A store randomly samples 602 shoppers over the course of a year and finds that 144 of them made their visit because of a coupon they'd received in the mail. Construct a 95% confidence interval for the proportion of all shoppers during the year whose visit was because of a coupon they'd received in the mail. (Round your answers to three decimal places.)

Answer:

[tex]x = \frac{26 + 8 \sqrt{10} }{9} [/tex]

or

[tex]x = \frac{26 - 8 \sqrt{10} }{9} [/tex]

Step-by-step explanation:

I apologise for my messy explanation.

The solution of the expression will be;

⇒ x = 5.7

or ⇒ x = 0.07

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ log ₂ (3x + 2) - log ₄ (x) = 3

Now,

Since, The expression is,

⇒ log ₂ (3x + 2) - log ₄ (x) = 3

Solve as;

⇒ log ₂ (3x + 2) - 1/2 log ₂ (x) = 3

⇒ log ₂ (3x + 2) - log ₂ √(x) = 3

⇒ log ₂ (3x + 2) / (√x) = 3

⇒ (3x + 2) / √x = 2³

⇒ (3x + 2) / √x = 8

⇒ (3x + 2) = 8√x

Taking square both side, we get;

⇒ (3x + 2)² = (8√x)²

⇒ 9x² + 12x + 4 = 64x

⇒ 9x² + 12x - 64x + 4 = 0

⇒ 9x² - 52x + 4 = 0

By applying quadratic formula, we get;

⇒ x = - (- 52) ± √ (-52)² - 4×9×4 / 2×9

⇒ x = 52 ± √ 2704 - 144 / 18

⇒ x = 52 ± √2560 / 18

⇒ x = 52 ± 50.6 / 18

This gives two solution as;

⇒ x = (52 + 50.6) / 18

⇒ x = 102.6/18

⇒ x = 5.7

And, We get;

⇒ x = 52 - 50.6 / 18

⇒ x = 1.4 / 18

⇒ x = 0.07

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Answer:

The inverse of f is x=8

Step-by-step explanation:

I did it

The graph which correct shows an image and pre-image after reflecting across the line; y = -x as required in the task content is; Option 1.

It follows from the task content that the answer choice which correctly represents an image ajd pre-image after reflecting across the line; y = -x.

First it is noteworthy to know that the line; y = -x is one which passes through the origin and has a negative slope of; -1.

On this note, by observation; when the line y = -x is drawn; the graph which represents the image and pre-image after reflecting across the line; y = -x is; Option 1.

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Answer:

x = 6

Explanation:

If x is reserved for the number of hours it'll take, then the first equation is saying that $6 is being multiplied by an x amount of hours, which is then added by $30. The second equation states that $11 is being multiplied by an x amount of hours, but there is no flat fee. This makes the equation:

6x + 30 = 11x

The steps to solving this are:

1) Make the variables on one side. In this case, it is easier to put them on the right.

11x - 6x = 5x

5x = 30

2) Divide both sides by 5.

5x / 5 = 30 / 5

x = 6

This means it will take 6 hours for them to charge the same amount of money.

The perimeter of the rectangle 24x + 1 feet. The perimeter of a geometric figure is the total length of its sides.

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations.

To find the perimeter of a rectangle, you need to add the lengths of all four sides of the rectangle.

The width of the rectangle is 4x-7.5 feet and the length is 7.5x+8 feet.

The perimeter is therefore equal to 2 times the sum of the width and the length,

= 2 * (4x-7.5 + 7.5x + 8) feet.

This simplifies to 2 * (12x + 0.5) feet,

which is equal to 24x + 1 feet.

The perimeter of the rectangle 24x + 1 feet

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The values of the angles x, y, z are x=56°, y=124°, z=56°

In Euclidean geometry, an angle is a figure made up of two rays that have a shared vertex, also known as a common terminus, and are referred to as the angle's sides. The angles of two rays are situated in the plane containing the rays. An angle is also created when two planes intersect at an angle. These are referred to as dihedral angles. Another technique to define two curves is to specify the angle generated by rays that are tangent to the intersection of two curves. Angle is another word for how long a rotation or angle is.

