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kiruha [24]
3 years ago
8

Find a formula for the described function. An open rectangular box with volume 3 m3 has a square base. Express the surface area

SA of the box as a function of the length of a side of the base, x.
Mathematics
1 answer:
Alex73 [517]3 years ago
4 0

Answer:

SA(x) = x^2 + \frac{12}{x}

Step-by-step explanation:

Given

V = 3m^3 --- volume

x \to base\ length

y \to height

Required

The surface area as a function of base length

The volume (V) is calculated as:

V = Base\ Area * Height

V = x*x*y

V = x^2*y

Make y the subject

y = \frac{V}{x^2}

Substitute 3 for V

y = \frac{3}{x^2}

The surface area of the open box is:

SA = x^2 + 2xy+2xy

SA = x^2 + 4xy

Substitute: y = \frac{3}{x^2}

SA = x^2 + 4x*\frac{3}{x^2}

SA = x^2 + 4*\frac{3}{x}

SA = x^2 + \frac{12}{x}

Hence, the function is:

SA(x) = x^2 + \frac{12}{x}

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20,25 and 35,50 and 10,15. Each pair would have a GCF of 5.
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3 years ago
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Select all values equivalent to -10/7<br> -10/-7<br> -3 1/7<br> 1 3/7<br> - -10/-7<br> -1 3/7
Kitty [74]
We know that

case 1) -10/-7-----> 10/7-------> is not <span>equivalent to -10/7

case 2) </span>-3 1/7----> (-3*7+1)/7----> -20/7 ------> is not equivalent to -10/7

case 3) 1 3/7-----> (1*7+3)/7----> 10/7 ------> is not equivalent to -10/7

case 4) - -10/-7---> +10/-7----> -10/7------>  is equivalent to -10/7

case 5) -1 3/7----> (-1*7+3)/7----> -4/7 ------> is not equivalent to -10/7

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5 0
3 years ago
7.109) The leading brand of dishwasher detergent has a 30% market share. A sample of 25 dishwasher detergent customers was taken
Rina8888 [55]

Answer:

0.9021 = 90.21% probability that 10 or fewer customers choose the leading brand

Step-by-step explanation:

For each customer, there are only two possible outcomes. Either they choose the leading brand, or they do not. The probability of a customer choosing the leading brand is independent of any other customer, 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.

The leading brand of dishwasher detergent has a 30% market share.

This means that p = 0.3

A sample of 25 dishwasher detergent customers was taken.

This means that n = 25

a. What is the probability that 10 or fewer customers choose the leading brand?

This is:

P(X \leq 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

In which

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

P(X = 0) = C_{25,0}.(0.3)^{0}.(0.7)^{25} = 0.0001

P(X = 1) = C_{25,1}.(0.3)^{1}.(0.7)^{24} = 0.0014

P(X = 2) = C_{25,2}.(0.3)^{2}.(0.7)^{23} = 0.0074

P(X = 3) = C_{25,3}.(0.3)^{3}.(0.7)^{22} = 0.0243

P(X = 4) = C_{25,4}.(0.3)^{4}.(0.7)^{21} = 0.0572

P(X = 5) = C_{25,5}.(0.3)^{5}.(0.7)^{20} = 0.1030

P(X = 6) = C_{25,6}.(0.3)^{6}.(0.7)^{19} = 0.1472

P(X = 7) = C_{25,7}.(0.3)^{7}.(0.7)^{18} = 0.1712

P(X = 8) = C_{25,8}.(0.3)^{8}.(0.7)^{17} = 0.1651

P(X = 9) = C_{25,9}.(0.3)^{9}.(0.7)^{16} = 0.1336

P(X = 10) = C_{25,10}.(0.3)^{10}.(0.7)^{15} = 0.0916

Then

P(X \leq 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0001 + 0.0014 + 0.0074 + 0.0243 + 0.0572 + 0.1030 + 0.1472 + 0.1712 + 0.1651 + 0.1336 + 0.0916 = 0.9021

0.9021 = 90.21% probability that 10 or fewer customers choose the leading brand

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3 years ago
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ElenaW [278]

Answer:

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5 0
3 years ago
What is a counterexample for the conjecture?
Dmitriy789 [7]

Answer:

A counterexample for a conjecture is the statement that disproves a conjecture.

Step-by-step explanation:

To find : What is a counterexample for the conjecture?

Solution :

A conjecture is an educated guess but not yet proven. It is possible that next example shown the conjecture wrong.

A counterexample is an example that disproves or disagree a conjecture.

For example : Prime numbers - 3,7,11,23

Conjecture  - All prime numbers are odd

Counterexample - 2

→ 2 is a prime number but not odd, it is an even number.

4 0
3 years ago
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