an independent group of food service personnel conducted a survey on tipping practices in a large metropolitan area. they collected information on the percentage of the bill left as a tip for 3535 randomly selected bills. the average tip was 12.7.7% of the bill with a standard deviation of 2.8%2.8%. assume that the tips are approximately normally distributed. construct an interval to estimate the true average tip (as a percent of the bill) with 99% confidence. round the endpoints to two decimal places, if necessary.

Answer:

(a)  15

(b)  270

Step-by-step explanation:

Given expression:

[tex]\left(\sqrt{5}\right)^2 \times \left(\sqrt{3}\right)^2[/tex]

[tex]\textsf{Apply the exponent rule}:\quad \left(\sqrt[n]{a}\right)^n=a,\quad \textsf{$n$ is odd or $a \geq 0$}[/tex]

[tex]\implies 5 \times 3[/tex]

Multiply the numbers:

[tex]\implies 15[/tex]

Given expression:

[tex]\left(\sqrt[3]{9} \right)^3 \times \left(\sqrt{30}\right)^2[/tex]

[tex]\textsf{Apply the exponent rule}:\quad \left(\sqrt[n]{a}\right)^n=a,\quad \textsf{$n$ is odd or $a \geq 0$}[/tex]

[tex]\implies 9 \times 30[/tex]

Multiply the numbers:

[tex]\implies 270[/tex]

Now we have to,

→ work out the value for the following.

We know that,

→ square ( ²) and square root (√) gets cancelled each other.

→ cube ( ³) and cube root (³√) gets cancelled each other.

a) (√5)² × (√3)² = ?

→ (√5)² × (√3)²

→ 5 × 3 = 15

Thus, the answer is 15.

b) (³√9)³ × (√30)² = ?

→ (³√9)³ × (√30)²

→ 9 × 30 = 270

Thus, the answer is 270.

Answer:

1 cm = 0.6 m.

Step-by-step explanation:

15 cm to 9 meters

= 15 cm to 900 cm

so 1cm = 900/15 cm

1cm = 60cm

1 cm = 0.6 m.

Answer:

Question 27

[tex]\textsf{(a)} \quad -\dfrac{6}{5}[/tex]

[tex]\textsf{(b)} \quad \dfrac{1}{10}[/tex]

[tex]\textsf{(c)} \quad \dfrac{4}{5}[/tex]

Question 28

[tex]\textsf{(a)} \quad \dfrac{6}{0}=\textsf{und\:\!efined}=\textsf{no gradient}[/tex]

[tex]\textsf{(b)} \quad -\dfrac{3}{10}[/tex]

[tex]\textsf{(c)} \quad \dfrac{3}{10}[/tex]

Step-by-step explanation:

The gradient of a straight line can be found by dividing the difference in the y-coordinates by the difference in the x-coordinates between two points on the line.

A positive gradient slopes up from left to right.

A negative gradient slopes down from left to right.

[tex]\boxed{\begin{minipage}{4.3cm}\underline{Gradient Formula}\\\\$m=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\end{minipage}}[/tex]

We can use the formula to find the gradients, or we can simply calculate the change in y and change in x by looking at the graph.

Example:

If we take line (a) from question 27 as an example.

Therefore, the gradient is -6/5.

Using the gradient formula, define two points on the line:

Input the points into the formula:

[tex]\textsf{Gradient}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-6}{5-0}=-\dfrac{6}{5}[/tex]

Solutions

Question 27

(a)  The gradient is -6/5, as calculated above.

(b)  The change in y is 1 unit and the change in x is 10 units. The line slopes up so the gradient is positive.  Therefore, the gradient is 1/10.

(c)  The change in y is 4 units and the change in x is 5 units. The line slopes up so the gradient is positive.  Therefore, the gradient is 4/5.

Question 28

(a)  The change in y is 6 units and the change in x is 0 units. Therefore, the gradient is undefined since anything divided by 0 is undefined.  Therefore, this line has no gradient.

(b)  The change in y is 3 units and the change in x is 10 units. The line slopes down so the gradient is negative.  Therefore, the gradient is -3/10.

(c)  The change in y is 3 units and the change in x is 10 units. The line slopes up so the gradient is positive.  Therefore, the gradient is 3/10.

