Describe how solving 1x + 4 = 0 is similar to solving
1x + 4 = 0.

The  volume of the largest right circular cone that can be inscribed in a sphere of radius r is  8/27 (volume of sphere)

Let r serve as the foundation. the volume of the area, and radius x is the separation between the base and the sphere's center. Height h of the cone = R + x

∴    V= 1/3πr² h= π/ 3 (R² −x²)(R + x)

       = π/3​ (R² + R² x − Rx² −x² )

∴   dV/ dx​ = π​ /3 [R²−2Rx−3x² ]

  d²V/ dx²​ = π/3​ [−2R−6x]

For max or min V dV/dx​ =0

∴   R² −2Rx−3x² =0

⇒(R + x)(x−3x)=0    

2) x=−R, x​/3 but x = −R

When x= R/3 d² V/dx² <0  V is max only when x= R/3

​∴   Max V= 1/3π(R² − R²/9 )(R+ R/3 )

= 32πR³/81

= 8/27 ( 4/3 πR³)

= 8/27 (volume of sphere)

To learn more about volume click here

brainly.com/question/1578538

#SPJ4

Answer:

2545

Step-by-step explanation:

Answer: -6

Step-by-step explanation: y= 17x -6

y=17•0 -6

y= -6

Just multiply by zero to know where the line will cross

The answer to this question is option (a) Multinomial population. A population where each element of the population is assigned to one and only one of several classes or categories is a multinomial population.

A population where each element of the population is assigned to one and only one of several classes or categories is a multinomial population. A multinomial population is a type of probability distribution that is used to calculate the likelihood of a particular event or outcome happening when there are more than two possible outcomes or categories. It is similar to a binomial distribution, which calculates the probability of an event occurring with two possible outcomes, except that a multinomial distribution can handle more than two outcomes. Therefore, the answer to this question is option (a) Multinomial population. Explanation of the category of a population is an essential aspect of statistics, and knowing the difference between a multinomial and other categories can be crucial in different types of researches.

To know more about probability visit: https://brainly.com/question/31828911

#SPJ11

Answer:

$60

Step-by-step explanation:

50 x 0.2 = 10

10 + 50 = 60

Therefore, the volume of the solid created upon dilation is 12960 cubic units.

Volume is a measure of the amount of space occupied by a three-dimensional object or shape. It is typically measured in cubic units, such as cubic meters, cubic centimeters, or cubic feet. The volume of an object can be calculated using its dimensions, such as length, width, and height, and various mathematical formulas depending on the shape of the object.

Here,

Assuming that the solid being referred to is a right prism with a rectangular base, the original volume can be calculated as follows:

Volume = base area x height

Base area = length x width

Base area = 9 x 15

Base area = 135 square units

The height of the prism can be calculated using the Pythagorean theorem:

h² = s1² - b²

h² = 15² - 9²

h² = 144

h = 12 units

Therefore, the original volume is:

Volume = base area x height

Volume = 135 x 12

Volume = 1620 cubic units

The new height of the prism can be calculated using the Pythagorean theorem:

h² = s1² - b²

h² = 30² - 18²

h² = 576

h = 24 units

Therefore, the new volume is:

Volume = base area x height

Volume = 540 x 24

Volume = 12960 cubic units

To know more about volume,

https://brainly.com/question/12237641

#SPJ1

To estimate the fraction of people who black out at 6 or more gs at 98% confidence level and an error of at most 0.03, a sample size of 1079 is required using the formula n = (2.33² * 0.5 * (1-0.5)) / 0.03², rounded up to the nearest integer.

To determine the sample size required to estimate the fraction of people who black out at 6 or more gs with an error of at most 0.03 and a 98% confidence level, we need to use the formula

n = (z² * p * (1-p)) / E²

where

n is the sample size

z is the z-score for the desired confidence level (2.33 for 98% confidence)

p is the estimated proportion of people who black out at 6 or more gs (unknown)

E is the maximum error (0.03)

We don't know the estimated proportion p, but we can assume that it is 0.5, which is the value that will give the maximum sample size. So, substituting the values into the formula, we get

n = (2.33² * 0.5 * (1-0.5)) / 0.03² = 1078.8

Rounding up to the nearest integer, we get a sample size of 1079. Therefore, a sample size of 1079 is required to estimate the fraction of people who black out at 6 or more gs at the 98% confidence level with an error of at most 0.03.

To know more about confidence interval:

https://brainly.com/question/29680703

#SPJ4

Answer: 5/42

Step-by-step explanation:

To find the y-coordinate of point P on the unit circle, given that its x-coordinate is 5/13, we can utilize the Pythagorean identity for points on the unit circle.

