[Maximum mark: 5] The diagram shows a sector AOB of a circle with centre O and radius r. The triangle AOB is equilateral and has perpendicular height 5 cm.
a) show that the radius of the sector is 10√3/3 cm.
b) find in terms of π, the perimeter P of the sector.

this is answer 44rrrrrrrrrrrrrrrrrrrrfrrrrrrrrrrr

England receives a total weighted score of [tex]1.9[/tex] , while Canada receives a score of [tex]1.6[/tex].

Instead of hiring an own accountant, a small business may choose to contract bookkeeping responsibilities to an accounting company in to cut expenses. Some companies find it advantageous to outsource HR department duties including payroll and medical coverage.

Outsourcing has several benefits, including better systems and service quality, access to the world's best workers, improved scheduling, avoiding personnel concerns, and many more.

a) Using the factor-rating method, we can calculate the total weighted score for each country as follows:

For England:

Total score [tex]= (2 * 0.1) + (3 * 0.6) + (1 * 0.2) + (1 * 0.1) = 1.9[/tex]

For Canada:

Total score [tex]= (3 * 0.1) + (1 * 0.6) + (3 * 0.2) + (2 * 0.1) = 1.6[/tex]

Therefore, based on the risk-avoidance criteria and weightings established by the executives, we would select Canada as the better choice.

b) If we double each of the weights used in part (a), the total weighted score for each country changes as follows:

For England:

Total score [tex]= (2 * 0.2) + (3 * 1.2) + (1 * 0.4) + (1 * 0.2) = 4.0[/tex]

For Canada:

Total score [tex]= (3 * 0.2) + (1 * 1.2) + (3 * 0.4) + (2 * 0.2) = 2.2[/tex]

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Actually, the correct identity is: cot(x + y) = (cot x cot y - 1) / (cot x + cot y) This identity can be derived from the sum formulas for tangent and cotangent: tan(x + y) = (tan x + tan y) / (1 - tan x tan y) cot(x + y) = (cot x cot y - 1) / (cot x + cot y) We can start by substituting cot(x + y) with its equivalent expression: cot(x + y) = cot x cot y - 1 / (cot x + cot y) Multiplying both sides by (cot x + cot y), we get: cot(x + y) (cot x + cot y) = cot x cot y - 1 Expanding the left side, we get: cot x cot y + cot x cot

The height h, on the other hand, denotes the slant height for oblique cylinders, which is the distance between the two circular bases on a straight line.

Two identical parallel spherical bases and a curving surface connecting the bases make up the three-dimensional geometric object known as a cylinder. It can be compared to a prism with rounded bases.

A line connecting the centres of the circle bases is the axis of a cylinder. The possibility that the axis is straight to the bases determines whether a cylinder is right or oblique.

Diagonal cylinders have bases that aren't perpendicular to the axis while right cylinders have bases that are perpendicular to the axis.

given

Both right and oblique cylinders can be calculated using the surface area of a cylinder formula, A = 2r2 + 2rh.

The height h, on the other hand, denotes the slant height for oblique cylinders, which is the distance between the two circular bases on a straight line.

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Answer:

  a) congruent

  b) not congruent

  c) congruent

Step-by-step explanation:

You want to know which sets of isosceles triangles are congruent.

An isosceles triangle has two congruent sides and two congruent angles. If those sides and angles match corresponding sides and angles in another isosceles triangle, then the triangles will be congruent.

Unless the triangle is equilateral, the two congruent base angles will have different measures than the angle between the congruent sides. Once any of the angle measures is known, the others are determined—provided that we also know which angle it is that is known.

The congruent side measures are the same, and the apex angle is the same. This triangle pair is congruent.

The base angle of one triangle is the same measure as the apex angle of the other. (Neither is 60°.) These triangles cannot be congruent.

The congruent side measures are the same, and the base angles are the same. This triangle pair is congruent.

The z-score of a student who scores 97 is 2.83. In this case, since the z-score is greater than 1.96, the student is in the top 1% of performers.

It is used to indicate how many standard deviations a certain value is from the mean. It is calculated by subtracting the mean from the observed value and then dividing the result by the standard deviation.

