Let G be the sales (in millions of dollars) of football jerseys. Let H be the sakes (in millions of dollars) of baseball jerseys. During a 5-year period, G and H can be modeled by the following equations, where t is the time (in years).

G = 15t^4 + 13t^3 + 10t^2 - 10t + 750

H - 11t^4 + 13t^3 + 9t^2 + 8t + 650

a. Find a polynomial function A for the total sales of football and baseball jerseys.
A = ?

b. Is the function A even, odd, or neither? Explain.

The graphed polynomial seems to have a degree of 2, so the degree can be 4 and not 5.

For a polynomial of degree N, we have (N - 1) changes of curvature.

This means that a quadratic function (degree 2) has only one change (like in the graph).

Then for a cubic function (degree 3) there are two, and so on.

So. a polynomial of degree 4 should have 3 changes. Naturally, if the coefficients of the powers 4 and 3 are really small, the function will behave like a quadratic for smaller values of x, but for larger values of x the terms of higher power will affect more, while here we only see that as x grows, the arms of the graph only go upwards (we don't know what happens after).

Then we can write:

y = a*x^4 + c*x^2 + d

That is a polynomial of degree 4, but if we choose x^2 = u

y = a*u^2 + c*u + d

So it is equivalent to a quadratic polynomial.

Then the graph can represent a function of degree 4 (but not 5, as we can't perform the same trick with an odd power).

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Answer:

x₁(2x₁x₂² - x₂ - 3) - 3x₂

Step-by-step explanation:

The expression you provided is a polynomial in two variables, x₁ and x₂. Let's simplify it step by step:

2x₁²x₂² - x₁x₂ - 3x₁ - 3x₂

To simplify, we can look for common terms that can be factored out:

x₁(2x₁x₂² - x₂ - 3) - 3x₂

Now let's simplify the expression inside the parentheses:

2x₁x₂² - x₂ - 3

Step-by-step explanation:

here's the answer to your question

Answer:

y^(2/3)

Step-by-step explanation:

( y ^ ( 7/3) * y^ ( 1/3)  ) ^ 1/4

Combine the terms in side the parentheses

a^b* a^c = a^(b+c)

( y ^ ( 7/3+ 1/3)  ) ^ 1/4

( y^( 8/3) )^1/4

We know a^b^c = a^(b*c)

y ^(8/3*1/4)

y^(2/3)

Answer:

This is an expression. To simplify it, we will combine like terms.

9d - 4p - 6 - 10d + 8 = (-9d - 10d) - 4p - 6 + 8 = -19d - 4p + 2

So the simplified expression is -19d - 4p + 2

Answer: 81

Step-by-step explanation: If you add all of the numbers, then you end up getting 81.35 and 81.35 estimated to the nearest whole number is 81 because that's the closest whole number to 81.35.

To determine the rows where the expression (p ∧ q) ∨ (p ∧ r) is true, we can construct a truth table with columns for p, q, r, p ∧ q, p ∧ r, (p ∧ q) ∨ (p ∧ r), as shown below:

```

p | q | r | p ∧ q | p ∧ r | (p ∧ q) ∨ (p ∧ r)

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

T | T | T | T | T | T

T | T | F | T | T | T

T | F | T | F | T | T

T | F | F | F | F | F

F | T | T | F | F | F

F | T | F | F | F | F

F | F | T | F | F | F

F | F | F | F | F | F

```

The rows where the expression (p ∧ q) ∨ (p ∧ r) is true are the first, second, and third rows, where the last column is true. Therefore, the rows where the expression is true are:

```

p | q | r

--------

T | T | T

T | T | F

T | F | T

```

The approach to probability exemplified by the formula Probability of an Event = Number of favourable Outcomes / Total number of possible outcomes is the Classical approach to probability.

The Classical approach to probability is based on the assumption of equally likely outcomes and is often used when dealing with simple and well-defined experiments or situations. It involves counting the number of favorable outcomes (those that satisfy the desired condition) and dividing it by the total number of possible outcomes. This approach assumes that all outcomes have an equal chance of occurring.

In contrast, the Empirical approach involves conducting experiments or observations to gather data and estimate probabilities based on the observed frequencies. The Subjective approach relies on personal judgments or subjective assessments of probabilities based on individual beliefs or opinions.

Therefore, the correct answer is A) Classical approach.

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The minimum sample size needed to be 99% confident that the sample mean is within 4 hours of the true population mean is 27.

