What is the area, in square feet, of the trapezoid below?

The appropriate probability distribution to use to test the null hypothesis in this scenario is the t distribution. This is because the sample size is small (n = 12) and the population standard deviation is unknown. The t distribution allows for estimation of the population mean based on the sample mean and standard deviation.

To test the null hypothesis for this problem, you should use the t-distribution. Here's an explanation of why:
1. You have a small sample size (n = 12), which is less than 30. When you have a small sample size, the t-distribution is more appropriate than the normal distribution.
2. The data consists of paired samples, with each person using the slicer and not using the slicer. This means you are comparing the mean differences within the paired samples.
3. The problem doesn't involve proportions or frequencies, so the chi-square and binomial distributions are not suitable here.

Based on these reasons, the appropriate probability distribution to use for this problem is the t-distribution (option B).

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a) The scale factor from shape A to shape B is given as follows: 4/5.

b) The value of t is given as follows: t = 5.6.

Similar triangles are triangles that share these two features listed as follows:

The concepts relating to similar shapes shape can be extended to any, hence the proportional relationship is given as follows:

5/4 = 7/t = 15/12.

Hence the value of t is obtained as follows:

5/4 = 7/t

5t = 28

t = 28/5

t = 5.6.

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Multiplicative Schwarz and Additive Schwarz are two different methods for solving partial differential equations numerically.

The idea behind both methods is to divide the problem domain into subdomains and solve the problem in each subdomain separately. The difference lies in how the solutions in each subdomain are combined to obtain the overall solution.

In Additive Schwarz, the solutions in each subdomain are added together to obtain the overall solution. This method is relatively simple and easy to implement, but it may require many iterations to converge to the correct solution.

In Multiplicative Schwarz, the solutions in each subdomain are multiplied together to obtain the overall solution. This method is more complex than Additive Schwarz, but it can converge to the correct solution much faster.

In summary, the main difference between these two methods is how they combine the solutions in each subdomain to obtain the overall solution.

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If the objective function is q=[tex]x^2y[/tex] and you know that x y=10, the objective function first in terms of x is q = 10x and then in terms of y is q = 100/y.

To write the objective function in terms of x, we can use the given value of xy = 10 and solve for y. Dividing both sides by x, we get:
y = 10/x
Now we can substitute this expression for y into the original objective function, q = [tex]x^2y[/tex], to get:
q = x^2(10/x)
Simplifying this, we get:
q = 10x
So the objective function in terms of x is q = 10x.
To write the objective function in terms of y, we can use the same approach. Solving the given equation xy = 10 for x, we get:
x = 10/y
Substituting this into the original objective function, q = [tex]x^2y[/tex], we get:
q = [tex](10/y)^2y[/tex]
Simplifying this, we get:
q = 100/y
So the objective function in terms of y is q = 100/y.

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To determine if there is significant evidence to suggest that the population of adolescents in a youth detention facility has a reading disability prevalence that is different from 9%, we need to conduct a hypothesis test. Let p be the proportion of adolescents in the population who have a reading disability. Our null hypothesis is that p=0.09, and the alternative hypothesis is that p is not equal to 0.09. We will use a significance level of 0.05.

Using the sample data, we can calculate the sample proportion, p-hat, which is 38/407=0.0933. To calculate the z-test value, we first need to calculate the standard error, which is sqrt(0.09*(1-0.09)/407)=0.0191. The z-test value is (0.0933-0.09)/0.0191=1.57. This z-test value can be compared to the critical value of the standard normal distribution at a significance level of 0.05/2=0.025. The critical value is 1.96. Since the calculated z-test value of 1.57 is less than the critical value of 1.96, we fail to reject the null hypothesis. Therefore, there is not significant evidence to suggest that the population of adolescents in a youth detention facility has a reading disability prevalence that is different than 9%.

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The length of arc KM is 11.09 units.

We have,

Arc length = 2πr x angle/360

From the figure,

∠KLM = 106

Radius = KL = 6

So,

Arc length KM

= 2πr x angle/360

= 2 x 3.14 x 6 x 106/360

= 11.09 unit

Thus,

The length of arc KM is 11.09 units.

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The orthocenter can be located on the exterior of the triangle, but this is not always the case is sometimes. D.

The orthocenter of a triangle is the point of intersection of the three altitudes of the triangle.

