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2 years ago

5

Josiah takes a multiple-choice quiz that has three questions. Each question has five answer options. If he randomly chooses his

answers, what is the probability that he will get all three correct?

2 answers:

ahrayia [7]2 years ago

6 0

The answer is 1/125.

k0ka [10]2 years ago

4 0

For E2020 users the answer is C (1/125)

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The angle whose sine is 0.39581 is

Lorico [155]

The angle whose sine is 0.39581 is 23.31650126° (round it how you want).
To calculate this, you need to do the inverse sine of 0.39581.

Inverse sine looks like $sin^{-1}$ , however, it is not the sine of the angle to the power of -1.

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2 years ago

Read 2 more answers

The rocks near the shore between two lighthouses at points A and B make the waters unsafe. The measure of arcAXB is 300. Waters

belka [17]

As a navigator of this ship, you must consider the measure of the arc. Using the distance between the two lighthouses and the arc measurement, you can find the radius and center of the circle to set a reasonable distance in keeping the ship in safe waters.

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2 years ago

Use Simpson's Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produ

SOVA2 [1]

$y=\ln(6+x^3)\implies y'=\dfrac{3x^2}{6+x^3}$

The arc length of the curve is

$\displaystyle\int_0^5\sqrt{1+\frac{9x^4}{(6+x^3)^2}}\,\mathrm dx$

which has a value of about 5.99086.

Let $f(x)=\sqrt{1+\frac{9x^4}{(6+x^3)^2}}$ . Split up the interval of integration into 10 subintervals,

[0, 1/2], [1/2, 1], [1, 3/2], ..., [9/2, 5]

The left and right endpoints are given respectively by the sequences,

$\ell_i=\dfrac{i-1}2$

$r_i=\dfrac i2$

with $1\le i\le10$ .

These subintervals have midpoints given by

$m_i=\dfrac{\ell_i+r_i}2=\dfrac{2i-1}4$

Over each subinterval, we approximate $f(x)$ with the quadratic polynomial

$p_i(x)=f(\ell_i)\dfrac{(x-m_i)(x-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+f(m_i)\dfrac{(x-\ell_i)(x-r_i)}{(m_i-\ell_i)(m_i-r_i)}+f(r_i)\dfrac{(x-\ell_i)(x-m_i)}{(r_i-\ell_i)(r_i-m_i)}$

so that the integral we want to find can be estimated as

$\displaystyle\sum_{i=1}^{10}\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx$

It turns out that

$\displaystyle\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx=\frac{f(\ell_i)+4f(m_i)+f(r_i)}6$

so that the arc length is approximately

$\displaystyle\sum_{i=1}^{10}\frac{f(\ell_i)+4f(m_i)+f(r_i)}6\approx5.99086$

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2 years ago

After dinner 3/4 of a pie remains. if tasha eats 1/6 of the remaining pie

astraxan [27]

Answer: 1/8

Step-by-step explanation: 3/4 x 1/6 = 24/3 (simplify to 1/8)

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2 years ago

Which equation below shows a correct first step for solving 3x = -12

Wewaii [24]

The answer is A. You just solve each one and you would find that it would be the same as 3x=-12.

5 0

1 year ago