To calculate the minimum sample size needed to be 99% confident that the sample mean is within 4 hours of the true population mean with a population standard deviation of 8 hours, follow these steps:

1. Identify the desired confidence level: In this case, it is 99%.
2. Find the corresponding Z-score for the confidence level: For a 99% confidence level, the Z-score is approximately 2.576.
3. Identify the population standard deviation: In this case, it is 8 hours.
4. Identify the margin of error: In this case, it is 4 hours.
5. Use the following formula to calculate the sample size:
  Sample size (n) = (Z-score^2 * population standard deviation^2) / margin of error^2

Plugging in the values, we get:
n = (2.576^2 * 8^2) / 4^2
n = (6.635776 * 64) / 16
n = 26.543104

Since we need to round up to the nearest integer, the minimum sample size needed is 27.

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Answer:

The length is 10 feet.

Step-by-step explanation:

The formula for the perimeter of a rectangle is 2(l + w) = P. If the perimeter is 50 and the width is 5 feet more than the length, the equation can be written as 2( (l + 5) + l) = 50, or 2(2l + 5) = 50. You can then solve for l.

2(2l + 5) = 50

2l + 5 = 25

2l = 20

l = 10

Answer:

Simplify ans: 3 x^2 y^-4

a no = x( x+2)

b no = 2x(x- 3)

c no = 5x(3- 2x^2)

d no.= 3x^2( 3+ x)

Hope this helps you

Answer:

see explanation

Step-by-step explanation:

Using the rules of exponents

\(\frac{a^{m} }{a^{n} }\) ⇔ \(a^{(m-n)}\) ( m > n)

\(\frac{a^{m} }{a^{n} }\) ⇒ \(\frac{1}{a^{(n-m)} }\) ( n > m )

Given

\(\frac{21x^6y^5}{14x^2y^9}\)

= \(\frac{21}{14}\) × \(x^{(6-2)}\) × \(\frac{1}{y^{(9-5)} }\)

= \(\frac{3}{2}\) × \(x^{4}\) × \(\frac{1}{y^{4} }\)

= \(\frac{3x^4}{2y^4}\) ← with positive exponents

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

(a)

x² + 2x ← factor out x from each term

= x(x + 2)

(b)

2x² - 6x ← factor out 2x from each term

= 2x(x - 3)

(c)

15x - 10x³ ← factor out 5x from each term

= 5x(3 - 2x²)

(d)

9x² + 3x³ ← factor out 3x² from each term

= 3x²(3 + x)

Lerchs-Grossman algorithm is a pit optimization software that helps in the determination of the most profitable final pit outline. The section of a copper porphyry ore body given has a cut-off grade of 0.45% Cu. Each block has dimensions of 16m x 16m x 16m (HxLxW).

The cost of mining a block of waste is $50, and the value of a block of ore is approximated to be $100 x (grade expressed in %). Firstly, we have to calculate the net present value (NPV) for all the blocks that are above the cut-off grade. NPV is calculated using the formula given below:

NPV = ((grade*100)*100)-50

Here, the cost of mining a block of waste is $50 and the value of a block of ore is approximated to be $100 x (grade expressed in %).

1. Firstly, the net present value (NPV) of each block above the cutoff grade is calculated.2. The blocks are then sorted in descending order of their NPVs.

3. Next, the algorithm calculates the limits of the pit at a sequence of levels, starting with the block of highest NPV.

4. It is assumed that the pit will extend downwards through the blocks from the highest NPV downwards.

5. If the pit reaches the edge of the ore body before reaching a certain level, it is truncated and the lower level is tried.

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Answer:

A and B

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

a standard wooden pencil typically measures around 7 inches to 7.5 inches in length.

The average length of a pencil can vary depending on factors such as the type of pencil, region, and manufacturer. However, a standard wooden pencil typically measures around 7 inches to 7.5 inches in length. This range encompasses the most common lengths found in the market.

It's important to note that there may be slight variations in length between different pencil brands and styles. Additionally, specialty or novelty pencils may have different lengths based on their design or intended purpose.

To obtain a more accurate average length for a specific set of pencils or a particular region, you would need to measure a representative sample of pencils and calculate the average length based on the measurements obtained.

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Answer:

yes

Step-by-step explanation:

Given the graph of any function, an x-intercept is simply the point, or points where the graph crosses the x-axis. There might be just one such point, no such point, or many, meaning a function can have several x-intercepts.

Answer

Step-by-step explanation:

Answer:

35/16      2 2/16

Step-by-step explanation:

1 1/4 = 5/4

1 3/4 = 7/4

5 * 7 = 35

4 * 4 = 16

35/16

Answer:

2 3/16

Step-by-step explanation:

First, we have to convert our mixed numbers to improper fractions, so our new equation is:

5/4 x 7/4 = 35/16

35/16 = 2 3/16

Answer:

maria : 1/3 =0.3 line on top of three

franco:1/4=0.25

Step-by-step explanation:

tried my best hope its right :)

Answer:

Maria: 1/3 cups for each gallon

Step-by-step explanation:

Maria: 2/3 for every 2 gallons.  2/3:2

Franco: 1 1/4 for every 5 gallons.  1 1/4/:5

Okay, so I'm actually going to do it my way.

