Your city has a sales tax rate of 6%. If you just spent $30 on sales tax, how much were your purchases?

A random variable x follows a normal distribution with mean d and standard deviation o=2. It is known that x is less than 5 abou

Vaselesa [24]

Answer:

The mean of this distribution is approximately 3.96.

Step-by-step explanation:

Here's how to solve this problem using a normal distribution table.

Let $z$ be the

$\displaystyle z = \frac{x - \mu}{\sigma}$ .

In this question, $x = 5$ and $\sigma = 2$ . The equation becomes

$\displaystyle z = \frac{5 - \mu}{2}$ .

To solve for $\mu$ , the mean of this distribution, the only thing that needs to be found is the value of $z$ . Since

The problem stated that $P(X \le 5) = 69.85\% = 0.6985$ . Hence, $P(Z \le z) = 0.6985$ .

The problem is that the normal distribution tables list only the value of $P(0 \le Z \le z)$ for $z \ge 0$ . To estimate $z$ from $P(Z \le z) = 0.6985$ , it would be necessary to find the appropriate

Since $P(Z \le z) = 0.6985$ and is greater than $P(Z \le 0) = 0.50$ , $z > 0$ . As a result, $P(Z \le z)$ can be written as the sum of $P(Z < 0)$ and $P(0 \le Z \le z)$ . Besides, $P(Z < 0) = P(Z \le 0) = 0.50$ . As a result:

$\begin{aligned}&P(Z \le z)\\ &= P(Z < 0) + P(0 \le Z \le z) \\ &= 0.50 + P(0 \le Z \le z)\end{aligned}$ .

Therefore:

$\begin{aligned}&P(0 \le Z \le z) \\ &= P(Z \le z) - 0.50 \\&= 0.6985 - 0.50 \\&=0.1985 \end{aligned}$ .

Lookup $0.1985$ on a normal distribution table. The corresponding $z$ -score is $0.52$ . (In other words, $P(0 \le Z \le 0.52) = 0.1985$ .)

Given that

$z = 0.52$ ,
$x =5$ , and
$\sigma = 2$ ,

Solve the equation $\displaystyle z = \frac{x - \mu}{\sigma}$ for the mean, $\mu$ :

$\displaystyle 0.52 = \frac{5 - \mu}{2}$ .

$\mu = 5 - 2 \times 0.52 = 3.96$ .

3 0

3 years ago

An equation is shown below: 6(2x-11)+15=21

mars1129 [50]

Hello!

To solve, we want to isolate the x on one side of the equation. We can use inverse operations to put numbers on the other side to find x.

First we undistribute our parentheses.

12x-66+15=21

We subtract 15 from both sides (it cancels out the 15 on the left side, making it 0).

12x-66=6

Now we add 66 to both sides, as -66+66=0

12x=72

Finally, we divide both sides by 12.

x=6

I hope this helps!

8 0

3 years ago

Read 2 more answers

What property is used to change the sum of 18+6 to the equivalent expression 6(3+1)

Fittoniya [83]

The distributive property is used to get the equivalent expression

Step-by-step explanation:

The properties on mathematical expressions are used to simplify or elaborate the expressions.

One of the propoerties is distributive properties

The distributive property states that:

Let a, b and c be three integers then

a(b+c) = ab+ac

The property can be used both ways

In given expression

18+6

$= 6.3+ 6.1\\=6(3+1)$

The distributive property is used to get the equivalent expression

Keywords: Properties

Learn more about properties at:

#LearnwithBrainly

7 0

3 years ago

What is the distance of P(1,-3) from y- axis

madam [21]

Answer:

1 unit to the right

Step-by-step explanation:

The y-axis is the vertical line and the point (1,-3) is one unit to the right of the vertical line

3 0

3 years ago

Factor completely. -5 x2y + 10 xy - 15 xy2<br><br> I need help.

ASHA 777 [7]

Answer:

$5\,x\,y\,(-x+2-3y)$

Step-by-step explanation:

Always proceed by first extracting all common factors to all terms:

Notice that the factors: 5, x, and y are present in all terms, so we can extract them from the trinomial:

$-5x^2y+10xy-15xy^2\\5\,x\,y\,(-x+2-3y)$

Now, the trinomial left (-x+2-3y) cannot be factored out, so then factoring is complete.

4 0

3 years ago