pi is an important symbol in mathematics. what does it look like

Answer:

Long solution

Step-by-step explanation:

(a) Let the height of the cone be h cm. The volume of the hemisphere is given by (1/2)(4/3)πr³ = (2/3)πr³. The volume of the solid is the sum of the volumes of the hemisphere and the cone, which is (2/3)πr³ + (1/3)πr²h. Since the volume of the hemisphere is one third of the volume of the solid, we have:

(2/3)πr³ = (1/3)πr²h

Simplifying, we get:

2r = h

Therefore, h is expressed in terms of r as h = 2r.

(b) The slant height of the cone can be found using the Pythagorean theorem. Let l be the slant height, then we have:

l² = r² + h²

Substituting h = 2r, we get:

l² = r² + (2r)² = 5r²

Taking the square root of both sides, we get:

l = r√5

Since k is an integer, we can write:

l = Vk cm, where k is an integer

Comparing the two expressions, we get:

Vk = r√5

Therefore, the value of k is k = ⌊r√5⌋, where ⌊x⌋ denotes the largest integer less than or equal to x.

(c) The total surface area of the solid is the sum of the curved surface area of the cone, the curved surface area of the hemisphere, and the area of the circular base of the cone. We have:

Curved surface area of the cone = πr l = πr(r√5) = πr²√5

Curved surface area of the hemisphere = 2πr²

Area of the circular base of the cone = πr²

Therefore, the total surface area of the solid, in cm², is given by:

πr²√5 + 2πr² + πr² = (πr²)(√5 + 3)

The pattern of the two charts and fill in the missing numbers is as follows:

For time 1,2, 3, 4, 5, 6, 7,8,9, and 10 the distance is 4, 8, 12, 16, 20, 24,28,32, 36, and 40 respectively.

When the time is increased by one(1) the corresponding distance is increased by 4.

Hence the pattern of increase in distance is:

T₁ = 4

T₂ = (4+ 4)

T₂ = 8

T₃ = (8 + 4)

T₃ = 12

T₄ = (12 + 4)

T₄ = 16

T₅ = (16 + 4)

T₅ = 20

T₆ = (20 + 4)

T₆ = 24

T₇ = (24 + 4)

T₇ = 28

T₈ = (28 + 4)

T₈ = 32

T₉ =  (32 + 4)

T₉ = 36

T₁₀ =  (36 + 4)

T₁₀ = 40

Learn more about Quantitative Reasoning on

https://brainly.com/question/15566375

#SPJ1

The 95% confidence interval for the difference between the proportion of the population who would survive at least 15 years can be used to estimate the range within which the true difference lies.

It provides a measure of uncertainty around the point estimate. The confidence interval can be interpreted as follows: we are 95% confident that the true difference in proportions of the population who would survive at least 15 years falls within the calculated interval. To construct the confidence interval, we first need to obtain sample data from the population. Let's assume we have collected data from two independent samples. From Sample 1, we find that out of n1 individuals, x1 survive at least 15 years. Similarly, from Sample 2, we have n2 individuals, with x2 surviving at least 15 years. To calculate the confidence interval, we use the formula: CI = (p1 - p2) ± Z * sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)) Where p1 = x1 / n1 and p2 = x2 / n2 are the sample proportions, and Z is the critical value corresponding to the desired confidence level (in this case, 95%). The critical value is determined based on the standard normal distribution. Once we have the confidence interval, let's say [lower limit, upper limit], we can interpret it as follows: We are 95% confident that the true difference in proportions between the two populations who would survive at least 15 years lies between the lower limit and the upper limit. In other words, there is a high likelihood that the actual difference falls within this range. The confidence interval allows us to make inferences about the population based on our sample data. It provides a range of plausible values for the difference in proportions, taking into account the variability of the sample. The wider the confidence interval, the greater the uncertainty in our estimate. Conversely, a narrower interval indicates a more precise estimation.

learn more about confidence interval here: brainly.com/question/29680703

#SPJ11

Answer:

A

Step-by-step explanation:

observe from the graph the curve hits the axis where y = 0 and x =-10 and x= 2

so points ( -10,0) and (2 ,0)

Answer:

\(17\)

Step-by-step explanation:

Since h=17 we use that

\(h(t) = \sqrt{17t} \)

\(h(t) = \sqrt{289} = 17\)

Yes, the mysteries equal 0.06 of the total books.