Attachment

I have marked the change in y (green) and the change in x (blue) for line (c) on both graphs.

There are 4 liters of solution are needed for the 10% acid solution.

Unitary method:

Unitary method is the way to find the value of a single unit and then multiply the value of a single unit to the number of units to get the necessary value.

Given,

In a chemistry class, 8 liters of a 4% acid solution must be mixed with a 10% acid solution to get a 6% acid solution.

Here we need to find how many liters of the 10% acid solution are needed.

First, we have to convert the percentage into decimal,

4% = 4/100 = 0.04

10% = 10/100 = 0.10

6% = 6/100 = 0.06

Let x be the required liter of solution.

So, based in the given details,

We have to write the equation as,

=> 0.04*8 + 0.10x = 0.06(8+x)

=> 0.32 + 0.10x = 0.48 + 0.06x

=> 0.10x - 0.06x = 0.48 - 0.32

=> 0.04x = 0.16

=> x = 0.16/0.04

=> x = 4

x = 4 liters of 10% solution is used.

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Answer:

2.62 x 10^16

Step-by-step explanation:

Step-by-step explanation:

Let look at the numerator:

(3.1 x 10^6)(6.97 x 10^4)

= (3.1 x 6.97) x 10^(6+4)

= 21.607 x 10^10

So  21.607 x 10^10      

      _______________        

      8.245 x 10^-6

= (21.607/8.245) x 10^(10 - -6)

= 2.62 x 10^(10 + 6)

= 2.62 x 10^16

I hope this helps

Answer:2.62061855 x 10^16

Step-by-step explanation:

Answer:

Step-by-step explanation:

e

The number of pages read by Soua in 10 minutes are 26.7 pages.

It is given in the question that Soua can read 8 pages in 3 minutes.

We have to find the number of pages that she will she read in 10 minutes.

We will use the unitary method for this question.

The method by which we find out the value of one unit and further use it to find the value of multiple units is known as the unitary method.

Pages read by Soua in 1 minute = 8/3 pages

Hence, we can write,

Pages read by Soua in 10 minutes = 10*(8/3) = 80/3 pages = 26 and(2/3) pages = 26.667 pages ≈ 26.7 pages.

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Answer: y = xw/v

Step-by-step explanation:

v = ( 1/y )*xw

⇒ y = xw/v

Keith credit card balance by next month is $664.88 if he doesn't make any additional charges

Information about the problem:

Calculating the amount he could not pay, we have:

Amount to pay= Total balance - minimum paid

Amount to pay= $732 - $75

Amount to pay= $657

Calculating the final balance he will pay:

Final balance = Amount to pay + (amount to pay * Charge fee/100)

Final balance = $657 + ($657 * 1.2/100)

Final balance = $657 + ($657 * 0.012)

Final balance = $657 + ($7.884)

Final balance = $664.88

Percentage is defined as the number that represents a ratio of a total that is divided by 100 equal parts. It is represented by the symbol %.

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Answer: 18.84 cm

circumference = 2πr, where r is the radius.

radius is half of the diameter.

6/2 = 3 so radius is 3

2x3.14x3= 18.84 cm

hope it helps.

Answer:

See Explanation

Step-by-step explanation:

So, the uncle has $3000.

The Oldest Niece gets double what the Younger Niece gets half her amount. The nephew gets the total of these 2 combined.

The Youngest Niece gets $500.

500x2=1000

The Oldest Niece gets $1000.

1000+500=1500

The Nephew gets $1500.

1500+1000+500=3000

Answer:

$15928.81

Step-by-step explanation:

hope this works

2000 x (0.98)^5 = ans

ans x (0.975)^5 = 15928.81442 which rounds to $15928.81

Answer:

Step-by-step explanation:

[tex]\displaystyle\\\frac{1}{2},\ \ \frac{4}{7},\ \ \frac{9}{14},\ \ \frac{5}{7} ,\ \ ... \\\\\frac{1*7}{2*7} ,\ \ \frac{4*2}{7*2} ,\ \ \frac{9}{14}, \ \ \frac{5*2}{7*2} ,\ \ ...\\\\\frac{7}{14},\ \ \frac{8}{14} , \ \ \frac{9}{14},\ \ \frac{10}{14},\ \ \frac{11}{14},\ \ ...,\ \ \frac{6+n}{14} , \ \ n=1,\ 2,\ 3,\ ...[/tex]

The required total of price area,  leather field, and sneakers field is evaluated with the help of arithmetic operations as 102.

Given that,
Joining 60.00 into the price, area joining 3.00 into the price of the leather field entering 38.00 into the price of sneakers field,
The sum of the components is to be determined.

In mathematics, it deals with a number of procedures according to the statements. There are four primary arithmetic operators, addition, subtraction, multiplication, and division,

Here,
Joining 60.00 into the price area,
Joining 3.00 into the price of the leather field.
entering 38.00 into the price of sneakers field,
The sum = 60.00 + 3.00 + 38.00
The sum = 102

Thus, the required total of entries is evaluated with the help of arithmetic operations as 102.

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Answer:

[tex]\frac{4}{5}[/tex]

Step-by-step explanation:

The method that can be used to write the equation of a line in slope-intercept form given two points is A. Find the slope using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept.

It should be noted that the equation of line passing through two point =  y = mx + b.

Also, b can find out via putting values of x, y, and m in the equation of the line to get y-intercept.

In this case, the slope of the line will be y2 - y1/x2 - x1.

In conclusion, the correct option is A.

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The order from least to greatest is  -8.222 <-7.43 < 8.333 < 8.366

The numbers given are:

The square root of 70 =√70 = 8.366

Negative 8.2 repeating = -8.222

Twenty five thirds = 25/3 = 8.333

Negative eight and Four sevenths = -8 and 4/7 = (-52)/7 = -7.43

So from least to greatest,

-8.222 <-7.43 < 8.333 < 8.366

That is,  Negative 8.2 repeating < Negative eight and Four sevenths < Twenty five thirds < The square root of 70

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The coordinates of K are (8,3).

There is a line segment JK with M as its midpoint. This means the length of JM = length of MK.

Also the coordinates of J is (-4,7) and the coordinates for M are (2,5).

As M is the midpoint, the x-distance and y-distance between (-4,7) and (2,5) are same as that between (2,5) and K.

x- distance between (-4,7) and (2,5) = 2- (-4) = 6

So x- coordinate of K = 2+6 = 8

y-distance between (-4,7) and (2,5) = 5-7 = -2

So y-coordinate of K = 5+(-2) = 3

Hence the coordinates of K are (8,3).

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Answer:

d) y - 8 = 7/3(x - 9)

Explanation:

[tex]\sf point-slope\:form :[/tex]

[tex]\sf y - y_1 = m(x - x_1) \ \ where \ (x_1, y_1), \ (x_2, y_2) \ are \ points \ and \ m \ the \ slope[/tex]

Find the slope:

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

[tex]\sf \rightarrow slope\ (m) : \dfrac{1-8}{6-9} = \dfrac{-7}{-3} = \dfrac{7}{3}[/tex]

Find the equation:

in point slope form:

[tex]\sf y - 8 = \dfrac{7}{3} (x - 9)[/tex]

[tex]\sf y = \dfrac{7}{3} x - 21+8[/tex]

in slope intercept form

[tex]\sf y = \dfrac{7}{3} x -13[/tex]

Answer:

Step-by-step explanation:

The scale factor is 3.

[tex]scale factor =\frac{scaled\ measure}{actual\ measure}[/tex]

∵ If sides of a polygon are changed by a scale factor 'a' then its perimeter is also changed by the same scale factor,

[tex]scale factor =\frac{scaled\ perimeter}{actual\ perimeter}[/tex]

The actual perimeter of the polygon = 10 unit,

Also, the scaled perimeter = 30 units

Hence,

[tex]scaled factor = \frac{30}{10} =3[/tex]

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The equation that relates the ages is as follows:

G = S + 5

Sara is 5 years younger than Geoff.

The equation that can be used to relates the age of Sara S and the age of Geoff G is as follows:

where

Therefore, Sarah is 5 years younger than Geoff.

