Which linear inequality is represented by the graph?

What is the total surface area of the rectangular prism?

bogdanovich [222]

Answer:

Total surface = 102.4 cm^2 (second answer in the list of options)

Step-by-step explanation:

Notice that we need to add the surface of 4 rectangles, two have smaller sizes than the other two. A pair of rectangles are 7.2 cm x 4 cm = 28.8 cm^2, while the other pair has 7.2 cm x 2 cm = 14.4 cm^2

There are also two equal bases each one of size 4 cm x 2 cm = 8 cm^2

Now we add two of each of the individual surfaces discussed above to complete the total surface area:

2 * 28.8 + 2 * 14.4 + 2 * 8 = 102.4 cm^2

which agrees with the second answer option provided.

3 0

3 years ago

Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and

Brums [2.3K]

Answer:

$t=\frac{51.6-48}{\frac{1.1}{\sqrt{10}}}=10.349$

$p_v =P(t_9>10.349)=1.34x10^{-6}$

If we compare the p value and the significance level given for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we reject the null hypothesis, and the the actual mean is significantly higher than 48 MPa at 5% of significance.

Step-by-step explanation:

1) Data given and notation

$\bar X=51.6$ represent the sample mean

$s=1.1$ represent the standard deviation for the sample

$n=10$ sample size

$\mu_o =48$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t 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 need to conduct a hypothesis in order to determine if the mean score is higher than 48, the system of hypothesis would be:

Null hypothesis: $\mu \geq 48$

Alternative hypothesis: $\mu > 48$

We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

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

t-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:

$t=\frac{51.6-48}{\frac{1.1}{\sqrt{10}}}=10.349$

Calculate the P-value

First we find the degrees of freedom:

$df=n-1=10-1=9$

Since is a one-side upper test the p value would be:

$p_v =P(t_9>10.349)=1.34x10^{-6}$

Conclusion

If we compare the p value and the significance level given for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we reject the null hypothesis, and the the actual mean is significantly higher than 48 MPa at 5% of significance.

5 0

3 years ago

A line with a slope of 3 passes through the point (-1, 2).

Rom4ik [11]

Answer:

y - 2 = 3(x + 1)

y - 2 = 3x + 3

y = 3x + 5

Step-by-step explanation:

8 0

3 years ago

What is the definition of a surd.<br>Give an example.

maria [59]

Answer:(of a number ) irrational

Step-by-step explanation:

4 0

3 years ago

Find the percent of change on an item that was $44 and now costs $66.

iVinArrow [24]

Answer:

33.3%

Step-by-step explanation:

the increase in price was $22. Find the ratio

$22

-------

$66

which comes out to 0.33333, or 33.3%.

The percent change in the price of the item is 33.3%.

4 0

3 years ago