Let [tex]\mu[/tex] be the population mean.
Null hypothesis : [tex]\mu=12[/tex]
Alternative hypothesis : [tex]\mu<12[/tex]
Since Alternative hypothesis is left tailed so , the test is a left tailed test.
Given : n=33 > 30 , so we use z-test.
Test statistic : [tex]z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
i.e. [tex]z=\dfrac{11.2-12}{\dfrac{1.6}{\sqrt{33}}}\approx-2.87[/tex]
Using z-value table,
P-value for left tailed test =[tex]P(z<-2.87)=0.0020524[/tex]
Since , the p-value (0.0020524) is less than the 0.05 level of significance, it means we reject the null hypothesis.
Therefore, we have enough evidence to support the claim that the mean completion time has decreased under new management.
Take as input two opposite corners of a rectangle: (x1,y1) and (x2,y2). Finally, the user is prompted for the coordinates of a third point (x,y). Find whether the point (x,y) lies inside the rectangle.
Answer:
The answer is a point [tex](x,y) / x1\leq x\leq x2 , y1\leq y\leq y2[/tex]
Step-by-step explanation:
That happens because the points you have are in opposite corners, which means that they are the limits of the rectangle. so any point inside the rectangle is between that segment
3. The population of Columbus, Ohio, in 2014 was about 823,000. The population of the United States was about 319 million in 2014. (a) Write each population in scientific notation. (b) About how many times larger was the population of the United States than the population of Columbus, Ohio? Show your work. Answer:
Answer:
The answer to your question is:
a)
8.23 x 10 ⁵
3.19 x 10⁸
b)
387.6 ≈ 388 times
Step-by-step explanation:
Columbus, Ohio population = 823, 000
United states population = 319 million
a)
823 000 = 8.23 x 10 ⁵ move the decimal point 5 places to the left
319 000 000 = 3.19 x 10⁸ move the decimal point 8 places to the left
b)
To find the answer, just divide the USA population by the Columbus, Ohio population
3.19 x 10⁸ / 8.23 x 10 ⁵ = 387.6 ≈ 388 times
Final answer:
a) The population of Columbus, Ohio in scientific notation is 8.23 × 10⁵ and that of the United States is 3.19 × 10⁸. and b) the US population is 388 times larger as compared to Columbus.
Explanation:
a)The population of Columbus, Ohio, in 2014 was about 823,000. This can be written in scientific notation as 8.23 × 10⁵.
The population of the United States in 2014 was about 319 million. In scientific notation, this is 3.19 × 10⁸.
b) To determine how many times larger the population of the United States was than the population of Columbus, Ohio, we divide the population of the United States by that of Columbus:
3.19 × 10⁸ / 8.23 × 10⁵ = 387.605 approx 388 times larger
Therefore, the population of the United States was about 388 times larger than the population of Columbus, Ohio in 2014.
solve each
14 is 38% of what?
92% of what is 110
please explain how to do i wanna understand
Answer:
36.84119.57Step-by-step explanation:
"Of" means "times"; "is" means "=". Write the English expression as a math expression and solve for "what".
14 = 38% × what
14/0.38 = what ≈ 36.84 . . . . . . divide by the coefficient of "what"
14 is 38% of 36.84
__
92% × what = 110
what = 110/0.92 ≈ 119.57 . . . . . divide by the coefficient of "what"
92% of 119.57 is 110.
a) 31 c) 30
b) 28 d) 61
Answer:
A) 31
Step-by-step explanation:
The difference of low-end values for successive classes is 31. This is the class width.
Simplify (-2)(-3)^2 -2(2 - 5)
To simplify the expression (-2)(-3)^2 - 2(2 - 5), you perform the calculations step by step. The final result is -12.
Explanation:To simplify the expression (-2)(-3)^2 - 2(2 - 5), we perform the calculations step by step:
First, we calculate (-3)^2, which is equal to 9.Next, we substitute the values in the expression: (-2)(9) - 2(2 - 5).Then, we simplify the expression inside the parentheses: (-2)(9) - 2(-3).Multiplying -2 by 9 gives us -18, and multiplying 2 by -3 gives us -6.Finally, we subtract -6 from -18 to get the final result, which is -12.Therefore, the simplified expression is -12.
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Zoey is reading a 100-page novel. If she averages reading 1 page in 1 minute, which is a reasonable estimate of the amount of time it will take her to read the novel? A) between 1 1/2 and 2 hours B) between 1 and 1/2 hours Eliminate C) between 2 and 3 hours D) between 0 and 1 hour
Answer:
The answer to your question is: letter A
Step-by-step explanation:
data
Book = 100 pages
Zoey reads 1 page per minute
Now we solve it using rule of three
1 page ------------------ 1 min
100 pages ---------------- x
x = 100x1/1 = 100 min will take Zoey to read the book
60 min ------------------ 1 hour
100 min --------------------- x
x = 100/60 = 10/6
and convert it to a mix fraction = 1 2/3 = 1 hour 40 minutes
Then, the answer is letter A
Answer:
A
Step-by-step explanation:
well since she reads 1 page per minute and there are 100 pages then that means it takes 100 minutes.
100 minutes= 1 2/3 hours which is in between 1 1/2 and 2 so the answer would be A
A cyclist rides his bike at a speed of 18 miles per hours.what is this speed in kilometers per hour? How many kilometers will the cyclist travel in 2 hours ?
Answer:
about 29 km/h57.94 kmStep-by-step explanation:
The conversion factor cancels units of miles and leaves units of km.
[tex]\dfrac{18\,mi}{h}\cdot\dfrac{1.609344\,km}{1\,mi}=\dfrac{28.968192\,km}{h}[/tex]
The speed rounds to 29 km/h.
Multiplying the distance per hour by the number of hours, we find the distance to be ...
(28.968192 km/h)×(2 h) = 57.936384 km ≈ 57.94 km
3. Jim is cutting up apples he is planning to serve 1/3 to each 8 people, how many apples does jim need to serve?
Answer:
3
Hope this helps! .. Do you need an explaination?
Answer:
3
Step-by-step explanation:
because I said
Simplify the radical expression.
[tex]\mathbb{ANSWER:}[/tex]
Refer to the attachment for the answer.
The area of the southern ocean is about 7.85 x 10^6 square miles. The difference between the areas of the indian ocean and the southern ocean is about 1.865 x 10^7 square miles. Explain how to find the area of the indian ocean. Then find the area.
Answer:
The answer to your question is: 2.65 x 10⁷ square miles
Step-by-step explanation:
Data
Southern ocean area = 7.85 x 10⁶ square miles
Difference between areas Indian ocean = 1.865 x 10⁷ square miles
and the southern ocean
Process
a) To find the area of the Indian ocean we need to sum of the values of the area of the Southern ocean and the area of the difference between the Indian ocean and the southern ocean.
b)
Area of the Indian Ocean = 1.865 x 10⁷ + 7.85 x 10⁶
= 2.65 x 10⁷ square miles
Answer:
The area of the Indian ocean is [tex]2.65\times 10^7[/tex]
Step-by-step explanation:
Given : The area of the southern ocean is about [tex]7.85\times 10^6[/tex] square miles. The difference between the areas of the Indian ocean and the southern ocean is about [tex]1.865\times 10^7[/tex] square miles.
To find : Explain how to find the area of the Indian ocean. Then find the area.