An altitude is a line segment drawn from a vertex of the triangle perpendicular to the opposite side or its extension.

The orthocenter can lie on the exterior of the triangle.

This occurs when the triangle is obtuse or when the altitude from one vertex of the triangle intersects the extension of the opposite side.

In such situations, the orthocenter will be located outside the triangle itself.

It is important to note that in other cases, such as with acute or right triangles, the orthocenter will lie within the interior of the triangle and not on the exterior.

The intersection of the triangle's three elevations is known as the orthocenter. A line segment known as an altitude is drawn from the triangle's vertex perpendicular to the other side or its extension.

It is possible for the orthocenter to be outside the triangle.

This happens if the triangle is acute or if the height from one of the triangle's vertices touches the extension of the other side.

The orthocenter will be outside of the triangle in such circumstances.

It's vital to keep in mind that the orthocenter will often reside inside the triangle and not on the outside in other scenarios, such as with acute or right triangles.

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The correct options are

The Chinese Remainder Theorem (CRT) is a mathematical principle that dates back to ancient Chinese mathematics. Its origins can be traced to Sun Tzu's "The Art of War," written in the 5th century BC, where he discussed a problem related to the deployment of troops.

However, the earliest known reference to the theorem as we know it today comes from the Chinese mathematician Sun Zi in the 3rd century AD. The theorem was later rediscovered and popularized in Europe by the mathematician Gottfried Leibniz in the 17th century.

The CRT has many practical applications in number theory, cryptography, and computer science. For example, it can be used to solve systems of linear congruences, which arise in a variety of mathematical problems. It is also used in Chinese remainder coding, a method for efficient data transmission in computer networks. In cryptography, the theorem is used to construct public-key cryptosystems, such as the RSA algorithm. Additionally, the CRT is used in the design of error-correcting codes and in the solution of problems related to modular arithmetic.

Overall, the Chinese Remainder Theorem is an ancient yet still relevant mathematical concept that has found a wide range of applications in modern times. Its history spans millennia and multiple cultures, from ancient China to Europe and beyond.

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Suppose that f(x) = −3x4 is an antiderivative of f(x) and g(x) = 2x3 is an antiderivative of g(x). The valsue of  ∫(f(x) g(x))dx is " -108/5 + C", where C is the constant of integration.

To find the integral of the product of two functions, we can use the formula ∫(f(x) g(x))dx = f(x) ∫g(x)dx - ∫[f'(x) (∫g(x)dx)]dx. Using this formula, we can evaluate the given integral as follows:

∫(f(x) g(x))dx = (-3x^4)(2x^3) - ∫[(-12x^3)(2x^3)]dx = -6x^7 + 24x^6/2 + C = -108/5 + C.

Therefore, the answer is " -108/5 + C".

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Yes, single-parent families tend to be more impoverished than families with two parents.  the findings suggest that family structure is an important factor in understanding the prevalence of poverty in a given population.

The study of the sample of 35 one-parent and 65 two-parent families found that a significantly higher percentage of single-parent families fell below the poverty level compared to two-parent families. This result is consistent with previous research that has shown that single-parent families, particularly those headed by women, are at a greater risk of poverty due to the challenges of raising children alone and the lack of dual incomes. Additionally, single-parent families often face more barriers to obtaining education and employment opportunities that could increase their income. Overall, the findings suggest that family structure is an important factor in understanding the prevalence of poverty in a given population.

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The length of x is,  32/9

And, The length of y is, 40/9

We have to given that;

Sides of triangle are, 8, 12 and 15.

Hence, By definition of proportionality we get;

⇒ CB / y = AB / x

⇒ 15 / y = 12 / x

⇒ x / y = 12 / 15

⇒ x / y = 4 / 5

So, Let x = 4a

y = 5a

Since, We have;

x + y = 8

4a + 5a = 8

9a = 8

a = 8/9

Hence, The length of x = 4a = 4 × 8/9 = 32/9

And, The length of y = 5a = 5 × 8/9 = 40/9

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The two values of b satisfy the equation are b = (5 + √13) / 6 and  b = (5 - √13) / 6

The average value of a function f(x) over an interval [a, b] is the mean value of the function on that interval. Mathematically, it is calculated using the following formula:

                  Average value = (1 / (b - a)) × ∫[a to b] f(x) dx

In this formula, the integral ∫[a to b] f(x) dx represents the definite integral of the function f(x) over the interval [a, b]. The integral measures the accumulated "area" under the curve of the function within that interval.

Here we have

The average value of f(x) = 7 + 10x − 9x² on the interval [0, b] is equal to 8.

To find the number 'b' such that the average value of the function

f(x) = 7(10x - 9x²) on the interval [0, b] is equal to 8, we need to set up the equation and solve for 'b'.

The average value of a function f(x) on the interval [a, b] is given by the formula:

=>  [tex]8 = \frac{1}{b} \int\limits^0_b {(7 + 10x - 9x^{2} ) } \, dx[/tex]

=>  [tex]8 = \frac{1}{b}[ \int\limits^b_0 {(7) dx +\int\limits^b_0 {10x} \ dx - 9\int\limits^b_0 {x^{2} } \, dx } \,][/tex]

=>   [tex]8 = \frac{7}{b} \int\limits^b_0 {(7) dx ] + \frac{10}{b} \int\limits^b_0 {x} \ dx - \frac{9}{b}\int\limits^b_0 {x^{2} } \, dx } \,[/tex]  

=>   [tex]8 = \frac{7}{b} (b) + \frac{10}{b} ( \frac{b^{2} }{2} ) - \frac{9}{b} (\frac{b^{3} }{3} )[/tex]

=>   [tex]8 = 7 + 5b - 3b^{2}[/tex]

=>   3b² - 5b + 8 - 7 = 0

=>   3b² - 5b + 1 = 0  

Here 3b² - 5b + 1 = 0 can solved as follows

b = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 3, b = -5, and c = 1.

Substituting these values into the quadratic formula:

b = (-(-5) ± √((-5)² - 4 × 3 × 1)) / (2 × 3)

= (5 ± √(25 - 12)) / 6

= (5 ± √13) / 6

Therefore, the solutions to the equation 3b² - 5b + 1 = 0 are:

b = (5 + √13) / 6

b = (5 - √13) / 6

Therefore,

The two values of b satisfy the equation are b = (5 + √13) / 6 and  b = (5 - √13) / 6

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Answer: C(2)

Step-by-step explanation: Count by 2's like 4,6,8

Answer:

Step-by-step explanation:

y-intercept is when x=0.

The rule here is y-x=3.

So when x=0, we get y=3.

SOLUTION: (D) 3

Ellen renovates his square farmhouse foyer that has a side of 15 feet. Therefore, the area of Ellen's square farmhouse foyer is 225 square feet.

The area of Ellen's square farmhouse foyer, with a side of 15 feet, is 225 square feet.

To find the area of a square, you need to multiply the length of one side by itself.

In this case, the side of the square foyer is 15 feet, so you simply need to multiply 15 by 15.

15 x 15 = 225

Therefore, the area of Ellen's square farmhouse foyer is 225 square feet. This measurement can be useful for determining how much flooring, paint, or other materials are needed to complete the renovation project.

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Since the total distance Xavier traveled by car is a function of time, we can plot the distance on the y-axis and the time on the x-axis. From the information given, we can break down the journey into three parts: 30 minutes of driving, 2 hours of shopping (which does not add to the distance traveled by car), and 15 minutes of driving followed by 1 hour of stopping at a friend's house.

Therefore, the graph would show a horizontal line for the time period of 2 hours (since no distance was traveled during this time), a positive slope for the first 30 minutes of driving, a horizontal line for the 1 hour of stopping at the friend's house (since no distance was traveled during this time), and a positive slope for the final 15 minutes of driving.

Of the four graphs shown, the one that most accurately represents this scenario is graph D, which shows a positive slope for the first and last sections of the journey, and horizontal lines for the periods of shopping and stopping at the friend's house.

I don't want your points, instead give me brainliest

The equation of the ellipse in standard form with center at the origin, with vertices at (-3,0) and (3,0), and co-vertices at (0,2) and (0,-2) is [tex](x^2/9) + (y^2/4) = 1[/tex].

Ellipses are important mathematical objects that can be used to describe various phenomena in science and engineering. An ellipse is a curve that is symmetric around two axes, and it can be defined in terms of its center, vertices, and co-vertices.

The equation of an ellipse in standard form with center at the origin is given by:

[tex](x^2/a^2) + (y^2/b^2) = 1[/tex]

where a and b are the lengths of the semi-major and semi-minor axes, respectively. The semi-major axis is the distance from the center to the farthest vertex, and the semi-minor axis is the distance from the center to the co-vertex.

To write the equation of an ellipse in standard form with center at the origin and given vertices and co-vertices, we first need to find the values of a and b. We can use the distance formula to find the lengths of the semi-major and semi-minor axes:

a = distance from (0,0) to (-3,0) = 3

b = distance from (0,0) to (0,2) = 2

Now we Substitute the values of a and b into the equation of the ellipse in standard form:

[tex](x^2/3^2) + (y^2/2^2) = 1[/tex]

Simplifying, we get:

[tex](x^2/9) + (y^2/4) = 1[/tex]

This is the equation of the ellipse in standard form with center at the origin, with vertices at (-3,0) and (3,0), and co-vertices at (0,2) and (0,-2).

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The required graph has been attached below which represents the given translation.

According to the shown figure, the coordinates of the given quadrilateral  can be written as:

The coordinates of vertice X are (-1, 4)

The coordinates of vertice V are (2, 0)

The coordinates of vertice W are (3, 4)

The coordinates of vertice Y are (-2, 1)

As the question, translation: (x, y)→ (x-3, y+1)

Then, the coordinates after translation can be written as:

The coordinates of vertice X' are: (-1-3, 4+1) = (-4, 5)

The coordinates of vertice V' are: (2-3, 0+1) = (-1, 1)

The coordinates of vertice W' are: (3-3, 4+1) = (0, 5)

The coordinates of vertice Y' are: (-2-3, 1+1) = (-5, 2)

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The mean of the given data is 6.

The given data is 3 ,3,6,5,8,11

we have to find the mean of the given data

To find the mean, you need to add up all the numbers and divide by the total number of numbers.

Mean = (3 + 3 + 6 + 5 + 8 + 11) / 6 = 36 / 6 = 6

Therefore, the mean of the given numbers is 6.

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The area of the three-petaled region is twice this value, or:  1/2 * (pi/5 + 1/10 * sin(2pi/5))

The area of the region enclosed by the three petals of r = cos(5) can be found by computing the integral of 1/2 * r^2 with respect to theta from 0 to pi/5, and then doubling the result.

This is because the curve r = cos(5) traces out each petal twice as theta varies from 0 to pi/5.

Thus, the area of one petal can be found by integrating 1/2 * (cos(5))^2 with respect to theta from 0 to pi/5:

A = 2 * ∫[0, pi/5] 1/2 * (cos(5))^2 d(theta)

Using the identity cos^2(x) = (1 + cos(2x))/2, we can simplify the integrand:

A = 2 * ∫[0, pi/5] 1/4 * (1 + cos(10)) d(theta)

= 1/2 * [theta + 1/10 * sin(10*theta)] evaluated from 0 to pi/5

= 1/2 * (pi/5 + 1/10 * sin(2pi/5))

area of the region. three petals of r = cos(5) = 1/2 * (pi/5 + 1/10 * sin(2pi/5))

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The number of intersections between the graphs of f(x) = Ix² - 4I and g(x) = 2ˣ is 3

From the question, we have the following parameters that can be used in our computation:

f(x) = Ix² - 4I

g(x) = 2ˣ

Next, we plot the graphs of the functions f(x) and g(x)

From the graph, we have the number of intersections between the graphs to be 3

The points of intersections are approximately (-2.1, 0.2), (-1.9, 0.3) and (1.3, 2.4)

Hence, the number of intersections between the graphs is 3

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To solve this problem, we can use the principle of inclusion-exclusion.
First, let's consider the total number of n digit ternary sequences. For each digit, we have 3 choices (0, 1, or 2), so the total number of n digit ternary sequences is 3^n.

Next, let's consider the number of n-digit ternary sequences in which no pair of consecutive digits are the same. To construct such a sequence, we can start with any digit (3 choices), and then for each subsequent digit, we must choose a different digit than the previous one (2 choices). Therefore, the number of n digit ternary sequences in which no pair of consecutive digits are the same is 3 x 2^(n-1).

Finally, to find the number of n digit ternary sequences in which at least one pair of consecutive digits are the same, we can use the principle of inclusion-exclusion. We want to subtract the number of n digit ternary sequences in which no pairs of consecutive digits are the same from the total number of n digit ternary sequences. However, if we simply subtract these two values, we will have double-counted the sequences in which there are two (or more) pairs of consecutive digits that are the same. So we need to add back in the number of sequences in which there are two (or more) pairs of consecutive digits that are the same, and so on.

The formula for the number of n digit ternary sequences in which at least one pair of consecutive digits are the same is:

3^n - 3 x 2^(n-1) + 3 x 2^(n-2) - 3 x 2^(n-3) + ... + (-1)^(n-1) x 3

So, for example, if n = 4, the number of n digit ternary sequences in which at least one pair of consecutive digits are the same is:

3^4 - 3 x 2^(4-1) + 3 x 2^(4-2) - 3 x 2^(4-3) = 81 - 24 + 12 - 6 = 63.

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Answer:

[tex]6\sqrt{3}[/tex]

Step-by-step explanation:

In a 30-60-90 triangle, the side opposite to the right angle is [tex]2x[/tex] , the side opposite to the 30 degrees is x and the side opposite to the 60 degrees is [tex]x\sqrt3[/tex]. Since 12 is on the side with [tex]2x[/tex], we can use reasoning to deduce that the unknown side is [tex]6\sqrt3[/tex].

The area of the triangle is 24 square units

From the question, we have the following parameters that can be used in our computation:

X(3, -4), Y(3, 2), and Z(7, -4).

The area of the triangle in square units is calculated as

Area = 1/2 * |x₁y₂ - x₂y₁ + x₂y₃ - x₃y₂ + x₃y₁ - x₁y₃|

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * |3 * 2 - 3 * 4 + 3 * -4 - 7 * 2 + 7 * -4 - 3 * -4|

Evaluate the sum and the difference of products

Area = 1/2 * 48

So, we have

Area = 24

Hence, the area of the triangle is 24 square units

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Step-by-step explanation:

For question 2, simplify the polynomial 3x²+6-2x+5x-4x²+9 by combining like terms:

3x² - 4x² + 5x + 6 + 9 = -x² + 5x + 15

Therefore, the simplified polynomial is: D. -x² + 7x + 15

For question 3, simplify the polynomial 2X²+6X-7X+8=3X²+1 by moving all terms to one side and combining like terms:

2X² + 6X - 7X - 3X² = 1 - 8

-X² - X - 7 = 0

Therefore, the simplified polynomial is: C. -X² - X + 9

The slope of the line is m = 2.49

Given data ,

Let's denote the number of meals delivered as x and the total cost as y.

Now , the cost is determined by two components

$4.98 for every 2 meals delivered and a $2.00 service fee

The first component, $4.98 for every 2 meals delivered, can be represented by the expression (4.98/2)x, which simplifies to 2.49x.

The second component is a fixed $2.00 service fee, which remains the same regardless of the number of meals delivered.

So , the total cost equation is:

y = 2.49x + 2.00

And , slope of this situation is the coefficient of x in the equation, which is 2.49

Hence , the slope of this situation is 2.49

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The equation of the parabola in vertex form is y = (-1/12)(x + 3)^2 + 2, which opens downwards since the leading coefficient is negative.

The equation of the given parabola in vertex form is y = a(x + 3)^2 + 2, where a is a constant that depends on whether the parabola opens up or down.

To determine the value of a, we can use the fact that the parabola passes through (-7, 2/3). Substituting these values into the equation, we get:

2/3 = a(-7 + 3)^2 + 2

2/3 = 16a + 2

16a = -4/3

a = -1/12

Therefore, the equation of the parabola in vertex form is

y = (-1/12)(x + 3)^2 + 2.

The vertex form of a parabola is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. In this case, we are given that the vertex is (-3, 2), so we can write the equation as y = a(x + 3)^2 + 2.

To find the value of a, we use the fact that the parabola passes through (-7, 2/3). Substituting these values into the equation, we get 2/3 = a(-7 + 3)^2 + 2. Simplifying this equation, we get 2/3 = 16a + 2, which we can solve for a to get a = -1/12.

Therefore, the final equation of the parabola in vertex form is y = (-1/12)(x + 3)^2 + 2, which opens downwards since the leading coefficient is negative.

