It is found that 15% of pupils at a school do not jog or swim or cycle, 8% do all three activities, 15% swim and cycle but do not jog, 15% do both jog and swim, 20% swim only, 18% cycle only and 42% do two or more activities
a) Define the cardinality of the complement of set
b) Workout the percentage of pupils who
i) Do both jog and cycle
ii) Swim or cycle
iii) Do not swim
iv) Do not jog, swim and cycle

1. The volume of water on the roof in cm and m is

240000 and 0.24 respectively.

2. The mass of water that fell on the roof is 2400kg

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also the capacity of a container.

Volume = l× b × h

l = 7.5 m

b = 4m

h = 12mm = 0.012

volume = 5 × 4 × 0.012

= 0.24 m³

in centimeter,

= 0.24 × 100³

= 240,000 cm³

2. The density of water is 1g/cm³

1g = 0.01kg

= 0.01kg/cm³

density = mass/volume

mass = density × volume

= 0.01 × 240000

= 2400 kg

therefore the mass of water that fell on the roof is 2400kg

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The order from utmost precise to least precise is

8.431 grams, 15.46 seconds, 980 meters, 900 miles.

Ranking the following in order from utmost precise to least precise

8.431 grams ( utmost precise) This dimension has the loftiest position of perfection as it includes three decimal places.

15.46 seconds - This dimension has two decimal places, indicating a advanced position of perfection compared to whole figures.

980 meters  measures This dimension is a whole number and lacks decimal places, making it less precise than measures with decimal values.

900 long hauls( Least precise) This dimension is also a whole number and lacks decimal places, making it the least precise among the given options.

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To determine the correct option, we need to check if the rates and times given in each option satisfy the condition of being inversely proportional.

Option A: 4 mph for 2.25 hours and 6 mph for 1.5 hours.

The product of the rate and time is not consistent: (4 mph) × (2.25 hours) = 9 and (6 mph) × (1.5 hours) = 9. Therefore, this option does not satisfy the condition.

Option B: 6 mph for 1.5 hours and 5 mph for 1.25 hours.

The product of the rate and time is not consistent: (6 mph) × (1.5 hours) = 9 and (5 mph) × (1.25 hours) = 6.25. Therefore, this option does not satisfy the condition.

Option C: 5 mph for 2 hours and 4 mph for 3 hours.

The product of the rate and time is consistent: (5 mph) × (2 hours) = 10 and (4 mph) × (3 hours) = 12. Therefore, this option satisfies the condition.

Option D: 4.5 mph for 3 hours and 6 mph for 4 hours.

The product of the rate and time is consistent: (4.5 mph) × (3 hours) = 13.5 and (6 mph) × (4 hours) = 24. Therefore, this option satisfies the condition.

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The probability that she rolls an odd number, or a number less than 10 is 0.7

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

Die = 20-sided

In the 20-sided die, we have

A = Odd numbers = 10

B = Numbers less than 10 = 9

A and B = Odd numbers less than 10 = 5

So, we have

P(A) = 10/20

P(B) = 9/20

P(A and B) = 5/20

The probability expression P(A or B)  can be calculated using

P(A or B) = P(A) + P(B) - P(A and B)

When the given values are substituted in the above equation, we have the following equation

P(A or B) = 10/20 + 9/20 - 5/20

Evaluate

P(A or B) = 0.7

Hence, the value of the probability P(A or B) is 0.7

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The slope of the given graph is determined as 1/3.

The slope of a line is a measure of its steepness of the graph. Mathematically, slope is calculated as rise over run or  change in y divided by change in x.

The formula is given as;

slope = Δy / Δx

where;

The slope of the given graph is calculated as follows;

choose the following coordinate points;

( x₁, y₁) = (-6, 0 )

( x₂, y₂) = ( 6 , 4 )

The slope = ( y₂ - y₁ ) / ( x₂ - x₁)

slope = ( 4 - 0 ) / ( 6 - - 6)

slope = ( 4 ) / ( 12)

slope = 1 / 3

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17.5 miles is the runner training distance in the tenth week.

We have,

A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Given,

The first​ week, she runs 4 miles during each training session

Each​ week, she increases her distance by 1.5 miles.

4,5.5,7,8.5....

The given sequence is a Arithmetic sequence, a is the first term and d is common difference

a=4,d=5.5

We need to find the distance in the tenth week.

n=10

aₙ=a+(n-1)d

a₁₀=4+(10-1)(1.5)

a₁₀=4+9(1.5)=4+13.5=17.5

Hence 17.5 is the runner training distance in the tenth week.

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complete question:

A runner is training for a marathon. The first​ week, she runs 4 miles during each training session. Each​ week, she increases her distance by 1.5 miles. Write a recursive definition for this sequence and use this definition to find her training distance in the tenth week.

Answer:

Length = 6.49 cm

Step-by-step explanation:

The formula for area of a rectangle is

A = lw, where

Since we're already given the area and width and want to find the length, we can first rewrite the area formula in terms of l:

A/w = l

Now, we can plug in 25.311 for A and 3.9 for w to solve for l, the length:

25.311 / 3.9 = l

6.49 cm = l

We can check that 6.49 is the correct length by plugging everything into the regular area formula and checking that we get 25.311:

25.311 = 6.49 * 3.9

25.311 = 25.311

For column A:

P(male | snickers) = number of males who like Snickers / total number of people who like Snickers = 230/410 = 23/41

P(M&M peanut | female) = number of females who like M&M peanuts / total number of females = 50/460 = 5/46

P(female | Reese's) = number of females who like Reese's / total number of people who like Reese's = 160/370 = 16/37

P(M&M plain | male) = number of males who like M&M plain / total number of males = 55/565 = 11/113

Therefore, the answers are:

A. 23/41

B. 5/46

C. 16/37

D. 11/113

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The magnitude and direction of the vectors is 12.65 and 161.6⁰ respectively.

The magnitude and direction of the vectors is calculated as follows;

The given vector, u = 2, v = 4

when the vectors are multiplied by 2 and 3 respectively, we will have;

2u = 2 x 2 = 4

3v = 3 x 4 = 12

The components of the vectors is calculated as follows;

2u (y component) = 4 x sin(90) = 4

2u (x component) = 4 x cos (90) = 0

3v (y component) = 12 x sin(180) = 0

3v (x component) = 12 x cos(180) = -12

sum of x and y component of the vectors is calculated as;

∑x = 0 -12 = -12

∑y = 4 + 0 = 4

The magnitude of the vectors is calculated as;

2u + 3v = √( (-12)² + 4²) = 12.65

The direction of the vectors is calculated as follows;

θ = arc tan (y/x)

θ = arc tan (4/-12)

θ = -18.4⁰ = 161.6⁰

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The sprinter's speed before he increased it was 8.2 miles per hour.

To find the sprinter's speed before he increased it, we can use the following steps:
Step 1: Identify the final speed and the increase in speed.
The sprinter's top speed is 23 miles per hour, and he increased his speed by 14.8 miles per hour.
Step 2: Subtract the increase in speed from the final speed.
We can determine the sprinter's initial speed by subtracting the increase in speed (14.8 miles per hour) from the final speed (23 miles per hour).
Initial speed = Final speed - Increase in speed
Initial speed = 23 miles per hour - 14.8 miles per hour
Step 3: Calculate the initial speed.
Now, we can perform the subtraction:
Initial speed = 8.2 miles per hour
So, the sprinter's speed before he increased it was 8.2 miles per hour.

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The sprinter's speed before he increased his speed was approximately 8.2 miles per hour. The correct option is D

We need to subtract the increase in speed from his top speed.

Assume that "x" miles per hour represents the sprinter's initial speed (before to the increase).

The sprinter improved his speed by 14.8 miles per hour, as indicated by the information, to reach a top speed of 23 miles per hour. This can be said as follows:

x + 14.8 = 23

To find the value of "x," we can solve this equation:

x = 23 - 14.8

x ≈ 8.2

Therefore, the sprinter's speed before he increased his speed was approximately 8.2 miles per hour.

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Answer to two decimal places: 34.13%
Approximately 34.13% of college women are between 65 and 68 inches tall.

The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations of the mean, and approximately 99.7% falls within three standard deviations of the mean.
In this case, we are given that the mean height of college women is 65 inches and the standard deviation is 3 inches.
z = (x - μ) / σ
z = (65 - 65) / 3
z = 0

To find the z-score for a height of 68 inches:
z = (x - μ) / σ
z = (68 - 65) / 3
z = 1
Using the standard normal distribution table, we can find that the area between z = 0 and z = 1 is approximately 0.3413.

The, approximately 34.13% of college women are between 65 and 68 inches tall.

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Answer:

The answer cannot be given as exact prices are not listed. How to do it could be explained as below:

Step-by-step explanation:

The first thing you have to do is find the price of the shoes. Then you take $250 (the amount of money in the gift card) and subtract it from the price of the shoes.

Then, we take the number we got from above and divide it by how much 1 pair of socks costs. You could get a decimal, and if you do, pretend that the numbers after the decimal don't exist. This number is the number of possible socks you could order only using the gift card.

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Therefore, the probability of drawing exactly 3 aces, 2 queens, and 1 king is approximately 0.000682.

We can solve this problem using the multiplication rule for independent events. The probability of drawing a specific card from a standard deck is 1/52, since there are 52 cards in the deck and each is equally likely to be drawn. We can use this probability to find the probability of drawing a specific combination of cards.

(a) To find the probability of drawing exactly 3 aces, 2 queens, and 1 king, we can break it down into three steps:

Find the probability of drawing exactly 3 aces: There are 4 aces in the deck, so the probability of drawing an ace on the first draw is 4/52. Since we need exactly 3 aces, the probability of drawing 3 aces and 3 non-aces (out of the remaining 48 cards) is given by the binomial probability formula:

P(3 aces) = (4/52)^3 * (48/52)^3 * C(6,3)

where C(6,3) is the number of ways to choose 3 cards out of 6. Using a calculator, we get:

P(3 aces) = 0.0080

Find the probability of drawing exactly 2 queens: There are 4 queens in the deck, so the probability of drawing a queen on the first draw is 4/52. Since we need exactly 2 queens, the probability of drawing 2 queens and 4 non-queens (out of the remaining 48 cards) is given by:

P(2 queens) = (4/52)^2 * (48/52)^4 * C(6,2)

where C(6,2) is the number of ways to choose 2 cards out of 6. Using a calculator, we get:

P(2 queens) = 0.2123

Find the probability of drawing exactly 1 king: There are 4 kings in the deck, so the probability of drawing a king on the first draw is 4/52. Since we need exactly 1 king, the probability of drawing 1 king and 5 non-kings (out of the remaining 48 cards) is given by:

P(1 king) = (4/52)^1 * (48/52)^5 * C(6,1)

where C(6,1) is the number of ways to choose 1 card out of 6. Using a calculator, we get:

P(1 king) = 0.4017

Now we can use the multiplication rule to find the probability of drawing exactly 3 aces, 2 queens, and 1 king:

P(exactly 3 aces, 2 queens, 1 king) = P(3 aces) * P(2 queens) * P(1 king)

= 0.0080 * 0.2123 * 0.4017

= 0.000682

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The area and circumference of the circles are solved

Given data ,

Let the area and circumference be represented as A and C

Now , the circles are

Circumference of circle = 2πr

Area of the circle = πr²

a)

Radius = 7 m

C = 2 ( π ) ( 7 )

C = 43.98 m

A = π ( 7 )²

C = 153.938 m²

b)

Diameter = 30 feet

C = 2 ( π ) ( 15 )

C = 94.24 feet

A = π ( 15 )²

C = 706.858 feet²

c)

Radius = 10.2 inches

C = 2 ( π ) ( 10.2 )

C = 64.088 inches

A = π ( 10.2 )²

C = 326.85 inches²

d)

Diameter = 9 mm

C = 2 ( π ) ( 4.5 )

C = 28.274 mm

A = π ( 4.5 )²

C = 63.617 mm²

Hence , the circles are solved

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The angle of depression that each chain makes with the ceiling are approximately 67° and 56°.

To solve the problem, use trigonometry. Let's call the angle of depression that the first chain makes with the ceiling x, and the angle of depression that the second chain makes with the ceiling y. Then:

In triangle ABC, where A is one of the hooks, B is the other hook, and C is the point where the chains meet:

AC = 1.9 m

BC = 2.2 m

angle BAC = 86°

Find angle BCA, which is the angle of depression that chain AC makes with the ceiling. Use the law of sines to find this angle:

sin BCA / AC = sin BAC / BC

sin BCA = AC sin BAC / BC

sin BCA = 1.9 sin 86° / 2.2

sin BCA ≈ 0.925

BCA ≈ 67.3°

So the angle of depression that chain AC makes with the ceiling is approximately 67 degrees.

Similarly, find the angle of depression that chain BD makes with the ceiling by considering triangle ABD:

AD = 2.8 m

BD = 2.2 m

angle ADB = 86°

Using the law of sines:

sin ADB / BD = sin BAD / AD

sin ADB = BD sin BAD / AD

sin ADB = 2.2 sin 86° / 2.8

sin ADB ≈ 0.836

ADB ≈ 56.4°

So the angle of depression that chain BD makes with the ceiling is approximately 56 degrees.

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Answer:

0.8

Step-by-step explanation:

In order to find its decimal form, we first need to divide the fraction.

[tex]4\div 5=0.8[/tex]

In decimal form, 4/5 = 0.8. The number is already rounded to the nearest tenth.

Answer:

The area of the right triangle is approximately 77.5 square yards.

Answer:

77.5 yards

Step-by-step explanation:

area of right-angled triangle = 0.5 x 7.75 X 20

= 10 X 7.75

=77.5 yards

Answer:

-------------------------------

Simplify in steps:

Answer:

Step-by-step explanation:

Here Is a Quick Explanation :)

To find the axis of symmetry and the vertex of the function, we can use the fact that the function is recursive, and we can write:

f(x) = f(x-1)² + 7

f(x-1) = f(x-2)² + 7

f(x-2) = f(x-3)² + 7

...

f(1) = f(0)² + 7

If we substitute the last equation into the previous one, we get:

f(x-1) = (f(0)² + 7)² + 7

f(x) = ((f(0)² + 7)² + 7)² + 7

This shows that the function depends only on the initial value f(0), and we can use this fact to find the axis of symmetry and the vertex.

To find the axis of symmetry, we need to find the value of x that makes f(x) equal to f(-x). We can write:

f(-x) = f(-(x-1))² + 7 = f(-x+1)² + 7

Now, if we substitute f(x) = f(x-1)² + 7 into the last equation, we get:

f(-x) = (f(x-1)² + 7)² + 7 = f(x)² + 7

This means that the axis of symmetry is the line x = 0, and not y = 7 as stated in option A.

To find the vertex, we need to find the maximum or minimum value of the function. Since f(x) = f(x-1)² + 7, the function is increasing if f(x-1) > -7, and decreasing if f(x-1) < -7. Since f(0) = 7, we can conclude that the function is increasing on the interval -∞ < x < 1, and decreasing on the interval x > 1. Therefore, the vertex is at x = 1, and the corresponding value is f(1) = 7.

Therefore, the correct statements are:

The axis of symmetry of f(x) is x = 0.

The vertex of the function is (1, 7).

f is increasing on the interval -∞ < x < 1.

f is decreasing on the interval x > 1.

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{7}{4}}x+2\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{7}{4}} ~\hfill \stackrel{reciprocal}{\cfrac{4}{7}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{4}{7} }}[/tex]

so we're really looking for the equation of a line whose slope is -4/7 and it passes through (2 , -2)

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{-2})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{4}{7} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{- \cfrac{4}{7}}(x-\stackrel{x_1}{2}) \implies y +2 = - \cfrac{4}{7} ( x -2) \\\\\\ y+2=- \cfrac{4}{7}x+\cfrac{8}{7}\implies y=- \cfrac{4}{7}x+\cfrac{8}{7}-2\implies {\Large \begin{array}{llll} y=- \cfrac{4}{7}x-\cfrac{6}{7} \end{array}}[/tex]

The probability of getting TTH or THH is (1/2) * (1/2) * (1/2) = 1/8, as each toss is independent and has a probability of 1/2.

To find the probability that a fair coin is flipped a multiple of three times before coming up heads, we can consider the possible outcomes. Let's denote H as heads and T as tails.

The first toss can either be T or H with equal probabilities of 1/2 each. If it's H, the experiment ends. If it's T, we move to the second toss.

For the second toss, the possibilities are TH or TT. If it's TH, the experiment ends. If it's TT, we move to the third toss.

For the third toss, the possibilities are TTH, TTT, or THH. If it's TTH or THH, the experiment ends. If it's TTT, we move to the fourth toss.

Following this pattern, we can see that the experiment ends when we get TTH, THH, TTTTH, TTTTTTH, or any sequence of T's followed by H. These are the outcomes where the coin is flipped a multiple of three times before coming up heads.

