Math question 20 PTS
(h – k)(3) =

The arrangement is as follows;

What is stock?

A stock is a colloquial phrase for any company's ownership certificates. On the other hand, a share alludes to a certain company's stock certificate. You become a shareholder if you possess shares of a specific corporation.

The given data about stock and investment can be arranged in order  from the highest risk and return potential to the lowest risk and return potential as mentioned above in the answer.

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Answer:

x = 3 or x = -1/2

Step-by-step explanation:

Solve for x:

2 x^2 - 5 x - 3 = 0

The left hand side factors into a product with two terms:

(x - 3) (2 x + 1) = 0

Split into two equations:

x - 3 = 0 or 2 x + 1 = 0

Add 3 to both sides:

x = 3 or 2 x + 1 = 0

Subtract 1 from both sides:

x = 3 or 2 x = -1

Divide both sides by 2:

Answer: x = 3 or x = -1/2

Length of the curve is e² - 1 .

What is function?

In arithmetic, a function from a group X to a group Y assigns to every part of X precisely one part of Y. The set X is termed the domain of the function and therefore the set Y is termed the codomain of the function

Main body:

A parametric curve is a function expressed in components form, such that

x=f(t) , y=g(t). The length of a parametric curve on the interval a ≤ t ≤ b is given by the definite integral :

L =  [tex]\int\limits^a_b {\sqrt{(\frac{dx}{dt} )^2 + (\frac{dy}{dt} )^2} } \, dt[/tex]

Let's begin by getting the first derivative of the components of the function with respect to the variable t.

x = e^t - t  

dx / dt = e^t−1

y = 4 e^t/2

dy /dt = 2 e^t/2

Substitute the derivatives into the following definite integral which computes the length of the parametric curve on the interval

[a,b]=[0,2].

L =[tex]\int\limits^a_b {\sqrt{(\frac{dx}{dt} )^2 + (\frac{dy}{dt} )^2} } \, dt[/tex]

L=  [tex]\int\limits^2_0 {\sqrt{(e^{t}-1 )^2 + (2e^{t/2} } )^2} } \, dt[/tex]

L =[tex]\int\limits^2_0 {e^{t} -1} \, dt[/tex]

Evaluate the solution at the limits of integration to get the length.

L = (e² - 1 )- (e⁰ - 1)

L = e² - 1 - 1 + 1

L= e² - 1

Hence , length of the curve is e² - 1 .

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Answer:

The Pacific Ocean is approximately 4.9 times larger than Lake Superior in terms of volume. This can be shown through the following mathematical argument:

First, divide the volume of the Pacific Ocean by the volume of Lake Superior to determine the size ratio:

6 x 10^8 cubic kilometers / 1.22 x 10^4 cubic kilometers = 4.9

This shows that the Pacific Ocean is approximately 4.9 times larger than Lake Superior.

To defend this solution, we can use the concept of ratio and proportion. We know that the ratio of the volumes of the two bodies of water is equal to the ratio of their respective sizes. Therefore, by finding the ratio of the volumes, we can determine the size ratio.

In this case, the ratio of the volumes is 6 x 10^8 cubic kilometers / 1.22 x 10^4 cubic kilometers, which simplifies to 4.9. This means that the Pacific Ocean is 4.9 times larger than Lake Superior in terms of volume.

This solution can be further supported by the fact that the Pacific Ocean is the largest ocean in the world, while Lake Superior is one of the Great Lakes and is much smaller in size.

Step-by-step explanation:

SELF EXPLANATORY

(a) The rectangles represent a left sum, as the rectangles are drawn starting from the left endpoints of the intervals.

(b) The rectangles lead to a lower estimate of the integral, as the rectangles are drawn underneath the curve of the function.

(c) The value of n is 5, as there are 5 rectangles drawn.

(d) The value of Δx is 1, as the interval between the limits 0 to 6 is divided into 5 equal parts.

