geno3141

By the graph there are 5 yellow, 5 red, 5 orange, 5 blue, and 5 green.

In total, there are 5 + 5 + 5 + 5 + 5 = 25.

The percentage, or probability of blue is 5/25.  [Which you will need to change into a decimal.]

Each of the other colors have the same probability.

Since AF is the perpendicular bisector both angle(AFD) and angle(AFB) are right angles; 

also, BF is congruent to DF.

Since AF is congruent to AF, triangle(ABF) is congruent to triangle(ADF)   ---   side-angle-side.

Therefore, AD = AB = 30 and DF = BF = 12.

You can now calculate AB + BF.

16 have all three ribbons.

Because 32 have a blue ribbon and a green ribbon and 16 have all three ribbons,

     32 - 16  =  16 have blue and green ribbons only (no white ribbon).

Because 31 have green and white ribbons and 16 have all three ribbons,

     31 - 16  =  15 have green and white ribbons only.

Because 39 have blue and white ribbons and 16 have all three ribbons,

     39 - 16  =  23 have blue and white ribbons only..

Since 62 have blue ribbons, subtracting those that have all three ribbons (16) and those that also have a green ribbon (16) and those that also have a white ribbon (23), we are left with 7 that have only a blue ribbon.

You can work in a similar fashion to determine how many only have a green ribbon and how many have only a white ribbon.

Finally, subtract all these non-overlapping groups to find out how many have no ribbons at all.

For #1:

Since a > b, it is longer (in the x-direction) than it is tall (in the y-direction.

If you draw the triangle that starts at the center of the hyperbola (0,0) to the right to the point (a,0) and then up to the point (a,b), you will be drawing a right triangle with the angle at the center of the hyperbola having 30°.

Therefore, a = sqrt(3) and b = 1.

If a door has a flower on its plant side, then it has a bird on its animal side.

You have to open every door that has a flower on its plant side   --->   so you have to open the door with a lily on it.

An equivalent logical statement is its contrapositive.

If a door does not have a bird on its animal side, the it does not have a flower on its plant side.

You have to open every door that does not have a bird on its animal side   --->   so you have to dopen the door with a fox on it.

You have to open two doors.

You don't have to open the other two doors.

I'm not certain what the "$" on each side of "x" represent.

If you are just considering all real numbers for the possibile replacements for x in the triangle whose sides are x + 15, 2x + 15, and 4x + 15, then, since the sum of any two sides of a triangle must be greater than the third side, there are these three possibilities:

I.    (x + 15) + (2x + 15) > 4x + 15     --->     3x + 30 > 4x + 15     --->     15 > x        --->     x < 15

II.   (x + 15) + (4x + 15) > 2x + 15     --->     5x + 30 > 2x + 15     --->     3x > -15     --->     x > -5

III.  (2x + 15) + (4x + 15) > x + 15     --->     6x + 30 > x + 15       --->     5x > -15     --->     x > -3    

The answer is (-3, 15)     [Using a value of -4 or -5 for x results in a side of the triangle being negative.]

Using "$x$ to refer to just "x", I can't get any possible of answers that work for questions 2 and 3.

There are 1000 grams in a kilogram; so in 1 1/2 kilograms of frosting, she has 1500 grams of frosting.

Since she uses 50 grams of frosting on each cupcake, she can frost  1500 / 50  =  answer  cupcakes.

y = a·sin(b·x) + c

c is the value of the midline; c = 70

a is the amplitude (high or low from the midline); a = 10      (found by high - midline)

b is the modification of the period; 360° in a 24 hour day; b = 360/24.

Since AB || CD, angle(APR) = angle(QRP)              [alternate interior angles]

Since PQ = QR, angle(QRP) = angle(QPR)             [base angles of an isosceles triangle]

Since angle(APR) = x, angle(QRP) = x                    [substitution, or transitivity]

angle(BPQ) + angle(QPR) + angle(RPA) = 180°      [they form a line]

Therefore:  (100° + x) + (x) + (x) = 180°

                               100° + 3x  =  180°

                                           3x  =  80°

                                             x  =  (80/3)°

In the problem, you have a "3"; in your answers, you have "13".

The graph will be horizontally compressed by the factor.

Check this out by graphing each one.