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4 years ago

What does x= in the equation?

Mathematics

1 answer:

vampirchik [111]4 years ago

4 0

Answer:

3.5

Step-by-step explanation:

2x + 5 = 12

-- minues five from both sides --

2x = 7

-- divide both sides by two ---

x = 3.5

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2. A sculptor is planning to make two triangular prisms out of steel. The sculptor will use ΔABC for the bases of one prism and

Phoenix [80]

Answer:

a) SAS

b) Volume of DEF is 4 times the Volume of ABC

Step-by-step explanation:

a) since they have one same/congruent angle (angle B and angle E) and other two sides are in the same ratio, they are similar by SAS similarity theorem.

40/20 = 30/15 = 2

Therefore Δ ABC is similar to Δ DEF

b) Volume of a prism

= base area × height

Let height be 'h cm'

With Base ABC:

Volume = ½×20×15×h = 150h cm³

With Base DEF:

Volume = ½×40×30×h = 600h cm³

600h/150h = 4

Prism with base DEF has a greater volume; it's 4 times of the volume of the prism with base ABC

7 0

4 years ago

Find f(g(h(x))) from functions below..

Lilit [14]

Answer:

$f(g(h(x))) = (\sqrt{x} - 8)^4 + 8$

Step-by-step explanation:

$f(x) = x^4 + 8$

$g(x) = x - 8$

$h(x) = \sqrt{x}$

$f(g(h(x))) = f(g(\sqrt{x})) = f(\sqrt{x} - 8) = (\sqrt{x} - 8)^4 + 8$

4 0

3 years ago

According to a study done by Otago University, the probability a randomly selected individual will not cover his or her mouth wh

nirvana33 [79]

Answer:

47.52% probability that among 10 randomly observed individuals fewer than 3 do not cover their mouth

Step-by-step explanation:

For each individual, there are only two possible outcomes. Either they cover their mouth when sneezing, or they do not. The probability of an individual covering their mouth when sneezing is independent of other individuals. So we use the binomial probability distribution 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.

According to a study done by Otago University, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267.

This means that $p = 0.267$