The polynomial function g(x) = 3x3 + 11x2 – 14x – 40 has a known factor of (3x + 5). Rewrite g(x) as theproduct of linear factors.

Answer:

1/5

Step-by-step explanation:

.7555555(repeating )

writing as a fraction

x = .755555555

10 x = 7.555555

Subtract the two

10x = 7.555555

-x =     .75555555

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

9x  =6.8

Divide each side by 9

x = 6.8/9

x = 68/90

Divide by 2

x = 34/45

We do the same  for .555555 repeating

y = .5555 repeating

10 y = 5.5 repeating

10y  = 5.5

-y =       .555

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

9y = 5

y = 5/9

Subtract x - y

34/45 - 5/9

Get a common denominator

34/45 - 25/45

9/45

1/5

The value of (fg)(x)= 3x³+ x²

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given:

f(x) = -3x+1

g(x) = \(x^{2}\)

Now, (fg)(x)

=f(x) * g(x)

=  (-3x+1) * (\(x^{2}\))

=-3x³+ x²

Hence, (fg)(x)= 3x³+ x²

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Complete Question

Part of the question is shown on the first uploaded image

The rest of the question

What is the predicted number of years a 40 year old will wait before remarrying?

Given that the study found that the average 40 year old waits 4 years before remarrying, what is the value of the residual for a 40 year old?

Based on the printout and the residual plot, does it appear that time and age have a linear relationship? If so, how strong does the predictive relationship appear to be?

Answer:

 a

  The predicted number of years a 40 year old will wait before remarrying is     \(Time = 4.99\)

  b

  The value of the residual for a 40 year old  is  \(t = 0.99 \ years\)

c

   Based on the print out , we can say that the time and the age has a linear relationship

  And looking the R-sq we can say the 43.7% of time variation is due to age

Step-by-step explanation:

   From the regression equation

         \(Time = 0.03 + 0.124 Age\)

And from the question we are told that Age is  40 years so

      \(Time = 0.03 + 0.124 (40 )\)

      \(Time = 4.99\)

Therefore the predicted time 40 year old will wait for 4.99 years before remarrying

    From the question,the study found that the average 40 year old waits 4 years before remarrying,

     So the residual for a 40 year old is  mathematically evaluated as

              \(t = 4.99 - 4\)

             \(t = 0.99 \ years\)

Based on the print out , we can say that the time and the age has a linear relationship

  And looking the R-sq we can say the 43.7% of time variation is due to age

Answer:

9 2/5 or 9.4

Step-by-step explanation:

(3 1/5 + 1 2/5) + 4 4/5
(4 3/5) + 4 4/5 =
8 7/5
1 = 5/5
7/5 = 1 2/5
8 + 1 /25 = 9 2/5

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

What was the answer

Answer:

A

Step-by-step explanation:

since mean is the most annoying to calculate I went through and did everything else, the range is the same as both charts go 0-6. The median is is the middle number which means store 1 has a higher number of 3' s but our option says store 2 is greater and B is the mode, the number that shows up the most.

Answer:

its b4 + 7b3 + 4b2 + b5 + 7b4+ 4b3= b5+8b4+11b3+4b2

Answer:

When multiplying, add the exponents, (example) remember if there is "7b" the exponent is one.

Multiply b^2 * b^3 = b^5  (add the exponent 2 + 3 = 5)

Multiply 7b * b^3 = 7b^4 (the exponent of 7b is one, add 1 + 3 for the exponent to become 4)

Multiply 4 * b^3 = 4b^3 (4 doesn't have a variable, the exponent will be 3)

b^2 * b*2 = b^4 (add exponents)

7b * b^2 = 7b^3 (add the exponents 1 + 2)

4 * b^2 = 4b^2

              b^2             +               7b             +        4

b^3           b^5              +           7b^4            +   4b^3

+                                                                                      

b^2           b^4             +           7b^3            + 4b^2

b^5 + 7b^4 + 4b^3 + b^4 + 7b^3 + 4b^2

\(b^5 + 7b^4 + 4b^3 + b^4 + 7b^3 + 4b^2\)

The probability of someone being a right-handed chess player is 0.962, or approximately 0.96

Now, We have to given that;

The probability of being right-handed (R) is 0.9 and the probability of playing chess (C) given that someone is left-handed (L) is 0.6.