From the given figure,

∠y=124°

∠x+124°=180°

∠x=180°-124°

∠x=56°

∠x=∠z=56°

Therefore, The values of the angles x, y, z are x=56°, y=124°, z=56°

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Using the Leading Coefficient Test the end behavior of the function  f(x) = 1234999x as the values of x increase towards infinity, ∞ is the functin also tends to infinity

The end behavior of function typically says the characteristics of the function at the ends

The given function is:

f(x) = 1234999x

The end behavior is determined by the leading Coefficient = 1234999, the problem has only one variable and hence the leading coefficient

x ⇒ ∞ f(x) ⇒ ∞

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Answer:

84 copies

Step-by-step explanation:

18 copies: $6 ==> 18:6

18:6 ==> 18/6 = 3

18 copies: $6 = 3 copies: $1  ==> common ratio of copies to cost

3 copies: $1 =

(3 copies: $1)*28 =  ==> multiply by 28 to get the number of copies for $28

3*28 copies: $28 = 84 copies: $28

Answer: 84 copies

Answer:

(18 copies for $6 = x copies for $28)

18:6 = x:28

6x = 18(28)

6x = 504

x = 84 copies

Copies       |     Dollars

  18             |       $6

  84           |      $28

Step-by-step explanation:

Answer:

(C) 12

Step-by-step explanation:

To solve this problem, we can use the following steps:

Find half of 80: 80/2 = 40

Add 20 to half of 80: 40 + 20 = 60

Find one fifth of the result: 60/5 = 12

Therefore, one fifth of twenty more than half of 80 is equal to 12. The correct answer is (C) 12.

Answer:

(C) 12

Step-by-step explanation:

What is one fifth of twenty more than half of 80

0.5 × 80 = 40

What is one fifth of twenty more than half of 80

40 + 20 = 60

What is one fifth of twenty more than half of 80

1/5 × 60 = 60/5 = 12

David's three exam scores are B. 84, 88, 98

From the information, David took three exams. The median score of his exams was 88, the mean score was 90, and the range was 14.

The scores are 84, 88, and 98. The middle number is 88. It's the median.

The mean is:

= (84 + 88 + 98) / 3

= 270 / 3.

= 90

Range will be:

= Highest number - Lowest number

= 98 - 84

= 14

In conclusion, the correct option is B.

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Answer:

the answer is < explanation at the step by step

Step-by-step explanation:

Do the Basic equation

2.18 x 10 - 6= 15.8

4.36 x 10 - 7= 36.6

Answer: x = 11

Step-by-step explanation: set both angles equal to 90 bc a triangle is 180 minus the 90 degree angle

The sampling methods here that are not examples of simple random sampling are;

A) Select the first 10 people from a list of members.

B) Ask 10 members in the gym on a Monday morning

E) Select every 20th person from a list of members until she has 10 .

F) Ask all members of the gym

A simple random sample is defined as a randomly selected subset of a particular population. In this method of sampling, it will be noticed that each member of the population has an exactly equal chance of being selected.

The importance of simple random sampling is that it removes every form of bias as every member has an equal chance of being selected. Thus, it will give a good representation of what we want to research.

A) Select the first 10 people from a list of members; This is not simple random sampling because it is not random but specific.

B) This is not random because it is specific which is just a monday morning and we don't have an idea of the type of people that come on the other days.

C) Use a random number generator to select 10 members from a list; This is simple random sampling because a random number generator is used.

D) Select 10 members' names from a box without looking; This is random because all members have an equal chance of being selected.

E) Select every 20th person from a list of members until she has 10; This is not random as all members don't have an equal chance of being selected.

F) Ask all members of the gym; This is not random selection.

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Therefore , the solution to the given problem of equation that the estimated rent comes out o be $1600.

The equivalent sign connects two expressions to form a mathematical statement known as an equation. An equation is, for instance, 2x - 5 = 15. By solving this equation, we can determine that the value of the variable x is 5.

Here,

In 2020, a one-bedroom apartment in New York City will cost $1600.

The formula for a straight line graph is often y = mx + c, where;

m = gradient

c is the vertical intercept.

With this knowledge, the graph clearly shows that the ideal line of fit for the data plot is y = 40x + 800.

This means that a one bedroom flat in New York City will cost; in the year 2020, which is 20 years after the year 2000;

y = 40(20) + 800 = $1600

Therefore , the solution to the given problem that the estimated rent comes out o be $1600.