(e) The approximate value of the integral g(x)dx between the limits 0 to 6 is 22.5.

left-end points:

[tex]g(0)[/tex]Δ[tex]x[/tex] [tex]+ g(2)[/tex]Δ[tex]x + g(4)[/tex]Δ[tex]x[/tex]

Right-end points:

[tex]g(2)[/tex]Δ[tex]x + g(4)[/tex]Δ[tex]x + g(6)[/tex]Δ[tex]x[/tex]

[tex](g(2)+g(4)+g(6))^{2}[/tex]

Δ[tex]x=\frac{b-a}{n}[/tex]

   [tex]2=\frac{6-0}{n} \\\\2=\frac{6}{n}\\\\n=\frac{6}{2}=3 \\\\n=3[/tex]

Δ[tex]x=2-0=2[/tex] (each sub-interval length)

[tex]g(x)=x^{2} \\\\\int\limits^6_0{g(x)} \, dx = \int\limits^6_0 {x^{2} } \, dx[/tex]

              [tex]=[\frac{x^3}{3} ]^6_0\\\\=\frac{6^3}{3} -0\\\\=72[/tex]

The integral can be evaluated using the Fundamental Theorem of Calculus, which states that the integral of a function [tex]f(x)[/tex] with respect to [tex]x[/tex]from [tex]a[/tex] to [tex]b[/tex] is equal to the difference between the values of the antiderivative of [tex]f(x)[/tex] evaluated at [tex]b[/tex] and at [tex]a[/tex].

Therefore, the integral of [tex]f(x)[/tex] from [tex]a[/tex] to [tex]b[/tex] is given by:

[tex]\int\limits f{(x)} \, dx =f(b)-f(a)[/tex]

where[tex]F(x)[/tex] is the antiderivative of [tex]f(x)[/tex].

In this case, the antiderivative of f(x) is given by [tex]F(x) = \frac{x2}2 + c[/tex], where [tex]c[/tex] is the constant of integration. Therefore, the integral of f(x) from [tex]a[/tex] to [tex]b[/tex] is given by:

[tex]\int\limits f(x)dx = F(b) - F(a)\\\\= (\frac {b2}{2} + c) - (\frac{a2}{2} + c)\\\\= \frac{(b2 - a2)}{2}[/tex]

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The value of natural logarithm, ln(1/0.32) where base "e" or e =2.7182 is 1.13943..

Logarithm, an exponent or power that must be raised to obtain a particular number. Expressed mathematically, x is the logarithm of n in base a, where x = logₐ n.

Basic Rules:

Wehave given that,

ln(1/0.32) here , a = 1 , b = 0.32

using formula, ln(1/0.32) = ln(1) - ln(0.32)

Now, from logarithm table , log(1) = 0

log(0.32)= ln(0.32) = - 1.13943

ln(1/0.32) = ln(1) - ln(0.32) = 0-(- 1.13943)

=> ln(1/0.32) = 1.13943

Hence, the value of ln(1/0.32) is 1.13943.

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Using the provided percentages, it is discovered that:

a) A randomly chosen dorm room has a 31% chance of having a TV but no refrigerator.

b) A randomly chosen dorm room has a 48% chance of having either a television or a refrigerator, but not both.

c) There is a 31% chance that a randomly chosen dorm room lacks both a refrigerator and a television.

Item a:

TVs were owned by 52% of people.

21% of them had a refrigerator as well.

52 - 21 = 31

A randomly chosen dorm room has a 31% chance of having a TV but no refrigerator.

Item b:

31% just have a TV.

Only 17% of people—38—have a refrigerator.

31 + 17 = 48

A randomly chosen dorm room has a 48% chance of having either a television or a refrigerator, but not both.

Item c:

The likelihood that at least one exists is:

P(A∪B) = P(A) + P(B) - P(A∩B)

Hence:

P(A∪B) = 0.52 + 0.38 - 21 = 0.69.