Solution :
The area of the southern ocean is about [tex]7.85\times 10^6[/tex] square miles.
i.e. [tex]A_s=7.85\times 10^6[/tex]
The difference between the areas of the Indian ocean and the southern ocean is about [tex]1.865\times 10^7[/tex] square miles.
i.e. [tex]A_i-A_s=1.865\times 10^7[/tex]
Substitute the value of [tex]A_s[/tex]
[tex]A_i-7.85\times 10^6=1.865\times 10^7[/tex]
[tex]A_i=1.865\times 10^7+7.85\times 10^6[/tex]
[tex]A_i=1.865\times 10^7+0.785\times 10^7[/tex]
[tex]A_i=(1.865+0.785)\times 10^7[/tex]
[tex]A_i=2.65\times 10^7[/tex]
Therefore, The area of the Indian ocean is [tex]2.65\times 10^7[/tex]
Gerry is looking to buy a new car and finds one she likes for $1,000. The dealership is currently offering 15% off. How much money will Gerry save if she buys the car? Select one: A. $15 B. $985 C. $850 D. $150
D 1000 X .15 = 150.
.15 = 15%
Answer:
D) $150.
Step-by-step explanation:
Gerry is looking to buy a new car and finds one she likes for $1000. It means 100% corresponds to $1000.
There is 15% off. It means, she can save 15% of the total value of the car. We need to calcualte the amount of money that she can save taking the 15% off (O)
O = $1000 * (15%)
O = $1000*(15/100)
O = $1000*(0.15)
O = $150.
100% corrsponds to $1000, and 15% corresponds to $150.If she takes 15% off, we can conclude that she can save $150.
Finally, the answer is D) $150.
NEED A QUICK ANSWER.
solve for x.
Enter your answer in the box.
x =
°
brainliest will be given to whoever answers correctly.
90 + x + 107 + 144 + 138 = 540
479 + x = 540
x = 540 - 479
x = 61
Answer:
x=61°
Step-by-step explanation:
There are 5 sides in a polygon.
Sum of interior angles = (n-2) times 180
[tex](5-2) \cdot 180=540[/tex]
The sum of interior angles in a polygon is 540 degree
Now add all the interior angles and set it to 540
Right angle is 90 degree
[tex]90+x+138+144+107= 540[/tex]
[tex]479+x= 540[/tex]
Subtract 479 from both sides
[tex]x=61[/tex]
Which of the following are exact numbers?
~The mass of a paperclip~The surface area of a dime~The number of inches in a mile~The number of ounces in a pound~The number of microseconds in a week~The number of pages in this worksheet (1)
Answer:
Explanation with the help of discrete variables and continuous variables.
Step-by-step explanation:
We have to tell that which of the following can be an exact number.
This can be done with the approach of discrete and continuous variables.
Discrete variables are the variables that are countable and cannot be expressed in decimal form. They are point estimated.
Continuous variable are the variable that are estimated with the help of an interval. Their values can be expressed with the help of a decimal expansion. They are not countable.
a) Mass of a paper clip, Surface are of dime, Inches in a mile, Ounces in pound, microseconds in a week
Since all mass, area, weight(ounces), time, length(inches) are continuous variable, they can be estimated with the help of an interval. Thus, they can have exact number but not always.
b) Number of pages in a worksheet
Since this is a discrete quantity and it is countable. Thus, it will always have a point estimation and are exact numbers always.
Sydney Blackwell manages an office building with leases of $60,000 per year. Her management agreement is for 7 years, with fees as follows: 7% the first year; 5% the second and third years; and 3 % the remaining years. What will be Sydney's total management fee?
Answer:
total management fee is $16200
Step-by-step explanation:
given data
leases = $60000 per year
time = 7 year
fees 1st year = 7%
fees 2nd and 3rd year = 5%
fees remaining year = 3%
to find out
total management fee
solution
we find here commission for each here
for 1st year = 7% of $60000 = $4200 ............1
for 2nd and 3rd year = 5% of $60000 = $3000 ............2
for remaining year = 3% of $60000 = $1800 ................3
and that is 4 year so fees = 1800 × 4 = $7200 ................4
now add all these to get total
total fees = 4200 + 3000 + 1800 + 7200
total fees = 16200
so total management fee is $16200
Sydney Blackwell's total management fee for a 7-year period, with varying annual rates applied to a $60,000 lease, amounts to $17,400.
