Consider the matrix that transforms a vector (x1, x2, x3) into (x2, x3, x1) in 3D:
1-Show that this is a rotation matrix.
2-Find the axis of rotation.
3-Find the angle of rotation

In a statistical test, the goal is to determine whether the null hypothesis (H0) is true or false based on the observed data. In this case, the null hypothesis is that the difference between the two population means (????T and ????????) is equal to zero, and the alternative hypothesis (H1) is that the difference is greater than zero.

The investigator initially compares the observed probability (Pobs) with the significance level (????) to make her decision. If Pobs is less than ????, then the null hypothesis is rejected, and if Pobs is greater than ????, then the null hypothesis is not rejected.

If the investigator had instead compared the observed test statistic (tobs) with the critical value (tcrit), she would have made the same decision. This is because the critical value is determined based on the significance level, and the test statistic is determined based on the observed data. If the test statistic is greater than the critical value, then the null hypothesis is rejected, and if the test statistic is less than the critical value, then the null hypothesis is not rejected.

Since the decision to reject or not reject the null hypothesis is based on the same criteria (whether the observed value is greater than or less than a predetermined value), the decision would be the same whether the investigator compares Pobs with ???? or tobs with tcrit.

In conclusion, the investigator would have made the same decision had she compared tobs with tcrit instead of Pobs with ???? because both methods are based on the same criteria for rejecting or not rejecting the null hypothesis.

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Answer:

x = 9

Step-by-step explanation:

given a line parallel to a side of the triangle and intersecting the other 2 sides, then it divides those sides proportionally.

[tex]\frac{x-1}{3x+1}[/tex] = [tex]\frac{6}{21}[/tex] = [tex]\frac{2}{7}[/tex] ( cross- multiply )

7(x - 1) = 2(3x + 1) ← distribute parenthesis on both sides

7x - 7 = 6x + 2 ( subtract 6x from both sides )

x - 7 = 2 ( add 7 to both sides )

x = 9

The area of this trapezoid is 66 cm².

To find the area of a trapezoid, we use the formula:

Area = (a + b) x h / 2

Where:

a and b are the lengths of the parallel sides of the trapezoid

h is the height

If we assume that the 22 cm and 11 cm sides are parallel sides, that is

a = 22

b = 11

and h = 4 cm

Now we can use the formula to find the area:

Area = (22 cm + 11 cm) x 4 / 2

Area = 66 cm²

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We can estimate that 900 people in attendance would prefer mustard on a hot dog.

What is proportion?

Proportion is a mathematical concept that refers to the relationship between two quantities, expressed as a ratio or a fraction. It represents the size of one quantity relative to another quantity, typically within a larger population or sample.

To determine the number of people who would prefer mustard on a hot dog, we need to use the proportion of people in the sample who prefer mustard and apply it to the total number of people in attendance.

The proportion of people in the sample who prefer mustard is:

27/150 = 0.18

To estimate the number of people who prefer mustard in the entire population of 5,000 attendees, we can multiply this proportion by the total number of attendees:

0.18 x 5,000 = 900

Therefore, we can estimate that 900 people in attendance would prefer mustard on a hot dog.

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Answer: C | SAS

Step-by-step explanation:

C. SAS - This acronym stands for Side-Angle-Side congruence. This criteria implies that △ABC≅△DEF if two sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle.

The height of the trapezoid is 23 cm.

What is a trapezoid?

A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs. The height of a trapezoid is the perpendicular distance between the two bases.

To find the height of a trapezoid given its parallel sides and area, you can use the formula:

height = 2 * area / (sum of bases)

In this case, the sum of the bases is 12 cm + 18 cm = 30 cm, and the area is 345 cm². Substituting these values into the formula, we get:

height = 2 * 345 cm² / 30 cm

height = 23 cm

Therefore, the height of the trapezoid is 23 cm.

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I would respond that Bonnie is correct. A pyramid with 6 vertices, or corners, would have a hexagonal base, which means it would be a pyramid with a base that is a hexagon. Therefore, the correct name for this type of pyramid is a hexagonal pyramid.

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The area of the rhombus is 16√39 sq. cm.

A four-sided polygon with equal-length sides is known as a rhombus. A rhombus is an unique kind of parallelogram, like a square, in which the opposing sides are parallel and congruent. Yet, a rhombus lacks right angles, unlike a square.

Given that, sides = 10cm and the diagonal = 16 cm.

Using the Pythagorean theorem, we can find the length of the other diagonal as follows:

a^2 + b^2 = c^2

(10/2)^2 + b^2 = 16^2/4

25 + b^2 = 64

b^2 = 39

b = √39

The length of the other diagonal is 2*√39 cm.

Now, we can use the formula for the area of a rhombus:

A = (d1d2)/2 = (162√39)/2 = 16√39

Hence, the area of the rhombus is 16√39 sq. cm.

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The area of the rhombus is approximately 62.4 cm².

A rhombus is a quadrilateral with four sides of equal length. It is also known as a diamond or a lozenge. A rhombus has two pairs of parallel sides, and opposite angles are equal to each other. The diagonals of a rhombus bisect each other at right angles, meaning they cut each other in half and form a right angle at their intersection point.

The properties of a rhombus are similar to those of a square, but unlike a square, a rhombus does not have right angles. However, a square can be considered a special case of a rhombus, where all four angles are right angles.

The area of a rhombus can be calculated using the formula:

Area = (diagonal 1 x diagonal 2) / 2

where diagonal 1 and diagonal 2 are the lengths of the two diagonals of the rhombus.

Let's use the Pythagorean theorem to find the length of the shorter diagonal. We know that a rhombus has two pairs of congruent right triangles. Let's call the length of the shorter diagonal d.

Using Pythagorean theorem:

(10/2)² + (d/2)² = (16/2)²

5² + (d/2)² = 8²

25 + (d/2)² = 64

(d/2)² = 39

d/2 = √(39)

d = 2 * √(39)

Now we can use the formula for the area of a rhombus:

Area = (diagonal1 * diagonal2) / 2

Area = (10 * 2 * √(39)) / 2

Area = 10 * √(39)

Therefore, the area of the rhombus is approximately 62.4 cm².

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Answer:

The surface area of the new prism increased by less than a scale factor of two.

Step-by-step explanation:

original prism:  S.A. = SA of 4 sides + Top + Bottom = 4(9x6) + 2 (3x6) = 252

scaled up prism:  SA = 4(18x6) + 2(3x6) = 468

height = 2(9) = 18

468/252 = 1.857 < 2

The surface area of the cylinder with a height of 8 yards and a radius of 82.13 yards is  46,486.93 sq. yards.

What is a cylinder?

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. One of the fundamental three-dimensional shapes in geometry is the cylinder, which has two distant, parallel circular bases. At a predetermined distance from the centre, a curved surface connects the two circular bases. The axis of the cylinder is the line segment connecting the centres of two circular bases. The height of the cylinder is defined as the distance between the two circular bases.

Given,

The height of the cylinder = 8 yards

 The circumference of the cylinder = 515.79 yards

We are asked to find the surface area of the cylinder.

Now the formula to find the surface area of a cylinder is:

SA = 2πr( r+h)

where r = radius

      h = height

Radius can be found from the circumference formula

2πr = 515.79

r = 515.79/ 2π = 515.79 / (2*3.14) = 82.13 yards

Then,

SA = 2πr( r+h) = 2*3.14*82.13 ( 82.13+8) = 46,486.93 sq. yards

Therefore the surface area of the cylinder with a height of 8 yards and a radius of 82.13 yards is  46,486.93 sq. yards.