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Answer:

x = 9

Step-by-step explanation:

Use Vertical Angles and Supplementary Angles to put all the given information inside the triangle.

Then use the idea that the three angles in a triangle add up to 180° to write an equation.

see image.

Actually also--shortcut! The 150° is an exterior angle, so it is equal to the

90° + 5x+15

90 + 5x + 15 = 150

this calculation comes out the same as the other.

Answer:

  x = 9

Step-by-step explanation:

Given a right triangle with an exterior angle of 150°, and a vertical angle to the other acute angle marked as 5x+15, you want to solve for x.

The exterior angle is equal to the sum of the remote interior angles. One of those is the right angle; the other is a vertical angle with respect to the one marked 5x+15. So, we have ...

  150 = 90 + (5x +15)

  45 = 5x . . . . . subtract 105

  9 = x . . . . . . divide by 5

The value of x is 9.

Answer:

Overall, as a doctor, I would prioritize treating Kundaval immediately due to their higher heart rate and larger projected deviation.

Step-by-step explanation:

As a doctor, I would prioritize treating the patient with the higher heart rate and larger projected deviation. In this case, that would be Kundaval, whose sum of heart rate readings is 400 and whose projected deviation is 3.16.

Heart rate is an important vital sign that reflects the health and function of the cardiovascular system. It is measured in beats per minute (bpm) and can vary based on factors such as age, activity level, and overall health. A high heart rate, especially in combination with a large projected deviation, can be a sign of a potential health problem or underlying condition that requires immediate medical attention.

In contrast, Kulazhi has a lower heart rate and smaller projected deviation, which may indicate that their cardiovascular system is functioning normally. However, it is still important to monitor and track their heart rate over time to ensure that it remains within a healthy range.

If I were a doctor, the immediate patient I would treat is; Kundaval because he has a higher projected deviation and a faster heart rate.

Instead of computation or experimentation, the standard deviation is an abstract concept based on observation.

A metric that is used to express the amount of variation or dispersion in a group of data is the standard deviation, which is also represented by the Greek letter sigma(σ).

To put it another way, it specifies the degree to which the members of a data group differ from the group's average value.

Given

The sum of heart rate readings taken five times for Kundaval is 400

The sum of heart rate readings taken five times for  Kulazhi is 360

and their projected deviation are 3.16 and 2.0,

Now, the standard deviation is a measure of how dispersed the data are in relation to the mean, whereas the mean simply refers to the average of a set of given data.

As a result, as a doctor, I would prioritize treating the patient whose heart rate and projected deviation are higher. As a result, we would conclude that Kundaval, with a projected deviation of 3.16 and a sum of 400 heart rate readings, should be treated first.

Therefore, The immediate patient I would treat if I were a doctor is; Kundaval because he has a faster heart rate and a higher projected deviation.

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Answer:

693.2

Step-by-step explanation:

6.932 · 100

Move the point two times to the right

693.2

Answer:

Step-by-step explanation:

You split it up into two 3-D triangles.

One of them has a volume of ((6*(5+5))/2)*8 = (60/2)*8=240

For the other one, you are missing a side on the 2-D face, so in order to apply pythagorean's theorem you need to split it into two more triangles. You know that 13^2=5^2+x^2    169-25=x^2         144=x^2  x=12

now that you know the missing side of the triangle you can recombine them. The volume of the remaining 3-D triangle is (((5+5)*12)/2)*8 = 60*8=480

480+240=720 meters cubed

The fourth term of the recursive sequence in this problem is given as follows:

[tex]a_4 = 15[/tex]

The nth term of a recursive sequence is obtained applying the recursive rule n times, considering that the first term of the sequence is given.

The recursive rule for this problem is given as follows:

[tex]a_n = 2a_{n - 1} + 1[/tex]

The first term of the sequence is given as follows:

[tex]a_1 = 1[/tex]

Then the second term of the sequence is given as follows:

[tex]a_2 = 2(1) + 1 = 2 + 1 = 3[/tex]

The third term of the sequence is given as follows:

[tex]a_3 = 2(3) + 1 = 6 + 1 = 7[/tex]

The fourth term of the sequence is given as follows:

[tex]a_4 = 2(7) + 1 = 14 + 1 = 15[/tex]

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Assume the account earns 7% simple interest. in your account now. You would need to deposit $3,007.52 in your account.

