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Anastaziya [24]

3 years ago

7

Consider a political discussion group consisting of 1010 Democrats, 1010 Republicans, and 55 Independents. Suppose that two gr

oup members are randomly selected, in succession, to attend a political convention. Find the probability of selecting two RepublicansRepublicans.

1 answer:

yan [13]3 years ago

3 0

Answer:

The probability is $\frac{3}{20}$

Step-by-step explanation:

Consider a political discussion group consisting of 10 Democrats, 10 Republicans, and 5 Independents.

Total members of the group = $10+10+5=25$

Selecting 2 republicans in succession means selecting 1st republican out of 10 republicans and total 25 members and then selecting 2nd republican out of 9 left republicans and 24 members.

Hence, probability becomes:

$\frac{10}{25}\times \frac{9}{24}$

= $\frac{90}{600} =\frac{3}{20}$

So, the probability is $\frac{3}{20}$

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3 years ago

City A is due north of City B. Find the distance between City A (36 degrees 6 prime36°6′ north latitude) and City B (21 degre

vitfil [10]

Answer:

distance = 994.75 miles

Step-by-step explanation:

given data

City A = 36°6′ = 36° + $\frac{6}{60}$ = 36.1° = 36.1° × $\frac{\pi}{180}$ = 0.6297 rad

City B = 21°42′ = 21° + $\frac{42}{60}$ = 21.7° = 21.7° × $\frac{\pi}{180}$ = 0.3785 rad

multiply by π/180 to convert the degree to radian

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5 0

3 years ago

What is x at most 30

andrezito [222]

Answer:

x < 30

Step-by-step explanation:

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7 0

3 years ago

Write an equation of a parabola that passes through (3,-30) and has x-intercepts of -2 and 18. Then find the average rate of cha

Nookie1986 [14]

Answer:

The equation of the parabola is $y = \frac{2}{5}\cdot x^{2}-\frac{32}{5}\cdot x -\frac{72}{5}$ . The average rate of change of the parabola is -4.

Step-by-step explanation:

We must remember that a parabola is represented by a quadratic function, which can be formed by knowing three different points. A quadratic function is standard form is represented by:

$y = a\cdot x^{2}+b\cdot x + c$

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$a$ , $b$ , $c$ - Coefficients, dimensionless.

If we know that $(3, -30)$ , $(-2, 0)$ and $(18, 0)$ are part of the parabola, the following linear system of equations is formed:

$9\cdot a +3\cdot b + c = -30$

$4\cdot a -2\cdot b +c = 0$

$324\cdot a +18\cdot b + c = 0$

This system can be solved both by algebraic means (substitution, elimination, equalization, determinant) and by numerical methods. The solution of the linear system is:

$a = \frac{2}{5}$ , $b = -\frac{32}{5}$ , $c = -\frac{72}{5}$ .

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$r = \frac{y(8)-y(-2)}{8-(-2)}$

$r = \frac{y(8)-y(-2)}{10}$

$x = -2$

$y = \frac{2}{5}\cdot (-2)^{2}-\frac{32}{5}\cdot (-2)-\frac{72}{5}$

$y(-2) = 0$

$x = 8$

$y = \frac{2}{5}\cdot (8)^{2}-\frac{32}{5}\cdot (8)-\frac{72}{5}$

$y(8) = -40$

$r = \frac{-40-0}{10}$

$r = -4$

The average rate of change of the parabola is -4.

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago