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3 years ago

In ΔABC, the lengths of a, b, and c are 22.5 centimeters, 18 centimeters, and 13.6 centimeters, respectively.

Mathematics

2 answers:

ehidna [41]3 years ago

8 0

Answer:

It is not 37.19 and 53.13.

Step-by-step explanation:

For newcomers who are using PLATO, I recently finished the test, and it is not the answer below. I don't know the right answer, unfortunately.

Irina-Kira [14]3 years ago

7 0

Given the values of the three sides of the triangle, we can apply the Cosine Law to find the angles of the triangle. Recall that for we can express the value of c through the equation below.

$c^{2} = a^{2} + b^{2} - 2abcosC$

Rearranging this equation, we can find the value ∠C as shown below.

$\cos C = \frac{a^{2}+b^{2}-c^{2}}{2ab}$
$C = cos^{-1} (\frac{a^{2}+b^{2}-c^{2}}{2ab})$

We can apply the same reasoning for finding the value of ∠B as shown.

$B = cos^{-1} (\frac{a^{2}+c^{2}-b^{2}}{2ac})$

Plugging in the values of the sides (see image attached) from the given. It will now be straightforward to compute for ∠B and ∠C.

$C = cos^{-1} (\frac{22.5^{2}+18^{2}-13.6^{2}}{2(22.5)(18)})$
$C \approx 37.19$

$B = cos^{-1} (\frac{22.5^{2}+13.6^{2}-18^{2}}{2(22.5)(13.6)})$
$B \approx 53.13$

Answer: ∠C = 37.19° and ∠B = 53.13°

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A certain NYC taxi driver has decided to start charging a rate of r cents per person per mile. How much, in dollars, would it co

katrin2010 [14]

Answer:

$\frac{3xr}{200}$

Step-by-step explanation:

A certain NYC taxi driver has decided to start charging a rate of r cents per person per mile

rate is cents . convert it in to dollars

1 cent = 1/100 dollars

r cents = r/100 dollars

Each people travels x miles

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For 3 people the cost is

$3\frac{r}{100} \cdot x$

Discount is 50%, so we divide by 2

$\frac{3\frac{r}{100} \cdot x}{2} =\frac{3xr}{200}$

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3 years ago

What is the square root of 5

Slav-nsk [51]

Hey There!

Answer:

2.23

Step-by-step explanation:

$\sqrt{x} 5$ = 2.23

The square root of 5 is 2.23

Hope this helps!!

Have a nice day!!:)

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3 years ago

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What is 30 over 12 written as a mixed number

Mila [183]

30 over 12 written as a mixed number is 2 and 6/12, which is simplified to 2 and 1/2.

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3 years ago

It seems to you that fewer than half of people who are registered voters in the City of Madison do in fact vote when there is an

Ad libitum [116K]

Answer:

a) Going to public places like restaurants, parks, theaters, etc in Madison and asking voters.

b) The 80% CI to estimate the true proportion of registered voters in the City of Madison who vote in non-presidential elections is (0.5533, 0.6667).

c) We are 80% sure that our confidence interval contains the true proportion of registered voters in the City of Madison who vote in non-presidential elections.

d) The lower limit of the interval is higher than 0.5. This means that it does seem that MORE than half of registered voters in the City of Madison vote in non-presidential elections.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence interval $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

Z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

(a) How might a simple random sample have been gathered?

Going to public places like restaurants, parks, theaters, etc in Madison and asking voters.

(b) Construct an 80% CI to estimate the true proportion of registered voters in the City of Madison who vote in non-presidential elections.

You take an SRS of 200 registered voters in the City of Madison, and discover that 122 of them voted in the last non-presidential election. This means that $n = 200, \pi = \frac{122}{200} = 0.61$ .

We want to build an 80% CI, so $\alpha = 0.20$ , z is the value of Z that has a pvalue of $1 - \frac{0.20}{2} = 0.90[tex], so [tex]z = 1.645$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{200}} = 0.61 - 1.645\sqrt{\frac{0.61*0.39}{200}} = 0.5533$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{200}} = 0.61 + 1.645\sqrt{\frac{0.61*0.39}{200}} = 0.6667$

The 80% CI to estimate the true proportion of registered voters in the City of Madison who vote in non-presidential elections is (0.5533, 0.6667).

(c) Interpret the interval you created in part (b).

We are 80% sure that our confidence interval contains the true proportion of registered voters in the City of Madison who vote in non-presidential elections.

(d) Based on your CI, does it seem that fewer than half of registered voters in the City of Madison vote in non-presidential elections? Explain.

The lower limit of the interval is higher than 0.5. This means that it does seem that MORE than half of registered voters in the City of Madison vote in non-presidential elections.

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3 years ago

Find the vertex of the parabola.

riadik2000 [5.3K]

Answer:

Correct answer is B. (-2,4)

Step-by-step explanation:

Given: y = 2x^2 + 8x + 12

if x = 2,

Use substitution: y = 2(-2)^2 + 8(-2) + 12

y = 8 - 16 + 12

y = -8 + 12

y = 4

So, (-2, 4) would be your answer.

I hope this helps!!!

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