Explanation:Calculating Sydney's Total Management Fee
To calculate Sydney Blackwell's total management fee for managing an office building, we need to apply the corresponding percentage rates to the annual lease amount over the span of the management agreement. The lease amount is $60,000 per year, and the management agreement spans 7 years with varying fees each year.
Here's the breakdown of fees per year and total fee calculation:
First year: 7% of $60,000 = $4,200Second and third years: 5% of $60,000 = $3,000 per year, for a total of $6,000 over two yearsRemaining four years: 3% of $60,000 = $1,800 per year, for a total of $7,200 over four yearsAdding up the fees from all years:
$4,200 + $6,000 + $7,200 = $17,400
Therefore, the total management fee Sydney will receive over the 7-year period is $17,400.
What are significant figures?
A. They are a close approximation of the actual value of what is being measured
B. They are all known digits in a measurement
C. The limit of a measurement
D. The gauge of the accuracy of a measurement
The best option is A: They are a close approximation of the actual value of what is being measured.
Significant figures, also known as significant digits, are a set of rules used to determine the precision or accuracy of a measured or calculated value. They indicate the reliability of the digits in a number and help communicate the level of certainty associated with a measurement or calculation.
The correct definition of significant figures is:
A. They are a close approximation of the actual value of what is being measured.
Significant figures represent the digits in a number that contribute to its precision. They include all the known digits in a measurement, as well as one estimated digit. The estimated digit is the least certain or the first uncertain digit in the measurement. The number of significant figures reflects the level of confidence in the measurement and helps convey the precision of the value.
Option B ("They are all known digits in a measurement") is incorrect because significant figures include both known digits and one estimated digit.
Option C ("The limit of a measurement") is incorrect because significant figures do not define a limit but rather represent the precision of the measurement.
Option D ("The gauge of the accuracy of a measurement") is partially correct, as significant figures can provide an indication of the accuracy, but they primarily convey the precision or reliability of the measurement rather than the overall accuracy.
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IF the navy pier ferris wheel in chicago has a circumference that is 56% of the circunference of the first ferris wheel built in 1893.
a. What is the radius of the navy pier wheel?
b. what was the radius of the first ferris wheel?
c. The first ferri wheel took nine minutes to make a complete revolution. how fast was the wheel moving?
Answer:
a. The radius of the navy pier wheel is 56% of the radius of the first ferris wheel
b. The radius of the first ferris wheel was 179% of the radius of the navy pier ferris wheel
c. The wheel was moving at 0.70 [tex]\frac{rad}{min}[/tex]
Step-by-step explanation:
Navy pier wheel circumference = Cn
First ferris wheel circumference = Cf
Cn = 0.56*Cf
a.
Circumference Perimeter = 2*π*Radius
Navy pier wheel radius = Rn
First ferris wheel radius = Rf
Cn = 0.56*Cf
2*π*Rn = 0,56*2*π*Rf (equation 1)
dividing both sides by 2π
Rn = 0,56*Rf
b.
From equation 1
2*π*Rn = 0,56*2*π*Rf
dividing both sides by 2π
Rn = 0.56*Rf
dividing both sides by 0.56
Rf = [tex]\frac{1}{0.56}[/tex]*Rn
Rf = 1.79*Rn
c.
9 minutes / revolution
1 revolution = 2π radians
The wheel makes 2π radians in 9 minutes
Wheel velocity = [tex]\frac{2\pi }{9} \frac{rad}{min}[/tex]
Wheel velocity = 0.70 [tex]\frac{rad}{min}[/tex]
Sherita's club is selling grapefruit to raise money. For every box they sell, they get $1.35 profit. They have sold 84 boxes already. How many more
boxes must they sell to raise $270?
A. 135 boxes
116 boxes
B.
c.
