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a) Numerical Expression

b) Variable Expression (c)

c) Variable Expression (x)

d) Numerical Expression

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Answer: V≈2144.66m³

Step-by-step explanation:

the product of any three (not necessarily distinct) elements of T is in T and that the product of any three elements of U is in U, show that at least one of the two subsets T, U is closed under multiplication.

Let S be a subset of R that is closed under multiplication (that is, if a and b are in S, then so is ab). Let Tand Ube disjoint subsets of S whose union is S .Given that the product of any three (not necessarily distinct) elements of T is in T and that the product of any three elements of U is in U, show that at least one of the two subsets T, U is closed under multiplication.

We start out with the assumption that neither T nor U is closed under multiplication and use proof by contradiction to prove that at least one of T or U must be closed under multiplication.

If t1, t2 ,t3 ∈T and u1 ,u2 , u3 ∈U, it is given by the problem that t1⋅t2⋅t3∈T

and u1⋅u2⋅u3∈U. Also, T and U are disjoint subsets of S and therefore, T∩U = ∅ Now let t3=u1⋅u2 and u3=t1⋅t2. These statements are valid because T and U are not closed under multiplication, so the product of u1⋅u2 must not be in the set U and the product of t1⋅t2 must not be in set T.

Then t1⋅t2⋅t3∈T is equivalent to t1⋅t2⋅u1⋅u2∈Tand u1⋅u2⋅u3∈U is equivalent to u1⋅u2⋅t1⋅t2∈U

However, this is a contradiction because these products both are the same —t1⋅t2⋅u1⋅u2— but T∩U= ∅ because Tand U are disjoint. Then the original assumption that "neither T nor U is closed under multiplication" must have been wrong, and at least one of T or U must be closed under multiplication.

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.

Answer:

8th term = 98

Step-by-step explanation:

Given equation,

→ Tn = 2n² - 3n - 6

Now the 8th term will be,

→ Tn = 2n² - 3n - 6

→ T8 = 2(8)² - 3(8) - 6

→ T8 = 2(64) - 24 - 6

→ T8 = 128 - 30

→ [ T8 = 98 ]

Hence, the 8th term is 98.

This answer states that when graphing a linear relationship (y = 2x) on a coordinate plane, the points form a straight line, indicating that the relationship is proportional. However, when graphing a non-linear relationship (y = x2) on a coordinate plane, the points form a parabolic curve, indicating that the relationship is not proportional.

A: Relationship 1:

The relationship between x and y is y = 2x.

When graphed on a coordinate plane, the points (0,0), (1,2), (2,4), (3,6), and (4,8) form a straight line, indicating that the relationship is proportional.

Relationship 2:

The relationship between x and y is y = x2.

When graphed on a coordinate plane, the points (0,0), (1,1), (2,4), (3,9), and (4,16) form a parabolic curve, indicating that the relationship is not proportional.

This answer states that when graphing a linear relationship (y = 2x) on a coordinate plane, the points form a straight line, indicating that the relationship is proportional. However, when graphing a non-linear relationship (y = x2) on a coordinate plane, the points form a parabolic curve, indicating that the relationship is not proportional.

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The equation that would answer this question is x + (2x + 1.5) = 12. where x is the number of hours that Fin volunteers, and 2x + 1.5 represents the number of hours that each of his friends volunteers.

In this scenario, you can set up an equation that represents the total amount of time Fin and his friends volunteer. Let 'x' be the number of Finn's volunteer hours. His friends volunteer 1.5 hours more than Finn, so the number of hours each friend volunteers can be represented by x + 1.5. The total number of hours that all three friends volunteered can be expressed as:

x + (x + 1.5) + (x + 1.5) = 12

Expansion of the 2nd and 3rd terms:

x + x + 1.5 + x + 1.5 = 12

Combining the same terms:

3x + 4.5 = 12

Subtract 4.5 from both sides:

3x = 7.5

Divide both sides by 3:

x = 2.5

So Fin volunteers his 2.5 hours. 

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The solution to the radical equation is 9/7

From the question, we have the following radical equation

√4z²-13z+9+3∛=3z

Complete the equation

So, we have the following representation

√4z² -13z + 9 + 3∛27 = 3z

Evaluate the radicals

The equation becomes

2z - 13z + 9 + 3 * 3 = 3z

So, we have

2z - 13z + 9 + 9 = 3z

Evaluate the like terms

So, we have the following

14z = 18

Divide both sides by 14

z = 9/7

Hence, the solution is 9/7

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Answer:

g(f(- 4)) = 40

Step-by-step explanation:

to evaluate g(f(- 4)) , evaluate f(- 4) and substitute the value obtained into g(x)

f(- 4) = (- 4)² + 3(- 4) + 6 = 16 - 12 + 6 = 4 + 6 = 10 , then

g(10) = 5(10) - 10 = 50 - 10 = 40

1. The unit g/cm³ is valid. So, division of measurements is possible.

2. The unit mm is valid. So, division of measurements is possible.

3. The unit L² is not valid. So, multiplication of measurements is not possible.

What are measurement units?