1 - 0.69 = 0.31

There is a 31% chance that a randomly chosen dorm room lacks a refrigerator or a television.

The Complete Question.

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Answer:

The probability that a randomly selected dorm room has a TV but no refrigerator is 0.31

What is Probability?

Probability is a branch of mathematics that quantifies the likelihood of an event occurring or the likelihood of a statement being true. The probability of an event is a number between 0 and 1, with approximately 0 indicating the improbability of the event and 1 indicating certainty.

According to question

The probability that a randomly selected dorm room has a TV but no refrigerator

Solution :

Suppose

A = event of having refrigerators,

B = event of having a TV,

We have,

P(A) = 34% = 0.34,

P(B) = 51% = 0.51,

P(A∩B) = 21% = 0.21

Therefore:

Probability of a TV but no refrigerator = P(A∩B')

= P(A) - P(A∩B)

= 0.34 - 0.21

= 0.31

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Answer:

-13

Step-by-step explanation:

combine the numbers and just add the - sign

hope this helps

Given that sin 30 degree = 1/2 and cos 30 degree = Squareroot 3/2the value of cot(30°) is  = Squareroot 3

Sine 30°=1/2

Cos 30° = √3/2

Sin 30 degrees has a value of 0.5. Sin 30 can also be expressed in radians as sin /6. The triangle's angles and side length are related by the trigonometric function, often known as an angle function.

The sine function, cosine function, and tangent function are the three trigonometric ratios that are the most well-known.

The ratio of the adjacent side to the hypotenuse is referred to as the cosine function. If the right triangle's angle is 30 degrees, then the cosine value at this angle, or the value of Cos 30 degrees, is expressed as 3/2.

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Answer:

3

Step-by-step explanation:

Answer:

Step-by-step explanation:

How do you solve 2x+7= −17?

2x + 7 = -17

2x = -17 - 7

2x = -24

x = -12

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

check

2 × (-12) + 7 = -17

-24 + 7 = -17

-17 = -17

The answer is good

(A) cylindrical coordinate = (r, θ, z) = (√2, -π/4, 1)

(B) cylindrical coordinate = (r, θ, z) = (14, -π/3, 7)

In the given question, we have to change from rectangular to cylindrical coordinates. (let r ≥ 0 and 0 ≤ θ ≤ 2π.)

A) (-1,1,1)

Given rectangular coordinates(x, y, z) = (-1,1,1)

The cylindrical coordinates are (r, θ, z)

So we find the value of r and θ one by one.

r = √x^2+y^2

r = √(-1)^2+(1)^2

r = √1+1

r = √2

θ = [tex]\tan^{-1}[/tex](y/x)

θ = [tex]\tan^{-1}[/tex](1/-1)

θ = [tex]\tan^{-1}[/tex](-1)

θ = -π/4

So cylindrical coordinate = (r, θ, z) = (√2, -π/4, 1)

B) (-7,7√3,7)

Given rectangular coordinates(x, y, z) = (-1,1,1)

The cylindrical coordinates are (r, θ, z)

So we find the value of r and θ one by one.

r = √x^2+y^2

r = √(-7)^2+(7√3)^2

r = √49+147

r = √196

r = 14

θ = [tex]\tan^{-1}[/tex](y/x)

θ = [tex]\tan^{-1}[/tex](7√3/-7)

θ = [tex]\tan^{-1}[/tex](-√3)

θ = -π/3

So cylindrical coordinate = (r, θ, z) = (14, -π/3, 7)

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Generally speaking, a S corporation is put up to reduce the tax obligations. It is Option (3).

A business form known as a S corporation is one that is allowed by the tax code to distribute its taxable income, credits, deductions, and losses to its shareholders directly. This provides it certain advantages over the more popular C corp. The S corp, an alternative to the limited liability company, is only available to small firms with 100 or fewer stockholders (LLC). S corporations and LLCs are both referred to as "pass-through entities" since they don't pay corporate taxes, instead, they pay their owners, who are then in charge of paying the necessary taxes.

