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2 years ago

14 − 3x < −1 What is x?

2 answers:

8 0

$14 -3x< -1\\\\\implies -3x < -1 -14\\\\\implies -3x< -15\\\\\implies x> \dfrac{-15}{-3}~~~~~~;[\text{Reverse the inequality when multiplying}\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~\text{or dividing by a negative number.}]\\\implies x> 5\\\\ \ \text{Interval,}~(5,\infty)$

almond37 [142]2 years ago

6 0

Answer:

Step-by-step explanation:

14 -3x < -1, subtract 14 from both sides

-3x < -1 -14, combine like terms

-3x < -15, divide both sides by -3

x > 5

! when solving inequalities if we multiply or divide by a negative number the sense of inequality changes.

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2 years ago

What is f(-2) of the function given below? * f(x) = 3x2 - 4x + 1

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Answer:

f(-2) = 21

Step-by-step explanation:

Step 1: Define

f(x) = 3x² - 4x + 1

f(-2) is x = -2

Step 2: Substitute and Evaluate

f(-2) = 3(-2)² - 4(-2) + 1

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2 years ago

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2 years ago

A particular sale involves four items randomly selected from a large lot that is known to contain 9% defectives. Let X denote th

umka2103 [35]

Answer:

The expected repair cost is $3.73.

Step-by-step explanation:

The random variable X is defined as the number of defectives among the 4 items sold.

The probability of a large lot of items containing defectives is, p = 0.09.

An item is defective irrespective of the others.

The random variable X follows a Binomial distribution with parameters n = 9 and p = 0.09.

The repair cost of the item is given by:

$C=3X^{2}+X+2$

Compute the expected cost of repair as follows:

$E(C)=E(3X^{2}+X+2)$

$=3E(X^{2})+E(X)+2$

Compute the expected value of X as follows:

$E(X)=np$

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The expected value of X is 0.36.

Compute the variance of X as follows:

$V(X)=np(1-p)$

$=4\times 0.09\times 0.91\\=0.3276\\$

The variance of X is 0.3276.

The variance can also be computed using the formula:

$V(X)=E(Y^{2})-(E(Y))^{2}$

Then the formula of $E(Y^{2})$ is:

$E(Y^{2})=V(X)+(E(Y))^{2}$

Compute the value of $E(Y^{2})$ as follows:

$E(Y^{2})=V(X)+(E(Y))^{2}$

$=0.3276+(0.36)^{2}\\=0.4572$

The expected repair cost is:

$E(C)=3E(X^{2})+E(X)+2$

$=(3\times 0.4572)+0.36+2\\=3.7316\\\approx 3.73$

Thus, the expected repair cost is $3.73.

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2 years ago

Which equations for the measures of the unknown

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Answer: Option B, Option C, Option E

Step-by-step explanation:

The options written correctly, are:

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For this exercise you need to use the following Inverse Trigonometric Functions:

$1)\ sin^{-1}(x)\\\\2)\ cos^{-1}(x)\\\\3)\ tan^{-1}(x)\\\\$

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$1)\alpha = sin^{-1}(\frac{opposite}{hypotenuse}) \\\\2)\ \alpha =cos^{-1}(\frac{adjacent}{hypotenuse})\\\\3)\ \alpha=tan^{-1}(\frac{opposite}{adjacent})$

Therefore, the conclusion is that the angles "x" and "y" can be found with these equations:

$x=sin^{-1}(\frac{c}{b})\\\\x= cos^{-1}(\frac{a}{b})\\\\x=tan^{-1}(\frac{c}{a})\\\\\\ y=sin^{-1}(\frac{a}{b})\\\\y=cos^{-1}(\frac{c}{b})\\\\y=tan^{-1}(\frac{a}{c})$

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3 years ago

Read 2 more answers