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Answer:

Step-by-step explanation:

It is given that ,

tanA=3/4 , [tex]\pi < A < \frac{3\pi }{2}[/tex]

so , angle are in 3rd Quadrant .

cosB = -15/17 ,[tex]\frac{\pi}{2} < B < \pi[/tex]

So, angle B are in 2nd Quadrant

We use Compound formula of tan(A+B)

[tex]tan(A+B) = \frac{tanA + tanB}{1- tanAtanB}[/tex]         ..........(1)

To use this formula , we need to find the value of tanA and tanB.

tanA = 3/4   ........ given

cos B =-15/17

Using Identity ,

[tex]sin^{2}B + cos^{2}B=1[/tex]

put the value of cosB

[tex]sin^{2}B + (-\frac{15}{17})=1\\ sin^{2}B = 1 - \frac{225}{289} \\sin^{2}B = \frac{64}{289} \\sinB = \frac{8}{17}[/tex]

we know that ,

tanB = sinB/cosB

put the value of sinB and CosB

[tex]tanB = \frac{\frac{8}{17} }{-\frac{15}{17}} \\tanB = - \frac{8}{15}[/tex]

[tex]tanB = -(-\frac{8}{15}) \\tanB = \frac{8}{15}[/tex]the value of tan in 2nd quadrant are negative .

We find the value of tanB and next we put the value of tanA and tanB in

equation(1)

[tex]tan(A+B) = \frac{tanA + tanB}{1- tanAtanB}\\tan(A+B) = \frac{\frac{3}{4}+\frac{8}{15}}{1 - \frac{3}{4}\frac{8}{15} } \\tan(A+B) = \frac{\frac{77}{60} }{1 - \frac{24}{60} } \\tan(A+B) = \frac{\frac{77}{60} }{\frac{36}{60} } }\\tan(A+B) = \frac{77}{36}[/tex]

Hopeful,this answer will help you!

If any wrong in this answer please let me know

Answer:

To find the value of b x6 when b = 7, we simply need to substitute 7 for b in the expression and perform the multiplication.

b x 6 = 7 x 6

Multiplying 7 by 6 gives us:

b x 6 = 42

Therefore, when b = 7, the value of b x 6 is 42.

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7527861800

Answer: -3

Step-by-step explanation:

The slope is the number being multiplied by x.

Answer:

m = -3

Step-by-step explanation:

Answer:

(x+4)^2=4

Step-by-step explanation:

Answer: By the Vertical Angles Theorem, we know that vertical angles are congruent. Therefore:

x + 8 = 5x - 148

Solving for x:

8 + 148 = 5x - x

156 = 4x

x = 39

So, we have:

x + 8 = 39 + 8 = 47 degrees

5x - 148 = 5(39) - 148 = 47 degrees (by the Vertical Angles Theorem)

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

that means we put -6 into every place, where n is showing in the expression, and then we simply calculate.

cubic root(4n - 3) + n

n = -6

cubic root(4×-6 - 3) - 6 = cubic root(-27) - 6 =

= -3 - 6 = -9

figure 1: length of sides are, 5[tex]\sqrt{2}[/tex] and 5

figure 2: height is 8[tex]\sqrt{3}[/tex] and base is 8

A triangle, with three sides, three angles, and three vertices, is one of the most fundamental and straightforward shapes in geometry. Any of the three sides and angles of a triangle can have various measurements. Depending on their angle dimensions and side lengths, triangles can be classified into various categories.

Equilateral triangles, for instance, are triangles with three equal sides and three equal 60-degree angles.

Right triangles, on the other hand, have one 90-degree angle, and the side opposite the right angle is known as the hypotenuse, with the other two sides called legs.

Isosceles triangles, whose two sides and angles are equal.

The values of figure 1: the angles are 45° 90° and 45° So, we can use right angle triangle and isosceles triangle rules in figure therefor, the base is 5[tex]\sqrt{2}[/tex] and other side is same as the another side which is 5.

Check the solution from the figure.

figure 2: height is 8[tex]\sqrt{3}[/tex] and base is 8

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The translated function from y=|x| that has a shrink of ( 1)/(4), a reflection over the x-axis and a vertical shift of 8 units down is y=-|(1)/(4)x|-8.

If f(x) is a function, then a translated function can be defined by adding or subtracting a constant value a to the variable x inside the function, resulting in a new function g(x) = f(x-a) or g(x) = f(x+a), respectively.

To create the translated function from y=|x|  we can follow these steps:
1. Shrink the function by multiplying the input by (1)/(4): y=|(1)/(4)x|
2. Reflect the function over the x-axis by multiplying the output by -1: y=-|(1)/(4)x|
3. Shift the function 8 units down by subtracting 8 from the output: y=-|(1)/(4)x|-8,

Therefore, the translated function is y=-|(1)/(4)x|-8.

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The values of the x in all triangles are:

1) x = 15. (2) x = 8. (3) x = 3. (4) x = 11.95. (5) x = √-5. (6) x = √104.

The Pythagorean theorem consists of a formula a²+b²=c² which is used to figure out the value of (mostly) the hypotenuse in a right triangle. The a and b are the 2 "non-hypotenuse" sides of the triangle (Opposite and Adjacent).

1) In this triangle:

Adjacent = 9mi

Opposite = 12 mi

Hypotaneous = x

so, x² =  (9)² + (12)²

x = √81 + 144

x = 15.

2) In this triangle:

Adjacent = x

Opposite = 6 in

Hypotaneous = 10 in

so, (10)² =  (x)² + (6)²

√100 - 36 = x

x = 8.

3) In this triangle:

Adjacent = x

Opposite = 4 ft

Hypotaneous = 5 ft

so, (5)² =  (x)² + (4)²

√25 - 16 = x

x = 3.

4) In this triangle:

Adjacent = x

Opposite = 5 yard

Hypotaneous = 13 yard

so, (13)² =  (5)² + (x)²

√168 - 25 = x

x = 11.95.

5) In this triangle:

Adjacent = x

Opposite = √13 mi

Hypotaneous = 2√2 mi

so, (2√2 )² =  (√13)² + (x)²

8 - 13 = x

x = √-5.

6)  In this triangle:

Adjacent = 13 yd

Opposite = √65 yd

Hypotaneous = x

so, (x)² =  (13)² + (√65 )²

169 - 65 = x

x = √104.

Hence, The values of the x in all triangles are:

1) x = 15. (2) x = 8. (3) x = 3. (4) x = 11.95. (5) x = √-5. (6) x = √104.

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The probabilities are given as follows:

The probabilities are different, as the theoretical probability is higher.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

Out of 20 tosses, 4 resulted in heads, hence the experimental probability is given as follows:

p = 4/20

p = 1/5.

A coin is equally as likely to be heads or tails, hence the theoretical probability is given as follows:

p = 1/2.

Over a large number of trials, it is expected that the two probabilities assume close values, but for a small number of trials such as 20 it is expected for there to be differences.

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Answer:

90 degrees clockwise rotation

Step-by-step explanation:

The way to do this is by looking at your transformation rules, where you will find that in a 90 degree clockwise rotation you take your original X and Y, swap them, and make Y negative (y, -x).

To find this, pick any two points from each rectangle (Each point must have the same letter) and compare them:

Example:

Q is at (4, 2) and Q' is at (2,-4). When comparing the two points you will find that X and Y have been swapped, and Y is now negative. This matches the 90 degree clockwise rotation rule

To find the level of production that maximizes the manufacturer's total revenue, we need to find the quantity, q, that maximizes the revenue function, R(q) = p*q.