This is calculated by subtracting the mean (80) from the student’s score (97) and dividing the result by the standard deviation (6).

97- 80/6

= 2.83

The z-score of 2.83 indicates that the student is in the top 1% of performers. This is because the z-score of 2.83 is greater than the z-score of 1.96, which is the z-score that is associated with the 1% percentile.

A z-score of 1.96 means that it is higher than 1% of the scores.

In this case, since the z-score is greater than 1.96, the student is in the top 1% of performers.

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Answer:

Y value is -128

Step-by-step explanation:

To find the y-value when x = -12, sub -12 for x in the equation.

y = -200 - 6(x)

y = -200 - 6(-12)

y = -200 + 72

y= -128

Answer:

the best answer would be 27

Step-by-step explanation:

Boom

After three years, Carlo is taller than Reggie. Carlo is 179 cm tall and Reggie is 175 cm tall.

A method for measuring temperature, length, volume, weight, and distance is known as the metric system. It is founded on three fundamental units that allow us to measure almost anything in the universe.

To compare the heights of Carlo and Reggie, we need to convert their heights to the same unit. We can convert Reggie's height from millimeters to centimeters by dividing by 10:

Reggie's height = 1680 mm ÷ 10 = 168 cm

Now we can compare their heights before and after three years:

After three years:

Therefore, after three years, Carlo is taller than Reggie. Carlo is 179 cm tall and Reggie is 175 cm tall.

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First question:

The cost of the t-shirt for the souvenir shop is $16.88. The shop adds $3.75 to the cost and then doubles the amount to get the price that the customer pays. So, the price that the customer pays before tax is:

2 x (16.88 + 3.75) = 2 x 20.63 = 41.26

Therefore, the answer is (D) 41.26.

Second question:

The cost of the t-shirt for the souvenir shop is $12.99. The shop adds $3.75 to the cost to get the price of the t-shirt. Then, the shop adds sales tax of $1.34 to the price to get the total amount that the customer pays. So, the total amount that the customer pays is:

12.99 + 3.75 + 1.34 = 18.08

Therefore, the answer is (C) 28.40.

Step-by-step explanation:

(1; 1,2)

Write any 4 decimal numbers that belong to this interval, for example:

1; 1,04; 1,08; 1,12; 1,16; 1,2

The eigen values of the first matrix is λ=4, λ=0 and λ=-3. The eigenvalues of the second matrix is 0 and 6.

If there is a scalar such that Ax = x, then a non-zero vector x is an eigenvector of A given a square matrix A. The scalar eigenvalue of the eigenvector x is known as the scalar.

To put it another way, when an eigenvector x is added to a matrix A, the outcome is a scalar multiple of x, where the scalar is the eigenvalue.

Many applications of linear algebra depend on eigenvectors and eigenvalues, such as the solution of differential equation systems, identifying the major variables in a dataset, and assessing the stability of dynamic systems.

The eigenvalues of the matrix can be found using the equation:

det(A - λI) = 0

Substituting the values we have:

[tex]\left[\begin{array}{ccc}4&2&0\\0&0&0\\1&0&-3\end{array}\right] - \lambda \left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc} 4 - \lambda &0&0\\0&- \lambda & 0\\1 &0 & -3 - \lambda\end{array}\right][/tex]

Now determine the det of the matrix:

(4 - λ) (-3λ + λ² ) - 0 + 0 = (4 - λ)(λ)(-3 + λ)

Thus the eigen values are:

λ= 4, λ = 0, and λ = 3.

For the second matrix we have:

Given that B has identical rows throughout, B has a rank of 1, and B's null space has a dimension of 2. With two eigenvalues equal to zero and one eigenvalue equal to the trace of B, which is 6, B has two eigenvalues equal to zero.

Hence, the eigenvalues of B are 0 and 6.

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The cos(θ) term cancels out and we are left with -1. Therefore, the equivalent expression is -1.

We can start by using the trigonometric identities:

cos(-θ) = cos(θ)

tan(-θ) = -tan(θ)

csc(θ) = 1/sin(θ)

Substituting these identities into the original expression, we get:

cos(θ) * (-tan(θ)) * (1/sin(θ))

Simplifying this expression, we can cancel out the cos(θ) and the sin(θ) terms:

-1 * cos(θ) * (1/(cos(θ))) The cos(θ) term cancels out and we are left with -1. Therefore, the equivalent expression is -1.

