What expression is equivalent to 14a+8?

Analyze the graph of the function f(x) to complete the statement.

ozzi

f(x) is the same as y, so we can say y = f(x)

Writing f(x) < 0 means we want to find when y < 0.

Visually, we are looking at the graph when the curve is below the horizontal x axis.

This is the portion in red that I have marked in the diagram (see attached image below). I apologize for the numbers being blurry.

The left red portion is from negative infinity to -3. In terms of a compound inequality we write $-\infty < x < -3$ which in interval notation is $(-\infty, -3)$ . The curved parenthesis tells the reader to exclude both endpoints.

The right red portion is from x = -1.1 to x = 0.9, excluding both endpoints. So we say $-1.1 < x < 0.9$ which becomes the interval notation $(-1.1, 0.9)$ . This is not ordered pair notation even though it looks identical to it.

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<h3>Answer in interval notation: $(-\infty, -3) \cup (-1.1, 0.9)$ </h3>

The "U" means "set union" which glues together the two separate intervals. Basically it's saying "x is either in the interval (-infinity, -3) or it is in the interval (-1.1, 0.9)"

5 0

3 years ago

An automobile manufacturer claims that its van has a 31.3 miles/gallon (MPG) rating. An independent testing firm has been contra

Yuliya22 [10]

Answer:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

$z=\frac{31.1-31.3}{\frac{1.3}{\sqrt{140}}}=-1.82$

$p_v =2*P(z$

If we compare the p value and the significance level given $\alpha=0.02$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true mean is NOT significantly different from 31.3 at 2% of signficance.

Step-by-step explanation:

Data given and notation

$\bar X=31.1$ represent the sample mean

$\sigma=1.3$ represent the population standard deviation for the sample

$n=140$ sample size

$\mu_o =31.3$ represent the value that we want to test

$\alpha=0.02$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We can assume that we conduct a hypothesis in order to check if the true mean is equal to 31.3 , the system of hypothesis would be:

Null hypothesis: $\mu =31.3$

Alternative hypothesis: $\mu \neq 31.3$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{31.1-31.3}{\frac{1.3}{\sqrt{140}}}=-1.82$

P-value

Since is a two-sided test the p value would be:

$p_v =2*P(z$

Conclusion

If we compare the p value and the significance level given $\alpha=0.02$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true mean is NOT significantly different from 31.3 at 2% of signficance.

5 0

3 years ago

What is the base 8 representation in the number 600

MAVERICK [17]

Answer:

Step-by-step explanation:

1*(8^3) + 1*(8^2) + 3*(8^1) + 0*(8^0) = 600

3 0

3 years ago

A store has clearance items that have been marked down by 40%. They are having a sale, advertising an additional 45% off clearan

Olegator [25]

Answer:

$P_2 = (1-0.45) *0.6 P_o =0.55*0.60 P_o=0.33 P_o$

So the discount is 33% and we are paying 67% of the value. The reason is given by the relative change:

$\% Change = \frac{|0.33P_o -P_o|}{P_o}*100 =67\%$

Step-by-step explanation:

First we have a first discount of 40% so then using this condition and assuming that $P_o$ represent the initial price, the price after the first discount $P_1$ is given by:

$P_1 = (1-0.4) P_o =0.6P_o$

That means 60% of the original value.

Now we have another discount of 45% for the 60% reamining after a 2 discount so let's $P_2$ represent the price after the second disccount we can can express this price in terms of $P_1$ or $P_o$ liek this:

$P_2 = (1-0.45) P_1=0.55 P_1$

$P_2 = (1-0.45) *0.6 P_o =0.55*0.60 P_o=0.33 P_o$

So the discount is 33% and we are paying 67% of the value. The reason is given by the relative change:

$\% Change = \frac{|0.33P_o -P_o|}{P_o}*100 =67\%$

4 0

3 years ago

For the graphed function f(x) = (2)^x + 2 + 1, calculate the average rate of change from x = -2 to x = 0

Monica [59]

X1=-2 and x2=0
We need to find y1 and y2 so
F(-2)=2^(-2+2)+1=2
The point(x1,y1)=(-2,2)
F(0)=2^(0+2)+1=5
The point(x2,y2)=(0,5)
Now, calculate the average rate of change (slope):
m = (y2 – y1) / (x2 – x1) =(5-2)/(0-(-2))
m=3/2
The answer is c
Hope it helps

5 0

4 years ago