what is the quadratic equation in standard form with rational coefficents that has a root of 5+4i?

The expected difference under null hypothesis can be understood by the following :

The required null and alternate hypothesis will be

Null hypothesis :  H0 : μ=μ0

Alternate Hypothesis: H1 : μ<μ0

To determine whether there is a difference in the means of two populations, the z test formula compares the z statistic to the z critical value.

The z critical value in hypothesis testing divides the distribution graph into acceptance and rejection regions. The null hypothesis can be rejected if the test statistic falls within the rejection region; otherwise, it cannot be rejected.

The z test formula  to set up the required hypothesis tests for a one sample and a two-sample z test is

z = (( x−μ) /σ/√n  )x

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The stock's average nominal risk premium is 6.70%, while its average real return is 7.47%.

The inflation rate can be obtained from the consumer price index or the GDP deflator. The real rate of return is the actual yearly rate of return after accounting for factors like inflation. It is computed by adding the nominal rate to the inflation rate and dividing the result by three.

The annual return factored in after taxes and inflation is known as the real rate of return. Taxes and inflation are not included in a nominal rate of return, which is what it is called. The same goes for a rate of return that is calculated using taxes or inflation.

From the information given, the average return will be calculated thus:

Average return = 0.540 / 5

                          = 0.108

Average return = 10.80%

Therefore, the average real return will be:

= [( 1 + Average return) / (1+ inflation rate)] - 1

substitute the values in the above equation, we get

= [(1+0.1080) / (1+0.081)] - 1

simplifying the above equation,

= 0.0747

= 7.47%

Also, the average nominal risk premium will be:

= Average Return - Risk free rate

= 0.1080 - 0.041

= 0.067

= 6.70%

Therefore, the stock's average nominal risk premium is 6.70%, while its average real return is 7.47%.

The complete question is:

You’ve observed the following returns on Yamauchi Corporation’s stock over the past five years: −10 percent, 24 percent, 21 percent, 11 percent, and 8 percent. The average inflation rate over this period was 3.1 percent and the average T-bill rate over the period was 4.1 percent. a. What was the average real return on the stock? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. What was the average nominal risk premium on the stock? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

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Answer:

by dividing 10.

Step-by-step explanation:

100 percent if full. so to find ten percent, do 100 divided by 10.

The value of θ is 45 degrees as sin45° is equal to 1/√2.

Trigonometric equation refers to an equation consists of a number of trigonometric ratios whose angle is unknown.

Generally trigonometric angles are represented by θ. while solving equations we get the values of θ ranges from 0 degree to 90 degrees.

Given, 2sin²θ = 1

solving the equation

      sin²θ = 1/2

     sinθ = 1/√2

we know sin45° has a specific value 1/√2

   sinθ = sin 45°

now, θ = 45°

hence, the solution is θ = 45 degrees.

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Answer: 25 oz for 2.30

Step-by-step explanation:

18oz Pepsi for $2.00

Take 2 divided by 18 = $0.11

25 oz for $2.30

Take 2.3 divided by 25 = $0.09

So 25 oz for 2.30 is better!

The equations of the tangents that pass through (2,−3) are y=−x−1 and  y= 11x−25.

What is an equation?

In arithmetic,an equation may be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.

Main BODY:

The gradient of the tangent to a curve at any particular point is given by the derivative of the curve at that point. So for our curve (the parabola) we have

y=x²+x

Differentiating wrt x we get:

dy / dx = 2x +1

Let P(α,β) be any generic point on the curve. Then the gradient of the tangent at P is given by:

m=2α+1                   (using the derivative)

And as P lies on the curve we also have:

β=α²+α                    (using the curve equation)

And so the tangent at P passes through (α,α²+α) and has gradient 2α+1, so using the point/slope form y−y₁=m(x−x₁) the equation of the tangent at P is;

y−(α²+α)=(2α+1)(x−α)

if this tangent also passes through

(2,−3) then;

⇒-3−(α²+α)=(2α+1)(2−α)

⇒-3 −α²- α = 3α−2α²+2

⇒α²−4α−5=0

∴α=−1,5

If  α=−1⇒β=0

, and the tangent equation becomes:

y−0=(−1)(x+1)

∴ y=−x−1

If α=5⇒β=30

, and the tangent equation becomes:

y−30=(11)(x−5

∴y−30=11x−55

∴y=11x−25

Hence the equations of the tangents that pass through (2,−3) are y=−x−1 and  y= 11x−25.

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Answer:

15

Step-by-step explanation:

In an equilateral triangle all the sides length are the same.  Set two sides equal to each other and solve for x

3x + 6 = 6x - 3    Subtract 3x from both sides

6 = 3x -3  Add 3 to both sides

9 = 3x  Divide each side by 3

3 = x

Now that we know x is 3, plug this into the expression for any side and find the side length

3x + 6

3(3) + 6

9 + 6 = 15

[tex]\boxed{20+40a \leq 280}\\\\1+2a \leq 14\\\\2a \leq 13\\\\a\leq \frac{13}{2}[/tex]

However, since there must be a whole number of people, this rounds down to [tex]\boxed{a \leq 6}[/tex]

According to the uniform distribution, there is a 0.1= 10% chance that a worker selected at random will have an annual wage between $45,000 and $60,000.

Uniform Distribution:

In statistics, uniform distribution refers to a type of probability distribution in which all outcomes are equally likely. A deck of cards has within it uniform distributions because the likelihood of drawing a heart, a club, a diamond, or a spade is equally likely.

An uniform distribution has two bounds, a and b.  

The probability of finding a value between c and d is:

P(c ≤ X ≤ d) = [tex]\frac{d-c}{b-a}[/tex]

given that , workers' salaries in your company are uniformly distributed between $10,000 and $60,000 per year

a = 10,000 , b= 60,000 , c = 45,000 and d = 50,000

The probability is

P(45,000 ≤ X ≤ 50,000) = [tex]\frac{50,000-45,000}{60,000-10,000}[/tex]

                                       = 0.1

0.1 = 10% probability that a randomly chosen worker earns an annual salary between $45,000 and $60,000

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In integration the bindefinite integral of 1/xlnx is

ln(|u|)+C=ln(|lnx|)+C with the aid of using parts, we've discovered whilst the specified formula.

The vital of the 2 capabilities are taken, with the aid of using thinking about the left time period as first feature and 2nd time period as the second one feature.

This technique is referred to as Ilate rule.The vital of xlnx is same to (x2/2) lnx - x2/4 + C, wherein C is the mixing constant. We can compare this vital the usage of the technique of integration with the aid of using parts.

We have the vital:

[tex]∫1xlnxdx

Use substitution. Let u=lnx so that du=1xdx . Note that each of those are presently gift withinside the vital.

∫1xlnxdx=∫(1lnx)1xdx=∫1udu

This is a not unusualplace vital:

∫1udu=ln(|u|)+C

Since u=lnx :

ln(|u|)+C=ln(|lnx|)+C[/tex]

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The number of days required to complete his task is 9 days.

What is a graph?

The graph of a relation R is the set of all points (x, y) in a coordinate plane such that x is related to y through the relation R.

Stewart loves playing Genshin Impact so much that he “forgets” to do his schoolwork. It’s really starting to impact his grades and he has 36 overdue assignments. The semester is almost over, and he really needs to improve his grades. He can realistically complete 4 overdue assignments each day.

So he will complete 4 assignments each day and he has to complete the 36 overdue assignments.

The number of days required to do this = 36/4

                                                                  = 9 days.

Hence, the number of days required to complete his task is 9 days. and this relation can be expressed on the graph as

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Answer:

116.9

Step-by-step explanation:

9.1(6) + 8.9(7)

54.6+62.3

116.9

The value of ∠JKI is  107⁰.

What is an angle of a triangle?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Given that ∠JKI = (5x−3)⁰, ∠KIJ=(2x+8)⁰, and ∠IJK=(x−1)⁰.

The sum of all angles of a triangle is 180⁰.