Maria : \(\frac{2}{3} = 4/6\\\frac{4}{6} /2 =2/6\)

So, I simply turn it into a bigger fraction and cut it in half!

So, Maria uses 1/3 of a cup for each gallon

Hope this will help you figure out Franco's!!!

Answer:

21.     5g - f = 25 - f

22.     100 - 3b = 6b

23.    4 (14 + c) = A2

24. 8o = 52

25. 12f = 30

26. 21 + 2w = P

27. f - 32 (5 / 9) = C

28. D = m / v

29. prt = I

Better understanding...

24. Let "o" refer to the number of octaves

25. Let "f" refer to the number of flats

26. Let "p" represent the Perimeter, Let "l" represent the length, Let "w" represent the width

28. Let "d" represent the density, Let "m" represent the mass, Let "v" represent the volume

29. Let "i" represent the simple interest

Sorry, this took so long.. Hopefully this helps! Feel free to mark barinliest!

The width of the path is 24 meters.

Let's call the width of the path "x".

The dimensions of the inner rectangle (the lawn without the path) are 46m by 34m. The dimensions of the outer rectangle (the lawn with the path) are (46+2x) by (34+2x).

Area of path = Area of outer rectangle - Area of inner rectangle

425m² = (46+2x)(34+2x) - (46)(34)

Simplifying and solving for x:

425m² = (2x+46)(2x+34)

425m² = 4x² + 80x + 1564

4x² + 80x - 1161 = 0

We only want the positive value for x, so:

x = (-80 + 272) / 8

x = 24m

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Answer:

center = \((-4,8)\)

Radius = 7 units

Step-by-step explanation:

Given: Equation of circle is \(x^2+y^2+8x-16y+31=0\)

To find: Radius and center of the circle

Solution:

Equation of circle is \((x-a)^2+(y-b)^2=r^2\)

Here, \((a,b)\) is the center and r is the radius.

\(x^2+y^2+8x-16y+31=0\\\left [ x^2+2(4)x+4^2 \right ]+\left [ y^2-2(8)y+8^2 \right ]+31=4^2+8^2\)

Use formula \((u+v)^2=u^2+v^2+2uv\)

\((x+4)^2+(y-8)^2=16+64-31\\(x+4)^2+(y-8)^2=49=7^2\)

On comparing this equation with equation of circle,

center = \((-4,8)\)

Radius = 7 units

Answer:

center: (4,-4)

Radius: 9

Step-by-step explanation:

KHAN ACADEMY

Yes, the line 1 and line 2 are parallel lines as the sum of both given angles is 180°.

Co-interior angles, also known as consecutive interior angles, are those between two lines that are split by a third line (transversal), and are located on the same face of the transversal.

The majority of the time, it comes from the latin word "com-," which often means "along with." Co-interior angles are located on the same face of a transversal as well as between two lines. The significant correlations angles in each diagram are referred to as co-interior angles. Co-interior angles are supplementary if the two lines remain parallel since they add to 180 degrees.

In the given diagram:

= 75 + 105 (co-interior angles)

= 180° (supplementary angles)

So,

line 1 || line 2

Thus, the line 1 and line 2 are parallel lines as the sum of both given angles is 180°.

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Answer:‘12.92

Step-by-step explanation:

Answer:

Step-by-step explanation:

$12.99

applying coupon

\(12.99(1-12\%) = 12.99*88\% = 11.4312\\11.4312 * (1+13\%) = 12.917=12.92\)

3. The current price of the common stock is $40.

4. The stock price considering the company quitting business after 25 years is $46.81.

5. The stock price assuming constant dividends is $26.67.

6. The stock price assuming constant dividends and the company quitting business after 25 years is $25.88.

3. The current price of the common stock can be calculated using the dividend discount model. The formula for the stock price is P = D / (r - g), where P is the stock price, D is the dividend, r is the required return, and g is the growth rate. In this case, the dividend is $4, the required return is 15% (0.15), and the growth rate is 5% (0.05). Plugging these values into the formula, we get P = 4 / (0.15 - 0.05) = $40.

