Construct a polynomial function with the following properties: fifth degree, 4 is a zero of multiplicity 3, −2 is the only other zero, leading coefficient is 2.

Answers

Answer 1

Answer:

[tex]\Large \boxed{\sf \bf \ \ 2(x-4)^3(x+2)^2 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

Construct a polynomial function with the following properties...

... fifth degree

It means that the polynomial can be written as below.

[tex]a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x+a_0 \ \text{ with }a_5\text{ different from 0}\\\\\text{ or } k(x-x_1)(x-x_2)(x-x_3)(x-x_4)(x-x_5) \\\\ \text{ with k different from 0 and } (x_i)_{1\leqi\leq 5 } \text { are the roots.}[/tex]

... 4 is a zero of multiplicity 3

We can write the polynomial as below.

[tex]k(x-4)(x-4)(x-4)(x-x_4)(x-x_5)=k(x-4)^3(x-x_4)(x-x_5)[/tex]

... −2 is the only other zero

Because this is the only other zero, we can deduce that -2 is a zero of multiplicity 2.

[tex]k(x-4)(x-4)(x-4)(x-x_4)(x-x_5)\\\\=k(x-4)^3(x-(-2))(x-(-2))\\\\=k(x-4)^3(x+2)^2[/tex]

... leading coefficient is 2.

Finally, it means that k = 2 and then the polynomial function is:

[tex]\large \boxed{2(x-4)^3(x+2)^2}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you


Related Questions

Carolyn and Paul are playing a game starting with a list of the integers $1$ to $n.$ The rules of the game are: $\bullet$ Carolyn always has the first turn. $\bullet$ Carolyn and Paul alternate turns. $\bullet$ On each of her turns, Carolyn must remove one number from the list such that this number has at least one positive divisor other than itself remaining in the list. $\bullet$ On each of his turns, Paul must remove from the list all of the positive divisors of the number that Carolyn has just removed. $\bullet$ If Carolyn cannot remove any more numbers, then Paul removes the rest of the numbers. For example, if $n=6,$ a possible sequence of moves is shown in this chart: \begin{tabular}{|c|c|c|} \hline Player & Removed \# & \# remaining \\ \hline Carolyn & 4 & 1, 2, 3, 5, 6 \\ \hline Paul & 1, 2 & 3, 5, 6 \\ \hline Carolyn & 6 & 3, 5 \\ \hline Paul & 3 & 5 \\ \hline Carolyn & None & 5 \\ \hline Paul & 5 & None \\ \hline \end{tabular} Note that Carolyn can't remove $3$ or $5$ on her second turn, and can't remove any number on her third turn. In this example, the sum of the numbers removed by Carolyn is $4+6=10$ and the sum of the numbers removed by Paul is $1+2+3+5=11.$ Suppose that $n=6$ and Carolyn removes the integer $2$ on her first turn. Determine the sum of the numbers that Carolyn removes.

Answers

Answer:

The sum of the numbers that Carolyn removes is 5.

Step-by-step explanation:

The provided instruction for the game are:

Carolyn always has the first turn. Carolyn and Paul alternate turns.On each of her turns, Carolyn must remove one number from the list such that this number has at least one positive divisor other than itself remaining in the list.On each of his turns, Paul must remove from the list all of the positive divisors of the number that Carolyn has just removed.If Carolyn cannot remove any more numbers, then Paul removes the rest of the numbers.

The value of n is supposed as 6.

And it is also provided that Carolyn removes the integer 2 on her first turn.

The table displaying the outcomes of the game are as follows:

Player          Removed             Remaining

Carolyn                2                    1, 3, 4, 5, 6

 Paul                    1                       3, 4, 5, 6

Carolyn                3                         4, 5, 6

 Paul                    6                           4, 5

Carolyn             None                        4, 5

 Paul                  4, 5                        None

The sum of the numbers that Carolyn removes is:

S = 2 + 3 = 5

Thus, the sum of the numbers that Carolyn removes is 5.

I believe the answer is 8, but I am not sure.

100 students are interviewed to see which of biology, chemistry or physics they prefer.
59 of the students are girls. 35 of the girls like biology best.
2 of the boys prefer physics.
6 out of the 30 who prefer chemistry are girls.
What percentage of the students prefer biology?

