2. Identify the leading coefficient, degree, and the end behavior for the following polynomial functions below.

​Future Value received at the end of  one year is 1065

Future Value received at the end of  two year is 1134.225

​Future Value received at the end of  three year is 1207.949

 discount rate of 6.5 percent

  present value of a $1,000

Present Value= [tex]\frac{FV}{(1+r)^{n} }[/tex]

​where:

FV=Future Value

r=Rate of return

n=Number of periods

Future Value received at the end of  one year

Future Value= Present Value * [tex](1+r)^{n}[/tex]

                      =  1000 * (1+ 6.5%)^1

                     =  1000* 1.065

                      = 1065

Future Value received at the end of  two year

Future Value= Present Value * [tex](1+r)^{n}[/tex]

                      =  1000 * (1+ 6.5%)^2

                     =  1000* 1.065^2

                      = 1000 * 1.134225

                      = 1134.225

​Future Value received at the end of  three year

Future Value= Present Value * [tex](1+r)^{n}[/tex]

                      =  1000 * (1+ 6.5%)^3

                     =  1000* 1.065^3

                      = 1000 * 1.207949

                      = 1207.949

​Future Value received at the end of  one year is 1065

Future Value received at the end of  two year is 1134.225

​Future Value received at the end of  three year is 1207.949

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The given polynomials are discussed and grouped into each given category as given below.

What is a polynomial?

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

We can now look into each polynomial.

a) x³ + 125

   125 is a cube of 5 and also  x³  is the power of x.

So this is a perfect cube.

b) 8p³ - 27

    8p³ is a perfect cube of 2p and 27 is a perfect cube of 3.

So it is a perfect cube.

c) 12x³-9

    This is neither a cube nor a square.

d) a²-100

   100 is a perfect square and so is a².

So this is a difference of perfect squares.

e) 4m² + 25

4m² is a square of 2m and 25 is a square of 5.

But the operator is +

So this is neither a cube nor a difference of a perfect square.

f) 16x²-9

16x² is a square of 4x and 9 is a square of 3.

Also, the operator is -

So this is a difference of perfect squares.

Therefore the above polynomials are discussed and grouped into each given category accordingly.

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One triangles can be made with these conditions.

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Answer:

The dimensions of the strongest rectangular beam that can be cut from the log are:

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

From observation of the given diagram, the diameter of the circle is the hypotenuse of a right triangle (with legs w and d).  Given that the diameter is 48 cm, substitute the values into Pythagoras' Theorem and rearrange to create an expression for d²:

[tex]\begin{aligned}w^2+d^2&=48^2\\w^2+d^2&=2304\\d^2&=2304-w^2\end{aligned}[/tex]

Substitute the found expression for d² into the given strength equation:

[tex]\begin{aligned}s&=kwd^2\\s&=kw(2304-w^2)\end{aligned}[/tex]

Hence showing that s = kw (2304 - w²).

To find the value of w that will maximise the strength of the rectangular beam, first differentiate the equation for s in terms of w:

[tex]\begin{aligned}s&=kw(2304-w^2)\\s&=2304kw-kw^3\\\implies \dfrac{\text{d}s}{\text{d}w}&=2304k-3kw^2\\&=3k(768-w^2)\end{aligned}[/tex]

Set the differentiated equation to zero and solve for w:

[tex]\begin{aligned}3k(768-w^2)&=0\\ 768-w^2&=0\\w^2&=768\\w&=\sqrt{768}\\w&=\sqrt{256 \cdot 3}\\w&=\sqrt{256}\sqrt{3}\\w&=16\sqrt{3}\\\end{aligned}[/tex]

Substitute the value of w that maximises the strength of the beam, together with the given hypotenuse of 48 cm, into Pythagoras' Theorem and solve for d:

[tex]\begin{aligned}w^2+d^2&=48^2\\768+d^2&=2304\\d^2&=2304-768\\d^2&=1536\\d&=\sqrt{1536}\\d&=\sqrt{256 \cdot 6}\\d&=\sqrt{256}\sqrt{6}\\d&=16\sqrt{6}\end{aligned}[/tex]

Therefore, the dimensions of the strongest rectangular beam that can be cut from the log are:

The total number of fish caught during the festival can be calculated by adding the number of fish caught for each value of n.