One sort of legal corporate structure that is popular among small businesses is the S corporation, commonly referred to as a S corp or S corp or S subchapter. Another is a limited liability company (LLC). A corporation with 100 shareholders or fewer can profit from incorporation while still being taxed as a partnership thanks to the requirements of a S corp. S corporations and LLCs are both pass-through companies, which means they don't pay corporate taxes and provide their owners and principals with limited liability protection. LLCs, however, offer more flexibility.

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Correct Question:

An S corporation is generally set up to:

1. implement an expansion strategy

2. attract capital

3. reduce tax burdens

4. easy entry into an industry

5. take advantage of limited liability

The value of the variable I (i.e interest) is $9

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

Principal, P =$400

Rate, R = 9%

Time, T = 0.25 years

The equation to calculate the interest is given as

I = PRT

Where

P, R and T are defined above

And I represents the interest

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

I = 400 * 9% * 0.25

Evaluate the products

I = 9

Hence, the interest is $9

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Answer:

3 years

Step-by-step explanation:

Lawson's tree starts at 14 inches and grows 3 inches every year, so we can represent that as 3x+14

Ezra's tree starts at 8 inches and grows 5 inches every year, so we can represent that as 5x+8

x=years

So, now that we have an equation for each tree, we will now set them as equal

5x+8=3x+14

Subtract 8 from each side

5x=3x+6

Subtract 3x from each side

2x=6

Divide each side by 2

x=3

It will take 3 years for the trees to reach the same height.

Step-by-step explanation:

a finite decimal number into a fraction is very easy.

remember what the different positions after the decimal point are worth :

tenths, hundredths, thousandths, tenthousandths, hundredthousandths, ...

0.225 covers thousandths.

how many ?

well, 225, of course.

so,

0.225 = 225/1000 = 9/40 × 25/25 = 9/40

The value of (1 + i)^5 is -2 * 2^1.5 * (1 + i). De Moivre's describes how the power of a complex number can be calculated using the properties of its modulus and argument.

De Moivre's theorem states that for any complex number z and any integer n, we have (z^n) = (r^n)(cos(nθ) + i * sin(nθ)), where r is the magnitude of z and θ is the angle that z makes with the positive real axis in the complex plane. Using this theorem, we can easily find the fifth power of 1+i as follows:

First, we need to express 1+i in polar form, which is given by z = r * cis(θ), where r is the magnitude of z and cis(θ) is the complex number with magnitude 1 and angle θ in the complex plane. In this case, we have z = 1+i = sqrt(2) * cis(π/4), where sqrt(2) is the magnitude of 1+i and cis(π/4) is the complex number with magnitude 1 and angle π/4 in the complex plane.

Next, we substitute this expression for z into the formula for (z^n) given by De Moivre's theorem, which gives us

(1 + i)^5 = √2^5 * (cos(5 * 45) + i * sin(5 * 45))

        = 2^2.5 * (cos(225) + i * sin(225))

(1 + i)^5 = 2^2.5 * (-cos(45) + i * -sin(45))

        = 2^2.5 * (-1 + i * -1)

        = -2 * 2^1.5 * (1 + i)

Therefore, the value of (1 + i)^5 is -2 * 2^1.5 * (1 + i).

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f(-7) will be equal to (-13) using given function and conditions.

What are function?

Function is an expression rule, or law that defines relationship between one variable and another variable.

An example of this would be y = x^2. If you put in anything for x, you get one output for y.

In given function,

y is represented by f(x),

f(x) = -x-6  for x ≠ 0

f(x) = 2      for x = 0

We need to find for x = -7 i.e. not equal to 0

So, we will take F(x) = -x-6

So, f(-7) = -7-6

             = -13

So, the value of f(-7) = -13.

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The stated inequality, x < 9 or x >=14, indicates that the two potential values for x are $8 and $14.

