Two angles are ____________________ if they are across from each other and are congruent (same measure).

Bingel [31]

The answer to your question is 1/3

8 0

3 years ago

A manufacturing company measures the weight of boxes before shipping them to the customers. If the box weights have a population

NikAS [45]

Answer:

The probability that the average weight of the boxes will exceed 94 pounds is 43.25%

Step-by-step explanation:

1. Let's review the information provided to answer the question correctly:

Mean of the population of box weights = 90 pounds

Standard deviation of the population of box weights = 24 pounds

Sample size = 36 boxes

2. What is the probability that the average weight of the boxes will exceed 94 lb?

For answering this question, we will use the z-scores table.

For using the correct z-score, we should use the correct standard deviation. In this case, we have that:

94 - 90 = 4 pounds above the mean.

4 pounds are 4/24 of the standard deviation,

therefore, simplifying:

4/24 = 1/6 = 0.1666......and we'll round to 0.17

z-score is 0.17 because 4 pounds is 1/6 of the standard deviation (24).

The probability of a z-score is 0.5675, but in this case we're asked by a weight over 94 pounds, not under 94 pounds, thus:

1 - 0.5675 = 0.4325

The probability that the average weight of the boxes will exceed 94 pounds is 43.25%

8 0

2 years ago

Write and simplify an expression to model the relationship expressed in the situation below.

spayn [35]

V(p) = x-n, where V(p) is the volume after the boxes have been together, x is the volume of the larger box, and n is the volume of the smaller box.
x = 15 cm x 25 cm x 20 cm = 7500 cubic centimeters (cm^3)
n = 10 cm x 10 cm x 10 cm = 1000 cm^3
V(p) = 7500 - 1000 = 6500 cm^3
So your answer is 6500 cubic centimeters.

6 0

3 years ago

You are making cupcakes and the recipe specifies 6 small eggs for every 27 cupcakes. You need to make 36 cupcakes. How many smal

astra-53 [7]

For every egg you can make 4.5 cupcakes so you will need 8 small eggs because 8 times 4.5 equals 36

6 0

3 years ago

10. 10. If AB bisects CAF, and m<EAF = 72°, then the m<BAF =

never [62]

The measure of ∠BAF is 54°.

Solution:

DF and CE are intersecting lines.

m∠EAF = 72° and AB bisects ∠CAF.

∠EAF and ∠DAC are vertically opposite angles.

Vertical angle theorem:

If two lines are intersecting, then vertically opposite angles are congruent.

∠DAC ≅ ∠EAF

m∠DAC = 72°

Sum of the adjacent angles in a straight line = 180°

m∠DAE + m∠EAF = 180°

m∠DAE + 72° = 180°

Subtract 72° from both sides.

m∠DAE = 108°

∠CAF and ∠DAE are vertically opposite angles.

⇒ m∠CAF = m∠DAE

⇒ m∠CAF = 108°

AB bisects ∠CAF means ∠CAB = ∠BAF

m∠CAB + m∠BAF = 108°

m∠BAF + m∠BAF = 108°

2 m∠BAF = 108°

Divide by 2 on both sides, we get

m∠BAF = 54°

Hence the measure of ∠BAF is 54°.

4 0

3 years ago