The Pythagorean identity states that for any point (x, y) on the unit circle, the following equation holds true:

x^2 + y^2 = 1

Since we are given the x-coordinate as 5/13, we can substitute this value into the equation and solve for y:

(5/13)^2 + y^2 = 1

25/169 + y^2 = 1

To isolate y^2, we subtract 25/169 from both sides:

y^2 = 1 - 25/169

y^2 = 169/169 - 25/169

y^2 = 144/169

Taking the square root of both sides, we find:

y = ±sqrt(144/169)

Since we are dealing with points on the unit circle, the y-coordinate represents the sine value. Therefore, the y-coordinate of point P is:

y = ±12/13

So, the y-coordinate of point P can be either 12/13 or -12/13.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Two samples can have the same mean but different standard deviations if one sample has more variability than the other. For example, one sample may have data points that are tightly clustered around the mean, while the other sample may have data points that are more spread out.

This can result in the same mean value for both samples, but different levels of variability.

Here's an example bar graph to illustrate this concept:

     Sample 1                Sample 2

 ╭────────────────╮   ╭────────────────╮

 │      Mean      │   │      Mean      │

 ├────────────────┤   ├────────────────┤

 │                │   │    ╭─╮         │

 │                │   │    │ │         │

 │                │   │    │ │         │

 │                │   │    ╰─╯         │

 │     o o o      │   │  o o o o o o  │

 │                │   │                │

 │                │   │                │

 │                │   │                │

 ╰────────────────╯   ╰────────────────╯

     Std. Dev.            Std. Dev.

In this example, both Sample 1 and Sample 2 have a mean value of 5. However, Sample 1 has lower variability with a standard deviation of 1, while Sample 2 has higher variability with a standard deviation of 3. The error bars on the graph represent the standard deviation for each sample.

To know more about variability refer here:

https://brainly.com/question/17344045

#SPJ11

Answer:

It's 5/7

Step-by-step explanation:

Total cards=black +red=2+5=>7

Total red = 5

Which gives 5/7

The ratio of corresponding sides for the given similar triangles is 2/5.

In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:

a. 10

This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.

b. 4/5

This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.

To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.

Dividing 4 and 5 by 1, we get:

4 ÷ 1 = 4

5 ÷ 1 = 5

Therefore, the simplified ratio is 4/5.

c. 10/85

This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.

Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.

For more such questions on triangles, click on:

https://brainly.com/question/17335144

#SPJ8

We can write the line's equation as y = 5.

To find the equation:

With the given conditions, we find the equation of the line.

We begin by recognizing that we can write the line's expression in the point-slope form, which is expressed as:

Where \(\left(x_0, y_0\right)\) is the point through which the line passes and m is the slope We have already been given the point:

Which the line passes through.

We now write the line's equation:

\(\begin{gathered}y-y_0=m\left(x-x_0\right) \\y-5=(0)(x-4) \\y-5=0 \\y=5\end{gathered}\)

Therefore, we can write the line's equation as y = 5.

Know more about the slope of a line here:

https://brainly.com/question/3493733

#SPJ4

The complete question is given below:
Find an equation of the line that satisfies the given conditions. Through (4,5), parallel to the x-axis.

Answer: I think it would be 15 inches but don't trust me I'm bad at math

Step-by-step explanation:

Answer:

I think it's 15 inches

Step-by-step explanation:

16-1

The probability that a person arriving to use the machine will find it idle is 1/3 or 0.3333. Option a is correct.

Use the concept of an M/M/1 queue to calculate the probability, which models a single-server queue with exponential interarrival times and exponential service times.

In this case, the interarrival time follows an exponential distribution with a rate parameter of λ = 5 persons per hour (or 1/12 persons per minute). The service time (copying time) also follows an exponential distribution with a rate parameter of μ = 1/8 persons per minute (since each person uses the machine for an average of 8 minutes).

In an M/M/1 queue, the probability that the system is idle (no person is being served) can be calculated as:

P_idle = ρ⁰ × (1 - ρ), where ρ is the traffic intensity, defined as the ratio of the arrival rate to the service rate. In this case, ρ = λ/μ.

Plugging in the values, we have:

ρ = (1/12) / (1/8) = 2/3

P_idle = (2/3)⁰ × (1 - 2/3) = 1/3

Therefore, the probability is 1/3 or approximately 0.3333.

Thus, option (A) is the correct answer.

Learn more about probability https://brainly.com/question/31828911

#SPJ11

The given supply and demand equations for a textbook are:p=1/4 q² (supply)p= -1/4 q²+ 40 (demand)Given:Price = $5Substituting $5 for p in the demand equation,-1/4 q²+ 40 = 5-1/4 q² = -35q² = 140q = ± √(140) = ±11.83 (approximately)However, quantity cannot be negative. So, q = 11.83 books are demanded when the price of a book is $5.So, at a price of $5, 11.83 books are demanded.Therefore, the demand for the book is 11.83 books when the price is $5.

#SPJ11

Learn more about price of books https://brainly.com/question/28571698

Answer:

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

3(2x-5) =15

6x-15=15

6x=15+15

6x= 30

6x/6=30/6

x=5

This can be derived using Chebyshev's inequality, as Chebyshev's inequality and the law of large numbers are different in nature.

Let M_n be the maximum of n independent U(0, 1) random variables.

To derive the exact expression for P(|M_n − 1| > ε), we need to follow the below steps:

First, we determine P(M_n ≤ 1-ε). The probability that all of the n variables are less than 1-ε is (1-ε)^n

So, P(M_n ≤ 1-ε) = (1-ε)^n

Similarly, we determine P(M_n ≥ 1+ε), which is equal to the probability that all the n variables are greater than 1+\epsilon

Hence, P(M_n ≥ 1+ε) = (1-ε)^n

Now we can write P(|M_n-1|>ε)=1-P(M_n≤1-ε)-P(M_n≥1+ε)

P(|M_n-1|>ε) = 1 - (1-ε)^n - (1+ε)^n.

Thus we have derived the exact expression for P(|M_n − 1| > ε) as P(|M_n-1|>ε) = 1 - (1-ε)^n - (1+ε)^n

Now, to show that $lim_{n\to\∞}$ P(|M_n - 1| > ε) = 0 , we can use Chebyshev's inequality which states that P(|X-\mu|>ε)≤{Var(X)/ε^2}

Chebyshev's inequality and the law of large numbers are different in nature as Chebyshev's inequality gives the upper bound for the probability of deviation of a random variable from its expected value. On the other hand, the law of large numbers provides information about how the sample mean approaches the population mean as the sample size increases.

Learn more about Chebyshev's inequality:

https://brainly.com/question/32750368

#SPJ11

The required probabilities are

a. At least 1 will survive for 10 years is 0.99902

b. At least 10 will survive for 10 years is 0.623

c. At least 15 will survive for 10 years is 0.008

The complement rule is a fundamental principle in probability theory that states that the probability of an event happening is equal to one minus the probability of the event not happening.

                               P(A') = 1 - P(A)

Here we have

The 10-year survival rate for bladder cancer is approximately 50%

The probability of one will survive for 10 years = 50% = 0.5

The probability of no one will survive for 10 years = 1- 0.5 = 0.5

To find the probability that at least 1 out of 20 people will survive for 10 years, use the complement rule,  

The probability that no one will survive for 10 years is:

P(0 survivors) = (0.5)²⁰ = 0.00098

Therefore,

The probability that at least 1 person will survive for 10 years is:

P(at least 1 survivor) = 1 - P(0 survivors) = 1 - 0.00098 = 0.99902

b. To find the probability that at least 10 out of 20 people will survive for 10 years, use the binomial distribution formula:

=> P(X ≥ 10) = 1 - P(X < 10) = 1 - ∑(k = 0 to k = 9) (20, k) × (0.5)²⁰

Using a binomial distribution table or a calculator, we can find that:

=> P(X < 10) = 0.377

Hence, the probability that at least 10 people will survive for 10 years is:

P(X ≥ 10) = 1 - P(X < 10) = 1 - 0.377 = 0.623

c. To find the probability that at least 15 out of 20 people will survive for 10 years, we can again use the binomial distribution formula:

P(X ≥ 15) = 1 - P(X < 15) = 1 - ∑(k= 0 to k = 14) (20 choose k) × (0.5)²⁰

Using a binomial distribution table or a calculator

=> P(X < 15) = 0.992

Hence, the probability that at least 15 people will survive for 10 years is:

=> P(X ≥ 15) = 1 - P(X < 15) = 1 - 0.992 = 0.008

Therefore,

The required probabilities are

a. At least 1 will survive for 10 years is 0.99902

b. At least 10 will survive for 10 years is 0.623

c. At least 15 will survive for 10 years is 0.008

Learn more about Probability

https://brainly.com/question/13655344  

#SPJ1

Answer:

both are 75 degrees

Step-by-step explanation:

the angles add up to 180, as they are also vertical angles

Answer:

b=c since they are vertical angles, b=75 and c=75

Step-by-step explanation: The angle opposite of the given is the same (105) that gives you two measure. Add 105+105 to get 210. A set of vertical angles=360 degrees, take away 210 from 360 to get the measure of b+c. Divide that by two to get the measure of either b or c.

