The Museum of Science in Boston has an exhibit in which metal balls drop down a chute, bounce around, and wind up in one of 21 b

Answer:

The proportion of goats at fair Y exceeds that of goats at fair X.

Step-by-step explanation:

From the bar chart,  we see there were 100 goats at both fairs X and Y.

Calculating the percentage of goats at each fair we find:

Fair X = 100/645 * 100 = 15.5%

Fair Y = 100/590 * 100 = 16.9%

This indicates that fair Y had a higher percentage of goats compared to fair X.

The original price stands at $450.

Step-by-step explanation:

Step 1:

Given information, Discount%, D% = 30 and Selling Price, SP = $315

Step 2:

Formulate the equation for determining the Original Price

Selling Price (SP) = Original Price (OP) - Discount (D)

Discount (D) = Original Price (OP) * (D%/100)

Step 3:

Plug in the known values into the formula

315 = OP - D

D =

D = 0.3 OP

Step 4:

Insert the value of D back into the initial equation

315 = OP - 0.3 OP

315 = OP (1 - 0.3) = 0.7 OP

A resulting Original Price of OP = 315/0.7 = $450

To find the value of z in triangle XYZ, we can utilize the law of sines. We know the following:

1. The measure of angle XYZ is 51 degrees.

2. The measure of angle YZX is 76 degrees.

3. The length of side XZ is 2.6 units.

From these angles, angle XZY can be calculated, and then we can apply the law of sines to determine z.

Thus, we proceed to solve for z using the sine relationship in the triangle.

We will round the result to one decimal place.

Answer:

2.CE lies on line m.

4.Ray AD is identical to ray AC.

6.Angle ECB is formed by CE and CB.

Step-by-step explanation:

A diagram has been provided.

Our task is to identify the valid statements regarding the diagram.

1.CB is found on line n.

CB does not align with line n since points C and B do not lie on that line.

Thus, this statement is false.

2.CE is situated on line m.

CE is indeed positioned on line m because points C and E are both on this line.

This statement is accurate.

3.Ray BC is equivalent to ray CB.

A ray begins at a single point and continues indefinitely without a terminal point.

Ray CB starts at point C and stretches out from point B.

However, ray BC does not exist.

This statement is therefore false.

4.Ray AD is equivalent to ray AC.

Both AD and AC are rays.

They are equivalent since both originate from point A and extend in the same direction.

5.Angle EAD is formed from AE and DA.

This is false because angle EAD is created by ray AE and ray AD, not by ray DA.

6.Angle ECB is generated by CE and CB.

This is true as angle ECB is made by ray EC and ray BC.