157 boxes
OD. 114 boxes
Answer: 156.7
Step-by-step explanation:
1.35x84= 113.4
270-113.4=156.60
Answer:
B
Step-by-step explanation:
1.35 x 84 = $113.40
270 - 113.40 = $156. 60
156.60 / 1.35 = 116 boxes
You are considering two securities. Security A has a historical average annual return of 7% and a standard deviation of 3%. Security B has a historical average annual return of 7% and a standard deviation of 9%. From this information you can conclude that:
Answer:
Security B is riskier than Security A.
Step-by-step explanation:
Security A and B have the same historical average annual return which is 7%, meaning that both of them have had the same results over the years.
However, the standard deviation of A is 3% and the standard deviation of B is 9%, therefore we can conclude that Security A is safer than Security B because a low standard deviation indicates that the annual returns tend to be close to the average (mean), while a high standard deviation indicates that the annual returns are spread out over a wider range of values.
For example:
Security A has this values over the years:
6, 7, 8, 7 where mean is 7.
Security B has this values over the years:
1, 13, 4, 12 where the mean is also 7.
But, A has a lower standard deviation and B a higher one, therefore, Security B is riskier.
What is the solution to this system of equations?
4x−3y=26
3x+2y=11
5,2
8,2
-2,5
5,-2
Answer:
(x, y) = (5, -2)
Step-by-step explanation:
A graphing calculator provides a quick and easy way to find the solution.
_____
There are several other ways to solve these equations. Or you can estimate where the answer might be using logic like this:
The intercepts of the first equation are ...
x-intercept = 26/4 = 6 1/2y-intercept = -26/3 = -8 2/3So the graph of it will form a triangle with the axes in the 4th quadrant.
The intercepts of the second equation are ...
x-intercept = 11/3 = 3 2/3y-intercept = 11/2 = 5 1/2So the graph of it will form a triangle with the axes in the 1st quadrant. The x-intercept of this one is less than the x-intercept of the first equation, so the two lines must cross in the 4th quadrant.
The only 4th-quadrant answer choice is (5, -2).
PLZ HURRY IT'S URGENT!!
The length of a rectangle is 4 inches longer than its width. The area of the rectangle is 12 square inches. What are the length and width?
Which equation models this problem?
w – (4 + w) = 12
w + (4 + w) = 12
w(4 + w) = 12
4 • w = 12
Answer:
w(4 + w) = 12 is the correct answer.
Step-by-step explanation:
You have to think that area is lenght x widht, so the first and second options musn't be correct. (you have + and -)
The last one, it isn't correct because, you have width but don't have lenght.
Length is not 4.
A softball team is ordering pizza to eat after their tournament. They plan to order cheese pizzas that cost $6 each and four-topping pizzas that cost $10 each. They order c cheese pizzas and f four-topping pizzas. Which expression represents the total cost of all of the pizzas they order?
The equation would be [tex]6c + 10f[/tex].
The expression which represents the total cost of all of the pizzas they order is 6c + 10f.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .
Now it is given that,
Cost of cheese pizza = $6
Cost of four-topping pizzas = $10
Number of cheese pizza order = c
Number of four-topping pizzas order = f
Hence,
Total cost cheese pizza = Cost of cheese pizza*Number of cheese pizza order
⇒Total cost cheese pizza = 6*c = 6c
Similarly,
Total cost of four-topping pizzas = Cost of four-topping pizzas*Number of four-topping pizzas order
⇒Total cost of four-topping pizzas = 10*f = 10f
Hence, total cost of all of the pizzas they order
= Total cost cheese pizza + Total cost of four-topping pizzas
⇒ total cost of all of the pizzas they order = 6c + 10f
Hence,The expression which represents the total cost of all of the pizzas they order is 6c + 10f.
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Could someone just show me how to solve this? I don't want an answer, I would like to solve it on my own, I just don't know how to write an equation for this. Please help!
