A wine producer believes that a new advertisement will increase product sales in LCBO by an average of 50 cases in a week. For a random sample of 20 LCBO stores, it was found that the average sales increase was 41.3 cases, and the sample standard deviation was 12.2 cases.
Test the null hypothesis that the population mean sales increase is at least 50 cases, stating any assumptions you can make. Use 5% as a significant level.
(You NEED to use BOTH the Critical-value approach and p-value approach to get a full mark).
To have a full mark, you NEED to show your calculation and solution (with all the STEPS) in the midterm exam file posted under Assessment-Assignment (Similar to Weekly Quizzes).
Do NOT use EXCEL
a) Reject the null hypothesis
b) Do not reject the null hypothesis
c) None of the answers are correct

A population consists of five members 2,3,6,8,1). consider all possible samples of size two which can be doamn with replacement from this positioning population.  The mean is  4 and standard deviation of the population is 1.67. The mean and standard error of sample mean (x) from the sampling distribution of x is 4 and 1.18 respectively

i) The mean and standard deviation of the population:

Mean = (2+3+6+8+1)/5 = 20/5 = 4

Standard deviation = √[(2-4)²+(3-4)²+(6-4)²+(8-4)²+(1-4)²]/5 = √14/5 = 1.67


ii) The mean and standard error of sample mean (x) from the sampling distribution of x:

Mean of sample mean = Mean of population = 4

Standard error of sample mean = Standard deviation of population/√n = 1.67/√2 = 1.18


The mean of a population is calculated by adding up all the values and dividing by the number of values in the population. The standard deviation of a population is calculated by finding the difference between each value and the mean, squaring those differences, adding them up, and then dividing by the number of values in the population.

The mean of the sample mean is the same as the mean of the population, and the standard error of the sample mean is the standard deviation of the population divided by the square root of the sample size.

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The answer is calculated by elementary row operations

To factor the given complex matrices into unitary times upper triangular, you will need to use elementary row operations. Specifically, you can use scaling, addition, subtraction, and multiplication of rows.

(i) i 1:

Row 1: Scale by i

Result: i2 1 = -1 1

(ii) 1+i 2-1:

Row 1: Subtract Row 2

Result: 1 0 -1

Row 2: Scale by i

Result: i 1 -i

(iii) i 1 0 , -1 2i 1-i -1 1 i 1

Row 1: Subtract i times Row 2

Result: 0 1 0 , -1 2i 0 -i -1 0 i

Row 2: Scale by i

Result: 0 1 0 , i 0 -1 -i -1 0 1

Row 3: Subtract Row 1

Result: 0 0 0 , i 0 -1 -i -1 0 1

(iv) 1 1 -i

Row 1: Subtract Row 2

Result: 1 0 -i

Row 2: Scale by i

Result: i 0 1+i

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We have compared a parallelogram, a rectangle, a square, a rhombus, a kite, and a trapezoid, with type, descriptions, and properties.

What is congruency?

The term “congruent” means exactly equal shape and size. This shape and size should remain equal, even when we flip, turn, or rotate the shapes.

Parallelogram:       A four-sided shape with opposite sides parallel. Opposite sides are parallel, opposite angles are congruent, diagonals bisect each other.

Rectangle: A four-sided shape with four right angles.

Opposite sides are parallel and congruent, all angles are right angles, diagonals are congruent and bisect each other.

Square: A four-sided shape with four congruent sides and four right angles.

All sides are congruent, all angles are right angles, diagonals are congruent and bisect each other.

Rhombus: A four-sided shape with four congruent sides. All sides are congruent, opposite angles are congruent, diagonals bisect each other, and are perpendicular bisectors of each other.

Kite:  A four-sided shape with two pairs of adjacent sides congruent. Diagonals are perpendicular, one diagonal bisect the other, opposite angles are congruent.

Trapezoid: A four-sided shape with one pair of parallel sides.

One pair of opposite sides are parallel, non-parallel sides may or may not be congruent, and diagonals intersect at a point inside the trapezoid.

Hence, we have compared a parallelogram, a rectangle, a square, a rhombus, a kite, and a trapezoid, with type, descriptions, and properties.

