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2 years ago

Find the missing probability. P(A)=15,P(A∪B)=1225,P(A∩B)=7100 ,P(B)=?

Mathematics

1 answer:

Llana [10]2 years ago

6 0

Answer:

Step-by-step explanation:

We will use the addition rule of probability of two events to solve the question. According to the rule given two events A and B;

p(A∪B) = p(A)+p(B) - p(A∩B) where;

A∪B is the union of the two sets A and B

A∩B is the intersection between two sets A and B

Given parameters

P(A)=15

P(A∪B)=1225

P(A∩B)=7100

Required

Probability of event B i.e P(B)

Using the expression above to calculate p(B), we will have;

p(A∪B) = p(A)+p(B) - p(A∩B)

1225 = 15+p(B)-7100

p(B) = 1225-15+7100

p(B) = 8310

Hence the missing probability p(B) is 8310.

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The area of a small pond is 78.5 yds. What is the diameter of the pond?

Zolol [24]

Answer:

Diameter of pound = 10 yd

Step-by-step explanation:

Given area of circular pond = 78.5 square yd

To find the diameter of the pond.

Solution:

The pond being circular in shape, the area of pond can be given as:

⇒ $\pi\ r^2$

where $r$ represents radius of the pond.

Thus, we have:

⇒ $\pi\ r^2=78.5$

Using $\pi=3.14$

⇒ $3.14r^2=78.5$

Solving for $r$

Dividing both sides by 3.14

⇒ $\frac{3.14r^2}{3.14}=\frac{78.5}{3.14}$

⇒ $r^2=25$

Taking square root both sides.

⇒ $\sqrt{r^2}=\sqrt{25}$

⇒ $r=\pm5$

So, radius = 5 yd, as distances are always positive.

Diameter = $2\times radius=2\times 5\ yd= 10\ yd$

Thus, diameter of pound = 10 yd

7 0

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

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

5 0

1 year ago

A trapezoid has a base of 4.5 inches, a height of 6 inches, and an area of 21 square inches. The equation below can be used to d

Troyanec [42]

Answer:

$b_2 = -2.5$

Step-by-step explanation:

Given

$\frac{1}{2}(4.5 + b_2) * 6 = 21$

Required

Determine the value of T

$\frac{1}{2}(4.5 + b_2) * 6 = 21$

Multiply both sides by 2

$2 * \frac{1}{2}(4.5 + b_2) * 6 = 21 * 2$

$(4.5 + b_2) * 6 = 42$

Divide through by 6

$4.5 + b_2 = 42/6``$

$4.5 + b_2 = 7$

$b_2 = 7 - 4.5$

$b_2 = -2.5$

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2 years ago

In an inventory of 100 sodas, 65 are

Ratling [72]

Answer:

5% I think

Step-by-step explanation:

Its mostly just a guess but I think its 5%

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Mrs. Epps buys 500 bags of balloons for the high school prom for $250. What is the cost per bag?

Andrej [43]

.50 is the answer I think, hope this helps

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1 year ago