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ANTONII [103]
3 years ago
15

One number is 9 less than the other. Find the two numbers if their product is 736.

Mathematics
1 answer:
Alika [10]3 years ago
6 0
x-first\ number\\x-9-second\ number\\\\x(x-9)=736\\x^2-9x-736=0\\\\\Delta=b^2-4ac\\\\\Delta=(-9)^2-4\cdot(-736)\cdot1=81+2944=3025\\\\\sqrt\Delta=55\\\\x_1=\frac{-b-\sqrt{\Delta}}{2a}\ \ x_1=\frac{9-55}{2*1}=\frac{-46}{2}=-23
\\\\ or \\
x_2=\frac{-b+\sqrt{\Delta}}{2a}\ \ x_2=\frac{9+55}{2*1}=\frac{64}{2}=32\\\\x_1\ is\ negative\ number\ so\ it\ can't\ be\ one\ of\ them\\\\32-9=23\\\\Searched\ number\ are\ 32\ and\ 23

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Answer: 1/24

Step-by-step explanation:

1/2 divided by 12

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Anastasy [175]

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2 × 8 × 15 ÷ 2 = 120

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4 0
3 years ago
If f(x) = -3x - 5 and g(x) = 4x - 2, find (f+ g)(x).
Stella [2.4K]

Answer:

\boxed{\sf x - 7}

Given:

f(x) = - 3x - 5

g(x) = 4x - 2

To Find:

(f + g)(x)

Step-by-step explanation:

\sf (f + g)(x) = f(x) + g(x) \\ \\   \sf \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:   \:  \:  \:  =  - 3x - 5 + 4x - 2 \\  \\  \sf \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:   \:  \:  \:  = 4x - 3x - 5 - 2 \\  \\  \sf \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:   \:  \:  \:  = x - 5 - 2 \\  \\  \sf \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:   \:  \:  \:  = x - 7

7 0
3 years ago
A fair coin is to be tossed 20 times. Find the probability that 10 of the tosses will fall heads and 10 will fall tails, (a) usi
lbvjy [14]

Using the distributions, it is found that there is a:

a) 0.1762 = 17.62% probability that 10 of the tosses will fall heads and 10 will fall tails.

b) 0% probability that 10 of the tosses will fall heads and 10 will fall tails.

c) 0.1742 = 17.42% probability that 10 of the tosses will fall heads and 10 will fall tails.

Item a:

Binomial probability distribution

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

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

The parameters are:

  • x is the number of successes.
  • n is the number of trials.
  • p is the probability of a success on a single trial.

In this problem:

  • 20 tosses, hence n = 20.
  • Fair coin, hence p = 0.5.

The probability is <u>P(X = 10)</u>, thus:

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

P(X = 10) = C_{20,10}.(0.5)^{10}.(0.5)^{10} = 0.1762

0.1762 = 17.62% probability that 10 of the tosses will fall heads and 10 will fall tails.

Item b:

In a normal distribution with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

  • It measures how many standard deviations the measure is from the mean.  
  • After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
  • The binomial distribution is the probability of <u>x successes on n trials, with p probability</u> of a success on each trial. It can be approximated to the normal distribution with \mu = np, \sigma = \sqrt{np(1-p)}.

The probability of an exact value is 0, hence 0% probability that 10 of the tosses will fall heads and 10 will fall tails.

Item c:

For the approximation, the mean and the standard deviation are:

\mu = np = 20(0.5) = 10

\sigma = \sqrt{np(1 - p)} = \sqrt{20(0.5)(0.5)} = \sqrt{5}

Using continuity correction, this probability is P(10 - 0.5 \leq X \leq 10 + 0.5) = P(9.5 \leq X \leq 10.5), which is the <u>p-value of Z when X = 10.5 subtracted by the p-value of Z when X = 9.5.</u>

X = 10.5:

Z = \frac{X - \mu}{\sigma}

Z = \frac{10.5 - 10}{\sqrt{5}}

Z = 0.22

Z = 0.22 has a p-value of 0.5871.

X = 9.5:

Z = \frac{X - \mu}{\sigma}

Z = \frac{9.5 - 10}{\sqrt{5}}

Z = -0.22

Z = -0.22 has a p-value of 0.4129.

0.5871 - 0.4129 = 0.1742.

0.1742 = 17.42% probability that 10 of the tosses will fall heads and 10 will fall tails.

A similar problem is given at brainly.com/question/24261244

6 0
2 years ago
Which figures demonstrate a reflection? Select each correct answer.
Romashka [77]

top right and bottom right

4 0
3 years ago
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