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3 years ago

Find the volume of a regular tetrahedron whose altitude measures 10 cm.

1 answer:

6 0

The answer is 118 cm³

The volume of tetrahedron (V), where a is its altitude, can be expressed as:
$V= \frac{ a^{3}}{6 \sqrt{2} } =$
$V = \frac{10 ^{3} }{6 \sqrt{2} } = \frac{1000}{6*1.41} = \frac{1000}{8.46} = 118.2 cm^{3}$ ≈ 118 cm³

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Simplify the following expression (x+y)²

MrMuchimi

Answer:

${x}^{2} + 2xy + {y}^{2}$

Step-by-step explanation:

1) Use square sum: (a + b)² = a² + 2ab + b².

${x}^{2} + 2xy + y^{2}$

Therefor, the answer is x² + 2xy + y².

8 0

3 years ago

A pharmaceutical company receives large shipments of ibuprofen tablets and uses an acceptance sampling plan. This plan randomly

Keith_Richards [23]

Answer:

0.7208 = 72.08% probability that this whole shipment will be accepted.

Step-by-step explanation:

For each tablet, there are only two possible outcomes. Either it meets the required specifications, or it does not. The probability of a tablet meeting the required specifications is independent of any other tablet, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

4% rate of defects

This means that $p = 0.04$

26 tablets

This means that $n = 26$

What is the probability that this whole shipment will be accepted?

Probability that at most one tablet does not meet the specifications, which is:

$P(X \leq 1) = P(X = 0) + P(X = 1)$

Thus

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{26,0}.(0.04)^{0}.(0.96)^{26} = 0.3460$

$P(X = 1) = C_{26,1}.(0.04)^{1}.(0.96)^{25} = 0.3748$

Then

$P(X \leq 1) = P(X = 0) + P(X = 1) = 0.3460 + 0.3748 = 0.7208$

0.7208 = 72.08% probability that this whole shipment will be accepted.

3 0

3 years ago

A student uses the ratio of 4 oranges to 6 fluid ounces to find the number of oranges needed to make 24 fluid ounces of juice. T

Lubov Fominskaja [6]

Answer:number of oranges needed to make 24 fluid ounces of juice. the student writes this proportion: equation explain the error in the student's work. ... Astudent uses the ratio of 4 oranges to 6 fluid ounces to find the number of ... Ratio is the relationship between two numbers, defined as the quotient of one number for the other.

Step-by-step explanation: hope it helps

5 0

3 years ago

A solid cylindrical metal is melted and recast into cubes of metal of sides 3cm . The base radius of the initial cylindrical met

Orlov [11]

Answer:

Approximately 809 cubes will be made

Step-by-step explanation:

To calculate the number if cubes to be made, we shall need to calculate the volume of both shapes

The volume of the cubes can be calculated using the formula L^3 = 3 * 3 * 3 = 27 cm^3

For the cylinder, the formula of the volume to use is

V = π * r^2 * h

The radius here is 10.5 cm and the height is 63 cm

V = 22/7 * 10.5^2 * 63 = 21,829.5 cm^3

The number of cubes that can be made is calculated by dividing the volume of the cylinder by that of the cube

That is 21,829.5/27 = 808.5 which is 809 to the nearest whole number

6 0

4 years ago

F(x) = 2x - 1, g(x) = 3x, h(x) = x2 + 1 Compute the following: h(f(9))

Tamiku [17]

H(2)=5-F+g(2)=(f • h)(2)=f

6 0

3 years ago