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The equation of a circle with center at (4, 8) and passing through (-10, -5) is [tex](x-4)^2 + (y-8)^2 = (6)^2.[/tex]

To find this equation, we need to use the distance formula: [tex]d = sqrt((x2-x1)^2 + (y2-y1)^2).[/tex]

We can substitute in the coordinates of the center of the circle and the point it passes through:

[tex]d = sqrt((-10-4)^2 + (-5-8)^2)[/tex]
[tex]d = sqrt( (6)^2 + (13)^2 )[/tex]

d = sqrt(36 + 169)

d = sqrt(205)

d = 14.2

Now, we have the radius of the circle. We can use this to form the equation of the circle:

[tex](x-4)^2 + (y-8)^2 = (14.2)^2[/tex]

[tex](x-4)^2 + (y-8)^2 = (6)^2[/tex]

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The expression [tex]cos^4(x)sin^2(x)[/tex] can be rewritten without exponents as [tex]cos^2(x) - (\frac{1}{2} )cos^4(x)[/tex].

The double angle, half angle, or power-reducing formula can be used to rewrite [tex]cos^4(x)sin^2(x)[/tex] without exponents. One of the approaches to rewriting is by applying the power-reducing formula. The power-reducing formula is a trigonometric identity that is used to reduce powers of sine and cosine functions.

To rewrite [tex]cos^4(x)sin^2(x)[/tex] without exponents, you can use the power reducing formula. This formula states that:
[tex]cos^2(x)*sin^2(x) = (\frac{1}{2} )(1-cos(2x))[/tex]

We can use this formula to break down [tex]cos^4(x)sin^2(x)[/tex] as follows:
[tex]cos^4(x)sin^2(x) = cos^2(x)sin^2(x)cos^2(x) = (\frac{1}{2} )(1-cos(2x))cos^2(x)[/tex]

Next, we can use the double angle formula, which states that:
[tex]cos(2x) = 2cos^2(x) - 1[/tex]

Plugging this into our equation, we get:
[tex]cos^4(x)sin^2(x) = (\frac{1}{2} )(1-2cos^2(x)+1)cos^2(x) = cos^2(x) - (\frac{1}{2} )cos^4(x)[/tex]


Therefore, the expression [tex]cos^4(x)sin^2(x)[/tex] can be rewritten without exponents as [tex]cos^2(x) - (\frac{1}{2} )cos^4(x)[/tex].

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Answer: x=-6

Step-by-step explanation:

8x+14=4x-10

-4x       -4x

4x+14=-10

-14       -14

4x=-24

/4    /4

x=-6

Given:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━

hope it helps ⸙

Answer:

To calculate the probability that the winner of the gift certificate bought a printer from Super Electronics, we need to use the total number of customers who participated in the survey as the denominator and the number of customers who bought printers as the numerator.

The total number of customers who participated in the survey is:

Total Customers = Number of Customers who bought Laptops + Number of Customers who bought Desktops + Number of Customers who bought Printers

Total Customers = 88 + 52 + 64

Total Customers = 204

The number of customers who bought printers is 64.

Therefore, the probability that the winner of the gift certificate bought a printer from Super Electronics is:

P(Bought a Printer) = Number of Customers who bought Printers / Total Customers

P(Bought a Printer) = 64 / 204

P(Bought a Printer) = 0.3137 (rounded to 4 decimal places)

So, the probability that the winner of the gift certificate bought a printer from Super Electronics is 0.3137 or approximately 31.37%.

The slope of line t is equal to 1/3.

The y-intercept of line t is equal to -1.

A table representing points on line s is shown below.

An equation that could represent line s is: IV. y = 1/3x +4​.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (0 - (-1))/(3 - 0)

Slope, m = 1/3

Based on the graph, the y-intercept of t is at point (0, -1)

Additionally, a table representing points on line s is given by;

x         y

-6       2

-3       3

0        4

3         5

Since line s has the same slope and passes through the point (0, 4), an equation that represents it is given by;

y = mx + c

y = x/3 + 4.

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Answer:

25, 27

Step-by-step explanation:

maybe ,,,,,,,,,hhy2u2u

Answer: Sum: 28 + 26 = 54

Difference: 28 - 26 = 2

Step-by-step explanation:

x + y = 54

x + 26 = 54

X = 28

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 6800\\ P=\textit{original amount deposited}\\ r=rate\to 2.7\%\to \frac{2.7}{100}\dotfill &0.027\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &16 \end{cases}[/tex]

[tex]6800 = P\left(1+\frac{0.027}{4}\right)^{4\cdot 16} \implies 6800=P(1.00675)^{64} \\\\\\ \cfrac{6800}{(1.00675)^{64}}=P\implies 4420\approx P[/tex]

i think it may be 16:36

explanation: if the 9 was multiplied by 4 which 9x4 is 36 it means that the 4 for the 4:9 will probably end up 16 hence 4x4 is 16 making the answer probably 16:36 to my own understanding

Measure of angles ∠Q,∠T,∠R are 98°, 98°, 82° respectively.

An isosceles trapezoid can be defined as a trapezoid whose non-parallel sides and base angles have the same measure. That is, if the two opposite sides (bases) of a trapezoid are parallel and the two non-parallel sides are of equal length, it is an isosceles trapezoid.

Given,

Isosceles trapezoid QRST

m∠S = 82°

Base angles are equal in Isosceles trapezoid

m∠R = m∠S

m∠R = 82°

and

m∠Q = m∠T

Sum of all interior angles of a quadrilateral is 360°

m∠Q + m∠T + m∠R + m∠S = 360°

m∠Q + m∠Q + 82° + 82° = 360°

2 m∠Q = 360° - 164°

2 m∠Q = 196°

m∠Q = 98°

m∠T = 98°

Hence, 98°, 98°, 82° are measure of angles ∠Q,∠T,∠R respectively.

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The company will have a loss of $46,605.60 by selling 40 items.

To find the profit, we need to subtract the cost from the price. The cost function C(q) gives us the cost of producing q items, and the price function p(q) gives us the price of selling q items.

First, let's plug in the value of 40 for q in both functions:

C(40) = 100(40) + 43,800 = 4,000 + 43,800 = 47,800

p(40) = 29.860(40) = 1,194.40

Now we can subtract the cost from the price to find the profit:

Profit = Price - Cost

Profit = 1,194.40 - 47,800

Profit = -46,605.60

Therefore, the company will have a loss of $46,605.60 by selling 40 items.

Note: It is important to make sure that the units for cost and price are the same. In this case, both are in dollars, so we can subtract them directly. If they were in different units, we would need to convert them to the same units before subtracting.

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Therefore, the mark-up percentage for the model solar system is 200%. This means that the selling price is twice the cost price.

We must divide the value by the entire value to find the percentage, then increase the resulting number by 100.

The mark-up percentage is the percentage by which the selling price exceeds the cost price.

In this case, the cost price of the model solar system is $24 and the selling price is $72. The mark-up amount is the difference between the selling price and the cost price, which is:

$72 - $24 = $48

To find the mark-up percentage, we divide the mark-up amount by the cost price and multiply by 100:

Mark-up percentage = (Mark-up amount / Cost price) x 100%

Mark-up percentage = ($48 / $24) x 100%

Mark-up percentage = 200%

Therefore, the mark-up percentage for the model solar system is 200%. This means that the selling price is twice the cost price.

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Answer:

15825.6 [tex]in^3[/tex]

Step-by-step explanation:

using 3.14 for pi you follow the formula for volume of a cylinder which is [tex]\pi r^2 h[/tex] when we plug in it comes to [tex]3.14\cdot3^{2}\cdot4[/tex] and then you solve that to get 113.04, but since you need 140 candles, we multiply the volume of one candle by 140 to get 15825.6 [tex]in^3[/tex]

If there are 360 students in the school, we can expect 108 students in the school to have a pet cat.

We can use proportion to solve the problem.

If 6 out of 20 students have a pet cat, then we can write:

6/20 = x/360

where;

x is the number of students in the school who have a pet cat.

To solve for x, we can cross-multiply:

20x = 6*360

20x = 2160

x = 108

Therefore, 108 students  are expected to have a pet cat in the school

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Answer: ur mom anyways jk

Step-by-step explanation:

6hrs and 7mins pls dont trust me on this answer and if u get it wrong im  sorry

The dimension of the new classroom is 8 meters of length and 5 meters of width.

Area of a two dimensional shape is the total region which is bounded by the object's shape.

Given that,

Area of the classroom = 20 square meters

Let x be the length and y be the width of the classroom.

Area of a rectangular classroom = Length × Width.

So, we get an equation,

xy = 20

x = 20/y [Equation 1]

If length is increased by 3 meters and the width is increased by 1 meter, the classroom will double in area.

(x + 3) (y + 1) = 20 × 2

(x + 3) (y + 1) = 40  [Equation 2]

Substitute [Equation 1] in [Equation 2]

((20/y) + 3) (y + 1) = 40  

Multiplying,

20 + 3y + (20/y) + 3 = 40

3y + (20/y) = 40 - 23

3y + (20/y) = 17

Multiplying throughout by y,

3y² + 20 = 17y

3y² - 17y + 20 = 0

3y² - 12y - 5y + 20 = 0

3y (y - 4) - 5 (y - 4) = 0

(3y - 5) (y - 4) = 0

3y - 5 = 0 or y - 4 = 0

y = 5/3 or y = 4

Let y = 4, then x = 20/4 = 5

Dimension of the new classroom is (x+3) = 8 meters and (y+1) = 5 meters

Hence the dimension of the new classroom is 8 meters and 5 meters.

