see attached the question is in an image attached

Step-by-step explanation:

Each number cube has 6 possible values, so there are 6⁴ = 1296 possible permutations.  Only 1 of those permutations is all ones.  Therefore, the probability is 1/1296.

Answer:

[tex]\boxed{\sf k=6}[/tex]

Step-by-step explanation:

[tex]\sf kx (x-2)+6=0[/tex]

Expand brackets.

[tex]\sf kx^2 -2kx+6=0[/tex]

This is in quadratic form.

[tex]\sf ax^2 +bx+c=0[/tex]

Since this is for equal roots:

[tex]\sf b^2 -4ac=0[/tex]

[tex]\sf a=k\\b=-2k\\c=6[/tex]

[tex]\sf (-2k)^2 -4(k)(6)=0[/tex]

[tex]\sf 4k^2-24k=0[/tex]

[tex]\sf 4k(k-6)=0[/tex]

[tex]\sf 4k=0\\k=0[/tex]

[tex]\sf k-6=0\\k=6[/tex]

Plug k as 0 to check.

[tex]\sf \sf 0x^2 -2(0)x+6=0\\6=0[/tex]

False.

So that means k must equal 6.

Answer:

A. 1 milliliter

Step-by-step explanation:

1000 milliliters = 1 liter

0.001 liters = 1 milliliter

Answer:

i) A = (3, 3), B = (12, 6), C = (6, 52) : Not orthogonal, ii) A = (-10, 5), B = (12, 16), C = (6, 52) : Not orthogonal, iii) A = (-8, 3), B = (12, 8), C = (18, 4) : Not orthogonal, iv) A = (12, -14), B = (-16, 21), C = (-11, 25) : Orthogonal, v) A = (-12, -19), B = (20, 45) : Impossible orthogonality, vi) A = (30, 20), B = (-20, -15) : Impossible orthogonality.

Step-by-step explanation:

The statement indicates that segments AB and BC must be orthogonal. Vectorially speaking, this can be expressed by using the following expression from Linear Algebra:

[tex]\overrightarrow {AB} \bullet \overrightarrow {BC} = 0[/tex]

[tex](AB_{x}, AB_{y})\bullet (BC_{x},BC_{y}) = 0[/tex]

[tex]AB_{x}\cdot BC_{x} + AB_{y}\cdot BC_{y} = 0[/tex]

Now, let is evaluate each choice:

i) A = (3, 3), B = (12, 6), C = (6, 52)

[tex]\overrightarrow {AB} = \vec B - \vec A[/tex]

[tex]\overrightarrow {AB} = (12, 6) - (3, 3)[/tex]

[tex]\overrightarrow {AB} = (12-3, 6-3)[/tex]

[tex]\overrightarrow {AB} = (9, 3)[/tex]

[tex]\overrightarrow {BC} = \vec C - \vec B[/tex]

[tex]\overrightarrow {BC} = (6, 52) - (12, 6)[/tex]

[tex]\overrightarrow {BC} = (6 - 12, 52 - 6)[/tex]

[tex]\overrightarrow {BC} = (-6, 46)[/tex]

[tex]\overrightarrow {AB} \bullet \overrightarrow {BC} = (9, 3)\bullet (-6, 46)[/tex]

[tex]\overrightarrow{AB} \bullet \overrightarrow {BC} = (9)\cdot (-6) + (3) \cdot (46)[/tex]

[tex]\overrightarrow{AB}\bullet \overrightarrow {BC} = 84[/tex]

AB and BC are not orthogonal.

ii) A = (-10, 5), B = (12, 16), C = (6, 52)

[tex]\overrightarrow {AB} = \vec B - \vec A[/tex]

[tex]\overrightarrow {AB} = (12, 16) - (-10, 5)[/tex]

[tex]\overrightarrow {AB} = (12+10, 16-5)[/tex]

[tex]\overrightarrow {AB} = (22, 11)[/tex]

[tex]\overrightarrow {BC} = \vec C - \vec B[/tex]

[tex]\overrightarrow {BC} = (6, 52) - (12, 16)[/tex]

[tex]\overrightarrow {BC} = (6 - 12, 52 - 16)[/tex]

[tex]\overrightarrow {BC} = (-6, 36)[/tex]

[tex]\overrightarrow {AB} \bullet \overrightarrow {BC} = (22, 11)\bullet (-6, 36)[/tex]

