Find the non-extraneous solutions of √x+6-5=x+1. (1 point)
Ox=-2
Ox=-6 and x = -5
Ox=-6 and x = -2
O x = 2

Answer:

A. The balloon rises 1 mile every 1/5 minute.

Step-by-step explanation:

1. Height = 1/5Time

2. For every mile risen, it takes 1/5 Minutes.

or if its easier to understand the other way around

For every 1/5 minutes, the balloon rises 1 mile

I hope my answer is correct and that you get a good grade!

The Total Proability will be 297 / 1015

What is Probability?

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

Solution:

Total Number of Regular Soft Drinks = 18

Total Number of Diet Soft Drinks = 12

Total Drinks = 18 + 12 = 30

Probability of selecting Diet Soft Drink in the first two attempt = 12/30 * 11/29 * 18/28 = 2376 / 24360

Probability of selecting Diet Soft Drink in the first and last attempt = 12/30  * 18/29 * 11/28 = 2376 / 24360

Probability of selecting Diet Soft Drink in the second and last attempt = 18/30  * 12/29 * 11/28 = 2376 / 24360

Total Probability = 3 * 2376 / 24360

Total Probability = 2376 / 8120

Total Probability = 297 / 1015

To learn more about Probability from the given link

https://brainly.com/question/25870256

#SPJ4

If this is sample data, the sample variance is 75.410  and the sample standard deviation is 8.68 .

The term variance refers to a statistical measurement of the spread between numbers in a data set. More specifically, variance measures how far each number in the set is from the mean (average), and thus from every other number in the set.

Variance is a statistical measurement used to determine how far each number is from the mean and from every other number in the set. You can calculate the variance by taking the difference between each point and the mean. Then square and average the results.

If this is population data, the population variance is 65.98  and the population standard deviation is8.12  .

If you were to recalculate the variance and standard deviation with the 80 instead of the 72,

Sample variance = 43.125

Sample standard deviation = 6.567

Population variance =  37.734

Population standard deviation = 6.14

Step-by-step explanation

Dats given are 88, 96, 72, 84, 95, 100, 92 and 90

Mean,  μ  = 89.625

Number of data, N = 8

Sample variance s2 =  Σ  ( xi -  μ  )2 / N-1

N -1 = 8-1 = 7

Given that xi -  μ  for each data are  -1.625, 6.375, -17.625, -5.625, 5.375, 10.375, 2.375  and 0.375

Σ  ( xi -  μ  )2  =  -1.6252 + 6.3752 + -17.6252 +-5.6252 + 5.3752 + 10.3752 + 2.3752 + 0.3752 = 527.870

Sample variance, s2 =  8−1−1.6252+6.3752+17.6252+5.622+5.3752+10.3752+2.3752+0.3752

 =  7527.870  = 75.410

sample standard deviation s =  75.410

= 8.68

Population variance ,  σ  2 =  Σ  ( xi -  μ  )2 / N

Population variance ,  σ  2  =  81.6252+6.3752+17.6252+5.6252+5.3752+10.3752+2.3752+0.3752

 =  8527.870

 = 65.96

Population standard deviation,  σ   =  65.98  = 8.12

If 72 is recalculated with  80 , datas are 88, 96, 80, 84, 95, 100, 92 and 90  888+96+80+84+95+100+92+90

New mean,  μ   =  888+96+80+84+95+100+92+90

= 90.625

The deviations from the mean ( xi -  μ  ) are -2.625, 5.375, -10.625, -6.625, 4.375 , 9.375, 1.375 and -0.625

Σ  ( xi -  μ  )2  = -2.6252 + 5.3752 + -10.6252+ -6.6252 + 4.3752 + 9.3752 +  1.3752 + -0.6252 = 301.875

Sample variance s2 =  Σ  ( xi -  μ  )2 / N-1

Sample variance s2  =  8−1−2.6252+5.3752+10.6252+6.6252+4.3752+9.3752+1.3752+0.6252

=  7301.875

  = 43.125

Sample standard deviation s =  43.125

 = 6.567

Population variance,  σ  2 =  Σ  ( xi -  μ  )2 / N

Σ  ( xi -  μ  )2  = -2.6252 + 5.3752 + -10.6252+ -6.6252 + 4.3752 + 9.3752 +  1.3752 + -0.6252 = 301.875

Population standard deviation,  σ^2   =   sqrt(37.734)

​Population standard deviation,  σ   = 6.14

To learn more about variance visit:

brainly.com/question/14116780

#SPJ4

A common at-home workout that features high-intensity cardio, and strength-building exercises, and focuses on total body fitness might be a 21-day or 60-day "challenge". Thus, the correct option is C.