The equation that relates the ages is as follows:

G = S + 5

Therefore, Geoff is 5 years older than Sarah. In other words, Sarah is 5 years younger than Geoff.

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The expression for the phrase is 5 * (x - 6) = 24

The phrase is given as:

the product of 5 minus 6 has a result of 24

Products means *

So, we have

5 * (x minus 6) has a result of 24

x minus 6 means x - 6

So, we have

5 * (x - 6) has a result of 24

has a result of 24 means = 24

So, we have

5 * (x - 6) = 24

Hence, the expression for the phrase is 5 * (x - 6) = 24

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Answer:

Y/6 = x

Step-by-step explanation:

Y = 6x

Y/6 = x

Answer:

x ≥ 1

Step-by-step explanation:

The number line shows that the dot is closed which means that the number it is on, is one of the solutions that works for the inequality. So x stands for/means that any number greater than 1 or equal to 1 is a solution.

Answer:

24 books can fit on 1 shelf.

Step-by-step explanation:

Question: Juan has 28 paperback books that measure 1 and 1/4 inches each. How many books will fit on one shelf if each shelf measures 30 inches?

Step-by-step:

We know that each book is 1 and 1/4 inches each. It might be easier to convert the fraction into a decimal.

1/4 inches is 1 divided by 4 which equals to 0.25 inches

1 inch + 0.25 inches = 1.25 inches

so, 1 and 1/4 inches = 1.25 inches

To find out how many books fit on a shelf, we need to find: length of 1 bookshelf divided by length of 1 book

We know that one bookshelf is 30 inches and 1 book is 1.25 inches

so, 30/1.25 or 30 divided by 1.25 = 24

Therefore, 24 books can fit on 1 shelf.

Answer: B

Step-by-step explanation:

Only makes sense its the same as the question I might be wrong

None of Chen and Mia have got the solution right for the given expression.

It is given that two students are asked to write an equivalent expression for (5v - 3 ) × 2.

We have to find out that which of the both students have got it correct ?

What is algebra ?

Algebra is the branch that deals with various symbols and the arithmetic operations such as addition , division , etc.

As per the question ;

The expression is (5v - 3 ) × 2.

Let's solve this equation to find out who of Chen and Mia is correct.

So ;

(5v - 3) × 2

= (5v  × 2) - (3 × 2)

= 10v - 6

So ; None of Chen and Mia is correct.

Thus , none of Chen and Mia have got the solution right for the given expression.

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Answer: Both Chen, and Mia are correct.

Step-by-step explanation:

The expression they gave us:

(5v^-3)^2.

Mia: 25/v^e

Chen: 25v^1

Now,

5v^-3)^2

Step 1: (5v^-3).= (5^2)v^3x2
Step 2: (5x5)v^3x2=25v^3x2
Step 3: 25v^-6. As you see Chen is correct. But..

Step 4: 25/1 x 1/v^6= 25/v^6

That also makes Mia to be correct.

So, in this problem there are two answers.

= 25v^-6, and 25/v^6.

Answer:

$7

Step-by-step explanation:

Since 100/20 = 5, 20% is 1/5, so 20% of 35 is 35/5, or 7

Answer:

If someone leave a 20% tip and the meal is 35$how much was the tip :

$35.00 ÷ 20% = $7.00

The correct option is the last one:

"Cousin; The distance is the absolute value of the difference of the numbers lined up with the beginning and the end of the object."

Now, remember that a rule is equivalent to a number line.

Now, suppose that you are measuring an element with a length of 16 centimeters.

If you measure it by lining up one of the ends of the element with the zero, then the other end will be at the line number 16.

And if you line it up from a different number, let's say 3cm, then the other end of the object (which still measures 16cm) will be at 19cm.

In both cases, to find the measure of the object that you are measuring with the ruler, you need to find the difference between the two numbers on the ruler that line up with the object ends.

If you line up with the zero, you need to subtract zero, so the measure is easier:

16cm - 0cm = 16cm

If you line up with other number, like the 3 in this case, you need to perform the subtraction:

19cm - 3cm = 16cm

In both cases, we will get the same measure. So your cousin is correct, and the correct option is the last one:

Cousin; The distance is the absolute value of the difference of the numbers lined up with the beginning and the end of the object.

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