describe what type of sampling approach you would implement to determine the rate of smoking among teenagers.

Using a trigonometric relation, we can see that the measure of angle W is 22.62°.

We can see a right triangle where we know the measures of all of its sides. Then we can use the trigonometric relation:

Sin(W) = (opposite cathetus)/hypotenuse

We can see that:

Opposite cathetus =15

hypotenuse = 39

Replacing these we will get:

Sin(W) = 15/39

Using the inverse sine function we will get:

W = Asin(15/39) = 22.62°

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The unit vector that has an angle θ= 2π/3 with the positive x-axis can be represented in component form as: (x, y) = (-1/2, √3/2).

The unit vector that makes an angle θ= 2π/3 with the positive x-axis can be represented as a vector in the form of (x, y) components. To solve for the components of this vector, we must use trigonometric functions. Using the trigonometric function SOH-CAH-TOA, we will solve for the components of the unit vector.

The x-component of the vector can be found using the SOH CAH TOA formula and the angle θ= 2π/3:

x-component = cos(2π/3)

Plugging in the angle yields: x-component = cos(2π/3) = -1/2

The y-component of the vector can be found using the SOH CAH TOA formula and the angle θ= 2π/3:

y-component = sin(2π/3)

Plugging in the angle yields: y-component = sin(2π/3) = √3/2

Therefore, the unit vector that has an angle θ= 2π/3 with the positive x-axis can be represented in component form as: (x, y) = (-1/2, √3/2).

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"Your question is incomplete, probably the complete question/missing part is:"

Find the component form of the vector: the unit vector that makes an angle theta=2pi/3 with the positive x-axis.

Step-by-step explanation:

for % problems always try to identify explicitly 100% and/or 1%.

everything else can be easily calculated out of that.

we need to find a 15% increase. of what ? that is the 100% in question.

so,

100% = 50

1% = 100%/100 = 50/100 = 0.5

15% = 1% × 15 = 0.5 × 15 = 7.5

so, 50 + 15% = 50 + 7.5 = 57.5

now, we could simply round (as a half-person or student does not make any sense).

the problem with the rounding is the small number of students overall.

if we round normally, we get 58 students.

but that are 8 students more, and 8 students are (remember, 1% = 0.5)

8/0.5 = 16%

if we round down, we get 57 students.

but that are 7 students more, and 7 students are

7/0.5 = 14%

so, every rounding to "whole students" actuality changes the % significantly.

there is no way to have 15% more students given the small number of students. only 14% more or 16% more.

if you need to give a number, do the normal rounding : 58.

but many greetings to your teacher with my additional comments.

FYI

once you understand the principle behind the % calculation, there are shortcuts to the calculations by combining 2 steps into 1 step :

x% of y is

y×x/100

or

y×0.x

in our case

50×0.15 = 7.5

x% added to y is

y×1.x

in our case

50×1.15 = 57.5

because

50 + 0.15×50 = (1 + 0.15)×50 = 1.15×50 = 57.5

The probability that the inspector in-charge is convinced that the suspect is guilty given he/she has brown hair is 0.882.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.

The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

[tex]P(C)[/tex] [tex]=P(C \mid G) P(G)+P(C \mid G c) P(G c)[/tex] = (1) (0.6) + (0.2) (0.4) =0.68

This is then used to update the inspector's belief in the suspect's guilt posterior to discovering that the suspect does have that characteristic.

[tex]$$\begin{aligned}& P(G \mid C)=(P(G) P(C \mid G)) / P(C) \\& =\frac{1(0.6)}{0.68} \\& =0.882\end{aligned}$$[/tex]

Therefore, the probability that the inspector in-charge is convinced that the suspect is guilty given he/she has brown hair is 0.882.

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Answer: $4.28

Step-by-step explanation:

We can set up the following equation to find the cost of the admission of play:

(14 students x $2x admission) + (14 students x $2 program) = (22 students x $x admission) + (22 students x $4 program)

We know the admission cost for the play is twice that of the musical, so we can substitute that into the equation:

(14 students x $2x admission) + (14 students x $2 program) = (22 students x ($2x/2) admission) + (22 students x $4 program)

Simplifying the equation:

28x + 28 = 22x + 88

Solving for x:

28x + 28 = 22x + 88

28x - 22x = 88 - 28

6x = 60

x = 60/6

So, x = 10 is the solution of the equation.