For example, if 10 contestants caught 4 fish, 5 caught 8 fish, 7 caught 10 fish, and 8 caught 7 fish, the total number of fish caught would be 104 + 58 + 710 + 87 = 330.

The argument states that the total number of fish caught during the Frostbite Falls Fishing Festival can be determined by adding the number of fish caught by each contestant.

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Answer: £15

Step-by-step explanation:

210/14 = 15

to check :14x15=210

Answer: One necklace costs $15

Step-by-step explanation:

We know Regan sold 14 necklaces but we do not know how many, we can use "x" to represent the amount of necklaces sold.

We will use the equation 14(x)=210 to represent our word problem

Use PEMDAS and divide both sides by 14, this will give you x=15

$15 per necklace is the answer

Answer: 17 units

Step-by-step explanation: A perimeter of a rectangle can be represented by the equation:

2(L)+2(W) = P

L represents length, W represents width and P represents perimeter

Lets say DC is width so AB has to be width aswell and then AD and BC are length.

We are given width and length as equations and P as 76 so we can substitute it into our equation to get:

2(3x-1) + 2(4x-3) = 76

We are trying to solve x so distributing would make it easy to obtain and we get:

6x - 2 + 8x - 6 = 76

Simplifying and solving for x gives us:

6x - 2 + 8x - 6 = 76

14x - 8 = 76

14x = 84

x = 6

Finally, we know AD represents our Width and AD = BC since we know BC is 3x-1, we can plug x in to get BC which is equal to AD to get:

3x - 1 = BC

3(6) - 1 = BC

17 = BC

since BC = AD

17 = AD

There are ${14 \choose 6}$ ways to select 6 of the babies from the group of 14, including Evie and Ben.

The question is asking how many ways there are to select 6 of the 14 babies from the group if Evie and Ben are included. This can be solved using the formula for combinations, which is ${n \choose r}$, where n is the total number of items and r is the number of items being selected. In this case, n = 14 and r = 6. Therefore, the answer is ${14 \choose 6}$. This means that there are 1001 ways to select 6 of the 14 babies, including Evie and Ben. To solve this, first the formula is used. Then, the total number of items, 14, is plugged into the formula. Finally, the number of items being selected, 6, is plugged into the formula. This yields the final answer of ${14 \choose 6}$.

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The bar diagram connect to the formula C = πd by taking π as 3

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

C = πd

Also from the bar diagram, we have

C = 3d

When the equations are compared, we have

C = πd = 3d

This gives

π = 3

Hence, the value of π is 3

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Answer: 2:5:7

Step-by-step explanation:

You need to find the greatest common factor of all three of them which is 5. Then, you divide each number by 5

The difference between the amounts of Nachelle and violet is $670.31

Starting young lets the students take advantage of the magic of "compound interest." Compound interest is the interest you earn on interest. This can be illustrated by using basic math: if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. At the end of the second year, you'll have $110.25.

Given here: Violet invested $5900 at 7.5% interest and Nachelle invested the same amount but at 6.875 %

After 10 years Violets Amount when compounded quarterly we get

A= 5900×(1+7.5%)⁴⁰

  =$12,403.86

Similarly after 10 years Nachelle's amount if it is compounded contionously we get

[tex]P(t)=P_{0}e^{rt}[/tex]

[tex]P(10)=5900e^{0.06875*10}\\ =11733.55[/tex]

∴The difference between their amounts is$12,403.86-11733.55=$670.31

Hence, The difference between the amounts of Nachelle and violet is $670.31

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Answer:670

Step-by-step explanation:

If you operate a small unmanned aircraft (UA) and deviate from your approved flight plan greater than 600 feet agl to avoid a possible collision with a manned airplane, you may need to report the deviation to;

the Federal Aviation Administration (FAA).

The FAA requires all small UAs to comply with certain regulations and guidelines, including the requirement to maintain an altitude of no more than 400 feet above ground level (AGL) unless otherwise authorized.