You would set up a ratio for the two known sides to equal the known side and x:
8/2 = 18/x
Cross multiply:
(2 * 18) = (8 * x)
Simplify:
36 = 8x
Solve for x by dividing both sides by 8:
x = 36/8
x = 4.5
For FHG find the measure of the smallest angle
Answer:
m∠HFG=16°
Step-by-step explanation:
we know that
The sum of the internal angles of a triangle must be equal to 180 degrees
In this problem
m∠HFG+m∠GHF+m∠HGF=180°
we have
m∠GHF=92°
m∠HGF=72°
substitute the given values and solve for m∠HFG
m∠HFG+92°+72°=180°
m∠HFG+164°=180°
m∠HFG=180°-164°
m∠HFG=16°
A package of 4 mechanical pencils comes with 2 free erasers. If you get a total of 12 free erasers, how many packages of pencils did you buy? If you get 18 free erasers,how many packages of pencils did you buy?
Answer:
6 packs, 9 packs
Step-by-step explanation:
The ratio of mechanical pencil to free eraser is 2:4, or 1:2.
So that means, for every free eraser you get, you bought the double amount of pencils.
12 free erasers x 2 = 24 pencils
18 free erasers x 2 = 36 pencils
And a pack of pencils contains 4.
24/4 = 6 packs
36/4 = 9 packs
Answer:
6 packs and 9 packs
Step-by-step explanation:
IF A SUBSCRIPTION IS $499 PLUS 8% TAX FOR 30 DAYS, BUT IS BEING PRORATED FOR 7 DAYS, PLUS THERE IS A $10 OFF COUPON, WHAT'S THE FINAL COST?
Answer:
Your final answer is $528.92
Step-by-step explanation:
[tex]499 + 8\% = 538.92[/tex]
[tex]538.92 - 10 = 528.92[/tex]
Answer:
$519.6048
Step-by-step explanation:
Cost of subscription is $499 + 8% tax for 30 days
Cost of subscription for 30 days = $499
Cost of subscription for 1 days = [tex]\frac{499}{30}[/tex]
So, Cost for (30-7 = 23)days = [tex]\frac{499}{30} \times 23 [/tex]
= [tex]382.56[/tex]
Cost of subscription for 23 days = [tex]382.56[/tex]
Sale tax = 8 %
Sales Tax = [tex]30.6048[/tex]
Cost of subscription = $499+$30.6048 = $529.6048
There is an off of $10
So, Final cost = $529.6048-$10= $519.6048
Hence The final cost is $519.6048
A certain library assesses fines for overdue books as follows. On the first day that a book is overdue, the total fine is $0.10. For each additional day that the book is overdue, the total fine is either increased by $0.30 or doubled, whichever results in the lesser amount. What is the total fine for a book on the fourth day it is overdue?
A. $0.60B. $0.70C. $0.80D. $0.90E. $1.00
Answer:
Option B. $0.70
Step-by-step explanation:
First day fine = $0.10
Second day fine (doubled or $0.30 which is lesser)
= $0.10 + $0.10 [$0.10 is lesser than $0.30]
= $0.20
Third day fine = $0.20 + $0.20 [ $0.20 is lesser than $0.30]
= $0.40
Fourth day fine = $0.40 + $0.30 = $0.70
[$0.30 is cheaper than doubling the amount $0.40 + $0.40]
Therefore, the total fine for a book on the fourth day is $0.70
To convert a quantity from km/h to m/s, you must a. multiply by 3600 and divide by 1000 b. multiply by 1000 and divide by 60 c. multiply by 60 and divide by 1000 d. multiply by 1000 and divide by 3600e. none of these is correct
Answer:
The correct answer is D
Multiply by 1000 and divide by 3600
Step-by-step explanation:
We know that in 1 km we have 1000 m and in 1 h we have 60 minutes and each minute have 60 seconds, then we multiply 60*60 to know how many seconds are in an hour and we have that 1 h have 3600 s. Using a conversion factor we have:
[tex]\frac{km}{h}(\frac{1000 m}{1km})(\frac{1h}{3600s})[/tex]
With this we can see that to convert a quantity from kn/h to m/s we must multiply by 1000 and divide by 36000
To convert from kilometers per hour to meters per second, you should multiply by 1000 (to convert kilometers to meters) and then divide by 3600 (to convert hours to seconds). An example with a speed of 50 km/h would result in approximately 13.9 m/s after conversion.
