A salon wants to conduct a survey in order to study the consumption pattern of its consumers. The population mean spending on visiting salon per month is unknown with the population standard deviation is assumed to be $200. A random sample of 55 customers is selected and the sample mean spending on visiting salon per month is $800.
(a) Construct a 95% confidence interval estimate for the population mean spending by a customer on visiting salon per month. (3 marks)
(b) It is suggested to do the second round inspection. This time, the sample size is 120. What is the sampling error at 95% confidence level? (2 marks)

Answer: width is 13.5 cm

Step-by-step explanation:

9 x 2 +2x =45

45-18

2x=27

2x/2=27/2

x=13.5

width is 13.5 cm

The Equation of the Line in Standard form is 4x - y = 3

What is Slope of a Line?

The slope formula is used to compute the inclination or steepness of a line. The slope of the lines is calculated using the x and y coordinates of the lines. It is the ratio of the y-axis change to the x-axis change.

Solution:

Slope of the Line passing through the points (1, 1), (2, 5)

is

m = 5-1/2-1 = 4

Equation of the line = (y - y1) = m(x - x1)

y - 1 = 4(x - 1)

y - 1 = 4x - 4

4x - y = 3

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The factored form of the polynomial x + 9x + 20 is (x + 4)(x + 5). To obtain this form, we can use the factoring method known as "FOIL," which stands for "First, Outer, Inner, Last." This method involves multiplying the first terms, the outer terms, the inner terms, and the last terms of the two factors to obtain the original polynomial.

In this case, if we let the factors be (x + 4) and (x + 5), we can use FOIL to multiply them and obtain the following:

(x + 4)(x + 5) = (x * x) + (4 * x) + (x * 5) + (4 * 5)

This simplifies to:

(x + 4)(x + 5) = x^2 + 9x + 20

As we can see, the result is the original polynomial. Therefore, the factored form of x + 9x + 20 is (x + 4)(x + 5)

The value of the factored form of the polynomial are,

⇒ (x + 4) (x + 5)

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The polynomial are,

⇒ x² + 9x + 20

Now, We can simplify as;

⇒ x² + 9x + 20

⇒ x² + 5x + 4x + 20

⇒ x (x + 5) + 4 (x + 5)

⇒ (x + 4) (x + 5)

Thus, The value of the factored form of the polynomial are,

⇒ (x + 4) (x + 5)

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Step-by-step explanation:

your question is strange.

first you tell us that 50 people like coffee, 25 like tea, and 13 like both.

and then you ask how many like coffee or tea or both.

is this a joke ? or do you rather mean how many like only coffee, or only tea, and how many don't like neither ?

since 13 people like coffee and tea, these 13 are also part of the group of 50 that like coffee, and of the group of 25 that like tea.

so, to get the number of people that like only one, we need to deduct the number of people, who like both from both groups.

the number of people that only like coffee is therefore

50 - 13 = 37

and the number of people that only like tea is

25 - 13 = 12

we know the number of people that like coffee and tea is 13.

together that are

37 + 12 + 13 = 62 people.

that means 70 - 62 = 8 people don't like neither coffee nor tea.

Answer: 62

Step-by-step explanation:

Those who like coffee only = 50 - 13 = 37. Those who like tea only = 25 - 13 = 12. Those who like either coffee, or tea, or both = 37 + 12 + 13 = 62.

In theory, the 70 people being surveyed could fall under any of the following four categories:

I have labelled the four categories 1, 2, 3 and 4 for convenient reference.

From the information provided in the question, category 1 contains 50 people, category 2 contains 25 people, while category 3 contains 13 people. We do not yet know how many people fall under category 4, but we shall calculate it.

We know from set theory that the four aforementioned categories are known formally as sets. A set is simply a group of objects or things that are similar in some way. Each of the objects in a set is called a member of that set. Two sets can intersect. The intersection of two sets is simply the collection of members that are in both of the two sets. Also, two sets can unite. The union of two sets is the collection of members that in either of the two sets.

For example, category 3 is the intersection of category 1 and 2. The question requires us to calculate the union of category 1 and 2.

Answer:

P=-15

Step-by-step explanation:

P-12=-27  |+27

P+15=0

P=-15

After solving the equation, we can conclude that Callie should rent the bicycle for a maximum of 3 hours.

The equals sign is indeed a symbol used in mathematical formulas to denote the equality of two reactions.

Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions.

For example, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.

So, according to the given information, form the equation as follows:

12x + 10 = 45

Where x is the number of hours Callie rents the cycle.