In other words, the original expression simplifies to -1 for all values of θ where it is defined (i.e. θ ≠ (2n + 1)π/2, where n is an integer). This means that as θ varies, the value of the expression will always be -1 when it is defined. Trigonometric identities are mathematical equations that involve trigonometric functions and are true for every possible value of the variables involved. There are various types of trigonometric identities, including:

Pythagorean Identities:

[tex]sin^2a + cos^2a= 1\\tan^2a + 1 = sec^2a\\1 + cot^2a = csc^2a[/tex]

Angle Sum and Difference Identities:

sin(α±β) = sin α cos β ± cos α sin β

cos(α±β) = cos α cos β ∓ sin α sin β

tan(α±β) = (tan α ± tan β) / (1 ∓ tan α tan β)

Double Angle Identities:

sin 2θ = 2 sin θ cos θ

cos 2θ =[tex]cos^2[/tex]θ - [tex]sin^2[/tex]θ = 2 [tex]cos^2[/tex]θ - 1 = 1 - 2[tex]sin^2[/tex]θ

tan 2θ = (2 tan θ) / (1 - [tex]tan^2[/tex]θ)

Half Angle Identities:

sin (θ/2) = ± √[(1 - cos θ) / 2]

cos (θ/2) = ± √[(1 + cos θ) / 2]

tan (θ/2) = ± √[(1 - cos θ) / (1 + cos θ)]

Product-to-Sum Identities:

sin α sin β = (1/2) [cos (α-β) - cos (α+β)]

cos α cos β = (1/2) [cos (α-β) + cos (α+β)]

sin α cos β = (1/2) [sin (α+β) + sin (α-β)]

Sum-to-Product Identities:

sin α + sin β = 2 sin [(α+β)/2] cos [(α-β)/2]

sin α - sin β = 2 cos [(α+β)/2] sin [(α-β)/2]

cos α + cos β = 2 cos [(α+β)/2] cos [(α-β)/2]

cos α - cos β = -2 sin [(α+β)/2] sin [(α-β)/2]

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Based on both the median and mean values, it appears that Bus 14 typically has a faster travel time compared to Bus 18.

What is the median and mean?

The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory. It could be referred to as "the middle" value for a data set.

Here,

Cοmparing the medians, we can see that Bus 14 has a higher median οf 14, while Bus 18 has a lower median οf 12. This suggests that Bus 14 may have a faster travel time οn average.

Hοwever, we alsο need tο cοnsider the means. Cοmparing the means, we can see that Bus 14 has a higher mean οf 14, while Bus 18 has a lower mean οf 12. This further supports the idea that Bus 14 may have a faster travel time οn average.

Hence, based on both the median and mean values, it appears that Bus 14 typically has a faster travel time compared to Bus 18.

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The BEST answer from the choices provided is Option (A) -2.

In summary in axis when x = 24, y = 41.1667.

Why is it?

If y varies inversely as x, then y = k/x for some constant k. To find k, we can use the initial values given:

y = k/x

38 = k/26

k = 38×26

k = 988

Now we can use k to find y when x = 24:

y = k/x

y = 988/24

y = 41.1667 (rounded to four decimal places)

Therefore, when x = 24, y = 41.1667.

In mathematics, an axis is a straight line that defines a reference direction for a coordinate system. It is used to locate or plot points, and describe geometric shapes in a plane or in space. In a two-dimensional coordinate system, there are two axes: the x-axis, which is horizontal, and the y-axis, which is vertical.

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The factors of [tex]16x^2yz[/tex]  are [tex]4xyz, xz, and 12.[/tex]yz, xz, and 12.

The factors of the given expression 16x^2yz are:

[tex]4xyz:[/tex]This is a valid factor of  [tex]16x^2yz[/tex] because it contains all the variables x, y, and z, and the exponent of x is 1, the exponent of y is 1, and the exponent of z is 1. Additionally, it contains a numerical factor of 4.