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A) Null hypothesis (H₀): The mean-life of the light bulbs is equal to 743 hours. Alternative hypothesis (H₁): The mean-life of the light bulbs is less than 743 hours. B)  The critical value for α = 0.05 and 20 degrees of freedom (n-1) to be -1.725. C) The standardized test statistic (t-score) is -2.157. D) Sufficient evidence to reject the manufacturer's claim that the mean-life of the light bulbs is at least 743 hours.

The sample mean of 714 hours, along with the population standard deviation of 57 hours and a significance level of 0.05, leads us to reject the null hypothesis in favor of the alternative hypothesis, indicating that the mean-life of the light bulbs is less than 743 hours.

B) To determine the critical values, we need to consider the significance level (α) of 0.05 and the one-tailed test since the alternative hypothesis is less than. Using a t-distribution table or software, we find the critical value for α = 0.05 and 20 degrees of freedom (n-1) to be -1.725.

C) The rejection region is the left tail of the distribution, where the test statistic is smaller than the critical value. In this case, since it's a one-tailed test, the rejection region corresponds to test statistics less than -1.725.The standardized test statistic (t-score) can be calculated using the formula:t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))[tex]= (714 - 743) / (57 / \sqrt{} (21))[/tex]= -2.157.

D) Since the standardized test statistic of -2.157 falls in the rejection region (-2.157 < -1.725), we can reject the null hypothesis. The evidence suggests that the mean-life of the light bulbs is less than 743 hours. This means there is enough evidence to reject the manufacturer's claim and conclude that the mean-life of the light bulbs is below the guaranteed value.

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The coordinates of the four corners of the rectangle are A(3, 2), B(0, 3), C(-3, -2), and D(0, -3).

The rectangle has two pairs of parallel sides and right angles at each corner, and the diagonals intersect at the origin. We can use this information to find the coordinates of the four corners of the rectangle.

Let's start by drawing a diagram and labeling the coordinates of the intersection point of the diagonals, (0, 0).

B ________ C

  |                |

  |                |

  |                |

  |________|D

       (0,0)

Since the rectangle is 6 units long and 4 units wide, we know that the distance from the origin to each corner is a multiple of 2 or 3 units (using the Pythagorean theorem). We can also use the fact that the diagonals bisect each other to find the coordinates of the corners.

Starting with corner A, we can use the fact that it is 3 units to the right and 2 units up from the origin to find its coordinates: A(3, 2). Similarly, we can find the coordinates of corner C, which is 3 units to the left and 2 units down from the origin: C(-3, -2).

Next, we can use the fact that corner B is equidistant from A and C to find its coordinates. Since the rectangle is symmetric, we know that corner B is 3 units up from the origin: B(0, 3). Finally, we can find the coordinates of corner D, which is 3 units down from the origin: D(0, -3).

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The approximate probability that a married woman selected at random is taller than her husband is 8.85%.

We can use the concept of sampling distribution of the difference between two means to approximate the probability that a randomly selected married woman is taller than her husband.

Let X be the height of a married man and Y be the height of a married woman. Then, the probability that a woman is taller than her husband can be expressed as P(Y > X).

The sampling distribution of the difference between two means can be approximated by a normal distribution if the sample sizes are large enough. In this case, since we have a large sample of 400 couples, we can assume that the sampling distribution of the difference in heights between married men and women is approximately normal.

The mean of the difference in heights between married men and women is

65 - 70 = -5 inches

The standard deviation is the

√(3² + 2.5²) = 3.7 inches.

We can then standardize the difference using the formula:

Z = (Y - X - (-5))/3.7

P(Y > X) = P(Z > (0 - (-5))/3.7) = P(Z > 1.35)

Using a standard normal table or calculator, we find that the probability of a woman being taller than her husband is approximately 0.0885 or 8.85%.

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Complete question is:

A random sample of 400 married couples was selected from a large population of married couples.

Heights of married men are approximately normally distributed with mean 70 inches and standard deviation of 3 inches.

Heights of married women are approximately normally distributed with mean 65 inches and standard deviation 2.5 inches.

There were 20 couples in which the wife was taller than her husband, and there were 380 couples in which the wife was shorter than her husband

suppose that a married man is selected at random and a married woman is selected at random. find the approximate probability that the woman will be taller than the man.