4. If the company quits business after 25 years, we need to calculate the present value of the dividends for those 25 years and add it to the final liquidation value. The present value of the dividends can be calculated using the formula PV = D / (r - g) * (1 - (1 + g)^-n), where PV is the present value, D is the dividend, r is the required return, g is the growth rate, and n is the number of years. In this case, D = $4, r = 15% (0.15), g = 5% (0.05), and n = 25. Plugging these values into the formula, we get PV = 4 / (0.15 - 0.05) * (1 - (1 + 0.05)^-25) = $46.81. Adding the final liquidation value, which is the future value of the stock price after 25 years, we get $46.81 + $0 = $46.81.

5. Assuming constant dividends, the stock price can be calculated using the formula P = D / r, where P is the stock price, D is the dividend, and r is the required return. In this case, the dividend is $4 and the required return is 15% (0.15). Plugging these values into the formula, we get P = 4 / 0.15 = $26.67.

6. If the company quits business after 25 years and assuming constant dividends, we need to calculate the present value of the dividends for those 25 years and add it to the final liquidation value. The present value of the dividends can be calculated using the formula PV = D / r * (1 - (1 + r)^-n), where PV is the present value, D is the dividend, r is the required return, and n is the number of years. In this case, D = $4, r = 15% (0.15), and n = 25. Plugging these values into the formula, we get PV = 4 / 0.15 * (1 - (1 + 0.15)^-25) = $25.88. Adding the final liquidation value, which is the future value of the stock price after 25 years, we get $25.88 + $0 = $25.88.

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On solving the question Interval notation and set builder notation is x≤ −4 , x≥ -3

This interval notation denotes that this set includes all real numbers between 8 and 12 where 8 is excluded and 12 is included. The set-builder notation is a mathematical notation for describing a set by representing its elements or explaining the properties that its members must satisfy.

We can write the given interval of a set in set builder form by using the required mathematical symbols and assuming a variable in each set. The interval given to us is \[\left( {6,12} \right)\] . Consider a symbol x to describe the element of the set or interval which is followed by a colon (:)

In set theory and its applications to logic, mathematics, and computer science, set-builder notation is a mathematical notation for describing a set by enumerating its elements, or stating the properties that its members must satisfy

Interval notation and set builder notation is x≤ −4 , x≥ -3

nterval notation is a way to describe continuous sets of real numbers by the numbers that bound them. Intervals, when written, look somewhat like ordered pairs. However, they are not meant to denote a specific point. Rather, they are meant to be a shorthand way to write an inequality or system of inequalities

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Answer:

A graph that is good for paired data called a scatterplot. The graph has  one coordinate axis and symbolises the paired data.

Step-by-step explanation:

Answer:

I live in the construction site and the life there is very hard and very difficult but I alsways taught my self to preict the beginnings of entity and enpipi

The unit rate of the juice is 0.5 carrot juice per green apple juice

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

This means that

Carrot juice = 2

Green apple juice = 4

Using the above as a guide, we have the following:

Unit rate = Carrot juice/Green apple juice

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

Unit rate = 2/4

Evaluate

Unit rate = 0.5

Hence, the unit rate is 0.5 carrot juice per green apple juice

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It will take 5 minutes to print a batch of newspapers if 20 printers are used.

What is proportionality?

Proportionality is a mathematical relationship between two variables, where one variable is a constant multiple of the other. In other words, two quantities are proportional if they maintain a constant ratio to each other, meaning that as one quantity increases or decreases, the other quantity changes in the same proportion.

We are given that the time it takes to print a batch of newspapers, m, is inversely proportional to the number of printers used, n, and the equation of proportionality is:

m = k/n

where k is a constant of proportionality. We are also given that when k = 100, the equation is satisfied. So we can substitute k = 100 into the equation to get:

m = 100/n

To find the time it will take to print a batch of newspapers if 20 printers are used, we can substitute n = 20 into the equation:

m = 100/20 = 5

So it will take 5 minutes to print a batch of newspapers if 20 printers are used. Rounded to 1 decimal place, the answer is 5.0 minutes.

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Answer:

depth, latitude, and seasons

Step-by-step explanation:

Three causes for water temperature variation in ocean water are depth, Latitude, and season. Then the correct option is A.

Surface water temperature depends on latitude and season. The temperature of the surface water in the ocean changes from place to place and from season to season.

Ocean temperature depends on the amount of solar energy absorbed. For example, tropical oceans receive a lot of direct overhead sunlight for much of the year, so the water is warm.

The temperature of the surface waters varies mainly with latitude. For example, The polar seas which are found in high latitude can be as cold as -2 degrees Celsius while the Persian Gulf which is in low latitude can be as warm as 36 degrees Celsius.

Hence, the correct option is A.

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Answer:

1:3.

Step-by-step explanation:

Probability(getting > 3 on one roll) = 3/6 = 1/2.

So on 2 cubes rolled the probability   of getting > 3 is 1/2 * 1/2 = 1/4.

As a ratio this is 1:3.