Selena walks from home to school each morning and back home each afternoon.altogether , she walks 2/3 mile each day . How far do
1 answer:
One days trip of to school from home and back home from school is 2/3 of a mile. We want to know how far it is to school from her house.
To solve this, we simply need to take half of the total distance (2/3)
Next, we need to turn the 2 into a fraction. Every whole number can be made into a fraction by putting it over 1.
Because we are dividing, we need to invert the second fraction and then multiply.
Next, we multiply the top of the first fraction by the top of the second and the bottom of the first fraction by the bottom of the second.
Once you reduce, you get:
To solve this, we simply need to take half of the total distance (2/3)
Next, we need to turn the 2 into a fraction. Every whole number can be made into a fraction by putting it over 1.
Because we are dividing, we need to invert the second fraction and then multiply.
Next, we multiply the top of the first fraction by the top of the second and the bottom of the first fraction by the bottom of the second.
Once you reduce, you get:
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Answer:
f(x) = {x-3 for x ≤ -1; -3x+14 for x > 5}
Step-by-step explanation:
To write the piecewise function, we can consider the pieces one at a time. For each, we need to define the domain, and the functional relation.
__
<h3>Left Piece</h3>The domain is the horizontal extent. It is shown as -∞ to -1, with -1 included.
The relation has a slope (rise/run) of +1, and would intersect the y-axis at -3 if it were extended.
The first piece can be written ...
f(x) = x-3 for x ≤ -1
__
<h3>Right Piece</h3>The domain is shown as 5 to ∞, with 5<em> not included</em>.
The relation is shown as having a slope (rise/run) of (-3)/(1) = -3. If extended, it would intersect the point (5, -1), so we can write the point-slope equation as ...
y -(-1) = -3(x -5)
y = -3x +15 -1 = -3x +14
The second piece can be written ...
f(x) = -3x +14 for x > 5
__
<h3>Whole function</h3>Putting these pieces together, we have ...
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<em>Additional comment</em>
Sometimes it is convenient to write inequalities in number-line order (using < or ≤ symbols). This gives a visual indication of where the variable stands in relation to the limit(s). Perhaps a more conventional way to write the domain for the second piece is, <em>x > 5</em>.
Answer:
The second choice: Approximately of the pretzel bags here will contain between 225 and 245 pretzels.
Step-by-step explanation:
This explanation uses a z-score table where each entry has two decimal places.
Let represent the mean of a normal distribution of variable
. Let
be the standard deviation of the distribution. The z-score for the observation
would be:
.
In this question,
.
.
Calculate the z-score for and
. Keep in mind that each entry in the z-score table here has two decimal places. Hence, round the results below so that each contains at least two decimal places.
.
.
The question is asking for the probability (where
is between two values.) In this case, that's the same as
.
Keep in mind that the probabilities on many z-table correspond to probability of (where
is no greater than one value.) Therefore, apply the identity
to rewrite
as the difference between two probabilities:
.
Look up the z-table for and
:
.
.
.