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2 years ago

What kind of transformation is illustrated in this figure?

Mathematics

2 answers:

Alinara [238K]2 years ago

6 0

Answer;

-Translation

Explanation;

-Any image in a plane could be altered by using different operations, or transformations. Translation is when we slide a figure in any direction.

-Translation involves sliding a figure in any direction without changing its size, shape or orientation.Translations are often referred to as slides. You can describe a translation using words like "moved up 3 and over 5 to the left" or with notation.

ad-work [718]2 years ago

3 0

The answer is a) translation, because only its position and not size or rotation changed and it also wasn't reflected

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A coin is thrown independently 10 times to test the hypothesis that the probability of heads is 0.5 versus the alternative that

mafiozo [28]

Answer:

(a) The significance level of the test is 0.002.

(b) The power of the test is 0.3487.

Step-by-step explanation:

We are given that a coin is thrown independently 10 times to test the hypothesis that the probability of heads is 0.5 versus the alternative that the probability is not 0.5.

The test rejects the null hypothesis if either 0 or 10 heads are observed.

Let p = <u><em>probability of obtaining head.</em></u>

So, Null Hypothesis, $H_0$ : p = 0.5

Alternate Hypothesis, $H_A$ : p $\neq$ 0.5

(a) The significance level of the test which is represented by $\alpha$ is the probability of Type I error.

Type I error states the probability of rejecting the null hypothesis given the fact that the null hypothesis is true.

Here, the probability of rejecting the null hypothesis means we obtain the probability of observing either 0 or 10 heads, that is;

P(Type I error) = $\alpha$

P(X = 0/ $H_0$ is true) + P(X = 10/ $H_0$ is true) = $\alpha$

Also, the event of obtaining heads when a coin is thrown 10 times can be considered as a binomial experiment.

So, X ~ Binom(n = 10, p = 0.5)

P(X = 0/ $H_0$ is true) + P(X = 10/ $H_0$ is true) = $\alpha$

$\binom{10}{0}\times 0.5^{0} \times (1-0.5)^{10-0} +\binom{10}{10}\times 0.5^{10} \times (1-0.5)^{10-10}$ = $\alpha$

$(1\times 1\times 0.5^{10}) +(1 \times 0.5^{10} \times 0.5^{0})$ = $\alpha$

$\alpha$ = 0.0019

So, the significance level of the test is 0.002.

(b) It is stated that the probability of heads is 0.1, and we have to find the power of the test.

Here the Type II error is used which states the probability of accepting the null hypothesis given the fact that the null hypothesis is false.

Also, the power of the test is represented by (1 - $\beta$ ).

So, here, X ~ Binom(n = 10, p = 0.1)

$1-\beta$ = P(X = 0/ $H_0$ is true) + P(X = 10/ $H_0$ is true)

$1-\beta$ = $\binom{10}{0}\times 0.1^{0} \times (1-0.1)^{10-0} +\binom{10}{10}\times 0.1^{10} \times (1-0.1)^{10-10}$

$1-\beta$ = $(1\times 1\times 0.9^{10}) +(1 \times 0.1^{10} \times 0.9^{0})$

$1-\beta$ = 0.3487

Hence, the power of the test is 0.3487.

3 0

2 years ago

If U = {all positive integers} and A = {x|x ∈ U and x is an odd positive integer}, which describes Ac?

tekilochka [14]

The answer is:

D. Ac = {xΙx ∈ U and is an even positive integer}

:)

6 0

3 years ago

Read 2 more answers

Given that ABCD is a rhombus, what is the value of x?<br>(3x - 26)

ExtremeBDS [4]

<h2>The required "option B) $20.75\°$ " is correct.</h2>

Step-by-step explanation:

You can refer figure:

brainly.com/question/4386376

To find, the value of x = ?

We know that,

Consecutive angles are supplementary

The diagonals bisect the angles.

$2x\°+2(3x+7)\°=180\°$

Divided by 2 both sides, we get

⇒ $x\°+(3x+7)\°=90\°$

⇒ $x\°+3x+7\°=90\°$

⇒ $4x=90\°-7\°$

⇒ 4x = $83\°$

⇒ $x=\dfrac{83\°}{4}$

⇒ $x=20.75\°$

∴ The value of x = $20.75\°$

Thus, the required "option B) $20.75\°$ " is correct.

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2 years ago

Read 2 more answers

Write an equation of a line that passes through the point (8,2) that is parallel and (b) perpendicular to the graph of the equat

oksian1 [2.3K]

For a parallel line the slope of the lines/equations will be the same but for perpendicular line the slope will be the negative reciprocal
-(1/4)*x+b
b=2-(-1/4)*8

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3 years ago

Use the discriminant to find the number of real roots in Y = x^2 – 6x + 9

BaLLatris [955]

So discriminant is being counted from that equation:
b^2-4ac = 36-36 = 0

As discriminant is 0, then there is just 1 root -> -b/2a = 6/2 = 3.

4 0

3 years ago