Marcella said that the mysteries equal 0.06 of the total books.

To check the mysteries equal 0.06 of the total books is correct or not.

We can follow these steps:

1. Identify the total number of books and the number of mysteries: Marcella read 100 books, and 60 of them were mysteries.

2. Calculate the fraction of mysteries: Divide the number of mysteries (60) by the total number of books (100) to find the fraction of mysteries.

3. Compare the fraction with Marcella's claim: If the calculated fraction equals 0.06, then she is correct.

Now let's perform the calculations:

60 mysteries ÷ 100 total books = 0.6

Since 0.6 ≠ 0.06, Marcella's claim that the mysteries equal 0.06 of the total books is incorrect. In reality, mysteries make up 0.6 or 60% of the total books she read.

A model to support this answer could be a pie chart, where the circle represents the 100 books, and the mysteries portion is shaded in. By dividing the circle into 10 equal sections, the mysteries would fill 6 of those sections, which represents 60% of the total books.

Learn more about books here,

https://brainly.com/question/31410086

#SPJ11

Answer:

the answer is a

Step-by-step explanation:

Answer:

c = \({\boxed{\boldsymbol{29}}}\) km

Step-by-step explanation:

Here's the required formula to find the missing side of triangle by pythagoras theorem :

\({\longrightarrow{\pmb{\sf{{(a)}^{2} + {(b)}^{2} = {(c)}^{2}}}}}\)

Substituting all the given values in the formula to find the third side of triangle :

\( \begin{gathered} \quad{\longrightarrow{\sf{{(a)}^{2} + {(b)}^{2} = {(c)}^{2}}}} \\ \\ \quad{\longrightarrow{\sf{{(20)}^{2} + {(21)}^{2} = {(c)}^{2}}}} \\ \\ \quad{\longrightarrow{\sf{(20 \times 20) + (21 \times 21) = {(c)}^{2}}}} \\ \\ \quad{\longrightarrow{\sf{(400) + (441) = {(c)}^{2}}}} \\ \\ \quad{\longrightarrow{\sf{400 + 441 = {(c)}^{2}}}} \\ \\ \quad{\longrightarrow{\sf{841= {(c)}^{2}}}} \\ \\ \quad{\longrightarrow{\sf{c = \sqrt{841}}}} \\ \\ \quad{\longrightarrow{\sf{\underline{\underline{\purple{c = 29 \: km}}}}}}\end{gathered}\)

Hence, the length of missing side of triangle is 29 km.

\(\rule{300}{2.5}\)

0.8 is greater than 0.3 an image is attached to show the plotting on the number line.

A number line is a one-dimensional horizontal line where we can represent any real number. The origin of the number line is represented by zero left to it are all negative real numbers and right to it are all positive real numbers.

Given, are two decimals 0.3 and 0.8.

We know 0.3 lies between 0 and 0.5 and 0.8 lies between 0.5 and 1.

∴ 0.8 > 0.3.

The plotting of the numbers is attached in the image.

learn more about number line here :

https://brainly.com/question/13425491

#SPJ1

Answer:

£13496.80

Step-by-step explanation:

We can ignore the £ sign for now, that is just units.

If we decrease a number by 4.5%, we will have to find \(100-4.5=95.5\)% of 14132.77.

We can easily do this by setting up a proportion.

\(\frac{x}{14132.77} = \frac{95.5}{100}\)

Multiply 14132.77 by 95.5:

\(14132.77\cdot95.5=1349679.535\)

Divide by 100:

\(1349679.535\div100=13496.79535\)

Rounding this to two decimal places, it simplifies to 13496.80.

Hope this helped!

The actual sum is 1.1.

Sum of the given numbers (-2.678), 4.5, (-0.68)

The sum can be defined as the result or answer after adding two or more numbers or terms. Thus, the sum is a way of putting things together.

(-2.678) + 4.5 + (-0.68)

= -2.678 + 4.5 - 0.68

= 4.5 - 3.358

= 1.142

Nearest tenth:

since .1 is in the tenth place and 42 isn't greater than 50, the answer would be 1.1.

The actual sum is 1.1.

Find out more information about sum here

https://brainly.com/question/4694239

#SPJ4

The relative frequency of selecting a diamond given the number of trials is 30%.

Relative frequency = (number of diamonds picked in the trial/ total number of trials) x 100

(12/40) x 100 = 30%

Therefore, 30% is the relative frequency of the selecting a diamond.

To learn more about percentages, please check: brainly.com/question/25764815

#SPJ1

Complete question:

A card was selected at random from a standard deck of cards. The suit of the card was recorded, and then the card was put back in the deck. The table shows the results after 40 trials.

Outcome - Club | Diamond | Heart | Spade

Number of trials- 8 | 12 | 11 | 9

What is the relative frequency of selecting a diamond?

A. 23%

B. 25%

C. 30%

D. 42%

Given:

Let's evaluate and find the quotient.

We have:

SInce it is not a repeating decimal, we are asked to leave to answer as it is.

A repeating decimal is a decimal with digits or group of digits that repeats endlessly.

The decimal 5.937

ANSWER:

5.9375

Answer:

Step-by-step explanation:

The slopes of both those lines are the same so there is no solution. Use slope triangles to find out the slope. They are both 1/4.

A. No solution

y = 1/4x+5

x - 4y = 4

You can simplify the second equation into y = 1/4x - 1

Since these equations both have the same slope, they are parallel. When two lines are parallel, they have no solutions.

Answer:

-24 is the correct answer

Step-by-step explanation:

The approximate total time using equations of motion takes for the ball to hit the ground is 3.49 seconds, and it travels approximately 69.8 meters horizontally before hitting the ground.

To begin with, we can use the equations of motion to solve for the time it takes for the ball to hit the ground. Since the ball is thrown horizontally, we can ignore the vertical component of the velocity and focus only on the horizontal motion.

First, let's find the horizontal distance the ball travels before hitting the ground. We know that the ball is thrown at a speed of 20 meters per second, so its horizontal velocity will remain constant throughout its motion. We can use the formula:

distance = velocity x time

Since the ball will hit the ground, we want to find the horizontal distance it travels in the time it takes to fall. We know that the height of the tower is 60 meters, so the vertical distance the ball falls is also 60 meters. We can use the formula for the time it takes to fall from a certain height:

time = \(\sqrt{(2 * height / gravity) }\)

where gravity is the acceleration due to gravity, approximately 9.8 meters per second squared. Plugging in the values, we get:

time = \(\sqrt{(2 x 60 / 9.8)}\) = 3.49 seconds

This is the total time it takes for the ball to hit the ground. Now, to find the horizontal distance it travels, we can use the formula above:

distance = velocity x time = 20 x 3.49 = 69.8 meters

Therefore, the approximate total time it takes for the ball to hit the ground is 3.49 seconds, and it travels approximately 69.8 meters horizontally before hitting the ground.

To learn more about equations of motion, refer here:

https://brainly.com/question/31314651#

#SPJ11

To understand why the function evaluates to -2 at -2.99, it is necessary to know the specific function and its definition or the rules. The value of the unknown function at -2.99 is -2.

In the given statement, it is indicated that the value of the unknown function at -2.99 is -2. This implies that when the input to the function is -2.99, the output is -2.

To provide a more detailed explanation, we need to know the specific function being referred to. Without this information, it is difficult to provide a precise explanation for why the function evaluates to -2 at -2.99. The behavior of a function depends on its definition, and different functions can have different rules or equations governing their behavior.

In general, functions can be represented by mathematical expressions or equations, and they map input values to corresponding output values. The function's behavior can be determined by its definition, which may involve various mathematical operations, constants, variables, or specific conditions.

Learn more about function here:

https://brainly.com/question/31062578

#SPJ11

The first term of the infinite geometric series is 625.Let's dive deeper into the explanation.

We are given that the sum of the infinite geometric series is \(\( \frac{15625}{24} \)\)and the common ratio is\(\( \frac{1}{25} \).\)The formula for the sum of an infinite geometric series is \(\( S = \frac{a}{1 - r} \)\), where \( a \) is the first term and \( r \) is the common ratio.
Substituting the given values into the formula, we have \(\( \frac{15625}{24} = \frac{a}{1 - \frac{1}{25}} \).\)To find the value of \( a \), we need to isolate it on one side of the equation.
To do this, we can simplify the denominator on the right-hand side.\(\( 1 - \frac{1}{25} = \frac{25}{25} - \frac{1}{25} = \frac{24}{25} \).\)
Now, we have \(\( \frac{15625}{24} = \frac{a}{\frac{24}{25}} \).\) To divide by a fraction, we multiply by its reciprocal. So, we can rewrite the equation as \( \frac{15625}{24} \times\(\frac{25}{24} = a \).\)
Simplifying the right-hand side of the equation, we get \(\( \frac{625}{1} = a \).\)Therefore, the first term of the infinite geometric series is 625.
In conclusion, the first term of the given infinite geometric series is 625, which corresponds to option (a).



learn more about geometric series here here

https://brainly.com/question/30264021



#SPJ11

Answer:

74

Step-by-step explanation:

All you have to do it first add f(x)+ g(x) and then plug in x=5.

(f+g) = f(x) + g(x)

= (7x- 2) + (9x-4)

= 7x - 2 + 9x - 4

= 16x - 6

(f + g)(5) = 16(5) - 6

= 80 - 6

= 74

A graph of the quadratic function y = (x + 4)² - 1 is shown below.

The vertex is (-4, -1) and another point for this function is (-5, 0).

In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:

f(x) = a(x - h)² + k

Where:

Based on the information provided about this quadratic function, we can determine the value of "a," "h," and "k" by comparison as follows:

y = a(x - h)² + k

y = (x + 4)² - 1

Therefore, the values of "a," "h," and "k" are:

a = 1

h = -4

k = -1

Vertex, (h, k) = (-4, -1)

Read more on vertex here: brainly.com/question/14946018

#SPJ1

Say it is two o'clock, draw an imaginary line between the hour hand and twelve o'clock to create the north-south line. You know the sun rises in the east and sets in the west so this will tell you which way is north and which way south. If you are in the Southern Hemisphere then it will be the other way round.

Problem

Write the rational number as A/B in simplest form 0.34​

Solution

For this case we can do the following:

And if we simplify we got:

The work done by the gas as indicated in the PV diagram is 6 atm L.

What is a rectangle?

A rectangle is a four-sided geometric shape with four right angles (90-degree angles) and opposite sides that are parallel and equal in length.

To determine the work done by the gas as indicated in the PV-diagram, we need to calculate the area enclosed by the graph.

The work done by the gas is equal to the area enclosed by the path in the PV diagram. In this case, we can see that the path is a closed shape that consists of two parts:

the work done by the gas as indicated in the PV diagram is 6 atm L.

Part 1: An isobaric process where the pressure is constant at P=3 atm, and the volume changes from V=1 L to V=3 L. The area of this rectangle is:

Work = P x ΔV = 3 atm x (3 L - 1 L) = 6 atm L

Part 2: An isochoric process where the volume is constant at V=3 L, and the pressure changes from P=3 atm to P=1 atm. The area of this rectangle is:

Work = 0 (since the volume does not change)

The total work done by the gas is the sum of the work done in each process:

Total Work = Work1 + Work2 = 6 atm L + 0 = 6 atm L.

Therefore, the work done by the gas as indicated in the PV diagram is 6 atm L.

To learn more rectangle from the given link:

https://brainly.com/question/29123947

#SPJ1

Option C represents a modified Hardy-Weinberg equation that incorporates the effects of natural selection on a population. The equation is given as:

$(p-3s)^2 + 2(p-s)q + q^2 = 1$

In this equation, various terms are included to express the impact of natural selection. Let's break down the equation and understand its components.

$p$ represents the frequency of the dominant allele in the population, while $q$ represents the frequency of the recessive allele. These frequencies are determined based on the initial allele frequencies in the population.