(5x−3)⁰ + (2x+8)⁰ + (x−1)⁰ = 180⁰

(5x + 2x + x) + ( - 3 + 8 -1) = 180

8x + 4 = 180

Subtract 4 from both sides:

8x = 176

x = 22

Putting x = 22 in ∠JKI = (5x−3)⁰:

∠JKI = (5×22 − 3)⁰

∠JKI = 107⁰

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Answer:

1600$

Step-by-step explanation:

By using the SI formula,

[tex]SI={PXRXT}/{100} \\SI=10000X2X8/100\\SI = 1600$\\\\Hence, the interest is 1600$[/tex]$

Option C) 1600$ is correct

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The equation to find how much money they will save after 3 weeks is y = 68x, and they will save $518, so yes they have enough money to buy the gift.

An assertion that two mathematical expressions have equal values is known as an equation. An equation simply states that two things are equal. The equal to sign, or "=," is used to indicate it.

Given:

Total money Jason and his 3 brothers have = $314,

Each of them will save $17 a week until they have at least $515,

At the end of three weeks, the money saved by Jason and his brothers,

Money saved = 17 × number of person × number of weeks

Assume the number of weeks is x and the money saved is y then,

y = 17x × 4

y = 68x

Money saved, y = 68 × 3

Money saved = $204

Total money after the end of three weeks = $314 + $204

Total money after the end of three weeks = $518

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The measure of z in the polygon is (a) z = 15

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

Shape = 9-sided polygon

Parameter to calculate = the measure of z

The sum of the interior angles is calculated using the following angle formula

The sum of the interior angles = ( n − 2 ) × 180 ∘ where n is the number of sides

In this case

n = 9

Substitute the known values in the above equation, so, we have the following representation

The sum of the interior angles = (9 − 2) × 180∘

Evaluate

The sum of the interior angles = 1260∘

So, the internal angle is

Angle = 1260/9

Evaluate

Angle = 140

This means that

5z + 65 = 140

So, we have

5z = 75

Divide by 5

z = 15

Hence, the angle is (a) z = 15

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if there appears to be a relationship in scatterplot 4,The linear relationship in scatterplot 4 appears to be negative.

When examining scatterplot 4, we can see that as the values of the x-axis increase, the values of the y-axis decrease in a linear relationship. This implies that as the values of the x-axis increase, the values of the y-axis decrease at a constant rate. This indicates a negative linear relationship between the two variables, meaning that as one variable increases, the other variable decreases in a linear fashion.

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Answer:

-9n - 6

Step-by-step explanation:

1. combine the n's

-3n - 6n = -9n

2. combine the constants

-7 + 1 = -6

Ages (in years) of a sample of retirement home inhabitants is option B. For the lowest wait time, the maximum frequency is anticipated to be right-skewed. A desert cannot have a maximum annual temperature of 60°F, and it is not conceivable to watch 60+ hours of TV in a single day.

Residents of senior living facilities are typically 84 years old. While there are many couples in these communities, the majority of people who live in independent living are women. Some people move in at or near the minimum age (often around 65), but most people do so between the ages of 75 and 84. Residents come from all different backgrounds.

Many people are choosing senior living in a community environment, including teachers, nurses, small business owners, big business CEOs, university professors, housewives, lawyers, engineers, musicians, and more. Current residents will attest that the rich diversity of origins fosters amazing interactions and relationships. And contrary to popular belief, the majority of residents of independent living are quite active.

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Correct Question:

Match the plot with a possible description of the sample.

60 70 80 90 100

Choose the correct answer below

A. Wait time (in minutes) for a sample of doctors offices

B. Ages (in years) of a sample of residents of a retirement home.

C. Highest yearly temperatures (F) for a sample of deserts.

D. Time (in hours_ spent watching TV in a day for a sample of teenagers.

The way is...

m x 10n

Answer: 780

Step-by-step explanation:

Two times 2 is 4

4 + 89 = 93

93 +765 = 858

858 - 78 = 780

Proof of  angle 6 is congruent to angle 4 is given.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

Angles of equal measure are said to have congruent angles.

