Answer:
Estimated Answer=
Exact Answer=
Step-by-step explanation:
Steady speed of the object =10 and one tenth km/h =
Distance to be Covered=4 and nine tenths km = km
To the nearest integer,
Steady speed of the object = 10 km/hr
Distance=5km
=
The estimated answer is 1/2 hr.
Next, we determine the exact answer.
The exact time taken is
Answer:
There is a difference between the two means.
Step-by-step explanation:
The hypothesis can be defined as:
<em>H₀</em>: The mean exam scores of my SAT 215 students with colorful calculators are same as the mean scores of my STA 215 students with plain black calculators, i.e. <em>μ</em>₁ - <em>μ</em>₂ = 0.
<em>Hₐ</em>: The mean exam scores of my SAT 215 students with colorful calculators are different than the mean scores of my STA 215 students with plain black calculators, i.e. <em>μ</em>₁ - <em>μ</em>₂ ≠ 0.
Assume that the significance level of the test is, <em>α</em> = 0.05. Also assuming that the population variances are equal.
The decision rule:
A 95% confidence interval for mean difference can be used to determine the result of the hypothesis test. If the 95% confidence interval contains the null hypothesis value, i.e. 0 then the null hypothesis will not be rejected.
The 95% confidence interval for mean difference is:
Compute the pooled standard deviation as follows:
The critical value of <em>t</em> is:
*Use a <em>t</em>-table.
Compute the 95% confidence interval for mean difference as follows:
The 95% confidence interval for mean difference is (-5.13, -0.87).
The confidence interval does not contains the value 0. This implies that the null hypothesis will be rejected at 5% level of significance.
Hence, concluding that the mean exam scores of my STA 215 students with colorful calculators are different than the mean scores of my STA 215 students with plain black calculators.
Answer:
One Angle = 110°
Other Angle = 70°
Step-by-step explanation:
A linear pair means that two angles are in a straight line (or, a straight angle).
A straight line is 180 degrees.
THey are supplementary.
We can say one angle is "a" and another one is "b".
<em>One angle is 10 MORE THAN 2/3rds of the other, we can write:</em>
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<em>Also, since they are supplementary (add up to 180), we can write:</em>
<em>a + b = 180</em>
<em />
We can now substitute 1st equation in this one and find b:
Since a + b = 180, we can write:
a + 110 = 180
so,
a = 180 - 110
a = 70
Thus,
One Angle = 110°
Other Angle = 70°
We have been given two ratios and we are supposed to compare our ratios whether they are proportional or not.
1. We will reduce our fractions to compare our ratios. Let us simplify each of our given fractions.
Let us divide numerator and denominator with greatest common factor. We can see that 21 is GCF of our ratio.
Now we will simplify our second ratio.
GCF of our fraction is 32. Upon dividing our fraction by 32 we will get,
We can see that our both ratios are similar.
2. Now we will find decimal values of our fractions.
We can see that .
Therefore, we can say that our ratios are proportional.