What are the steps to simplifying -(x)³-x³ and what is the answer?

A textbook costs $65.49 before tax. The tax on the textbook is 6.5%. What is the total cost of the textbook? Round your answer t

Ghella [55]

Answer: $69.75.

Step-by-step explanation:

Given: Cost of textbook before tax=$65.49

The tax on the textbook = 6.5%

∴ The tax amount = 6.5% of $65.49

$=\frac{65}{1000}\times65.49=4.25685\approx4.26$

⇒The tax amount = $4.26

The total cost of the textbook=Cost of textbook before tax+tax amount

=$65.49+$4.26

=$69.75

∴ The total cost of the textbook is $69.75.

3 0

3 years ago

On the day that a certain celebrity proposes marriage, 252525 people know about it. Each day afterward, the number of people who

Serhud [2]

Answer:

A

Step-by-step explanation:

The graphs are attached.

First of all, the day proposal goes out, 25 people know, so the initial condition is y = 25 at x = 0.

Hence, graph would start at y = 25.

Looking at the graphs, we can eliminate B and D immediately because they start at 50.

Now, it says every day, this number (y) triples, so 1 day after, it would be:

25 * 3 = 75

So, the graph would show x = 1 and y = 75

We can eliminate "C" as it doesn't show 75 at x = 1.

And we look at A and it is correct.

So,

A is the graph of the situation represented.

6 0

3 years ago

Read 2 more answers

ZE is the angle bisector of AngleYEX and the perpendicular bisector of Line segment G F. Line segment G X is the angle bisector

frozen [14]

Answer:

Point A is the center of the circle that passes through points E, F, and G and the center of the circle that passes through points X, Y, and Z.

Step-by-step explanation:

A is the intersection of angle bisectors, so is the incenter of triangle EFG. It is also the intersection of the perpendicular bisectors of the sides of triangle EFG, so is the circumcenter.

The altitudes at X, Y, and Z are perpendicular to sides EF, EG, and FG, and pass through the incenter, so X, Y, Z are points on the incircle.

A is the center of circles through E, F, and G, and through X, Y, and Z.

6 0

3 years ago

Read 2 more answers

To better understand how husbands and wives feel about their finances, Money Magazine conducted a national poll of 1010 married

Xelga [282]

Answer:

a. See the table below

b. See the table below

c. 0.548

d. 0.576

e. 0.534

f) i) 0.201, ii) 0.208

Explanation:

First, order the information provided:

Table: "Who is better at getting deals?"

Who Is Better?

Respondent I Am My Spouse We Are Equal

Husband 278 127 102

Wife 290 111 102

a. Develop a joint probability table and use it to answer the following questions. 

The joint probability table shows the same information but as proportions. Hence, you must divide each number of the table by the total number of people in the set of responses.

1. Number of responses: 278 + 127 + 102 + 290 + 111 + 102 = 1,010.

2. Calculate each proportion:

278/1,010 = 0.275
127/1,010 = 0.126
102/1,010 = 0.101
290/1,010 = 0.287
111/1,010 = 0.110
102/1,010 = 0.101

3. Construct the table with those numbers:

Joint probability table:

Respondent I Am My Spouse We Are Equal

Husband 0.275 0.126 0.101

Wife 0.287 0.110 0.101

Look what that table means: it tells that the joint probability of being a husband and responding "I am" is 0.275. And so for every cell: every cell shows the joint probability of a particular gender with a particular response.

Hence, that is why that is the joint probability table.

b. Construct the marginal probabilities for Who Is Better (I Am, My Spouse, We Are Equal). Comment.

The marginal probabilities are calculated for each for each row and each column of the table. They are shown at the margins, that is why they are called marginal probabilities.

For the colum "I am" it is: 0.275 + 0.287 = 0.562

Do the same for the other two colums.

For the row "Husband" it is 0.275 + 0.126 + 0.101 = 0.502. Do the same for the row "Wife".

