How many DVDs can you buy with $192 if one DVD costs $16?”
1 answer:
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Answer:
The true statement is UV < US < SR ⇒ 1st statement
Step-by-step explanation:
"I have added screenshot of the complete question as well as the
diagram"
* <u><em>Lets revise the hinge theorem</em></u>
- If two sides of one triangle are congruent to two sides of another
triangle, and the measure of the included angle between these two
sides of the first triangle is greater than the measure of the included
angle of the second triangle then the length of the third side of the
first triangle is longer than the length of the third side of the second
triangle
* <em>Lets solve the problem</em>
- The figure has three triangles have a common vertex T
- m∠UTV < m∠UTS < m∠STR
- <u><em>From the hinge theorem above</em></u>
∵ The side opposite to ∠UTV is VU
∵ The side opposite to ∠UTS is US
∵ The side opposite to ∠STR is SR
∵ m∠UTV < m∠UTS < m∠STR
∴ UV < US < SR
* The true statement is UV < US < SR
Answer:
84.13% of bottles will have volume greater than 994 mL
Step-by-step explanation:
Mean volume = u = 1000
Standard deviation = = 6
We need to find the proportion of bottles with volume greater than 994. So our test value is 994. i.e.
x = 994
Since the data is normally distributed we will use the concept of z-score to find the required proportion. First we convert 994 to its equivalent z-score, then using the z-table we will find the corresponding value of proportion. The formula to calculate the z score is:
Substituting the values, we get:
This means 994 is equivalent to a z score of -1. Now we will find the proportion of z values which are greater than -1 from the z table.
i.e. P(z > -1)
From the z-table this value comes out to be:
P(z >- 1) = 1 - P(z < -1) = 1 - 0.1587 = 0.8413
Since, 994 is equivalent to a z score of -1, we can write that proportion of values which will be greater than 994 would be:
P( X > 994 ) = P( z > -1 ) = 0.8413 = 84.13%