[tex]\overrightarrow{AB} \bullet \overrightarrow {BC} = (22)\cdot (-6) + (11) \cdot (36)[/tex]

[tex]\overrightarrow{AB}\bullet \overrightarrow {BC} = 264[/tex]

AB and BC are not orthogonal.

iii) A = (-8, 3), B = (12, 8), C = (18, 4)

[tex]\overrightarrow {AB} = \vec B - \vec A[/tex]

[tex]\overrightarrow {AB} = (12, 8) - (-8, 3)[/tex]

[tex]\overrightarrow {AB} = (12+8, 8-3)[/tex]

[tex]\overrightarrow {AB} = (20, 5)[/tex]

[tex]\overrightarrow {BC} = \vec C - \vec B[/tex]

[tex]\overrightarrow {BC} = (18, 4) - (12, 8)[/tex]

[tex]\overrightarrow {BC} = (18 - 12, 4 - 8)[/tex]

[tex]\overrightarrow {BC} = (6, -4)[/tex]

[tex]\overrightarrow {AB} \bullet \overrightarrow {BC} = (20, 5)\bullet (-6, -4)[/tex]

[tex]\overrightarrow{AB} \bullet \overrightarrow {BC} = (20)\cdot (-6) + (5) \cdot (-4)[/tex]

[tex]\overrightarrow{AB}\bullet \overrightarrow {BC} = -140[/tex]

AB and BC are not orthogonal.

iv) A = (12, -14), B = (-16, 21), C = (-11, 25)

[tex]\overrightarrow {AB} = \vec B - \vec A[/tex]

[tex]\overrightarrow {AB} = (-16,21) - (12, -14)[/tex]

[tex]\overrightarrow {AB} = (-16-12, 21+14)[/tex]

[tex]\overrightarrow {AB} = (-28, 35)[/tex]

[tex]\overrightarrow {BC} = \vec C - \vec B[/tex]

[tex]\overrightarrow {BC} = (-11,25) - (-16, 21)[/tex]

[tex]\overrightarrow {BC} = (-11+16, 25-21)[/tex]

[tex]\overrightarrow {BC} = (5, 4)[/tex]

[tex]\overrightarrow {AB} \bullet \overrightarrow {BC} = (-28,35)\bullet (5, 4)[/tex]

[tex]\overrightarrow{AB} \bullet \overrightarrow {BC} = (-28)\cdot (5) + (35) \cdot (4)[/tex]

[tex]\overrightarrow{AB}\bullet \overrightarrow {BC} = 0[/tex]

AB and BC are orthogonal.

v) A = (-12, -19), B = (20, 45)

It is not possible to determine the orthogonality of this solution, since point C is unknown.

vi) A = (30, 20), B = (-20, -15)

It is not possible to determine the orthogonality of this solution, since point C is unknown.

Answer:

623

Step-by-step explanation:

Given that margin of error (E) = 3 unit, standard deviation (σ) = 29, sample size (n) = ?

a) The confidence (C) = 99% = 0.99

α = 1 - C = 1 - 0.99 = 0.01

α/2 = 0.01 / 2 = 0.005

From the normal distribution table, The z score of α/2 (0.005) is the critical value and it corresponds to the z score 0.495 (0.5 - 0.005) which is 2.58.

[tex]critical\ value = z_{\frac{\alpha}{2} }=z_{0.005}=2.58\\[/tex]

b) The margin of error (E) is given as:

The minimum sample size (n) is 623

Answer:

16+x²

Step-by-step explanation:

Answer:

x = 1.5

Step-by-step explanation:

5(4x-10)+10x=4(2x-3)+2(x-4)

Distribute(5)

20x-50+10x=4(2x-3)+2(x-4)

Distribute(4)

20x-50+10x=8x-12+2(x-4)

Distribute(2)

20x-50+10x=8x-12+2x-8

Combine like terms

30x-50=10x-20

Subtract(10x)

20x-50=-20

Add(50)

20x=30

Divide(20)

x = 1.5

Hope it helps <3

Answer:

Step-by-step explanation:

5 ( 4x - 10) + 10x = 4(2x - 3) + 2(x - 4)

Expand the terms

That's

20x - 50 + 10x = 8x - 12 + 2x - 8

Simplify

30x - 50 = 10x - 20

Group the constants at the right side of the equation

That's

30x - 10x = - 20 + 50

20x = 30

Divide both sides by 20

x = 3/2

Hope this helps you

Answer:

Part A: no solution

Part B: Distributive property of multiplication over addition.

Step-by-step explanation:

Part A:

4x + 2(x – 3) = 4x + 2x – 11

4x + 2x - 6 = 6x - 11

6x - 6 = 6x - 11

-6 = -11

Since -6 = -11 is a false statement, there is no solution.

Number of solutions: 0

Part B:

Property used: Distributive property of multiplication over addition.

Part A: Here are the steps I used to solve this equation-

4x + 2(x – 3) = 4x + 2x – 11

4x + 2x - 6 = 6x - 11

6x - 6 = 6x - 11

-6 = -11

Since -6 = -11 is a false statement, there is no solution.

The final number of solutions: 0

Part B: I used the distributive property of multiplication over addition.

The graph D shows a line with slope zero.

Since graph A, B and C doesn't make horizontal line, it is not a zero slope/ horizontal line.

Graph D is a horizontal line. It doesn't depend on any y value. It is neither increasing nor decreasing.

Therefore, graph D shows a line with a slope of zero.

Learn more about slope here:

https://brainly.com/question/3493733

#SPJ2

Since "a line has a slope of zero when it does not have any vertical rise. It will be a straight horizontal line." the answer is D

Answer:

  5

Step-by-step explanation:

The limit of f(x) at x=-1 is 5 when approached from the left or right. Since those limits are the same, the limit exists and is ...

  [tex]\boxed{\lim\limits_{x\to-1}f(x)=5}[/tex]

Answer:

  0.12 g/cm³

Step-by-step explanation:

Density is the ratio of mass to volume. The volume of the brownie is the cube of its side dimension:

  V = s³ = (5 cm)³ = 125 cm³

Then the density is ...

  ρ = M/V = (15 g)/(125 cm³) = 0.12 g/cm³

The density of the brownie is 0.12 g/cm³.

Answer:

8.2

Step-by-step explanation:

When you calculate it by 100, there are two zeros, so you move two decimals to the right.

This makes 8.2, and 8.2 will be the answer.

Another example could be... 0.082✖️10.

In this case, there is 1 zero, so you move the decimal to the right once, making it 0.82.

Hope this helps!!!

Answer:

8.2

Step-by-step explanation:

When you calculate it by 100, there are two zeros, so you move two decimals to the right.

so you will get 8.2

hope it helps you

Answer:

x=8/3 OR 2.7

Step-by-step explanation:

-1.3+4.6x=0.3+4x

4.6x-4x=0.3+1.3

0.6x=1.6

x=1.6/0.6=8/3

x=8/3 OR 2.7

Hope this helps!

Answer:

[tex]\boxed{x = 2\frac{2}{3} }[/tex]

Step-by-step explanation:

[tex]-1.3+4.6x = 0.3 +4x[/tex]

Collecting like terms

[tex]4.6 x -4x = 0.3+1.3[/tex]

[tex]0.6x = 1.6[/tex]

Dividing both sides by 0.6

x = 1.6 / 0.6

x = 2 2/3

Answer:

The answer is option 2.

Step-by-step explanation:

Quadratic function is always written in the form of ax² + bx + c where the highest power of x is 2.

In the options above :

Option 1 is Cubic function.

Option 2 is Quadratic function.

Option 3 and 4 are Linear function.

Answer:

I guess....

Step-by-step explanation:

option 2............

Answer:

101.98 yards.

Step-by-step explanation:

Please refer to the diagram that I drew (sorry for the messiness; I do not own a stylus and so I was using my mouse to try to draw it).

Since the triangle is a right triangle, you can use SOH CAH TOA. In this case, you are trying to figure out the opposite length, but you are given the adjacent. So, we will use tangent to solve this (TOA = Tangent, Opposite over Adjacent).

The angle is 22.6 degrees, and the tangent of the angle is equivalent to the opposite length, x, divided by the adjacent length, 245 yards.

tan(22.6) = x / 245

x / 245 = tan(22.6)

x = tan(22.6) * 245

x = 0.4162598242 * 245

x = 101.9836569

So, you are about 101.98 yards from the cabin.

Hope this helps!

Answer: Because 4 is the base of what is being exponentially multiplied, you can multiply 256 by 4 to get 4^5

Hi there! Hopefully this helps!