And, We are also told that dominant hand and playing chess are independent, so this means that the probability of playing chess is the same regardless of whether someone is left-handed or right-handed.

Hence, the probability of someone being a right-handed chess player, we can use the following formula:

P(R and C) = P(R) x P(C)

We know that P(R) = 0.9,

and since playing chess is independent of handedness,

P(C) = P(C|L) + P(C|R) = 0.6 + P(C|R).

We want to find P(C|R), the probability of playing chess given that someone is right-handed.

We can use the fact that the probabilities must add up to 1 to solve for P(C|R):

P(C|R) = 1 - P(not C|R)

We know that;

P(not C|R) = 1 - P(C|R),

so we can substitute to get:

P(C|R) = 1 - (1 - P(C|R)) = 2P(C|R) - 1

Now we can substitute this back into the original formula and solve for P(R and C):

P(R and C) = P(R) x P(C) P(R and C) = 0.9 x (0.6 + P(C|R))

P(R and C) = 0.54 + 0.9P(C|R)

Finally, we use the fact that the probabilities must add up to 1 to solve for P(C|R):

P(C|R) = 1 - P(not C|R) P(C|R)

= 1 - P(no C and R) / P(R) P(C|R)

= 1 - P(R and not C) / P(R) P(C|R)

= 1 - (0.1 x 0.4) / 0.9

P(C|R) = 0.5333

Now we can substitute this back into the equation for P(R and C) to get:

P(R and C) = 0.54 + 0.9(0.5333...)

P(R and C) = 0.962

Therefore, the probability of someone being a right-handed chess player is 0.962, or approximately 0.96

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Answer:

Step-by-step explanation:

A discriminate of -8 is never going to give you a real root. D is wrong

You cannot have just 1 complex root, nor can you have just 1 real root unless the discriminate is 0. A and C are both wrong for the same reason. 1 complex root is impossible. They come in pairs.

So the answer is B. You have 2 complex roots.

The inequality needed is

Answer:

a $12 discount like what is it soupoust to be

Approximately 7 employees took a break longer than 49 minutes.

We have,

In a box-and-whisker plot, the box represents the interquartile range (IQR), which includes the middle 50% of the data.

The line within the box represents the median.

The "whiskers" extend to the minimum and maximum values, excluding any outliers.

Given the information provided:

Median = 41

Q1 = 37

Q3 = 49

Largest = 55

Smallest = 35

Since Q3 represents the upper quartile and corresponds to the boundary for the upper 25% of the data, we can conclude that 25% of the employees took a break longer than 49 minutes.

Now,

The number of employees who took a break longer than 49 minutes can be estimated by calculating 25% of the total number of employees:

25% of 27 employees

= (25/100) x 27

= 6.75

Since we cannot have a fractional number of employees, we round up to the nearest whole number.

Therefore,

Approximately 7 employees took a break longer than 49 minutes.

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Answer:

$14

Step-by-step explanation:

35/20 = 1.75

8*1.75 = 14

Answer

$14

Step-by-step explanation:

You divide 35 by 20 so you get the cost of each individual comic book (35/20=$1.75 each)

then you multiply 8 by $1.75 which is equal to: $14

The answer is 14 dollars during the sale.

The functions f(4x-3)≥f(2-x^2) and f(5-x^2)≥f(3x-5) are quadratic functions

The values of the inequalities are -5 ≤ x ≤ 1 and -5 ≤ x ≤ 2

Inequality 1: f(4x - 3) ≥ f(2 - x^2), Df = (-8 , 4)

The function increases at (-8,4).

