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3 years ago

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In triangle ABC, the size of angle B is 3 times the size of angle A, and the size of angle C is 1° less than 6 times the size

of angle A.

1 answer:

andriy [413]3 years ago

8 0

Answer:

<em>18.1 -->Measure of A</em>

<em>54.3° -->Measure of B</em>

<em>107.6° -->Measure of C</em>

Step-by-step explanation:

<u>Equations</u>

The sum of the interior angles of a triangle is 180°. Let's call:

x = measure of angle A

The measure of angle B is 3 times the measure of A, thus:

3x = measure of angle B

The measure of angle C is 1 degree less than 6 times of x, thus:

6x - 1 = measure of angle C

The equation to solve is:

x + 3x + 6x - 1 = 180

Simplifying:

10x - 1 = 180

Adding 1:

10x = 181

Dividing by 10:

x = 18.1 -->Measure of A

3x = 54.3° -->Measure of B

6x-1 = 107.6° -->Measure of C

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Identify a transformation of the function f(x) = x by observing the equation of the function g(x) = x − 90.

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The transformation of a function may involve any change. The transformation of the function is Right shift by 90 units.

<h3>How does the transformation of a function happen?</h3>

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units:

y=f(x+c) (same output, but c units earlier)

Right shift by c units:

y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: $y = k \times f(x)$

Horizontal stretch by a factor k: $y = f\left(\dfrac{x}{k}\right)$

Since the function is transformed from f(x)=x to g(x)=x-90, therefore, the transformation of the function is Right shift by 90 units.

Learn more about Transforming functions:

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2 years ago

The pre-image is

yKpoI14uk [10]

It is the last one.

A pre-image is the original before another shape is created from it, either dilated, translated, reflected, or rotated.

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3 years ago

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A sample of 200 observations from the first population indicated that x1 is 170. A sample of 150 observations from the second po

igor_vitrenko [27]

Answer:

a) For this case the value of the significanceis $\alpha=0.05$ and $\alpha/2 =0.025$ , we need a value on the normal standard distribution thataccumulates 0.025 of the area on each tail and we got:

$z_{\alpha/2} =1.96$

If the calculated statistic $|z_{calc}| >1.96$ we can reject the null hypothesis at 5% of significance

b) Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{170+110}{200+150}=0.8$

c) $z=\frac{0.85-0.733}{\sqrt{0.8(1-0.8)(\frac{1}{200}+\frac{1}{150})}}=2.708$

d) Since the calculated value satisfy this condition 2.708>1.96 we have enough evidence at 5% of significance that we have a significant difference between the two proportions analyzed.

Step-by-step explanation:

Data given and notation

$X_{1}=170$ represent the number of people with the characteristic 1

$X_{2}=110$ represent the number of people with the characteristic 2

$n_{1}=200$ sample 1 selected

$n_{2}=150$ sample 2 selected

$p_{1}=\frac{170}{200}=0.85$ represent the proportion estimated for the sample 1

$p_{2}=\frac{110}{150}=0.733$ represent the proportion estimated for the sample 2

$\hat p$ represent the pooled estimate of p

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

$\alpha=0.05$ significance level given

Concepts and formulas to use

We need to conduct a hypothesis in order to check if is there is a difference between the two proportions, the system of hypothesis would be:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

a.State the decision rule.

For this case the value of the significanceis $\alpha=0.05$ and $\alpha/2 =0.025$ , we need a value on the normal standard distribution thataccumulates 0.025 of the area on each tail and we got:

$z_{\alpha/2} =1.96$

If the calculated statistic $|z_{calc}| >1.96$ we can reject the null hypothesis at 5% of significance

b. Compute the pooled proportion.

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{170+110}{200+150}=0.8$

c. Compute the value of the test statistic.

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.85-0.733}{\sqrt{0.8(1-0.8)(\frac{1}{200}+\frac{1}{150})}}=2.708$

d. What is your decision regarding the null hypothesis?

Since the calculated value satisfy this condition 2.708>1.96 we have enough evidence at 5% of significance that we have a significant difference between the two proportions analyzed.

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3 years ago

The bill at a restaurant came to $136.40. The patrons decided to leave a 15% tip. What was the total bill including tip?

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Answer:

156.86

Step-by-step explanation:

136.40 + 15% is 20.46 added to 136.40 is 156.86

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Winning the jackpot in a particular lottery requires that you select the correct four numbers between 1 and 42 and, in a separa

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Answer:

$\dfrac{1}{3,357,900}$

Step-by-step explanation:

There are

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different ways to select the four numbers between 1 and 42. Only one of this ways is correct (successful to win).

There are 30 different ways select the single number between 1 and 30. Only one of them is correct.

The probability of winning the jackpot is

$\dfrac{1}{111,930}\cdot \dfrac{1}{30}=\dfrac{1}{3,357,900}$

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