All categories

3 years ago

If y varies directly as x, and y is 20 when x is 4, what is the constant of variation for this relation?

Mathematics

2 answers:

Nuetrik [128]3 years ago

6 0

The variation would be x5. 4*5=20

Levart [38]3 years ago

6 0

Answer: 5

Step-by-step explanation:

Let k be the constant of variation for this relation.

If y varies directly as x, then the equation of direct variation is given by ;-

$y=kx$ , where k is the constant of variation for the relation.

$\Rightarrow\ k=\dfrac{y}{x}$

Now, for the given value of y = 20 and x=4, the value of constant of variation is given by :-

$\Rightarrow\ k=\dfrac{20}{4}=5$

Hence, the value of constant of variation for this relation k = 5.

You might be interested in

If 8 pencils cost 3 dollars, then how many pencils can you buy with 27 dollars?

Kisachek [45]

Answer:

72 pencils

Step-by-step explanation:

i used a calculator

8 0

3 years ago

Read 2 more answers

Which of the following is the equation of a line perpendicular to the line y =

makvit [3.9K]

Answer:

y = $\frac{1}{10}$ x + $\frac{13}{2}$

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 10x + 1 ← is in slope- intercept form

with slope m = - 10

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{-10}$ = $\frac{1}{10}$ , thus

y = $\frac{1}{10}$ x + c ← is the partial equation

To find c substitute (5, 7) into the partial equation

7 = $\frac{1}{2}$ + c ⇒ c = 7 - $\frac{1}{2}$ = $\frac{13}{2}$

y = $\frac{1}{10}$ x + $\frac{13}{2}$ ← equation of line

5 0

3 years ago

Military radar and missile detection systems are designed to warn a coutry of an enemy attack. Assume that a particular detectio

Tom [10]

Answer:

0.96 = 96% probability that at least one of them detect an enemy attack.

Step-by-step explanation:

For each radar, there are only two possible outcomes. Either it detects the attack, or it does not. The missiles are operated independently, which means that we use the binomial probability distribution to solve this question.

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.

Assume that a particular detection system has a 0.80 probability of detecting a missile attack.

This means that $p = 0.8$

If two military radars are installed in two different areas and they operate independently, the probability that at least one of them detect an enemy attack is

This is $P(X \geq 1)$ when $n = 2$ . So