The two expressions that make up an equation or an inequality are connected in a mathematical statement. The equal sign (=) in an equation denotes the equality of the two expressions. The symbols >,,, or are used to denote an inequality, when the two expressions aren't always equal.

x < 9 or x ≥ 14

This indicates that x must be more than 9 but not equal to 14.

In the choices

All values below nine are

$8

There are no values larger than or equal to 14.

$14

The stated inequality, x < 9 or x >=14, indicates that the two potential values for x are $8 and $14.

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The number of apples obtained from the product of the fraction represented by the apples and the total number of fruits is 5 apples.

A fraction is a representation of the proportion or part of a whole quantity.

The fraction of the fruit that are apples = One quarter = 1/4

The fraction of the fruit that are oranges = One quarter of the number of fruits

The number of bananas = 4

Number of pear = 3

Number of plums = 3

The fraction of the whole fruit are represented by  apples and oranges = (1/4) + (1/4) = 1/2

The fraction of the total number of fruits represented by the bananas, pear and plum = 1 - (1/4 + 1/4)) = 1/2

Therefore;

Half of the total number of fruits = 4 + 3 + 3 = 10 fruits

Half of the fruits = 10

The total number of fruits is therefore, n = 2 × 10 = 20

The number of fruits that are apples = (1/4) × The total number of fruits

Therefore, the number of apples = (1/4) × 20 = 5

The number of fruits that are apples are 5 fruits

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On solving the provided question, the equation will be [tex]y^2 = - 4ax[/tex] and the factors - This cannot be determined from the information given

When points on a curve are equally spaced from a fixed point and line, the curve is said to have a parabola as its equation. The parabola's fixed point is referred to as the focus, and its fixed line is referred to as the directrix. Remember that the fixed point is not on the fixed line as well. A parabola is the locus of any point that is equidistant from both a focus and a straight line. A conical curve of interest in coordinate geometry is a parabola.

The equation will be

=> [tex]y^2 = - 4ax[/tex]

=> [tex]y^2 = -24x[/tex]

Factors - This cannot be determined from the information given

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Answer:

6

Step-by-step explanation:

Trust the process

Analysts recommend using Alpha Aesthetics. The alpha aesthetic makes some points on the chart more transparent than others in order to draw attention to specific data points.

How can a scatterplot be explained?

A scatterplot represents a group of points displayed on both the horizontal and vertical axes. Scatter plots are very important in the field of statistics because they can show the degree of correlation that exists between the values ​​of observed quantities or events (called variables). Scatter plots are used to show the degree to which one variable is influenced by another by plotting data points on horizontal and vertical axes. This is done to show how closely related the two variables are.

The positions of the markers that symbolize each row of the data table are determined by the values ​​placed in the columns along the X and Y axes.

Refer to this complete question:

A data analyst creates a scatterplot. The analyst wants to put a text label on the plot to call out specific data points. What function does the analyst use?

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The probability that the two pets selected are of the same species  is 0.2426   .

In the question ,

it is given that ,

the number of puppies in the pet store = 6

the number of kittens in the pet store = 9

the number of lizards in the pet store = 4

the number of snakes in the pet store = 5

total animals = 24

the probability of selecting 2 puppies = ⁶C₂/²⁴C₂

the probability of selecting 2 kittens = ⁹C₂/²⁴C₂

the probability of selecting 2 lizards = ⁴C₂/²⁴C₂

the probability of selecting 2 snakes = ⁵C₂/²⁴C₂

So , the required probability is

= ⁶C₂/²⁴C₂  + ⁹C₂/²⁴C₂ + ⁴C₂/²⁴C₂  + ⁵C₂/²⁴C₂  

Simplifying further ,

we get ,

= 5/92 + 3/23 + 1/46 + 5/138

= 0.0543 + 0.1304 + 0.0217 + 0.0362

= 0.2426

Therefore , the required probability is 0.2426   .