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The function shown in graph is nether odd nor even function.

If f(−x)=f(x) for all x with in domain of f, then a function f is even. If f(x)=f(x) for every x in f's domain, a function f is odd.

In the given graph.

The graph of the function is nether increasing nor decreasing as, the y value of the function is going along both y - axis and -y axis.

Thus, the function shown in graph is nether odd nor even function.

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Answer:

Area of a circle = πr²

Plug in values (radius is half of the diameter so radius = 8)

π8² = 64π ≈ 201.0619 feet (rounded to four decimal places)

Hope this helps!

Answer:

45

Step-by-step explanation:

Answer: The surface area of a cylinder is given by the formula:

S = 2πr^2 + 2πrh

where r is the radius of the base, h is the height of the cylinder, and π is the mathematical constant pi.

In this case, the radius is 28 mm and the height is 30 mm.

Substituting these values into the formula, we get:

S = 2π(28)^2 + 2π(28)(30)

Simplifying the equation:

S = 2π(28)(28 + 30)

S = 2π(28)(58)

S = 32176π

Using a calculator, we can approximate the value of S to 3 significant figures:

S ≈ 101285.744 mm^2

Therefore, the surface area of the cylinder is approximately 101286 mm^2 (rounded to 3 significant figures).

Step-by-step explanation:

The determinant of a 3x3 matrix can be found using the following formula:
\[ \left|\begin{array}{ccc} a & b & c \\ d & e & f \\ g & h & i \end{array}\right| = a(ei - fh) - b(di - fg) + c(dh - eg) \]

In this case, we can substitute the values from the given matrix into the formula:
\[ \left|\begin{array}{ccc} d+b & d & d \\ d & d+b & d \\ d & d & d+b \end{array}\right| = (d+b)((d+b)(d+b) - d^2) - d(d(d+b) - d^2) + d(d^2 - d(d+b)) \]
Simplifying the expression gives:
\[ = (d+b)(d^2 + 2bd + b^2 - d^2) - d(d^2 + bd - d^2) + d(d^2 - d^2 - bd) \]
\[ = (d+b)(2bd + b^2) - d(bd) + d(-bd) \]
\[ = 2bd^2 + 2b^2d + b^3 - bd^2 - bd^2 \]
\[ = b^3 + 2b^2d \]

Therefore, the determinant of the given matrix is \[b^3 + 2b^2d\].

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Using analyzing functions, The correct answer is B. X. A parabola declines through (negative 3, 4), (negative 2 point 5, 2), (negative 2, 1), (negative 1, 0), (0, 1), (0 point 5, 2) and (1, 4) on the x y coordinate plane.

Studying a mathematical function's characteristics and behavior is the process of doing an analysis of a function.

Telling a function's story involves detailing all of its attributes and features.

When you analyze a function, you are telling your side of the story and outlining how you came to your conclusions.

A thorough study involves global information from graphs and precise information from algebra. The graphical and algebraic data should be in agreement, so you may use either to support the other as you do the analysis.

The function [tex]g(x) = (x + 1)^2[/tex] is a vertical shift of the function [tex]f(x) = x^2[/tex]. The vertex of the parabola representing g(x) is shifted one unit to the left, and one unit up.

The graph for option X matches these specifications and passes through the given points, so it represents the function g(x) = [tex](x + 1)^2.[/tex]

Hence, The correct answer is B. X.

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Answer:14+15=19, 15+16=31, 15+22=37

Step-by-step explanation:

The area of the circle is  490. 625 cm²

The formula for calculate the circumference of a circle is expressed as;

C  = 2πr

Given that;

From the information given, we have that;

Substitute the value of the circumference

25π = 2πr

Divide by the coefficient of r

r = 12. 5cm

Area of a circle = πr²

Substitute the values

Area = 3.14 × (12.5)²

Find the square

Area = 490. 625 cm²

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Answer:

  39°

Step-by-step explanation:

You want to know the measure of the third angle in a triangle with two angles given as 39° and 102°.

The angle sum theorem tells you the sum of angles in a triangle is 180°.

  39° +102° +x = 180°

  x = 39° . . . . . . . . . . . . subtract 141° from both sides

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Answer: The employee payed $36 for the item.

Step-by-step explanation:

Take $40 and since the employee gets a 10% discount

do $40 times 10% and you get 4

so take 4 away from the $40

40-4=36