Answers

Answer:

50%

Step-by-step explanation:

Girls                                            Boys

total:                 59                     total:                              41

- Chemistry       35                   - Physics                           2

                       = 24                                    =                     39

                                                 - Chemistry ( 30 - 6 )      24

                                                                   =                     15

Total boys and girls for Biology = 35 + 15 = 50

% = 50/100*100

   = 50%

Hope it helps and also mark it as brainliest!!!!

3
Select the correct answer.
Which equation represents the line that is parallel to y= 2 and passes through (-1,-6)?
OA x=-1
OB
X= 2
OCy= -6
OD. y= 2x - 4
Reset
Next

Answers

Hey there! I'm happy to help!

Lines that are parallel have the same slopes because they are increasing or decreasing at the same rate and therefore will never bump into each other.

We see that y=2 has a slope of 0 because there is no x that we can see in the equation. This is just a flat line.

If the line we are looking for is flat; it stays at the same y-value the entire time. We see that  the y-value for this line of ours is -6. Therefore, the answer is C. y=-6.

I hope that this helps! Have a wonderful day!

Answer:

Lines that are parallel have the same slopes because they are increasing or decreasing at the same rate and therefore will never bump into each other.

We see that y=2 has a slope of 0 because there is no x that we can see in the equation. This is just a flat line.

If the line we are looking for is flat; it stays at the same y-value the entire time. We see that  the y-value for this line of ours is -6. Therefore, the answer is C. y=-6.

Step-by-step explanation:

; ) BELIEVE IN YOURSELF!!!!!!!!!!!!!!!!!

In rectangle ABCD, point E lies half way between sides AB and CD and halfway between sides AD and BC. If AB=10 and BC=2, what is the area of the shaded region? Answer as a decimal, if necessary. Little confused on this one.

Answers

Answer:

10 units²

Step-by-step explanation:

Consider the unshaded region to consists of 2 triangles, ∆AED and ∆BEC, which are both of equal dimensions. Their bases and heights are both the same. Both triangles are embedded inside a rectangle ABCD.

Area of the shaded region = Area of rectangle - area of the 2 triangles.

Area of rectangle = l*w

l = 10

w = 2

[tex] Area_R = 10*2 = 20 units^2 [/tex]

Area of the 2 triangles = 2(½*b*h)

b = 2

h = 5

[tex]Area_T = 2(\frac{1}{2}*2*5)[/tex]

[tex] Area_T = 1*2*5 = 10 units^2 [/tex]

Area of shaded region = 20 - 10 = 10 units²

What are the zeros of the quadratic function represented by this graph?
У
A
6
2
X
-6
- 2
6
2-
-6-
A.
1 and 3
OB.
-3 and -1
C.
-3 and 1
D. -1 and 3

Answers

Answer: C.  -3 and 1

Look where the parabola crosses the x axis. This is where the x intercepts are located. The term "x intercept" is the same as "root" and also the term "zero".

Find a • b. a = 5i + 7j, b = -4i + 3j (5 points)
<1, 10>
<-20, 21>
1
41

Answers

Answer:

[tex]a\cdot b[/tex] = 1

Step-by-step explanation:

Given that,

Vector [tex]a=5i+7j[/tex]

Vector [tex]b=-4i+3j[/tex]

We need to find [tex]a{\cdot} b[/tex] means the dot product of a and b. So,

[tex]a{\cdot} b=(5i+7j){\cdot} (-4i+3j)[/tex]

We know that,

[tex]i{\cdot}i, j{\cdot}j,k{\cdot}k=1\ \text{and}\ i{\cdot}j= j\cdot i=0[/tex]

So,

[tex]a{\cdot} b=(5i+7j){\cdot} (-4i+3j)\\\\=5i{\cdot}(-4i)+5i{\cdot} 3j+7j\cdot(-4i)+7j\cdot 3j\\\\=-20+21\\\\=1[/tex]

So, the value of [tex]a\cdot b[/tex] is 1.

Answer:

1

Step-by-step explanation:

The Colonel spots a campfire at a bearing N 59∘59∘ E from his current position. Sarge, who is positioned 242 feet due east of the Colonel reckons the bearing to the fire to be N 34∘34∘ W from his current position.
Determine the distance from the campfire to each man, rounded to the nearest foot.
Colonel is about............................ feet away from the fire
Sarge is about............................... feet away from the fire

Answers

Answer:

i. Colonel is about 201 feet away from the fire.

ii. Sarge is about 125 feet away from the fire.

Step-by-step explanation:

Let the Colonel's location be represented by A, the Sarge's by B and that of campfire by C.

The total angle at the campfire from both the Colonel and Sarge = [tex]59^{0}[/tex] + [tex]34^{0}[/tex]

                                           = [tex]93^{0}[/tex]

Thus,

<CAB = [tex]90^{0}[/tex] - [tex]59^{0}[/tex] = [tex]31^{0}[/tex]

<CBA = [tex]90^{0}[/tex] - [tex]34^{0}[/tex] = [tex]56^{0}[/tex]

Sine rule states;

[tex]\frac{a}{Sin A}[/tex] = [tex]\frac{b}{Sin B}[/tex] = [tex]\frac{c}{Sin C}[/tex]

i. Colonel's distance from the campfire (b), can be determined by applying the sine rule;

[tex]\frac{b}{Sin B}[/tex] = [tex]\frac{c}{Sin C}[/tex]

[tex]\frac{b}{Sin 56^{0} }[/tex] = [tex]\frac{242}{Sin 93^{0} }[/tex]

[tex]\frac{b}{0.8290}[/tex] = [tex]\frac{242}{0.9986}[/tex]

cross multiply,

b = [tex]\frac{0.8290*242}{0.9986}[/tex]

  = 200.8993

Colonel is about 201 feet away from the fire.

ii. Sarge's distance from the campfire (a), can be determined by applying the sine rule;

[tex]\frac{a}{Sin A}[/tex] = [tex]\frac{c}{Sin C}[/tex]

[tex]\frac{a}{Sin 31^{0} }[/tex] = [tex]\frac{242}{Sin 93^{0} }[/tex]

[tex]\frac{a}{0.5150}[/tex] = [tex]\frac{242}{0.9986}[/tex]

cross multiply,

a = [tex]\frac{0.5150*242}{0.9986}[/tex]

  = 124.8073

Sarge is about 125 feet away from the fire.

Help me please ?! ❤️❤️

Answers

Answer:

Hey there!

Point K has coordinates of (-2, -5)

Hope this helps :)

Answer:

Point K

Step-by-step explanation:

Since they're asking us to find (-2,-5) first we need to move 2 points to the left and then 5 points down.

Emile is a long-distance trucker. In one week he drives miles from his home in Fort Lauderdale, FL, to Benson, NC. He then drives miles to Barstow, CA, and continues driving miles to Bakersfield, CA. From there, Emile drives miles to Seattle, WA. Estimate the total distance Emile travels by first rounding each distance to the nearest hundred. Do not put units in your answer.

Answers

Answer:

Estimated total distance is 1,900 miles.

Step-by-step explanation:

We begin by adding each distance traveled by Emile:

1. Fort Lauderdale, FL, to Benson, NC = 748 miles

2. Barstow, CA, to Bakersfield, CA = 130 miles

3. Bakersfield, CA.  to Seattle, WA = 1030 miles

Total miles = 1,908.

Therefore, in one week Emile's total distance to the nearest hundred is 1,900.

Note: the distances where gotten via Google Map.

PLEASE HELP ME!!! The students in Suzanne's school are painting a rectangular mural outside the building that will be 15 feet by 45 feet. To prepare they are create a scale drawing that represents 20% of the given dimensions. What is the length and width of the scale drawing?

Answers

Answer:

length of scale drawing = 9 feet

width of scale drawing = 3 feet

Step-by-step explanation:

Actual dimension  15 feet by 45 feet.

length = 45 feet

width = 15 feet

Dimension on drawing is 20% of actual dimension.

20% = 20/100

Thus,

20% of 15 feet = 20/100 * 15 feet = 3 feet

20% of 45 feet = 20/100 * 45 feet = 9 feet

Thus, length of scale drawing = 9 feet

width of scale drawing = 3 feet

A museum curator is hanging 7 paintings in a row for an exhibit. There are 4 Renaissance paintings and 3 Baroque paintings. From left to right, all of the Renaissance paintings will be hung first, followed by all of the Baroque paintings. How many ways are there to hang the paintings

Answers

Answer:

144 ways

Step-by-step explanation:

Number of paintings = 7

Renaissance = 4

Baroque = 3

We are hanging from left to right and we will first hang Renaissance painting before baroque painting.

For Renaissance we have 4! Ways of doing so. 4 x3x2x1 = 24

For baroque we have 3! Ways of doing so. 3x2x1 = 6

We have 4!ways x 3!ways

= (4x3x2x1) * (3x2x1) ways

= 144 ways

Therefore we have 144 ways to hang the painting.

domain and range A) D: (–7, –2], (–1, 3] R: (–10, 9.2] B) D: [–7, –2], [–1, 3] R: [–10, 9.2] C) D: (–7, 3] R: (–10, 9.2] D) D: (–7, –2), (–1, 3) R: (–10, 9.2)

Answers

Answer:

[tex]\Large \boxed{\mathrm{C) \ D: (-7, 3] \ R: (-10, 9.2]}}[/tex]

Step-by-step explanation:

The domain is the set of all possible x values.

The range is the set of all possible y values.

For the domain, we observe the graph, the graph will contain all the x values shown on the x-axis.

[tex]\mathrm{D= (-7,3] }[/tex]

For the range, we observe the graph, the graph will contain all the y values shown on the y-axis.

[tex]\mathrm{R= (-10,9.2] }[/tex]

Salina currently has an account balance of $1,047.69. Her initial deposit on the account was $630 and it earned 3.9% simple interest. How long has Salina held the account?

A - 17 years

B - 26 years

C - 10 years

D - 43 years

Answers

Answer:

A. 17 years

Step-by-step explanation:

Use the simple interest equation, I = prt, where I is the interest money gained, p is the starting amount of money, r is the interest rate in decimal form, and t is the time in years.

Plug in the values to solve for t:

417.69 = (630)(0.039)(t)

417.69 = 24.57t

17 = t

= 17 years

So, the correct answer is A, 17 years

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9 } A= {1, 2, 3, 4} and B= {4, 5, 6, 7}. Draw the Venn diagram of A ∩B. Answer with full explanation and diagram will be marked as brainliest for sure!!!

Answers

Step-by-step explanation:

Its mean the same number for both A and B which is only 4.

Match the provided functions to a graphed function with the same zero(s).

Answers

Answer:

1st:

[tex] {x}^{3} - 3 { x}^{2} - 3[/tex]

2nd:

[tex] {x}^{2} - 5x + 4[/tex]

3rd:

[tex] - 4x - 8[/tex]

Step-by-step explanation:

Graph all of them and see which ones cross the x- axis at the same points.

Area And Perimeter! Find the Area and the Perimeter of the Triangle!!! and explain.... ( help hurry!!)

Answers

perimeter of triangle: P = l+w+h

9+12+10= 31in.

area of triangle: A=b×h÷2

21 + 21 = 42in^2

which polynomial correctly combines the like terms and expresses the given polynomial in standard form? 9xy³ -4y⁴ -10x²y² + x³y + 3x⁴ + 2x²y² - 9y⁴

Answers

Answer:

3x^4+(x^3)y-8x^2y^2+9xy^3-13y^4

Step-by-step explanation:

3x^4+(nothing)=3x^4

x^3y+(nothing)=x^3y

-10x^2y^2=2x^2y^2=-8x^2y^2

9xy^3+(nothing)=0

-4y^4-9y^4=-13y^4

Add it all up and write the terms by descending order of exponent value, and u get my answer.

find out what's wrong with this graph

Answers

Answer:

The y-axis is upside down, meaning that instead of the values increasing as they go up, they decrease.

A rectangular tank that is 2048 ft cubed with a square base and open top is to be constructed of sheet steel of a given thickness. Find the dimensions of the tank with minimum weight.

Answers

Answer:

16ft by 16ft by 8ft.

Step-by-step explanation:

Let the total surface area of the rectangular tank be S = 2LW+2LH+2WH where;

L is the length of the box

W is the width of the box

H is the height of the box.