If you deviate from your approved flight plan, such as by climbing to an altitude greater than 600 feet AGL to avoid a possible collision with a manned airplane, you may need to report the deviation to the FAA.

It is important to follow all FAA regulations and guidelines for small UAs to ensure the safety of other aircraft and people on the ground. If you are unsure about how to report a deviation or what regulations apply to your specific UA, you can contact the FAA for guidance.

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The quadratic function with vertex (-1,-6), that passes through (1,2), is given as follows:

y = 2x² + 4x - 4.

The equation of a quadratic function, of vertex (h,k), is given by the following rule:

y = a(x - h)² + k

In which:

Considering the vertex at x = -1, y = -6, the parameters h and k are given as follows:

h = -1, k = -6.

Hence:

y = a(x + 1)² - 6.

When x = 1, y = 2, hence the leading coefficient a is obtained as follows:

2 = a(2)² - 6

4a = 8

a = 2.

Hence:

y = 2(x + 1)² - 6.

In standard form, we have that:

y = 2x² + 4x + 2 - 6

y = 2x² + 4x - 4.

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Answer:

Hi, I'm Za'Riah! I will gladly assist you with your problem. (see explanation)

Step-by-step explanation:

Solution:

We need to simplify the following expression: (5-7y+10)1/5

[tex]\frac{(5-7y+10)*1}{5}[/tex]

Grouping together numerical values

[tex]\frac{(-7y+5+10)*1}{5}[/tex]

We reduce the integers that can be added together: 5+10=15

= [tex]\frac{(-7y+5+10)*1}{5}[/tex]

By reorganizing/simplifying/expanding the terms that are amenable to

[tex]3 -\frac{7}{5}y[/tex]

Answer:

Yes they are in fact equivalent.

(Hope this helped!)

The range of the regression coefficient of y on x is (-∞, ∞).

The parameter β (the regression coefficient) represents the amount by which change in x must be multiplied to give the interconnected average change in y or the amount y changes for a unit increase in x. In this manner, it represents the degree to which the line slopes upwards or downwards.

The regression coefficient of x on y, β, represents the change in y per unit change in x. The regression coefficient of y on x, β', represents the change in x per unit change in y.

The range of the regression coefficient of y on x is (-∞, ∞). This is because the relationship between x and y can be positive, negative, or zero, leading to positive, negative, or zero regression coefficients.

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The imaginary part of the given expression 1/ ( 1+i ) is -i / 2.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is 1 / ( 1 + i). The imaginary part will be calculated as:-

E = 1 / ( 1 + i)

Rationalize the numbers,

E = 1 / ( 1 + i)

E = [ 1 / ( 1 + i) ] [ ( 1 - i ) / ( 1 - i ) ]

E = ( 1 - i ) / ( 1² +1 )

E = ( 1 - i ) / 2

E = ( 1 / 2 ) - ( i / 2 )

The imaginary part will be -( i / 2 ).

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Therefore , the solution of the given problem of triangle comes out to be a value is 3.5154 unit.

Triangles are polygons because they have four sides or more. Its form is simple and geometric. An angle square with the letters ABC is known as a triangle. When the sides remain not collinear, Euclidean geometry generates a singular plane or square. Having three parts and three corners makes a triangle a polygon. The corners of a triangle are where the three sides meet. Angles in a triangle add up at 180 °.

Here,

Given :

=> Tan 38° =  a/4.5

=> 0.7812 = a /4.5

=> a = 4.5 * 0.7812

=> a = 3.5154 unit

Therefore , the solution of the given problem of triangle comes out to be

a value is 3.5154 unit.

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The amount of state income tax owed on a $60,000 per year salary is $3,000.

A progressive tax is one in which the tax rate rises in proportion to the taxable amount. The term progressive refers to the manner in which the tax rate rises from low to high, resulting in a taxpayer's average tax rate being less than the person's marginal tax rate.

We are given that the income is $60,000. The applicable Progressive tax for this income range is 5%.

