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2 years ago

Instructions: Find the surface area of the figure below. Round your answers to the nearest tenth, if necessary.

Mathematics

1 answer:

Y_Kistochka [10]2 years ago

6 0

The surface area of the figure given is of: 61.3 yd².

<h3>What is the combined surface area of a figure?</h3>

The combined surface area of a figure is the area of each figure.

This figure is composed by:

A circle of radius 3 yd.

A triangle with base 6 yd and one leg 11.4 yd.

The area of the circle is given as follows:

$A = \pi r^2 = \pi \times 3^2 = 9\pi$

For the triangle, we need to find it's height, which is the <u>leg of a right triangle, in which one of the sides is 3 and the hypotenuse is 11.4</u>, hence:

h² + 3² = 11.4²

$h = \sqrt{11.4^2 - 3^2}$

h = 11 yd.

Hence the area of the triangle is:

A = 0.5 x 6 x 11 = 33 yd²

The surface area of the figure is:

9pi + 33 yd² = 61.3 yd².

More can be learned about the surface area of at brainly.com/question/21208177

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The weekly salaries of sociologists in the United States are normally distributed and have a known population standard deviation

Lostsunrise [7]

Answer:

$ME =z_{\alpha/2} \frac{\sigma}{\sqrt{n}}$

The confidence level is 0.98 and the significance is $\alpha=1-0.98 =0.02$ and $\alpha/2 =0.01$ and the critical value using the table is:

$z_{\alpha/2}= 2.326$

And replacing we got:

$ME=2.326 \frac{425}{\sqrt{22}}= 210.760\ approx 210.76$

Step-by-step explanation:

For this case we have the following info given:

$\sigma = 425$ represent the population deviation

$n =22$ the sample size

$\bar X =1520$ represent the sample mean

We want to find the margin of error for the confidence interval for the population mean and we know that is given by:

$ME =z_{\alpha/2} \frac{\sigma}{\sqrt{n}}$

The confidence level is 0.98 and the significance is $\alpha=1-0.98 =0.02$ and $\alpha/2 =0.01$ and the critical value using the table is:

$z_{\alpha/2}= 2.326$

And replacing we got:

$ME=2.326 \frac{425}{\sqrt{22}}= 210.760\ approx 210.76$

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2 years ago

3.1 Find the equation of the line passing through (4, 5) and parallel to the line 3x – 2y = 4.

valentinak56 [21]

$\rule{50}{1}\large\blue\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}$

<em>Find the equation of the line passing through (4, 5) and parallel to </em>

<em />

<em> </em> $\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}$

First of all, We need to convert this equation from standard form (ax+by=c) into slope-intercept form (y=mx+b).

$\rightarrow$ First, add 2y on both sides:-

$\Large\textsf{3x+2y=4}$

$\rightarrow$ Now, subtract 3x on both sides:-

$\Large\textsf{2y=-3x+4}$

$\rightarrow$ Divide by 2 on both sides

$\Large\text{$y=-\displaystyle\frac{3}{2}x +2$}$

$\rule{300}{3}$

Now, let's find the equation of the line that's parallel to the given line.

Remember, if lines are parallel to each other, then their slope's the same.

So the slope of the line that's parallel to the line whose equation we just found, is

$\Large\text{$-\displaystyle\frac{3}{2}$}$

Now let's write the equation in point-slope form:-

$\hookrightarrow\sf{y-y_1=m(x-x_1)}$

Replace numbers with letters, as follows:-

$\sf{y-5=-\displaystyle\frac{3}{2} (x-4)}$

The equation above is the equation in point-slope form.

Incase you need it converted to slope intercept form, refer to the steps below ~

Multiply -3/2 times x and -4:-

$\hookrightarrow\sf{y-5=-\displaystyle\frac{3}{2} x-6}$

Now, Add 5 on both sides:-

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

$\Uparrow\sf{Our\:equation\:in\:slope\;intercept\;form}$

<h3>Good luck with your studies.</h3>

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