a. what is the area of the window seat when x=3
b. write a polynomial that helps represent the area of the window seats

The height is changing at the rate of 1/20in per minute in the given right cylindrical tank.

So, the changing the rate of the height:

Calculate height as follows:

Therefore, the height is changing at the rate of 1/20in per minute in the given right cylindrical tank.

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The simplified expression of (5.1)(5.1^2)^4 is (5.1)^9

The expression is given as:

(5.1)(5.12)4

Rewrite the expression properly as follows:

(5.1)(5.1^2)^4

Rewrite the expression properly as follows:

(5.1)(5.1^2)^4 = (5.1) * (5.1^2)^4

Apply the power law of indices

(5.1)(5.1^2)^4 = (5.1) * (5.1^8)

Apply the power law of indices

(5.1)(5.1^2)^4 = (5.1)^(1 + 8)

Evaluate the sum

(5.1)(5.1^2)^4 = (5.1)^9

Hence, the simplified expression of (5.1)(5.1^2)^4 is (5.1)^9

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Answer:

The value is ten thousands

Step-by-step explanation:

The value of polynomial for x = 2 that is f(2) will be 32.  

In many branches of mathematics and science, polynomials are used. For instance, they are used to define polynomial functions, which show up in settings ranging from basic chemistry and physics to economics and social science.

They are also used in calculus and numerical analysis to approximate other functions. Polynomial equations are used to form these functions. Polynomial rings and algebraic varieties, two fundamental ideas in algebra and algebraic geometry, are constructed in advanced mathematics using polynomials.

We have given polynomial f(x)=3x²8x+4

We have to find the value of f(2

We have to find the value of polynomial for x = 2

So for finding this value we have to just put x = 2 in polynomial

So f(2) will be

So the value of polynomial for x = 2 will be 32

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The price per quart of juice is $2.44.

To determine the price per quart of juice, we need to convert the 3-gallon volume to quarts and then divide the cost by the number of quarts.

There are 4 quarts in 1 gallon, so 3 gallons is equal to:

3 gallons × 4 quarts/gallon = 12 quarts

Next, we can divide the total cost of $29.28 by the number of quarts:

$29.28 ÷ 12 quarts = $2.44 per quart

Therefore, the price per quart of juice is $2.44.

It's important to note that the price per quart may vary depending on the brand and type of juice. Additionally, it's important to consider the nutritional value of the juice and whether it aligns with your dietary needs and preferences.

When comparing prices, it's also important to look at the unit price (price per ounce or price per serving) to ensure that you are getting the best value for your money.

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Answer: 4

Step-by-step explanation:

The algebraic expression of the statement given as the difference of 27 and 5​ is 27 - 5

The statement is given as:

the difference of 27 and 5​

Difference means minus.

The minus sign is represented as -

This means that the statement given as: the difference of 27 and 5​

Can be represented as

27 minus 5

So, have

27 - 5

Hence, the algebraic expression of the statement given as the difference of 27 and 5​ is 27 - 5

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Answer:

d

Step-by-step explanation:

took it on edg

The graph d represents the solution set of the inequalities 2x^2 < y and -x^2 + 5 > y

First, we represent the mathematical statements as an equation or inequalities

Mathematically, the statements in the questions are:

Where x and y represents the two numbers

So, we plot the graphs of 2x^2 < y and -x^2 + 5 > y

The graph d represents the solution set of the inequalities 2x^2 < y and -x^2 + 5 > y

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The area of region R in terms of k is given by (A) \(k^3/6\). That is bounded by the polar curves \(r=\theta\) and \(\theta = k\).

What are polar curves ?

In mathematics, polar coordinates are an alternative coordinate system to rectangular coordinates (x, y) for representing points in a plane.

To find the area of the region R bounded by the polar curves r = θ and θ = k in the first quadrant, we can integrate the area element dA in polar coordinates.

The polar area element dA is given by dA = (1/2) \(r^2\) dθ.