The state income tax owed on a $60,000 per year salary goes as follows:

= $60,000 * 5%

= $3,000

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Answer:

n = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

for the equation to be true for all values of x , then both sides have to be the same.

expand both sides and equate like terms

left side

12(3n - [tex]\frac{1}{2}[/tex] x) ← distribute each term in the parenthesis by 12

= 36n - 6x

right side

- [tex]\frac{2}{3}[/tex] (9x - 18) ← distribute each term in the parenthesis by - [tex]\frac{2}{3}[/tex]

= - 6x + 12

we require

36n - 6x = - 6x + 12

that is

36n = 12 ( divide both sides by 36 )

n = [tex]\frac{12}{36}[/tex] = [tex]\frac{1}{3}[/tex]

for the equation to be true for all x then n = [tex]\frac{1}{3}[/tex]

Answer:

Use the scale, 400:100

Step-by-step explanation:

400 on x axis, 100 on y axis
800 on x axis, 200 on y axis
Join the points with a line, extend it
That's it!

An integral for the volume of the solid obtained by rotating the region in the first quadrant bounded by the curves y = tan² x, y = 3, and x = 0 about the line y = 3 is V = ∫[0, arctan(√3)] 2πx(3 - tan²(x)) dx.

The method of cylindrical shells can be used to set up the integral for the solid's volume after rotating the first quarter region defined by the curves y = tan² x, y = 3, and x = 0 about the line y = 3.

We must take into account an infinitesimally thin strip of width dx at a distance x from the y-axis in order to set up the integral.

This cylindrical shell's volume can be estimated by multiplying its height, radius, and thickness (dx) together. Consequently, each shell's volume is as follows:

dV = 2πx(3 - tan²(x)) dx

Setting 3 = tan²(x), we have:

tan²(x) = 3

tan(x) = √3

x = arctan(√3)

Thus, the integral for the volume of the solid is: V = ∫[0, arctan(√3)] 2πx(3 - tan²(x)) dx

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Answer:

Step-by-step explanation: Distributing the -10 to the parentheses, we get:

-20m -10 = -50

Adding 10 to both sides:

-20m = -40

dividing both sides by -20:

m = 2

So the solution for m is 2.

Answer:

-7

Step-by-step explanation:

Distribute the -10: -20-10m=50

Add 20 to both sides: -10m=70

Divide by -10 to isolate 70

m = -7

rAnswer: x-intercept: (-0.75, 0)

y-intercept: (0, 3/7)

Step-by-step explanation: An x and y intercept is the point when the line crosses the x and y axis respectively. When a line crosses the x axis, the y value is 0 and when the line crosses y axis, the x value is 0. This means   we can set y and x equal to 0 and solve for the other variable.

To solve for the x intercept, we set y equal 0 so:

-4x + 7(0) = 3

-4x = 3

x = -(3/4)

so we get

(-3/4, 0) or (-0.75, 0) for our x int

For the y intercept we set x equal 0:

-4(0) + 7y = 3

7y = 3

y = 3/7

so we get

(0, 3/7) for our y int

7 + 6m is solution of parenthesizes equation .

What is parentheses in maths ?

These are also referred to as round brackets and are represented by the following symbols: ( ). The most typical brackets are those mentioned above.

                                 They are utilized to combine several numbers and formulae. In an equation, terms are grouped together or the order of operations is stated using parentheses or "round brackets."

Rewrite 12-(5+6m)

= 12 - 5 + 6m

=  7 + 6m

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In Triangle ABC which is an Isosceles triangle. AB = BC where mLB = 34° so mLA = 73°

Triangles that have at least two sides of equal length are said to be isosceles.

Sum of all angle of a traingle is 180°

So mLA + mLB +mLC = 180

2(mLA) + mLB = 180

2(mLA ) = 180 - 34

2(mLA ) = 146

mLA = 73°

An isosceles triangle has three angles, which, like other triangles, sum up to 180 degrees. The angles other than the apex angle among the three inner angles are identical in size. According to the isosceles triangle theorem, an isosceles triangle has equal-sized angles on either side of its equal sides. As a result, we have B = C in the isosceles triangle ABC where AB = AC.