Body fitness may be defined as an ability of a person to perform daily physical activities with normal performance, endurance, and strength. This fitness assists the individual in the regulation of disease, fatigue, and stress and reduced inactive behavior.

People who performed high-intensity cardio, and strength-building exercises, in their home and focus on total body fitness must be actively involved in the 21-day or 60-day "challenge".

A 21-day or 60-day "challenge" would be self-selected by an individual in order to maintain their overall physical fitness.

Therefore, the correct option for this question is C.

To learn more about Body fitness, refer to the link:

https://brainly.com/question/3524635

#SPJ4

Step-by-step explanation:

Parallel lines cut by a transversal coloring activity is an activity that helps students understand the pattern of angles when parallel lines are cut by a transversal. The activity involves coloring the angles formed by the parallel lines and the transversal in different colors. This helps students identify the different types of angles formed and their relationships with each other.

Answer:

Open circle at 3 going to the right.

Step-by-step explanation:

Let’s look at this.

first, let’s simplify the inequality. 2x +3-3>9-3

2x>6

x>3

since this is just a greater than or less than, it will be an open circle.

now that we have established that, we can see that x is BIGGER than 3. In that case, it will be an open circle at 3 going to the right.

Answer:

C

Step-by-step explanation:

The measurements of AB = 20 in and AC = 10 in

Triangles that are similar to each other have corresponding sides that are proportional to one another and corresponding angles that are equal to one another.

Triangles with similar appearances can have varying diameters. In a set of similar triangles, the ratio of corresponding sides will be equal.

Here we have

Two Similar  triangles ABC and CDE  

Since the two triangles are Similar

=> AB/DE = AC/EC = BC/DC

Substitute each measurement of the sides

=> AB/16  = AC/8 = 15/12  

Take, AB/16 = 15/12  

=> AB/16 = 5/4

=> AB = 5(16)/4

=> AB = 20 in  

Take AC/8 = 15/12  

=> AC = 15(8)/12

=> AC = 15(2)/3

=> AC = 10

Therefore,

The measurements of AB = 20 in and AC = 10 in

Learn more about Similar triangles at

https://brainly.com/question/14926756

#SPJ1

Answer:

98

Step-by-step explanation:

b(c(3))

b(3(3)-2)

2(3(3)-2)^2

2(9-2)^2

2(7)^2

2(49)

98

Yes the graph of the function represents a linear piecewise function of x.

From the graph we can see that the function can be broken down into 3 distinct parts.

Let us take the first part of the graph which represents the function:

For values of x ranging from negative infinity to 0, the value of y is 2 .

So the function is of the form y = 2.

Now for the second slanting part of the function.

The function passes through the points (0,2) and (2,-2)

Slope of the line = (-2-2)/(2-0) = -2

Equation of the line :

y-2 = -2(x)

or, y + 2x = 2.

Now for the third part of the function is y = -2 for all x>2

Hence the piecewise function can be represented as for the domain of x:

     {2 , x < -2 }

y = {2-2x , -2 ≤ x ≤ 2}

     {-2 , x > 2}

Hence all parts are linear so the function is linear in nature.

To learn more about function visit:

https://brainly.com/question/21107621

#SPJ9

Answer:

The change in elevation of the seagull is -16 ft

Step-by-step explanation:

Displacement

The displacement, unlike distance, considers the direction of the lengths occurring in the systems.

To solve the problem, we need to set a zero-level reference. Let's assume the sea level as zero height, any position above this reference as positive, and any position below this reference as negative.

The seagull is flying at a height of 10 ft above the ocean. Thus, its position is positive +10 feet.

The seagull then dives into the water to catch a fish at a depth of 6 feet. This position is negative: -6 ft.

The change in elevation is found by subtracting the final elevation and the initial elevation:

change = -6 ft - 10 ft = -16 ft

The change in elevation of the seagull is -16 ft

(a) The marginal density functions fX and fY is FY(y) = 3y(2y+1)

(b)The probability that X + Y ≤ 1 is P(X + Y ≤ 1) = 5/16

(a) To discover the negligible thickness work of X, we coordinated the joint thickness work with regard to y over the extent of conceivable values of y:    

fX(x) = ∫ f(x,y) dy = ∫ 3(2−x)y dy,   0<x<2

Assessing the necessary, we get:

fX(x) = (3/2)*(2-x)²,   0<x<2

To discover the negligible thickness work of Y, we coordinated the joint thickness work with regard to x over the extent of conceivable values of x:

FY(y) = ∫ f(x,y) dx = ∫ 3(2−x)y dx,   0<y<1

Assessing the necessary, we get:

FY(y) = 3y(2y+1),   0<y<1

(b) To calculate the likelihood that X + Y ≤ 1, we got to coordinate the joint thickness work over the locale of the (x,y) plane where X + Y ≤ 1:

P(X + Y ≤ 1) = ∫∫ f(x,y) dA,   where A is the locale X + Y ≤ 1

We will modify the condition X + Y ≤ 1 as y ≤ 1−x. So the limits of integration for y are to 1−x, and the limits of integration for x are to 1:

P(X + Y ≤ 1) = \(∫0^1 ∫0^(1−x)\) 3(2−x)y dy dx

Evaluating the inner integral, we get:

\(∫0^(1−x)\) 3(2−x)y dy = (3/2)*(2−x)*(1−x)²

Substituting this into the external indispensably, we get:

P(X + Y ≤ 1) = ∫0^(3/2)*(2−x)*(1−x)²dx

Assessing this necessarily, we get:

P(X + Y ≤ 1) = 5/16

Hence, the likelihood that X + Y ≤ 1 is 5/16.

To know more about probability refer to this :

https://brainly.com/question/24756209

#SPJ4

Yes it is correct that the expected value of a random variable can be interpreted as a long-run average.

The expected value of a random variable is a concept used in probability theory and statistics. It is a way to summarize the average behavior or central tendency of the random variable.

To understand why the expected value represents the average value that the random variable would take in the long run, consider a simple example. Let's say we have a fair six-sided die, and we want to find the expected value of the outcomes when rolling the die.

The possible outcomes when rolling the die are numbers from 1 to 6, each with a probability of 1/6. The expected value is calculated by multiplying each outcome by its corresponding probability and summing them up.

To know more about random variable,

https://brainly.com/question/29851447

#SPJ11

Answer:

6000.000 + 900.000 + 0 + 5 + 3/10 + 2/100 + 7/1000

six thousand nine hundred and five ones point(.) three tenths two hundredths and seven thousandths

Step-by-step explanation:

right!!!

Answer:

\(18\sqrt{3} + 55\sqrt{3} = 73\sqrt{3}\)

Step-by-step explanation:

27= 3 * 3 * 3

75 = 3 * 5*5

18 sqr 3 + 55 sqr 3 = 73 sqr 3

Answer:

B, C and D

Step-by-step explanation:

Ema found the surface area of a cone as:

\(S.A = \pi(14^2) + \pi(14)(29)\)

Surface Area of a Cone \(S.A.=\pi r^2+\pi rl\)

Therefore:

Radius, r =14 units

Slant Height, l = 29 Units

(B)The diameter of the cone is 28 units.

SInce Diameter =Radius X 2

Diameter = 14 X 2= 28 Units

(C)The base area of the cone is \(196\pi$ units^2.\)

Base Area of a Cone \(=\pi r^2\)

Since r=14 Units

Base Area = \(=\pi 14^2=196\pi $ square units\)

(D)The lateral area is the product of pi, the radius(r), and the slant height(l).

\(L$ateral Area of a cone =\pi rl\)

Therefore, B, C andDapplies.

Answer:

A,B,D

Step-by-step explanation:

Answer:

-47.8 feet

Step-by-step explanation:

Answer:

47.8 feet below

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Answer:

none is

Step-by-step explanation:

The statement "I estimate that the probability of my getting married in the next 3 years is 0.7" does make sense.

As individuals, we can make personal estimates or predictions about events that are relevant to our lives, such as the probability of getting married in a certain timeframe. These estimates are based on our own subjective beliefs, experiences, and expectations. While they may not be based on precise mathematical calculations or rigorous statistical analysis, they can still reflect our personal opinions or perceptions.

In this case, the person is providing an estimate that they believe there is a 0.7 (or 70%) probability of getting married within the next 3 years. This estimate is a subjective assessment of their own chances based on various factors such as their current relationship status, personal goals, or cultural norms.

It is important to note that personal estimates like this are not necessarily based on concrete evidence or universally applicable probabilities. They can vary greatly from person to person and are subjective in nature. However, they can still hold personal meaning and influence one's decision-making or expectations regarding future events.

Learn more about probability here:

https://brainly.com/question/31828911

#SPJ11

"meso-" and "medi-" both relate to the middle or intermediate position, but they may be used in different contexts and have distinct origins (Greek and Latin, respectively).