Since r = θ and the curves intersect at the origin (θ = 0), we need to integrate from θ = 0 to θ = k.

The area of region R can be calculated as:

\(A = \int_0^k (1/2) (\theta^2) d\theta\)

Integrating the above expression, we have:

\(A = (1/2)\int _0^k \theta^2 d\theta\)

Using the power rule of integration, the integral simplifies to:

\(A = (1/2) [\theta^3/3]\) evaluated from 0 to k

\(A = (1/2) [(k^3/3) - (0^3/3)]\)

\(A = (1/2) (k^3/3)\)

Simplifying further, we get:

\(A = k^3/6\)

Therefore, the area of region R in terms of k is given by \(k^3/6\).

Hence, the answer is (A) \(k^3/6\).

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The complete question is :

Let R be the region in the first quadrant that is bounded by the polar curves r = theta and theta = k where k is a constant, 0 < k < \(\pi/2\), as shown in the figure above. What is the area of R in terms of k? (A) \(k^3/6\) (B) \(k^3/3\)(C) \(k^3/2\) (D) \(k^2/4\) (E) \(k^2/2\)

Answer:

1. 89 2. 91

Step-by-step explanation:

180-29-62=118-29=89

180--89=91

Answer:

91 and 89 degrees respectively

Step-by-step explanation:

Sooooo, the exterior angle of any angle in a triangle is equal to the sum of the  2 other adjacent interior angles in a triangle. Therefore, we just need to do 29+62, which is 91 degrees, so the Exterior angle is 91 degrees. Next, to find the last unknown angle of a triangle, we can take the sum of the 2 other interior angles and subtract it from 180. Doing this here, we get 180-91, which is 89 degrees.

The property of the triangle congruence state that a ≅ B then B ≅ A are:

The triangle is a polygon that has 3 edge and vertices. Triangle is one of the basic shape in the geometric. The area of the triangle is formulated as base of the triangle * height of triangle x 0,5. The value of three triangle edge degree is 180°.

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The rate at which the pail is collecting the water is \(\frac{2}{5}\) of an inch per minute.

What is rate in mathematics?

A rate is the ratio of two related quantities expressed in different units. the numerator of the ratio expresses the corresponding rate of change in the other (dependent) variable. One unit of one of these quantities is used to represent the ratio's denominator, and if it can be altered consistently, then the ratio can be stated as follows: (i.e., is an independent variable).

The rate can be configured as.

Rate = \(\frac{1/3}{5/6}\)

Rate = \(\frac{2}{5}\)

Hence, the rate at which the pail is collecting the water is \(\frac{2}{5}\) of an inch per minute.

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Answer:

a) y = 9.95(x-3) + 20.00

b) Cost of 5 software packages = $39.90

Step-by-step explanation:

Given that:

Cost of 3 software at sale = $20

Cost of regular = $9.95

Let,

x be the number of software purchased.

We will subtract 3 from x because they cost $20.

y be the total cost.

y = 9.95(x-3)+ 20.00

Putting x=5 in expression

y = 9.95(5-3) + 20.00

y = 2(9.95) + 20.00

y = 19.90 + 20.00

y = $39.90

Hence,

a) y = 9.95(x-3) + 20.00

b) Cost of 5 software packages = $39.90

Answer:

See explanation below

Step-by-step explanation:

Flat fee = $25

Cost per mile = $0.60

Let

C = total cost

m = number of miles travelled by the truck

The equation is

C = 25 + 0.60m

The independent variable is miles,m travelled

The dependent variable is total cost, C

$25 is the constant

It is impossible to determine with certainty which number of pushups Bucky will never do in any game, as this depends on Bucky's physical abilities, training, and determination.

It is possible that Bucky may be able to do a very large number of pushups in a game, or he may not be able to do very many. It is also possible that there may be certain numbers of pushups that Bucky finds more challenging or difficult to do than others, but this would depend on his individual physical abilities and strengths. Ultimately, the number of pushups that Bucky will be able to do in any given game will depend on a variety of factors, and it is not possible to predict with certainty which numbers he will never do.