First, we need to find the revenue function by substituting the demand function for p in the revenue function:
R(q) = p*q = (−0.13q+156)*q = -0.13q^2 + 156q
Next, we need to find the quantity that maximizes this function. To do this, we can take the derivative of the revenue function and set it equal to zero:
R'(q) = -0.26q + 156 = 0
Solving for q, we get:
q = 600
This means that the quantity that maximizes the manufacturer's total revenue is 600 units.
To find the maximum revenue, we can plug this quantity back into the revenue function:
R(600) = -0.13(600)^2 + 156(600) = 46,800

Therefore, the maximum revenue is $46,800.

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Therefore , the solution of the given problem of unitary method comes out to be in a group of 15, we would anticipate that 5 pupils would choose a candy.

To finish a job using the unitary method, divide the lengths of just this minute subsection by two. In a nutshell, the unit method eliminates a desired item from both the characterized by a set and colour subsets. 40 pens, for instance, will cost Rupees ($1.01). It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait. There are changes and unanswered issues (mathematics, algebra).

Here,

There are a total of 12 sweets in the bag: 5 + 1 + 2 + 4 candies. Given that there are 4 gold-wrapped candies out of a total of 12, the chance of choosing one during any given draw is 4/12 = 1/3.

. Therefore, regardless of how many draws have been conducted before, the chance of choosing a gold-wrapped treat is always 1/3.

In a class of 15 pupils, the predicted proportion of students who would choose a gold-wrapped treat would be:

Expected number of gold-wrapped candies = (1/3) * (number of draws) * (probability of choosing gold-wrapped candy on one draw) = 5

Therefore, in a group of 15, we would anticipate that 5 pupils would choose a candy that was wrapped in gold.

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Answer:

75

Step-by-step explanation:

This is an example of a biased sample, because the sample was not chosen at random from the entire population. It is possible that certain groups of people were more likely to have their names drawn from the hat, such as people who were sitting near the person doing the drawing.

To predict how many guests at the party have blonde hair, we can use the proportion of people in the sample who had blonde hair (3 out of 8), and apply it to the entire population of 200 guests:

(3/8) x 200 = 75

Therefore, we can predict that approximately 75 guests at the party have blonde hair.

Answer:

1. Unbiased sample

2. 75

If Alan and Robert worked together, it would take them 6.857 hours to move the inventory from the truck to the shelves

If Robert can move the inventory from his store from the truck to the shelves in 12 hours and Alan can do the same job in 16 hours, then we can find the time it would take for them to do the job together by using the formula for combined work rate:

1/t = 1/12 + 1/16

Multiplying both sides of the equation by 48t gives us:

48 = 4t + 3t

Simplifying and solving for t gives us:

48 = 7t

t = 48/7

t = 6.857 hours

It would take Alan and Robert approximately 6.857 hours to move the inventory working together.

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Answer:

The answer is -4

Step-by-step explanation:

The slot of the line can be calculated using the formula : y2 - y1/ x2 - x1.

So, you would plug in the values making the equation 5 - (-7)/ -1 - 2 and solve.

Anstoo blurry

Step-by-step explanation:

The circumference of the circle is approximately 31.4 cm to the nearest tenth.

Use this formula to get a circle's circumference:

C = 2πr

where C is the circumference, pi (roughly 3.14), is a mathematical constant, and r is the circle's radius.

If you have the diameter of the circle, you can find the radius by dividing the diameter by 2.

Once you have the radius, you can plug it into the formula to find the circumference.

For example, if the radius is 5 cm:

C = 2πr

C = 2 x 3.14 x 5

C = 31.4

So the circumference of the circle is approximately 31.4 cm to the nearest tenth.

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The pair of expressions which represents the price of an order that was originally x dollars are x - 0.15x and 0.85x

Percentage discount = 15%

Original price of an order = x dollars

New price = Original price of an order - (Percentage discount × Original price of an order)

= x - (15% of x)

= x - 0.15x

= 0.85x

Therefore, x - 0.15x and 0.85x are the expressions which represent the price of an order that was originally x dollars

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