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

So, we know that 4 to the 4th power equals 256.

4 to the 4th power = 4 x 4 x 4 x 4.

So we can add another 4 to the equation to quickly get out answer for 4 to the 5th power.

4 to the 5th power = 4 x 4 x 4 x 4 x 4 = 1024.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Or you could break the equation into parts.

For example, there are FOUR 4s in the equation.

4 x 4 = 16.

4 x 4 = 16.

16 x 16 = 256.

Now since we've added ANOTHER 4, it should look like this:

16 x 16 = 256.

256 x 4 = 1024.

Answer:

x = ±sqrt(7)

Step-by-step explanation:

x^2 - 8 = -1

Add 8 to each side

x^2 - 8+8 = -1+8

x^2 = 7

Take the square root of each side

sqrt(x^2) = ±sqrt(7)

x = ±sqrt(7)

Answer:

D. 11.8 cm.

Step-by-step explanation:

This is a 30-60-90 triangle, which means that the hypotenuse is 2x, the short leg is x, and the long leg is x[tex]\sqrt{3}[/tex].

In this case, the hypotenuse is 5.

5 / 2 = 2.5. That is the short leg.

The long leg is 2.5 * [tex]\sqrt{3}[/tex] = 4.330127019.

5 + 2.5 + 4.330127019 = 7.5 + 4.330127019 = 11.83012702, which is about D. 11.8 cm.

Hope this helps!

Answer:

100yd²

Step-by-step explanation:

length=4x

width=x

perimeter=2(l+w)

50=2(4x+x)

50=2(5x)=10x

50=10x

x=5yd

width=5yd

length=20yd

area=length×width

=20×5

=100yd²

Answer:

[tex]\boxed{\red{100 \: \: {yd} ^{2}}} [/tex]

Step-by-step explanation:

width = x

length = 4x

so,

perimeter of a rectangle

[tex] p= 2(l + w) \\ 50yd = 2(4x + x) \\ 50yd= 2(5x) \\ 50yd= 10x \\ \frac{50yd}{10} = \frac{10x}{10} \\ x = 5 \: \: yd[/tex]

So, in this rectangle,

width = 5 yd

length = 4x

= 4*5

= 20yd

Now, let's find the area of this rectangle

[tex]area = l \times w \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 20 \times 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 100 {yd}^{2} [/tex]

Answer:

2 inches

Step-by-step explanation:

x= smallest

3x=largest

2x=medium

x+3x+2x=12

6x=12

x=2

so smallest is 2

largest is 6 (3x)

medium is 4 (2x)

2+6+4=12

Answer:

(0,0), (-4,0), (0,-5).

Step-by-step explanation:

Note: Matrices are not in proper format.

Consider the given matrix is

[tex]T=\begin{bmatrix}0&4&0\\0&0&5\end{bmatrix}[/tex]

It means vertices are (0,0), (4,0) and (0,5).

Transformation matrix is

[tex]A=\begin{bmatrix}-1&0\\0&-1\end{bmatrix}[/tex]

To find the coordinates of the transformed triangle multiply both matrices and calculate matrix AT.

[tex]AT=\begin{bmatrix}-1&0\\0&-1\end{bmatrix}\begin{bmatrix}0&4&0\\0&0&5\end{bmatrix}[/tex]

[tex]AT=\begin{bmatrix}\left(-1\right)\cdot \:0+0\cdot \:0&\left(-1\right)\cdot \:4+0\cdot \:0&\left(-1\right)\cdot \:0+0\cdot \:5\\ 0\cdot \:0+\left(-1\right)\cdot \:0&0\cdot \:4+\left(-1\right)\cdot \:0&0\cdot \:0+\left(-1\right)\cdot \:5\end{bmatrix}[/tex]

[tex]AT=\begin{bmatrix}0&-4&0\\ 0&0&-5\end{bmatrix}[/tex]

It means coordinates of the transformed triangle are (0,0), (-4,0), (0,-5).