1541 days = 4.2219 years

Hence,

Time = 4.2219 years

Interest rate = 7%

Principal = $4,000

Hence,

4000=Po(1+.07)^4.2219 years

4000=1.33×Po

Po = 4,000 /1.33

Po = $3,007.52

Therefore the amount you need to deposit is  $3,007.52.

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The mean number of misprints per page on manuscript is 0.5 and If a page is selected then the probability that it has 3 misprints is 0.0126..

The Poisson distribution is a theoretical discrete probability, also known as the Poisson distribution probability mass function. It is used to find the probability that independent events occur at regular time intervals and have a constant average rate. λ is the Poisson rate parameter, the expected average number of events over a given time interval.

Using the Poisson distribution formula:

P(X = x) = (e-λ (λˣ) )/x!

where λ is mean number or poisson rate parameter ; x = 0, 1, 2, 3...

e is the Euler's number(e = 2.718)

We have given that,

Total number of Manuscript Pages = 400

total misprinted pages = 200

let X be random variable that the page is misprinted .

Mean number, λ = 200/400 = 0.5

the probability that it has 3 misprints, P(X= 3) = (e⁻⁰·⁵ (0.5)³ )/3!

= e⁻⁰·⁵ ( 0.125 )/6 =0.075816/6 = 0.0126

Hence, the required probability is 0.0126..

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Complete question:

Misprints on Manuscript Pages In a 400-page manuscript, there are 200 randomly distributed misprints Part 1 of 2 Find the mean number of misprints per page. Round the answer to one decimal place as needed. If a page is selected, find the probability that it has 3 misprints.

Answer:

Doing the math, it should be 7.25/1

The hypothesis, at the 0.05 significance level,

H₀ : the observed distribution of X may be fitted by the geometric distribution

Hₐ : the observed distribution of X may not be fitted by the geometric distribution

we conclude p-Value > α so, cannot reject null hypothesis. The observed distribution of X may be fitted by the geometric distribution g(x ; 1 / 2), x=1,2,3

A coin is thrown until a head occurs and the number X of tosses recorded.

The probability that head occur on toss ,p = 0.5

Consider the null and alternative hypothesis,

H₀ : the observed distribution of X may be fitted by the geometric distribution

Hₐ : the observed distribution of X may not be fitted by the geometric distribution

The chi square test statistic here as:

χ² = ∑( Oᵢ - Eᵢ)²/Eᵢ

where Oᵢ--> observed value

Eᵢ --> expected value

and the expected frequencies for each X here E(x) = P(X = x) = 256×g(x)

The probability mass function of geometric distribution with parameter 1/2 is g(x) = (1/2)(1 - 1/2)⁽ˣ⁻¹⁾

where x = 0, 1,2 ,3,......

Observed values are f :136 60 34 12 9 1 3 1

Using the data,we calculate the expected values

E₁ = P( x = 1) = 256×g(1) = 256×(1/2)(1/2)⁰

= 128

E₂ = P( x =2) = 256×g(2) = 256×(1/2)(1/2)¹

= 64

E₃ = P( x = 3) = 256×g(3) = 256×(1/2)(1/2)² = 32

E₄ = P( x = 4) = 256×g(4) = 256×(1/2)(1/2)³

= 16

E₅ = P( x = 5) = 256×g(5) = 256×(1/2)(1/2)⁴

= 8

E₆ = P( x = 6) = 256×g(6) = 256×(1/2)(1/2)⁵

= 4

E₇ = P( x = 7) = 256×g(7) = 256×(1/2)(1/2)⁶

= 2

E₈ = P( x = 8) = 256×g(8) = 256×(1/2)(1/2)⁷

= 1

Hence, χ² = ∑( Oᵢ - Eᵢ)²/Eᵢ

= (136 - 128)²/128 + (60 - 64)²/64 + (34 - 32)²/32 + (12-16)²/16 +(9 - 8)²/8 + (1 - 4 )²/4 + (3 - 2)²/2 +(1 - 1)²/1

= 0.5 + 0.25 + 0.125 + 1 + 0.125 + 2.25 + 0.5 =4.75

Significance level is α =0.05

Using the χ² table, the p- value for χ² is 0.6290 .. Now P value > 0.05 , therefore the test is not significant here and we cannot reject the null hypothesis here. Therefore we have sufficient evidence here that the frequencies given are fitted by the geometric (p = 0.5) distribution.