Since the box is openend at the top, S = lw + 2lh+ 2wh

If the base is a square base then, l = w

S = l(l) + 2wh+2wh

S = l²+4wh ............... 1

If volume = lwh

lwh = 2028 ft³

wh = 2048/l ................ 2

Substitute equation 2 into 1;

S = l²+4(2048/l)

S = l²+8192/l

dS/dl = 2l - 8192/l²

If dS/dl = 0 (since we are looking for dimensions of the tank with minimum weight.)

2l - 8192/l² = 0

2l = 8192/l²

2l³ = 8192

l³ = 8192/2

l³ = 4096

l =∛4096

l = 16 ft

Since the length is equal to the width, hence the width = 16ft (square based tank)

Given the volume V = lwh = 2048

lwh = 2048

16*16*h = 2048

256h = 2048

divide both sides by 256

256h/256 = 2048/256

h = 8ft

Hence, the dimensions of the tank with minimum weight is 16ft by 16ft by 8ft.

What is the name of a number that can be written in the form a + bi where a and b are nonzero real
numbers? (1 point)
a pure imaginary number
an imaginary unit
a real number
a complex number

Answers

Answer:

Complex numbers

Step-by-step explanation:

Given

[tex]a + bi[/tex]

Required

Determine the type of number in that form

Numbers written in [tex]a + bi[/tex] are referred to as complex numbers

Where [tex]a \neq 0[/tex]; [tex]b\neq 0[/tex] and [tex]i = \sqrt{-1}[/tex]

Note that a and b can either integers or non integers and a and be can also be positive or negative

The following are valid examples of complex numbers

[tex]2 + 3i[/tex]

[tex]2.4 - 5i[/tex]

[tex]-3 - i[/tex]

and lots more..

Question 2 (1 point)
Saved
A year ago, Rebecca purchased 100 shares of Havad stock for $20 per share.
Yesterday, she placed a limit order to sell her stock at a price of $33 per share before
the market opened. The stock's price opened at $23 and slowly increased to $26 in
the middle of the day, before declining to $22 by the end of the day. The stock did
not pay any dividends over the period in which Rebecca held it. Given Rebecca's
initial investment of $ 20 per share, her return is

Answers

Answer:

Rebecca does not have a return yet because the stock was not sold since there was a limit order at $33.

However, the value of her investment can be put around $2,400 (100 x $24 average price).

Step-by-step explanation:

Price of Havad Stock bought a year ago = $20

No. of shares = 100

Limit order selling price = $33

Stock prices during the limit order day = $23, $26, and $22

The stock cannot be sold, since its price did not reach $33.

Rebecca's limit order is an order to buy or sell her stock in Havad at $33 or better. Since her order is a sell limit order, it can only be executed at the limit price of $33 or higher.  Unfortunately, the price of the stock did not reach the limit order on that particular day.  This implies that her limit order is not guaranteed to execute.

If the true mean is 50 and we reject the hypothesis that μ = 50, what is the probability of Type II error? Hint: This is a trick question.

Answers

Answer:

Zero

Step-by-step explanation:

Given that:

the true mean is 50 and we reject the hypothesis that μ = 50

The probability of the Type II error will be zero, given that we reject the null hypothesis. This has nothing to do with if it is true or false.

Type II error is occurs when you accept a false null hypothesis. The probability of this error is denoted by beta which relies on sample size and population variance.

The probability of rejecting is equal to one minu beta. i.e it is the researchers goal to reject a false null hypothesis.

Solve the equation for x by graphing.-4x-1 5x=4

Answers

Answer: Undefined

Step-by-step explanation:

slope is undefined

no y intercept

This line is vertical

Do not use spaces in your answer. Solve for x. -5x + 12x - 8x = -24 x = ___ a0

Answers

Answer:

[tex]\Huge \boxed{x=24}[/tex]

Step-by-step explanation:

[tex]-5x + 12x - 8x = -24[/tex]

Combine all like terms.

[tex](-5+ 12- 8)x = -24[/tex]

[tex]-x=-24[/tex]

Multiply both sides by -1.

