if at least one child in a family with 2 children is a boy, what is the probability that both children are boys?​

Answers

Answer 1

Answer:

The probability of both children being boys in a family with 2 children is  

3

1

.

There are 3 possible outcomes for the gender of each child: boy, girl, or unknown. There are 2 children, so there are 3

2

=9 possible combinations of genders for the 2 children.

Of these 9 combinations, 3 of them have both children being boys: BB, BG, and GB. So the probability of both children being boys is  

9

3

=

3

1

.

However, this is only the probability if we don't know the gender of the first child. If we know that the first child is a boy, then the probability of both children being boys is  

2

1

. This is because there are only 2 possible outcomes for the gender of the second child: boy or girl. If the first child is a boy, then the second child must be a boy in order for both children to be boys. So the probability is  

2

1

.

Step-by-step explanation:

Let's use the following notation for the children:

B: Boy G: Girl

There are 4 possible combinations for a family with 2 children:

1. BB (Both children are boys)

2. BG (First child is a boy, second child is a girl)

3. GB (First child is a girl, second child is a boy)

4. GG (Both children are girls)

Since we know that at least one child is a boy, we can eliminate the 4th combination (GG) as it doesn't meet the condition. Now we have 3 possible combinations left:

1. BB

2. BG

3. GB

Now, to find the probability that both children are boys (BB) from the remaining combinations, we can calculate it as follows:

Probability = (Number of favorable outcomes) / (Total possible outcomes)

Probability = 1 (BB) / 3 (BB, BG, GB)

Probability = 1/3

So, the probability that both children are boys is 1/3.


Related Questions

You purchased 96 ounces of fruit. Fruit costs $3 per pound. The cashier says you owe $4,608 for the fruit, but you know that is not correct. Look at the cashier's work and figure out how much you should pay. Explain what the cashier did wrong. 96 x 16 = 1,536 pounds 1,536 pounds x $3 = $4,608 ​

Answers

Answer: you pay 18$

Step-by-step explanation:96 ounce×1pound/16ounce×3$/1pound=18$

The amount the cashier charged is incorrect. Based on the given information, the amount of fruit purchased is 96 ounces, which is equivalent to 6 pounds. Therefore, the total cost of the fruit should be 6 pounds x $3 per pound = $18.


The error the cashier made was converting ounces to pounds incorrectly. 96 ounces is equivalent to 6 pounds, not 1,536 pounds. The cashier multiplied 96 by 16 (the number of ounces in a pound) instead of dividing by 16 to get the number of pounds.

What is the probability that it will land on tails twice and heads once?

Answers

Answer:

3/8

Explanation:

I just know :) (;

a mean of 589 grams with standard deviation of 16 grams . if you pick 23 fruits at random then 14% of the time their mean weight will be greater than how many grams?

Answers

14% of the time the mean weight of 23 fruits will be greater than approximately 594.33 grams.

What is the Central Limit Theorem (CLT)?

According to the CLT, the distribution of sample means from a population with mean μ and standard deviation σ, will be approximately normal with mean μ and standard deviation σ/√n, where n is the sample size.

In this case, the population mean is 589 grams and the population standard deviation is 16 grams. We are picking a sample of 23 fruits at random, so the standard deviation of the sample means will be:

σ/√n = 16/√23 ≈ 3.33

To find the value of x such that 14% of the time the sample mean will be greater than x, we need to find the z-score that corresponds to the 86th percentile of the standard normal distribution. We can use a table or a calculator to find that z-score:

z = invNorm(0.86) ≈ 1.08

The sample mean is normally distributed with a mean of 589 grams and a standard deviation of 3.33 grams. Using the formula for z-score:

z = (x - μ) / (σ / √n)

We can solve for x:

x = z × (σ / √n) + μ

x = 1.08 × (16 / √23) + 589

x ≈ 594.33 grams

Therefore, 14% of the time the mean weight of 23 fruits will be greater than approximately 594.33 grams.

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87,178 time what equals 458,930

Answers

Answer: 5.26

Step-by-step explanation:

458,930/87,178 =
5.264 =
5.26

Can someone please help me

Answers

Answer:

Step-by-step explanation:

Find the indicated measure. Lines that appear to be tangent are tangents(help pls)

Answers

Step-by-step explanation:

This is basically an inscribed angle in a circle which encompasses twice as many degrees of arc (246) as the angle measure : angle 3 = 123 degrees

Given the graph of y=f(x) below, find the value f(4).

Answers

The numeric value of the function at x = 4 is given as follows:

f(4) = 0.

How to obtain the numeric value of the function?

The expression for the numeric value of the function in this problem is given as follows:

f(4).

This means that the input is given as follows:

x = 4.

Passing a vertical line through x = 4 the value of y in which the vertical line crosses the graph is given as follows:

y = 0.

Hence the numeric value is given as follows:

f(4) = 0.

Missing Information

The graph is given by the image presented at the end of the answer.

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Calculate the height of the Zeta Tower as a percentage of the height of the Delta tower

Answers

The height of the Zeta Tower as a percentage of the height of the Delta tower is the 94.72%

How to find the the height of the Zeta Tower as a percentage of the height of the Delta tower?

Here we know that:

height of the Delta tower = 55m

The epsilon tower is 23% taller than the delta one, then the height is:

H = 55m*(1 + 0.23) = 67.65 m

And we know that the Zeta tower is 23 short than the epsilon one, then the height of this twoer is.

H' = 67.65m*(1 - 0.23) = 52.0905 m

The height of the delta tower is 55m, this is our 100%.

Then the height of the zeta tower written as a percentage will be:

(52.0905 m/55m)*100% = 94.72%

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Find the value of x.

Answers

Answer: x=22

Step-by-step explanation:

see image for explanation

calculate the distance that P is :
a. north of Q b.east of Q​

Answers

The distance of P at north of Q is 34.98 km.

The distance of P at east of Q is 19.39 km.

What is the distance of P?

The distance of P at the given directions is calculated by resolving the vector into vertical and horizontal components.

The distance of P at north of Q is calculated as follows;

Py = d sinθ

Py = 40 km x sin (61)

Py = 34.98 km

The distance of P at east of Q is calculated as follows;

Px = d cosθ

Px = 40 km x cos (61)

Px = 19.39 km

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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2

Answers

The three equivalent equations are:

2 + x = 5
x + 1 = 49
-5 + x = -2
Explanation:

Subtracting 2 from both sides of the equation 2 + x = 5 gives x = 3, which is the solution to the equation.
Subtracting 1 from both sides of the equation x + 1 = 49 gives x = 48, which is the solution to the equation.
Adding 5 to both sides of the equation -5 + x = -2 gives x = 3, which is the solution to the equation.

From the set {21, 29, 49}, use substitution to determine which value of x makes the equation true. 8(x - 20) = 304 A. 49 B. none of these C. 29 D. 21

Answers

Answer:

We can solve this equation by using substitution. We substitute each value of x in the given set and check which one makes the equation true.

Let’s start with A. 8(x - 20) = 304 becomes 8(49 - 20) = 304 which simplifies to 8(29) = 304 which is not true.

Let’s try B. 8(x - 20) = 304 becomes 8(none of these - 20) = 304 which simplifies to 8(-20) = 304 which is not true.

Let’s try C. 8(x - 20) = 304 becomes 8(29 - 20) = 304 which simplifies to 8(9) = 304 which is not true.

Finally, let’s try D. 8(x - 20) = 304 becomes 8(21 - 20) = 304 which simplifies to 8(1) = 304 which is not true.

Therefore, none of these values of x make the equation true

Step-by-step explanation:

nd the compound interest and future value. Do not round intermediate steps. Round your answers to the neare Principal Rate Compounded Time $865 4% Annually 10 years The future value is $ and the compound interest is $ X Start over Ś​

Answers

All the values are,

Compound interest = $1280.2

Future value = $1280.2 + $x

Given that;

P = $865

r = 4%

T = 10 years

Formula is,

Compound Interest = P(1 + r)^t

Where, Principal = P, Interest rate = r, Number of compounds = n, Interest time = t

Plug, p = 865, r = 0.04, t = 10

Compound Interest = 865 (1 + 0.04)¹⁰

Compound Interest = 865 (1.04)¹⁰

Compound Interest = 865 x 1.48

Compound Interest = 1280.2

Hence, We get;

Future value = Compound Interest + Principal

Future value = $1280.2 + $x

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Exercise 6.2.8: Solve ′′′ + = 3( − 1) for initial conditions (0) = 1 and ′(0) = 0, ′′(0) = 0.

