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Answer:
Step-by-step explanation:
-5 (-6k + 10)
= 30k - 50
IMAGE below!
Answer:
x =22.5
Step-by-step explanation:
x+3x = 90
x and 3x are complementary so they add to 90 degrees
Combine like terms
4x =90
Divide each side by 4
4x/4 = 90/4
x =22.5
answer: x = 22.5
explanation:
as the 3x and x are on a straight line with the angle of 90° we know that
3x +x = 90
4x = 90
x = 22.5
Answer:
x = -2 and 3/4
Step-by-step explanation:
3x - 4 = 0
3x = 4
x = 3/4
x + 2 = 0
x = -2
Hopefully this helps!
Brainliest please?
Answer: 18 pine trees / 12 elm trees
Step-by-step explanation:
To meet the requirement of at least 16 but no more than 30 trees with a 3:2 ratio of elm to pine trees, we can choose:
Elm Trees: 3x
Pine Trees: 2x
Where x is a positive integer. To stay within the given constraints:
3x + 2x ≥ 16 (at least 16 trees)
5x ≥ 16
x ≥ 16/5
x ≥ 3.2
We need to find the largest integer value for x while staying below 30 (no more than 30 trees). Since x must be an integer, the largest valid value for x is 6 (as 7 would exceed 30).
So, for the example:
Elm Trees = 3x = 3 * 6 = 18
Pine Trees = 2x = 2 * 6 = 12
In this case, there would be 18 elm trees and 12 pine trees, totaling 30 trees, which falls within the range of at least 16 but no more than 30 trees and maintains the 3:2 ratio of elm to pine trees.
Answer:
0.9533
Step-by-step explanation:
(a) Probability that a randomly selected woman's height is less than 65 inches:
Using the z-score formula:
�
=
�
−
�
�
Z=
σ
X−μ
Where:
�
X = 65 inches
�
μ = 64.3 inches
�
σ = 2.7 inches
�
=
65
−
64.3
2.7
≈
0.2593
Z=
2.7
65−64.3
≈0.2593
Now, find the probability associated with this z-score, which is approximately 0.6010 (rounded to four decimal places).
(b) Probability that the mean height of 43 randomly selected women is less than 65 inches:
Using the Central Limit Theorem:
�
μ (mean of the sample means) remains 64.3 inches.
�
sample mean
σ
sample mean
(standard deviation of the sample means) is calculated as
2.7
43
≈
0.4115
43
2.7
≈0.4115.
Now, find the z-score for a sample mean of 65 inches:
�
=
65
−
64.3
0.4115
≈
1.6924
Z=
0.4115
65−64.3
≈1.6924
The probability associated with this z-score is approximately 0.9533 (rounded to four decimal places).