The given question is incomplete , the complete question is

The pet store has 6 puppies , 9 kittens , 4 lizards and 5 snakes . if you select two pets from the store randomly, what is the probability that they are both the same species ?

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Answer:

m=-1/3

Step-by-step explanation:

The equation of the perpendicular line to the given line is, [tex]y = \frac{4}{5}x - 8[/tex].

What is perpendicular lines?

When two geometric objects intersect at a right angle, they are considered to be perpendicular in elementary geometry. By using the perpendicular symbol,, the condition of perpendicularity can be graphically represented. Between two lines, a line and a plane, or between two planes can be used to define it.

Consider the given equation of line

5x + 4y = 10

Convert it into the form y = mx + c

⇒ 4y = -5x + 10

y = -5/4x + 10/4

y = -5/4x + 5/2

Here the slope of line is, -5/4.

The slope of perpendicular line is negative reciprocal of the slope of given line.

So, the slope of perpendicular line is,

[tex]-\frac{1}{(-5/4)} = \frac{4}{5}[/tex]

Also the line passes through the point (5, -4).

By using the point slope form to find the equation of line

[tex]y-y_1 = m(x-x_1)\\y-(-4) = \frac{4}{5}(x-5)\\ y+4=\frac{4}{5}x - 4\\ y = \frac{4}{5}x - 4 - 4\\ y = \frac{4}{5}x - 8[/tex]

Hence, the equation of the perpendicular line to the given line is, [tex]y = \frac{4}{5}x - 8[/tex].

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Generate two-digit random numbers, 00-99. 00 – 02 represent a birth defect. 03 – 99 represent no defect

It has already occurred. The rating for number five, which discusses birth problems, is three out of one hundred. The digit 99 Ah, chosen at random, stands for 100 numbers.

If I'm given the task, I'll choose one to two to stand in for a birth defect. A sign that reads "No birth malformations" is present. I am able to generate a random number and examine two digits. Keep track of your trial numbers and your results so that you can get an idea of how that percentage will be.

If the number comes back as 000 teams, which represents the effect of birds, and then if it comes back as 0 to 99 teams, which indicates no effect of birds, keep track of your trial numbers and results.

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The solution of the equation after completing the square of the equation is found as; x = ±√19 + 2.

The given steps are-

x² - 4x = 15.

(b/2)² = (-2)²

x² - 4x + (-2)² = 15 +(-2)²

x² - 4x + 4 = 19

There are various ways to display the outcome.

(x - 2)² = 19

x = ±√19 + 2

Thus, the solution of the equation after completing the square of the equation is found as; x = ±√19 + 2.

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43920  is the lowest amount that a teacher needs to make and still be one of the top 7% earners with a mean of $38,000 and a standard deviation of $4,000

According to information provided to us, the pay for elementary school teachers in a certain nation is generally distributed, with a mean of $38,000 and a standard deviation of $4,000 per year.

To resolve the issue at hand, we shall make use of the normal distribution table. Finding the z-score corresponding to the top 7% or the 93% probability from the normal distribution table (0.93).

The normal distribution table provides us with the 1.48 z-score we need.

We will now solve for the sample score using the z-score formula as follows:

z = x - μ/σ

1.48 = x - 38,000/4000

1.48 × 4000 = x - 38,000

5920 = x - 38000

x = 5920+38000

x = 43920

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Answer:

its 3

Step-by-step explanation:

the rate is 3

The estimate for f(4.8) using the local linear approximation for f at x= 5 is obtained as 2.2.

For the stated function;

f(5)=3 and f′(5)=4

the linear approximation indicates that you believe the function is linear.

So just do this:

f(5) + f'(5) (x-5)

Put the values in the obtained function;

In this particular instance, it works out.

= 3 + 4 (4.8 - 5)

= 3 + 4 (-0.2)

= 2.2

Thus, the estimate for f(4.8) using the local linear approximation for f at x= 5 is obtained as 2.2.

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