Answers

Answer:

Step-by-step explanation:

To solve the differential equation:

y′′′ + y = 3(y′ − 1)

we first find the characteristic equation:

r^3 + 1 = 0

The roots of this equation are:

r = -1, 0 ± i

So, the general solution of the homogeneous equation (y′′′ + y = 0) is:

y_h(t) = c1 e^(-t) + c2 cos(t) + c3 sin(t)

To find a particular solution of the non-homogeneous equation (3(y′ − 1)), we assume a solution of the form:

y_p(t) = a t + b

Taking the first, second and third derivatives of y_p(t), we get:

y′_p(t) = a

y′′_p(t) = 0

y′′′_p(t) = 0

Substituting these into the differential equation, we get:

0 + (a t + b) = 3(a - 1)

Solving for a and b, we get:

a = 1

b = 2

Therefore, the particular solution of the non-homogeneous equation is:

y_p(t) = t + 2

So, the general solution of the non-homogeneous equation is:

y(t) = y_h(t) + y_p(t) = c1 e^(-t) + c2 cos(t) + c3 sin(t) + t + 2

To find the values of c1, c2 and c3, we use the initial conditions:

y(0) = c1 + c2 + 2 = 1

y′(0) = -c1 + c2 + c3 = 0

y′′(0) = c1 - c2 = 0

Solving these equations simultaneously, we get:

c1 = c2 = 1/2

c3 = -1/2

So, the solution of the differential equation with initial conditions (0) = 1, ′(0) = 0, ′′(0) = 0 is:

y(t) = 1/2 e^(-t) + 1/2 cos(t) - 1/2 sin(t) + t + 2

-2 x + 4 =2 x - 4 solve .

Answers

Answer:

[tex]\sf{x = 2}[/tex]

Step-by-step explanation:

Question type: solving equations with variables on both sides.

[tex]\textsf{This is a question with variables on both sides, to solve this we need to get the variable x }[/tex]

[tex]\textsf{alone. (getting the x on one side)}[/tex]

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

[tex]\sf{-2x~+~4~=~2x~-~4[/tex]

Subtract 4 from both sides.

[tex]\sf{-2x~=~2x~-8[/tex]

Subtract 2x from both sides.

[tex]\sf{-4x~=~-8}[/tex]

Divide both sides by -4.

[tex]\bf{x~=~2[/tex]

Therefore, x would be 2.

[tex]-jurii[/tex]

Answer:

x=2

Step-by-step explanation:

how to find 6 rational numbers between 3 and 4? ​

Answers

The six rational numbers between 3 and 4 are: 3.1, 3.2, 3.3, 3.4, 3.5 and 3.6

Listing the rational numbers between 3 and 4

To find 6 rational numbers between 3 and 4, we can start by finding the difference between 4 and 3, which is 1.

We can then divide this difference by any number and add it to 3

So that the number will be less than 4 but greater than 3

Now, we can add this gap size successively to 3, starting with the first rational number after 3, to find the six rational numbers between 3 and 4:

3.1, 3.2, 3.3, 3.4, 3.5, 3.6

So, the six rational numbers between 3 and 4 are: 3.1, 3.2, 3.3, 3.4, 3.5 and 3.6

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Comparing Rates of Change Station Cards
Two students are texting.

Student A is texting at the rate given in the table.
Number of
Tests Sent
0
1
2
3
4
12
Number of Texts Sent
てん
0
10.
5
10
Student B is texting at the rate given in the graph.
15
20
2 3 4
Minutes
5
7+
What is the different in the texting rate of these two students?
what is student A's rate ?
Student B's rate ?
what is

Answers

Answer:

To compare the texting rates of Student A and Student B, we need to calculate their respective rates of change.