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Answer:

It will take him 9 hours to mow 12 lawns.

Step-by-step explanation:

We can use a proportion. We see that the answer choices are in hours, so let's first convert the given information to hours.

180 minutes × (1 hour)/(60 minutes) = 3 hours

180 minutes to mow 4 lawns = 3 hours to mow 4 lawns

Proportion:

3 hours is to 4 lawns as x hours is to 12 lawns

3/4 = x/12

4x = 3 × 12

4x = 36

x = 9

Answer: It will take him 9 hours to mow 12 lawns.

The volume of the cylinder is 36.8 cm³

We have,

The diameter of the cylinder = 2.5 cm

The radius of the cylinder = 2.5 / 2 = 1.25 cm

The height of the cylinder.

= 2.5 + 2.5 + 2.5

= 7.5 cm

Now,

The volume of the cylinder.

= πr²h

= 3.14 x 1.25 x 1.25 x 7.5

= 36.8 cm³

Thus,

The volume of the cylinder is 36.8 cm³

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Answer: c

Step-by-step explanation:

The coordinates of the quadrilateral after a reflection over the line with equation y = x are:

Ordered pair (1, -3).

Ordered pair (2, -4).

Ordered pair (5, -5).

Ordered pair (5, -3).

In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative.

Furthermore, a reflection across the line y = x would interchange (switch) the x-coordinate and y-coordinate and this is given by this transformation rule:

(x, y)                                    →              (y, x)

Ordered pair (-3, 1)    →        Ordered pair (1, -3).

Ordered pair (-4, 2)    →        Ordered pair (2, -4).

Ordered pair (-5, 5)    →        Ordered pair (5, -5).

Ordered pair (-3, 5)    →        Ordered pair (5, -3).

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The volume of Cylinder #2 is about 157 cm³ greater than the volume of Cylinder.#1 The correct answer is D. 157 cm³.

To compare the volumes of the two cylinders, we will use the formula for the volume of a cylinder, which is V = πr²h, where V is the volume, r is the radius, and h is the height.
Cylinder #1:
Radius (r1) = 5 cm
Height (h1) = 18 cm
Volume of Cylinder #1 (V1) = π × r1² × h1 = π × 5² × 18 = π × 25 × 18 = 450π cm³
Cylinder #2:
Radius (r2) = 5 cm (same as Cylinder #1)
Height (h2) = 20 cm
Volume of Cylinder #2 (V2) = π × r2² × h2 = π × 5² × 20 = π × 25 × 20 = 500π cm³
Now, we will find the difference in volumes:
Difference = V2 - V1 = 500π cm³ - 450π cm³ = 50π cm³ ≈ 157 cm³
So, the volume of Cylinder #2 is about 157 cm³ greater than the volume of Cylinder #1. The correct answer is D. 157 cm³.

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The correct answer is not listed among the given options. None of the listed options is a CSS3 2D transformation function that resizes an object by a factor of x horizontally.

Here are brief explanations of the given options:

a. scaleY(y) - This function scales an object vertically by a factor of y.

b. rotate(angleY) - This function rotates an object around the y-axis by the specified angle.

c. translateY(offY) - This function translates an object vertically by the specified offset.

d. skewY(angleY) - This function skews an object along the y-axis by the specified angle.

To resize an object horizontally by a factor of x, you can use the scaleX(x) function. This function scales an object horizontally by a factor of x.

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Answer:

he needs 9 cans

Step-by-step explanation:

first,

43L/5L

= 8.6 cans

8.6 cans is not logical therefore u need to round up to 9 cans

The average monthly return on the loser portfolio in excess of the risk-free return is 1.26 percent, the standard deviation of its monthly excess returns is 8.7 percent, the monthly Sharpe ratio is 0.145, the annualized Sharpe ratio is 0.5, and the annualized Sharpe ratio of the overall market index is 0.54.

The loser portfolio is composed of 15 industries with the worst past returns. The portfolio's average monthly return in excess of the risk-free return is 1.26 percent, while its standard deviation of monthly excess returns is 8.7 percent. The monthly Sharpe ratio is 0.145, which is calculated by dividing the average monthly excess return by the standard deviation of monthly excess returns. The annualized Sharpe ratio is 0.5, which is the monthly Sharpe ratio multiplied by the square root of 12. The annualized Sharpe ratio of the overall market index is 0.54.

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