the formula for the volume of a cylinder is v = πr2h. The cylinder to the right has an exact volule of 500π cubic meters. Find its height

The given statement "the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring." is False.

The union of two events A and B represents the event that at least one of the events A or B occurs. The probability of the union of two events can be calculated using the formula:

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

On the other hand, the intersection of two events A and B represents the event that both events A and B occur. The probability of the intersection of two events can be calculated using the formula:

P(A and B) = P(A) * P(B|A)

where P(B|A) is the conditional probability of B given that A has occurred.

It is possible for the probability of the union of two events to be greater than the probability of the intersection of two events if the two events are not mutually exclusive.

In this case, the probability of both events occurring together (the intersection) may be relatively small, while the probability of at least one of the events occurring (the union) may be relatively high.

In summary, the probability of the union of two events occurring can sometimes be greater than the probability of the intersection of two events occurring, depending on the relationship between the events.

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The fraction of the surface of the cube which is white is 14/27

Given 27 cubes of 1 centimetre are conjoined to form a large cube of 3x3x3

To maximise the value of the surface area, in this case, taken as white, other than the cube in the centre, the rest of the cubes must have their white surface area exposed.

• Total Number of cubes where white surface area is exposed is = 27 – 1 = 26

Although, on each surface of the 3x3x3 cube, there are 9 smaller cube surfaces, and there will be a total of 6 surfaces for the bigger cube.

•      Total number of cube surfaces exposed in blue = 9 * 6 = 54

• Therefore, the greatest fraction in blue= 26/54 = 13/27

Therefore the fraction of the surface of the cube is white is = 1-\(\frac{13}{27}\)= 14/27

The fraction of the surface of the cube which is white is 14/27 is the answer

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The fraction of the surface area of the cube which is white is 14/27

Given 27 cubes of 1 centimetre are conjoined to form a large cube of 3x3x3

To maximise the value of the surface area, in this case, taken as white, other than the cube in the centre, the rest of the cubes must have their white surface area exposed.

• Total Number of cubes where white surface area is exposed is = 27 – 1 = 26

Although, on each surface of the 3x3x3 cube, there are 9 smaller cube surfaces, and there will be a total of 6 surfaces for the bigger cube.

•      Total number of cube surfaces exposed in blue = 9 * 6 = 54

• Therefore, the greatest fraction in blue= 26/54 = 13/27

Therefore the fraction of the surface of the cube is white is = 1-(13/27)

= 14/27

The fraction of the surface of the cube which is white is 14/27 is the answer.

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Answer:

x = 1 and y = -8/3

step-by-step explanation:

solve for x

\(\sf 6x+3\left(\frac{4}{3}x-4\right)=-2\)

\(\sf 6x+4x-12=-2\)

\(\sf \rightarrow 10x = -2 +12\)

\(\sf \rightarrow 10x = 10\)

\(\sf \rightarrow x = 1\)

solve for y

\(\hookrightarrow \sf y = \frac{4}{3} x-4\)

\(\hookrightarrow \sf y = \frac{4}{3} (1)-4\)

\(\hookrightarrow \sf y=-\frac{8}{3}\)

Answer:

x=1 and y=-8/3

Step-by-step explanation:

The easiest way to solve this is by substitution because the first equation is already in slope-intercept form.

First, take y= 4/3x -4 and substitute it into the second equation as follows: 6x + 3(4/3x -4) = -2

Next, simplify that equation to get 6x + 12/3x -12 = -2.

After that, combine all like values: 10x - 12 = -2.

Finally, add 12 to each side and divide by 10 to get x=1.

To find the y-value, substitute x=1 into either equation and solve for x (I'm choosing the first equation). y= 4/3(1) -4

In order to make simplifying this easier, I find that -4 = -12/3.

Finally, simplify: y= 4/3 - 12/3 = -8/3.

The solution to the system of equations is (1, -8/3), or x=1 and y=-8/3.

An hour later, the number of bacteria in the population was 6656.

To solve the how many bacteria are there in the population, use the exponential growth function.

Exponential growth and decay functions are written in standard form as

A = A₀•b^kt

where A =  final amount

A₀ = initial amount = 104

b = growth factor = 2

k = growth rate = 1/10 minutes

t = time = 1 hour = 60 minutes

Plug in the values to the equation and solve for the final amount, A.