The group of units used to quantify different physical quantities collectively known as the units of measurement. Since ancient times, we have measured these things using many units, including length, mass, volume, current, and temperature.

1. 63g/7cm³ = 9 g/cm³

The density of a substance indicates how dense it is in a given area. Mass per unit volume is the definition of a material's density. In essence, density is a measurement of how closely stuff is packed. It is a particular physical characteristic of a specific thing.

The unit g/cm³ is a unit for measuring density.

Therefore, the division of measurements is possible.

2. The m or mm must be converted so that the units are the same.  

1 m = 1000 mm.

Convert the meters to mm:  

0.080 m = 80 mm.

480 mm²/80 mm = 6 mm

The word "area" refers to a free space. A shape's length and width are used to compute its area. Unidimensional length is expressed in terms of feet (ft), yards (yd), inches (in), etc.

The mm² is a unit for measuring area.

The m is a unit for measuring length or width.

Therefore, the division of measurements is possible.

3.  (4.5 dL) × (0.70 L)

Liquid volume is a term used to describe how much 3-D space a given amount of liquid takes up.

Volume of a liquid is measured in litres (L).

Squaring Litres doesn't make any sense.

Therefore, the multiplication of measurements is not possible.

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The intercepts and the asymptotes of h(x) using the graph is  x-intercept -4 and y-intercept =-1

The y-intercept of a function y = f(x) is a point where its graph would meet the y-axis and is obtained by substituting x = 0. Understand the y-intercept and its formula with derivation

From the given graph

Y-intercept is the point where the curves crosses the y-axis

From the graph, the coordinate of the y-intercept is (0, -1)

X-intercept is the point where the curves crosses the x-axis

From the graph, the coordinate of the x-intercept is (-4, 0)

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Answer:

The vertical asymptote is -5

Step-by-step explanation:

You basically have to set it to 0 and then solve the equation. You should get x= -5

By removing both of the equations in system A and by bringing the first equation of system A, we may create system B from system A.

Multiple equations are compiled into systems of equations.

5x+y=3

4x−7y=8

System B

5x+y=3

x+8y=−5

1) From System A, how do we go to System B?

CORRECT (SELECTED) (SELECTED)

Substitute the difference or sum of the two equations in one equation.

2) Are the systems equal in the light of the prior response? Do they share the same solution, in other words?

CORRECT (SELECTED) (SELECTED)

Yes

As a result, we can obtain system B from system A by Subtracting the solutions to the two equations in system A

Additionally, by rewriting system A's initial equation

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The volume of the ark is about 1.44 million cubic feet.

What is unit conversion mean?

A unit conversion expresses the same property as a different unit of measurement. For instance, time can be expressed in minutes instead of hours, while distance can be converted from miles to kilometers, or feet, or any other measure of length.

First, we need to convert the measurements from cubits to inches.

We know that one cubit is equal to six palms and that one palm is equal to 2.5 inches. So, we can convert the measurements of the ark by multiplying the number of cubits by the number of inches per cubit:

Length of ark = 300 cubits x 6 palms/cubit x 2.5 inches/palm = 4500 inches

Width of ark = 50 cubits x 6 palms/cubit x 2.5 inches/palm = 750 inches

Height of ark = 30 cubits x 6 palms/cubit x 2.5 inches/palm = 450 inches

Next, we can find the volume of the ark by multiplying these dimensions together:

Volume of ark = 4500 inches x 750 inches x 450 inches = 1.42 x 10^9 cubic inches

Finally, we can convert cubic inches to cubic feet by dividing by the conversion factor of 1 cubic foot = 12 x 12 x 12 cubic inches.

1.42 x 10^9 cubic inches / (12x12x12 cubic inches/cubic foot) = 1.44 x 10^6 cubic feet

Hence, the volume of the ark is about 1.44 million cubic feet.

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Answer:

a) e^x (3 - e^x)^4 dx

Using the formula [ f'(x)[f(x)"]dx =[ [f(x)]^n+1 / n+1] + c, where n = 1,

we have:

e^x (3 - e^x)^4 dx = (e^x)^5 (3 - e^x)^4 / 5 + c

= (e^5x - 4e^4x + 6e^3x - 4e^2x + e^x) / 5 + c

b) 3e^2x √(1 + e²x) dx

Using the formula [ f'(x)[f(x)"]dx =[ [f(x)]^n+1 / n+1] + c, where n = 1,

we have:

3e^2x √(1 + e²x) dx = (3e^2x)^2 * (1 + e²x)^(3/2) / 2 + c

= (9e^4x + 3e^2x) / 2 + c

c) 3e^-2x / (1 + e^-2x)^3 dx

Using the formula [ f'(x)[f(x)"]dx =[ [f(x)]^n+1 / n+1] + c, where n = 1,

we have:

3e^-2x / (1 + e^-2x)^3 dx = -(3e^-2x)^2 / (1 + e^-2x)^2 + c

= -(9e^-4x) / (e^-4x + 2e^-2x + 1) + c

d) 4 cos 2x sin³ 2x dx

Using the formula [ f'(x)[f(x)"]dx =[ [f(x)]^n+1 / n+1] + c, where n = 1,

we have:

4 cos 2x sin³ 2x dx = -4 cos 2x (sin 2x)^4 / 4 + c

= -(cos 2x) (1 - cos 4x)^2 / 2 + c

e) sec² 3x tan³ 3x dx

Using the formula [ f'(x)[f(x)"]dx =[ [f(x)]^n+1 / n+1] + c, where n = 1,

we have:

sec² 3x tan³ 3x dx = -sec² 3x (tan 3x)^4 / 4 + c

= -sec² 3x (sec² 3x - 1)^2 / 4 + c

f) 2+tan ² x / cos² x dx

Using the formula [ f'(x)[f(x)"]dx =[ [f(x)]^n+1 / n+1] + c, where n = 1,

we have:

2+tan ² x / cos² x dx = ln|sec x| + c

It's worth noting that all these integrals are indefinite, which means that the constant c is arbitrary, and the actual antiderivative depends on the problem context.

Step-by-step explanation:

The amount  of marginal product of the 13th worker is 10 units of output, which is the difference between the quantity of output when L = 12 (122) and when L = 13 (132).

The marginal product of the 13th worker can be calculated as follows:

Marginal product = Quantity of output for L = 13 - Quantity of output for L = 12

Marginal product = 132 - 122

Marginal product = 10 units of output

The marginal product of the 13th worker is the additional output created by hiring one additional worker. This is calculated by taking the difference between the quantity of output when the number of workers is 12 and when it is 13. In this case, the quantity of output when L = 12 is 122, and when L = 13 it is 132, so the marginal product is 10 units of output. This calculation shows that the 13th worker is adding 10 units of output to the firm's total production. This is an important concept in production economics, as it helps firms determine the optimal number of workers to hire in order to maximize their output and profits.

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Area of the parallelogram attached in the figure is solve to be

The area of parallelogram is solved using the formula

= base x height

From the problem it can be deduced that

base = 12 cm - 2 cm = 10 cm

height = 4 cm

Area of the parallelogram = 10 * 4

Area of the parallelogram = 40 square cm

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The greatest integer x is 3  in the given expression.

Some function [] rounds DOWN a number to the nearest integer. For example [1.5]=1, [2]=2, [-1.5]=-2

A number can be an integer if it is both whole and negative. Accordingly, a set of integers is formed if we combine negative numbers with whole numbers. An integer is a positive or negative number, including zero, that has no decimal or fractional parts. -5, 0, 1, 5, 8, 97, and 3, 043 are a few examples of integers. Z is the symbol for a collection of integers.

Thus

[-1.6]+[3.4]+[2.7]

=-2+3+2

=3

The greatest integer function rounds off the given number to the nearest integer. Hence, the formula to find the greatest integer is very simple.

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The liters of water that will completely fill the test tube, can be found to be 0. 0084 liters.

Both cubic centimeters and liters can be used to describe the volume of an object in terms of the amount of fluid that can fill them up.

A liter can be converted to be 1, 000 cubic centimeters.

This means that if a test tube has a volume of 8. 4 cubic centimers, it can be filled up by:
= 8. 4 / 1, 000

= 0. 0084 liters of water

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Answer:

Step-by-step explanation:

a) Percent of already washed cars?

→ (67/260) × 100

→ 6700/260

→ 25.769

→ ≈ 25.77%

b) Wax job done each week will be?

→ (260/100) × 15

→ 2.6 × 15

→ 39 wax jobs

Hence, these are required answers.