Table Marginal probabilities:

Respondent I Am My Spouse We Are Equal Total

Husband 0.275 0.126 0.101 0.502

Wife 0.287 0.110 0.101 0.498

Total 0.562 0.236 0.202 1.000

Note that when you add the marginal probabilities of the each total, either for the colums or for the rows, you get 1. Which is always true for the marginal probabilities.

c. Given that the respondent is a husband, what is the probability that he feels he is better at getting deals than his wife? 

For this you use conditional probability.

You want to determine the probability of the response be " I am" given that the respondent is a "Husband".

Using conditional probability:

P ( "I am" / "Husband") = P ("I am" ∩ "Husband) / P("Husband")

P ("I am" ∩ "Husband) = 0.275 (from the intersection of the column "I am" and the row "Husband)

P("Husband") = 0.502 (from the total of the row "Husband")

P ("I am" ∩ "Husband) / P("Husband") = 0.275 / 0.502 = 0.548

d. Given that the respondent is a wife, what is the probability that she feels she is better at getting deals than her husband?

You want to determine the probability of the response being "I am" given that the respondent is a "Wife", for which you use again the formula for conditional probability:

P ("I am" / "Wife") = P ("I am" ∩ "Wife") / P ("Wife")

P ("I am" / "Wife") = 0.287 / 0.498

P ("I am" / "Wife") = 0.576

e. Given a response "My spouse," is better at getting deals, what is the probability that the response came from a husband?

You want to determine: P ("Husband" / "My spouse")

Using the formula of conditional probability:

P("Husband" / "My spouse") = P("Husband" ∩ "My spouse")/P("My spouse")

P("Husband" / "My spouse") = 0.126/0.236

P("Husband" / "My spouse") = 0.534

f. Given a response "We are equal" what is the probability that the response came from a husband? What is the probability that the response came from a wife?

What is the probability that the response came from a husband?

P("Husband" / "We are equal") = P("Husband" ∩ "We are equal" / P ("We are equal")

P("Husband" / "We are equal") = 0.101 / 0.502 = 0.201

What is the probability that the response came from a wife:

P("Wife") / "We are equal") = P("Wife" ∩ "We are equal") / P("We are equal")

P("Wife") / "We are equal") = 0.101 / 0.498 = 0.208

6 0

3 years ago

Given that −4i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable. f

GalinKa [24]

Answer:

$\large \boxed{\sf \bf \ \ f(x)=(x-4i)(x+4i)(x+3)(x-5) \ \ }$

Step-by-step explanation:

Hello, the Conjugate Roots Theorem states that if a complex number is a zero of real polynomial its conjugate is a zero too. It means that (x-4i)(x+4i) are factors of f(x).

$\text{Meaning that } (x-4i)(x+4i) =x^2-(4i)^2=x^2+16 \text{ is a factor of f(x).}$

The coefficient of the leading term is 1 and the constant term is -240 = 16 * (-15), so we a re looking for a real number such that.

$f(x)=x^4-2x^3+x^2-32x-240\\\\ =(x^2+16)(x^2+ax-15)\\\\ =x^4+ax^3-15x^2+16x^2+16ax-240$

We identify the coefficients for the like terms, it comes

a = -2 and 16a = -32 (which is equivalent). So, we can write in $\mathbb{R}$ .

$\\f(x)=(x^2+16)(x^2-2x-15)$

The sum of the zeroes is 2=5-3 and their product is -15=-3*5, so we can factorise by (x-5)(x+3), which gives.

$f(x)=(x^2+16)(x^2-2x-15)\\\\=(x^2+16)(x^2+3x-5x-15)\\\\=(x^2+16)(x(x+3)-5(x+3))\\\\=\boxed{(x^2+16)(x+3)(x-5)}$

And we can write in $\mathbb{C}$

$f(x)=\boxed{(x-4i)(x+4i)(x+3)(x-5)}$

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

7 0

3 years ago