The prefixes "meso-" and "medi-" have different meanings:

Meso-: The prefix "meso-" generally means "middle" or "intermediate." It is derived from the Greek word "mesos," which carries the same meaning. In scientific and medical terminology, "meso-" is often used to indicate something that is located in the middle or intermediate position.

For example:

Mesoderm: The middle germ layer in the early development of an embryo.

Mesozoic: The era between the Paleozoic and Cenozoic eras, often referred to as the "Age of Reptiles."

Medi-: The prefix "medi-" typically means "middle" or "between." It is derived from the Latin word "medius," which conveys a similar sense. In various contexts, "medi-" is used to indicate something that is in the middle or intermediary position.

For example:

Median: Referring to the middle value in a set of numbers or the middle line or point dividing something into equal halves.

Mediastinum: The central area within the thoracic cavity, located between the lungs, which contains the heart, great vessels, and other structures.

Learn more about prefix here, https://brainly.com/question/30382110

#SPJ11

a) The area of the first circle is approximately 254.34 square inches

b) The area of the second circle is approximately 70650 square inches.

a) The area of a circle can be calculated using the formula A = πr², where π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

For the first circle with a diameter of 18 inches, we can find the radius by dividing the diameter by 2:

r = 18/2 = 9 inches

Now we can calculate the area using the formula:

A = πr² = 3.14 x 9² = 254.34 square inches

Therefore, the area of the first circle is approximately 254.34 square inches.

b) For the second circle with a diameter of 25 feet, we need to convert the diameter to inches, since our formula uses radius in inches:

25 feet = 25 x 12 inches = 300 inches

Then we can find the radius by dividing by 2:

r = 300/2 = 150 inches

Now we can calculate the area using the formula:

A = πr² = 3.14 x 150² = 70650 square inches

Therefore, the area of the second circle is approximately 70650 square inches.

Note that the units for the second calculation are in square inches, not square feet, because we used the formula that requires radius in inches.

To learn more about area click on,

https://brainly.com/question/16599566

#SPJ1

Yes, any list of five real numbers can be considered a vector in the set of real numbers with dimension 5, denoted as ℝ5.

A vector is a mathematical object that represents a quantity with both magnitude and direction. In the case of ℝ5, this set includes all possible lists of five real numbers, which can be thought of as five-dimensional vectors. Each number in the list represents a component or coordinate of the vector, indicating how far it extends in each of the five dimensions.

Therefore, any list of five real numbers can be considered a vector in the set of real numbers with dimension 5, denoted as ℝ5.


In mathematics, a vector is an element of a vector space, which is a set of objects that can be added together and multiplied by scalars (real numbers). The set ℝ⁵ is a vector space consisting of all 5-tuples (lists) of real numbers, written as (a₁, a₂, a₃, a₄, a₅), where each element aᵢ is a real number. Any list of five real numbers forms a vector in ℝ⁵ because it satisfies the required conditions to be an element of the vector space.

A list of five real numbers is indeed a vector in the set of real numbers ℝ⁵, as it meets the necessary criteria to be a part of the vector space.

To know more about vector space, visit:

https://brainly.com/question/13058822

#SPJ11

When 293 college students are randomly selected and surveyed, it is found that 114 own a car. The upper limit for the 90% confidence interval for the percentage of all college students who own a car is 46.3%.

The given problem is an example of confidence intervals in statistics. The formula for finding the confidence interval in percentage is given below:

Confidence Interval in Percentage = P ± Z Score x √ (PQ/n)

where

P = Sample proportion

Q = 1 - P

n = Sample Size

Z Score is obtained from the Z-Table where the confidence level is given.

To obtain the upper limit, the following formula should be used:

Upper Limit of the Confidence Interval = P + Z Score x √ (PQ/n)

Substitute the given values of the question into the formula:

P = 114/293 = 0.3891

Q = 1 - 0.3891 = 0.6109

n = 293

The upper limit for the 90% confidence interval is given by the Z-Table at 1.645:

Upper Limit of the Confidence Interval = 0.3891 + 1.645 x √ [(0.3891 x 0.6109)/293]

≈ 0.3891 + 1.645 x 0.0467

≈ 0.3891 + 0.07701

≈ 0.4661 = 46.3%

Therefore, the answer is 46.3%.