A = A₀•b^kt

A = 104•(2)^(1/10 minutes)(60 minutes)

A = 104•(2)^(6)

A = 104•64

A = 6656

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The standard error of the sampling distribution of the sample proportion is given by:

The standard error for the sampling distribution of the sample proportion when n = 50 is approximately 0.059.

SE = sqrt[p(1-p)/n]

where p is the population proportion and n is the sample size.

For n = 20 and p = 0.12, we have:

SE = sqrt[(0.12)(1-0.12)/20] ≈ 0.083

Therefore, the standard error for the sampling distribution of the sample proportion when n = 20 is approximately 0.083.

For n = 50 and p = 0.12, we have:

SE = sqrt[(0.12)(1-0.12)/50] ≈ 0.059

Therefore, the standard error for the sampling distribution of the sample proportion when n = 50 is approximately 0.059.

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Jim purchased notebooks. they were dollars each. Therefore, the equation to represent the total cost that Jim paid is:y = x dollars.

The amount or equivalent paid or charged for something : price. The average cost of a college education has gone up dramatically.

the outlay or expenditure (as of effort or sacrifice) made to achieve an object. He achieved fame, but at the cost of losing several friends.

Given that Jim purchased notebooks which were x dollars each, we can write an equation to represent the total cost that Jim paid as follows:

Let the total cost Jim paid be y.

Then, since he purchased x notebooks, the equation that represents the total cost that Jim paid is:

y = x dollars

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a)The total inside length of the curved ends of the track will be 25.13 meters

b)The total distance around the inside of the track will be 275.13 meters

c)The area inside the track is 10050 square meters.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.

Given that:-

A stadium has a central rectangular area 125m long by 80m wide. there are two semi-circular ends. a running track goes all the way around.

a) what is the total inside length of the curved ends of the track?

The length of the curved track means it is a perimeter of the circle so the radius of the semicircle will be 4 meters.

So the length will be = π r + πr = 2 πr

                                  = 2 x π x 4 = 25.13

b) what is the total distance around the inside of the track?

The total distance of the track will be the sum of the length of the two semicircles and the longer side of the rectangle.

Total length = 125 + 125 + 25.13

                     = 275.13 meters

c) what is the area inside of the track?

The area will be equal to the area of the two semicircular tracks and the rectangular track.

Total Area = Area of semicircle + Area of semicircle + Area of rectangle

                  = ( π/2 ) r² + (π/2) r² + ( L x W )

                  =  π  r² + (  L x W)

                  = π ( 4 )² + ( 125 x 8 )

                  = 10050.26 square meters.

Therefore the total inside length of the curved ends of the track will be 25.13 meters. The total distance around the inside of the track will be 275.13 meters. The area inside the track is 10050 square meters.

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Answer:

x = 2

Step-by-step explanation:

Since this is an isosceles triangle the unmarked side is also √2

Since this is also a right triangle use the pythagorean theorem to find x.

x² = (√2)² + (√2)²

x² = 2 + 2

x² = 4

x = 2

The value of x is 2.

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

Given:

H= x, P= √2, B= √2

Now, using Pythagoras theorem

H² = P² + B²

x² = (√2)² + (√2)²

x² = 2 + 2

x² = 4

x = 2

Hence, the value of x is 2.

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The value of b² is 125.44 units since b equals 11.2 units when c equals 13 units and an equals 6.6 units.

The Pythagorean theorem is a mathematical theorem that asserts that the square of the length of the hypotenuse (the side opposite the right angle) in a right-angled triangle is equal to the sum of the squares of the other two sides. It is mathematically stated as c2 = a2 + b2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

Here,

c=13²

a=6.6²

a²+b²=c²

b=√(c²-a²)

=√(13²-6.6²)

b=11.2 units

b²=125.44 units

The value of b² is 125.44 units as b is equal to 11.2 units when c is 13 units and a is 6.6 units.

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Answer:

Joe will run 22.08 miles in 230 minutes.

Step-by-step explanation:

so Joe running the miles in 1 minute is = 12/125 = 0.096 miles

As Joe runs 0.096 miles in one minute.

Thus, in 230 minutes, Joe will run = 0.096 × 230 = 22.08 miles

Therefore, Joe will run 22.08 miles in 230 minutes.

Answer:

113.1 cm³

Step-by-step explanation:

diameter = 2 X radius

Volume of sphere = (4/3) X π X r ³

= (4/3) π (3)³

= 36π

= 113.1 cm³ to nearest tenth

Answer:92.84

Step-by-step explanation: 39+27+13.5+13.5 because the two sides are longer than 12

The perimeter of the trapezium is 143.94 ft.

We have,

The perimeter of an isosceles trapezium can be found by adding the lengths of all four sides.

In this case, the trapezium has height = 12 ft and parallel sides of length 27 ft and 39 ft.

To find the length of the non-parallel sides we can use the Pythagorean theorem:

a² = (39 - 27/2)² + 12²

a² = 1440

a ≈ 37.95 ft

Therefore,

The perimeter of the trapezium is:

P = 27 + 39 + 2a

P ≈ 27 + 39 + 2(37.95)

P ≈ 143.9 ft

Rounding to the nearest hundredth place,

we get P ≈ 143.94 ft.

Thus,

The perimeter of the trapezium is 143.94 ft.

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Answer:

-5/4

Step-by-step explanation:

slope = rise/run

Start at the lower right point. Go up 5. The rise = 5. Go left 4. The run -4.

slope = 5/-4 = -5/4

Answer:

Option c

Step-by-step explanation:

multiply the expression in the parentheses by 4 and you get 12x+16

a doesn't fit, x³ is x*x*x, not plus

b 14x-2x is 12x, not 16x

d got a 5x expression with no correspondence on the other side and 12x² isn't 17x²

Answer:

x= -2; y= -2

Step-by-step explanation:

The opposite sides of a parallelogram are congruent, and therefore we can make two observations:

9=-9x-9
19=-10y-1

Then we can just solve each of the equations to get x and y:

9 = -9x - 9
+ 9       +9

18=-9x

----------
-9

-2=x

19=-10y-1
+1        +1

20=-10y
------------

-10

-2=y

Answer:

Step-by-step explanation:

$18-$7.50= $10.50

Answer:

f(x)=3x

f(x)=x+2

f(x)=3√3+x2

Step-by-step explanation:

By using the law of sine, the measure of ∠C is 39°

Law of sine:

Law of sine refers the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.

Given,

Here we have the triangle.

Now, we have to find the angle ∠C.

While we looking into the given diagram,

We have the length of,

AB = 6

AC = 9

∠B = 105°

So, based on the law of sine it can be written as,

=> sin 105° / 9 = sin x°/6

Apply the value of sin 105° = 0.97, then we get,

=> 0.97/9 = sin x° / 6

Cross multiply them, then we get,

=> 5.82/9 = sin x°

=> 0.64 = sin x°

=> x = sin⁻¹ (0.64)

=> x = 39°

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Answer:

\(A_X=\frac{15x^2}{16}\)

Step-by-step explanation:

From the question we are told that:

Base of Flower bed \(b=\frac{x}{2}\)

Height of Flower bed \(h=\frac{x}{4}\)

Generally the equation for Area of garden left A_X is mathematically given by

 \(A_X=Area\ of\ Garden\ A_g\ - Area\ of\ flower\ bed\ A_f\)

Where

 \(A_f=b*h\)

 \(A_f=\frac{1}{2}*\frac{x}{2}*\frac{x}{4}\)

 \(A_f=\frac{x^2}{16}\)

Therefore

 \(A_X= A_g - A_f\)

 \(A_X=x^2-\frac{x^2}{16}\)

 \(A_X=\frac{15x^2}{16}\)

b) 50 hectares of white spruce trees are required to make the paper.

This estimate is based on the assumption that a large metropolitan American newspaper prints about 500,000 copies on an average weekday and each newspaper requires roughly 0.1 square meters of paper. To produce 500,000 newspapers, we need about 50,000 square meters or 5 hectares of paper. However, it takes about 10 trees to produce one ton of newsprint paper, so 5 hectares of paper require approximately 500 tons of paper.

Thus, it would take about 50 hectares of white spruce trees to produce enough paper for a typical midweek issue of a large metropolitan American newspaper for one day. It's worth noting that this is just an estimate and the actual number could vary depending on the newspaper's circulation, page count, and paper size.

The answer is approximately 50 hectares of white spruce trees.

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\(625=5^{7x-3}\implies 5^4=5^{7x-3}\implies 4=7x-3 \\\\\\ 7=7x\implies \cfrac{7}{7}=x\implies 1=x\)

Answer:

3 and 1/4

Step-by-step explanation:

Answer:

the slope of the line is 2

Step-by-step explanation:

Answer:

m = 4

Step-by-step explanation:

Think of the slope as rise/run

each time you move 4 points up you move 1 point to the right

giving you 4/1  

Answer:

The minimum value of the function is 12

Answer:

d. multiply the second equation by 4

After answering the provided question, we can state that As a result, expression rather than a rating of 6, it would be more appropriate to use the median to describe the centre of this data set.

An expression in mathematics is a collection of interpretations, digits, and transnational corporations that resemble a causative link or regimen. A real number, a mutable, or a combination of the two can be used as an expression. Mathematical operators include extension, subtraction, rapid spread, separation, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.

Because the dot plot is not symmetrical and the distribution appears to be skewed towards higher ratings, a rating of 6 may not be a good description of the centre of this data set. The numbers 8, 9, and 10 are more common than the numbers 0-7, indicating that the data set has a right skew.

As a result, the centre of the data set may be better described by a measure of central tendency that accounts for data skewness, such as the median.

As a result, rather than a rating of 6, it would be more appropriate to use the median to describe the centre of this data set.

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If sentence 6 states that ¬C is true, and sentence 7 presents a conditional statement with C as the antecedent and Q as the consequent, we can use modus ponens to infer that Q is false.

Modus ponens is a deductive reasoning rule that allows us to derive a conclusion from a conditional statement and its antecedent. Therefore, we can apply modus ponens to sentence 7 given that we know ¬C from sentence 6.
Since from sentence 6 we know ¬C, we can apply modus ponens to sentence 7. To do this, follow these steps:
1. Identify the premises: One premise is sentence 6, which states ¬C. The other premise should be a conditional statement, such as "If ¬C, then P" (replace P with the relevant proposition).
2. Apply modus ponens: Modus ponens is a rule of inference that allows us to deduce a conclusion from the given premises. If we have the premises "If ¬C, then P" and "¬C", we can conclude "P" using modus ponens.
3. State the conclusion: After applying modus ponens, we can conclude "P" based on the given premises, which include sentence 6 (¬C) and the conditional statement.

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To answer this question, we can proceed as follows:

We have that the complete way to obtain this division is that the quotient is equal to 1.38.

However, in a division in which we have the remainder, we can express this division as:

D = d * C + R

Where

D is the dividend (69)

d is the divisor (50)

C is the quotient.

R is the remainder

So having the remainder, and not having decimals part in the division, we can say that this division is equal to:

69 = 50 * 1 + 19.

We can express this as follows:

69 is the Dividend, 50 is the divisor, 1 is the quotient, and 19 is the remainder.

Therefore, the division 69 / 50 = 1 + 19. We can divide the number 69 by 50 and we have that we can divide it in 1, but we have 19 as the remainder, then we have:

69 = 50 * 1 + 19

Answer:

0= -42

Step-by-step explanation:

Simplify then add 6 to both sides after simplify again and subtract 2x from both sides then finally combine like terms and simplify the expression.

Answer:

4^-8

Step-by-step explanation:

When multiplying two exponents with the same base, in this case, 4, you need to add the two powers (-6 + -2), to get -8.

Answer: 41%

Step-by-step explanation:

15 girls prefer biology.

Find the boys who prefer biology;

There are 36 girls in total so;

= 100 - 36

= 64 boys interviewed

14 boys prefer Physics

= 64 - 14

= 50 boys prefer Biology and Chemistry

7 out of the 31 who prefer chemistry are girls so the boys who prefer chemistry are;

= 31 - 7

= 24 boys

Boys who prefer Biology;

= 50 - 24

= 26 boys

Total who prefer biology;

= 15 girls + 26 boys

= 41 students

Percentage = 41/100 = 41%