All categories

3 years ago

What is the answer to this equation h(x)= -9 - x; h(2k-5

Mathematics

1 answer:

dezoksy [38]3 years ago

7 0

The answer is h(2k - 5) = -4 - 2k

Step-by-step explanation:

In a function f(x) = y, we can find the value of y for any given value of x

Examples:

If f(x) = 2x - 3, and we need to find f(3), that means substitute x by 3 in f(x), so f(3) = 2(3) - 3 = 6 - 3 = 3, that means f(x) = 3 at x = 3
If f(x) = 8 - 5x, and we need to find f(a - 2), substitute x by (a - 2) in f(x), so f(a - 2) = 8 - 5(a - 2) = 8 - 5a + 10 = 18 - 5a, that means f(a - 2) = 18 - 5a at x = a - 2

∵ h(x) = -9 - x

- We need to find h(2k - 5), that means substitute x by 2k - 5

∵ x = 2k - 5

∴ h(2k - 5) = -9 - (2k - 5)

- Simplify the right hand side

∴ h(2k - 5) = -9 - 2k - (-5)

- Remember (-)(-) = (+)

∴ h(2k - 5) = -9 - 2k + 5

- Add the like terms in the right hand side

∴ h(2k - 5) = (-9 + 5) - 2k

∴ h(2k - 5) = -4 - 2k

The answer is h(2k - 5) = -4 - 2k

Learn more:

You can learn ore about the functions in brainly.com/question/5337932

#LearnwithBrainly

You might be interested in

Can someone help me with this.?

prohojiy [21]

Answer:

Below.

Step-by-step explanation:

To find the answer, you have to compare the two equations:

$y=\frac{1}{10}x+60$ and $y=\frac{1}{5}$

So first, the graph looks different because the two slopes are different. The first one will be more vertical than the second one.

The second difference is the y - intercepts. The first equation starts at (0, 60) and the second starts at the origin.

4 0

3 years ago

A manufacturer of Christmas light bulbs knows that 10% of these bulbs are defective. It is known that light bulbs are defective

andriy [413]

Answer:

(a) P(X $\leq$ 20) = 0.9319

(b) Expected number of defective light bulbs = 15

(c) Standard deviation of defective light bulbs = 3.67

Step-by-step explanation:

We are given that a manufacturer of Christmas light bulbs knows that 10% of these bulbs are defective. It is known that light bulbs are defective independently. A box of 150 bulbs is selected at random.

Firstly, the above situation can be represented through binomial distribution, i.e.;

$P(X=r) = \binom{n}{r} p^{r} (1-p)^{2} ;x=0,1,2,3,....$

where, n = number of samples taken = 150

r = number of success

p = probability of success which in our question is % of bulbs that

are defective, i.e. 10%

Now, we can't calculate the required probability using binomial distribution because here n is very large(n > 30), so we will convert this distribution into normal distribution using continuity correction.

So, Let X = No. of defective bulbs in a box

Mean of X, $\mu$ = $n \times p$ = $150 \times 0.10$ = 15

Standard deviation of X, $\sigma$ = $\sqrt{np(1-p)}$ = $\sqrt{150 \times 0.10 \times (1-0.10)}$ = 3.7

So, X ~ N( $\mu = 15, \sigma^{2} = 3.7^{2})$

Now, the z score probability distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

(a) Probability that this box will contain at most 20 defective light bulbs is given by = P(X $\leq$ 20) = P(X < 20.5) ---- using continuity correction

P(X < 20.5) = P( $\frac{X-\mu}{\sigma}$ < $\frac{20.5-15}{3.7}$ ) = P(Z < 1.49) = 0.9319