QUESTION 3 Which inequality is a true statement?

Mathematics

1 answer:

Vilka [71]3 years ago

8 0

Answer: B

Step-by-step explanation: the first number is a negative so it’s less than the second number

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What is the equation of the line that is perpendicular to and has the same y-intercept as the given line?

Anastasy [175]

ANSWER

The required equation is

$y = 5x + 1$

EXPLANATION

The given line passes through the point

$(5,0) \: and \: (0,1)$

The slope of this line is given by the formula,

$m=\frac{y_2-y_1}{x_2-x_1}$

This implies that,

$m = \frac{1 - 0}{0 - 5}$

$m = - \frac{1}{5}$

The product of the slope of the two perpendicular lines should be negative one.

Thus,

$m_1\times m_2=-1$
This implies that,

$- \frac{1}{5} \times m_2=-1$

We multiply through by
$- 5$
to obtain,

$m_2=-1 \times - 5$

$m_2=5$
Therefore the slope of the line perpendicular to the given line is
$5.$

We use the slope intercept formula
$y =m x + b$

where
$b = 1$
is the y-value of the y-intercept.

We therefore have,

$y = 5x + 1$

as the required equation.

The correct answer is C.

8 0

3 years ago

Read 2 more answers

A financial talk show host claims to have a 55.3 % success rate in his investment recommendations. You collect some data over th

baherus [9]

Answer:

There is a 25.52% probability of observating 4 our fewer succesful recommendations.

Step-by-step explanation:

For each recommendation, there are only two possible outcomes. Either it was a success, or it was a failure. So we use the binomial probability distribution to solve this problem.

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.

In this problem we have that:

$p = 0.553, n = 10$

If the claim is correct and the performance of recommendations is independent, what is the probability that you would have observed 4 or fewer successful:

This is

$P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$