a plane is defined by any three points that are in the plane. if a plane contains the points p(1,0,0), q(1,1,1), and r(2,−1,3), then find a vector orthogonal to the plane.

The required probability of randomly selected person to be a man or a heavy smoker is given by 0.5525.

Total number of people is equals to 1124

Total number of men is equals to 531

Total number of heavy smoker is equals to 90

Man and Heavy smoker are mutually exclusive events.

Let 'M' represents man

And 'H' represents heavy smoker

Probability of randomly selected person is a man or a heavy smoker

= P( M ∪ H )

= Probability of a man  + Probability of a heavy smoker

= P( M ) + P (H)

= ( 531 / 1124 ) + ( 90 / 1124 )

= ( 621 / 1124 )

= 0.5525

Therefore, the probability of a person to be a man or a heavy smoker is equals to 0.5525.

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The above question is incomplete, the complete question is:

If one of the 1124 people is randomly selected, find the probability that the person is a man or heavy smoker.

table is attached.

The marginal cost function is given by:C'(x) = 0.18x(24√x + 19) dollars per unit. If it costs $3,800 to produce 100 units, we need to determine the constant of integration in the cost function. We know that when x = 100, the cost is $3,800.

Hence, we can write:C'(100) = 0.18(100)(24√100 + 19) = 0.18(100)(24 × 10 + 19) = 0.18(100)(240 + 19) = 0.18(100)(259) = 4,476 dollars per unit (approximately).Therefore, the cost function is given by: To obtain the cost function, we have to integrate the marginal cost function:C(x) = ∫[0, x] C'(t) dt + Cwhere C is the constant of integration. From the marginal cost function, we get:C'(x) = 0.18x(24√x + 19) dollars per unit Integrating both sides with respect to x, we get:

C(x) = ∫[0, x] 0.18t(24√t + 19) dt + C= ∫[0, x] (4.32t³/2 + 0.18t²) dt + C= (1.44x⁵/2 + 0.06x³) - (1.44(0)⁵/2 + 0.06(0)³) + C= 1.44x⁵/2 + 0.06x³ + C

When x = 100, C(100) = 3,800. Hence, we get:

3,800 = 1.44(100)⁵/2 + 0.06(100)³ + C= 1.44(10,000) + 0.06(1,000,000) + C= 14,400 + 60,000 + C= 74,400 + C

Therefore, C = 3,800 - 74,400 = -70,600. Thus, the cost function is given by:C(x) = 1.44x⁵/2 + 0.06x³ - 70,600.

The cost function is given by:C(x) = 1.44x⁵/2 + 0.06x³ - 70,600 dollars.

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Answer:

-11

Step-by-step explanation:

First we plug -2 in for c

4(-2)-3=-8-3=-11

By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

WHat is Divisibility?

Divisibility is a mathematical property that describes whether one number can be divided evenly by another number without leaving a remainder. If a number is divisible by another number, it means that the division process results in a whole number without any remainder. For example, 15 is divisible by 3

To prove that 4 evenly divides 11n - 7n for any positive integer n, we can use mathematical induction.

Base Case:

When n = 1, 11n - 7n = 11(1) - 7(1) = 4, which is divisible by 4.

Inductive Step:

Assume that 4 evenly divides 11n - 7n for some positive integer k, i.e., 11k - 7k is divisible by 4.

We need to prove that 4 evenly divides 11(k+1) - 7(k+1), which is (11k + 11) - (7k + 7) = (11k - 7k) + (11 - 7) = 4k + 4.

Since 4 evenly divides 4k, and 4 evenly divides 4, it follows that 4 evenly divides 4k + 4.

By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

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The solution to the inequality "four-thirds times the absolute value of the quantity one fourth times x plus 3 end quantity is less than 4" is: C. x > −24 and x < 0.

In order to determine the solution to the given inequality, we would first of all translate the word description into an absolute value function (inequality) as shown below.

The word description "Four-thirds times the absolute value of the quantity one fourth times x plus 3 end quantity is less than 4" is given by:

Expression = 4/3 × |x/4 + 3| < 4

Expression = 4/3|x/4 + 3| < 4

By solving the expression within absolute value symbol, we have:

x/4 + 3 = (x + 12)/4

4/3|(x + 12)/4| < 4

Multiplying both sides of the inequality by 3/4, we have the following:

4|(x + 12)/4| < 12

(x + 12)/4 < 3

x + 12 < ±12

x > -12 - 12

x > -24

x + 12 < ±12

x < -12 + 12

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Answer:

−24<x<0, so x > -24 and x < 0

Step-by-step explanation:

So its C if im wrong my bad

The sequence diverges and the the limit to the expression  is\(lim(n- > \infty) a_n = \infty - 1 = \infty\)

To determine the convergence of the sequence, we can simplify the expression for the nth term and then apply the limit laws.

\(a_n = n - \sqrt(n + n^2) * \sqrt(n + 3)\)

simplify the term under the square root as follows

\(\sqrt(n + n^2) * \sqrt(n + 3) = \sqrt(n*(1+n)) * \sqrt(n+3) \\= \sqrt(n) * \sqrt(n+1) * \sqrt(n+3)\)

Substitute this back into the original expression for \(a_n\)

\(a_n = n - \sqrt(n) * \sqrt(n+1) * \sqrt(n+3)\)

Now, use the limit laws to evaluate the limit as n approaches infinity.

\(a_n = n - \sqrt(n) * \sqrt(n+1) * \sqrt(n+3) * ((\sqrt(n+1) * \sqrt(n+3)) / (\sqrt(n+1) * \sqrt(n+3)))\\= n - \sqrt(n^2 + 4n + 3) / (\sqrt(n+1) * \sqrt(n+3))\\= n - [(n+1)^2 - 1]^(1/2) / [(n+1)*(n+3)]^(1/2)\)

Now, we can apply the limit laws:

\(lim(n- > \infty) n = \inftylim(n- > \infty) [(n+1)^2 - 1]^(1/2) / [(n+1)(n+3)]^(1/2) = 1/\sqrt(11) = 1\)

Therefore, the limit of the sequence is\(lim(n- > \infty) a_n = \infty - 1 = \infty\)

Since the limit of \(a_n\) as n approaches infinity is infinity, the sequence diverges.

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The population of birds to increase by 50% in 31.25 years.

The differential equation for the population of birds is:

dp/dt = 0.016P

where P is the population of birds and t is time in years.

To obtain the time it takes for the population to increase by 50%, we need to solve for t when P increases by 50%.

Let P0 be the initial population of birds, and P1 be the population after the increase of 50%.

Then we have:

P1 = 1.5P0 (since P increases by 50%)

We can solve for t by integrating the differential equation:

dp/P = 0.016 dt

Integrating both sides, we get:

ln(P) = 0.016t + C

where C is the constant of integration.

To obtain the value of C, we can use the initial condition that the population at t=0 is P0:

ln(P0) = C

Substituting this into the previous equation, we get:

ln(P) = 0.016t + ln(P0)

Taking the exponential of both sides, we get

:P = P0 * e^(0.016t)

Now we can substitute P1 = 1.5P0 and solve for t:

1.5P0 = P0 * e^(0.016t

Dividing both sides by P0, we get:

1.5 = e^(0.016t)

Taking the natural logarithm of both sides, we get:

ln(1.5) = 0.016t

Solving for t, we get:

t = ln(1.5)/0.016

Using a calculator, we get:

t ≈ 31.25 years

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Answer:

a. 120 Degrees

b. 180-120=60 60 Degrees

Step-by-step explanation:

A straight line has a maximum of 180 degrees.

ABC is 120, so CBD is 60

a) The size of angle ABC is 120 degrees.

b) The size of reflex angle CBD is 240 degrees.

a) The size of angle ABC is 120 degrees by inspecting at the protractor and counting from 0° 1o 120°

Reflex angles are formed by extending one of the sides of an angle beyond the straight line, creating an angle greater than 180 degrees. They can be visualized as the "extra" portion of a rotation around a point, beyond the 180-degree mark

b) To determine the size of reflex angle CBD,  consider that a reflex angle measures more than 180 degrees but less than 360 degrees. Since angle ABC is 120 degrees, subtract this angle from 360 to find the remaining measure of the reflex angle CBD.

Reflex angle CBD = 360 degrees - 120 degrees

= 240 degrees.

Therefore, the size of reflex angle CBD is 240 degrees.

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The correct answer is option c) infinitely many solutions..

To solve the system of equations using the substitution method, we'll substitute the value of y from the second equation into the first equation and solve for x.

Given:

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

y = 3x + 4 ---(2)

Substitute equation (2) into equation (1):

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

Simplify:

-6x + 6x + 8 = 8

8 = 8

We obtained a true statement (8 = 8), which means the two equations are equivalent. This solution shows that the system has infinitely many solutions.

Therefore, the correct answer is option c) infinitely many solutions..

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Answer:

\(A=P+P\times S\%\)

Step-by-step explanation:

For calculating the sales tax of a product, it is required to first multiply the original cost price of the product by the sales tax percentage.  

Once the sales tax has been computed add it to the original cost price in order to determine the total cost of the product.

The formula of final amount is:

\(A=P+P\times S\%\)

Here,

A = final amount

P = original cost price

S = sales tax percentage

Answer:

1.$25.68

2.$51.36

3. 77.04

Step-by-step explanation:

I just took the test.

the equation of the tangent to the curve at the point where x = 1 is:

y = 8x - 6

To find the equation of the tangent to the curve at the point where x = 1, we need to determine the slope of the tangent at that point and then use the point-slope form of a line to find the equation.

First, let's find the slope of the tangent. We can do this by finding the derivative of the function f(x) = x√(1 + 3x²) and evaluating it at x = 1.

f(x) = x√(1 + 3x²)

Taking the derivative of f(x) with respect to x:

f'(x) = √(1 + 3x²) + x * (1/2√(1 + 3x²)) * (6x)

Now, we can evaluate f'(x) at x = 1:

f'(1) = √(1 + 3(1)²) + 1 * (1/2√(1 + 3(1)²)) * (6(1))

Simplifying this expression:

f'(1) = √(1 + 3) + (1/2√(1 + 3)) * 6

f'(1) = √4 + (1/2√(4))* 6

f'(1) = 2 + (1/2)(2) * 6

f'(1) = 2 + 1 * 6

f'(1) = 2 + 6

f'(1) = 8

So, the slope of the tangent at x = 1 is 8.

Now that we have the slope, we can use the point-slope form of a line, which is:

y - y₁ = m(x - x₁)

Where:

m is the slope

(x₁, y₁) is the point on the line (x = 1, f(1))

Using the point-slope form, we can write the equation of the tangent:

y - f(1) = 8(x - 1)

Now, substitute the value of f(1) into the equation:

y - f(1) = 8(x - 1)

y - f(1) = 8x - 8

Since we know that f(1) = 1√(1 + 3(1)²), we can substitute it into the equation:

y - √(1 + 3(1)²) = 8x - 8

y - 2 = 8x - 8

y = 8x - 6

Therefore, the equation of the tangent to the curve at the point where x = 1 is:

y = 8x - 6

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Both the graphs have same slope and are parallel and g(x) is translated 3 units down the y - axis.

The general equation of a straight line is -

y = mx + c

Where -

[m] is the slope of the line.

[c] is the y - intercept

We have the following functions -

f(x) = -4x

g(x) = -4x - 3

Refer to the graph attached. The graph of g(x) is the graph of f(x) shifted 3 units downwards. Both the graphs have same slope and are parallel.

Therefore, both the graphs have same slope and are parallel and g(x) is translated 3 units down the y - axis.

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Answer:

25%

Step-by-step explanation:

The total number of 7th grade students = 9 + 11 + 11 + 13 = 44

Out of the 44 students 11 play bass

Probability that a seventh grader chosen at random will play the base is:

11/44 = 1/4 = 0.25

As a percentage, this would be 0.25 x 100 = 25%

Answer:

A. $1.50

B. $4

Step-by-step explanation:

7.5% of $20.00 is $1.50 and 20% of $20.00 is 4.

Yes, the sample size would be large enough if the population is school-aged children and young adults in the United States as this is a simple random sampling.

Simple random sampling is used for randomly selecting the sample size for research. No member in the population has a higher chance in comparison to others for selection in sampling. Every individual has an equal chance to be a part of the sample for the study. This is a type of probability sampling method.

The probability sampling method states that every individual has a fair and equal chance to be selected as a research sample. It includes simple random sampling, stratified sampling, systematic sampling, and cluster sampling. Here the researchers have picked around 150 students and young adults which is an appropriate amount of simple random sample for the study.

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The actual value of the sample average may vary due to chance, and the typical distance it is away from the expected value is about 0.24 feet.

Given that a large population of Indian elephants has an average height of 9 feet with an SD of 0.75 feet, we can use this information to answer the following questions.
If 10 elephants are selected at random, the expected average height of these 10 elephants is still 9 feet. This is because the population average height of 9 feet remains unchanged, even if we randomly select a smaller group of elephants.
However, the actual value of the sample average may vary due to chance. This variation in the sample average is measured by the standard error of the mean (SEM). The SEM is calculated as the standard deviation of the sample divided by the square root of the sample size. For a sample size of 10, the SEM would be 0.24 feet.
Therefore, the typical distance the sample average is away from its expected value is about 0.24 feet. This means that if we were to repeat this random sampling process many times, the average height of the 10 elephants would vary by approximately 0.24 feet on average.
In summary, if 10 elephants are randomly selected from a large population of Indian elephants with an average height of 9 feet and an SD of 0.75 feet, we can expect the average height of these 10 elephants to be 9 feet.

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Data that are accurate, consistent, and available in a timely fashion are considered C) high-quality.

High-quality data is characterized as being reliable, consistent, and timely. High-quality data offers a strong foundation for analysis and decision-making because it is accurate, error-free, and consistent.

It is a valuable asset for organizations because it promotes accurate reporting and analysis, increases operational efficiency, and allows for informed decision-making. Although database management systems like Oracle and Microsoft SQL Server can assist with managing and storing data, the quality of the data is unrelated to the particular technology or program employed.

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Answer:

16/22, 24/33, and 40/55

or

72.7272...% = Percentage form

0.7272... = Decimal form

Hope this helps :)

Pls brainliest...

T he joint moment generating function of x and y is M(t1, t2) = (1/36)Σx=1^6Σz=1^6 e^(t1x + t2z)

Let X be the value of the first die, which takes on values {1, 2, 3, 4, 5, 6} with equal probability of 1/6 each. Let Y be the sum of the values of two dice, so Y takes on values {2, 3, ..., 12}.

The joint moment generating function of X and Y is given by:

M(t1, t2) = E[e^(t1X + t2Y)]

To compute this, we can use the law of total probability and conditioning on the value of X:

M(t1, t2) = E[e^(t1X + t2Y)]

= Σx P(X=x) E[e^(t1X + t2Y) | X=x]

= (1/6)Σx=1^6 E[e^(t1x + t2Y) | X=x]

Now we need to compute E[e^(t1x + t2Y) | X=x]. We can use the fact that the sum of two dice is the sum of two independent uniform random variables on {1, 2, 3, 4, 5, 6}:

E[e^(t1x + t2Y) | X=x] = E[e^(t1x + t2(x+Z))]

= E[e^(tx) e^(t2Z)]

= MZ(t2) e^(tx)

where Z is a uniform random variable on {1, 2, 3, 4, 5, 6} and MZ(t2) is its moment generating function, which is:

MZ(t2) = E[e^(t2Z)]

= (1/6)Σz=1^6 e^(t2z)

Substituting this back into the expression for M(t1, t2), we get:

M(t1, t2) = (1/6)Σx=1^6 E[e^(t1x + t2Y) | X=x]

= (1/6)Σx=1^6 MZ(t2) e^(tx)

= (1/6)Σx=1^6 [(1/6)Σz=1^6 e^(t2z)] e^(tx)

Simplifying the expression, we get:

M(t1, t2) = (1/36)Σx=1^6Σz=1^6 e^(t1x + t2z)

This is the joint moment generating function of X and Y.

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The tilde approximation of the growth function f(n) = n + 5n^4 + nlg(n) is ~5n^4.

The tilde notation is used to describe the asymptotic behavior of a function, which means how the function grows relative to other functions as the input gets very large.

To determine the tilde approximation of the function f(n) = n + 5n^4 + nlg(n), we need to identify the term that grows the fastest as n becomes very large.

Analyze the first term: n. As n gets larger, the term n becomes relatively smaller compared to the other terms in the function.

Analyze the second term: 5n^4. This term grows much faster than the first term as n becomes larger.

Analyze the third term: nlg(n). The logarithmic term grows slower than the polynomial term, meaning that it becomes relatively smaller as n becomes larger.

Based on the analysis above, we can conclude that the dominant term in the function is 5n^4.

Therefore, the tilde approximation of the function f(n) = n + 5n^4 + nlg(n) is ~5n^4, meaning that the function grows approximately as n^4 when n becomes very large.

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Answer

110

Step-by-step explanation:

35+35=70

180-70=110

Answer:

4. 3/10

Step-by-step explanation:

I believe it would be answer 4 because there are 10 coins in all and 3 pennies, making the ratio 3:10

The marginal product of capital is 3000 units of output when 5 units of capital and 10 units of labor are employed.

The marginal product of capital (MPK) is defined as the additional output that results from adding one more unit of capital while holding other inputs constant.

To find the MPK when 5 units of capital and 10 units of labor are employed, we need to take the partial derivative of the production function with respect to capital, holding labor constant at 10:

MPK = ∂q/∂k | l=10

Taking the partial derivative of the production function with respect to k, we get:

\(∂q/∂k = 12k^2l\)

Substituting k=5 and l=10, we get:

MPK = ∂q/∂k | l=10 = \(12(5)^2(10) = 3000\)

Therefore, the marginal product of capital is 3000 units of output when 5 units of capital and 10 units of labor are employed.

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Ok, we need find the price of each dvd unit, then for this we are going to take the total price of the dvd's and divide it by the quantity that was compared.

So we have this:

Total dvd price: 76.57

Number of dvd: 13

Dividing we get:

76.57/13=5.89

The long division is:

76/13 equals 5 and we have a remainder of 11 that goes down, we went down on the 5th of ten, 115 divided by 13 equals 8 and there are 11 remainders left, we lower the 7 of the hundredths, and 117 divided 13 equals 9.

So finally we get that the unitary price of dvd is $5.89.

Answer:

313(?)

Step-by-step explanation:

qasxx c.f. tikhg

Answer:

Hey there!

The line 4x-3y=-9 can be converted to y=mx+b form.

4x-3y=-9

-3y=-4x-9

3y=4x+9

y=4/3x+3

The slope of a line perpendicular to this line would be -3/4.

The slope of a line parallel to this line would be 4/3.

Hope this helps :)