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3 years ago

A bill at a restaurant is $48.50. There is a 5% tax

Mathematics

1 answer:

Nitella [24]3 years ago

4 0

Answer:

$61.11

Step-by-step explanation:

When the price of something has a certain percent added to it, you can first convert that percentage to a decimal and then add 1, since 1 is the original price. Therefore, we can set up the following equation:

48.50*1.05*1.20=$61.11

Hope this helps!

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g A fair coin is tossed 20 times. The number of heads observed is the count X of successes. Give the distribution of X . Choose

Nuetrik [128]

Answer:

We assume that we have a fair coin that is $p(Head)=p(Tails)=0.5$

For this case we define the random variable X as "number of heads observed in 20 times". The distribution for X is given by:

$X \sim Binom(n=20, p=0.5)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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

Step-by-step explanation:

Previous concepts

A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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

Solution to the problem

We assume that we have a fair coin that is $p(Head)=p(Tails)=0.5$

For this case we define the random variable X as "number of heads observed in 20 times". The distribution for X is given by:

$X \sim Binom(n=20, p=0.5)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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

3 0

3 years ago

a manufacturer has determined that if his company sells x items per day then their profit is given by P=-x^2+ 700 x-10000 euros.

Radda [10]

Answer:

Step-by-step explanation:

To find the minimum amount of items, x, that need to be sold for the manufacturer to make a profit, we can use the quadratic formula

$x = \frac{-b+\sqrt{b^{2}-4ac } }{2a}; x= \frac{-b-\sqrt{b^{2}-4ac } }{2a}$

$x= \frac{-700+\sqrt{700^{2}-4(a)(-10000) } }{2(1)}; x= \frac{-700-\sqrt{700^{2}-4(a)(-10000) } }{2(1)}$

$x= \frac{-700+\sqrt{530000} }{2}; x= \frac{-700-\sqrt{530000} }{2}$

$x=\frac{-700+100\sqrt{53} }{2}; x=\frac{-700-100\sqrt{53} }{2};$

$x=-350 + 50\sqrt53 = 14.005; x = -350 - 50\sqrt53 = -714.005$

In context of the problem, we can only rely on the positive value, as the negative value would lead to a loss of profit.

$(-714.005)^2+700(-714.005)-10000=-0.360$

Furthermore, we must round to the nearest whole number, as you cannot make part of an item.

Lastly, if you were to plug in 14 into the equation for Profit, you would still have a negative number (i.e. a negative profit), thus requiring the manufacturer to make no less than 15 items to make a profit:

$(14)^2+700(14)-10000=-4\\\\(15)^2+700(15)-10000=725$

3 0

2 years ago

2. Jolie manages an annual film festival in her town. Every year, one movie from every genre is chosen as a finalist to win best

Ad libitum [116K]

Answer:

Step-by-step explanation:

All votes: 10*3+18+22+15*3+20+8=143

143*0.2(20%)=28.6 about 28vote (Scifi)

Scifi, 10 adults, 18 children, which is 20% of the votes.

4 0

3 years ago

Randy won 36 out of 54 games of tic tac toe. what percent of the games did he win

Archy [21]

36/54 = x/100

54x = 100 * 36
54x = 3600
x = 3600 ÷ 54
x = 66.666666.... so 66.67

First put it into a proportion and then cross multiply. After that you divide both sides by 54 to get x alone which gives you 66.66666 which is rounded to 66.67

Answer: 66.67%

7 0

3 years ago

Read 2 more answers

The sum of 3 and a number is less than 5 times the number plus 2.

Leno4ka [110]

Answer:

3+x<5x+2

Step-by-step explanation:

the sum of the number 3+xis less than so 3+x<5×x+2

so final ans is 3+x<5x+2

4 0

3 years ago