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2 years ago

Simplify the expression. [90 – (12 + 13)](15 ÷ 3)

Mathematics

2 answers:

slega [8]2 years ago

6 0

$[90-(12+13)](15:3)= \\\\=(90-25)*5=\\\\= 65*5=\\\\=\boxed{325}$

Eduardwww [97]2 years ago

4 0

First, solve the brackets. 13+12= 25. 15÷3= 5. So te equation is now: 90-25 × 5. Do 90-25 first, it equals 75. All that's left is 75×5, which is 375.

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Solve. | 3x + 1 | = 2

qwelly [4]

Since this is an absolute value equation, it will have two answers. For the first answer, take away the absolute value bars and solve 3x + 1 = 2. Subtract 1 from both sides to get 3x = 1 and divide each side by 3 to get x = 1/3. Now onto the second solution. This time, take away the absolute value bars and make the other side of the equation, the 2, negative, to get 3x + 1 = -2. Now solve this by subtracting 1 from each side to get 3x = -3 and divide each side to get the other answer which is x = -1. The answer is x = -1 or 1/3, hope this helps!

8 0

2 years ago

Read 2 more answers

Solve the system using elimination. * 2x + 3y = - 10 -4x + 5y = -2 Your answer

sesenic [268]

Answer:

2x + 3y=-10 is incorrect (I think)

When you mulitply something with no negative you get something with no negative

Hope this helps :)

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8 0

2 years ago

A monkey is swinging from a tree. On the first swing, she passes through an arc whose length is 24 m 24 m24, start text, space,

Alchen [17]

Answer:

$24(\frac{1}{2})^{n-1}$

Step-by-step explanation:

Complete Question:

A monkey is swinging from a tree. On the first swing, she passes through an arc whose length is 24 m. With each swing, she travels along an arc that is half as long as the arc of the previous swing. Which expression gives the total length the monkey swings in her first n swings?

Solution:

First Swing:

24 m

Second Swing:

Half of first, so

24(1/2)

Third Swing:

Half of second, so:

24(1/2)(1/2)

Fourth Swing:

24(1/2)(1/2)(1/2)

So we see the general formula as:

$24(\frac{1}{2})^{n-1}$

Note: n -1 because (1/2) plays a role from second swing, which is n - 1

where n is the number of swings

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2 years ago

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The perimeter of a rectangle is 108 inches. the rectangle is 34 inches long. how wide is it?

mixer [17]

$\frac{108 - 34 - 34}{2}$
= 20 inches

In a rectangle, there are 2 similar length measurements & 2 similar width measurements

7 0

2 years ago

An automobile manufacturer finds that 1 in every 2500 automobiles produced has a particular manufacturing defect. (a) Use a bin

Advocard [28]

Answer:

a) 0.1558 = 15.58% probability of finding 4 cars with the defect in a random sample of 7000 cars.

b) 0.1557 = 15.57% probability of finding 4 cars with the defect in a random sample of 7000 cars. These probabilities are very close, which means that the approximation works.

Step-by-step explanation:

Binomial 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.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

To use the Poisson approximation for the binomial, we have that:

$\mu = np$

1 in every 2500 automobiles produced has a particular manufacturing defect.

This means that $p = \frac{1}{2500} = 0.0004$

a) Use a binomial distribution to find the probability of finding 4 cars with the defect in a random sample of 7000 cars.

This is $P(X = 4)$ when $n = 7000$ . So

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

$P(X = 4) = C_{7000,4}.(0.0004)^{4}.(0.9996)^{6996} = 0.1558$

0.1558 = 15.58% probability of finding 4 cars with the defect in a random sample of 7000 cars.

(b) The Poisson distribution can be used to approximate the binomial distribution for large values of n and small values of p.

Using the approximation:

$\mu = np = 7000*0.0004 = 2.8$ . So

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 4) = \frac{e^{-2.8}*(2.8)^{4}}{(4)!} = 0.1557$

0.1557 = 15.57% probability of finding 4 cars with the defect in a random sample of 7000 cars. These probabilities are very close, which means that the approximation works.

6 0

2 years ago