Please help me, just need the answer and thank you!

What is the range of the function f(x)=-2|x+1|?

schepotkina [342]

Answer:

The correct answer to given question is option (a).

Step-by-step explanation:

Given function: f(x)= -2|x+1|

we need to put random values of x in given function to see that range of the given function f(x) is all real numbers.

when:

x=0; f(0)= -2|0+1|= -2|1|= -2

when x is positive i.e. x>0

x=1; f(1)= -2|1+1|= -2|2|= -4

x=2; f(2)= -2|2+2|= -2|4|= -8

when x is negative i.e. x<0

x= -1; f(-1)= -2|-1+1|= -2|0| =0

x=-2; f(-2)= -2|-2+1|= -2|-1|=2 (with the help of mod property |-1|=1)

hence, we saw that

when we take x>0; f(x)<0

when x<0; f(x)>0

we can conclude from above steps that the range of function f(x)= -2|x+1| is all real numbers.

7 0

4 years ago

Read 2 more answers

Whats 10+-6. is it<br><br>16<br><br>-4<br><br>4<br><br>-16

zaharov [31]

Answer:

-16

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

What area of the grass is being watered by this sprinkler

Novay_Z [31]

<h3>♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫</h3>

➷ Use this formula:

Area of circle = $\pi r^{2}$

However, as we are using 3.14 for 'pi', we can write it like this:

Area = $(3.14)r^{2}$

'r' is the radius which is 12ft

Substitute this value into the equation:

Area = $(3.14)12^{2}$

Solve:

Area = 452.16

Multiply this value by 0.75 to get the answer:

452.16 x 0.75 = 339.12

339.12 square feet is being watered

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

5 0

3 years ago

The number of surface flaws in plastic panels used in the interior of automobiles has a Poisson distribution with a mean of 0.08

kvv77 [185]

Answer:

a) 44.93% probability that there are no surface flaws in an auto's interior

b) 0.03% probability that none of the 10 cars has any surface flaws

c) 0.44% probability that at most 1 car has any surface flaws

Step-by-step explanation:

To solve this question, we need to understand the Poisson and the binomial probability distributions.

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.

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 with a mean of 0.08 flaws per square foot of plastic panel. Assume an automobile interior contains 10 square feet of plastic panel.

So $\mu = 10*0.08 = 0.8$

(a) What is the probability that there are no surface flaws in an auto's interior?

Single car, so Poisson distribution. This is P(X = 0).

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

$P(X = 0) = \frac{e^{-0.8}*(0.8)^{0}}{(0)!} = 0.4493$

44.93% probability that there are no surface flaws in an auto's interior

(b) If 10 cars are sold to a rental company, what is the probability that none of the 10 cars has any surface flaws?

For each car, there is a $p = 0.4493$ probability of having no surface flaws. 10 cars, so n = 10. This is P(X = 10), binomial, since there are multiple cars and each of them has the same probability of not having a surface defect.