Suppose n balls are distributed in n boxes in such a way that each ball chooses a box indepen- dently of each other. (a) What is the probability that Box #1 is empty? (b) What is the probability that only Box #1 is empty? (c) What is the probability that only one box is empty? (d) Given that Box #1 is empty, what is the probability that only one box is empty? (e) Given that only one box is empty, what is the probability that Box #1 is empty?

Answer:

6/49  

Step-by-step explanation:

-2/7  *   -3/7   = (-2 * -3) / (7*7) =  6/49

The result of the function f(p) = \(p^2\) + 3p + 1  for p = -2 is -1

The function is

f(p) = \(p^2\) + 3p + 1  

The function is the expression that represents the relationship between the one variable and another variable. If one variable is dependent variable then the another variable will be independent variable.

The values of p = -2

Substitute the value of p in the function and find the solution

f(p) = \(p^2\) + 3p + 1  

f(-2) = \((-2)^2\) + 3×-2 + 1

f(-2) = 4 - 6 + 1

f(-2) = -1

Hence, the result of the function f(p) = \(p^2\) + 3p + 1  for p = -2 is -1

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The amount that Matthew was paid per hour is given as follows:

$6.

The amount that Matthew was paid per hour is obtained applying the proportions with the amounts given in this problem. A proportion is a fraction of a total amount, using to obtain amounts in the context of a problem.

He then spent $3 and had $12 remaining, hence the total amount earned is calculated as follows:

x - 3 = 12

x = 12 + 3

x = $15.

(total amount - spent amount = remaining amount).

He earned $15 in 2.5 hours, hence the amount that Matthew was paid per hour is found applying the division of 15 by 2.5, as follows:

15/2.5 = $6.

(amount per hour = total amount divided by the number of hours).

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The final answer is $\frac{1}{12}$.

We need to evaluate the triple integral $\iiint e y , dv$ over the region $e$ bounded by the planes $x = 0$, $y = 0$, $z = 0$, $x + y + z = 1$, and $x + y = 2$.

To evaluate this triple integral, we can use the limits of integration obtained by considering the intersection of the planes. From the plane equations $x+y+z=1$ and $x+y=2$, we can solve for $z$ and $x$ in terms of $y$ to obtain the limits:

0≤z≤1−x−yand0≤x≤2−y.

Since $e$ is bounded by the planes $x=0$ and $y=0$, we have $0 \leq x \leq 2-y$ and $0 \leq y \leq 2$. Thus, we can set up the triple integral as follows:

Next, integrating with respect to $x$, we obtain∫

02[22−22]

02−∫ 02 [eyx− 2eyx 2 − 2ey 2 x​ ] 02−ydy.Simplifying this expression, we get

∫02(2−522+32)

.∫ 02​ (2ey− 25​ ey 2 + 2ey 3 )dy.

Evaluating the integral, we get the final answer of $\frac{1}{12}$.

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question:-Evaluate the triple integral $\int!!\int!!\int e y ,dv$, where $e$ is bounded by the planes $x = 0$, $y = 0$, $z = 0$, $x + y + z = 1$ and $x + y = 2$.

Answer:

false

Step-by-step explanation:

The range of the function on the graph would be: D. all real numbers greater than or equal to 2

To obtain the range, observe the y values whose result can be obtained by the function of x. To obtain this range, we examine the graph and note that the range begins from 2 on the y-axis and extends upwards.

So, if we wish to define our range, we will enter all real numbers that are equal to or greater than 2 as seen in the direction of the graph.

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Answer:If an N-gon (polygon with N sides) has perimeter P, then each of the  

N sides has length P/N.  If we connect two adjacent vertices to the  

center, the angle between these two lines is 360/N degrees, or 2*pi/N  

radians.  (Do you understand radian measure well enough to follow me  

this far?)

The two lines I just drew, plus the side of the polygon between them,  

form an isosceles triangle.  Adding the altitude of the isosceles  

triangle makes two right triangles, and we can use one of them to  

derive the equation

 sin(theta/2) =  s/(2R)

where theta is the apex angle (which I said is 2*pi/N radians), R is  

the length of the lines to the center (the radius of the circumscribed  

circle), and s is the length of the side (which I said is P/N).

Putting those values into the equation, we have

 sin(pi/N) = P/(2NR)

so that

 P = 2NR sin(pi/N)

gives the perimeter of the N-gon with circumradius R.

Can we see a connection between this formula and the perimeter of a  

circle?  The perimeter of the circumcircle is 2*pi*R.  As we increase  

N, the perimeter of the polygon should get closer and closer to this  

value.  Comparing the two, we see

 2NR*sin(pi/N) approaches 2*pi*R

 N*sin(pi/N)   approaches pi

You can check this out with a calculator, using big numbers for N such  

as your teacher's N=1000.  If you calculate the sine of an angle in  

degrees rather than radians, the formula will look like

 N*sin(180/N) --> pi

Step-by-step explanation:

Therefore, the solutions to the equation 0 = |3x + 3| + 3 are x = -2 and x = 0.

