Answer:
35 minutes
Step-by-step explanation:
<u><em>Martin can run a kilometer in 7 minutes. If he keeps at this pace how many minutes will it take him to run a 5k race?</em></u>
<u><em /></u>
To solve this, we simply need to use proportion.
Let x represent the number of minutes that will take Martin to run a 5 kilometer race
1 kilometer = 7 minutes
5 kilometer = x
cross-multiply
1 × x = 7 × 5
x = 35 minutes
Therefore, it will take Martin 35 minutes to run a 5 kilometer race.
7 to 1 is the reduced ratio.
Answer:
WDQA
Step-by-step explanation:
Notice that angle P has two arc marks. Look for the same marks in the other polygon: angle W has two arc marks. So P and W are corresponding angles.
Repeat for the rest of the letters:
G → D
Y → Q
X → A
Matching each letter, the similarity statement is:
PGYX ~ WDQA
Answer:
A 90% confidence interval for <em>p</em> will be <u>narrower </u>than the 99% confidence interval.
Step-by-step explanation:
The formula to compute the (1 - <em>α</em>) % confidence interval for a population proportion is:
Here is the sample proportion.
The margin of error of the confidence interval is:
The MOE is dependent on:
- Confidence level
- Standard deviation
- Sample size
The MOE is directly related to the confidence level and standard deviation.
So if any of the two increases then the MOE also increases, thus widening the confidence interval.
And the MOE is inversely related to the sample size.
So if the sample increases the MOE decreases and vice versa.
It is provided that the sample size and the sample proportion are not altered.
The critical value of <em>z</em> for 90% confidence level is:
And the critical value of <em>z</em> for 99% confidence level is:
So as the confidence level increases the critical value increases.
Thus, a 90% confidence interval for <em>p</em> will be narrower than the 99% confidence interval.
The integral is path-independent if we can find a scalar function <em>f</em> such that grad(<em>f</em> ) = <em>A</em>. This requires
Take the first PDE and integrate both sides with respect to <em>x</em> to get
where <em>g</em> is assumed to be a function of <em>y</em> alone. Differentiating this with respect to <em>x</em> gives
which would mean <em>g</em> is *not* a function of only <em>y</em>, but also <em>x</em>, contradicting our assumption. So the integral is path-dependent.
Parameterize the unit circle (call it <em>C</em>) by the vector function,
with <em>t</em> between 0 and 2π.
Note that this parameterization takes <em>C</em> to have counter-clockwise orientation; if we compute the line integral of <em>A</em> over <em>C</em>, we can multiply the result by -1 to get the value of the integral in the opposite, clockwise direction.
Then
and the (counter-clockwise) integral over <em>C</em> is
and so the integral in the direction we want is -2π.
By the way, that the integral doesn't have a value of 0 is more evidence of the fact that the integral is path-dependent.