And I got $2.14 from x = 60/28 = 2.14

That was the value that makes the equation true in the first step (14 students x $2x admission) + (14 students x $2 program) = (22 students x $x admission) + (22 students x $4 program)

So x = 2.14 is the price of the musical admission.

x = $2.14

Therefore, the admission cost for each student that is going to the play is $2x = $2.14 x 2 = $4.28.

For dy/dt = (1 + t^2)/ (3y - y^2), the hypotheses of Theorem 2.4.2 are satisfied, and a unique solution exists in some interval around the initial point if y ≠ 0 and y ≠ 3.

The hypotheses of Theorem 2.4.2 state that for the initial value problem

dy/dt = f(t, y), y(t₀) = y₀

to have a unique solution in some interval t₀ - h < t < t₀ + h within α < t < β, provided that:

f and its partial derivative with respect to y, ∂f/∂y, are continuous in a rectangle α < t < β, γ < y < δ that contains (t₀, y₀).

To determine if the hypotheses are satisfied for the given differential equation we need to check if f and ∂f/∂y are continuous in a rectangle that contains the initial point (t₀, y₀). If they are, then the hypotheses of Theorem 2.4.2 are satisfied, and a unique solution exists in some interval around the initial point.

dy/dt = (1 + t^2)/ (3y - y^2)

dy/ dt = (1 + t^2)/ y(3 - y)

So dy/dt is not continuous at y = 0 and y = 3.

So the hypotheses of Theorem 2.4.2 are satisfied, and a unique solution exists in some interval around the initial point if y ≠ 0 and y ≠ 3.

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The charge to wrap the small gift is $3 and the charge to wrap the large gift is $10.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that, a local service organization is wrapping gifts at the mall to raise money for charity.

Let the charge for wrapping small gift be x and the charge for wrapping large gift be y.

Yesterday, they wrapped 39 small gifts and 16 large gifts, earning a total of $277.

39x+16y=277 ------(I)

Today, they wrapped 35 small gifts and 42 large gifts, and earned $525.

35x+42y=525

5x+6y=75 ------(II)

Multiply equation (I) by 3, we get

117x+48y=831 ------(III)

Multiply equation (II) by 8, we get

40x+48y=600 ------(IV)

Now, subtract equation (IV) from the equation (III), we get

117x+48y-(40x+48y)=831-600

77x=231

x=231/77

x=3

Substitute x=3 in equation (II), we get

5(3)+6y=75

6y=60

y=10

Therefore, the charge to wrap the small gift is $3 and the charge to wrap the large gift is $10.

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If by the SAS similarity theorem, in ΔABE ≈ΔACD the AD is 24 units.

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

Triangles that resemble one another but may not be exactly the same size are said to be comparable triangles. When two objects have the same shape but different sizes, they can be said to be comparable. This indicates that comparable shapes superimpose one another when amplified or demagnified.

If the sides are in the same ratio or proportion and the angles are equal (corresponding angles), two triangles will be similar (corresponding sides). Similar triangles may have varied side lengths when compared individually, but they must all have equal angles and the same ratio of their side lengths.

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The value of x in the given right triangle is 4.58

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Given is a right triangle, with an acute angle of 74° and sides 16 and x,

Considering the 74° as reference angle,

Using trigonometric ratio,

We know that, the tangent of an angle in a right triangle is the ratio of the hypotenuse to its base,

Therefore,

tan 74° = 16 / x

x = 16 / tan 74°

x = 4.58

Hence, the value of x in the given right triangle is 4.58

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1/3 is the fraction of the flags are either indigo or green

It is a branch of mathematics that deals with the occurrence of a random event.

Given that Of the flags in Nate's Flag Shop, 1/4 are indigo and another 1/12 are green.

P(I)=1/4

P(G)=1/12

Fraction of the flags are either indigo or green

P(IUG)=P(I)+P(G)

=1/4+1/12

=3+1/12

=4/12

=1/3

Hence, 1/3 is the fraction of the flags are either indigo or green

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Therefore, the smaller part = 41.29 and the greater part = 57 - 41.29 = 15.71.

Let the smaller part be x.

