dhdrbzdsdbSFBDFbdff'shgv'sdlkhvlSDKhvbsldKnvb"LN

The answers to all subquestions would be

Part A: \(P(X=x)= {15 \choose x} (0.15)^{x} (0.85)^{15-x}\), x= 0, 1, 2, 3, ..., 15.

Part B: P(X = 1) = 0.2312

Part C: P(X = 2) = 0.2656

Part D: P(X ≥ 2) = 0.6814

Part E: P(X = 0) = 0.0874

What is a binomial distribution?

The binomial distribution with parameters n and p in probability theory and statistics is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-no question and each with its own Boolean-valued outcome: success or failure.

Let X be the random variable.

The number of trials n = 15, P=0.15

X ~ Bin(n, p)

Part A:

      \(P(X=x)= {n \choose x} (p)^{x} (1-p)^{n-x}\)

      \(P(X=x)= {15 \choose x} (0.15)^{x} (0.85)^{15-x}\), x=0, 1, 2, 3,..., 15.

Part B:

    \(P(X=1)= {15 \choose 1} (0.15)^{1} (0.85)^{15-1}\\\\P(X=1)= {(15)} (0.15) (0.85)^{14}\\\\P(X=1)=0.2312\)

Part C:

     \(P(X=2)= {15 \choose 2} (0.15)^{2} (0.85)^{15-2}\\\\P(X=2)= {(105)} (0.15)^2 (0.85)^{13}\\\\P(X=2)=0.2856\)

Part D:

 \(P(X\geq 2)= 1-P(X < 2)\\\\P(X\geq 2)=1-P(X=0)-P(X=1)\\\\P(X\geq 2)=1-0.0873-0.3212\\\\P(X\geq2)=0.6814\)

Part E:

  The probability of none of the children getting the disease will be

             \(P(X=0)= {15 \choose 0} (0.15)^{0} (0.85)^{15-0}\\\\P(X=0)= {(1)} (1) (0.85)^{15}\\\\P(X=1)=0.8734\)

Hence,

Part A: \(P(X=x)= {15 \choose x} (0.15)^{x} (0.85)^{15-x}\), x= 0, 1, 2, 3, ..., 15.

Part B: P(X = 1) = 0.2312

Part C: P(X = 2) = 0.2656

Part D: P(X ≥ 2) = 0.6814

Part E: P(X = 0) = 0.0874

To learn more about binomial distribution, visit:

https://brainly.com/question/9325204

#SPJ4

For two matrices to be multiplicative inverse of each other, the product of the matrix must be equal to an identity matrix I.

For two matrices to be multiplicative inverse of each other, the product of the matrix must be equal to an identity matrix I.

Since the 2 by 2 matrix is given, hence the resulting value of I must be a 2 by 2 matrix.

Multiply the row of the first matrix with the column of the second to have:

\(\left[\begin{array}{ccc}-3&7\\-2&5\\\end{array}\right] \left[\begin{array}{ccc}-5&-7\\-2&3\\\end{array}\right] =\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right]\)

Learn more on identity matrix here: https://brainly.com/question/2361951

#SPJ1

Given, `f(x) f¹(x) = 1/(x + 4)`

We need to find the exponential function passing through the points (-1,-5) and (2,45).Let, y = ae^(bx)

Here, we have two unknowns a and b.

To find them we will use the given points

(-1,-5) and (2,45).Putting (x,y) = (-1,-5) in the equation of exponential function,

we get-5 = ae^(-b) ----(1)Putting (x,y) = (2,45) in the equation of exponential function,

we get45 = ae^(2b)-----(2)

\(Dividing equation (2) by equation (1), we get:45/-5 = e^(2b)/e^(-b) = > -9 = e^(3b) = > ln(-9) = 3b = > b = ln(-9)/3Therefore, putting value of b in equation (1), we get:-5 = ae^(-ln(-9)/3) = > -5 = a(-9)^(1/3) = > a = -5/-9^(1/3)\)

Hence, the required formula for the exponential function is:y = (-5/-9^(1/3))*e^(ln(-9)x/3) or y = (5/9^(1/3))*e^(-ln9x/3

)Therefore, the required exponential function is y = (5/9^(1/3))*e^(-ln9x/3).

To know more about exponential function visit:

https://brainly.com/question/26130204

#SPJ11

Answer:

x = 12°

∠RST = 40°

∠STR = 100°

Step-by-step explanation:

Taking into account the definition of a system of linear equations, the amount of adult tickets sold is 356 and the amount of child tickets sold is 144.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

The maximum capacity for seating in a theater is 500 people. If they sold out on a certain showtime, this is represented by x+y=500.

On the other side, the theater sells two types of tickets, adult tickets for $7.25 each and child tickets for $4 each and the made a total of $3,157. This is represented by 7.25x +4y=3157.

So, the system of equations to be solved is

\(\left \{ {{x+y=500} \atop {7.25x+4y=3157}} \right.\)

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable x from the first equation you get:

x=500 - y

Substituting this expression in the second equation you get:

7.25× (500 -y) +4y=3157

7.25×500 - 7.25y +4y=3157

3625 - 7.25y +4y=3157

- 7.25y +4y=3157 -3625

-3.25y= -468

y= (-468)÷ (-3.25)

y= 144

Substituting this value in the expression x=500 - y you get:

x=500 - 144

x=356

Remembering that "x" is the amount of adult tickets sold and "y" is the amount of child tickets sold, you get that the amount of adult tickets sold is 356 and the amount of child tickets sold is 144.

Learn more about system of equations:

brainly.com/question/14323743

brainly.com/question/1365672

brainly.com/question/20533585

brainly.com/question/20379472

Answer:

896 meters sq

Step-by-step explanation:

Step 1. Find the area of each square

Big square: 36 x 36 = 1296

Small square: 20 x 20 = 400

Step 2. Find the area of the shaded region only

big square A - small square A = ONLY shaded region area

1296 - 400 = A

896 \(m^{2}\) = A

I hope this helps!

Answer:

this isn't an answer but i think we do the same online school HAHAHA

Based on the two-tangent theorem, the value of x is calculated in the circle as: x = 2.

Based on the two-tangent theorem, if two tangents are drawn from a circle to meet each other at any point outside the circle, then the lengths of the tangents are congruent to each other, that is, they are equal.

Therefore, we would create the following equation based on the two-tangent theorem:

20x + 6 = 10x + 26

Combine like terms:

20x - 10x = -6 + 26

10x = 20

Divide both sides by 10:

10x/10 = 20/10

x = 2

Learn more about the two-tangent theorem on:

https://brainly.com/question/31548143

#SPJ1

Answer:

x=3,x=4

Step-by-step explanation:

(x-3)(x-4)=0

x=3, 4

Answer:

x = 3

x = 4

Step-by-step explanation:

"find the roots" means to find the solutions to the equation.

Roots are solutions are zeros are x-intercepts.

You are being asked to solve the equation.

First, factor the quadratic.

x^2 -7x + 12 = 0

(x - 3)(x - 4) = 0

This works because -3 × -4 is 12 and

-3 + -4 is -7

You see the 12 in the equation is the constant and the -7 is the middle term, the x-term in the trinomial.

So we have

(x - 3)(x - 4) = 0

Separate the two factors into two separate tiny, one-step equations.

x - 3 = 0 , x - 4 = 0

Solve.

x = 3 , x = 4

These are the roots (solutions, zeros and x-intercepts)

The Logarithmic function is a mathematical operation that is used to determine the logarithm of a number.

The logarithm of a number x is the exponent to which a fixed number, the base, must be raised to produce x. The most common bases used are 10 and e. The formula for determining the logarithm of a number x base d is: log base d of x = (log base d of x)/(log base d of b).

For example, if we want to calculate the log base 10 of a number x, we would use the formula: log base 10 of x = (log base 10 of x)/(log base 10 of b). We can calculate the log base 10 of a number x by taking the logarithm of x and dividing it by the logarithm of the base, 10. The result will be the log base 10 of x.

For example, if we want to calculate the log base 10 of 25, we would calculate the logarithm of 25 and divide it by the logarithm of 10. The calculation would be: log base 10 of 25 = (log base 10 of 25)/(log base 10 of 10) = (1.3979)/(1) = 1.3979. This means that the log base 10 of 25 is 1.3979.

Learn more about Logarithmic function here:

https://brainly.com/question/16909003

#SPJ4

Answer: A. 4(8m-2) and 32m -8

Step-by-step explanation: First distribute the 4 to 8m and -2 to get 32m - 8 which is equal to 32m - 8.

32m - 8 = 32m - 8

Hope this helps! :)

Answer:

The first one

Step-by-step explanation:

4(8m-2)=32m-8

Answer:

115

Step-by-step explanation:

Answer:

Step-by-step explanation:

$86.50

There were 33 questions on Clytie's test and she got a grade of 85%.

The number of right answers was:

The result is approximately 28, thus:

Clytie got 28 answers right

Answer:in decimal form it is 0.12. in 12/100

Step-by-step explanation:

Answer:Examples of Spiral Movement are:

Step-by-step explanation:

1)Cyclone

2)Spiral fern

The examples of a spiral motion include cyclone, motion of electron in uniform magnetic field.

The path of a point in a plane moving around a central point while continuously receding from or approaching it.

Given is a spiral motion.

The examples of a spiral motion include cyclone, motion of electron in uniform magnetic field.

Therefore, the examples of a spiral motion include cyclone, motion of electron in uniform magnetic field.

To solve more questions on spiral motion, visit the link below -

https://brainly.com/question/11020427

#SPJ2

To find C∇f·dr, where C is a constant and f has parametric equations\(x = t^2 + 1\) and \(y = t^3 + t\) for 0 ≤ t ≤ 1, we need to evaluate the line integral. The line integral ∇f·dr represents the work done along the curve defined by the parametric equations.

To calculate C∇f·dr, we first need to find the gradient of the function f. The gradient of f is given by ∇f = (∂f/∂x, ∂f/∂y), where ∂f/∂x and ∂f/∂y are the partial derivatives of f with respect to x and y, respectively.

Taking the partial derivatives of f = (x, y) with respect to x and y, we get ∂f/∂x = 2t and ∂f/∂y = \(3t^2\) + 1.

Next, we need to parameterize the curve defined by the given parametric equations. The curve is defined for 0 ≤ t ≤ 1.

To evaluate the line integral C∇f·dr, we substitute the gradient components (∂f/∂x, ∂f/∂y) and the differential elements (dx, dy) with their corresponding expressions in terms of t.

Finally, we integrate the dot product C(∂f/∂x dx + ∂f/∂y dy) along the curve from t = 0 to t = 1. The result will depend on the constant C and can be computed using the given table of values for x and y.

Learn more about parametric equations here:

https://brainly.com/question/29275326

#SPJ11

The complete question is:

A Table Of Values Of A Functionfwith Continuous Gradient Is Given. Find

A table of values of a functionfwith continuous gradient is given. FindCnablaf�dr, whereChas parametric equationsx=t2+ 1,y=t3+t, 0t1.

x\y 0 1 2

0 2 7 5

1 4 6 8

2 9 3 10

The t-test yields the probability (p value) that the null hypothesis is option (B) incorrect

The p-value in a t-test represents the probability of obtaining the observed test statistic (or one more extreme) assuming that the null hypothesis is true. The null hypothesis is typically a statement of "no effect" or "no difference" between two groups being compared in the test.

Therefore, a low p-value (generally less than 0.05) indicates that the observed data is unlikely to have occurred by chance under the null hypothesis and suggests that the null hypothesis is likely to be false.

In other words, a low p-value provides evidence against the null hypothesis and in favor of the alternative hypothesis (which typically represents the hypothesis that the researchers are interested in testing).

Thus, the p-value does not directly tell us whether the null hypothesis is correct or incorrect, but rather whether the evidence supports rejecting it or not.

Therefore, the correct option is (B) incorrect

Learn more about p-value here

brainly.com/question/30461126

#SPJ4

Answer:

$16/5tickets

Step-by-step explanation:

it be in simplest form mate.

The transfer price set by the selling division should be equal to the selling price less the variable costs plus the foregone contribution to the organization of making the transfer internally. Option D.

The transfer price refers to the price at which goods or services are transferred between divisions within the same organization. When the selling division sets the transfer price, it needs to consider various factors. Option D, selling price less the variable costs plus the foregone contribution to the organization of making the transfer internally, is the most appropriate choice.

The selling price less the variable costs ensures that the selling division covers its direct costs associated with the transferred goods or services. This ensures that the division remains financially viable and does not incur losses. However, it is also important to consider the opportunity cost of making the transfer internally.

The foregone contribution to the organization represents the potential profit or contribution that the selling division could have made if it had sold the goods or services to external customers instead of transferring them internally. By including this foregone contribution in the transfer price, the selling division accounts for the potential value it could have added to the organization.

In conclusion, the transfer price set by the selling division should consider both the variable costs associated with the transfer and the foregone contribution to the organization. Option D, selling price less the variable costs plus the foregone contribution to the organization of making the transfer internally, captures both of these factors and provides a comprehensive approach to setting the transfer price.

Learn more about divisions here: https://brainly.com/question/28598725

#SPJ11

Answer:

[AF is equal to FE, CD + DE = CE]

a).

\(AM = \frac{1}{2} AD \\ \\ AM = \frac{15}{2} \\ \\ AM = 7.5\)

b).

\(MF = \frac{1}{2} CF \\ \\ MF = \frac{7}{2} \\ \\ MF = 3.5\)

c).

\(MB = ME \\ 6 = 4x - 5 \\ 4x = 11 \\ x = \frac{11}{4} \\ \\ x = 2.75\)

The probability of choosing a 5 and then a 6 is 1/49

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

The tiles

Where we have

Total = 7

The probability of choosing a 5 and then a 6 is

P = P(5) * P(6)

So, we have

P = 1/7 * 1/7

Evaluate

P = 1/49

Hence, the probability of choosing a 5 and then a 6 is 1/49

Read more about probability at

https://brainly.com/question/31649379

#SPJ1

Question

You randomly choose one of the tiles. Without replacing the first tile, you choose a second tile. Find the probability of the compound event. Write your answer as a fraction or percent rounded to the nearest tenth. The probability of choosing a 5 and then a 6

Answer:

I would say yes if Im wrong im deeply sorry

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Note that I will be using a, b, and y instead of their Greek counterparts.

First, we know that sin(c+d) = sin(c)cos(d) + cos(d)sin(a) and sin(c-d) = sin(c)cos(d) - cos(d)sin(a). We can apply these here to get

sin(b+y) = sin(b)cos(y) + cos(b)sin(y)

sin(b-y) = sin(b)cos(y) - cos(b)sin(y)

sin(a+y) = sin(a)cos(y) + cos(a)sin(y)

sin(a-y) = sin(a)cos(y) - cos(a)sin(y)

Plugging these into our equation, we get

(sin(b)cos(y) + cos(b)sin(y) - (sin(b)cos(y) - cos(b)sin(y)))

/

(sin(a)cos(y) + cos(a)sin(y)-(sin(a)cos(y) - cos(a)sin(y)))

=

2cos(b)sin(y) / 2cos(a)sin(y)

= cos(b)sin(y)/cos(a)sin(y)

= cos(b)/cos(a)

Next, we can see that a+b = π, so we can subtract b from both sides to get a = π -b. Plugging that in for a in our equation, we get

cos(b) / cos(π-b)

After that, we know that cos(c-d) = cos(c)cos(d) - sin(c)sin(d). Plugging that in here, we get

cos(π-b) = cos(π)cos(b) - sin(π)sin(b)

= -cos(b) + 0

= -cos(b)

Plugging that back into our equation, we get

cos(b) / -cos(b) = -1

Answer:

(a) $1.98

(b) $6.30

Step-by-step explanation:

(a)

The new value =

1.80 + The value of the percentage increase =

1.80 + (10% × 1.80) =

1.80 + 10% × 1.80 =

(1 + 10%) × 1.80 =

(100% + 10%) × 1.80 =

110% × 1.80 =

110 ÷ 100 × 1.80 =

110 × 1.80 ÷ 100 =

198 ÷ 100 =

1.98

Calculate the actual change (the absolute difference) between the two values

The actual change =

The new value - 1.80 =

1.98 - 1.80 =

0.18

Proof of calculation.

Calculate the percentage increased value...

... and see if we get as a result...

... the actual change (the absolute difference).

Calculate the percentage increased value:

The value of the percentage increase =

10% × 1.80 =

10 ÷ 100 × 1.80 =

10 × 1.80 ÷ 100 =

18 ÷ 100 =

0.18

So we have proven that the calculations are correct.

For positive numbers

The actual change =

The value of the percentage increase

The answer:

1.80 increased by 10% = 1.98

The actual change:

1.98 - 1.80 = 0.18

(b)

Calculate the New value
The new value =

42.0 + The value of the percentage increase =

4.20 + (50% × 4.20) =

4.20 + 50% × 4.20 =

(1 + 50%) × 4.20 =

(100% + 50%) × 4.20 =

150% × 4.20 =

150 ÷ 100 × 4.20 =

150 × 4.20 ÷ 100 =

63,000 ÷ 100 =

630

(but its as a dollar so its 6.30)

Calculate the actual change (the absolute difference) between the two values

The actual change =

The new value - 4.20 =

6.30 - 4.20 =

2.10

Proof of calculation.

Calculate the percentage increased value...

... and see if we get as a result...

... the actual change (the absolute difference).

Calculate the percentage increased value:

The value of the percentage increase =

50% × 4.20 =

50 ÷ 100 × 4.20 =

50 × 4.20 ÷ 100 =

21,000 ÷ 100 =

210

(but its as a dollar so its 2.10)

So we have proven that the calculations are correct.

For positive numbers

The actual change =

The value of the percentage increase

The answer:

4.20 increased by 50% = 6.30

The actual change:

6.30 - 4.20 = 2.10

Step-by-step explanation:

25 1/2 = 51/2

1 1/2 = 3/2

51/2 / 3/2 = 17

therefore,

b >15

just find the roots and substitute

a(x - "first root") (x - "second root")

The equivalent equation after combining like terms is x-7=1. To solve this equation, simply add 7 to both sides of the equation and you will get x=8.

An equivalent equation is an equation that is mathematically equal to another equation, meaning that both equations have the same solutions. For example, the equation "2x + 5 = 11" is equivalent to the equation "2x = 6". Both equations have the same solution, x = 3.

This is done by subtracting 2x from both sides, and then adding 9 to both sides. Doing so eliminates the -2x and -9 terms, leaving just x on one side, and 7 on the other. Combining like terms is a useful way to simplify equations, and it is important to understand how to do it in order to solve more complex equations.

To know more about  equation click-
https://brainly.com/question/2972832
#SPJ1

The correct option is -2f (x - 4) as it accurately represents how f(x) is transformed to get g(x) using the given function g(x) = a · f (x b). -2f (x - 4))

To transform f(x) into g(x) using the given function g(x) = a · f (x b), we need to substitute the values of a and b into the function.

Let's go through each option and see how f(x) is transformed: –2f (x 4): To transform f(x) to g(x), we substitute a = -2 and b = 4 into the given function.

Therefore, g(x) = -2 · f (x 4). –2f (x – 4):

Similar to the previous option, we substitute a = -2 and b = -4 into the given function. Hence, g(x) = -2 · f (x - 4). –f (x 4):

By substituting a = -1 and b = 4 into the function, we obtain g(x) = -1 · f (x 4). –f (x – 4):

Lastly, we substitute a = -1 and b = -4 into the function, giving us g(x) = -1 · f (x - 4).

In conclusion, the correct option is -2f (x - 4) as it accurately represents how f(x) is transformed to get g(x) using the given function g(x) = a · f (x b). -2f (x - 4))

The correct option is -2f (x - 4).

To transform f(x) into g(x) using the function g(x) = a · f (x b), we substitute the values of a and b into the function. In this case, a = -2 and b = -4.

Therefore, g(x) = -2 · f(x - 4). The negative sign indicates a reflection about the x-axis. The factor of 2 signifies that the graph of g(x) is vertically stretched or compressed by a factor of 2 compared to the graph of f(x). The value of -4 in the function represents a horizontal shift to the right by 4 units. So, g(x) will be obtained by shifting the graph of f(x) to the right by 4 units, reflecting it about the x-axis, and vertically compressing it by a factor of 2. Hence, the correct option is -2f (x - 4).)  

To Know More about reflection visit:

brainly.com/question/15487308  

#SPJ11

Answer:

(2, –3) is a solution to the system of linear equations.

Step-by-step explanation:

Given: Equations:

3x - y = 9 --------(1),

4x + y = 5 --------(2),

Add Equation (1) + Equation (2),

3x + 4x = 9 + 5

7x = 14  ( Combine like terms )

x = 2   ( Divide both sides by 7 ),

From equation 1:

3(2) - y = 9

6 - y = 9

-y = 9 - 6    ( Subtraction 6 on both sides )

-y = 3

y = - 3     ( Multiplying -1 on both sides )