Given,

∠1 ≅ ∠3

And we know from the vertical angles, property;

The angles opposite each other when two lines cross.

They are always equal.

And here we have two pairs of vertical angles,

So, ∠1 = ∠4

and ∠3 = ∠6

And ∠1 ≅ ∠3 is given.

So,  ∠1 ≅ ∠4

and ∠3 ≅ ∠6

Comparing, we get

∠4 ≅ ∠6

Therefore, ∠4 ≅ ∠6 is proved.

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The answer is 35

140 times 0.25

The linear function that passes through (-8,4) and (4,5) will be y = (1/12)x + 14/3.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

A linear equation or function is given as ;

y = mx + b

The slope (m) associated with two points (x₁, y₁) and (x₂, y₂) is given by

Slope = (y₂ - y₁)/(x₂ - x₁)

The slope associated with (-8,4) and (4,5) will be as,

m = (5 - 4)/(4 + 8) = 1/12

Thus, y = (1/12)x + b

Put (4,5)

5 = (1/12)4 + b

b = 5 - 1/3

b = 14/3

Thus, y = (1/12)x + 14/3

Hence "The linear function that passes through (-8,4) and (4,5) will be y = (1/12)x + 14/3".

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Answer:

ST = 2.6

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{ST}{PQ}[/tex] = [tex]\frac{SU}{PR}[/tex] ( substitute values )

[tex]\frac{ST}{18}[/tex] = [tex]\frac{5.2}{36}[/tex] ( cross- multiply )

36 × ST = 18 × 5.2 = 93.6 ( divide both sides by 36 )

ST = 2.6

The random variable x's mean and standard deviation are 8 and 2, respectively. W=7+ 4x is the formula for the random variable w. The mean of w is E(W) =39

A dataset's mean is calculated by dividing the sum of all values by the total number of values. The term "average" is frequently used to describe it because it is the most widely used central tendency metric.

Divide the entire number of values by the total number of numbers to find the average. A mean is the term used to describe the mathematical average of a set of two or more data values. Average is also referred to as mean or arithmetic mean.

The mean is the average value of the data. It's easy to calculate: just add up all the numbers, then divide by the total number of numbers. Or, to put it another way, it is equal to the sum divided by the quantity.

The mean is then determined as follows:

E(W) = E (7 + 4X)

This results

E(W) = 7 + 4 E (X)

We thus have:

E(W) = 7 + 4 x 8

E(W) =39

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Standard deviation = 8 and mean = 39.

What is standard deviation?

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the anticipated value) of the collection.

Given, the formula for mean is E(W) = 7 + 4(X)

∴ E(W) = 7 + 4E(X)

Mean, E(X) equals to 8, hence substituting in the above equation, we get,

E(W) = 7 + 4×8

⇒E(W) = 39

Since, E(W) = 7 + 4(X)

Var(W) = Var(7) + Var(4X)

Since, Var(constant)=0,

Var(W) = Var(4X)

Var(W) = 4²×Var(X), where Var(X)=σₓ²

⇒ Var(W) = 16×σₓ², where σₓ²=2²

⇒ Var(W) = 16×4

⇒ Var(W) = 64

Standard Deviation (SD) = √64 = 8

Thus, standard deviation = 8 and mean = 39.

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Answer:17cm x 19cm

Step-by-step explanation:

Answer: length is 19 inches  

               width is 17 inches

Step-by-step explanation:

Let the length and the width are x>0 and (x+2)>0

Hence,

x(x+2)=323

x²+2x=323

x²+2x-323=0

x²+(19x-17x)-323=0

(x²+19x)-(17x+323)=0

x(x+19)-17(x+19)=0

(x+19(x-7)=0

x+19=0

x=-19∉ (x>0)

x-17=0

x=17 inches

x+2=17+2

x+2=19 inches

Answer:Square

Step-by-step explanation:

A square is a quadrilateral with four right angles and four congruent sides. All squares are rectangles and rhombuses.

Answer:

D. square

Step-by-step explanation:

As an explanation, I have attached a picture of the 4 quadrilaterals and their internal angles and sides.

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