Then, the greater part = 57 - x

According to the question,

1/2 (57-x) = 11 + 1/5x

Solve for x:

1/2 (57-x) - 1/5x = 11

7/10 (57-x) = 11

7/10 (57-x) - 11 = 0

7/10 (57-x) = 11

57-x = 11 * (10/7)

57-x = 15.71

x = 57 - 15.71

x = 41.29

The equation for this problem is:

x + y = 57

1/2 x = 11 + 1/5 y

y = 57 - x

1/2 x = 11 + 1/5 (57 - x)

2x = 11 + 57 - 5x

7x = 68

x = 68/7

x = 9.71

y = 57 - x

y = 57 - 9.71

y = 47.29

Therefore, the two parts of 57 are 9.71 and 47.29.

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There are 69300 possible ways of selecting six bottles randomly with two bottles of each variety.

Probability is a branch of mathematics concerned with numerical descriptions of how likely an event is to occur or how likely a statement is to be true. In the given question, we have to select 6 bottles randomly with two bottles of each variety,

= ¹⁰C₂× ⁸C₂ × ¹¹C₂

¹⁰C₂= [1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10] / [(1 × 2)(1 × 2 × 3 × 4 × 5 × 6 × 7 × 8)]

= 90/2

= 45

Similarly,  ⁸C₂  = 28

In the same way ¹¹C₂= 55

= ¹⁰C₂× ⁸C₂× ¹¹C₂

= 45 × 28 × 55

= 69300

Therefore, there are 69300 possible ways of selecting 6 bottles with two bottles of each variety.

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The data are found to be normally distributed with a mean of 5.82 and a standard deviation of 1.43. The answer will be the later. 90.62% 

To find the percentage of first names with 7 letters or less, we need to use the Z-score formula to determine how many standard deviations the value 7 is from the mean.

Z = (7 - 5.82) / 1.43

The Z-score indicates how many standard deviations the value 7 is from the mean. A positive z-score indicates a value above the average, and a negative z-score indicates a value below the average.

A Z-score table or calculator can then be used with the standard normal distribution function to find the cumulative probability to which the Z-score compare. This cumulative probability is the percentage of data values ​​that are 7 or less. In this case, Z = 1.36 and the cumulative probability is approximately 0.9062. This means that about 90.62% of given names are seven letters or less of him. So the answer will be the later. 90.62% 

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Step-by-step explanation:

44.10 dollars after the sales tax

Answer: $44.10

Step-by-step explanation:

So to start take $42.00 and multiply it by 5% or 0.05

when you do that you will get 2.10 that is the amount you will add to the 42.00 to see how much it will be

Two values of frequency can be used to calculate the final value in a particular row or column.

Statistic is the study of mathematics which deal with relations between comprehensive data.

Here,

If a table already includes some data and we need to add more, we simply search for a row or column that holds the additional data. These two values can be used to calculate the final value in a particular row or column.

Thus, two values of frequency can be used to calculate the final value in a particular row or column.

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The number of Students like folk music but not rock music  = 30 + 6 = 36

There are 190 pupils overall.

Let R, F, and C stand for a group of students who enjoy classical, folk, and rock music, respectively.

I The percentage of students who don't like any of the three types

= 190 - (90 + 9 + 5 + 10 + 30 + 6 + 20)

= 190 - 170 = 20

(ii) The number of Students like any two types only. = 9 + 6 + 10 = 25

(iii) The number of Students like folk music but not rock music

= 30 + 6 = 36

The complete question is:

A radio station surveyed 190 students to determine the types of music they liked. The survey revealed that 114 liked rock music, 50 liked folk music and 41 liked classical music, 14 liked rock music and folk music, 15 liked rock music and classical music, 11 liked classical music and folk music, 5 liked all the three of music.

Find:

(i) How many did not like any of the 3 types?

(ii) How many liked any two types only?

(iii) How many liked folk music but not rock music?

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Answer: the measure of arc A B is 180°.

Step-by-step explanation:

mArc A B = mArc B O + mArc O A Because line segments B D and A C are diameters, they are also chords of the circle and therefore bisect each other. This means that angle A O C and angle B O C both measure x.

A radius drawn to cut angle C O C into 2 equal angle measures of x, it means that angle C O C measure 2x. So, arcs A O and B O are also equal.

Since angle A O C and angle B O C both measure x, and arcs A O and B O are equal, it means that mArc A B = mArc B O + mArc O A = x + x = 2x

As angle C O C measure 2x, and x angle measures are equal to each other. It means that x = (2x)/2 = x = angle C O C/2 = (180°)/2 = 90°

So, mArc A B = 2x = 2(90°) = 180°

Therefore, the measure of arc A B is 180°.

Answer: Hi

Step-by-step explanation:

The equation for the line y = p - 3x can be rearranged as y + 3x = p.

Substituting this into the system of equations, we get:

4x - (y + 3x) = 6

4x - y - 3x = 6

x = 6

2x - 5y = 12

2(6) - 5y = 12

12 - 5y = 12

-5y = 0

y = 0

So the point of intersection is (6, 0).

Substituting these values into y = p - 3x, we get:

0 = p - 3(6)

0 = p - 18

p = 18

Therefore, the value of p that makes the line y = p - 3x pass through the point of intersection of the lines 4x - y = 6 and 2x - 5y = 12 is 18.

If these pigs produce a total of three piglets, then the probability that all will be pink is 0.016

The heterozygous black pig can be represented as "Bb" , where B is the dominant for black skin color and b is the recessive for pink skin color.

When two heterozygous black pigs are crossed, each pig can contribute either B or b to each offspring, giving us four possible combinations for each offspring: BB (black) , Bb (black) , bB (black) , bb (Pink)  .

For all piglets to be Pink , we need all pink piglets to be "bb" .

Probability of getting a black pigs = 3/4 and that of pink pigs = 1/4 ;

To find probability of getting all  pink pig ;

it can be produced in only one way : .

(i) Pink, Pink, Pink

So probability to get all  pink pig ;

⇒ 1/4 × 1/4 × 1/4        

⇒  1/64    

⇒ 0.015625 ≈ 0.016

Therefore , the probability that all will be pink 0.016 .

The given question is incomplete , the complete question is

Black skin color is dominant to pink skin color in pigs. Two heterozygous black pigs are crossed.

If these pigs produce a total of three piglets,  what is the probability that all will be pink? express your answer using three significant figures.

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Step-by-step explanation:

a =

[tex] \frac{1}{6} [/tex]

Answer:

14.9 minutes per day

Step-by-step explanation:

We know

Angela ran 104.3 minutes in 7 days

How many minutes did she run per day?

104.3 divided by 7 = 14.9 minutes per day

So, she ran 14.9 minutes per day.

Answer: Henry drove 7 3/4 miles last week.

Step-by-step explanation:

First, you need to find the GCF of both numbers which is 4.

7 1/2 -----> 7 2/4

1/4 -------->    1/4

Add the numbers together.

          7 3/4

Therefore, Henry drove 7 3/4 miles in total last week. Hope this helps!

The first option is correct. The series of transformations that would result in an image being similar but not congruent to its preimage is reflection over the x-axis, reflection over the y-axis, and translation up 3.

The state of being in agreement or concord is referred to as congruency. It is a notion that is employed in many fields of life, including mathematics, psychology, and philosophy. Congruency is the belief that in order for an idea, system, or process to be effective, all of its components must agree with each other.

Reflection along the x-axis: This transformation includes reflecting the shape along an imaginary line drawn across the coordinate plane's origin. This produces a mirror copy of the original shape, with the left side of the shape mirrored to the right side and the right side of the shape reflected to the left.

Reflection along the y-axis: This transformation includes reflecting the shape along an imaginary line drawn across the coordinate plane's origin. This produces a mirror copy of the original shape, with the top side of the shape reflecting to the bottom side and the bottom side of the shape reflecting to the top side.

Translation up 3: In this transformation, the shape is moved up by a given number of units. The form will be pushed forward three units without affecting its size or orientation as a result of this.

Reflection over the x-axis, reflection over the y-axis, reflection over the x-axis: This transformation requires reflecting the shape twice across an imaginary line drawn through the coordinate plane's origin. This produces a mirror copy of the original shape, with the left side of the shape mirrored to the right side and the right side of the shape reflected to the left.

Dilation by a scale factor of 3: This modification enlarges or contracts the shape by a certain scale factor. This causes the form to be three times larger or smaller than it was before, without affecting its orientation.

180° anticlockwise rotation: This transformation includes rotating the shape by a given amount. This will spin the form 180° anticlockwise without affecting its size or orientation.

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The total number of text messages Connor sent last month is 171 text messages.

Number text messages Jonah sent = 73

Number of text messages Connor sent = x

So,

1/3x + 16 = 73

Subtract 16 from both sides

1/3x = 73 - 16

1/3x = 57

divide both sides by 1/3

x = 57 ÷ 1/3

multiply by the reciprocal of 1/3

x = 57 × 3/1

x = 171 text messages

Therefore, last month, Connor sent 171 text messages.

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The linear charge density of a thin wire bent into a circle remains constant, due to the fact that the linear charge density is determined by the number of electrons in the wire and the length of the wire.

Linear charge density refers to the amount of charge per unit length of a charged object.

In the case of a thin wire bent into a circle, the linear charge density remains constant despite the change in shape.

The reason for this is that the linear charge density is determined by the number of electrons in the wire and the length of the wire.

When the wire is bent into a circle, the length of the wire remains constant, while the number of electrons remains the same. As a result, the linear charge density remains constant.

It is important to note that the total charge in the wire changes when it is bent into a circle. The total charge is equal to the product of the linear charge density and the circumference of the wire.

So, while the linear charge density remains constant, the total charge in the wire increases as the wire is bent into a circle.

Complete Question:

What is the linear charge density of a thin wire bent into a circle (or ring) of radius if the total charge on the wire is constant?

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Domain is (-∞,∞) and Range is (-16,∞) and -16 is the lowest possible value of the function.

The provided function is,

f(x) = x² - 16 → (1)

Because the coefficient of is x² positive, it is an upward parabola.

A parabola's vertex form is

f(x) = a(x - h)²  + k → (2)

an is the constant, and (h,k) is the vertex.

(1) and (2) result in,

a = 1, h = 0, k = -16

As a result, the vertex of the parabola is (0,-16).

The following are key features:

For all x values, the given function is defined. So,

Domain = (-∞,∞)

The value of an upward parabola function cannot be less than the y-coordinate of its vertex.

Range = (-16,∞)

Minimum Value = vertex's y-coordinate = -16

It is a quadratic function.

For f(x)=0,

= x² - 16

16 = x²

x = ± 4

As a result, the x-intercepts are -4 and 4.

decreasing function before vertex = (-∞,0)

The function that increases after the vertex = (0,∞)

For x=0,

f(0) = (0)² - 16

= -16

As a result, the y-intercept is -16.

Positive Function = (-∞,-4) ∪ (4,∞)

Negative function = (-4,4)

Domain Increasing Interval = (0,∞)

Range of decreasing intervals = (-∞,-16)

The complete question:

"1-1 Reteach to Build Understanding

Key Features of Functions

Linear, quadratic, and absolute-value functions can be graphed using key features

that the equation identifies. Key features can be labeled using either set builder

notation or interval notation. Interval notation represents a set of real numbers by

a pair of values. Parentheses are used when the points are not included. Brackets

are used for when a boundary point is included.

1. Use the function f(x) = x2 – 16 and identify the key features that are listed in

the table for the graph. Label the graph with the key features.

Key Feature

Domain

Range

Minimum Value

Function is Function is

x-intercept

decreasing increasing

10

y-intercept

LEAD) 14.0VA

Function is Positive

-2 O

Function is Negative

TO

Interval Increasing

Domain:

Interval Decreasing

Range:

-20160-16)."

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Answer: The last one

Step-by-step explanation: The area of a parallelogram is base x height, so you know the original area of the parallelogram is 2 x 1, which is 2.

Great, so now you have to find the area of the new parallelogram. The question says the base is halved, so the new base is now 1, and the height is quadrupled, so the height is now 4, because 1 x 4 = 4. Plugging that into the equation for the area of a parallelogram, you get an area of 4, because 1 x 4 = 4.

Now, you have to find the ratio between the two areas, and you can see that all the answer choices want the area to be new area:old area. Well, you just solved the new area, and you know the old area, so putting those two in a ratio gives you 4:2. Wait! But you have to simplify it first, or else the answer will be wrong. To simplify, you need to divide both sides by two, since it is the greatest common factor, or GCF. Dividing both sides by 2 will now give you 2:1, which is what the last answer choice says.

There are 25 2-digit positive integers have 2 different factors

A 2-digit positive integer has two different factors if it is a prime number.

There are 25 prime numbers between 1 and 100.

For example, the prime number 7 has only two factors: 1 and 7. A positive integer that is not prime is called a composite number and has more than two factors.

Therefore, there are 25 2-digit positive integers that have 2 different factors.

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