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Number of push-ups Bucky will never perform in any game is impossible to predict with confidence because it relies on Bucky's physical prowess, training, and willpower.

In a game, Bucky might be able to perform a lot of push-ups or he might not be able to perform many at all. It's also likely that Bucky will find some numbers of push-ups harder or more difficult to complete than others; however, this will depend on his particular physical prowess and capabilities.

In the end, Bucky's ability to do a certain number of push-ups throughout a game will rely on a multitude of variables, and it is impossible to say with certainty certain numbers he will never complete.

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Answer:

it is c

Step-by-step explanation:

i learned it last year

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . .  .  . . . . . .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

We are asked to find the value of \(\mathrm{36x-8y^2}\) when x=3 and y=-6.

So, we substitute the values of the variables instead of the variables:

\(\mathrm{36(3)-8(-6)^2}\)

Square -6 first:

\(\mathrm{36(3)-8\times36}\)

Multiply 36 times 3 and 8 times 36:

\(\mathrm{108-288}\)

Upon subtraction, we obtain

\(\bigstar~\mathrm{\underline{-180}}\)

Hope it helps you out! :D

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Answer:

X =20

X+24=2(x+22)

X+24=2x+44

X=44-24

X=20

So, the y-value of the solution to the system of equations 3x + 5y = 17 and 4x + 4y = -13 is not possible to find, because the system is inconsistent and has no solution.

To find the y-value of the solution to the system of equations 3x + 5y = 17 and 4x + 4y = -13, we can use one of the methods for solving systems of equations, such as substitution, elimination, or graphing. In this case, we will use elimination method.

The first step of elimination method is to eliminate one of the variables by adding or subtracting the equations. In this case, we will multiply the first equation by 4 and the second equation by -3 and add them:

4(3x + 5y) = 4(17)

12x + 20y = 68

-3(4x + 4y) = -3(-13)

-12x - 12y = 39

then we can add these two equations:

12x + 20y = 68

-12x - 12y = 39

0 = 29

This is an impossible equation, which means that the system has no solution.

Therefore, the y value of the solution to the system of equations 3x + 5y = 17 and 4x + 4y = -13 is not possible to find, because the system is inconsistent and has no solution.

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Therefore, the probability that the team is comprised of 2 men and 2 women is approximately 0.4545, which is true.

To calculate the probability that the team is comprised of 2 men and 2 women, we need to determine the number of favorable outcomes (teams with 2 men and 2 women) and the total number of possible outcomes (all possible teams).

The number of ways to choose 2 men from 6 men is given by the combination formula: C(6, 2) = 6! / (2! * (6-2)!) = 15.

Similarly, the number of ways to choose 2 women from 6 women is also C(6, 2) = 15.

Therefore, the number of favorable outcomes is the product of the number of ways to choose 2 men and 2 women: 15 * 15 = 225.

Now, let's calculate the total number of possible outcomes. We need to choose 4 members from a total of 12 members, which is given by C(12, 4) = 12! / (4! * (12-4)!) = 495.

The probability that the team is comprised of 2 men and 2 women is the ratio of favorable outcomes to the total number of outcomes: 225/495 = 45/99 ≈ 0.4545 (rounded to four decimal places).

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At present, Tyrone is 48 years old and his daughter is 24 years old.

Let's start by using variables to represent the ages of Tyrone and his daughter.

Let T be Tyrone's current age and D be his daughter's current age.

We know that Tyrone is twice as old as his daughter, so we can write:

T = 2D

We also know that in 6 years, Tyrone's age will be three times what his daughter's age was six years ago. Six years ago, Tyrone's age was T - 6 and his daughter's age was D - 6. So we can write:

T + 6 = 3(D - 6)

Now we have two equations with two variables, so we can solve for T and D.

First, substitute T = 2D from the first equation into the second equation:

2D + 6 = 3(D - 6)

Simplifying this equation, we get:

2D + 6 = 3D - 18

Add 18 to both sides:

2D + 24 = 3D

Subtract 2D from both sides:

24 = D

So Tyrone's daughter is 24 years old now.

