According to the Corporate Travel Index compiled by Business Travel News, the average daily cost for business travel in the United States rose to per day (Executive Travel website). The file Travel contains sample data for an analogous study on the estimated daily living costs for an executive traveling to various international cities. The estimates include a single room at a four-star hotel, beverages, breakfast, taxi fares, and incidental costs.

City Daily Living Cost ($) City Daily Living Cost ($)
Bangkok 242.87 Mexico City 212
Bogota 260.93 Milan 284.08
Cairo 194.19 Mumbai 139.16
Dublin 260.76 Paris 436.72
Frankfurt 355.36 Rio de Janeiro 240.87
Hong Kong 346.32 Seoul 310.41
Johannesburg 165.37 Tel Aviv 223.73
Lima 250.08 Toronto 181.25
London 326.76 Warsaw 238.2
Madrid 283.56 Washington, D.C. 250.61

Required:
a. Compute the sample mean.
b. Compute the sample standard deviation.
c. Compute a 95% confidence interval for the population standard deviation.

Answer:

Step-by-step explanation:

You have omitted relevant parts of the question. What is the question? Are you looking for the area of the yard? The amount of fencing needed?

What units are used? (Feet, yards, meters, etc.)

area of yard = 75×55 = 4125 units²

amount of fencing needed = perimeter of rectangle = 2(75+55) = 260 units.

The total length of the fencing is the perimeter of the rectangular yard which is P = 260 feet

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P = 2 ( Length + Width )

Given data ,

The width of the rectangular yard W = 55 feet

The length of the rectangular yard L = 75 feet

Let the perimeter of the rectangular yard be = P

And , the required fencing = Perimeter of rectangular yard

Perimeter of rectangular yard P = 2 ( L + W )

Substituting the values in the equation , we get;

Perimeter of rectangular yard P = 2 ( 55 + 75 )

Perimeter of rectangular yard P = 2 ( 130 )

Perimeter of rectangular yard P = 260 feet

Therefore , the value of P is 260 feet

Hence , the perimeter of yard is 260 feet

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Mr. Fuller wants to put fencing around his rectangular-shaped yard. the width of the yard is 55 feet and the length is 75 feet. how many feet of fencing does Mr. Fuller

Let

x -----> the number of cups

so

The solution is the interval {1,4}

In a number line the solution is the shaded area at right of x=1 (closed circle) and at left of x=4 (closed circle)

The median, mean, range and mode will be 6, 5.4, 9 and 7.

What is median?

The median is the middle number in the data set when the data set is written from least to greatest.

The median is the number in the middle when arranged in an ascending order. The numbers will be:

0, 3, 4, 6, 6, 7, 7, 7, 9.

The median is 6.

The range is the difference between the highest and lowest number which is: = 9 - 0 = 9

The mode is the number that appears most which is 7.

The mean will be the average which will be:

= (0 + 3 + 4 + 6 + 6 + 7 + 7 + 7 + 9) / 9.

= 49/9

= 5.4

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Answer:

\(\sqrt{106}\) units

Step-by-step explanation:

Calculate the distance d using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (- 9, 5)

d = \(\sqrt{(-9-0)^2+(5-0)^2}\)

   = \(\sqrt{(-9)^2+5^2}\)

   = \(\sqrt{81+25}\)

    = \(\sqrt{106}\)

A) The value of x in log₄(x² - 12x + 48) = 2, is x = 4 OR x = 8

B) The value of x in 27^(4x-6) =(1/9)^(2x-7), is x = 2

From the question, we are to solve the given equations

The given equation is log₄(x² - 12x + 48) = 2

From one of the laws of logarithm, we have that

logₐ x = n ⇒ x = aⁿ

Thus,

log₄(x² - 12x + 48) = 2 becomes

(x² - 12x + 48) = 4²

x² - 12x + 48 = 16

x² - 12x + 48 - 16 = 0

x² - 12x + 32 = 0

Solve the quadratic equation

x² - 12x + 32 = 0

x² - 8x - 4x + 32 = 0

x(x - 8) -4(x - 8) = 0

(x - 4)(x - 8) = 0

x - 4 = 0 OR x - 8 = 0

x = 4 OR x = 8

B) 27^(4x-6) =(1/9)^(2x-7)

Solve for x

27^(4x-6) =(1/9)^(2x-7)

Express the bases in index form

3^3(4x-6) =(3)^-2(2x-7)

Equate the powers

3(4x - 6) = -2(2x - 7)

12x - 18 = -4x + 14

12x + 4x = 14 + 18

16x = 32

Divide both sides by 16

16x/16 = 32/16

x = 2

Hence, the value of x is 2

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a) The customs duty on the car would be $1,350,000.

b) The imported price of the bus would be $858,000.