For Student A, we can use the formula for the slope of a line:

slope = (change in y) / (change in x)

In this case, the "y" variable represents the number of texts sent, and the "x" variable represents the number of tests sent. Looking at the table, we can see that Student A sent 10.5 texts after sending 1 test, and 10 texts after sending 2 tests. So the change in y is -0.5 (10.5 - 10), and the change in x is 1. Therefore:

slope = (-0.5) / 1 = -0.5

So Student A's texting rate is -0.5 texts per test.

For Student B, we can look at the graph and find the slope of the line connecting any two points. Let's choose the points (2, 15) and (5, 23) because they are easy to read off the graph. The change in y is 8 (23 - 15), and the change in x is 3 (5 - 2). Therefore:

slope = 8 / 3 = 2.67

So Student B's texting rate is 2.67 texts per minute.

To find the difference in their texting rates, we simply subtract:

difference = Student B's rate - Student A's rate

difference = 2.67 - (-0.5) = 3.17

So the difference in their texting rates is 3.17 texts per test.

Step-by-step explanation:

Lin is tracking the progress of her plant's growth. Today the plant is
5 cm high. The plant grows 1.5 cm per day.
a. Write a linear model that represents the height of the plant after d
days.
(Equation)
b. What will the height of the plant be after 20 days?

Answers

Answer:

a. The linear model that represents the height of the plant after d days can be expressed as:

h(d) = 1.5d + 5

where h(d) is the height of the plant in centimeters after d days, and 1.5d represents the growth rate of 1.5 cm per day multiplied by the number of days (d). The constant term 5 represents the initial height of the plant, which is 5 cm.

b. To find the height of the plant after 20 days, we can substitute d = 20 into the linear model:

h(20) = 1.5(20) + 5

= 30 + 5

= 35

So, the height of the plant after 20 days will be 35 cm.

1. Four family members attended a
family reunion. The table below
shows the distance each person
drove and the amount of time each
person traveled.

Family Reunion Travel:

•Name
Hank
Laura
Nathan
Raquel

•Distance
176 miles
150 miles
112.5 miles
286 miles

• Travel Time
3 hours 12 minutes
2 hours 30 minutes
2 hours 15 minutes
4 hours 24 minutes

If each person drove at a constant rate, who drove the fastest (in miles per hour)?

A. Hank
B. Laura
C. Nathan
D. Raquel

Answers

If each person drove at a constant rate, the person who drove the fastest (in miles per hour) is: C. Nathan.

What is speed?

In Mathematics and Science, speed is the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured by using the following unit of measurement;

Miles per hour (mph).Kilometers per hour (kph).Meter per seconds (m/s).

How to calculate the speed?

In Mathematics and Science, the speed of any a physical object can be calculated by using this formula;

Speed = distance/time

For Hank, we have:

Speed = 176/3.2 = 55 miles per hour.

For Laura, we have:

Speed = 150/2.5 = 60 miles per hour.

For Nathan, we have:

Speed = 112.5/2.25 = 50 miles per hour (Fastest).

For Raquel, we have:

Speed = 286/4.4 = 65 miles per hour.

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The Dahlia Flower Company has earnings of $3.64 per share. if the benchmark PE for the company is 21, how much will you pay for the stock?

Answers

Answer:

Step-by-step explanation:

To calculate the stock price, you can multiply the earnings per share (EPS) by the benchmark PE ratio.

The stock price would be:

$3.64 x 21 = $76.44

So you would pay $76.44 per share for the stock of The Dahlia Flower Company.

Express the answers in simplest form. If a die is rolled one time, find the probability of (a) Getting a 6. (b) getting an even number (c) number greater than 3 (d) number greater than 0 (E) number greater than 4 and an odd number?​

Answers

a) 1/6 b) 1/2 c) 1/2 d) 1 e) 1/6

Answer:

a) 1/6

b) 1/2

c) 1/2

d) 1

e) 1/6

Step-by-step explanation:

a)Getting a six

=1/6

b)Gettingan even number =3/6=1/2

c)number greater than 3

=3/6=1/2

d)number greater than 0

=6/6=1

e)number greater than 4 and an odd number

=1/6

Clinton and Stacy decided to travel from their home near Austin, Texas, to Yellowstone National Park in their RV.

- The distance from their home to Yellowstone National Park is 1,701 miles.
- On average the RV gets 10.5 miles per gallon.
- On average the cost of a gallon of gasoline is $3.60.