[tex]2xy:[/tex]This is not a factor of 16x^2yz because it does not include the variable z, which is present in the given expression.

[tex]xz:[/tex] This is not a factor of [tex]16x^2yz[/tex] because it does not include the variable y, which is present in the given expression.

[tex]12:[/tex] This is not a factor of [tex]16x^2yz[/tex] because it is a numerical factor and does not contain any of the variables x, y, or z.

[tex]xyz:[/tex] This is not a factor of [tex]16x^2yz[/tex] because it does not contain any numerical factor. It only includes the variables x, y, and z without any exponents.

Therefore, the factors of [tex]16x^2yz[/tex]  are [tex]4xyz, xz, and 12.[/tex]

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Answer:

Yes

Step-by-step explanation:

Angle RDE =angle TVA=28°

REV=TAV=42°

DRE=VTA=110°

THEREFORE TRIANGLE DER IS SIMILAR TO TRIANGLE ATV

The cumulative relative frequency for flossing 3 times per week is 58.57%.

a. Let's complete the table.

We can calculate the missing relative frequency for 0 times flossing per week by dividing the frequency (4) by the total number of people (70).

Relative Frequency for 0 times flossing = 4/70 = 0.0571 (rounded to 4 decimal places)

For 6 times flossing per week, the frequency is missing.

We can calculate it by summing up the frequencies for all other days and subtracting that from the total number of people.

Missing frequency for 6 times flossing = 70 - (4 + 11 + 15 + 11 + 6 + 7 + 6) = 70 - 60 = 10

Now, let's calculate the cumulative frequency for 5 times flossing per week.

Cumulative Frequency for 5 times flossing = Cumulative Frequency for 4 times flossing + Frequency for 5 times flossing = 47 + 7 = 54

The completed table looks like this:

of times floss per week | Frequency | Relative Frequency | Cumulative Frequency

0 | 4 | 0.0571 | 4

1 | 11 | 0.1571 | 15

2 | 15 | 0.2143 | 30

3 | 11 | 0.1571 | 41

4 | 6 | 0.0857 | 47

5 | 7 | 0.1 | 54

6 | 10 | 0.1429 | 64

7 | 6 | 0.0857 | 70

b. The cumulative relative frequency for flossing 3 times per week is the cumulative frequency for 3 times flossing divided by the total number of people (70).

Cumulative Relative Frequency for 3 times flossing = Cumulative Frequency for 3 times flossing / Total number of people = 41 / 70 = 0.5857 (rounded to 4 decimal places)

The cumulative relative frequency for flossing 3 times per week is 58.57%.

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The estimated probability that a randomly selected consumer will recognize Costco is 0.988 or approximately 98.8%.

What is Probability ?

Probability is a branch of mathematics that deals with the study of random events or outcomes. It is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

In this brand recognition study, we are given that 897 consumers knew of Costco and 10 did not.

The probability of a randomly selected consumer recognizing Costco can be estimated as the number of consumers who knew of Costco divided by the total number of consumers in the study:

P(recognizing Costco) = number of consumers who knew of Costco : total number of consumers in the study

P(recognizing Costco) = 897 : (897 + 10)

P(recognizing Costco) = 897 : 907

P(recognizing Costco) = 0.988 or approximately 98.8%

Therefore, the estimated probability that a randomly selected consumer will recognize Costco is 0.988 or approximately 98.8%.

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The two cylinders have the exact same volume given by:

V = pi*r²*h

The volume of a cylinder of radius r and height h is given by:

V = pi*r²*h

Where pi = 3.14

While the volume for a slanted cylinder, like the one in the image, is computed in the same way, as long as the height h is measured with a line normal from the bases (like in the image).

Now, notice that the first cylinder has a diameter of 2r and height h, so its radius is 2r/2 = r, and the volume is:

v = 3.14*r²*h

The second cylinder has a radius r and a height h, so its volume is

v = 3.14*r²*h

So yea, both cylinders have the same volume.

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According to the given information, the mean age of 25 people in the cinema is 24, which means the total age of all 25 people is:

25 people * 24 years = 600 years

When the new person arrives, the total age becomes:

26 people * 25 years = 650 years

The difference between the two totals is the age of the new person:

650 years - 600 years = 50 years

Therefore, the age of the new person is 50 years old.

