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Marina86 [1]
3 years ago
13

PLEASE HELP

Mathematics
2 answers:
Inga [223]3 years ago
4 0
<h3>Answer: The scale factor is 5 used to create the dilation.</h3>

Step-by-step explanation: We are given original image ABCD.

The coordinates of the image ABCD are

A (1, 2)

B ( 2, 2)

C ( 2, 1)

D ( 1, 1).

And coordinates of dilated image A'B'C'D' are :

A' (5, 10)

B' ( 10, 10)

C' ( 10, 5)

D' ( 5, 5).

We can see that (x,y) --> (5x, 5y) rule is being applied there.

<em>Therefore, each x and y-coordinate is being multiplied by 5.</em>

<h3>Therefore, the scale factor 5 is used to create the dilation.</h3>
Rama09 [41]3 years ago
3 0
<span>image ​ A′B′C′D′ is 5 times bigger than pre-image ABCD

scale factor = 5</span>
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Gemiola [76]

Answer:

(a) <em>H</em>₀: <em>μ ≥ 5.70 </em><em>vs. </em><em>Hₐ</em>:<em>μ < 5.70</em>

(b) The rejection region is (<em>t₀.₀₁,₉</em> <em>≤ -2.821</em>).

(c) The value of the test statistic is -4.33.

(d) The true mean breaking strength of the new bonding adhesive is less than 5.70 Mpa.

Step-by-step explanation:

A hypothesis test should be conducted to determine that the if the true mean breaking strength of the new bonding adhesive is less than 5.70 Mpa.

(a)

The hypothesis is:

<em>H</em>₀: The true mean breaking strength of the new bonding adhesive is not less than 5.70 Mpa, i.e. <em>μ ≥ 5.70</em><em>.</em>

<em>Hₐ</em>: The true mean breaking strength of the new bonding adhesive is less than 5.70 Mpa, i.e. <em>μ < 5.70</em><em>.</em>

(b)

The alternate hypothesis indicates that the hypothesis test is left-tailed.

The rejection region for the left tailed test will be towards the lower tail of the t<em>-</em>distribution curve.

The significance level of the test is: <em>α</em> = 0.01.

The critical value is:

t_{\alpha ,(n-1)}=t_{0.01,(10-1)}=t_{0.01,9}

Use the <em>t-</em>table for the critical value.

t_{\alpha ,(n-1)}=t_{0.01,9}=-2.821

Since rejection region is in the lower tail the critical value will be negative.

Thus, the rejection region is (<em>t₀.₀₁,₉</em> <em>≤ -2.821</em>).

(c)

The test statistic value is:

t=\frac{\bar x-\mu}{s/\sqrt{n}}

Given:

\bar x=5.07\\s=0.46\\n=10\\\mu=5.70

Compute the value of the <em>t</em>-statistic as follows:

t=\frac{\bar x-\mu}{s/\sqrt{n}}=\frac{5.07-5.70}{0.46/\sqrt{10}} =-4.33

The value of the test statistic is -4.33.

(d)

The value of the test is less than the critical value.

t=-4.33

This implies that the test statistic lies in the rejection region.

Hence the null hypothesis will be rejected at 1% significance level.

<u>Conclusion:</u>

As the null hypothesis is rejected it can be concluded that the true mean breaking strength of the new bonding adhesive is less than 5.70 Mpa.

(e)

The conditions required for the <em>t-</em>test for single mean to be valid is:

  • The data should be continuous.
  • The parent population should be normally distributed.
  • The sample should be randomly selected.

5 0
3 years ago
Express ratio as a fraction in simplest form
Zanzabum

Answer:

\frac{3}{1}

Step-by-step explanation:

The dimensions must be the same

10 yards = 10 × 3 feet = 30 feet

ratio = \frac{30}{10} = \frac{3}{1}

6 0
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Simplify it and you get : -5/2

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7 0
2 years ago
Read 2 more answers
One more question pls help thanx
Arada [10]
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(I'm not entirely sure what the question is asking as some of it is blocked out from the drop down box?)
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On a recent day, one U.S dollar was worth 0.81 euros. If you were to exchange 222 euros, how many U.S dollars would you receive?
Juli2301 [7.4K]

<em>Answer:</em>

<em>254.22</em>

<em>Step-by-step explanation:</em>

<em>222 euros equal 254.22</em>

7 0
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