To know more about confidence interval visit:

https://brainly.com/question/32546207

#SPJ11

The equation of the line as it passes through the point (-6, 1) is

y = 3x/2 + 10

Slope is the same as gradient which is the ratio of change in y to change in x. That is,

gradient m = Δy / Δx

Given that the equation of the line passes through the point (-6, 1) and is perpendicular to the graph of 2x + 3y = -5

Let us first find the slope, 3y = -2x - 5

y = -2x/3 - 5/3

Slope m = -2/3

Let us use the formula Mm = -1

M = -1/m

M = -1 × -3 /2

M = 3/2

The equation of the line as it passes through the point (-6, 1) will be

M = (Y - Y1) / (X - X1)

3/2 = (y - 1) / (x + 6)

Cross multiply

2(y - 1) = 3(x + 6)

2y - 2 = 3x + 18

Collect the like time

2y = 3x + 18 + 2

2y = 3x + 20

y = 3x/2 + 10

Therefore, the equation of the line as it passes through the point (-6, 1) is y = 3x/2 + 10

Learn more about Gradient here: https://brainly.com/question/21727173

#SPJ1

18 is the answer to this question

The given parabolic equation is y = 4x - x² and the point is (1, 3). We are to determine the slope of the tangent line at (1, 3) and then obtain an equation of the tangent line.  we must first calculate the derivative of the given equation.

We can do this by using the power rule of differentiation. The derivative of x² is 2x. So the derivative of y = 4x - x² is dy/dx = 4 - 2x.Since we want to find the slope of the tangent line at (1, 3), we need to substitute x = 1 into the equation we just obtained. dy/dx = 4 - 2x = 4 - 2(1) = 2. Therefore, the slope of the tangent line at (1, 3) is 2.We can now write the equation of the tangent line. We know the slope of the tangent line, m = 2, and we know the point (1, 3).

We can use the point-slope form of the equation of a line to obtain the equation of the tangent line. The point-slope form of the equation of a line is given as: y - y₁ = m(x - x₁)where m is the slope, (x₁, y₁) is a point on the line.Substituting in the values we have, we get:y - 3 = 2(x - 1)We can expand this equation to obtain the slope-intercept form of the equation of the tangent line:y = 2x + 1Therefore, the equation of the tangent line to the parabola y = 4x - x² at the point (1, 3) is y = 2x + 1.

To Know about intercept visit:

brainly.com/question/14180189

#SPJ11

The given statement " limn→infinity=0 using an ϵ/N " is true and proved by showing that for any given ϵ > 0, there exists an N such that if n > N, then |√n+2−√n| < ϵ.

Let ϵ > 0 be given. We want to find an N such that |√n+2−√n| < ϵ for n > N.

First, we can simplify |√n+2−√n| as follows:

|√n+2−√n| = |(√n+2−√n) * (√n+2+√n) / (√n+2+√n)| = |(n+2−n) / (√n+2+√n)| = 2 / (√n+2+√n)

Now, we need to find an N such that 2 / (√n+2+√n) < ϵ for n > N. Multiplying both sides by (√n+2−√n), we get:

2 < ϵ(√n+2+√n)

2/ϵ < √n+2+√n

Squaring both sides, we get:

4/ϵ^2 < n+2+2√n(n+2)+n

4/ϵ^2 < 2n+2√n(n+2)

n > (4/ϵ^2 - 2)/(2√n+2)

Since we want n > N, we can choose N to be any integer greater than or equal to (4/ϵ^2 - 2)/(2√N+2). Then, for any n > N, we have:

n > (4/ϵ^2 - 2)/(2√n+2)

2 / (√n+2+√n) < ϵ

|√n+2−√n| < ϵ

This completes the proof.

To know more about Limit approaches to infinity:

https://brainly.com/question/15293030

#SPJ4

x = -1 and y = -13, (-1,-13) is the solution to the system of equation y = 3x - 10 and y = -2x - 15.

Given the system of equation in the question;

To find the solution to the system of equation, replace the occurrence of y in the second equation with y = 3x - 10  and solve for x.

y = -2x - 15

3x - 10 = -2x - 15

Add 10 to both sides

3x - 10 + 10 = -2x - 15 + 10

3x = -2x - 15 + 10

Add 2x to both sides

3x + 2x = -2x + 2x - 15 + 10

3x + 2x = - 15 + 10

Add like terms

5x = -5

x = -5/5

x = -1

Now, to solve for y, replace all occurrence of x with -1 in the first equation and solve for y.

y = 3x - 10

y = 3( -1 ) - 10

y = -3 - 10

y = -13

Therefore, the solution to the system of equation is (-1,-13).

Learn more about simultaneous equation here: brainly.com/question/16763389

#SPJ1

Answer:

D = 18

Step-by-step explanation: