A Shampoo Problem: A bottle contains 25.4 fluid ounces of shampoo. Katie uses 0.25 of the bottle. How much shampoo is left? a. I
1 answer:
Answer:
a) There is no a word problem for both expressions ( and
), b) A bottle contains 25.4 fluid ounces of shampoo. Katie uses 0.75 of the bottle. How much shampoo is left? A bottle contains 25.4 fluid ounces of shampoo. Katie uses 0.25 fluid ounces of the bottle. How much shampoo is left?
Step-by-step explanation:
a) The shampoo problem is a word problem for:
(Final content) = (Initial content) - (Used content)
Then,
Or:
Hence, there is no a word problem for both expressions ( and
).
b) The word problem for is:
A bottle contains 25.4 fluid ounces of shampoo. Katie uses 0.75 of the bottle. How much shampoo is left?
The word problem for is:
A bottle contains 25.4 fluid ounces of shampoo. Katie uses 0.25 fluid ounces of the bottle. How much shampoo is left?
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Answer:
The students have to score 0.74 standard deviations above the mean to be publicly recognized.
Step-by-step explanation:
A random variable <em>X</em> is said to have a normal distribution with parameters <em>µ</em> (mean) and <em>σ</em>² (variance).
If , then
, is a standard normal variate with mean, E (<em>Z</em>) = 0 and Var (<em>Z</em>) = 1. That is,
.
The distribution of these <em>z</em>-scores is known as the standard normal distribution.
The <em>z</em>-score is a standardized form of the raw score, <em>X</em>. It is a numerical measurement of the relationship between a value (<em>X</em>) and the mean (<em>µ</em>) in terms of the standard deviation (<em>σ</em>). A <em>z</em>-score of -1 implies that the data value is 1 standard deviation below the mean. And a <em>z</em>-score of 1 implies that the data value is 1 standard deviation above the mean.
Let <em>X</em> be defined as the scores of students at the National Financial Capability Challenge Exam.
It is provided that the students who score in the top 23% are recognized publicly for their achievement by the Department of the Treasury.
That is, P (X > x) = 0.23.
⇒
⇒
The value of <em>z</em> for this probability value is:
<em>z</em> = 0.74.
*Use a <em>z</em>-table.
Thus, the students have to score 0.74 standard deviations above the mean to be publicly recognized.
Answer:
Option (1). 34°
Step-by-step explanation:
From the figure attached, CE and CD are the radii of the circle C.
Central angle CED formed by the intercepted arc DE = 68°
Since measure of an arc = central angle formed by the intercepted arc
Therefore, m∠CED = 68°
Since m∠EFD = [Central angle of an intercepted arc measure the double of the inscribed angle by the same arc]
Therefore, m∠EFD =
= 34°
Therefore, Option (1) 34° will be the answer.
Answer:
Step-by-step explanation:
Finding the 8th term of this sequence will be much easier with an explicit formula, so we will find that, find the 8th term, then write the equation for the recursive. The recursive formula is only good if you know all the terms before the one you're looking for. That means if we want the 8th term, we first have to find the 7th term, but before that we have to find the 6th term, etc...
We can find the explicit formula for this using the info we have about the 5th term and the 3rd term. The explicit formula looks like this, in general terms:
where a1 is the first term and r is the common ratio. We can solve for both, one at a time. First, using the fact that the 5th term is 3888:
and subbing in and simplifying:
and we will solve that for a1:
Now the other equation we need for this system, using the fact that the third term is 108:
and we sub in our expression for a1:
which simplifies to
and
so
r = 6. Now we'll plug 6 in for r to find a1:
so
a1 = 3. Now we have the a and r for the explicit formula:
and we simply put in an for n:
and
which gives us the 8th term as
a8 = 839808
The recursive formula is
and it works, also, but again, you have to have all the terms that come before the one you want or this formula is useless. Explicit is always better, in my opinion.