So, we have:

4x - 3 ≥ 2 - x^2

Rewrite as:

x^2 + 4x - 2 - 3 ≥ 0

Evaluate the like terms

x^2 + 4x - 5 ≥ 0

Expand

x^2 + 5x - x - 5 ≥ 0

Factorize the expression

x(x + 5) - 1(x + 5) ≥ 0

Factor out x + 5

(x - 1)(x + 5) ≥ 0

Solve for x

x ≥ 1 or x ≥ -5

Rewrite as:

-5 ≤ x ≤ 1

Inequality 2: f(5 - x^2) ≥ f(3x - 5), Df=(-∞,4)

The function decreases at (-∞,4).

So, we have:

5 - x^2 ≥ 3x - 5

Rewrite as:

x^2 + 3x - 5 - 5 ≤ 0

Evaluate the like terms

x^2 + 3x - 10 ≤ 0

Expand

x^2 + 5x - 2x - 10 ≤ 0

Factorize the expression

x(x + 5) - 2(x + 5) ≤ 0

Factor out x + 5

(x - 2)(x + 5) ≤ 0

Solve for x

x ≤ 2 or x ≤ -5

Rewrite as:

-5 ≤ x ≤ 2

Hence, the values of the inequalities are -5 ≤ x ≤ 1 and -5 ≤ x ≤ 2

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Answer: (-1) x 2² x 3

Happy to help:)

Because the denominators of both fraction have been changed to 7/8=21/24 and 5/6=20/24, respectively,

In mathematics, a denominator is the lowest number in such a fraction that indicates how many equal parts are split into a whole. It is a fraction's divisor.

Divisor is another synonym for denominator. In a common fraction, the integer under the line is described by both of these terms. Similar to this, when discussing statistical values, the term "denominator" refers to the entire population or number out of which samples are selected.

Common denominator is going to be \(24\)

\(8=2*2*2\\6=2*3\\24=2*2*2*3\)

\(8\) should be multiplied by \(3\)

\(6\) should be multiplied by \(4\)

\(7/8=(7*3)/(8*3)=21/3\\5/6=(5*4)/(6*4)=20/24\\7/8=21/24\\5/6=20/24\)

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The values into the slope-intercept form, we have y = -5x - 6

The slope-intercept form of a linear equation is given by:

y = mx + b

where 'm' represents the slope of the line, and 'b' represents the y-intercept.

In this case, the y-intercept is (0, -6), which means that the line crosses the y-axis at the point (0, -6).

The slope is given as -5.

Therefore, substituting the values into the slope-intercept form, we have:

y = -5x - 6

This equation represents the line with a y-intercept of (0, -6) and a slope of -5.

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The balance for each value of n is calculated by using the formula A = P(1 + r/n) ^nt. The rounded balance values are shown in the last column of the table above.

To complete the table and find the balance A if $3100 is invested at an annual percentage rate of 4% for 10 years and compounded n times a year.

The formula for calculating compound interest is as follows:

A = P(1 + r/n) ^nt,

where P represents the principal investment amount, r is the interest rate, n is the number of times the interest is compounded, t represents the time in years, and A represents the total amount, which includes the principal amount and the interest earned.

The table is given below:
\(\begin{array}{|c|c|c|} \hline \text{n} &

\text{A = P(1 + r/n) }^{nt} &

\text{Balance (rounded to nearest cent)} \\ \hline \text{1} &

\text{3100(1 + 0.04/1)}^{1*10} &

\text{\$4788.03} \\ \hline \text{2} &

\text{3100(1 + 0.04/2)}^{2*10} &

\text{\$4798.76} \\ \hline \text{4} &

\text{3100(1 + 0.04/4)}^{4*10} &

\text{\$4817.46} \\ \hline \text{12} &

\text{3100(1 + 0.04/12)}^{12*10} &

\text{\$4861.94} \\ \hline \end{array}\)

The balance is obtained by substituting the values of P, r, n, and t into the compound interest formula.