Answer: 2 hours 40 minutes

Step-by-step explanation: 2/3 x 4 = 8/3 simplified to 2 2/3

2 hours and 2/3 of an hour = 2 hours 40 minutes

The prοbabiIity οf seIecting 3 peanut M&M's at randοm, and having aII 3 be a different cοIοr, is P(aII 3 are different) = 1 * 5÷6 * 2÷3 = 0.556

The study οf randοm events οr οccurrences is the fοcus οf the mathematical field οf prοbability. It is a measurement οf the likelihοοd that an event will οccur, expressed as a number between 0 and 1, where 0 denοtes an imprοbable event and 1 denοtes a specific event.

Based οn the infοrmatiοn prοvided, we are given the fοIIοwing prοbabiIities fοr the different cοIοrs οf peanut M&M's:

P (brοwn) = 0.12

P (yeIIοw) = 0.15

P (red) = 0.12

P (bIue) = 0.23

P (οrange) = 0.23

P (green) = 0.15

We can use this infοrmatiοn tο answer variοus prοbabiIity questiοns. Fοr exampIe:

What is the prοbabiIity οf selecting a bIue οr an οrange peanut M&M?

P (bIue οr οrange) = P(bIue) + P(οrange) = 0.23 + 0.23 = 0.46

Therefοre, the prοbabiIity οf selecting a bIue οr an οrange peanut M&M is 0.46 οr apprοximateIy 0.460.

What is the prοbabiIity οf nοt selecting a green peanut M&M?

P(nοt green) = 1 - P(green) = 1 - 0.15 = 0.85

Therefοre, the prοbabiIity οf nοt selecting a green peanut M&M is 0.85 οr apprοximateIy 0.850.

If yοu seIect 3 peanut M&M's at randοm, what is the prοbabiIity that aII 3 are a different cοIοr?

The prοbabiIity οf the first M&M being any cοIοr is 1, since we have nοt seIected any M&M's yet. The prοbabiIity οf the secοnd M&M being a different cοIοr than the first is:

P(secοnd is different) = 1 - P(secοnd is same)

P(secοnd is different) = 1 - (1÷6) = ÷/6

(The prοbabiIity οf the secοnd M&M being the same cοIοr as the first is 1/6, since there are 6 cοIοrs and οnIy οne οf them is the same as the first cοIοr.)

SimiIarIy, the prοbabiIity οf the third M&M being a different cοIοr than the first twο is:

P(third is different) = 1 - P(third is same as first οr secοnd)

P(third is different) = 1 - (2÷6) = 2÷3

(The prοbabiIity οf the third M&M being the same cοIοr as the first οr secοnd is 2/6, since there are twο cοIοrs that have already been seIected.)

Therefοre, the prοbabiIity οf seIecting 3 peanut M&M's at randοm, and having aII 3 be a different cοIοr, is:

P(aII 3 are different) = 1 * 5÷6 * 2÷3 = 0.556

Therefοre, the prοbabiIity οf selecting 3 peanut M&M's at randοm, and having aII 3 be a different cοIοr, is apprοximateIy 0.556.

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Answer:

7/8, 1/5, 1/3, 5/9, 11/12, 2/5, 3/5, 3/20, 9/25, 3/7, 3/8, 4/9, 8/15, 4/5, 5/7, 1/8, 7/12, 21/25, 1/6, 3/14, 1/4, 8/27, 3/4, 2/3, 5/6, 2/15, 27/40, 9/10, 5/12

the secret message spells "YES"

Step-by-step explanation:

you cant divide any of the numbers above by the same number and not get a decimal.

Answer: The word is yes

Step-by-step explanation:

Shade in 7/8, 1/5, 2/5, 3/7, 8/15, 3/14, 3/4, 5/9, 3/8, 4/5, 1/4, 2/3, 1/3, 3/5, 5/7, 1/8, 5/6, 2/15, 11/12, 3/20, 9/25, 4/9, 7/12, 21/25, 1/6, 8/27, 9/10, 27/40, and 5/12.