Answer:
x = 7
Step-by-step explanation:
Notice that in the triangle, the angle is either known or in terms of x. This means we can make an equation: 82 + (9x - 6) + (6x - 1) = 180. Now, add up tthe terms to get 15x + 75 = 180, or 15x = 105 or x = 7.
Using the normal distribution, it is found that 0.26% of the items will either weigh less than 87 grams or more than 93 grams.
In a <em>normal distribution</em> 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.
In this problem:
- The mean is of 90 grams, hence
.
- The standard deviation is of 1 gram, hence
.
We want to find the probability of an item <u>differing more than 3 grams from the mean</u>, hence:



The probability is P(|Z| > 3), which is 2 multiplied by the p-value of Z = -3.
- Looking at the z-table, Z = -3 has a p-value of 0.0013.
2 x 0.0013 = 0.0026
0.0026 x 100% = 0.26%
0.26% of the items will either weigh less than 87 grams or more than 93 grams.
For more on the normal distribution, you can check brainly.com/question/24663213
6p^3+29p^2+22p-21 i believe!
The perimeter of the triangle is 40 units
<h3>Perimeter of a triangle</h3>
From the question, we are to determine the perimeter of the given triangle
From the given diagram, we can observe that the triangle is a right triangle
The vertical length of the triangle is 15 units
and the horizontal length of the triangle is 8 units
Thus,
We can find the hypotenuse by using the<em> Pythagorean theorem </em>
Let the hypotenuse be h
Then,
h² = 15² + 8²
h² = 225 + 64
h² = 289
h = √289
h = 17 units
Now, for the perimeter of the triangle
The perimeter of a triangle is the sum of all its three sides
Thus,
The perimeter. P, of the triangle is
P = 15 + 8 + 17
P = 40 units
Hence, the perimeter of the triangle is 40 units
Learn more on Calculating perimeter here: brainly.com/question/17394545
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Answer:

Step-by-step explanation:
The formula relating distance (d), speed (s), and time (t) is
d = st
1. Calculate the distance
d = 269 s × 4.6 m·s⁻¹ = 1240 m
2.Calculate the track radius
The distance travelled is the circumference of a circle
