3х – 2y < 10<br> solve inequality and explain how to graph

*The rectangle to the left is divided into 12 shapes. One of them is a rectangle labeled with #1 and the remaining 11 shapes are

Mandarinka [93]

Given that the length of side of shaded area is 1 ft.

Making equal square of size of shaded area we have:

Horizontally number of shaded area are 12

Vertically number of shaded area are 11

So, the horizontal length of big rectangle is 12 ft.

The vertical length of big rectangle is 11 ft.

Area of big rectangle is 12*11

Area of given rectangle is 132 sq.ft.

6 0

2 years ago

The mean annual cost of an automotive insurance policy is normally distributed with a mean of $1140 and standard deviation of $3

DerKrebs [107]

Using the normal distribution, it is found that the probabilities are given as follows:

a) 0.8871 = 88.71%.

b) 0.0778 = 7.78%.

c) 0.8485 = 84.85%.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

$Z = \frac{X - \mu}{\sigma}$

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

The parameters in this problem are given as follows:

$\mu = 1140, \sigma = 310, n = 16, s = \frac{310}{\sqrt{16}} = 77.5$

Item a:

The probability is the <u>p-value of Z when X = 1250 subtracted by the p-value of Z when X = 1000</u>, hence:

X = 1250:

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{1250 - 1140}{77.5}$

Z = 1.42

Z = 1.42 has a p-value of 0.9222.

X = 1000:

$Z = \frac{X - \mu}{s}$

$Z = \frac{1000 - 1140}{77.5}$

Z = -1.81

Z = -1.81 has a p-value of 0.0351.

0.9222 - 0.0351 = 0.8871 = 88.71% probability.

Item b:

The probability is <u>one subtracted by the p-value of Z when X = 1250</u>, hence:

1 - 0.9222 = 0.0778 = 7.78%.

Item c:

The probability is the <u>p-value of Z when X = 1220</u>, hence:

$Z = \frac{X - \mu}{s}$

$Z = \frac{1220 - 1140}{77.5}$

Z = 1.03

Z = 1.03 has a p-value of 0.8485.

0.8485 = 84.85% probability.

More can be learned about the normal distribution at brainly.com/question/4079902

#SPJ1

3 0

2 years ago

Which equation has the solutions x= 5 ± 2 square root 7 all over 3

Verdich [7]

Let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

Then the equation is (x-x₁)(x-x₂) = 0

If you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

You can see that a=1 (there is just an x²)
b = (-5 -2√7 + 2√7 - 5)/3 = -10/3
c = ((-5-2√7)/3 ) * (-5+2√7)/3) = -1/3

So the equation you're looking for is:

$\frac{3 x^{2} -10x - 1}3 = 0$

7 0

3 years ago

If f(x) = <img src="https://tex.z-dn.net/?f=%5Csqrt%7Bx%7D%20%2B3" id="TexFormula1" title="\sqrt{x} +3" alt="\sqrt{x} +3" align=

Delvig [45]

Answer:

$f^{-1}(x) = x^{2}-6x+9$ is the answer.

Step-by-step explanation:

If the function is f(x) = √x + 3

We will write the function as an equation

y = √x + 3

√x = y - 3

x = (y -3)²

x = y² -6y +9

Now we will convert the equation into a function

$f^{-1}(x) = x^{2}-6x+9$

Therefore the inverse function f(x) = x²-6x+9

7 0

3 years ago

Read 2 more answers

A consensus forecastis the average of a large number of individual analysts’ forecasts. Suppose the individual forecasts fora pa

Crank

Answer:

a) $P(X\geq 3.5)=P(\frac{X-\mu}{\sigma}\geq \frac{3.5-\mu}{\sigma})=P(Z\geq \frac{3.5-5.0}{1.2})=P(Z\geq -1.25)$

And we can find this probability using the z table or excel

$P(Z \geq$

b) $P(X\leq 6.0)=P(\frac{X-\mu}{\sigma}\leq \frac{6.0-\mu}{\sigma})=P(Z\leq \frac{6.0-5.0}{1.2})=P(Z\leq 0.833)$

And we can find this probability using the z table or excel:

$P(Z \leq$

c) $P(3.5$

And we can find this probability on this way:

$P(-1.25$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(-1.25$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the interest rate of a population, and for this case we know the distribution for X is given by:

$X \sim N(5.0,1.2)$