\sqrt{5}\\x+4-4&=-4\pm\sqrt{5}\\x&=-4\pm\sqrt{5}\end{aligned}\)

Therefore, the x-intercepts are:

\(x = -4+\sqrt{5}, \quad x = -4-\sqrt{5}\)

---------------------------------------------------------------------

Given function:

\(f(x)=x^2+10x+14\)

Change to vertex form by completing the square.

Add and subtract the square of half the coefficient of x:

\(\implies f(x)=x^2+10x+14+\left(\dfrac{10}{2}\right)^2-\left(\dfrac{10}{2}\right)^2\)

\(\implies f(x)=x^2+10x+14+25-25\)

\(\implies f(x)=x^2+10x+25+14-25\)

\(\implies f(x)=x^2+10x+25-11\)

Factor the perfect trinomial:

\(\implies f(x)=(x+5)^2-11\)

Therefore, the vertex is (-5, -11).

To find the x-intercepts, set the function to zero and solve for x:

\(\begin{aligned}f(x) & = 0\\\implies (x+5)^2 -11 & = 0\\(x+5)^2 & = 11\\\sqrt{(x+5)^2} & = \sqrt{11}\\x+5&=\pm\sqrt{11}\\x+5-5&=-5\pm\sqrt{11}\\x&=-5\pm\sqrt{11}\end{aligned}\)

Therefore, the x-intercepts are:

\(x = -5+\sqrt{11}, \quad x = -5-\sqrt{11}\)

---------------------------------------------------------------------

Given function:

\(f(x)=-(x^2-2x-15)\)

Change to vertex form by completing the square.

Add and subtract the square of half the coefficient of x:

\(f(x)=-\left(x^2-2x-15+\left(\dfrac{-2}{2}\right)^2-\left(\dfrac{-2}{2}\right)^2\right)\)

\(f(x)=-\left(x^2-2x-15+1-1\right)\)

\(f(x)=-\left(x^2-2x+1-15-1\right)\)

\(f(x)=-\left(x^2-2x+1-16\right)\)

Factor the perfect trinomial:

\(f(x)=-\left((x-1)^2-16\right)\)

Simplify:

\(f(x)=-(x-1)^2+16\)

Therefore, the vertex is (1, 16).

To find the x-intercepts, set the function to zero and solve for x:

\(\begin{aligned}f(x) & = 0\\\implies -(x-1)^2 +16 & = 0\\(x-1)^2 -16 & = 0\\(x-1)^2 & = 16\\\sqrt{(x-1)^2} & = \sqrt{16}\\x-1&=\pm4\\x-1+1&=1\pm4\\x&=5,-3\end{aligned}\)

Therefore, the x-intercepts are:

\(x = 5, \quad x=-3\)

Answer:

B: No error has occured

Step-by-step explanation:

In statistical hypothesis testing, we have two types of errors namely Type I error and Type II error.

Type I error occurs when we reject the null hypothesis although it is true. Meanwhile, Type II error occurs when we fail to reject the null hypothesis null hypothesis even though it is false.

Now, we are given the null and alternative hypothesis as;

Null Hypothesis: μ ≤ 67.16

Alternative Hypothesis: μ > 67.16.

Where μ represents the statewide average bill.

We are also given the true statewide average bill is $51.28.

Now, the true statewide average bill falls within the range of the null hypothesis given.

Thus, we can't reject the null hypothesis since it is true.

Now, we are told the null hypothesis is not rejected and that is correct.

Thus, there is no error as it doesn't fall into the type I or the type II error.