[tex]x=24[/tex]

Answer:

x must be 24

Step-by-step explanation:

I assume you meant " -5x + 12x - 8x = -24

Combine the x terms on the left side, obtaining -x = -24.

Then x must be 24

Henry takes out a $650 discounted loan with a simple interest rate of 12% for a period of 7 months. How much money does Henry receive into his bank account when the loan is drawn down? Give your answer to the nearest cent.

Answers

Answer:

$546

Step-by-step explanation:

Given

Amount, P = $650

Rate, R = 12%

Period, T = 7 months

Required

Determine the amount paid.

We'll solve this using simple interest formula, as thus

[tex]I = \frac{PRT}{100}[/tex]

Substitute values for T, R and P

[tex]I = \frac{\$650 * 12 * 7}{100}[/tex]

[tex]I = \frac{\$54600}{100}[/tex]

[tex]I = \$546[/tex]

Hence, Henry's withdrawal is $546

PLEASE HELP !!! (5/5) -50 POINTS-

Answers

Answer:

at least one solution

Step-by-step explanation:

Consistent solutions have at least one solution, but may have more than one solution.  Intersecting lines and  Lines that are the same are consistent solutions

Answer:

[tex]\boxed{Atleast\ one \ Solution}[/tex]

Step-by-step explanation:

A consistent system of equations have at least one solution. It can be more than that. There are no compulsions.

determine each unknown addend ___ + 41=-18

Answers

Answer:

-59

Step-by-step explanation:

x+41=-18

x= -18-41

x = -59

We want to model the daily movement of a particular stock (say Amazon, ticker = AMZN) using a homogeneous markov-chain. Suppose at the close of the market each day, the stock can end up higher or lower than the previous day’s close. Assume that if the stock closes higher on a day, the probability that it closes higher the next day is .65. If the stock closes lower on a day, the probability that it closes higher the next day is .45.

(a) What is the 1-step transition matrix? (Let 1 = higher, 2 = lower)

(b) On Monday, the stock closed higher. What is the probability that it will close higher on Thursday (three days later)

Answers

Answer:

See the explanation and attached images for the answers.

Step-by-step explanation:

a) 1-step transition matrix:

See the attached image for transition matrix.

Let the matrix be M

if the stock closes higher on a day, the probability that it closes higher the next day is 0.65.

If the stock closes lower on a day, the probability that it closes higher the next day is 0.45

if the stock closes higher on a day, the probability that it closes lower the next day is 1 - 0.65 = 0.35

if the stock closes lower on a day, the probability that it closes lower the next day is 1 - 0.45 =0.55

b)

To compute probability for 3 days later multiply matrix M (from part a) thrice i.e. M*M *M

[tex]M^{3} = \left[\begin{array}{ccc}0.65&0.35\\0.45&0.55\end{array}\right]*\left[\begin{array}{ccc}0.65&0.35\\0.45&0.55\end{array}\right]*\left[\begin{array}{ccc}0.65&0.35\\0.45&0.55\end{array}\right][/tex]

   

[tex]M^{3} = \left[\begin{array}{ccc}0.65 * 0.65 + 0.35 * 0.45 &0.65 * 0.35 + 0.35 * 0.55 \\0.45 * 0.65 + 0.55 * 0.45 &0.45 * 0.35 + 0.55 * 0.55 \end{array}\right] * \left[\begin{array}{ccc}0.65&0.35\\0.45&0.55\end{array}\right][/tex]

[tex]M^{3} = \left[\begin{array}{ccc}0.58&0.42\\0.54&0.46\end{array}\right]*\left[\begin{array}{ccc}0.65&0.35\\0.45&0.55\end{array}\right][/tex]

   

[tex]M^{3} = \left[\begin{array}{ccc} 0.58 * 0.65 + 0.42 x 0.45&0.58 * 0.35 + 0.42 * 0.55 \\0.54 * 0.65 + 0.46 * 0.45 &0.54 * 0.35 + 0.46 * 0.55 \end{array}\right][/tex]

[tex]M^{3} = \left[\begin{array}{ccc}0.566&0.434\\0.558&0.442\end{array}\right][/tex]

The probability that it will close higher on Thursday is 0.566. See the transmission matrix of M³ for higher-higher. This can be interpreted as:

if the stock closed higher on Monday, the probability that it closes higher the on Thursday (three days later) is 0.566

Need help finding the value for A

Answers

Answer:

[tex]\text{n}(A \bigcup B)[/tex] = 6.

