All Answers 354507 Answers

I think you are saying the number of mosquitoes is given by   -x^2 + 14x     where x is the cm of rain?

max will be at   cm of rain = - b/2a     where b = 14   and   a = -1    

                                              - 14/ -2 = 7cm of rain will produce max mosquitoes

Question 16889 (the one with Carl)

So there's 7 parts total, 2 parts are black cards, and 5 parts are red cards.

The fraction of red cards then is 5/7, which is C.

For the next question, if a is 100% more than b, it is simply double b. Because b = 100%, 100% + 100% is 200% (which is double). So, the ratio between a and b will be 2:1, which is C.

Wheee

Need more info   but basically the pizza circumference would be     pi x d       where d = diameter of the pie  (round pie assumed)

x = faster tap

(x+20) = slower tap

1/x  + 1/(x+20) = 1/24

x + 20 + x = (x^2+20x)/24

48x + 480 = x^2 + 20x

x^2 -28x-480 = 0                        Use quadratic formula to find x = 40 min

There are 7 red, 5 blue, and 6 green marbles, for a total of 18 marbles.

What is the probability of getting a red marble?     7/18

Replacing it, and getting a blue marble?                5/18

What is probability of doing both?                          7/18 x 5/18  =  35/324

A regular square pyramid has a base edge of 20 mm and total area of 1440 mm².

The area of the base is 20 mm x 20 mm  =  400 mm²

Subtracting this from the total area gives an area of 1440 mm² - 400 mm²  =  1040 mm² for the sides.

Since there are four congruent triangles for the sides, each triangle will have 1040 mm² / 4  =  260 mm².

The area of each of these triangles can be found by the formula:  Area  =  ½ · base · height.

Placing the values into this formula:  260 mm²  =  ½ · 20 mm · height     --->     height  =  26 mm.

This is the slant height of the pyramid.

To find the height of the pyramid, draw a right triangle from the peak down to the middle of the base (side a = unknown height) to tme middle of one of the sides (side b = 10) and back up to the peak (the hypotenuse = 26)

Using the Pythagorean Theorem:  a² + 10²  =  26²     --->     a  =  24 mm

This is the height of the pyramid.

Volume of the pyramid:  V  =  (1/3) · (Area of the Base) · (Height of the Pyramid)

                                       V  =  (1/3) · (400 mm²) · (24m)  =  3200 mm³  

Ight, first find the area of the triangles. That would be (4 * 9) / 2 for one triangle but since there are two it's just 4*9 = 36 yd² (for the triangles)

The rectangle facing the right has dimensions of 5 yd and 12 yd, so the area of that is 5 * 12 = 60 yd².

The rectangle opposite of that (the one on the left, not the bottom one) has dimensions of 8 yd * 12 yd, so its area is 8 * 12 = 96 yd².

The bottom rectangle has dimensions 9 yd * 12 yd, so its area is 108 yd².

Adding all the areas up, you get 36 + 60 + 96 + 108 = 300. Yey

We could solve this with some unknowns.

Let's say C is the # of cars, and T is the # of trucks.

We know that C = 12 + T, and T : C = 3 : 5.

As T / C = 3 / 5, we can cross multiply to get that 5T = 3C.

So, C = 12 + T, and 5T = 3C. I hope you can solve this on your own now!

In case you want to check, here's the solution.

Substitute (12 + T) into 5T = 3C

5T = 3(12 + T)

Distribute to get:
 

5T = 36 + 3T

Isolate the variable: 5T - 3T = 36

2T = 36

Divide by 2, and te number of trucks is 18.

The number of cars is 12 + 18, which is 30.

:)

I believe that the largest value will occur when a = b.

A right triangle with a = b and c the hypotenuse is a 45^o - 45^o - 90^o triangle.

The ratio of the sides of this triangle is sqrt(2) : sqrt(2) : 2

making  (a + b) / 2  =  ( sqrt(2) + sqrt(2) ) / 2  =  2·sqrt(2) / 2  =  sqrt(2) / 1  =  sqrt(2).

Sleep

Since 2 students play both sports, 3 students play only basketball and 10 play only baseball.

There is a problem with the word "or". It has two separate meanings (each one ccan be correct).

There is an "exclusive or" that means either one or the other but not both.

In this case, there are 13 students who play basketball or baseball (but not both).

