Point D is at (1,5) and point G is at (13,-1). If O is on the segment DG, and DO is twice as long as OG, what are the coordinates of O? 

Answer:

Yes. the Psychologist can confirm his theory that the attitudes have changed over time, based on the first and second surveys.

The expected value for the number of respondents who are optimistic is:

= 16.25

Step-by-step explanation:

Attitude                   1st Survey      2nd Survey

Optimistic                     7%                    6%

Slightly Optimistic       9%                     6%

Slightly Pessimistic    31%                   37%

Pessimistic                53%                   51%

Expected value of optimistic respondents:

Attitude                    

Optimistic      Expected Value

1st Survey        8.75 (250 * 7% * 50%)  

2nd Survey      7.50 (250 * 6% * 50%)

Total EV         16.25

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

Learn more about integrations here:

https://brainly.com/question/30217024

#SPJ1

Answer:

$25×0 02

Step-by-step explanation:

i have done this before

The solution for the given expression is 14∛x. The correct option is (C).

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given expression is as below,

5∛x + 9∛x

The given expression can be simplified as follows,

5∛x + 9∛x

Here, both the terms have equivalent variables. So, both are like terms.

As per the rules like terms can be added or subtracted keeping the variable as the same.

Thus, 5∛x + 9∛x = 14∛x

Hence, the given expression can be evaluated as 5∛x + 9∛x = 14∛x.

To know more about algebraic expression click on,

brainly.com/question/953809

#SPJ1

Answer:

Your answer is: \(6x^2-12y+13x\)

Simplify the expression.

Step-by-step explanation:

Hope this helped : )

Answer:

ACD

Step-by-step explanation:

jo welcome

Answer:

Step-by-step explanation:

General form of equation of a circle is expressed as \((x-a)^{2} + (y-b)^{2} =r^{2}\) where r is the radius of the circle and (a, b) is the center of the circle.

Given the equation of a circle to be \((x-20)^{2}+(y-0.05)^{2} = 81\), rewriting the equation to conform to the general equation above we have;

\((x-20)^{2}+(y-0.05)^{2} = 9^{2}\)

Comparing the equation given to the general equation above, a = 20, b = 0.05 and the radius of the circle will be 9. The center (a, b) will be (20, 0.05).

The probability that the chosen ball is blue is 55.3%.

If the chosen ball is blue, the probability would be 3.33% that it came from the first urn.

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

(a) To find P(A|B1), we use the formula P(A|B) = P(A and B)/P(B).

In this case, P(A and B1) is the probability of choosing a blue ball from the first urn, which is 7/20.

The probability of choosing the first urn is 1/2, so P(B1) = 1/2.

Plugging these values into the formula gives us P(A|B1) = (7/20)/(1/2) = 14/20 = 7/10.

To find P(A|B2), we use the same formula.

In this case, P(A and B2) is the probability of choosing a blue ball from the second urn, which is 14/19.

The probability of choosing the second urn is 1/2, so P(B2) = 1/2.

Plugging these values into the formula gives us P(A|B2) = (14/19)/(1/2) = 28/19.

To find P(A and B2), we use the formula P(A and B) = P(A|B) * P(B).

In this case, we already know that P(A|B2) = 28/19 and P(B2) = 1/2, so P(A and B2) = (28/19) * (1/2) = 28/38.

To find P(A or B2), we use the formula P(A or B) = P(A) + P(B) - P(A and B).

In this case, P(A) is the probability of choosing a blue ball overall, which is 21/38.

P(B2) is the probability of choosing the second urn, which is 1/2.

P(A and B2) is the probability of choosing a blue ball from the second urn, which is 28/38.

Plugging these values into the formula gives us P(A or B2) = 21/38 + 1/2 - 28/38 = 15/38.

The probability that the chosen ball is blue is P(A) = 21/38 = 55.3%.

(b) If the chosen ball is blue, the probability that it came from the first urn is P(B1|A) = P(B1 and A)/P(A).

We already know that P(B1 and A) is the probability of choosing a blue ball from the first urn, which is 7/20.

We also know that P(A) is the probability of choosing a blue ball overall, which is 21/38.

Plugging these values into the formula gives us P(B1|A) = (7/20)/(21/38) = 7/21.

This probability is equal to 33.3%.

Learn more about probability, here https://brainly.com/question/29582649

#SPJ4

f(x, y) = 3x + 2y + C

To know if a vector field is conservative, we have to check if it is the gradient of a scalar function.

The gradient of the function f(x, y) is given by

∇f(x, y) = (∂f/∂x, ∂f/∂y)

If a vector field F(x, y) is the gradient of a scalar function f(x, y), then the following conditions must be satisfied:

F(x, y) = ∇f(x, y)

Whether a given vector field satisfies this condition can be checked by taking the partial derivative with respect to x and y.

∂F/∂x = ∂(6x + 5y)/∂x = 6

∂F/∂y = ∂(5x + 4y)/∂y = 4

The partial derivative of a given vector field is the constant, the gradient of the scalar function. So vector fields are conservative and we can find a potential function f(x, y) such that F(x, y) = ∇f(x, y).

To find the potential function, we can integrate the partial derivative of F(x, y) with respect to x and y.

f(x, y) = ∫∂F/∂xdx + ∫∂F/∂ydy

= ∫6dx + ∫4dy

= 3x + 2y + C

where C is the constant of integration. So the potential function for a given vector field is

f(x, y) = 3x + 2y + C

Read more about conservative vectors on brainly.com/question/4864916

#SPJ4

Answer:

6 students are wearing shirts that aren't blue or white

Step-by-step explanation:

1/6 + 2/3 = 5/6  

5/6 are wearing either blue or white so 1/6 isn't wearing blue or white

there are 36 student and 1/6 means 36 divided by 6

36 divided by 6 = 6

Answer:

Below

Step-by-step explanation:

From 7 to 10 AM is THREE hours (if the times are all on the same day)

percent row: 120%      0.03%            15%

Decimal row: 1.2          0.0003          0.15

Fraction row: 12/ 10      3/10000         3/20

A relation that has more than one output of each input. That is not a function. A function only has one output of each input. Function a and function b are linear functions. Function a is represented by the table values. function b is represented by the equation y=3x+4.

Domain, is a term that is used to measure the independent variable’s values. Also known as the “x” values. It tells you what values of “x” are applicable in the function. What values will satisfy the function.

Range, is a term used to measure the dependent variable’s values. Also known as the “y” values. It tells you what values of why does the graph of the function extends till.

To learn more about functions visit:

https://brainly.com/question/29051369?referrer=searchResults

#SPJ1

The height of rectangular prism B is 5 yards.

Let's first find the volume of rectangular prism B:

The volume of the solid figure = Volume of prism A + Volume of prism B

180 = 75 + length × width × height of prism B

105 = length × width × height of prism B

We know that the length of prism B is 7 yards and the width is 3 yards,

Substitute those values:

105 = 7 × 3 × height of prism B

105 = 21 × height of prism B

height of prism B = 105/21

height of prism B = 5

Therefore, the height of rectangular prism B is 5 yards.

To know more about rectangular prism follow

https://brainly.com/question/30799424

#SPJ1

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

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

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

Read more about tangent lines at

https://brainly.com/question/21595470

#SPJ1

Answer:

64 inches squared

Step-by-step explanation:

Type I error is "Megan's results show significant improvements in health associated with a whole foods diet."

A Type I error occurs when the null hypothesis is rejected, even though it is true.

In this case, the null hypothesis states that a whole foods diet would not have any impact on general health.

Therefore, a Type I error would occur if Megan's results show significant improvements in health associated with a whole foods diet.

This means that Megan would reject the null hypothesis and conclude that a whole foods diet does have an impact on general health, even though it is not true.

So, the statement that would indicate a Type I error is "Megan's results show significant improvements in health associated with a whole foods diet."

To learn more on Null hypothesis click:

https://brainly.com/question/30821298

#SPJ1

Answer:

See explanation below.

Step-by-step explanation:

Let's say, \(x\) represents the sale price of radio.

Then the marked price of the radio is \(1.25x\)

The cost price of the radio is \((1.25x)(0.70)\)

The discount is simply 25% because the radio is being sold at 25% less then the marked price.

The gain percent is given as:

\(\frac{x-1.25x\times \:0.70}{x}\times 100\\\\=12.5\%\)

The radio is being sold at 12.5% gain.

Best Regards!

The number of country A forces in country B decreased to approximately 34,000 in 2014 from a high of about 10,000 in 2008. X represents the number of years after January 2007, this means that the amount of funding was approximately $10.5 billion in the year 2.135 years after January 2007, or approximately September 2009.

Generally, To find the year in which the amount of funding was approximately $10.5 billion, we need to solve the equation:

f(x) = 10.5

Substituting the given function for f(x), we get:

-1.384x^{2} + 5.253x + 5.517 = 10.5

We can solve this quadratic equation by using the quadratic formula:

\(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

where a = -1.384, b = 5.253, and c = 5.517.

Substituting these values into the formula, we get:

\(x = \frac{5.253 \pm \sqrt{5.253^2 - 4(-1.384)(5.517)}}{2(-1.384)}\)

Simplifying this expression gives us:

\(x = \frac{5.253 \pm \sqrt{27.747029}}{-2.768}\)

Since x represents the number of years after January 2007, we are only interested in the positive solution. Therefore, we can ignore the negative solution.

\(x = \frac{5.253 + \sqrt{27.747029}}{-2.768}\)

Simplifying this expression further gives us:

x = 2.135

Read more about funding

https://brainly.com/question/14705214

#SPJ1

The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

for more such questions on sampling method

https://brainly.com/question/13219833

#SPJ8

Expression represents the probability of the given number of attempts and the success rate is given by option E. B( 60 , 45 , 30 ).

As given in the question,

In the given situation,

Let us consider 'n' represents the number of trials attempt by the weightlifter.

'p' represents the probability of success in his number of trials.

And 'r' represents the number of success out of his total number of attempts.

Here n = 60

p = 45%

r = 30

Using binomial distribution method we can represents the expression of the probability for the given condition  :

B( n , p , r )

Substitute the values we get,

= B( 60, 45, 30 )

Therefore, for the given total number of lifts , success rate the expression represents the probability is given by option E . B ( 60, 45 , 30 ).

Learn more about probability here

brainly.com/question/30034780

#SPJ4

Given the circle L

KL represents the radius of the circle, r = 10

We will find the length of the arc KM using the following formula:

Note: the given angle is in degree, we have converted it to radian

Round to the nearest hundredth.

So, the answer will be, the length of the arc = 9.42

Using the formula of volume of a sphere and hemisphere, the volume of the figures are given as;

1. 2144.57 m³

2. 696.6 m³

3. 20569.1m³

4. 2637ft³

5. 56.5km³

6. 6381.79 in³

The volume of a sphere is given as 4/3πr³

Where π is a constant whose value is equal to 3.14 approximately. “r” is the radius of the hemisphere.

1. The volume of the sphere is;

v = 4/3 * 3.14 * 8³ = 2144.57m³

2. The volume of the sphere is;

v = 4/3 * 3.14 * (11/2)³ = 696.6m³

3. The volume of the sphere is;

v = 4/3 * 3.14 * 17³ = 20569.1m³

4. The volume of the hemisphere is;

v = 2/3 * 3.14 * 10.8³ = 2637ft³

5. The volume of the hemisphere is;

v = 2/3 * 3.14 * 3³ = 56.5km³

6. The volume of the hemisphere is;

v = 2/3 * 3.14 * (29/2)³ = 6381.79in³

Learn more on volume of sphere here;

https://brainly.com/question/22807400

#SPJ1

The equation of the line is with the coordinates f(-6) = 9 and f (20) = 5. is y = (-2/13)x + 117/13.

Y = mx + b, where m is the line's slope and b is the y-intercept, is the slope-intercept form of a linear equation. This form is helpful since it provides information about the line's slope and y-intercept in a clear and understandable manner. We can quickly determine the slope of the line (m) and its point of intersection with the y-axis by glancing at the equation (b). By beginning at the y-intercept and using the slope to determine other locations along the line, we can also graph the line using this method.

The slope of the line is given as:

m = (y2 - y1) / (x2 - x1)

Substitute the given coordinates:

m = (5 - 9) / (20 - (-6))

m = -4 / 26

m = -2 / 13

Using the point slope form we have:

y - y1 = m(x - x1)

Using the point (-6, 9):

y - 9 = (-2/13)(x - (-6))

y - 9 = (-2/13)x - 12/13

y = (-2/13)x + 117/13

So the equation of the line is y = (-2/13)x + 117/13.

Learn more about slope intercept form here:

https://brainly.com/question/29146348

#SPJ1

Answer:

a) The minimum sample size is 601.

b) The minimum sample size is 2401.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

The margin of error is:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

For this problem, we have that:

We dont know the true proportion, so we use \(\pi = 0.5\), which is when we are are going to need the largest sample size.

95% confidence level

So \(\alpha = 0.05\), z is the value of Z that has a pvalue of \(1 - \frac{0.05}{2} = 0.975\), so \(Z = 1.96\).

a. If a 95% confidence interval with a margin of error of no more than 0.04 is desired, give a close estimate of the minimum sample size that will guarantee that the desired margin of error is achieved. (Remember to round up any result, if necessary.)

This is n for which M = 0.04. So

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.04 = 1.96\sqrt{\frac{0.5*0.5}{n}}\)

\(0.04\sqrt{n} = 1.96*0.5\)

\(\sqrt{n} = \frac{1.96*0.5}{0.04}\)

\((\sqrt{n})^2 = (\frac{1.96*0.5}{0.04})^2\)

\(n = 600.25\)

Rounding up

The minimum sample size is 601.

b. If a 95% confidence interval with a margin of error of no more than 0.02 is desired, give a close estimate of the minimum sample size necessary to achieve the desired margin of error.

Now we want n for which M = 0.02. So

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.02 = 1.96\sqrt{\frac{0.5*0.5}{n}}\)

\(0.02\sqrt{n} = 1.96*0.5\)

\(\sqrt{n} = \frac{1.96*0.5}{0.02}\)

\((\sqrt{n})^2 = (\frac{1.96*0.5}{0.02})^2\)

\(n = 2401\)

The minimum sample size is 2401.

Answer:

0

Step-by-step explanation:

Any number that is written in fraction form including integers is called a Rational number.

0 is a whole number, this is not an integer.

The volume of the closet space = 207,936 in³

The volume of the one roll of toilet paper = 141.3in³

To calculate the volume of the closet, the formula that should be used is the formula for the volume of a rectangle = length×width×height.

Where;

length = 57 in

width = 57

height = 64

volume = 57×57×64 = 207,936 in³

The volume of the toilet paper with the shape of a cylinder would be = πr²h

where;

radius = diameter/2= 6/2=3in

height = 5 in

volume of cylinder = 3.14×3×3×5 =141.3in³

Learn more about volume here:

https://brainly.com/question/30794567

#SPJ1