Answer:

A

Step-by-step explanation:

E2020

Answer:

[tex]\large \boxed{\sf \ \ 6 \ and \ 11 \ \ }[/tex]

Step-by-step explanation:

Hello,

Let's note a and b the two numbers.

a = b - 5

[tex]a^2+b^2=157[/tex]

We replace a in the second equation and we solve it

[tex](b-5)^2+b^2=157 \\ \\ \text{*** develop the expression ***} \\ \\b^2-10b+25+b^2=157 \\ \\ \text{*** subtract 157 from both sides ***} \\ \\2b^2-10b+25-157=2b^2-10b-132=0 \\ \\ \text{*** divide by 2 both sides ***} \\ \\b^2-5b-66=0[/tex]

It means that the sum of the two roots is 5 and the product is -66.

because

     [tex](x-\alpha )(x-\beta )=x^2-(\alpha +\beta )x+\alpha \beta \\ \\ \text{ where } \alpha \text{ and } \beta \text{ are the roots }[/tex]

And we can notice that 66 = 6 * 11 and 11 - 6 = 5

So let's factorise it !

    [tex]b^2-5b-66=0 \\ \\b^2+6b-11b-66=0 \\ \\b(b+6)-11(b+6)=0 \\ \\(b-11)(b+6) =0 \\ \\ b=11 \ or \ b=-6[/tex]

It means that the solutions are

(6,11) and (-6,-11)

I guess we are after positive numbers though.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Step-by-step explanation:

Let b represent the number of cups of butter needed.

Let s represent the number of cups of sugar needed.

Let o represent the number of cups of oat needed.

Let f represent the number of cups of flour needed.

The recipe calls for two times as many cups of sugar as butter. It means that

s = 2b

Two times as many cups of oats as sugar. It means that

o = 2s

Two times as many cups of flour as oats. It means that

f = 2o

If Duane puts in one cup of butter, it means that b = 1

Therefore,

s = 2 × 1 = 2 cups

o = 2s = 2 × 2 = 4 cups

f = 2o = 2 × 4 = 8 cups

Therefore, he needs to add 8 cups of flour

Answer: Let b represent the number of cups of butter needed. Let s represent the number of cups of sugar needed. Let o represent the number of cups of oat needed. Let f represent the number of cups of flour needed. The recipe calls for two times as many cups of sugar as butter. It means that s = 2bTwo times as many cups of oats as sugar. It means that o = 2sTwo times as many cups of flour as oats. It means that f = 2oIf Duane puts in one cup of butter, it means that b = 1Therefore, s = 2 × 1 = 2 cupso = 2s = 2 × 2 = 4 cupsf = 2o = 2 × 4 = 8 cups Therefore, he needs to add 8 cups of flour

Step-by-step explanation:

Answer:

The answer is below

Step-by-step explanation:

Let x represent the big buses and y represent small buses. The large buses can carry 30 students and the small buses can carry 15 students. The total number of students are 450, this can be represented by the inequality:

30x + 15y ≤ 450

They are only 20 drivers, therefore only 20 buses can be used. It is represented by:

x + y ≤ 20

They  are only 19 small buses and 18 large buses:

x ≤ 18

y ≤ 19

After plotting the graph, the minimum solution to the graph are at:

A (15,0), B(18,0), C(10, 10), D(18, 2).

The cost function is given as:

The total cost of operating one large bus is $225 a day, and the total cost of operating one small bus is $100 per day.

​

F(x, y) = 225x + 100y

At point A:

F(x, y) = 225(15) + 100(0) = $3375

At point B:

F(x, y) = 225(18) + 100(0) = $4050

At point C:

F(x, y) = 225(10) + 100(10) = $3250

At point D:

F(x, y) = 225(18) + 100(2) = $4250

The minimum cost is at point C(10, 10) which is $3250

Answer: min = 12, Q1 =17,  median =23.5 , Q3 = 30, max = 37 .

Step-by-step explanation:

The five-number summary for this data set consists  of  min, Q1,

median, Q3, max.

Given data: 12, 15, 17, 20, 22, 25, 27, 30, 33, 37, which is already arranged in a order.

Minimum value = 12

Maximum value = 37

since , number of observations = 10 (even)

So , Median = Mean of middle most terms

Middle most terms = 22, 25

Median =[tex]\dfrac{22+25}{2}=23.5[/tex]

First quartile ([tex]Q_1[/tex])= Median of first half ( 12, 15, 17, 20, 22)

= middle most term

= 17

Third quartile ([tex]Q_3[/tex]) = Median of second half (25, 27, 30, 33, 37)

= middle most term

= 30

Hence, five-number summary for this data set :

min = 12, Q1 =17,  median =23.5 , Q3 = 30, max = 37 .

Answer:

9 in.

Step-by-step explanation:

Given that the line 10 in. and line 4 in. are parallel, then the two triangles are similar.

As such, the ratio of the sides would give the same results.

Hence,

4/6 = 10/(6 + x)

cross multiplying

4(6 + x) = 60

Dividing both sides by 4

6 + x = 15

collecting like terms

x = 15 - 6

= 9

Answer:

[tex]x = -5[/tex]

Step-by-step explanation:

We can simplify this equation down until x is isolated.

[tex]2x - 3 + 3x = -28[/tex]

We can combine the like terms of x.

[tex]5x - 3 = -28[/tex]

Add 3 to both sides.

[tex]5x = -25[/tex]

Now we can divide both sides by 5.

[tex]x = -5[/tex].

So x = -5.

Hope this helped!

Answer:

x=-5

Step-by-step explanation:

first combine like terms

5x-3=-28

add on both sides

5x=-25

divide

x==-5

Answer:

[tex]a^9 + b^ 5 + c^{13}[/tex]

Step-by-step explanation:

[tex](a^5 \times a^4)+(b^2 \times b^3) + (c^7 \times c^6)[/tex]

When bases are same and it is multiplication, then add the exponents.

[tex](a^{5+4})+(b^{2+3})+(c^{7+6})[/tex]

[tex](a^9)+(b^ 5) + (c^{13})[/tex]

Apply rule : [tex](a^b)=a^b[/tex]

[tex]a^9 + b^ 5 + c^{13}[/tex]

Answer:

[tex]a^9+b^5-c^{13[/tex]

Step-by-step explanation:

[tex](a^5*a^4) + (b^2*b^3)-(c^7*c^6)[/tex]

When bases are same, powers are to be added.

=> [tex](a^{5+4})+(b^{2+3})-(c^{7+6})[/tex]

=> [tex]a^9+b^5-c^{13[/tex]

Answer:  60

Step-by-step explanation:

Formula to calculate sample size (n):

[tex]n=(\dfrac{\sigma\times z^*}{E})^2[/tex]

, where [tex]\sigma[/tex] = population standard deviation, E Margin of error , z* = critical value for the confidence interval.

As per given , we have

E =5

[tex]\sigma=15[/tex]

Critical value for 99% confidence = 2.576

Then,

[tex]n=(\dfrac{15\times2.576}{5})^2\\\\\Rightarrow\ n=59.721984\approx60[/tex]

So, Required sample size = 60 .

Complete Question

A magazine provided results from a poll of 500 adults who were asked to identify their favorite pie. Among the 500 ​respondents, 12 ​% chose chocolate​ pie, and the margin of error was given as plus or minus 5 percentage points.What values do ​ [tex]\r p , \ \r q[/tex], ​n, E, and p​ represent? If the confidence level is 90​%, what is the value of [tex]\alpha[/tex] ​?

Answer:

a

   [tex]\r p[/tex] is the sample proportion   [tex]\r p = 0.12[/tex]

   [tex]n[/tex] is the  sample size is  [tex]n = 500[/tex]

   [tex]E[/tex] is the  margin of error is [tex]E = 0.05[/tex]

   [tex]\r q[/tex] represents the proportion of those that did not chose chocolate​ pie i.e                        [tex]\r q = 1- \r p[/tex]

b

   [tex]\alpha = 10\%[/tex]

Step-by-step explanation:

Here

    [tex]\r p[/tex] is the sample proportion   [tex]\r p = 0.12[/tex]

   [tex]n[/tex] is the  sample size is  [tex]n = 500[/tex]

    [tex]\r q[/tex] represents the proportion of those that did not chose chocolate​ pie i.e  

      [tex]\r q = 1- \r p[/tex]

      [tex]\r q = 1- 0.12[/tex]

      [tex]\r q = 0.88[/tex]

     [tex]E[/tex] is the  margin of error is [tex]E = 0.05[/tex]

Generally [tex]\alpha[/tex] is the level of significance and it value is mathematically evaluated as

     [tex]\alpha = ( 100 - C )\%[/tex]

Where  [tex]C[/tex] is the confidence level which is given in this question as  [tex]C = 90 \%[/tex]

So  

    [tex]\alpha = ( 100 - 90 )\%[/tex]

    [tex]\alpha = 10\%[/tex]