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3 years ago

Which is the best description of an extraneous solution?

Mathematics

1 answer:

Degger [83]3 years ago

8 0

Answer:

A solution that results in a false statement when substituted back into the original equation.

Step-by-step explanation:

An extraneous solution is one that arises in a solution of equations, but which on closer inspection is not a solution to the original equation. Therefore, they imply an error in the development of the solution of the equation, so they cannot be taken as a valid solution since, when replacing the result with the missing variable, the equation does not obtain the desired result.

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The largest 4 digit number exactly divisible by 88 is: a.9944 b.9768 c.9988 d.8888

serious [3.7K]

Answer:

Step-by-step explanation:

8 0

3 years ago

So, the additive inverse of -7/8 is

zlopas [31]

Answer:

Im prett sure its 7/8

Step-by-step explanation:

The additive inverse of a number is a number that, when added, goes to zero. For example, 7 is -7 because when added it equals 0 (or 7-7)

8 0

3 years ago

(10 points)Assume IQs of adults in a certain country are normally distributed with mean 100 and SD 15. Suppose a president, vice

vesna_86 [32]

Answer:

0.0139 = 1.39% probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

Step-by-step explanation:

To solve this question, we need to use the binomial and the normal probability distributions.

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.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

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

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

The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Probability the president will have an IQ of at least 107.5

IQs of adults in a certain country are normally distributed with mean 100 and SD 15, which means that $\mu = 100, \sigma = 15$

This probability is 1 subtracted by the p-value of Z when X = 107.5. So

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

$Z = \frac{107.5 - 100}{15}$

$Z = 0.5$

$Z = 0.5$ has a p-value of 0.6915.

1 - 0.6915 = 0.3085

0.3085 probability that the president will have an IQ of at least 107.5.

Probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

First, we find the probability of a single person having an IQ of at least 130, which is 1 subtracted by the p-value of Z when X = 130. So

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

$Z = \frac{130 - 100}{15}$

$Z = 2$

$Z = 2$ has a p-value of 0.9772.

1 - 0.9772 = 0.0228.

Now, we find the probability of at least one person, from a set of 2, having an IQ of at least 130, which is found using the binomial distribution, with p = 0.0228 and n = 2, and we want:

$P(X \geq 1) = 1 - P(X = 0)$

In which

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

$P(X = 0) = C_{2,0}.(0.9772)^{2}.(0.0228)^{0} = 0.9549$

$P(X \geq 1) = 1 - P(X = 0) = 0.0451$

0.0451 probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

What is the probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130?

0.3085 probability that the president will have an IQ of at least 107.5.

0.0451 probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

Independent events, so we multiply the probabilities.

0.3082*0.0451 = 0.0139

8 0

3 years ago

Please help and thank you.

pashok25 [27]

Answer:

s(x) is t(x) ...

horizontally compressed by a factor of 2,
reflected across the y-axis, and
translated downward 5 units.

Domain and Range

t(x) has a domain of x ≤ 0, and a range of y ≥ 0.
s(x) has a domain of x ≥ 0, and a range of y ≥ -5.

Step-by-step explanation:

t(x) is the square root function reflected across the y-axis and compressed horizontally by a factor of 2. That is, in f(x) = √x, the x has been replaced by -2x.

s(x) has the function t(x) reflected back across the y-axis and compressed horizontally by another factor of 2. It is also translated downward by 5 units, so that its origin (vertex) is at (0, -5).

_____

The graph shows you the domain and range of s(x). The domain is all numbers to the right of x=0, including x=0. That is ...

domain: x ≥ 0

The range is all numbers -5 or above:

range: y ≥ -5

___

For t(x), the argument of the square root function must not be negative, which means the value of x cannot be positive.

domain: x ≤ 0

For non-negative values of radicand, the t(x) function will have non-negative values. So, the range is ...

range: y ≥ 0

_____

Comment on solving problems like this

Your graphing calculator can be your friend.

6 0

3 years ago

Y=x^2+3x-4 y=3x+5 what does x and y equal

Rom4ik [11]

Answer:

y = x^2+3x-4 y=3x+5

(3, 14)

Step-by-step explanation:

hope this helps and have a nice day!! :)

And also you should try to use Desmos calculator it really helps with these problem/ equations!! you just have to put y = x^2+3x-4 then press enter and on the second one you put y=3x+5 and then it shows you a graph and plus the answer!! :))

4 0

2 years ago