Answer:
The last expression is correct
Step-by-step explanation:
We have been given the following expression for simplification;
The bases of the two expressions are the same. They are both equal to 4. When multiplying numbers with the same base, we simply add their exponents. In this case our exponents are;
4 and -9
adding them we have;
4 + (-9) = -5
The simplified expression thus becomes;
Answer:
5, 7, 9
Step-by-step explanation:
Using the information given we get:
<em>Add 7 to both sides</em>
<em>Subtract 2x from both sides</em>
<em>Divide both sides by 3</em>
Using these equations:
and
We get:
Answer:
T = 4.541
Step-by-step explanation:
We don't have the standard deviation for the population, so we use the t-distribution.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 4 - 1 = 3
98% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 3 degrees of freedom(y-axis) and a confidence level of . So we have T = 4.541
Answer:
The length of rope is 20.0 ft . Hence, <u>option (1) </u> is correct.
Step-by-step explanation:
In the figure below AB represents pole having height 10 ft and AC represents the rope that is from the top of pole to the ground. BC represent the ground distance from base of tower to the rope.
The rope and the ground form a 30 degree angle that is the angle between BC and AC is 30°.
In right angled triangle ABC with right angle at B.
Since we have to find the length of rope that is the value of side AC.
Using trigonometric ratios
Putting values,
We know,
On solving we get,
AC= 20.0 ft
Thus, the length of rope is 20.0 ft
Hence, <u>option (1)</u> is correct.
Answer:
15, 840.
Step-by-step explanation:
-HCM(GCM)
105's factor are 1, 3, 5, 7, <em>15</em>, 21, 35, 105.
125's factor are 1, 2, 3, 4, 5, 6, 8, 10, 12, <em>15</em>, 20, 24, 30, 40, 60, 120.
so, the answer is 15!