Step-by-step explanation:

We are given that n(A) = 4, n(B) = 5, and [tex]\text{n}(A \bigcap B)[/tex] = 3.

And we have to find the value of [tex]\text{n}(A \bigcup B)[/tex].

As we know that the union formula is given by;

[tex]\text{n}(A \bigcup B) = \text{n}(A) + \text{n}(B) - \text{n}(A \bigcap B)[/tex]

Now, substituting the values given in the question in the above formula, we get;

[tex]\text{n}(A \bigcup B) = 4+5-3[/tex]

[tex]\text{n}(A \bigcup B) = 9-3[/tex]

[tex]\text{n}(A \bigcup B) = 6[/tex]

Hence, the value of [tex]\text{n}(A \bigcup B)[/tex] = 6.

Find the missing term in the
geometric sequence.
13,[ ? ],208

Answers

Answer:

110.5

Step-by-step explanation:

208=13+(3-1)d

208=13+2d

-13. -13

195=2d

÷2. ÷2

97.5=d. (d means difference)

13(first term)+97.5=110.5

Answer: 676

Step-by-step explanation: r/13=208/r

                                             r²=2704

                                               r=52

                                               13x52=676

                                               

Other Questions
Find the average rate of change of g(x)= x2 over the interval [ 8, 2]. Write your answer as an integer, fraction, or decimal rounded to the nearest tenth. Simplify any fractions. A bill passes the general assembly, but the governor vetoes it. Its chances or becoming law are now slim. What is the most likely reason for the bill's slim chances? A. The bill must receive two-thirds of the vote in the house of delegates and a majority in the Senate to override the veto.B. The bill must receive a certain number of signatures from the voters of Maryland to override the veto.C. The bill must receive three-fifths of the vote in both chambers of the general assembly to override the veto.D. The bill must receive unanimous support by all the seven judges on the court of appeals to override the veto. 4. A 0.100 M solution of NaOH is used to titrate an HCl solution of unknown concentration. To neutralize the solution, an average volume ofthe titrant was 38.2 mL. The starting volume of the HCI solution was 20 ml. What's the concentration of the HCI?O A.0.284 MB. 3.34 MC. 0.191 MD. 0.788 M Why is millet grown in the Sahel? A. It tastes better than wheat or barley. B. It is cheaper to grow than wheat or barley. C. It requires less water to grow than other grains. D. It has a longer cultivation cycle than other grains. Q3) Creative Sports Design (CSD) manufactures a standard-size racket and an oversize racket. The firms rackets are extremely light due to the use of a magnesium-graphite alloy that was invented by the firms founder. Each standard-size racket uses 0.125 kilograms of the alloy and each oversize racket uses 0.4 kilograms; over the next two-week production period only 80 kilograms of the alloy are available. Each standard-size racket uses 10 minutes of manufacturing time and each oversize racket uses 12 minutes. The profit contributions are $10 for each standard-size racket and $15 for each oversize racket, and 40 hours of manufacturing time are available each week. Management specified that at least 20% of the total production must be the standard-size racket. How many rackets of each type should CSD manufacture over the next two weeks to maximize the total profit contribution? Assume that because of the unique nature of their products, CSD can sell as many rackets as they can produce. Which of the following completes the sentence, '________ gamers value realism in the game's contextual clues and challenge in the game's activities, while _________ gamers value ease of use and immediate gratification'? Identify the sample as biased or unbiased and describe its type. John wanted to know about the popularity of a particular movie. He surveyed 20% of the people in 5 different theaters. Throughout his sermon Jonathan Edwards discusses peoples relationships with god. How does Edwards change or refine the idea of god and peoples relationship with god from the beginning to the end of the excerpt Q1) Determine the force in each member of thetruss and state if the members are in tension orcompression. Set P1 = 10 kN, P2=15 KN The parallelogram to be a square,x=? a project that will last for 8 years is expected to have equal annual cash flows of $97,900. If the required return is 7.6 percent, what maximum initial cash flows of $97,900 PLS ANSWER! According to scientific research, a student must study an instrument for how many years before they will perform better on tests of listening, motor skills, vocabulary, and reasoning? Select one: a. one year b. two years c. three years d. five years Raul tried to evaluate an expression step by step. Water flows at 0.00027 m3/s through a 10-m long garden hose lying on the ground, with a radius of 0.01 m. Water has a viscosity of 1 mPa.s What is the magnitude of gauge pressure in Pa of the water entering the hose the volume of a solid come is 616cm^3. Find it's height if the base radius is 7cm Suppose you invest equal amounts in a portfolio with an expected return of 16% and a standard deviation of returns of 18% and a risk-free asset with an interest rate of 4%. Calculate the expected return on the resulting portfolio. Group of answer choices PLEASE HELP!!! ILL MAKE YOU BRAINLKYEST!! 