Now, calculate for x as follows:

12x + 10 = 45

12x = 45 - 10

12x = 35

x = 35/12

x = 2.91

Rounding off: 3

Therefore, after solving the equation, we can conclude that Callie should rent the bicycle for a maximum of 3 hours.

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Complete question:

Callie is on vacation and wants to rent a bicycle to explore the town. She pays a $10 flat fee and then $12 per hour for the rental.

If Callie has $45 to spend, what is the greatest number of full hours she can rent the bicycle?

The solution of the inequality will be;

⇒ x > 5

And, The solution is shown on number line.

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is,

⇒ - 2/5x < - 2

Now,

Solve the inequality as;

⇒ - 2/5x < - 2

⇒ - 2x < - 2 × 5

⇒ - 2x < - 10

Multiply by - 1,

⇒ 2x > 10

⇒ x > 5

Thus, The solution of the inequality = x > 5

And, The solution is shown on number line in figure.

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The slope of the line that passes through the given two points is m = 26/25.

Consider a line that passes through the points (x1, y1) and (x2, y2).

So, the slope of the line is calculated by

m = (y2 - y1)/(x2 - x1)

The given line passes through points (1, 3) and (26, 29).

So, we can consider (x1, y1) = (1, 3) and (x2, y2) = (26, 29).

Then, the slope of the line is

m = (y2 - y1)/(x2 - x1)

   = (29 - 3)/(26 - 1)

   = 26/25

Therefore, the slope of the given line is 26/25.

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Answer:

Hope the picture will help you

Answer: y = -5/6x - 23/6

(Read the explanation first to make sure it's correct)

Step-by-step explanation:

A parallel line means that it has the same slope as the equation:

5x + 6y = 11

Let's first convert this standard form equation into slope-intercept form:

y = -5/6x + 11/6

So that means that our new line also has a slope of:

-5/6

So far, for our new equation we have:

y = -5/6x + b

Next, let's plug in the values of our point to the equation:

-3 = 5/6 + b

So b = -23/6

So the equation in slope-intercept form is:

y = -5/6x - 23/6

The population of the city after eight years is 35,125,731,743

Population growth is the increase in the number of people in a population or dispersed group. The expression P(t) = P(o)(1+r)^t can be used to determine the growth rate of a population.

Where P(t) is the population at a particular time

P(o) is the initial population , t is the time and r is the growth rate.

Here the growth rate has been given, but we are to find p(t).

P(t) = 330,000(1+3.25)⁸

P(t) = 330,000(4.25)⁸

P(t) = 330,000× 106441.61

P(t) = 35,125,731,743( nearest billion)

Therefore the population of the city after 8years is 35,125,731,743

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Answer:

Step-by-step explanation:

13

Answer: 13

Step-by-step explanation:

I hope it helps

Answer: e

Step-by-step explanation:

4+6= 10 and then divide by 50 and add 25 so 0.2+25+25.02 so then subtract 4 so about 21 or 21.02

Answer:

height = 4cm

Step-by-step explanation:

volume of right-circular cylinder = πr²h

h = r

so

πr²r or πr³

πr³ = 64π

r³ = 64

r = 4

h = 4

Answer:10

Step-by-step explanation:3/5x10=6

So our goal is to determine the mean test score, which we don't know, we know to raw scores, we know one raw score is 38 that's one standard deviation below the mean, which by definition of a Z score that Z equals negative one. one

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Answer:

Step-by-step explanation:

A vending machine

The user puts in money, punches a specific button, and a specific item drops into the output slot. (The function rule is the product price. The input is the money combined with the selected button. The output is the product, sometimes delivered along with coins in change, if the user has entered more money than required by the function rule.)

Answer: it is mean to state a real world relationship that consisted a state of a input and output

Step-by-step #hopethishelps

The values that make the inequality true are (a) 2.11 (c) 1.1 and (d) 1.63

From the question, we have the following parameters that can be used in our computation:

0.3m ≥ 0.55-0.2m

Evaluate the like terms

0.5m ≥ 0.55

Divide both sides by 0.5

So, we have the following representation

m ≥ 1.1

This means that the true values are at least 1.1

In this case, they are 1.1, 1.63 and 2.1

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The required values of x and y are x = 2 and y = 11.

We have been given that parallelogram PQRS which has:

PT = ​y, TR = 5x+​1, QT = 2​y, TS = 6x+10

We know that the diagonals of a parallelogram bisect each other.

So, PT = TR and QT = TS

Substitute the values and we have a system of equations:

y = 5x + ​1    ....(i)

2y = 6x + 10 ....(ii)

Substitute the value of the equation y = 5x + ​1 in equation (ii), and solve for x

2(5x + ​1) = 6x + 10

10x + 2 = 6x + 10

10x - 6x = 10 - 2

4x = 8

x = 8/4

x = 2

Substitute the value of x = 2 in equation (i), and solve for y

y = 5(2) + ​1

y = 10 + 1

y = 11

Therefore, the required values of x and y are x = 2 and y = 11.

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Answer:

Slope is undefined. { Infinity }

Step-by-step explanation:

Formula we use,

→ Slope(m) = (y2 - y1)/(x2 - x1)

Now required slope will be,

→ m = (y2 - y1)/(x2 - x1)

→ m = (8 + 12)/(17 - 17)

→ m = 20/0

→ [ m = 0 ]

Hence, the slope is undefined.

The slope of the line passing through the points ( 17 , -12 ) and ( 17 , 8 ) is undefined

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 17 , -12 )

Let the second point be Q ( 17 , 8 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 8 - ( -12 ) ) / ( 17 - 17 )

On simplifying the equation , we get

Slope m = ( 8 + 12 ) / 0

Slope m = 20 / 0

So , the slope is undefined

Hence , the slope of the line is m = undefined

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In the given equation, the coefficient of b is 183/23 and the constant coefficient is -30.

The given equation is 8b= b/23 +30.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Now, 8b= b/23 +30

⇒ 8b-b/23 -30=0

⇒ 8b-b/23 -30=0

⇒ 183b/23 -30=0

Here, the coefficient of b is 183/23 and the constant coefficient is -30.

Therefore, in the given equation, the coefficient of b is 183/23 and the constant coefficient is -30.

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Answer:

0.38

Step-by-step explanation:

imagine a circle, with C being the center, and 13 being the radius.

the triangle is then representing the trigonometric functions. remember, they are all multiplied by the radius as the circle is much higher than the norm circle (radius 1).

so,

5 = sin(C) × 13

sin(C) = 5/13 = 0.384615385... ≈ 0.38

Answer:

Hope the picture will help you

The stated statement indicates that the takt time is 5.38 minutes for each section.

Takt time is calculated as the amount of manufacturing time that is available divided by the volume of orders. Takt time, for instance, is two minutes if a factory makes widgets for 480 minutes a day and clients need 240 widgets per day. Similar to this, the takt time is one week if clients desire two new goods per month.

Takt time depends on client demand and the amount of time that is available, and for many items, it is always changing as the demand from the market shifts. Takt time is unaffected by system changes, although cycle time is affected.

Available hours are 7 * 60 minutes, which is 420 minutes.

No. of parts = 78 units

Available time for work / No of parts = Takt time

               = 420/ 78

               = 5.38 minutes per part

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Answer:

D) [tex]f^{-1}(x)=(x-3)^2+2[/tex]

Step-by-step explanation:

[tex]f(x)=\sqrt{x-2}+3 \implies x=\sqrt{f^{-1}(x)-2}+3 \\ \\ x-3=\sqrt{f^{-1}(x)-2} \\ \\ (x-3)^2=f^{-1}(x)-2 \\ \\ f^{-1}(x)=(x-3)^2+2[/tex]

Note we take the positive case because the domain of the original function is the same as the range of the inverse, and the domain of [tex]f(x)[/tex] is [tex][2, \infty)[/tex].

Answer:

19°

Step-by-step explanation:

m<A + m<B + m<C = 180°

a + 17° + 49° + 5a = 180°

6a + 66° = 180°

6a = 114°

a = 19°

x=7/6

---------------

The value of x is 9.

The value of y is 5.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

Two triangles in a composite triangle.

We see that,

m∠UST = m∠STR

This means,

x + 4 = 13

x = 13 - 4

x = 9

The sum of the angles in a triangle is 180 degrees.

One triangle is an equilateral triangle.

All three angles are equal.

This means,

The angle has to be 60°.

m∠UTR + m∠URT + m∠TUR = 180

3m = 180

m = 60

Now,

m∠URS = 180

m∠URT + m∠SRT = 180

60 + m∠SRT = 180

m∠SRT = 120

The isosceles triangle has two equal angles.

m∠RTS = m∠RST

m∠SRT + m∠RTS + m∠RST = 180

120 + 6y + 6y = 180

12y = 180 - 120

12y = 60

y = 5

Thus,

The value of x and y are 9 and 5.

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it would be inconsistent. Meaning it won't have a solution