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We have proved that the ray FE is parallel to the ray GC.

What is meant by parallel lines?

In geometry, parallel lines are coplanar straight lines that do not intersect at any point. Parallel planes are planes in the same three-dimensional space that never meet. Parallel curves are curves that do not touch each other or intersect and keep a fixed minimum distance.

Angle DEF intersects at B

which results in angle DEF corresponding to the angle  ACG.

As DEF = 45 so angle ACG = 45

So by the above discussion, we can say that the ray FE is parallel to the ray GC.

Hence, we have proved that the ray FE is parallel to the ray GC.

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The associative property states that the order in which three or more numbers are added or multiplied does not affect the result of the operation. You can apply the associative property to the expressions A. 9-5-2, B. 5+3-2, and D. 7+3+1.

In expression A, 9-5-2, you can rearrange the numbers as follows: 9-5-2 = (9-5)-2 = 4-2 = 2.

In expression B, 5+3-2, you can rearrange the numbers as follows: 5+3-2 = (5+3)-2 = 8-2 = 6.

In expression D, 7+3+1, you can rearrange the numbers as follows: 7+3+1 = (7+3)+1 = 10+1 = 11.

You cannot apply the associative property to expression C, 8÷4÷1, as this is a division expression, and the associative property does not apply to division.

Overall, the associative property allows you to rearrange the order of addition or multiplication of three or more numbers without affecting the result of the operation.

The expressions that you apply the associative property to will be (9 - 5 - 2), (5 + 3 - 2), and (7 + 3 + 1). Then the correct options are A, B, and D.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

A mathematical principle that states the product of a multiplication issue is unaffected by the way the elements are organized.

The associative property for addition and multiplication is valid but not for division.

The expressions that you apply the associative property to will be (9 - 5 - 2), (5 + 3 - 2), and (7 + 3 + 1). Then the correct options are A, B, and D.

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The amount of money earned by Zach each week will be equal to $9 per week.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given data in the question,

Total amount earned by Zach = $36

The time taken to earn the amount = 4 weeks

Then, the amount earned each week will be.

= $36/4

= $9 per week

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The probability of drawing a king, a king or queen, a diamond, or a black card from a deck of 52 cards is 1/52, 4/52, 13/52, and 26/52, respectively.

(a) The probability that a king is drawn is 1/52, since there is only one king in the deck and 52 total cards. This means that if we draw one card from the deck, the probability that it will be a king is 1/52.

(b) The probability that a king or a queen is drawn is 4/52, since there are four kings and queens in the deck and 52 total cards. This means that if we draw one card from the deck, the probability that it will be a king or queen is 4/52.

(c) The probability that a diamond is drawn is 13/52, since there are 13 diamonds in the deck and 52 total cards. This means that if we draw one card from the deck, the probability that it will be a diamond is 13/52.

(d) The probability that a black card is drawn is 26/52, since there are 26 black cards in the deck and 52 total cards. This means that if we draw one card from the deck, the probability that it will be a black card is 26/52.

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The equation is y = 15x + 90. The initial value is 90. Rate of change is: 15.

To host a party at a local restaurant, you must pay $90 to rent it and $15 per guest.

To write a linear equation that models a situation in slope-intercept form, y = mx + b, find the following:

Given the table above, the value of y when x = 0 is 90. This means the initial value (b) = 90.

Using two pairs of values from the table, (0, 90) and (6, 180):

Rate of change (m) = (180 - 90) / (6 - 0) = 15

Substitute m = 15 and b = 90 into y = mx + b, to write the equation:

y = 15x + 90.

The graph of y = 15x + 90 is shown below.

The complete table is:

x   |  y  

0    90

3    135

6    180

9    225

12   270

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Measure of angle AKQ is 90°.

There are several different kinds of angles in geometry. Angle is one of the most significant and fundamental units. When two rays or lines are connected at their common terminus, an angle is created. Angles are used in many facets of daily life, including the construction of buildings, dams, and statues, starting with a pizza slice. Angle has a crucial role in civil engineering. A pair of rays (half-lines) with a shared terminal are combined to form an angle. The latter is referred to as the angle's vertex, and the rays are sometimes referred to as the angle's legs and other times as its arms.

Given

Measure of angle AKQ is 90°.

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