To solve the equation 0 = |3x + 3| + 3, we need to eliminate the absolute value. Remember that the absolute value of a number is always non-negative.

First, let's isolate the absolute value term on one side of the equation:

|3x + 3| = -3

Since the absolute value cannot be negative, there are no solutions to the equation as it stands. However, if we modify the equation to make the right side positive, we can find a solution.

To eliminate the absolute value, we can rewrite the equation as two separate equations, considering both the positive and negative cases:

   3x + 3 = -3

   -(3x + 3) = -3

Solving equation 1:

3x + 3 = -3

3x = -6

x = -2

Solving equation 2:

-(3x + 3) = -3

-3x - 3 = -3

-3x = 0

x = 0

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Keegan's error is assuming that the product of the slopes of any two sides of a triangle should be -1 for the triangle to be a right triangle.

To determine if the triangle LMN is a right triangle, Keegan should instead calculate the lengths of the three sides of the triangle and check if they satisfy the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

To correct his approach, Keegan should calculate the lengths of sides LM, MN, and NL using the coordinates of the vertices and then check if the Pythagorean theorem holds true.

If the squared length of one side is equal to the sum of the squares of the other two sides, then the triangle LMN is a right triangle.

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Answer:

positive and odd

Step-by-step explanation:

If a is a negative odd number, then a² can't be negative, because a number squared is always positive.

I'll illustrate this with an example.

Let's choose -7 as an example. Instead of a.

-7² = 49

So we see that the result is positive & odd.

So the words that describe a^2 are positive and odd.

Answer:

d) 30

Step-by-step explanation:

1% of 10 inch is 0.1 inch

10 inch + 0.1 inch = 10.1 inch

10 inch - 0.1 inch = 9.9 inch

V = s³

For s = 9.9 in., V = (9.9 in.)³ = 970.299 in.³

For s = 10.1 in., V = (10.1 in.)³ = 1030.301 in.³

For 10 in., V = (10 in.)³ = 1000 in.³

|1000 in.³ - 970.299 in.³| = 29.701 in.³

|1000 in.³ - 1030.301 in.³| = 30.301 in.³

The error is 30 in.³.

The best estimate of how much she will spend on movies and eating out is given as follows:

$162.

The best estimate of how much she will spend on movies and eating out is obtained applying the proportions in the context of the problem.

The percentages associated with movies and eating out are given as follows:

The amount that she has left is given as follows:

$300.

Hence the best estimate of how much she will spend on movies and eating out is obtained as follows:

(0.3 + 0.24) x 300 = 0.54 x 300 = $162.

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Answer:

Step-by-step explanation:

slope of y=7 is 0

As line is parallel to y=7 therefore m=0

equation of line is given by y=mx+c

m=0

therefore y=c

substituting y=4

therefore value of c=4

hence equation of line is given by y=0(x)+4

Step-by-step explanation:

f(3)=2(3)+1

6+1

7

answer is 7

Answer:

f(3)=15

Step-by-step explanation:

just put 3 instead of x

The current market price for the bond is $870 the yield to maturity is 14.13%

The approximate yield to maturity of this bond is 11.25%, which is above the annual coupon rate of 10% by 1.25%. You can then use this value as the rate (r) in the following formula: C = future cash flows/coupon payments. r = discount rate (the yield to maturity)

knowing that:

the formula is:

\(P = (C / (1 + r))^1 + (C / (1 + r))^2 + ... + (C + F) / (1 + r)^n\)

Putting the values:

\($870 = (130 / (1 + r))^1 + (130 / (1 + r))^2 + ... + (130 + 1,000) / (1 + r)^13\)

Using the math we find that the percentage is  approximately 14.13%;

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The table of values that could be used to graph g(x), a reflection of f(x) across the x-axis is table (c)

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

f(x) = One-third(6)x

When this statement is represented as an equation, we have the following representation

f(x)= 1/3(6)ˣ

The transformation is given as

A reflection of f(x) across the x-axis

This means that

g(x) = -f(x)

So, we have

g(x) = -1/3(6)ˣ

What this means is that the values of f(x) are negated to get g(x)

The table that represents this is table (c)

Hence, the table of values is table (c)

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Answer: C

Step-by-step explanation:

As a Roman citizen looking for a place to settle in the Roman Empire, the best region for me to settle in would be the region of Italy, more specifically, the Italian Peninsula.

There are several reasons why this region is better than the other two regions to settle in.

Let's take a look at the advantages and disadvantages of the three regions: Advantages of settling in the Italian Peninsula: 1. Center of Power: Italy was the center of power in the Roman Empire.

This meant that all the most significant buildings, activities, and political events took place in Italy.

For instance, the Roman Senate and the Colosseum were all located in Rome.

2. Access to Sea Trade: Italy is located on the coast, giving citizens access to sea trade routes.

This meant that they could easily trade with other nations across the sea.

3. Fertile Land: The Italian Peninsula has rich soil, making it suitable for farming.

This meant that farmers could grow crops like olives, grapes, and wheat.

4. Better Protection: The Italian Peninsula was protected by the Alps mountain range to the north and the Mediterranean Sea to the south.

Disadvantages of settling in the Italian Peninsula: 1. High population density: Due to the advantages that the Italian Peninsula offered, it was highly populated, which could lead to competition for resources and limited living space.

2. Higher living costs: Since Italy was the center of power, it was more expensive to live in Italy than in other regions of the empire.

Advantages of settling in Gaul: 1. More Living Space: Gaul was less populated than the Italian Peninsula, meaning that there was more living space for the citizens.

2. Fertile Land: Gaul had rich soil, making it suitable for farming. Disadvantages of settling in Gaul: 1. Further from the Center of Power: Since Gaul was further from Rome, it meant that it was less involved in political decisions.

2. Limited Sea Trade: Gaul was further from the coast, which meant that there was limited sea trade.

Advantages of settling in Greece: 1. Access to Sea Trade: Greece was located on the coast, meaning that citizens had access to sea trade routes.

2. Rich Cultural History: Greece had a rich cultural history, meaning that there were many festivals, traditions, and myths that people could learn about.

Disadvantages of settling in Greece: 1. High Competition for Resources: Greece was highly populated, meaning that there was competition for resources and limited living space.

2. High living costs: Greece was a popular tourist destination, meaning that it was more expensive to live in Greece than in other regions of the empire.

In conclusion, the best region for me to settle in the Roman Empire would be the Italian Peninsula.

It had many advantages, including being the center of power, having access to sea trade, fertile land, and better protection, and disadvantages such as a higher population density and higher living costs.

Gaul and Greece also had advantages and disadvantages, such as having more living space and access to sea trade, respectively, but had more significant drawbacks like limited sea trade and high competition for resources.

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Hello!

area

= 2*25 + (20 - 2)*(25-8)

= 50cm² + 306cm²

= 356cm²

The name of the figure illustrated in the image of AD is Side B. PO.

From the diagram in the question, Figure ABCD is the Image of PMNO, that is each vertex is a corresponding pair of the other image. This implies that P with AM with BN with CO with D

The same can be applied to the sides in the two images ABCD correspond with PMNO, also each corresponding side will be AD to PO. In this case, AB to PMBC to MNDC to ON.

Therefore, the image of side AD must be PO.

In conclusion, the correct option is B.

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the value of the investment when she retires is $26434.92.

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

Formula:

A = P(1 + {r}/{n})^{n.t}

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

here, we have,

given that,

Leilamade a one-time investment of $12 000.00 in a

registered retirement savings plan (RRSP) at 2.65%, compounded

semi-annually.

She plans to withdraw the money when she retires in 30

years.

So, she get finally is,

using the formula we get,

$26434.92

hence,  the value of the investment when she retires is $26434.92.

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Answer:

276.25

Step-by-step explanation:

1.25x+275x

=276.25

no like terms

Answer:

\(q=45\)

Step-by-step explanation:

Notice that \((q+2)^{\circ}\) and \((3q-2)^{\circ}\) form a linear pair, that is, they sum to \(180^{\circ}\) as follows:

\((q+2)^{\circ}+(3q-2)^{\circ}=180^{\circ}\\(q+2+3q-2)^{\circ}=180^{\circ}\\(4q)^{\circ}=180^{\circ}\\4q=180\\q=\frac{180}{4}\\q=45\)

Answer: A

In looking for solutions in the graph of y=f(x) where f(x) = 0, you're looking for the x-intercepts.  The catch is that you only want the x-value of the intercepts.

The intercepts are (-4,0) and (7,0), so the solutions are -4 and 7.

Answer:

$10300

Step-by-step explanation:

Given data

Marked price= Rs 10,000

discount= 10%

VAT= 13%

Let us compute the discount and the VAT

Discount

=10/100*10,000

=0.1*10,000

=$1000

VAT

=13/100*10,000

=0.13*10,000

=$1300

Hence the cost of the good will be

=10000-1000+1300

=$10300

Answer:

m=25/28

Step-by-step explanation:

The lengths of the segments x and y in the right triangles are x = 6√2 and y = 12√2

The given shape is the right-angled triangle

Such that

We have angles = 30 degrees and 45 degrees

The measure of y can be calculated using the following sine ratio

sin(45) = y/24

Make y the subject

So, we have

y = 24 * sin(45)

When evaluated, we have

y = 12√2

The length x is calculated as

sin(30) = x/y

So, we have

x = y * sin(30)

This gives

x = 12√2 * 1/2

Evaluate

x = 6√2

Hence, the value of x in the triangle is 6√2

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The value of the expression 18 + 4(28) will be 130.

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The expression is given below.

⇒ 18 + 4(28)

Simplify the expression, then the value of the expression will be

⇒ 18 + 4 x (28)

⇒ 18 + 4 x 28

⇒ 18 + 112

⇒ 130

Thus, the value of the expression 18 + 4(28) will be 130.

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