Explanation:To convert a quantity from kilometers per hour (km/h) to meters per second (m/s), the correct approach is (a) multiply by 1000 and then divide by 3600. This is because 1 km is equal to 1000 meters, and 1 hour is equal to 3600 seconds. Therefore, to change the unit from km/h to m/s, you need to perform these conversion operations.
Let's consider an example. If you have a speed of 50 km/h and want to convert it into m/s, here's the step-by-step process:
Multiply 50 (km/h) by 1000 to convert kilometers into meters. You'll get 50000 m/h.Next, divide 50000 m/h by 3600 to convert hours into seconds. The result is approximately 13.9 m/s.Learn more about Unit Conversion here:https://brainly.com/question/19420601
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Midpoint of ST is (5,-8). T is (4.5,-2.5) Find S.
Answer:
(5.5, -13.5)
Step-by-step explanation:
Midpoint M satisfies ...
M = (S +T)/2
So ...
2M = S + T
2M -T = S
2(5, -8) -(4.5, -2.5) = S = (10 -4.5, -16 +2.5)
S = (5.5, -13.5)
City A is due north of City B. Find the distance between City A (37 degrees 2 prime north latitude) and City B (19 degrees 44 prime north latitude). Assume that the radius of Earth is 3960 miles.
Answer:
1196 mi
Step-by-step explanation:
The latitude difference is 17°18', so is about 0.301942 radians. Then the arc length is ...
s = r·θ = (3960 mi)(0.301942) ≈ 1196 mi
The distance between City A and City B, given their latitudes and the radius of the Earth, is found using the arc length formula (length = radius x angle in radians) to be approximately 2011 miles.
Explanation:The subject of this question is Geography and it entails finding the distance between two cities located at different latitudes on Earth. The difference between the two latitudes is used to find the distance. Since the Earth is a sphere, we can use the formula for the length of an arc to find the distance between these two cities. To do so, subtract the latitude of City B (19 degrees 44 prime) from the latitude of City A (37 degrees 2 prime) to get the difference in degrees which is equal to 17 degrees 18 prime. Convert this to decimal form by dividing the prime by 60 (17 + 18/60 = approx. 17.3 degrees).
Then use the formula for the length of an arc: length = radius x angle (in radians). The radius of the Earth is given as 3960 miles and the angle in radians is obtained by multiplying the angle in degrees by π/180. Therefore, the distance is 3960 miles x 17.3 x π/180 = approximately 2011 miles. As such, City A and City B are estimated to be about 2011 miles apart.
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Alice and Bob play the following game: they start with an empty 2008x2008 matrix (p.s. take a wild guess which year this was) and take turns writing numbers in each of the 20082 positions. Once the matrix is filled, Alice wins if the determinant is nonzero and Bob wins if the determinant is zero. If Alice goes first, does either player have a winning strategy?
Answer:
Bob wins
Step-by-step explanation:
Think first in a simpler case. In a 2x2 matrix the determinant is zero if two columns or rows are proportional. So Alice writes the first number, then Bob write the same number in the same column but in the other row. Bob repeat the procedure after Alice's second number, and win.
If the matrix is nxn where n is even (like 2008) Bob will win following the previous procedure. Alice writes a number anywhere, Bob writes the same number in the same column in the above (or below) row. Every time Alice write a number in the same row as her first one, Bob copy that number in the above (or below) row. Any other rows are not important, i.e, the determinant will be zero with any values in them.