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2 years ago

15

Find the domain of the function. (enter your answer using interval notation.) f(x) = x + 3 if x < −1 −2x if |x| ≤ 1 −2 if x &

gt; 1

1 answer:

Ivenika [448]2 years ago

4 0

The domain of the function is the union of all of the "if" parts of the function definition:

... (-∞, -1) ∪ [-1, 1] ∪ (1, ∞) = (-∞, ∞)

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Suppose a shipment of 120 electronic components contains 3 defective components. to determine whether the shipment should be ac

Likurg_2 [28]

For this problem, the most accurate is to use combinations

Because the order in which it was selected in the components does not matter to us, we use combinations

Then the combinations are $nC_r = \frac{ n! }{r! (n-r)!}$

n represents the amount of things you can choose and choose r from them

You need the probability that the 3 selected components at least one are defective.

That is the same as:

(1 - probability that no component of the selection is defective).

The probability that none of the 3 selected components are defective is:

$P = \frac{_{117}C_3}{_{120}C_3}$

Where $_{117}C_3$ is the number of ways to select 3 non-defective components from 117 non-defective components and $_{120}C_3$ is the number of ways to select 3 components from 120.

$_{117}C_3 = 260130$

$_{120}C_3 = 280840$

So:

$P = \frac{260130}{280840} = 0.927$

Finally, the probability that at least one of the selected components is defective is:

$P = 1-0.927 = 0.0737$

P = 7.4%

3 0

3 years ago

Find the length of EF

Lisa [10]

Answer:

9

Step-by-step explanation:

1. First, we need to set up an equation to find the value of x and then the length of EF.

2. We know that DG is equal to 33, so we can add all the three sections it's cut into altogether to get 33. Therefore, we get an equation of: $3x - 28 + 3x - 30 + x = 33$

3. (Solving for x)

Step 1: Simplify both sides of the equation.

$3x - 28 + 3x - 30 + x = 33$
$(3x+3x+x) + (-28-30)=33$
$7x - 58 = 33$

Step 2: Add 58 to both sides.

$7x - 58 + 58 = 33 + 58$
$7x = 91$

Step 3: Divide both sides by 7.

$\frac{7x}{7} = \frac{91}{7}$
$x = 13$

4. Now that we know x is equal to 13, we can plug that value in for the expression 3x - 30.

$3(13)-30$
$39 - 30$
$9$

Therefore, the length of EF is 9.

7 0

2 years ago

Jonathan’s age is one-third Belindas age now in 12 years time Belinda will be M years old

chubhunter [2.5K]

Step-by-step explanation:

quisiera ayudarte pero no hablo inglés :(

4 0

2 years ago

Use the equation 1/2 (x - 4) = 1/3x + 2

Anon25 [30]

Answer:

1/2(x-4)= 1/3x+2

6x1/2(x-4)=6x1/3x+2x6

3(x-4)=2x+12

3x-12=2x+12

3x-2x=12+12

x=24

5 0

2 years ago

Read 2 more answers

You deposit $2200 Into three separate bank accounts for each pay 3% annual interest. How much interest does each account earn af

Hatshy [7]

The formula to find the amount is

$A=P(1+r)^n$

Here A = amount

P is the principal

r is the rate

n is the number of years

Then to find the interest we subtract principal from amount.

Interest = A - P

Here

P= 2200, r = 3% = 0.03 , n = 6 years

$A = 2200 (1+0.03)^6=2626.92$

Hence the interest earned = 2626.92-2200 = $426.92

Now if the total of $2200 was deposited in three banks then each account earns $\frac{426.92}{3}= 142.31$

Each account earns $142.31

5 0

3 years ago