We can use the first equation to find Tyrone's age:

T = 2D = 2(24) = 48

Therefore, Tyrone is 48 years old now.

So at present, Tyrone is 48 years old and his daughter is 24 years old.

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Tyrone is twice as old as his daughter. in 6 years Tyrone's age will be three times what his daughters age was six years ago. how old will they be at present?

Answer:

x=9

Step-by-step explanation:

step 1. restate the equation

2x+10=28

step 2. subtract 10 from both sides of the equations

2x+10-10=28-10

2x=18

step 3. get x alone by dividing 2 from both sides

2x/2=18/2

step 4. the answer

x=9

The equations will be re-written such that the expression on one side can be graphed and the x-intercepts of the graph would indicate the solution.

A) 3X² = 81

Rewritten, we have  3X² - 81 = 0

This is also = 3(X² - 27) = 0

B) (X - 1)(X + 1) - 9 = 5X

Open the brackets and we have X² - 1 - 9 - 5x = 0

Simplified, we have X² - 5X - 10 = 0

C) X² - 9x + 10 = 32

Collect like terms and we have:
X² - 9X - 22 = 0

D) 6x(x - 8) = 29

Expand the bracket and collect like terms such that the equation is equal to zero and we have

6X² - 48x - 29 = 0

Using Desmos Graphing, the following results can be obtained showing that x intercepts at:

(a) (-5.196, 0) & (5.196, 0)

(b) (-1.531, 0) & (6.531, 0)

(c) (-2, 0) & (11, 0)

(d) (-0.564, 0) & (8.564, 0)

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The sample is a three-stage cluster sample

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It would be 20% of hours is spent walking.

Answer:

total cost is £244.4

Step-by-step explanation:

( 37 * 4 ) + ( 15 * 4 ) = 208

208 * .175 = 36.4

208 + 36.4 = 244.4

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If the alternative hypothesis is that the proportion of items in population 1 is larger than the proportion of items in population 2, then the null hypothesis should be that there is no significant difference in the proportion of items between population 1 and population 2.

Based on the information provided, the null hypothesis should be:

The null hypothesis is that the proportion of items in population 1 is less than or equal to the proportion of items in population 2.

This is denoted as H₀: P₁ ≤ P₂. The alternative hypothesis, as you mentioned, is that the proportion of items in population 1 is larger than the proportion of items in population 2, which is represented as H₁: P₁ > P₂.

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Step-by-step explanation:

this is my answer you should mind your own business

We can conclude that (5, -2, -3) is the vector that the linear 1-form acts on by taking a dot product.

To find the vector that the given linear 1-form acts on by taking a dot product, we need to express the linear 1-form in terms of a vector.

Let's start by writing the given linear 1-form in terms of differentials of the coordinate functions:

\(2dy-3 dz + 5 dx - 4 dy = 5 dx - 2 dy - 3 dz\)

We can recognize this expression as the dot product of a vector with components (5, -2, -3) with the differential of a general vector function (dx, dy, dz).

Therefore, the vector that the linear 1-form acts on by taking a dot product is simply (5, -2, -3).

To verify this, let's take the dot product of the given linear 1-form with the given vector V:

\((2 dy - 3 dz + 5 dx - 4 dy) * (it 3+ 4) = 5 dx * i + (-2 dy) * t + (-3 dz) * 1 = 5(1) + (-2)(3) + (-3)(4) = 5 - 6 - 12 = -13\)

Now let's take the dot product of the same vector with the vector (5, -2, -3):

\((it 3+ 4) * (5, -2, -3) = (3)(5) + (4)(-2) + (0)(-3) = 15 - 8 + 0 = 7\)

Since the dot product of the given linear 1-form with the vector V is equal to the dot product of the same vector with the vector (5, -2, -3), we can conclude that (5, -2, -3) is the vector that the linear 1-form acts on by taking a dot product.

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