Based on the average gas mileage of their RV and the average cost of gasoline, how much will Clinton and Stacy spend on gasoline for the round trip to Yellowstone National Park and back home?

A. $1,166.40
B. $2,480.63
C. $583.20
D. $64,297.80

Answers

this is the total cost for the round trip, the answer is (C) 583.20.

what is round trip ?

A round trip refers to a journey from a starting point to a destination and then back to the starting point. In other words, it involves traveling to a place and then returning to the original location.

In the given question,

To calculate the cost of gasoline for the round trip, we need to first find the total amount of gasoline they will use. We can calculate this by dividing the distance of the trip by the RV's average gas mileage:

Total gasoline used = distance ÷ gas mileage

Total gasoline used = 1,701 miles ÷ 10.5 miles per gallon

Total gasoline used = 162 gallons (rounded to the nearest whole number)

Now, we can find the total cost of gasoline by multiplying the total amount of gasoline used by the average cost of a gallon of gasoline:

Total cost of gasoline = total gasoline used × cost per gallon

Total cost of gasoline = 162 gallons × 3.60 per gallon

Total cost of gasoline = 583.20

Since this is the total cost for the round trip, the answer is (C) 583.20.

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The platoon drank 155 liters of water. How many milliliters did the platoon drink?

Answers

Answer:

155000 milliliters of water

Step-by-step explanation:

We Know

The platoon drank 155 liters of water.

How many milliliters did the platoon drink?

1 liter = 1000 milliliters

155 liters = 155 x 1000 = 155000 milliliters of water

So, the platoon drank 155000 milliliters of water.

The platoon drank 155,000 milliliters of water.

1 liter = 1000 milliliters

Therefore, 155 liters = 155,000 milliliters

So, the platoon drank 155,000 milliliters of water.

2as = vf2-vo2 despejar para a

Answers

Para despejar "a" de la ecuación 2as = vf^2 - vo^2, podemos seguir los siguientes pasos:

1. Sumar vo^2 a ambos lados de la ecuación:

2as + vo^2 = vf^2

2. Dividir ambos lados de la ecuación por 2s:

a = (vf^2 - vo^2) / 2s

Por lo tanto, la fórmula para calcular "a" a partir de la distancia de desplazamiento "s", la velocidad final "vf" y la velocidad inicial "vo" es:

a = (vf^2 - vo^2) / 2s

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[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]

[tex]\textcolor{blue}{\small\texttt{If you have any further questions,}}[/tex] [tex]\textcolor{blue}{\small{\texttt{feel free to ask!}}}[/tex]

♥️ [tex]{\underline{\underline{\texttt{\large{\color{hotpink}{Sumit\:\:Roy\:\:(:\:\:}}}}}}\\[/tex]

Find the length of the third side of the right triangle 19, 21 and c

Answers

The length of the hypotenuse is 28.3

What is Pythagoras theorem?

Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

A right angle triangle is a triangle that has one of it's angles has 90°. And Pythagoras theorem is applied to only right angled triangle.

If a and b are the legs of the triangle and c is the other side(hypotenuse) then,

c² = a²+b²

c² = 19² +21²

c² = 361+441

c² = 802

c = √802

c = 28.3

therefore , if the two legs are 19 and 21, the length of the other side is 28.3

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The length of the hypotenuse is 28.3

What is Pythagoras theorem?

Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

A right angle triangle is a triangle that has one of it's angles has 90°. And Pythagoras theorem is applied to only right angled triangle.

If a and b are the legs of the triangle and c is the other side(hypotenuse) then,

c² = a²+b²

c² = 19² +21²

c² = 361+441

c² = 802

c = √802

c = 28.3

therefore , if the two legs are 19 and 21, the length of the other side is 28.3

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Graph the solution to the inequality |2x + 2) > 6.

Answers

The solution to the inequality is all the values of x that are either greater than 2 or less than -4. The required graph of inequality is given below.

What is Inequality :

In mathematics, an inequality is a statement that compares two values, often using the symbols "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

Inequality graphs show the region of the coordinate plane that satisfies an inequality. The graph of inequality can be determined in a similar way to the graph of an equation, but with some additional steps.

Here we have

The inequality |2x + 2| > 6

To graph the solution to the inequality |2x + 2| > 6,

we can start by rewriting the inequality as two separate inequalities without the absolute value:

2x + 2 > 6 or 2x + 2 < -6

Simplifying these inequalities, we get:

2x > 4 or 2x < -8

x > 2 or x < -4

Therefore,

The solution to the inequality is all the values of x that are either greater than 2 or less than -4. The required graph of inequality is given below.

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math please help me on thissssssss hurry

Answers

The standard form based on the information given will be:

a) 2.35 x 10^-3 = 0.00235 (in standard form)

b) 2.35 x 10^3 = 2350 (in standard form)

How to explain the standard form

It should be noted that in mathematics and computer science, a normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical expression.

Often, it is one which provides the simplest representation of an object and allows it to be identified in a unique way

he standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form.

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Find the value of x, y, and z in the rhombus below.

Answers

The value of x, y, and z in the rhombus below x = 20, y = -7, z = -11

How to find the values of x, y and z?

Recall that a  rhombus is an equilateral parallelogram with both pairs of opposite sides parallel and all sides the same length.

Sum of interior angles of a rhombus = 360°

The opposite angles of a rhombus are equal to each other.

The adjacent angles are supplementary (add up to 180°)

Therefore,

66 + (6x - 6) = 180

⇒ 66 + 6x - 6 = 180

⇒ 6x = 180 - 66 + 6

⇒ 6x = 120

⇒ x = 120 ÷ 6

⇒ x = 20

66 + (-10z + 4) = 180

⇒ 66 - 10z + 4 = 180

⇒ -10z= 180 - 66 - 4

⇒ -10z = 110

⇒ z = 110 ÷ -10

⇒ z = -11

(6x - 6) + (-10y - 4) = 180

⇒ 6x - 6 - 10y - 4 = 180

⇒ 120 - 6 - 10y - 4 = 180

⇒ -10y = 180 - 120 + 6 + 4

⇒ -10y = 70

⇒ y = 70 ÷ -10

⇒ y = -7

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The second option is to issue new preferred stock at a market price of $56,000, with a $5.00 annual dividend. The net proceeds per share after paying flotation costs are $51.50.

Answers

The cost of capital for the second option, issuing new preferred stock, is 0.00356, or 0.356%. This means that for every dollar of capital raised through issuing preferred stock, the company will need to pay 0.356 cents in annual interest or dividend payments.

To calculate the cost of capital for the second option, we need to first calculate the cost of the preferred stock. The cost of preferred stock is the dividend yield, or the annual dividend divided by the market price of the stock. In this case, the annual dividend is $5.00 and the market price is $56,000.

Cost of preferred stock = Annual dividend / Market price of stock

Cost of preferred stock = $5.00 / $56,000

Cost of preferred stock = 0.000089

To calculate the cost of capital, we need to weight the cost of preferred stock with the proportion of capital that is financed by preferred stock. Let's assume that the preferred stock will finance 40% of the total capital.

Cost of capital = Cost of preferred stock * Proportion of capital financed by preferred stock

Cost of capital = 0.000089 * 0.40

Cost of capital = 0.0000356

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Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. √5,5i​

Answers

The polynomial function of lowest degree with rational coefficients P(x) = x⁴ + 20x² - 125

What is a polynomial?

A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.

To find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. √5,5i​.

Since √5 and 5i​ are zeros, then their conjugates -√5, and -5i​ are also zeros.

So,

x = √5,x = 5i​.x = -√5,x = -5i

So, the factors of the polynomial are

x  - √5,x - 5i​.x + √5,x + 5i

So, multiplying the factors together, we get the polynomial.

So, P(x) = (x  - √5)(x - 5i)(x + √5)(x + 5i)

= (x  - √5)(x  + √5)(x - 5i)(x + 5i)

= [x² - (√5)²][x² - (5i)²]

= [x² - 5][x² - (5²i²)]

= [x² - 5][x² - 25(-1))]

= [x² - 5][x² + 25]

Expanding the brackets, we have

= [x² - 5][x² + 25]

= [x² × x² + 25x² - 5x² + 25 × (-5)]

= x⁴ + 20x² - 125

So, P(x) = x⁴ + 20x² - 125

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