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scoundrel [369]
3 years ago
15

∠AOB is shown on a coordinate plane. Select all of the following transformations that would preserve the measure of ∠AOB . Answe

r Choices reflection in the x -axis counterclockwise rotation by 90° the translation P(x,y)→P′(x+2,y+3) the horizontal dilation P(x,y)→P′(2x,y)
Mathematics
1 answer:
SSSSS [86.1K]3 years ago
3 0
<span>reflection in the x -axis, counterclockwise rotation by 90° ,the translation P(x,y)→P′(x+2,y+3)</span>
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A researcher is planning to compare the effects of two different types of lights on the growth of bean plants. She expects that
kicyunya [14]

Answer:

The sample size is  n  = 36

Step-by-step explanation:

From the question we are told that

   The sample standard deviation is  s =  1.5

  The mean difference of the two groups is  \=x _ 1 - \=x_2 =  1

   The standard error is  SE =  \frac{ \= x_1 - \= x_2}{4}

=>                                      SE =  \frac{1}{4}

Let assume that the confidence level is 95% hence the level of significance is  

   \alpha = (100-95)\%

=> \alpha = 0.05

So the critical value of  \frac{\alpha }{2} obtained from the normal distribution table is

     Z_{\frac{\alpha }{2} } = 1.96

Generally the margin of error is mathematically evaluated as

     E =  Z_{\frac{\alpha }{2} } * SE    

   E =  1.96 * \frac{1}{4}

    E = 0.49

Generally the sample size is mathematically represented as

  n =[ \frac{Z_{\frac{\alpha }{2}  * s^2}}{E}]^2

=> n  = [\frac{1.96 * 1.5}{0.49} ]^2

=> n  = 36

6 0
3 years ago
-12p^2 - 27p +27 = 0
EleoNora [17]

Answer:

that's the right answer

Step-by-step explanation:

6 0
3 years ago
Please help with this question, thanks!
sweet [91]

The first box would be 2 and the second box would be 11.

49-65=2(3-11)

-16=2(-8)

-16= -16


4 0
3 years ago
A 11 inch by 8 inch piece of cardboard squares cut out of the corners and is folded up to make up an open-top-box. If the volume
Arada [10]
<h3>Answer:  b. either 2.5 inches or about .716 inches</h3>

=====================================================

Work Shown:

I have attached two images below. The first shows figures 1 through 4. The second image shows figure 5.

Start with figure 1. Work your way left to right, top to bottom til you get to figure 4. This is the basic process to turn a flat piece of cardboard into a 3D folded box.

The dashed lines in figure 1 are x inches long.

Figure 2 is the result of cutting out the dashed lines you see in figure 1.

When you fold along the dashed lines in figure 2, you'll end up with something similar to figure 3.

Figure 4 is the completed open-top-box. In other words, this box does not have a lid.

The green portions in figures 3 and 4 indicate where the flaps used to be in reference to figure 2.

-------------------

Since those dashed lines in figure 1 were x inches long, this means that the distance from A to B is 11-x-x = 11-2x inches long.

This makes segment BD to be 8-2x inches long. We are subtracting off 2 copies of x each time for each dimension.

------------------

length = AB = 11-2x

width = BD = 8-2x

Since we want the length to be positive, this means 11-2x > 0 which solves to x < 5.5

Since we want the width to be positive, this means 8-2x > 0 which solves to x < 4

Overall, we must make x < 4 to make both inequalities 11-2x > 0 and 8-2x > 0 to be true at the same time.

Furthermore, x is some length itself, so it cannot be negative either. Therefore x > 0 or 0 < x

Combine 0 < x and x < 4 to get 0 < x < 4

The restriction 0 < x < 4 will be used later.

------------------

For now, let's compute the volume.

Volume = Length*Width*Height

Volume = (AB)*(BD)*x

Volume = (11-2x)*(8-2x)*x

Volume = (88-22x-16x+4x^2)*x

Volume = (88-38x+4x^2)*x

Volume = 88x-38x^2+4x^3

This is the algebraic way of representing the volume in terms of the cut length x

We want this volume to be 45 cubic inches. We set  88x-38x^2+4x^3 equal to 45 and solve for x

88x-38x^2+4x^3 = 45

4x^3-38x^2+88x-45 = 0

At this point we try to factor by grouping or we turn to a calculator. Cubics are often very difficult to solve by hand, so I recommend using a calculator (unless you can quickly spot how to factor by grouping, but I don't see a quick way of doing that). Note: based on the answer choices that aren't whole numbers (assuming choice C is a non-answer), this heavily implies we do not have rational roots, and therefore factoring over the rationals will be impossible. In other words, the answer choices tell us to immediately use a graphing calculator to find the roots.

Using geogebra (see figure 5), I find the three approximate roots to be

x = 0.716 (shown as point A)

x = 2.5 (point B)

x = 6.284 (point C)

Recall that earlier we made 0 < x < 4. The first two roots satisfy this inequality, but x = 6.284 is outside this range. So we ignore it. It looks like your teacher put 6.284 as a trick answer in choice A.

5 0
3 years ago
Part B Lawyer B charges an hourly rate and an up-front fee of $650. He
Anastasy [175]

Answer:

(5490-650) ÷ 22 = Y

Step-by-step explanation:

3 0
2 years ago
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