The term $(p-3s)^2$ represents the expected frequency of the homozygous dominant genotype in the next generation. The factor $3s$ denotes the selection coefficient, where $s$ represents the frequency of homozygous recessive individuals who do not survive due to natural selection. By subtracting $3s$ from $p$, we account for the reduction in the frequency of the dominant allele due to selection.

The term $2(p-s)q$ represents the expected frequency of the heterozygous genotype in the next generation. This term incorporates both the initial frequency of the heterozygous individuals, represented by $(p-s)$, as well as the transmission of alleles through reproduction, given by $q$. The factor of 2 accounts for the two possible combinations of alleles in the heterozygous genotype.

Finally, $q^2$ represents the expected frequency of the homozygous recessive genotype in the next generation. This term considers the transmission of the recessive allele, represented by $q$, and its squared value accounts for the homozygous recessive genotype.

The equation is set equal to 1, as the frequencies of all genotypes should sum to 1 in a population.

To know more about Hardy-Weinberg equation

https://brainly.com/question/5028378

SPJ11#

a) The probability of the second ball being drawn from Urn 2 is 2/3.

b) The probability that the second ball is black given that it is drawn from Urn 2 is 3/4.

c) The probability that the second ball is black is 11/24.

d) The probability that the second ball was drawn from Urn 1 given that it is black is 4/11.

e) The probability that the first ball drawn was red, given that the second ball drawn is black is 4/11.

f) The probability that both balls drawn are red is 1/6.

Given that Urn 1 contains two red balls and two black balls, the probability of drawing one ball is 1/2. Urn 2 contains one red ball and three black balls, the probability of drawing one ball is 1/4. Urn 3 contains two red balls and one black ball, the probability of drawing one ball is 1/3.

Let R1 and R2 represent the events of drawing a red ball from Urn 1 and Urn 2, respectively.

Also, let B1 and B2 represent the events of drawing a black ball from Urn 1 and Urn 2, respectively.

For this probability problem, we need to consider the three conditional events: drawing a second ball from Urn 2 if the first ball is red from Urn 3, drawing a second ball from Urn 1 if the first ball is black from Urn 3, and the overall probability of drawing a second ball that is black.

a) If the first ball is red from Urn 3, then there are two possible scenarios. Either the second ball is drawn from Urn 1, or it is drawn from Urn 2. The probability of the second ball being drawn from Urn 2 is 2/3, and the probability of it being drawn from Urn 1 is 1/3.

b) The probability that the second ball is black given that it is drawn from Urn 2 is 3/4.

c) If we consider all possible scenarios, the probability that the second ball is black is

(1/3)×(1/2)+(2/3)×(3/4) = 11/24.

d) The probability that the second ball was drawn from Urn 1 given that it is black is P(B1)×P(1|B1) / P(B),

where P(B1) is the probability of drawing a black ball from Urn 1, P(1|B1) is the probability of drawing from Urn 1 given that the first ball is black, and P(B) is the probability of drawing a black ball regardless of which urn it is drawn from. Plugging in the values,

we get (1/2)×(1/2) / (11/24) = 4/11.

e) The probability that the first ball drawn was red given that the second ball drawn is black is P(R1|B2) = P(B2|R1)×P(R1) / P(B2), where P(R1) is the probability of drawing a red ball from Urn 1, and P(B2|R1) is the probability of drawing from Urn 2 given that the first ball is red. Plugging in the values, we get (3/4)×(1/2) / (11/24) = 4/11.

f) The probability that both balls drawn are red is P(R1)×P(R2|R3) = (1/2)×(1/4) = 1/8.

Therefore, the probability of the second ball being drawn from Urn 2 is 2/3. The probability that the second ball is black given that it is drawn from Urn 2 is 3/4. The probability that the second ball is black is 11/24. The probability that the second ball was drawn from Urn 1 given that it is black is 4/11. The probability that the first ball drawn was red given that the second ball drawn is black is 4/11. The probability that both balls drawn are red is 1/6.

To know more about probability visit:

brainly.com/question/31828911

#SPJ11