(a) To calculate the customs duty on a car with an imported price of $3,000,000, we can multiply the imported price by the duty rate of 45%:

Customs duty = $3,000,000 * 0.45 = $1,350,000.

(b) To calculate the imported price of a bus if the amount paid, including customs duty, is $1,560,000, we need to determine the portion of the total amount that represents the customs duty. Since the customs duty is 45% of the imported price, we can set up the following equation:

Customs duty = $1,560,000 * 0.45.

Solving for the customs duty:

Customs duty = $702,000.

Now, we can subtract the customs duty from the total amount to find the imported price:

Imported price = $1,560,000 - $702,000 = $858,000.

In summary, the customs duty on a car with an imported price of $3,000,000 would be $1,350,000. On the other hand, if the amount paid for a bus, including customs duty, is $1,560,000, the imported price of the bus would be $858,000.

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The inequality that can be used to determine x, the number of outfits Tamika can purchase is; 539.63+ 52.93x ≤ 800

The given parameters are:

Budget = $800

New bicycle = $482.62

3 bicycle reflectors = $10.84 each

Pair of a bike gloves = $24.49.

New biking outfits = $52.93each.

Let the number of new biking outfits be x So, we have;

New bicycle + 3 . price of bicycle reflectors + Pair of a bike gloves + New biking outfits <= Budget

This gives;

482.62 + 3( 10.84) + 24.49+ 52.93x ≤ 800

This gives;

539.63+ 52.93x ≤ 800

Solve the inequality;

52.93x ≤ 260.37

Divide by 52.93

x ≤  4.91

Hence, the inequality is 539.63+ 52.93x ≤ 800

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Given statement solution is :- It takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

To determine the number of months it takes to pay off the credit card and the total amount paid, including interest, we can follow these steps:

Step 1: Calculate the monthly interest rate.

The APR (Annual Percentage Rate) is given as 9.5%. To find the monthly interest rate, we divide this by 12 (the number of months in a year):

Monthly interest rate = 9.5% / 12 = 0.0079167

Step 2: Determine the monthly payment.

The monthly payment is given as $400.

Step 3: Calculate the interest and principal paid each month.

The interest paid each month can be calculated by multiplying the monthly interest rate by the current balance.

Principal paid = Monthly payment - Interest paid

Step 4: Track the remaining balance each month.

Starting with the initial balance of $1,367.90, subtract the principal paid each month to determine the new balance.

Step 5: Repeat Steps 3 and 4 until the balance reaches zero.

Continue calculating the interest and principal paid each month, updating the balance, until the remaining balance becomes zero.

Step 6: Determine the total number of months and the total amount paid.

Count the number of months it takes to reach a balance of zero. Multiply the number of months by the monthly payment ($400) to find the total amount paid.

Let's calculate the number of months and the total amount paid, including interest:

Month 1:

Interest paid = 0.0079167 * $1,367.90 = $10.84

Principal paid = $400 - $10.84 = $389.16

New balance = $1,367.90 - $389.16 = $978.74

Month 2:

Interest paid = 0.0079167 * $978.74 = $7.75

Principal paid = $400 - $7.75 = $392.25

New balance = $978.74 - $392.25 = $586.49

Month 3:

Interest paid = 0.0079167 * $586.49 = $4.64

Principal paid = $400 - $4.64 = $395.36

New balance = $586.49 - $395.36 = $191.13

Month 4:

Interest paid = 0.0079167 * $191.13 = $1.51

Principal paid = $400 - $1.51 = $398.49

New balance = $191.13 - $398.49 = -$207.36 (Paid off)

It takes 4 months to pay off the credit card. Now, let's calculate the total amount paid, including interest:

Total amount paid = 4 * $400 = $1600

Therefore, it takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

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1.19 is the cost to download a single song.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that The proportional relationship between the number of songs Nachelle downloads, s, and the total cost in dollars and cents, c, can be represented by the equation c=1.19s

c equal to one point one nine s.

We need to find the cost to download a single song

so s=1

c=1.19×1

c=1.19

Hence, 1.19 is the cost to download a single song.

