<em><u>Step-by-step explanation:</u></em>
FIRST, we want to understand every property:
Associative Property: The associative property states that you can add or multiply regardless of how the numbers are grouped so (5 + 4) + 3 = 5 + (4 + 3)
Commutative Property: Commutative is the one that refers to moving stuff around so 3 + 2 = 2 + 3
Additive Inverse Property: This is the number that when added to the original number, equals 0 or it's the opposite of the number so 5 <- is the original number and -5 <- is the additive inverse.
Simplify: Is just to add like terms, and make the equation the simplest.
1. ORIGINAL EXPRESSION
2. Additive Inverse Property
3. Commutative property
4. Associative Property
5. Simplify
6. Simplify
120 square centimeters i think?
3.3 x 5 = 16.5 cm
Happy to Help!
Answer:
- <u><em>A dilation by a scale factor of 4 and then a reflection across the x-axis </em></u>
Explanation:
<u>1. Vertices of triangle FGH:</u>
- F: (-2,1)
- G: (-3,3)
- H: (0,1)
<u>2. Vertices of triangle F'G'H':</u>
- F': (-8,-4)
- G': (-12,-12)
- H': (0, -4)
<u>3. Solution:</u>
Look at the coordinates of the point H and H': to transform (0,1) to (0,-4) you can muliply each coordinate by 4 and then change the y-coordinate from 4 to -4. That is<em> a dilation by a scale factor of 4 and a reflection across the x-axis.</em> This is the proof:
- Rule for a dilation by a scale factor of 4: (x,y) → 4(x,y)
(0,1) → 4(0,1) = (0,4)
- Rule for a reflection across the x-axis:{ (x,y) → (x, -y)
(0,4) → (0,-4)
Verfiy the transformations of the other vertices with the same rule:
- Dilation by a scale factor of 4: multiply each coordinate by 4
4(-2,1) → (-8,4)
4(-3,3) → (-12,12)
- Relfection across the x-axis: keep the x-coordinate and negate the y-coordinate
(-8,4) → (-8,-4) ⇒ F'
(-12,12) → (-12,-12) ⇒ G'
Therefore, the three points follow the rules for <em>a dilation by a scale factor of 4 and then a reflection across the x-axis.</em>
Using the normal distribution, it is found that there is a 0.9192 = 91.92% probability that the total amount of product is less than 575 g.
In a normal distribution with mean 
and standard deviation 
, the z-score of a measure X is given by:
- It measures how many standard deviations the measure is from the mean.
- After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
- When two normal variables are added, the mean is the sum of the means while the standard deviation is the square root of the sum of the variances.
In this problem, the product is composed by flakes and raisins, and we have that:
Hence, the distribution for the total amount of product has <u>mean and standard deviation</u> given by:
The probability that the total amount of product is less than 575 g is the <u>p-value of Z when X = 575</u>, hence:
has a p-value of 0.9192.
0.9192 = 91.92% probability that the total amount of product is less than 575 g.
A similar problem is given at brainly.com/question/22934264
