A laboratory blood test is 99% effective in detecting a certain disease when it is in fact, present. However, the test also yields a false positive result for 0.5% of the healthy person tested (i.e. if a healthy person is tested, then, with probability 0.005, the test will imply he has the disease). If 0.1 percent of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive ?
A. 0.1654
B. 0.1982
C. 0.1827
D. 0.1346

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.    

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.

Answer:

  A)  31

Step-by-step explanation:

The difference of low-end values for successive classes is 31. This is the class width.

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]

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

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]

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)

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 ...

So the graph of it will form a triangle with the axes in the 4th quadrant.

The intercepts of the second equation are ...

So 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).

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.

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:

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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.

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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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

Answer:

Step-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.

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

Answer:

   3

Hope this helps! .. Do you need an explaination?

Answer:

3

Step-by-step explanation:

because I said

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:

[tex]\mathbb{ANSWER:}[/tex]

Refer to the attachment for the answer.

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.

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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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.

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:

Adding 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.

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

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. 

Answer:

Step-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

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°

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

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

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]

Answer:

here merchandise sell is $6000

correct option is A

Step-by-step explanation:

given data

salary = $300 + 10 % commission

paid = $900

to find out

merchandise sell

solution

we consider here sell is x

so paid will be                

paid = salary + 10% of x

so here put value

900 = 300 + 10% ×  x

900 - 300 = 10% ×  x

x = 600 / 10%                

x = 6000                  

so here merchandise sell is $6000

correct option is A

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.

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.

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.

To simplify the expression (-2)(-3)^2 - 2(2 - 5), you perform the calculations step by step. The final result is -12.

To simplify the expression (-2)(-3)^2 - 2(2 - 5), we perform the calculations step by step:

Therefore, the simplified expression is -12.

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