Answer:

x=2

AB=8

BC=8

AC=16

Step-by-step explanation:

7x-6=12-2x

7x+2x=12+6

9x=18

x=2

AB=7x-6=7(2)-6=14-6=8

BC=12-2x-12-2(2)=12-4=9

AC=8+8=16

Answer:

\(5*\frac{1}{2}\)

Step-by-step explanation:

We have a picture and are being asked to identify the multiplication problem that represents it.

So we have 5 triangles, all of which are color-coded in red, but only half of them are filled. When multiplying, the number that is before the * sign is the amount there is, while the number that is after the * is the amount going to multiply the amount of items there are. So looking at the picture, we can see 5 triangles, therefore :

5 *

2 * 1/5 is scratched out as an answer. As is starts with 2.

As for the second number, we acknowledge that all triangles are half in red, therefore the number is 1/2.

5 * 1/2

Scratching all other answers.

We have the following details

mean = 554

n = 60

bar x = 567

alpha = 0.01

A. h0. u = 554

H1. u > 554

B. Given that the standard deviation is known what we have to make use of is the independent z test

test statistics calculation

567-554/(39/√60)

= 2.582

d. at alpha = 0.01 and test statistics = 2.582, the value of the p value = 0.0049

0.0049  < 0.01. So we have to reject the null hypothesis.

e. Yes We have to accept that  we support the preparation course's claim that the population mean SAT score of its graduates is greater than 554

Read more on statistics here:

https://brainly.com/question/19243813

#SPJ1

The probability that two particular people, A and B, will be seated next to each other in a random arrangement of n people in a row of n seats depends on the total number of possible arrangements and the number of arrangements where A and B are seated together. The probability can be calculated as (n-1)/n.

Let's consider the two people, A and B, as a single unit. So, we have (n-1) units (including the unit of A and B together) to arrange in a row of n seats. The total number of possible arrangements is n!, which is the factorial of n.

Now, we focus on the number of arrangements where A and B are seated next to each other. Since A and B can be arranged in two ways (A followed by B or B followed by A), we can treat them as a single unit, giving us (n-1) units to arrange in a row.

The number of arrangements with A and B seated together is then (n-1)!. Therefore, the probability of A and B being seated next to each other is ((n-1)!)/n!. This simplifies to (n-1)/n, which is the final probability.

In conclusion, the probability that two particular people, A and B, will be seated next to each other in a random arrangement of n people in a row of n seats is (n-1)/n.

Learn more about probability here: https://brainly.com/question/31828911

#SPJ11

The probability that the sum of the two values showing is 5 is 1/9 which is approximately 0.111 or 11.11%.

There are a total of 36 possible outcomes when rolling two fair 6-sided dice. Since the dice are fair, each outcome is equally likely. To find the probability of getting a sum of 5, we need to determine how many of the 36 possible outcomes will result in a sum of 5.

The possible outcomes that add up to 5 are (1,4), (2,3), (3,2) and (4,1). These are 4 possibilities, so the probability of getting a sum of 5 when rolling two fair 6-sided dice is 4/36 or 1/9 which is approximately 0.111 or 11.11%.

In general, the probability of getting a certain sum when rolling two fair dice is determined by the number of ways that the two dice can combine to give that sum.

Therefore, the probability that the sum of the two values showing is 5 is 1/9 which is approximately 0.111 or 11.11%.

Learn more about probability here: https://brainly.com/question/24756209

#SPJ4

The type of influence on wellness that this represents is given as follows:

A. Social.

An influence on wellness is an activity that improves the morale of certain aspect of our lives.

The aspect improved in this problem is the social aspect, along with the physical aspect, as follows:

Since this is an example of social bonding, option A gives the correct option regarding which type of influence on wellness this is an example of.

For example, reading a book would be intellectual influence, while recycling would be environmental influence.

More can be learned about influences on wellness at https://brainly.com/question/4639722

#SPJ1

Answer:

30

Step-by-step explanation:

Answer:

\({ \tt{question \: 1 : }} \\ 2 {x}^{2} - 4x - 3 = 0 \\ x = 2.58 \: \: and \: \: - 0.58 \\ \\ { \tt{question \: 2 : }} \\ x(x - 2) = 4 \\ x = 4 \: \: and \: \: 6 \\ \\ { \tt{question \: 3 : }} \\ {9x }^{2} + 12x + 4 = 0 \\ (3x + 2)(x - 9) = 0 \\ x = \frac{ - 2}{3} \: \: and \: \: 9 \\ \\ { \tt{question \: 4 : }} \\ {x}^{2} + 2x = 1 \\ {x}^{2} + 2x - 1 = 0 \\ x = 0.41 \: \: and \: \: - 2.41\)