In this case, the investment is $3100, the annual interest rate is 4%, the investment is for 10 years, and n is the number of times the interest is compounded.

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Answer:

y=mx+b

Step-by-step explanation:

m=4/3×-6

I think this is the answer

Answer: ST = 6

Step-by-step explanation:

the segment sum is...

QR + RS + ST = QR

QR + 2 + ST= 10... use given values

Since R is the midpoint of QS, we know QR = RS = 2. Now, we have...

 ST = 10 -2 -QR = 10 -2 -2 = 6

The length of ST is 6.

Answer:

18 Bowls of Candy

Step-by-step explanation:

Camila has 6 bags of candy, and she can pour 1/3 of a bag into a bowl. To determine how many bowls of candy she can make in total, we need to divide the total amount of candy by the amount of candy per bowl.

Since Camila can pour 1/3 of a bag into a bowl, it means she can make 3 bowls of candy with a full bag.

Now, we can calculate the total number of bowls of candy:

Total bowls of candy = (Number of bags) x (Bowls per bag)

Total bowls of candy = 6 bags x 3 bowls per bag

Total bowls of candy = 18 bowls

Therefore, Camila can make a total of 18 bowls of candy with her 6 bags of candy.

We can respond to that by addressing the problem at hand As a equation  result, Felicia's equation has a slope of B and a y-intercept of 0, whereas Bruce's equation has a slope of A and a y-intercept of 0.

A math equation is a procedure that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the calculation 3x + 5 = 14, the equal sign places a space between the values 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The logo and the specifically software are frequently the same. as in, 2x - 4 Equals 2, for instance.

Let A represent the area that each tile covers. Following that, the area that Bruce covered, y, in terms of the quantity of tiles he employed, x, is given by:

y = Ax

Similarly, Felicia covered the space, y, by using the following number of tiles, x:

y = Bx

B is the area that each tile utilised by Felicia covers.

d) The equations are as follows when written in slope-intercept form:

For Bruce, y = Ax + 0.

For Felicia, y = Bx + 0.

As a result, Felicia's equation has a slope of B and a y-intercept of 0, whereas Bruce's equation has a slope of A and a y-intercept of 0.

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5n+2k = 25k or 7n but u have to divide by 2

25k divided by 2 = 12.5

7n divided by 2 = 3.5

12.5 + 3.5 = 16 therefore the answer is 16

Answer:

An acute angle

Step-by-step explanation:

An acute angle is smaller than an obtuse ad right angle.

hope this helps and hope it was right 'cause I really don't know what you meant. :)

Answer:

$609

Step-by-step explanation:

In water, a strong acid will dissociate completely into its component ions, while a weak base will undergo partial dissociation.

When a strong acid is dissolved in water, it will dissociate completely into its component ions. For example, if we consider hydrochloric acid (HCl), it will dissociate into hydrogen ions (H+) and chloride ions (Cl-) in water:

HCl → H+ + Cl-

In contrast, a weak base will undergo partial dissociation in water. It will only release a fraction of its component ions. For example, if we consider ammonia (NH3) as a weak base, it will partially dissociate into ammonium ions (NH4+) and hydroxide ions (OH-) in water:

NH3 + H2O ⇌ NH4+ + OH-

The equilibrium arrow (⇌) indicates that the reaction can occur in both directions, with the weak base partially dissociating and reforming in water.

The difference between strong acids and weak bases lies in their ability to dissociate in water. Strong acids have strong bonds that easily break in water, leading to complete dissociation. On the other hand, weak bases have weaker bonds, resulting in partial dissociation.

It's important to note that the degree of dissociation for weak bases can vary depending on factors such as concentration and temperature. However, in general, weak bases do not completely break down into their component parts like strong acids do in water.

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