1. How could John Adams defend the British soldiers but still be seen as a Patriot? A. Adams knew that many Patriots wanted the British soldiers to be set free. B. Adams defended the soldiers because many Patriots asked him to. C. Adams defended the soldiers while defending the Patriots' belief in justice. D. Adams defended the soldiers because he thought it would make the British pity the Patriot cause. 2. Our Colonies must be the biggest Beggars in the World, if such small Duties appear to be intolerable Burdens in their Eyes. Pacificus, Maryland Gazette, March 20, 1766 Use the excerpt to answer the question. This excerpt is from a citizen in England in response to the colonial outrage toward the Stamp Act. What central argument of the American colonists against the Stamp Act is not understood by the writer? A. that trade was heavily restricted due to the taxes, which made it difficult for the colonists to make enough money to live let alone pay the taxes B. that although the tax is small, it is the idea that the colonists have to repay the British government for a war they did not support that is unjust C. that it is not the amount of tax that is the problem but rather the fact that the colonists were not involved in passing the tax D. that the tax may seem small to those in England but for the American colonists it is a very large amount of money 3. Why did the British feel justified imposing the Stamp Act on the colonists? Select all that apply. A. British citizens living in England faced increased taxes due to wars in the colonies. B. The taxes protected colonists living in the Ohio River valley from Native Americans. C. Britain had spent money protecting colonists from the French. D. The taxes were being used to raise money for more supplies for the colonists. 4. What was the purpose of the Olive Branch Petition? A. to declare war on England B. to raise a colonial army C. to declare allegiance to the King of England D. to convince France to enter the war 5. Why were colonial minutemen so prepared for the arrival of the British in Concord? Select all that apply. A. When Washington saw the British, he fired three canon shots sending a warning signal. B. Paul Revere had warned villages that the redcoats were coming. C. The Green Mountain Boys hid in the bushes and warned the Continental Army. D. When the British headed out, Americans hung two lamps as a warning signal. 6. How did Washington gain control of Boston? A. He sent 16,000 troops to launch a surprise attack on the British fort protecting Boston. B. He surrounded the harbor, giving them no option other than to surrender. C. He strategically placed cannons overlooking the harbor which forced out the British. D. He gained the trust of Native Americans who led a deadly attack on the British. 7. Compare the tactics used by the French troops in the French and Indian War with those of the American patriots during the Revolution. Select the correct answer. Assume that you are a member of a special interest group that wants to raise taxes on certain items. Who would you present your idea to if you wanted it to be proposed as a bill? A. a Supreme Court justice B. the president C. the American people D. a senator E. a member of the House PLEASE HELP ASAPNo explanation neededThe Kellen school district gives awards to its schools based on overall student attendance. The data for attendance are shown in the table, where Low represents the fewest days attended and High represents the most days attended for a single student. School Low High Range Mean Median IQR High School W 108 180 72 169 150 47.5 29.5 High School X 112 180 68 160 124 49.5 32.4 High School Z 130 180 50 162 151 39.5 27.5 Part A: If the school district wants to award the school that has the most consistent attendance among its students, which high school should it choose and why? Justify your answer mathematically. Part B: If the school district wants to award the school with the highest average attendance, which school should it choose and why? Justify your answer mathematically. What part of the line does the midpoint identify? The half-way coordinate between the end points. The second quartile The top part The bottom quartile