Probability:  13/27

There is an "inclusive or" that means one or the other or both.

In this case, there are 15 students who play basketball or baseball (and perhaps both).

Probability:  15/27.

Which answer is correct? Until the person who asks the question tells you which "or" they intend, you don't know.

Draw a Venn Diagram      12 students do not play those sports    15 students DO play those sports

15 out of 27       15/27

Area of circle = pi r^2    =    64 pi   

      subtract 1/2 (unshaded area) = 32 pi

         subtract area of triangle  1/2 b h = 1/2 16 8 = 64

(32 pi - 64) / (64 pi)

By Thales' Theorem: angle BAC = 90 degrees(it subtends an arc of 180 degrees)

Because we know that, we know that triangle BAC is a right triangle with angle measurements of 45, 45, 90

Next, realize that the hypotenuse of said triangle is the diameter BC, which has length 16( which is 8 *2).

Now that we have our hypotenuse, realize that the ratio of a 45-45-90 triangle is 

x, x, \(x\sqrt{2}\)

That means that our leg of our right triangle is equal to:

\(16\over{\sqrt{2}}\)= \(16\sqrt{2}\over2\) by rationalizing the denominator(multiplying it by \(\sqrt{2}\over\sqrt{2}\))

This equals 

\(8\sqrt{2}\)

Triangle area formula is 1/2 * b * h

Since the base and height are the same in this scenario, we have that the area of triangle BAC is:

\((8\sqrt{2})^2/2 = 64*2/2 = 64\)

The area of the entire circle is 64pi, so half of it is 32pi. Our area of the shaded region is then:

\(32\pi-64\)

The probability is then this part divided by the entire area of the dart board, which is 64pi, so our answer is:

\(32\pi-64\over64\pi\)

An alternative method is draw the altitude from C to AB. Then calculate the area, and I got 31.25 as well.

xf=xi+vit+1/2gt^2   put in the values you are given

xf = 1  +   vi t + 1/2 g t^2       ( I think that should be  MINUS 1/2 gt^2)

     anyway   xi is initial position = 1 m    (given)

I am a bit confused as to what you ae looking for?    You ask for xi    and then vi   and then xf    and you have a t = .01   (what is that?)

Angle A subtends to arc BC, which is equal to 180. Therefore angle A is 180/2 = 90. Knowing that it is a 45-45-90 triangle, can you figure out the area of the triangle? After that, just subtract it from the area of the semi-circle.

Thanks how about 4 out of 9 compared to 10 out of 10

Your question is not well formatted/entered     v = 32 pi     or   .32 pi

                                                                          depth is 66   or  6   ft ?

Volume of a CONE = 1/3 pi r^2 h      V = 32 pi ft³      h = 66 ft    r = ?

                     32 pi   = 1/3  66  r²

                               ^{r = 2.14 ft                              perhaps that was 6 ft deep?    then r =  7 .1 ft}

The lines y = -2x + 8 and y = x/2 - 2 meet at (4,0), as shown. What is the area of the triangle formed by these two lines and the line x = -2?

Since the committee must include Mark

  there are 9 memebers left from which to choose 2 remaining committee members

    9 c 2 = 36 ways

PAB is similar to PDC by AA. The ratio of sides AB:DC is 1:3. That means the ratio of the areas must be 1:9.

_____________________________________________________________________________________

Call the area of PAB \(x\).

 - The area of PDC is obviously \(x+224\)

Since the ratio is 1:9, then we have the following proportion.

 - \(\frac{x}{x+224}=\frac{1}{9}\)

\(x\) is the area of PAB. I leave the rest of the question up to you.

With a probability of 0.500

2 out of 2 times occurs 1 our of every 4 times (  (1/2)²  =  1/4 )

while 10 out of 10 times occurs 1 out of every 1024 times ( (1/2)¹⁰  =  1/1024 ).

1 out of every 1024 times is 1/256^th as likely to occur as 1 out of every 4 times (because 1024 / 4  =  256).

Or, 1 out of every 2 times is 256 times as likely to occur as 1 out of every 1024 times.

2 3 5 7 11 13 17 19

there are   8 x 7/2 = 28 combos

here are some possibles   2 3 = 5

  2 5 = 7

 2 11 = 13

  2 17 = 19

I don't think there are any more.....can you find any more?    4 out of 28