One measure of student success for colleges and universities is the percent of admitted students who graduate. Studies indicate that a key issue in retaining students is their performance in so-called gateway courses. These are courses that serve as prerequisites for other key courses that are essential for student success. One measure of student performance in these courses is the DFW rate, the percent of students who receive grades of D, F, or W (withdraw). A major project was undertaken to improve the DFW rate in a gateway course at a large midwestern university. The course curriculum was revised to make it more relevant to the majors of the students taking the course, a small group of excellent teachers taught the course, technology (including clickers and online homework) was introduced, and student support outside the classroom was increased. The following table gives data on the DFW rates for the course over three years. In Year 1, the traditional course was given; in Year 2, a few changes were introduced; and in Year 3, the course was substantially revised.


Year DFW Rate Number of Students Taking Course


Year 1 42. 1% 2408


Year 2 24. 3% 2325


Year 3 19. 4% 2126


1. Do you think that the changes in this gateway course had an impact on the DFW rate? (Use α = 0. 1. )


2. State the null and alternative hypotheses.


3. State the Ï2 statistic, degrees of freedom, and the P-value.

The approximate area of the figure is 40 square meters. So, the correct answer is B).

Recall the formula for the area of a kite, which is

Area = (1/2) x Base x Height

where "Base" is the length of one of the diagonals and "Height" is the length of the other diagonal.

Identify the base and height of the given kite from the problem statement. Here, it is given that the height is 10 meters and the base is 8 meters.

Substitute the values of the base and height into the formula for the area of a kite

Area = (1/2) x 8 meters x 10 meters

Simplify the expression by multiplying the base and height together and dividing by 2

Area = 40 square meters

Round the answer to the nearest whole number or keep the answer as a decimal, depending on the instructions of the problem.

Therefore, the approximate area of the given kite is 40 square meters. So, the correct answer is B).

To know more about Area:

https://brainly.com/question/31749625

#SPJ4

If the fifth and tenth terms of an arithmetic sequence, respectively, are -2 and 53, the seventh term of the arithmetic sequence is 20.

To find the seventh term of the arithmetic sequence, we need to first find the common difference (d) of the sequence. We know that the fifth term is -2 and the tenth term is 53.

The formula for the nth term of an arithmetic sequence is: an = a1 + (n-1)d

Using this formula, we can set up two equations:

-2 = a1 + 4d  (since the fifth term is a1 + 4d)
53 = a1 + 9d  (since the tenth term is a1 + 9d)

We now have two equations with two variables (a1 and d). We can solve for either variable using substitution or elimination. I'll use elimination:

-2 = a1 + 4d
53 = a1 + 9d

Subtracting the first equation from the second equation, we get: 55 = 5d

Therefore, d = 11

Now that we know the common difference is 11, we can use the formula for the nth term again to find the seventh term:

a7 = a1 + (7-1)d
a7 = a1 + 6d

We still don't know a1, but we can solve for it using one of the previous equations:

-2 = a1 + 4d
-2 = a1 + 4(11)
-2 = a1 + 44
a1 = -46

Now we can substitute a1 and d into the formula for the seventh term:

a7 = -46 + 6(11)
a7 = -46 + 66
a7 = 20

Therefore, the seventh term of the arithmetic sequence is 20.

More on arithmetic sequence: https://brainly.com/question/31439905

#SPJ11

The maximum number of students allowed to attend the field trip is 59.

To determine the maximum number of students allowed to attend the field trip, given the ticket cost and money raised, we'll need to follow these steps:
1. Subtract the adult ticket cost from the total money raised.
2. Divide the remaining amount by the cost of a student ticket.
Subtract the adult ticket cost from the total money raised.
$580 (money raised) - $75 (adult ticket cost) = $505 (remaining amount)
Divide the remaining amount by the cost of a student ticket.
$505 (remaining amount) / $8.50 (student ticket cost) = 59.41
Since we can't have a fraction of a student, we round down to the nearest whole number.
The maximum number of students allowed to attend the field trip is 59.

Learn more about money here, https://brainly.com/question/24373500

#SPJ11

To get it why radians  have fractional answers, one can use the unit of a circle .  the unit circle could be a circle with a radius of 1, centered at the root of a coordinate plane. To measure points in radians on the unit circle, we measure the  arc length of the comparing other part of the circle, as shown within the image attached:

Radian measures angles based on arc length equal to the radius of a circle, resulting in fractions for non-whole arcs. The unit circle has a radius of 1 and is centered at the origin.

This explains why radians can be fractional. To measure angles in radians, we use arc length on the unit circle. Most angles correspond to fractions of a full circle, like π/2 for a quarter circle.

The angle in radians for one-eighth of a circle is approximately 0.79 (π/4), as most circle arcs are not exact multiples of the radius. Most circle arcs cannot be expressed as a whole number of radii.

Learn more about radians  from

https://brainly.com/question/19278379

#SPJ1

(a) The expressions for the length, width, and height can be 3x, (2x + 5), and (x - 3).

(b) The least possible integer value of x for the rectangular solid to exist is 4.

a. To express the length, width, and height of the right rectangular prism in terms of x, we can factor the volume expression, 6x³ - 3x² - 45x.

Factoring out the greatest common factor, 3x:

3x(2x² - x - 15)

Now, factor the quadratic expression:

3x(2x² - x - 15)

To factor the quadratic expression further, find two numbers whose product equals the constant term (-15) and whose sum equals the coefficient of the linear term (-1). These two numbers are -5 and 3.

3x(2x + 5)(x - 3)

Thus, the expressions for the length, width, and height can be 3x, (2x + 5), and (x - 3)

b. For the rectangular solid to exist, all dimensions (length, width, and height) must be positive. Let's examine the constraints on x for each dimension:

1. 3x > 0
2. 2x + 5 > 0 → x > -5/2
3. x - 3 > 0 → x > 3

Since x must satisfy all three inequalities, the least possible integer value of x for the rectangular solid to exist is x = 4.

Learn more about factor here: https://brainly.com/question/28589848

#SPJ11

The area of the triangle ∆WXY is derived to be 5.7 to the nearest tenth.

When two side length of a triangle and the angle between them is given, the area is half the multiplication of the two sides and the sine of the angle.

Area of the triangle = 1/2 × 4.7 × sin162

Area of the triangle = 11.4738/2

Area of the triangle = 5.7369.

Therefore, the area of the triangle ∆WXY is derived to be 5.7 to the nearest tenth.

Read more about area here:https://brainly.com/question/29123926

#SPJ1

Answer:

62.29

Step-by-step explanation:

100 - 3(4.25) - 13 - 4(2.99)

= 100 - 12.75 - 13 - 11.96

= 62.29

explanation in the picture

the answer is

62,29

The solution to the inequality given is false.

To determine whether x = 5 is a solution of the inequality x + 3 > 12, we substitute x = 5 into the inequality and see if the resulting statement is true or false:

5 + 3 > 12

8 > 12

In this case, when we substitute x = 5 into the inequality, we get the statement 5 + 3 > 12, which simplifies to 8 > 12. This statement is false, since 8 is not greater than 12. Therefore, x = 5 is not a solution of the inequality x + 3 > 12.

Find out more on inequalities at https://brainly.com/question/28755685

#SPJ1

The full question is:

Tell whether the given value is a solution of the inequality X + 3 > 12; x = 5

The estimated population proportion is 0.622, with a margin of error of +/- 0.096.

The value of the population proportion of people from Hawaii who exercised for at least 30 minutes a day 3 days a week can be estimated using the sample proportion of 62.2%. However, we need to calculate the margin of error to determine a range in which the true population proportion is likely to fall.

Using the formula for the margin of error:

Margin of error = z*sqrt(p*(1-p)/n)

where z is the z-score for the desired level of confidence (let's use 95% confidence, which corresponds to a z-score of 1.96), p is the sample proportion (0.622), and n is the sample size (100).

Plugging in the values, we get:

Margin of error = 1.96*sqrt(0.622*(1-0.622)/100) = 0.096

So the margin of error is 0.096, meaning that we can be 95% confident that the true population proportion of people from Hawaii who exercise for at least 30 minutes a day 3 days a week falls within a range of 0.622 +/- 0.096.

To know more about the margin of error refer to

https://brainly.com/question/10218601

#SPJ11

To find the height of the rocket after 2.5 seconds,

you'll need to plug in t = 2.5 into the given equation h(t) = 160t - 16t².

h(2.5) = 160(2.5) - 16(2.5)²
h(2.5) = 400 - 100
h(2.5) = 300 meters

The height of the rocket after 2.5 seconds is 300 meters.

To know more about Height Equations:

https://brainly.com/question/28122539

the backup goalie saved 42 shots. Answer: 42 shots. We can start by setting up an equation using the information given

what is equation ?

An equation is a mathematical statement that asserts that two expressions are equal. It is typically written with an equal sign (=) between the two expressions. For example, the equation 2x + 3 = 7 is a statement that asserts that the expression 2x + 3 is equal to 7.

In the given question,

We can start by setting up an equation using the information given:

save percentage = (number of shots saved / total number of shots attempted)

For the backup goalie, we know that their save percentage is 0.560, and we also know the total number of shots attempted on the goal is 75. Let's let the number of shots saved by the backup goalie be represented by the variable "t". Then we can write:

0.560 = t / 75

To solve for t, we can cross-multiply:

0.560 * 75 = t

t = 42

Therefore, the backup goalie saved 42 shots. Answer: 42 shots.

To know more about equation, visit:

https://brainly.com/question/29538993

#SPJ1

The discrepancy in the results: The theoretical probability may not be calculated correctly and enough trials have not been performed to give the desired result

In the given scenario, 81% of money spent at full-service restaurants in America is through debit, credit, or pre-paid cards. However, one restaurant found that 421 out of 973 customers used these payment methods. Possible reasons for the discrepancy in the results are:

1. The theoretical probability may not be calculated correctly: The 81% figure might not accurately represent the actual proportion of customers using cards in full-service restaurants. It could be due to incorrect data collection or interpretation.

3. Enough trials have not been performed to give the desired result: The data from one restaurant for one week might not be enough to accurately reflect the overall trend. A larger sample size and longer time frame would give a more accurate representation.

It's important to note that there might not necessarily be a discrepancy in the result; it could be a difference due to variations in individual restaurant data compared to the overall average.

To know more about theoretical probability, refer here:

https://brainly.com/question/24037367#

#SPJ11

We have found the altitude of the aircraft, we can determine its distance from station P, which is simply the value of d1

We can use the concept of triangulation to find the distance of the aircraft from station P. Let's assume that the aircraft is at point A, and let d1 and d2 be the distances of the aircraft from stations P and Q, respectively. Then we have:

[tex]d1^2 + h^2 = r1^2 ------ (1)\\d2^2 + h^2 = r2^2 ------ (2)[/tex]

where h is the altitude of the aircraft, r1 and r2 are the distances from the aircraft to stations P and Q, respectively. We want to find d1, which is the distance of the aircraft from station P.

We know that the distance between the two radar stations is 120 miles, so we have:

[tex]r2 = r1 + 120 (3)[/tex]

Subtracting equation (1) from equation (2), we get:

[tex]d2^2 - d1^2 = r2^2 - r1^2\\d2^2 - d1^2 = (r1+120)^2 - r1^2\\d2^2 - d1^2 = 120*240 + 120^2\\d2^2 - d1^2 = 40800[/tex]

Adding equations (1) and (3), we get:

[tex]2h^2 + 2*r1*120 = r1^2 + (r1+120)^2\\2h^2 + 2*r1*120 = 2*r1^2 + 120^2\\2h^2 = 4*r1^2 - 2*r1*120 + 120^2\\h^2 = 2*r1^2 - r1*120 + 120^2 / 2\\h^2 = r1^2 - r1*60 + 120^2 / 4[/tex]

Substituting h^2 into equation (1), we get:

[tex]d1^2 + (r1^2 - r1*60 + 120^2 / 4) = r1^2\\d1^2 = r1*60 - 120^2 / 4\\d1^2 = 15*r1^2 - 18000[/tex]

Substituting d2^2 - d1^2 from the previous calculation, we get:

[tex]d2^2 - (15*r1^2 - 18000) = 40800\\d2^2 = 15*r1^2 + 58800[/tex]

Now we have two equations with two unknowns (d1 and r1). Solving for r1 in equation (4) and substituting into equation (5), we get:

[tex]d2^2 = 15*(d1^2 + 120*d1) + 58800\\d2^2 = 15*d1^2 + 1800*d1 + 58800\\15*d1^2 + 1800*d1 + 58800 - d2^2 = 0[/tex]

This is a quadratic equation in d1, which can be solved using the quadratic formula:

[tex]d1 = (-b \± sqrt(b^2 - 4ac)) / 2[/tex]

where a = 15, b = 1800, and c = 58800 - d2^2. Note that we should take the positive root, since d1 is a distance and therefore cannot be negative.

Once we have found d1, we can use equation (1) to find h, the altitude of the aircraft, as:

[tex]h = sqrt(r1^2 - d1^2)[/tex]

Finally, the distance of the aircraft from station P is simply d1.

Learn more about Distance

brainly.com/question/29689299

#SPJ11

If regular hexagon, regular octagon are inscribed in circle, perimeter of hexagon is greater than perimeter of octagon, each perimeter is greater than circumference of circle. Therefore, statement B is true.

The perimeter of a polygon is the sum of the lengths of all its sides. In a regular polygon, all sides have equal length, so the perimeter is simply the number of sides multiplied by the length of one side. The circumference of a circle is the distance around its outer edge.

Since both polygons are inscribed in the same circle, they have the same circumcircle, which means that their perimeters are both less than the circumference of the circle.

To compare the perimeters of the two polygons, we need to know the number of sides of each polygon and the length of one side. A regular hexagon has six sides, and a regular octagon has eight sides. Since the circle is inscribed in both polygons, the sides of each polygon are tangents to the circle, forming right angles with the radii of the circle.

Thus, we can draw a right triangle with the radius of the circle as the hypotenuse, and the side of the hexagon (or octagon) as one leg. Using trigonometry, we can find the length of one side of the hexagon (or octagon) in terms of the radius of the circle.

After calculating the lengths of one side of each polygon, we can compare their perimeters. It turns out that the perimeter of the octagon is greater than the perimeter of the hexagon, since the octagon has more sides.

Therefore, statement B is true.

To learn more about hexagon click on,

https://brainly.com/question/10209400

#SPJ4

Complete question is:

A regular hexagon and a regular octagon are both inscribed in the same circle. which of these statements is true?

A) the perimeter of the hexagon is less than the perimeter of the octagon, and each perimeter is less than the circumference of the circle.

B) the perimeter of the hexagon is greater than the perimeter of the octagon, and each perimeter is greater than the circumference of the circle.

The ordered pair that is a reflection over the x-axis for the point shown include the following: A. (6, 4)

In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y).

This ultimately implies that, a reflection over or across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative or negative to positive.

Next, we would apply a reflection over or across the x-axis to the point;

(x, y)                →      (x, -y)

(6, -4)                →      (6, -(-4)) = (6, 4)

Read more on reflection here: brainly.com/question/27912791

#SPJ1

Answer:

252 mi

Step-by-step explanation:

volume= L x W x H

9x 7 x 4 = 252 mi

Note that where the above function is given, the equation in function notation is f(x) = (-2/3)x + 490. This function represents the profit Sal makes from lunch specials based on the number of sandwich and wrap lunch specials sold. See the graph attached.

To change the given equation to slope-intercept form, we need to solve for y.

2x + 3y = 1470

3y = -2x + 1470

y = (-2/3)x + 490

Therefore, the slope of the line is -2/3 and the y-intercept is 490.

To graph this line using the slope-intercept method, we can plot the y-intercept first, which is (0, 490). Then, using the slope of -2/3, we can find another point by moving 2 units to the right and 3 units down from the first point. We can continue this pattern to plot additional points and then draw a straight line through them.

The equation in function notation is f(x) = (-2/3)x + 490. This function represents the profit Sal makes from lunch specials based on the number of sandwich and wrap lunch specials sold.

To graph the function, we can plot the intercepts (0, 490) and (735, 0), where 735 is the x-intercept. Then, using the slope of -2/3, we can find other points and draw a straight line through them.

If Sal's total profit on lunch specials for the next month is $1,593, then the equation would be 2x + 3y = 1593. The graphs of the functions for both months would have the same slope of -2/3, indicating that the profit per lunch special sold remains constant.

However, the y-intercept would be different, indicating a different starting profit for the month. The graphs would have different intercepts and intersect the y-axis at different points, reflecting the difference in starting profits.

Learn more about graphs  at:

https://brainly.com/question/17267403

#SPJ1

For the solutions to the inequality *> 145, you can consider the given terms: 1. Fractions larger than 14 1/2: These are solutions since 14 1/2 is equivalent to 145/2, which is smaller than 145. 2.

Decimals larger than 14 1/2: These are also solutions as any decimal larger than 14.5 (14 1/2 as a decimal) will be greater than 145/2 and thus smaller than 145. 3. Whole numbers larger than 14 1/2: These are solutions as well, since any whole number greater than 14 is greater than 14 1/2 and therefore greater than 145/2. The numbers that are not solutions to the inequality are: 1. Fractions smaller than 14 1/2 2. Decimals smaller than 14 1/2 3. Whole numbers smaller than 14 1/2 These values are all less than 145/2 and therefore do not satisfy the inequality *> 145.

For more questions like fractions visit the link below:

https://brainly.com/question/24181320

#SPJ11

The group of natural numbers is a subset of the whole numbers.

What is Whole number ?

Whole numbers are a set of numbers that includes all positive integers (1, 2, 3, ...) and zero (0). They do not include negative numbers or fractions. Whole numbers are often used to count objects or represent quantities that cannot be divided into smaller parts.

Out of the given options, the group of natural numbers is the only one that is a subset of whole numbers. The other options - Rational numbers, Real numbers, Irrational numbers, and Integers - are not subsets of the whole numbers.

Rational numbers include fractions and decimal numbers, which can be expressed as a ratio of two integers, including non-whole numbers.

Real numbers include all rational and irrational numbers, including non-whole numbers. Irrational numbers are non-repeating, non-terminating decimals that cannot be expressed as a fraction. Integers include both positive and negative whole numbers, as well as zero.

The subset of whole numbers is called natural numbers.

Therefore, the group of natural numbers is a subset of the whole numbers.

To learn more about Whole number from given link.

https://brainly.com/question/29766862

#SPJ1

the inflection points are x = 0 and x = 2, and the intervals of concavity are (-∞, 0) and (2, ∞) for concave down, and (0, 2) for concave up.

To find the inflection points and intervals of concavity of the function f(x) = x^4 - 4x^3, we need to find its second derivative.

f'(x) = 4x^3 - 12x^2
f''(x) = 12x^2 - 24x

The inflection points occur where f''(x) = 0 or is undefined. Therefore, we set 12x^2 - 24x = 0 and solve for x.

12x(x - 2) = 0
x = 0 or x = 2

These are the two possible inflection points.

To determine the intervals of concavity, we need to look at the sign of the second derivative in each interval. We can use test points to determine the sign.

Test point x = 1:
f''(1) = 12 - 24 = -12, so the function is concave down on the interval (-∞, 0) and concave up on the interval (0, ∞).

Test point x = 3:
f''(3) = 108 - 72 = 36, so the function is concave up on the interval (2, ∞) and concave down on the interval (-∞, 2).

To learn more about second derivative click here

brainly.com/question/29090070

#SPJ11

Final Answer:  a. The number of units that should be sold in order to maximize the profit is 7 thousand units.

b. The  maximum profit is approximately $5.51

Conceptual part:   a. In order to find maximum profit we need to differentiate the profit function

[tex]dp/dx = (-3x^2+18x+21)/-x^3+9x^2+21x+1[/tex] = 0

[tex]-3x^2+18x+21=0[/tex]

[tex](x-7) (x+1) = 0[/tex]

as profit can't be negative.

hence x=7.

b. We can determine the maximum profit by substituting x=7 in profit function.

[tex]p(7) = ln(-7^3+9*7+21*7+1)[/tex]

[tex]p(7) = ln(246)[/tex]

p(7) = 5.51

To learn more about maximization  of profit visit: brainly.com/question/30639135

Hashtag:  #SPJ11

When the pretax financial income is negative (indicating a loss), the taxable income will also be negative. This means that the company can use the loss to offset future profits and reduce its tax liability.

To calculate the taxable income (loss) for each year, we need to apply the corresponding tax rate to the pretax financial income (or loss) figures. Here's the breakdown:

2017:

Taxable income = Pretax financial income * Tax rate

Taxable income = $77,000 * 0.25

Taxable income = $19,250

2018:

Taxable income = Pretax financial income * Tax rate

Taxable income = ($38,000) * 0.20

Taxable income = ($7,600)

2019:

Taxable income = Pretax financial income * Tax rate

Taxable income = ($33,000) * 0.20

Taxable income = ($6,600)

2020:

Taxable income = Pretax financial income * Tax rate

Taxable income = $122,000 * 0.20

Taxable income = $24,400

2021:

Taxable income = Pretax financial income * Tax rate

Taxable income = $90,000 * 0.20

Taxable income = $18,000

Please note that when the pretax financial income is negative (indicating a loss), the taxable income will also be negative. This means that the company can use the loss to offset future profits and reduce its tax liability.

Learn more about Pretax financial income,

https://brainly.com/question/31953594

#SPJ11

The best point estimate for the population mean score on the nationwide examination in psychology is the sample mean of 492.

When we take a sample from a population, the sample mean is a point estimate of the population mean. A point estimate is an estimate of a population parameter based on a single value or point in the sample. In this case, the sample mean of 492 is the best point estimate for the population mean, because it is an unbiased estimator.

An estimator is unbiased if it is expected to be equal to the true population parameter. In this case, the expected value of the sample mean is equal to the population mean. This means that if we were to take many different samples from the population and calculate the sample mean for each sample, the average of all these sample means would be equal to the population mean.

Learn more about sample mean here

brainly.com/question/14127076
#SPJ4

The given question is incomplete, the complete question is:

You would like to construct a 95% confidence interval to estimate the population mean score on a nationwide examination in psychology, and for this purpose we choose a random sample of exam scores. The sample we choose has a mean of 492 and a standard deviation of 78. What is the best point estimate, based on the sample, to use for the population mean?

The first derivative of g(a) is [tex]g'(x) = 18x^2 - 18x - 36.[/tex]

To find the first derivative of g(a), we need to use the power rule and the constant multiple rule.

First, we use the power rule to take the derivative of each term:

[tex]- The derivative of 6x^3 is 18x^2

- The derivative of -9x^2 is -18x

- The derivative of -36x is -36[/tex]

Next, we use the constant multiple rule to combine these derivatives:

g'(a) = 18x^2 - 18x - 36

Therefore, the first derivative of g(a) is [tex]g'(x) = 18x^2 - 18x - 36.[/tex]

To know more about constant multiple rule, refer here:

https://brainly.com/question/29015896

#SPJ11

The solution of the given inequality, x - 3 ≤ -2, is solved as the possible value of x which is determined as: x ≤ 1.

Given the inequality x - 3 ≤ -2, to find the solution, wr would have to solve for x as explained below:

x - 3 ≤ -2 [given]

Add 3 to both sides:

x - 3 + 3 ≤ -2 + 3 [addition property of equality]

x ≤ 1

This means that the values of x are less than or equal to 1, which is from 1 below.

Thus, the solution to the inequality is solved by finding the possible value of x, which is x ≤ 1.

Learn more about inequality on:

https://brainly.com/question/24372553

#SPJ1

The number of different combo meals possible in a restaurant that is serving a special dinner combo meal is 90.

We are given that the customers can choose from 5 drinks, 6 main dishes, and 3 desserts. We have to find that how many different combos are possible. It means that we have to do an arrangement for such a situation. Arrangement of things means to group them in a systematic order, in all the possible ways.

We know that the number of possible ways to arrange is n! where n is the number of objects. As we know that the dinner includes 5 drinks, 6 main types of dishes, and 3 types of desserts. The number of different combo meals possible can be found by simply multiplying all the meals. Thus,

n = 5 * 6 * 3

n = 90

Therefore, the number of different combo meals possible in a restaurant that is serving a special dinner combo meal that includes a drink, a main dish, and a dessert is 90.

To learn more about the arrangement;

brainly.com/question/6032811

#SPJ1

Note that the probability that he gives the lifejackets to just two of the three non-swimmers​ is 3/250 or 0.012

Let's define the following events...

A: Two of the three non-swimmers get lifejackets

B: Three lifejackets are given to two non-swimmers and one swimmer

We want to calculate P(A), the probability that two of the three non-swimmers get lifejackets. We can do this using the formula/...

P(A) = P(A|B) * P(B) + P(A|not B) * P(   not B)

P (B), the probability that the Captain gives the lifejackets to two non-swimmers and one swimmer....

P(B )  = (3/5 ) x (2/4) x (1/3) = 1/ 10

Note that  he number of ways to choose 2 non-swimmers from 3 is 3, and the number of ways to choose 1 swimmer from 2 is 2.

The total No.  of ways to choose 3 passengers from 5 is 10, hence

P(A | B) = (3 choose 2) x (2 choose 1) / (10 choose 3) = 6 /50

The No. of ways to choose 2 non-swimmers from 2 is 1, and the number of ways to choose 1 swimmer from 3 is 3. The total number of ways to choose 3   passengers from 5 is 10

P(A|not B) = (1 choose 2) x (3 choose 1) / (10 choose 3) = 0

Plugging in the values, we get....the followint

P(A) = (6/50) * (1/10) + (0) * (9/10) = 3/ 250

Learn more about probability:
https://brainly.com/question/30034780

#SPJ1

The geometric term that can be used to describe the crossing sign shown is intersecting lines.

In geometry, intersecting lines are two lines that cross one another at a location known as the point of intersection. It is possible to use the point of intersection to solve issues concerning angles, segments, and geometric shapes because it is the sole point that both lines share.

Two pairs of opposite angles that are equal to one another are formed when two lines connect, giving rise to four angles.

Learn more about geometry:https://brainly.com/question/31408211

#SPJ1

1/70 is the probability of having slips numbered 1, 2, 3, and 4 drawn in order from the box.

To calculate the probability of drawing slips numbered 1, 2, 3, and 4 in order from a box containing slips numbered 1 through 8, we need to first find out the total number of possible outcomes when drawing four slips without replacement from the box.

The number of ways to draw 4 slips from a set of 8 slips without replacement is given by the combination formula:

= 8!/4!(8-4)! = 70

This means there are 70 possible outcomes when drawing four slips from the box.

To calculate the probability of drawing slips 1, 2, 3, and 4 in that order, we need to consider that there is only one way to draw the slips in that specific order, out of the 70 possible outcomes.

Therefore, the probability of drawing slips 1, 2, 3, and 4 in order is:

P(1,2,3,4 in order) =  number of favorable outcomes/total number of possible outcomes = 1/70

So the probability of drawing slips numbered 1, 2, 3, and 4 in order from the box is 1/70.

To learn more about probability refer here:

https://brainly.com/question/30034780

#SPJ11

The total length of the race is approximately 28.24 miles.

To determine the total length of the race, we can use the given information: Piotr has completed 24 miles, which represents 85% of the race. We can set up a proportion to find the total length. Let 'x' represent the full length of the race:

(24 miles) / x = 85% / 100%

To solve for 'x', we can first convert the percentage to a decimal by dividing 85 by 100, resulting in 0.85:

24 / x = 0.85

Next, we can cross-multiply:

0.85 * x = 24

Now, we can solve for 'x' by dividing both sides by 0.85:

x = 24 / 0.85

x ≈ 28.24 miles

Therefore, the total length of the race is approximately 28.24 miles. Piotr has completed 85% of this distance, which means he has run 24 miles and has around 4.24 miles remaining to finish the race.

Learn more about percentage here: https://brainly.com/question/24339661

#SPJ11