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Answer:

Step-by-step explanation:

4. short leg= 4

      hyp= 8

5. leg 2= 5

    hypotenuse= 5√2

6. both legs = 2√2

Okun's law states that changes in unemployment and production are inversely related, with a coordinate of -2.

(a) When the unemployment rate stays the same in a given year, Okun's law's number 3.5 indicates the anticipated percent rise in yearly US national production.

(b) In accordance with Okun's law, a year in which unemployment increases from 5% to 8% results in a 1% decrease in national production.

(c) In accordance with Okun's law, a year in which production is equal to the previous year results in a decline of 1.75% in the unemployment rate.

(d) The inverse link between the unemployment rate and national output is represented by the coefficient -2 in Okun's law, which states that a rise in the unemployment rate would result in a fall in national production.

According to Okun's Law, the annual US national production's percent change (y) and the unemployment rate's percent change are connected (u). When the unemployment rate stays constant in a given year, the projected percent increase in national production is represented by the constant 3.5 in Okun's law. The inverse link between the unemployment rate and national output, represented by the coefficient -2 in Okun's law, states that a rise in the unemployment rate will result in a fall in national production. As a result, if unemployment increases from 5% to 8%, national production will decline by 1%. The change in the unemployment rate would need to be a decrease of 1.75 percent for national production to be the same as it was the previous year.

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The best explanation for the difference between Doctor A’s and Doctor B’s posterior probability for the hypothesis that you have cogscitis is that Doctor A thought the hypothesis that you have cogscitis was more likely than Doctor B before either of them saw the results from Test 1.

After getting the results from Test 1, Doctor A's posterior probability for the hypothesis that you have cogscitis can be calculated as follows:

P(cogscitis|test 1 positive) = (P(test 1 positive|cogscitis) × P(cogscitis)) / P(test 1 positive)

where P(cogscitis) = 0.70 (Doctor A's prior probability) and P(test 1 positive|cogscitis) = 0.70 (probability of positive test result given cogscitis).

P(test 1 positive) can be calculated as the sum of probabilities of getting a positive result for both hypotheses:

P(test 1 positive) = P(test 1 positive|cogscitis) × P(cogscitis) + P(test 1 positive|not cogscitis) × P(not cogscitis)

where P(not cogscitis) = 0.3 (Doctor A's prior probability for not cogscitis).

Substituting the values, we get:

P(cogscitis|test 1 positive) = (0.70 × 0.70) / (0.70 × 0.70 + 0.10 × 0.30) = 0.87 (rounded to two decimal places).

So, Doctor A's posterior probability for the hypothesis that you have cogscitis after seeing the positive result of Test 1 is 0.87.

Similarly, Doctor B's posterior probability for the hypothesis that you have cogscitis after seeing the positive result of Test 1 can be calculated as follows:

P(cogscitis|test 1 positive) = (P(test 1 positive|cogscitis) × P(cogscitis)) / P(test 1 positive)

where P(cogscitis) = 0.20 (Doctor B's prior probability) and P(test 1 positive|cogscitis) = 0.70 (probability of positive test result given cogscitis).

P(test 1 positive) can be calculated as the sum of probabilities of getting a positive result for both hypotheses:

P(test 1 positive) = P(test 1 positive|cogscitis) * P(cogscitis) + P(test 1 positive|not cogscitis) × P(not cogscitis)

where P(not cogscitis) = 0.8 (Doctor B's prior probability for not cogscitis).

Substituting the values, we get:

P(cogscitis|test 1 positive) = (0.70 × 0.20) / (0.70 × 0.20 + 0.10 × 0.80) = 0.15 (rounded to two decimal places).

So, Doctor B's posterior probability for the hypothesis that you have cogscitis after seeing the positive result of Test 1 is 0.15.

The best explanation for the difference between Doctor A’s and Doctor B’s posterior probability for the hypothesis that you have cogscitis is c) Doctor A thought the hypothesis that you have cogscitis was more likely than Doctor B before either of them saw the results from Test 1.

Hence, the correct answer is c.

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