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Answer:

D) The vertex of the equation is \(f(x) = \frac{2}{3}\cdot (x+3)^{2}-6\). The standard form of the equation is \(f(x) = \frac{2}{3}\cdot x^{2}+4\cdot x\).

Step-by-step explanation:

Let \(A(x,y) = (0,0)\) and \(V(x,y) = (-3, -6)\) (vertex).

If we know that \(x = 0\), \(y = 0\), \(h = -3\) and \(k = -6\), then the standard equation results in:

\(a\cdot (0+3)^{2}-6 = 0\)

And the value of \(a\) is:

\(9\cdot a - 6 = 0\)

\(a = \frac{2}{3}\)

And the vertex form of the equation is \(f(x) = \frac{2}{3}\cdot (x+3)^{2}-6\).

Lastly, the standard form of the equation is found by algebraic means:

\(f(x) = \frac{2}{3}\cdot (x^{2}+6\cdot x +9)-6\)

\(f(x) = \frac{2}{3}\cdot x^{2}+4\cdot x\)

The standard form of the equation is \(f(x) = \frac{2}{3}\cdot x^{2}+4\cdot x\).  

In consequence, the right answer is D.

Answer:

16

Step-by-step explanation:

3^x +1 = f(X)

2x-4 = g(x)

find f(2)-g(-1)

we substitute in function f(X) by value (2), and in function g(X) by value (-1)

1. 3^x +1 becomes 3^2+1 =9+1=10

2. 2(-1)-4= -2-4=-6

then f(2)-g(-1)

= 10-(-6) =10+6=16

Answer:

3,952 ft

Step-by-step explanation:

Use the sine function since you need to find the hypotenuse but know the opposite side of the angle, since sine is equal to opposite/hypotenuse.

sin8°=\(\frac{550}{c}\)

csin8°=550

c=550/sin8°

c= 3,952

Answer:

X + Y = 180°

Step-by-step explanation:

We know that vertical opposite angles are equal

So,

Angle A = Angle B

So,

Assume;

Angle A = x

So,

Angle A + Y = 180°

So,

X + Y = 180°

Answer:

12 hours

Step-by-step explanation:

The formula for distance is \(d=rt\), distance = rate multiplied by time.

We know that you travel at 50 mph, which is our rate, and we travelled for 42 hours, which is the time.

So the distance is \(42\cdot 50 = 2100\) miles.

However, we weren't constantly driving at a speed of 50 mph - once in a while we were driving at 0 mph because we had taken rests.

That means the total miles lost for taking rests will be \(2100-1500 = 600\) miles.

Since we travel at a speed of 50 mph, that means we spent a total of \(600\div 50 = 12\) hours not driving.

Hope this helped!

Answer:

infinite number of solutions

all numbers are solutions

Step-by-step explanation:

5(x + 9) = 5x + 45

Distribute on the left side.

5x + 45 = 5x + 45

Since the two sides are equal, there is an infinite number of solutions. All numbers are solutions of the equation.

We get the following answers:

A) The least square regression line is:

yi = 88.73 - 2.827(xi)

B) The slope  is β₁ = -2.827 and The intercept is β₀ = 88.73.

C) e*₆ = -0.6964, final grade is below average grade.

E) It would not be reasonable since no of absence increases the score decreases, it works well for small no of absences but will not work for large number of absences since it may give absurd final grade.

we have Xi = No of absences

Yi = Final grade

The regression model is

Yi = β₀ +  β₁Xi + i

β₀ = y -  β₁x

we have n = 10, x bar = 4.5 , y bar = 76.01

cov(x,y) = -23.325 and var(x) = 9.1667

therefore,  β₀ = 88.73 and  β₁ = -2.827

A) Least square regression line is given by:

yi =  β₀+ β₁Xi

yi = 88.73 - 2.827(xi)

B) The slope  β₁ = -2.827 which means when no of absence is increased by 1 duty then the final grade will decrease by 2.827

The intercept  β₀ = 88.73 when there are 0 days absence the average grade is 88.73

C) Predicted graph for student who misses five class periods is

x = 5

y*5 = 88.73 - 2.827(5) = 74.5964

Hence for corresponding residual is:

e*₆ = 73.9 - 74.5964

e*₆ = -0.6964, final grade is below average grade.

D) please see graph

E) when student miss 15 class periods the final grade will be

X = 5

y* = 88.73 - 2.827(15)

= 46

It would not be reasonable since no of absence increases the score decreases, it works well for small no of absences but will not work for large number of absences since it may give absurd final grade.

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The simplified exponential expression for this problem is given as follows:

D. 1/49.

The exponential expression for this problem is defined as follows:

\(7^{-\frac{5}{6}} \times 7^{-\frac{7}{6}}\)

When two terms with the same base and different exponents are multiplied, we keep the base and add the exponents.

Hence the exponent is given as follows:

-5/6 - 7/6 = -12/6 = -2.

The negative exponent is moved to the denominator, hence:

1/7² = 1/49.

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Answer: 4:00 pm

Step-by-step explanation:

Answer: 138 inches

Step-by-step explanation:

We can use proportions here, let h = height of the statue

height/height = shadow/shadow

\(\frac{h}{69} = \frac{94}{47}\)

h/69 = 2

*69 (h/69 = 2) *69

h = 138 inches

Answer:

mathanyics it will help a little

Step-by-step explanation:

Answer:

$840.77

Step-by-step explanation:

The equation is 5.25x = 21  and number of weeks should be 4 weeks to exercise 21 hours.

Since Gary exercises 1.75 hours on Mondays, Wednesdays, and Saturdays.

So here we know that the week contain 7 days so here, the equation should be

3(1.75)x = 21

5.25x = 21

Here x be the number of weeks

So, the number of week should be 4

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Answer:

(10, 5π/3)

Step-by-step explanation:

To convert rectangular coordinates (5, -5√3) to polar form, we can use the following formulas:

r = √(x^2 + y^2)

θ = arctan(y/x)

Substituting the given values, we get:

r = √(5^2 + (-5√3)^2) = √(25 + 75) = √100 = 10

θ = arctan((-5√3)/5) = arctan(-√3) = -π/3

Note that the value of θ is in the fourth quadrant, which corresponds to a negative angle. However, we need to express the angle θ in the range 0 ≤ θ < 2π. To do this, we can add 2π to the angle if it is negative:

θ = -π/3 + 2π = (5π/3)

Therefore, the rectangular coordinates (5, -5√3) in polar form are (10, 5π/3).

This is false, undetermined coefficients is a method of "guessing" the particular solution of a inhomogeneous differential equation.

Answer:

Rick: 2 miles

Tina: 1,5

Step-by-step explanation:

60mn=1h

reck: 1/2x60÷15=2

tina: 1/4x60÷10=1,5

The distance each hiked in 1 hour is for Tina 3/2 miles and for rick 1/2 miles.

The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

Given:

Rick hiked 1/2 mile every 15 minutes or 1/4 hour.

Tina 10 minutes to hike 1/4 mile.

We have to find the distance each hiked in 1 hour.

According to given question we have

Rick:

1/2 miles= 15 minutes or 1/4 hour

1 miles=  1/4*2=2 hour

2 hour =1 miles

1 hour=1/2 miles

Tina:

1/4  miles = 10 minutes or 10/60=1/6 hour

1 miles=  =1/6*4=2/3 hour

2/3 hour=1 miles

1 hour = 1*3/2=3/2 miles

Therefore, the distance each hiked in 1 hour is for Tina 3/2 miles and for rick 1/2 miles.

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Answer:

A. 5/6 B. 5/6 C. 1/4 D. 1/24

Step-by-step explanation:

A. 12+3= 15 = 5

— — —

18. 18. 6

B. 4+6=10= 5

— — —

12. 12. 6

C. 4-2=2 = 1

— — —

8. 8. 4

D. 9-8 = 1

— —

24. 24

Answer:

3 lessons

Step-by-step explanation:

150-40=110

110/35=3

she can take 3 lessons and it not cost more than $150

Answer:

Step-by-step explanation:

Step one:

Given that the capacity of the gas tank is 24 gallons.

we know that 1 mile will consume 0.06 gallons

therefore x miles will consume 0.06x gallons.

the consumption for any distance is given as

0.06x gallons.

Step two:

if x=240 miles

then the gallons consume will be

0.06(240)=14.4 gallons

Step three:

the remaining gallons of gas in the tank will be

24-14.4=9.6 gallons

The reamining gallons will be 9.6 gallons

Given:

A snail moves 1 1/8 meters in 1 1/2 minutes.

The snail's rate is given as,

Answer: The snail's rate is 3/4 meter per minute.