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2 years ago

Find the volume of the rectangular

Mathematics

1 answer:

Kobotan [32]2 years ago

4 0

Answer:

Hope this will help you

Step-by-step explanation:

$volume \: of \: rectangular \: prism = l \times b \times h \\ = 0.6 ft\times 0.8 ft\times 3.8ft \\ = 1.824 {ft}^{3}$

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Simplify the radical expression.

tresset_1 [31]

To simplify this fraction, multiply the entire fraction by the conjugate of the denominator. The conjugate of a square root and a number being added to it would be the number <em>subtracted </em>from the square root. In other words, the conjugate of $\sqrt{a} + b$ would be $\sqrt{a} - b$ .

Applying that information to our fraction shown here, the conjugate of the denominator would be $\sqrt{3} - 4$ . We will multiply both the numerator and denominator of our original fraction by this expression to obtain our answer, as shown below.

$\Big(\dfrac{1}{\sqrt{3} + 4}\Big)\Big(\dfrac{\sqrt{3} - 4}{\sqrt{3} - 4}\Big)$

$\dfrac{\sqrt{3} - 4}{3 - 16}$

$\dfrac{4 - \sqrt{3}}{13}$

Our answer is $\boxed{\dfrac{4 - \sqrt{3}}{13}}$ .

5 0

2 years ago

Equation of the line passing through (7,5) and (1, 2)

Trava [24]

Answer:

$y = \frac{1}{2}x + \frac{3}{2}$

Step-by-step explanation:

Assuming this is a linear equation in the form of $y = mx + b$ , we can first solve for the slope using $\frac{y_2 - y_1}{x_2 - x_1}$ , for these points, the slope would be $\frac{1}{2}$ . Now we plug in the points to get the equation:

plugging in (7,5), we get $5 = \frac{1}{2}$ × $7$ + $b$

and solving for b, we get b = $\frac{3}{2}$

therefore, the equation of the line passing through (7,5) and (1,2) is $y = \frac{1}{2}x + \frac{3}{2}$ .

hope this helps!

6 0

1 year ago

The perimeter of a rectangle is 42 inches. If the width of the rectangle is 6 inches, what is the length?

snow_lady [41]

Answer:

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

An automobile manufacturer would like to know what proportion of its customers are not satisfied with the service provided by th

monitta

Answer:

a) n =1623

b) $ME=2.0538\sqrt{\frac{0.21 (1-0.21)}{1623}}=0.0208$

Step-by-step explanation:

1) Notation and definitions

$n$ random sample taken

$\hat p=0.19$ estimated proportion of customers are not satisfied with the service provided by the local dealer

Confidence =0.96 or 96%

Me= 0.02 represent the margin of error

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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 population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Part a

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 96% of confidence, our significance level would be given by $\alpha=1-0.96=0.04$ and $\alpha/2 =0.02$ . And the critical value would be given by: