Gold Corp. has an ROE of 12% and a payout ratio of 20%.
What is its sustainable growth rate? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answers

Answer 1

The sustainable growth rate is calculated by subtracting the payout ratio from the ROE.

The sustainable growth rate is calculated by subtracting the payout ratio from the ROE. To calculate the sustainable growth rate for Gold Corp., we must first calculate the retention ratio. The retention ratio is calculated by subtracting the payout ratio from 100%. In this case, the retention ratio would be 100% - 20% = 80%. The sustainable growth rate is then calculated by multiplying the retention ratio by the ROE. In this case, the equation would be 80% * 12% = 9.6%. The sustainable growth rate for Gold Corp. is 9.6%, which can be rounded to 9.6%.

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Related Questions

Charlotte and Pablo are each making purple paint by mixing blue
paint and red paint. Charlotte uses 1 cup of red paint for every
2 cups of blue paint. Pablo uses 2 cups of red paint for every
3 cups of blue paint. Whose paint is a bluer shade of purple?

Answers

Answer:

Charlotte's mix has a bluer shade of purple

Step-by-step explanation:

Since we are asked whose paint is a bluer shade it would be easier to express the ratios of the paint mix as blue:red

Charlotte: 1 cup red for every 2 cups blue ==> 2 cups blue for every 1 cup red

This can be expressed as the ratio
[tex]\dfrac{ 2 \;blue}{1\;red} = \dfrac{2}{1} = 2[/tex]

[tex]-------------------[/tex]

Pablo : 2 cups red for every 3 cups blue ==> 3 cups blue for every 2 cups red

The ratio of blue to red
= [tex]\dfrac{3 \;blue}{2\;red} = \dfrac{3}{2} = 1\dfrac{1}{2} \;\; (or\; 1.5)[/tex]

Since
[tex]2 > 1\dfrac{1}{2} \;\;\;(or\; 2 > 1.5)[/tex]  

Charlotte's mix has a bluer shade of purple

what is the value of the expression shown below when x=7? 3x^2 - 2x+3

Answers

The expression value of 3x^2 - 2x+3 is 6x^2 - 13x + 6

What is expression value?

Value of an Expression The value of the expression is the result of the calculation described by this expression when the variables and constants in it are assigned values. Letters can be used to represent numbers in an algebraic expression.

Apply the distributive property:

→ 3x (2 - 3) - 2 (2x - 3)

Apply the distributive property:

→ 3x (2x) + 3x ⋅ -3 - 2 (2x - 3)

Apply the distributive property:

→ 3x (2x) + 3x ⋅ -3 - 2 (2x) - 2 ⋅ -3

Simplify each term:

→ 6x^2 - 9x - 4x  + 6x

Subtract 4x from -9x

→ 6x^ - 13x + 6

Therefore, the expression value of 3x^2 - 2x+3 is 6x^2 - 13x + 6

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The value of the expression given is 136.

What are Expressions?

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given expression is,

3x² - 2x + 3

We have to find the value of the expression when x = 7.

Substitute x = 7.

(3 × 7²) - (2 × 7) + 3 = (3 × 49) - 14 + 3

                               = 147 - 14 + 3

                               = 136

Hence the value of the expression is 136.

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The length of life Y1 AND Y2
for fuses of a certain type is modeled by the exponential distribution, with
(The measurements are in hundreds of hours.)
a. If two such fuses have independent lengths of life and , find the joint probability density function for and .
b. One fuse in part (a) is in a primary system, and the other is in a backup system that comes into use only if the primary system fails. The total effective length of life of the two fuses is then Find .

Answers

a) The joint probability density function is [tex]f(y_1,y_2) = f(y_1) * f(y_2) = (1/3e^{(-y1/3)})(1/3e^{-y2/3})[/tex]

b) The total effective length of life of the two fuses is less than or equal to one.

The exponential distribution is a probability distribution that models the length of life of fuses, and its probability density function can be used to find the joint probability density function for the lengths of two independent fuses.

a) To find the joint probability density function for the lengths of two independent fuses, we simply multiply the probability density functions of each individual fuse. In this case, we have

[tex]= > f(y_1,y_2) = f(y_1) * f(y_2) = (1/3e^{(-y1/3)})(1/3e^{-y2/3})[/tex]

for y₁, y₂ > 0. This is a function that gives the probability of a given pair of lengths (y₁,y₂) occurring.

b) To find P(Y₁ + Y₂ ≤ 1), we must first determine the cumulative distribution function for the sum of the lengths of the two fuses. This is given by

=> F(y) = P(Y₁ + Y₂ ≤ y) = ∫∫f(x,y)dxdy,

where the integral is taken over the region x+y ≤ y. We can simplify this by changing the order of integration:

=> [tex]F(y) = \int0^y\int0^{y-x}f(x,y)dxdy.[/tex]

Using the probability density function given in part (a), we have

=> [tex]F(y) = \int0^y\int0^{y-x}(1/9)e^{-(x+y)/3}dxdy[/tex]

This can be solved using integration by parts or by using the fact that the exponential function integrates to itself, giving

=> [tex]F(y) = 1 - e^{-y/3)(y+3)}[/tex]

Finally, we can find P(Y₁ + Y₂ ≤ 1) by evaluating F(1) - F(0), which gives

=> [tex]P(Y_1 + Y_2 ≤ 1) = 1 - e^{(-1/3)(4/3)}[/tex].

This is a function that gives the probability that the total effective length of life of two fuses is less than or equal to one.

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Complete Question:

The length of life Y1 AND Y2 for fuses of a certain type is modeled by the exponential distribution, with

[tex]f(y) = \left \{ {1/3e^{-y/3} y > 0,} \atop {0, else where }} \right.[/tex]

(The measurements are in hundreds of hours.)

a) If two such fuses have independent lengths of life Y1 and Y2, find the joint probability density function for Y1 and Y2.

b) One fuse in part (a) is in a primary system, and the other is in a backup system that comes into use only if the primary system fails. The total effective length of life of the two fuses is then Y1 + Y2. Find P(Y1 + Y2 ≤ 1).

mack is selling beaded necklaces and beaded wristbands at the craft market. a. a necklace requires 40 minutes to make. b. a wristband requires 25 minutes to make. c. mack has 360 minutes to make the necklaces and wristbands. additionally, a. mack wants to make no more than 12 items. b. when mack sells the necklaces and wristbands at the craft market, he will make $3.00 profit per necklace and $2.00 profit per wristband. let x = the number of necklaces mack maker.
Let y = the number of wristbands mack makes.

Answers

Mack should make 4 necklaces and 8 wristbands to maximize his profit while staying within his time and quantity constraints.

His profit would be:

Profit = 3(4) + 2(8) = $20.

What is the system of equations?

One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.

From the information given, we know:

a) Necklace requires 40 minutes to make.

Let x be the number of necklaces made, then the total time spent on necklaces is 40x.

b) Wristband requires 25 minutes to make.

Let y be the number of wristbands made, then the total time spent on wristbands is 25y.

c) Mack has a total of 360 minutes to make necklaces and wristbands. Therefore, the equation for time is:

40x + 25y = 360

d) Mack wants to make no more than 12 items, so we have the inequality:

x + y ≤ 12

e) Mack makes a profit of $3.00 per necklace and $2.00 per wristband. Therefore, the equation for profit is:

Profit = 3x + 2y

Now we have the following system of equations:

40x + 25y = 360

x + y ≤ 12

Profit = 3x + 2y

From equation (2), we have y = 12 - x.

Substitute y = 12 - x into equations (1) and (3):

40x + 25(12 - x) = 360

Profit = 3x + 2(12 - x)

Simplify and solve for x:

40x + 300 - 25x = 360

15x = 60

x = 4

Substitute x = 4 into equation (2) to find y:

y = 12 - x = 12 - 4 = 8

Therefore, His profit would be, Profit = 3(4) + 2(8) = $20.

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A tower made of wooden blocks measures​114 feet high. Then a block is added that increases the height of the tower by 8 inches.

What is the final height of the block tower?

Answers

Depends how the answer "should" be formatted but 114 2/3 feet should do the trick

Which sign makes the statement true?

792 3/20

792 1/2

Answers

The sign that makes the statement true is 792 3/20 ≠ 792 1/2.

What is a fraction?

A fraction is written in the form of p/q, where q ≠ 0.

There are two types of fractions: proper fractions in which the numerator is less than the denominator and,

Improper fractions in which the numerator is larger than the denominator.

Given, Are two fractions 792 3/20 and 792 1/2.

The sign that makes the statement true is 792 3/20 ≠ 792 1/2.

Some other signs, for example, Inequalities can also make the statement true.

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It takes 6 hours to travel 372 miles. How long
will it take to travel 279 miles?

Answers

The time to travel 279 miles is 4.5 hours

How to determine the time taken

We can use the formula:

time = distance ÷ speed

To find the time it will take to travel 279 miles, given that it takes 6 hours to travel 372 miles.

The speed is constant, so we can find it by dividing the distance by the time for the first trip:

speed = distance ÷ time = 372 miles ÷ 6 hours = 62 miles/hour

Now we can use the speed to find the time it will take to travel 279 miles:

time = distance ÷ speed = 279 miles ÷ 62 miles/hour ≈ 4.5 hours

Hence, it will take approximately 4.5 hours to travel 279 miles at this speed.

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¿ Como despejar B en esta variable

Answers

The simplified form of the expression (4 - a²b³)/5 = (9 - 3b³)/7 is

b³(15 - 7a²) = 17.

What is an equation?

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

Given, An equation (4 - a²b³)/5 = (9 - 3b³)/7,  in variables 'a' and 'b'.

7(4 - a²b³) = 5(9 - 3b³).

28 - 7a²b³ = 45 - 15b³.

15b³ - 7a²b³ = 45 - 28.

b³(15 - 7a²) = 17.

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Bill will run at least 31 miles this week. So far, he has run 16 miles. What are the possible numbers of additional miles he will run? Use t for the number of additional miles he will run. Write your answer as an inequality solved for t.

Answers

Answer:

The inequality to set up is [tex]t+16 \ge 31[/tex]

It solves to [tex]t \ge 15[/tex]

Bill needs to run at least 15 more miles.

================================================

Explanation:

He has run 16 miles so far. Add on another t miles to get 16+t or t+16 to represent the total amount he runs. This expression must be 31 or larger

Either t+16 > 31 or t+16 = 31

Those two items condense to [tex]t+16 \ge 31[/tex]

To solve for t, we subtract 16 from both sides to undo the +16.

[tex]t+16 \ge 31\\\\t+16-16 \ge 31-16\\\\t \ge 15\\\\[/tex]

Bill needs to run at least 15 more miles.

Meaning that t = 15, t = 16, t = 17, etc.

I will give brainlist for the right answer!!

use one of these equations to solve!

1. Separation of variables
2.Homogeneous equation
3. Exact equation

I need answer ASAP please!​

Answers

Answer:

the solution to the differential equation is:

y + (1/3)y^3 = e^x + 1/3.

Step-by-step explanation:

We can use the equation e^x=(1/(1+y^2))dy/dx to solve this differential equation using separation of variables.

First, we can rewrite the equation as:

(1+y^2)dy = e^x dx

Next, we can separate the variables:

(1+y^2)dy = e^x dx

∫ (1+y^2)dy = ∫ e^x dx

y + (1/3)y^3 = e^x + C

where C is the constant of integration.

Now we can use the initial condition to solve for C. Let's say the initial condition is y(0) = 1, then we have:

1 + (1/3)(1)^3 = e^0 + C

4/3 = 1 + C

C = 1/3

Therefore, the solution to the differential equation is:

y + (1/3)y^3 = e^x + 1/3.

What values of x
and y
satisfy the system {y=−2x+3
{y=5x−4?

Enter your answer as an ordered pair, like this: (42, 53)

If there is no solution, enter "no"; if there are infinitely many solutions, enter "inf."

Answers

The solution to the system of equation y = -2x + 3 and y = 5x - 4 is (1,1).

What is the solution to the system of equation?

Given the system of equation in the question;

y = -2x + 3

y = 5x - 4

To solve the system of equation, plug equation one to into equation two and solve for x.

y = 5x - 4

Plug in y = -2x + 3

-2x + 3 = 5x - 4

Solve for x

-2x - 5x = - 4 - 3

-7x = -7

x = -7 / -7

x = 1

Now, plug x = 1 into equation one and solve for x.

y = -2x + 3

Plug in x = 1

y = -2( 1 ) + 3

y = -2 + 3

y = 1

Therefore, the value of x is 1 and y is also 1.

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Show that in any parallelogram the sum of the squares of the lengths of the four sides equals the sum of the squares of the lengths of the two diagonals.

Answers

The statement "parallelogram the sum of the squares of the lengths of the four sides equals the sum of the squares of the lengths of the two diagonals." is proved.

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are congruent, meaning they have the same length. Similarly, the opposite angles of a parallelogram are congruent, meaning they have the same measure.

Now, let's consider a parallelogram ABCD with sides AB, BC, CD, and DA. We want to show that:

AB² + BC² + CD² + DA² = AC² + BD²

where AC and BD are the diagonals of the parallelogram.

First, let's draw the diagonals AC and BD. This divides the parallelogram into four triangles: triangle ABC, triangle BCD, triangle CDA, and triangle DAB.

Next, let's use the Pythagorean theorem in each of these triangles. Recall that the Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

In triangle ABC, we have:

AC² = AB² + BC²

Similarly, in triangle CDA, we have:

AC² = CD² + DA²

Adding these two equations together, we get:

2AC² = AB² + 2BC² + CD² + 2DA²

Now, let's look at triangle ABD. We have:

BD² = AB² + DA²

Similarly, in triangle BCD, we have:

BD² = BC² + CD²

Adding these two equations together, we get:

2BD² = AB² + 2BC² + CD² + 2DA²

Finally, adding the two equations we obtained for AC² and BD², we get:

2AC² + 2BD² = 2AB² + 4BC² + 2CD² + 2DA²

Simplifying this expression, we get:

AC² + BD² = AB² + BC² + CD² + DA²

Therefore, we have proven that in any parallelogram, the sum of the squares of the lengths of the four sides is equal to the sum of the squares of the lengths of the two diagonals.

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convert the binary fractional number 0.000112 to a decimal representation. you can use fractions or floating point values, but your answer must be precise. you can use expressions if that's useful.

Answers

The decimal representation of the given binary fractional number 0.000112 is 0.109375.

Binary numbers are composed of only 0s and 1s, while decimal numbers are composed of 0-9. Additionally, binary numbers follow a different place value system, where each digit represents a power of 2 rather than a power of 10.

Now, let's focus on the given problem - converting a binary fractional number 0.000112 to a decimal representation. We can use the following formula to convert any binary fraction to decimal:

(decimal equivalent) = (binary digit 1/2¹) + (binary digit 2/2²) + (binary digit 3/2³) + ...

Using this formula, we can start by breaking down the given binary fraction 0.000112 into its individual binary digits:

0.000112 = 0/2¹ + 0/2² + 0/2³ + 1/2⁴ + 1/2⁵ + 1/2⁶

Now, we can simply evaluate each term in the equation and add them up to get the decimal equivalent:

0/2¹ = 0

0/2² = 0

0/2³ = 0

1/2⁴ = 0.0625

1/2⁵ = 0.03125

1/2⁶ = 0.015625

(decimal equivalent) = 0 + 0 + 0 + 0.0625 + 0.03125 + 0.015625 = 0.109375

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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each area to its corresponding radius or diameter of the circle.(All areas are approximate.)
area: 221.5584 square units
area: 78.5 square units
area: 452.16 square units
area: 36.2984 square units
area: 314 square units
area: 886.2336 square units
radius: 12 units
arrowBoth
diameter: 16.8 units
arrowBoth
radius: 3.4 units
arrowBoth
diameter: 10 units
arrowBoth

Answers

The areas, diameters, and radii can be grouped as follows:

1. Area: 221.5584 square units

Diameter: 16. 8 units

Radius: 8.4 units

2. Area: 78.5 square units

Diameter: 10 units

Radius: 5 units

3. Area: 452.16 square units

Diameter: 24 units

Radius: 12 units

4. Area: 36.2984 square units

Diameter: 6.8 units

Radius: 3.4 units

5. Area: 314 square units

Diameter: 20 units

Radius: 10 units

6. Area: 886.2336 square units

Diameter: 33.6 units

Radius: 16.8 units

How to calculate the diameter and radius

First, we are given the area of the circles. Next, we need to note the formula of the area of a circle and this is: πr²

To get the radius, we can use the formula: √(A/π)

For the first case, we have:

Area = 221.5584 square units

Thus, radius = √(221.5584/3.14)

= 8.4

Since diameter is = 2r, then diameter in this case

= 16.8 units.

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5. without solving, identify 3 equations that you think would be the least difficult to solve and 3 equations that you think would be the most difficult to solve. Explain you reasoning.

Answers

Three equations that you think would be the least difficult to solve are,

∛(t + 4) = 3

∛ (r³ - 19) = 2

4 + ∛- m + 4 = 6

And, 3 equations that you think would be the most difficult to solve are,

∛z + 9 = 0

6 - ∛b = 0

∛2n + 3 = - 5

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, By all the expressions;

Some expression gives easily real solution after solving.

But here some expression have complex solution after solving and tough to solve.

Thus, By all the expressions,

Three equations that you think would be the least difficult to solve are,

∛(t + 4) = 3

∛ (r³ - 19) = 2

4 + ∛- m + 4 = 6

And, 3 equations that you think would be the most difficult to solve are,

∛z + 9 = 0

6 - ∛b = 0

∛2n + 3 = - 5

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If RSTU is a parallelogram,
find the length of SU.
please help :)

Answers

The length of the diagonal SU will be 46 units.

What is parallelogram?

A parallelogram is a quadrilateral with two pairs of equal sides.

Given is a parallelogram RSTU.

The diagonals of a parallelogram bisect each other. This means that -

SV = VU

2x + 3 = 4x - 17

17 + 3 = 4x - 2x

20 = 2x

x = 10

The length SU will be -

SU = SV + VU

SU = 2x + 3 + 4x - 17

SU = 6x - 14

SU = 60 - 14

SU = 46 units

Therefore, the length of the diagonal SU will be 46 units.

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The Wakefield High School football team won the regional championship in 2022. A record of their wins and losses is shown, in which the relationship between wins and losses is sorted by number of points scored.


≥ 21 points < 21 points Total
Win 25 45
Loss 3
Total 50

Does the data give evidence of an association between scoring at least 21 points and the football team winning the game?
There is a strong, negative association.
There is a strong, positive association.
There is a weak, negative association.
There is a weak, positive association.



≥ 21 points < 21 points Total

Win 25 45

Loss 3

Total 50


Does the data give evidence of an association between scoring at least 21 points and the football team winning the game?

Answers

Does the data give evidence of an association between scoring at least 21 points and the football team winning the game?

Ans. There is a weak, negative association.

What is a Weak, Negative Association?

A weak, negative association refers to a relationship between two variables where an increase in one variable is associated with a decrease in the other variable, but the association is not strong.

In statistics, the strength of the association between two variables is measured by a correlation coefficient.

A correlation coefficient ranges from -1 to 1, where -1 represents a perfect negative correlation, 0 represents no correlation, and 1 represents a perfect positive correlation.

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Suppose a basketball player makes 55.3% of shots and that the probability of making each shot is independent. If the basketball player attempts 6 shots, what is the probability of making at least one shot?

Answers

There is a probability of 98.1% or around 0.98 of making at least one shot.

We can solve this problem using the binomial distribution. Let X be the number of shots the basketball player makes out of 6 attempts. Then X follows a binomial distribution with parameters n = 6 (number of trials) and p = 0.553 (probability of success).

The probability of making at least one shot can be calculated as the complement of the probability of missing all six shots. That is:

P(X ≥ 1) = 1 - P(X = 0)

Using the binomial probability formula, we can calculate P(X = 0) as:

P(X = 0) = (6 choose 0) * (0.553)^0 * (1 - 0.553)^(6-0) = 0.019

where (6 choose 0) = 1 is the number of ways to choose 0 shots out of 6.

Therefore,

P(X ≥ 1) = 1 - P(X = 0) = 1 - 0.019 = 0.981

So the probability of making at least one shot is approximately 0.981 or 98.1%.

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What is the length of XZ? Step by step.

Answers

The measure of XZ is equivalent to 24. Option C is correct

Solving similar triangles

The given triangles in question are similar in nature. For every similar triangles, the ratio of the similar sides of the triangle is equal to a constant as shown:

k+3/36 = k+5/44

Cross multiply and expand

36(k + 5) = 44(k + 3)

36k + 180 = 44k + 132

36k - 44k = 132-180|

-8k = -48

k = 6

For the measure of XZ

k/XZ = k+5/44

6/XZ = 11/44
6/XZ = 1/4
XZ = 24

Hence the measure of XZ from the given diagram is equivalent to 24

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Use the remainder theorem and synthetic division to find the value of
f(3) if f(3) = x^3 - 6x^2 + 13x - 11
SHOW THE STEPS OF THE SYNTHETIC DIVISION!

Answers

The quotient is x² - 3 - 4 and remainder is 1.

So, The value of f (3) is, 1

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

The value of f(3) is told by the remainder theorem to be the remainder from division of f(x) by (x -3). That division is shown in the attachment. The remainder is 1, hence we have;

⇒ f(3) = 1

The number at upper left in the synthetic division table is the value of x for which we are evaluating f(x).

When the polynomial is written in Horner Form:

⇒ f(x) = ((x -6)x +13)x -11

Here, the coefficient of x at each point in the evaluation is the same as the number on the bottom row of the synthetic division. The result of the evaluation is the same as the remainder from the division.

Now, Add the obtained result to the next coefficient of the dividend and write down the sum as;

3 | 1  - 6  13         - 11

         3  - 9        3x4 = 12

-----------------------

   1  - 3    4    (- 11)  + 12 = 1

Thus, We have complete table and have obtained the resulting coefficient are,

1 , - 3, 4, 1

Thus, The quotient is x² - 3 - 4 and remainder is 1.

So, The value of f (3) is, 1

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the waiting time, in hours, between successive speedersspotted by a radar unit is a continuous random variable wthcumulative distribution function
F(x)=
Find probability of waiting less than 12 min. betweensuccessive speeders?
a) using the cumulative distribution function of X
b) using the probability density function of X

Answers

The probability of waiting less than 12 minutes between successive speeders is 0.02.

The time elapsed between successive speeders detected by a radar unit is a  random variable with a cumulative distribution function:

F(x) = 0 when x = 0.

x/10, for 0 x ten 1, for x ten

a) Using the cumulative distribution function, to calculate the probability of waiting less than 12 minutes (0.2 hours) between successive speeders: F(0.2):

F(0.2) = 0.2/10 = 0.02

So, the probability of waiting less than 12 minutes between speeders is 0.02.

b) Using the probability density function, we can differentiate the cumulative distribution function with respect to x to find the probability:

For x = 0, f(x) = dF(x)/dx = 0.

1/10 for 0 x 10 0, 0 for x 10

The area under the probability density function up to x=0.2 represents the probability of waiting less than 12 minutes:

P(0 < w < 0.2) = ∫0.2 0 f(x) (x) dx = ∫0.2 0 (1/10) dx = (1/10) * [x] 0.2 = 0.02

Using either the cumulative distribution function or the probability density function, the probability of waiting less than 12 minutes between successive speeders is 0.02.

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Albinism in humans is autosomal and fully recessive to normal color. A couple, who are both normal, have a daughter who is albino and a son who is normal. The couple wants to have 3 more children. What is the probability that they will have 3 normal girls?

Answers

The probability that the couple will have 3 normal girls is approximately 0.422

Since both parents are normal, they both have to be heterozygous carriers for the recessive allele that causes albinism. We can represent the normal allele with the letter N and the albino allele with the letter n. Then, we can write the genotypes of the parents as Nn x Nn.

The daughter is albino, so her genotype must be nn. The son is normal, so his genotype must be Nn.

We want to find the probability that the couple will have 3 normal girls. We can use the multiplication rule of probability to find this probability:

P(3 normal girls) = P(normal girl) x P(normal girl) x P(normal girl)

The probability of having a normal girl is 3/4 since there are three possible genotypes that result in a normal phenotype (NN, Nn, Nn) out of a total of four possible genotypes. The probability of having a normal boy is also 3/4, for the same reason.

Therefore, the probability of having 3 normal children (in this case, girls) is:

P(3 normal girls) = (3/4) x (3/4) x (3/4) = 27/64 ≈ 0.422

So, the probability that the couple will have 3 normal girls is approximately 0.422, or about 42.2%.

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Find the equation of the plane that passes through the line of intersection of the planes 2x−3y−z+1=0
and 3x+5y−4z+2=0, and that also passes through the point (3,−1,2)

Answers

The equation of the plane that passes through the line of intersection of the two planes and passes through the point (3,-1,2) is x - 2y + 7z - 17 = 0  .

The Plane we want to find passes through the line of intersection of the planes, so it is perpendicular to the normal vectors of both planes.

The Normal Vector of the plane 2x - 3y - z + 1 = 0 is (2, -3, -1), and

the normal vector of the plane 3x + 5y - 4z + 2 = 0 is (3, 5, -4).

The cross product of these two vectors gives a vector which is perpendicular to both of them, and

hence , it lies along the line of intersection of the two planes:

the cross product of (2, -3, -1) x (3, 5, -4) is  = (-7, -2, 1)  ;

The vector (-7, -2, 1) is the direction vector of the line of intersection.

Now to find the equation of the plane that passes through the point (3, -1, 2) and is perpendicular to this direction vector.

we let , equation of the plane be ax + by + cz + d = 0. We know that the point (3, -1, 2) lies on the plane, so we have:

⇒ a(3) + b(-1) + c(2) + d = 0  ;

⇒ 3a - b + 2c + d = 0  ;

We also know that the plane is perpendicular to the direction vector (-7, -2, 1), so we have:

⇒ a(-7) + b(-2) + c(1) = 0  ;

⇒ -7a - 2b + c = 0  ;

Let  say a = 1. Then we have :

⇒ a = 1

⇒ -7a - 2b + c = 0

⇒ 3a - b + 2c + d = 0

Substituting a = 1 into the first equation gives:

⇒ -7 - 2b + c = 0  ;

Solving for c in terms of b gives:

⇒ c = 2b + 7

Simplifying ,

we get ;

⇒ 3 - b + 2(2b + 7) + d = 0  ;

Solving for d in terms of b gives:   ⇒ d = -2b - 17  ;

Therefore, the equation of the plane is x - 2y + 7z - 17 = 0 .

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A shipment of 1500 washers contains 400 defective and 1100 non-defective washers. Two hundred washers are chosen at random (without replacement) and classified as defective or non-defective_ a) What is the probability that exactly 90 defective washers are found? (Do NOT compute out:) b) What is the probability that at least 2 defective items are found? (Do NOT compute out:)

Answers

The probability that exactly 90 defective washers are found is (400 choose 90) * (1100 choose 110) / (1500 choose 200). and the probability that at least 2 defective items are found is (400 choose 1) * (1100 choose 199) / (1500 choose 200).

Let X be the number of defective washers in a sample of 200 washers.

We can model X as a hypergeometric distribution with parameters N = 1500 (total number of washers), K = 400 (total number of defective washers), and n = 200 (sample size).

a) The probability of finding exactly 90 defective washers is:

P(X = 90) = (400 choose 90) * (1100 choose 110) / (1500 choose 200)

This is because we need to choose 90 defective washers from the 400 defective washers, and 110 non-defective washers from the 1100 non-defective washers, out of the total of 200 washers chosen.

b) The probability of finding at least 2 defective items can be calculated as the complement of the probability of finding 0 or 1 defective item in the sample:

P(X >= 2) = 1 - P(X = 0) - P(X = 1)

To compute P(X = 0), we need to choose 0 defective washers from the 400 defective washers, and 200 non-defective washers from the 1100 non-defective washers, out of the total of 1500 washers:

P(X = 0) = (400 choose 0) * (1100 choose 200) / (1500 choose 200)

To compute P(X = 1), we need to choose 1 defective washer from the 400 defective washers, and 199 non-defective washers from the 1100 non-defective washers, out of the total of 1500 washers:

P(X = 1) = (400 choose 1) * (1100 choose 199) / (1500 choose 200)

Once we have computed P(X = 0) and P(X = 1), we can substitute these values into the expression for P(X >= 2) to obtain the desired probability.

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jenny made $126 in 9 hours of work at the same rate how many hours would she have to work to make 252

Answers

126 x 2=252
9 hours x 2 = 18 hours
Answer : 18 hours

7. The total of 13 cherries, 8 more cherries, and 2 more cherries is c.​

Answers

The value of c is given as follows:

c = 23.

How to obtain the value of c?

The problem states that the total of 13 cherries, 8 more cherries, and 2 more cherries is c, hence the value of c is obtained with the addition of these amounts, as follows:

c = 13 + 8 + 2.

Adding these three amounts, the numeric value of c is given as follows:

c = 23.

Missing Information

The problem asks for the numeric value of c.

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The scores of a certain population on the Wechsler Intelligence Scale for Children (WISC) are thought to be Normally distributed with mean μ and standard deviation σ = 10. A simple random sample of 25 children from this population is taken and each is given the WISC. The mean of the 25 scores is = 104.32.
Based on these data, a 95% confidence interval for μ is
104.32 ± 0.78.
104.32 ± 3.29.
104.32 ± 3.92.
104.32 ± 19.60

Answers

If the scores of a certain population are Normally Distributed , and the mean is 104.32 , then the 95% confidence interval is (b) 104.32 ± 3.29   .

The Scores of the population of WISC are Normally Distributed ;  

and the Mean(μ) of the 25 scores is = 104.32  ;

the standard deviation(σ) for the population is = 10  ;

the sample size(n) = 25  ;

For  the 95% confidence, critical value is = 1.96 ;

So,  Confidence interval is written as =  μ ± 1.96(σ/√n)

Substituting the required values  ,

we get ;

⇒ 104.32 ± 1.96(10/√25)

⇒ 104.32 ± 1.96×2

⇒ 104.32 ± 3.92

Therefore , the required 95% confidence interval is (104.32 ± 3.92) .

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The given question is incomplete , the complete question is

The scores of a certain population on the Wechsler Intelligence Scale for Children (WISC) are thought to be Normally distributed with mean μ and standard deviation σ = 10. A simple random sample of 25 children from this population is taken and each is given the WISC. The mean of the 25 scores is = 104.32.

Based on these data, a 95% confidence interval for μ is

(a) 104.32 ± 0.78.

(b) 104.32 ± 3.29.

(c) 104.32 ± 3.92.

(d) 104.32 ± 19.60

use fractions from the number lines in problem 1 complete the sentence. use words, pictures, or numbers to explain how you made that comparison ​

Answers

Based on the data, we can infer that the following numbers fill in the blanks: 100 is greater than 10.

How to fill in the blanks?

To fill in the blanks we must carefully read the information in the fragment. Once we understand this information we can select the two numbers that meet the rule mentioned in the statement.

According to the above, a correct statement would be:

100 is greater than 10.

Additionally, we could put other values that comply with this rule, for example:

1000 is greater than 10020 is greater than 1012 is greater than 9

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Find, using the method of volumes by SLICES, the volume of a pyramid of height h with an equilateral triangle base with side a.

Answers

The volume of the pyramid  of height h with an equilateral triangle base with side a, by using the method of volumes by SLICES  is V = a²h/3.

We can use the method of volumes by slices to find the volume of the pyramid.

Consider a slice of the pyramid that is perpendicular to the base and at a distance x from the apex. This slice has a cross-sectional area of a square with side length (base of pyramid) s, We can use the Pythagorean theorem to find that the

Height of the slice is [tex]\sqrt{(a^2 - (a/2)^2 - x^2)} = \sqrt{(3a^2/4 - x^2).[/tex]

Therefore, the volume of the slice is given by the product of its cross-sectional area and height:

dV = s^2 dh = (a^2 - 4x^2)/4 dh

To find the total volume of the pyramid,

we integrate dV from x=0 to x=h:

V = ∫₀ʰ (a²-4x²)/4 dx

Simplifying the integrand, we get:

V = (1/4) ∫₀ʰ (a² - 4x²) dx

V = (1/4) [a²x - (4x³)/3] from x=0 to x=h

V = (1/4) [a²h - (4h³)/3]

V = a²h/3

Therefore, the volume of the pyramid is V = a²h/3.

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The displacement (in meters) of a particle moving in a straight line is given by the equation of motions = 4/t2, where t is measured in seconds. Find the velocity of the particle at times t = a, t = 1, t = 2, and t = 3(a) Find the average velocity during each time period. (i) [1, 2] cm/s (ii) [1, 1.1] cm/s
(b) Estimate the instantaneous velocity of the particle when t = 1. cm/s

Answers

The velocity of the particle at times t = a, t = 1, t = 2, and t = 3 are:

a) 4/a^2 m/s, 4 m/s, 1 m/s, 4/9 m/s.

b) The instantaneous velocity of the particle when t=1 is 4 m/s.

To find the velocity, we need to take the derivative of the displacement function with respect to time. The derivative of s = 4/t^2 is ds/dt = -8/t^3. So, the velocity of the particle at time t is given by v = ds/dt = -8/t^3.

For t = a, the velocity is v = -8/a^3 m/s. For t = 1, the velocity is v = -8 m/s. For t = 2, the velocity is v = -2 m/s. For t = 3, the velocity is v = -8/27 m/s.

To find the average velocity during the time period [1, 2], we need to find the displacement at t = 2 and t = 1, then calculate the change in displacement divided by the time interval: (4/4 - 4/1)/1 = 0 cm/s. To find the average velocity during the time period [1, 1.1], we need to find the displacement at t = 1.1 and t = 1, then calculate the change in displacement divided by the time interval: (4/1.1^2 - 4/1)/0.1 = -19.60 cm/s.

To estimate the instantaneous velocity of the particle at t = 1, we can plug in t = 1 to the derivative we found earlier: v = -8/1^3 = -8 m/s. Therefore, the instantaneous velocity of the particle when t = 1 is 4 m/s.

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