Answer:
The answer is
±
in exact form or
,
in decimal form.
Step-by-step explanation:
To solve this problem, start by moving all terms to the left side of the equation and simplify. Simplify the equation by subtracting 12 from both sides of the equation and squaring
, which will look like
. Next, simplify the equation again, which will look like
.
Then, use the quadratic formula to find the solutions. The quadratic formula looks like
.
For this problem, the quadratic variables are as follows:



The next step is to substitute the values
,
, and
into the quadratic formula and solve. The quadratic formula will look like
. To simplify the equation, start by simplifying the numerator, which will look like
. Then, multiply 2 by 1 and simplify the equation, which will look like
. The final answer is
±
in exact form. In decimal form, the final answer is
,
.
Answer:
Step-by-step explanation:
<u>The volume of the prism:</u>
<u>If each of the dimensions is doubled, then the volume becomes:</u>
- V₁ = 2l*2w*2h = 8lwh = 8V
The larger prism has 8 times greater volume
Answer:
The 99% two-sided confidence interval for the average sugar packet weight is between 0.882 kg and 1.224 kg.
Step-by-step explanation:
We are in posession of the sample's standard deviation, so we use the student's t-distribution to find the confidence interval.
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 = 16 - 1 = 15
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 35 degrees of freedom(y-axis) and a confidence level of
). So we have T = 2.9467
The margin of error is:
M = T*s = 2.9467*0.058 = 0.171
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 1.053 - 0.171 = 0.882kg
The upper end of the interval is the sample mean added to M. So it is 1.053 + 0.171 = 1.224 kg.
The 99% two-sided confidence interval for the average sugar packet weight is between 0.882 kg and 1.224 kg.
Answer:
approx. 9.06 for one pound
Step-by-step explanation:
Answer:
1/2
Step-by-step explanation:
Remaining fraction will be (1-3/8)=5/8
Given that in the second hour he delivered 4/5 of 5/8, then the fraction delivered in the second hour will be:
4/5 of 5/8
=4/5×5/8
=1/2
He delivered 1/2 (in fraction)