DS2011

A = 0.67

B = 1536

C = 0.32

D = -16

E = 4.24

Smallest to biggest:

D, C, A, E, B, or -16, 0.32, 0.67, 4.24, 1536

Answer: D, C, A, E, B

Answer: -16, 0.32, 0.67, 4.24, 1536

Well, we can see that this is a special right triangle, a 30-60-90 triangle, where m angle A = 30, m angle C = 60, and m angle B = 90.

The side lengths are in the ratio 1:sqrt3:2, which in our case is 12:12 x sqrt3:24

12 x sqrt 3 = 20.7846096908 or approx 20.8 as shown in the graph below:

ALERT:     Sorry, the top point is meant to be A, the bottom left one B, and the bottom right one C.

We can multiply 12x 20.7846 x 1/2 and get:

124.7076

or approximately

124.71

Answer: 124.71

We can solve by substituting:

\(\frac{s}{2}+5t=3+3s-6\)

\(3t-6s=9+2s+7t\)

We can do:

\(5t=\frac{5}{2}s-3\)

\(t=0.5s-0.6\)

Substituting:

\(1.5s-1.8-6s=9+2s+3.5s-4.2\)

\(-10s=10.8-4.2\)

\(-10s=6.6\)

\(s=-0.66\)

Plugging in -0.66 for s, we get:

\(-0.33+5t=3-1.98-6\)

\(5t=-4.65\)

\(t=-0.93\)

We get (-0.66,-0.93)

Answer: ( -0.66 , -0.93 )

We can write this as an equation, getting:

\(45^\circ+45^\circ+x+45^\circ+2x=180^\circ\)

\(135^\circ+3x=180^\circ\)

\(3x=45^\circ\)

\(x=15^\circ\)

We can now add \(2x\) to \(45^\circ\) and get:

\(30^\circ+45^\circ\)

\(75^\circ\)

We get that angle \(C=75^\circ\)

Answer: 75°

We know that the angles of the triangle are in the ratio 3:5:10, and we know that the sum of the three interior angles of a triangle is 180°, so we can do:

\(3x + 5x + 10x = 180°\)

\(18x=180°\)

\(x=10°\)

We can now multiply 3, the smallest interior angle, by x.

\(3\cdot 10\)

\(30°\)

Answer: 30°

I tried simplifying the equation and then maybe putting all the \(c\) 's on one side, but I don't know what to do after or if i'm in the right direction.

\(3^{2c+1} = 28\cdot 3^c - 9 + 4 \cdot 3^c - 25\)

\(3^{2c+1} = 32\cdot 3^c-34\)

\(3^{2c+1}+34 = 32\cdot 3^c \)

\(3^{c+1}+\frac{34}{3^c} = 32\)

\(3^{c+1}+34\cdot3^{-c} = 32\)

I don't know 😒

Well, the probability that the mean will be between 121 and 133 pounds is 0.9836, so the probability that the mean will be more than 133 pounds or less than 121 pounds is 1 - 0.9836 = 0.0164

Answer: 0.0164