A rectangular prism is 3 meters long, 4 meters wide, and has a total surface area of 94 square meters. What is its height?3 m
4 m
5 m
6 m


Answer 1
Answer:     S = 2lw + 3lh + 2wh
  94 = 2(3)(4) + 2(3)(h) + 2(4)(h)
  94 = 2(12) + 2(3h) + 2(4h)
  94 = 24 + 16h + 8h
  94 = 24 + 14h
- 24  - 24
  70 = 14h
   14     14
    5 = h

The answer is C.
Answer 2

Answer: answer is C

Step-by-step explanation:

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An airline company is considering a new policy of booking as many as 354 persons on an airplane that can seat only 330. (Past studies have revealed that only 88% of the booked passengers actually arrive for the flight.) Estimate the probability that if the company books 354 persons, not enough seats will be available



See the explanation.

Step-by-step explanation:

It is given that, if 100 persons book their seats, then only 88 passengers come.

The probability of 1 passenger to come is (88)/(100) = 0.88.

There will not be enough seats only when, 331 or more than 331 passengers will come.

The probability of 1 passenger will not come is (1 - 0.88)= 0.12.

Out of 354 passengers the probability that n passengers will come is ^(354)C_n (0.88)^n (0.12)^(354 - n).

The required probability is ∑^(354)C_n (0.88)^n (0.12)^(354 - n), where 331\leq n \leq 354.

The half-life of radium-226 is 1620 yr. Given a sample of 1 g of radium-226, the quantity left Q(t) (in g) after t years is given by:Q(t)= 1/2^t/1620

a. Convert this to an exponential function using base e.
b. Verify that the original function and the result from part (a) yield the same result for Q(0), Q(1620), and Q(3240).



(a)e^(-0.000428 t)

Step-by-step explanation:

We are given that

Half life of radium-226=1620 yr

The quantity left Q(t) after t years is given by


a. We have to convert the given function into an exponential function using base e.



=e^(ln(1/2) t/1620)


=e^(-0.000428 t)


Q(0)=e^(-0.000428 * 0)


From original function




From exponential function

Q(1620)=e^(-0.000428 * 1620)

=0.499\approx 0.5


Q(3240)=e^(-0.000428 * 3240)

Q(3240)=0.249=\approx 0.25

Hence, verified.

At a point on the ground 20 feet from a building, a surveyor observes the angle of inclination to the top of the building to be pi/3 radians. How tall is the building?



34.64 ft

Step-by-step explanation:

Distance from the building = 20 ft

Angle of inclination = π/3 radians

The tangent of the angle of inclination must equal the height of the building divided by the distance of the observer from the building:

tan( \pi/3) = (h)/(20) \nh = 20*1.73205\nh=34.64\ ft

The building is 34.64 ft tall

I need help please!!



2 remainder 5 ily

Step-by-step explanation:

Juan makes a measurement in a chemistry laboratory and records the result in his lab report. The standard deviation of students' lab measurements is σ σ = 10 milligrams. Juan repeats the measurement 4 times and records the mean x x of his 4 measurements.


Final answer:

Juan is applying basic statistical principles in a chemistry laboratory by reviewing the standard deviation of the lab measurements and repeating his measurements multiple times to find a more accurate mean. The more Juan repeats his measurements, the closer he gets to a normal distribution or an accurate mean as per the central limit theorem.


In this chemistry laboratory scenario, you're dealing with a situation in statistics known as repeated measurements. Essentially, you are considering the standard deviation of the lab measurements, which is a typical measure of the dispersion of a set of values. The standard deviation is denoted by σ, and it is given as 10 milligrams.

When Juan repeats the measurement 4 times and records the mean of his measurements, he's using another common measure of central tendency, the arithmetic mean.

According to the central limit theorem in statistics, the distribution of the mean of a large number of independent, identically distributed variables will be approximately normal, regardless of the underlying distribution. In this case, as Juan repeats his measurements, the mean of these measurements is likely to be more accurate (closer to the true value) than a single measurement.

Learn more about Standard Deviation and Mean here:



Final answer:

The standard deviation a measure of dispersion in a data set, lower values indicating data points closer to the mean of the data set, and higher values indicating a wide range of the data points. The scenario discusses the calculation of standard deviation for repeated measurements, with the standard error calculated as the original standard deviation divided by the square root of the number of measurements.


The subject matter of the question pertains to statistical concepts, primarily the standard deviation. In statistics, the standard deviation is a measure of the amount of variation or dispersion in a data set. A low standard deviation indicates that the data points tend to be close to the mean of the data set, while a high standard deviation indicates that the data points are spread out over a wider range.

In the scenario provided, Juan makes a measurement in a chemistry lab and the standard deviation of the students' lab measurements is 10mg. He repeats the measurement 4 times and records the mean of his 4 measurements. When you repeat a measurement multiple times and take the mean, the standard deviation of the mean tends to be smaller than the standard deviation of the individual measurements. In statistical terms, the standard deviation of the mean, also known as the standard error, is given by the original standard deviation σ divided by the square root of the number of measurements n. In this case, n is 4, so the standard error would be σ/√n = 10mg/√4 = 5mg.

Learn more about Standard Deviation here:



Please Explain/Show Your Work! Thank You!



  10.8 yards

Step-by-step explanation:

Since she has 19.7 yards left over, the amount she used for curtains is ...

  84.5 - 19.7 = 64.8 . . . . yards

Then each of the 6 identical curtains used 1/6 of this amount, or ...

  (64.8 yards)/6 = 10.8 yards


You can write an equation if you like. Let c represent the yardage used for each curtain. Then the total number of yards of fabric Jennifer has is ...

  6c +19.7 = 84.5

We can find the value of c by subtracting 19.7, then dividing by 6 (as above).

  6c = 64.8 . . . . subtract 19.7

  c = 10.8 . . . . . divide by 6

Jennifer used 10.8 yards of fabric per curtain.