Answer:

a)  25.8%

b)  39

Step-by-step explanation:

Given information:

To find the percent of the total expected cars that have already been washed, divide the number of cars already washed by the average number of cars washed per week:

[tex]\implies \dfrac{67}{260}=0.257692307...=25.8\%\; \sf (nearest\;tenth)[/tex]

To find the number of cars that get a wax job each week, find 15% of 260:

[tex]\begin{aligned}\implies 15\%\; \textsf{of}\;260&=\dfrac{15}{100} \times 260\\\\&=\dfrac{3900}{100}\\\\&=39\end{aligned}[/tex]

Therefore, 39 wax jobs are done each week.

C: It is not a function.  

It doesn't pass the vertical line test.

Answer:

2/5 = w

Step-by-step explanation:

area = length x width

1/4 = 5/8w

isolate 'w' by dividing each side by 5/8

remember, when dividing fractions you must multiply by the reciprocal

1/4 x 8/5 = w

8/20 = w

simplify:

2/5 = w

Assuming David’s height off the floor is continuous and differentiable, the statement that is true is: B. The Mean Value Theorem does not apply.

Based on the details we can vividly states that the Mean Value Theorem does not apply based on the fact that the function that help to described David's height off the floor is not continuous and differentiable.

This  function would only be differentiable if David's movement off the couch and landing on the floor could be described by a mathematical function, which is highly unlikely.

Therefore the correct option is B.

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The likelihood that a randomly selected youngster is under 49 inches tall is 0.989

The likelihood that a randomly selected child would be taller than 48.8 inches is 0.875.

Let the X represent a ten-year-old child's height measurements.

As a result, with a mean of 56.2 inches and a standard deviation of 3.3 inches, X follows the normal distribution.

A) We need to calculate the likelihood that a youngster selected at random is under 63.75 inches tall.

Specifically,

P(X < 63.75)

The Z score calculation gives us

Z = (X - μ)/σ

where mean is and standard deviation is.

Z = (63.75 - 56.2)/3.3

Z = 2.288 as a result.

According to the z distribution table, the value is around 0.989

B) Similar to this, the Z score formula gives us

Z = (X - μ)/σ

where μ mean is and σ standard deviation is.

Therefore, we must determine the likelihood that a child picked at random will be taller than 60 inches.

Z = (60 - 56.2)/3.3

Z = 1.1515

The number is around 0.875 according to Z score.

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The types of words must be capitalized is

A) A government position when it comes before a specific name

In writing systems with a case distinction, capitalization (American English) or capitalisation (British English) refers to writing a word with its initial letter as a capital letter (uppercase letter) and the other characters in lower case. The phrase could also be used to describe the choice of text case.

Given:

In English, the initial word of a phrase and all proper nouns are written in capital letters (words that name a specific person, place, organization, or thing).

The initial word in a quotation and the first word following a colon may occasionally both need to be capitalized.

So, the types word can be capitalized is a government position when it comes before a specific name like President Obama.

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The value of function showing the total cost of hiring your neighbor (y) for a certain amount of hours (x) is,

⇒ y = 10 + 20x

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

A neighbor charges $10 to mow your lawn plus $20 per hour.

Let the total cost of hiring your neighbor = y

And, Number of amount of hours = x

Hence, We can formulate;

The function which showing the total cost of hiring your neighbor (y) for a certain amount of hours (x) is,

⇒ y = 10 + 20x

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The slope of line L1 is obtained to be m = -1.7.

The slope of line L2 is obtained to be m = 1.

The slope of line L3 is obtained to be m = 0.

What is a slope?

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

The line L1 indicated with red colour moves from quadrant 2 to quadrant 4 which means the slope will be negative. It moves 1.7 unit down and 1.7 unit right.

The three options for slope is -

m = 0

m = 1

m = -1.7

Therefore, m = -1.7 is the slope for line L1.

The line L2 indicated with blue colour moves from quadrant 3 to quadrant 1 which means the slope will be positive. It moves 1 unit up and 1 unit right.

The three options for slope is -

m = 0

m = 1

m = -1.7

Therefore, m = 1 is the slope for line L2.

The line L3 indicated with green colour moves from quadrant 3 to quadrant 4 forming a straight horizontal line parallel to x-axis which means the slope will be zero. It moves 0 right.

Therefore, m = 0 is the slope for line L3.

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Answer: 3/4

Step-by-step explanation:why do u need explaination]

Answer 3:

At the end of the first hour, there would be 5 amoebas from the first group and 53=15 amoebas from the second group, a total of 5+15 = 20 amoebas.

At the end of the second hour, there would be 55 = 25 amoebas from the first group and 153 = 45 amoebas from the second group, a total of 25+45 = 70 amoebas.

At the end of the third hour, there would be 5^3 = 125 amoebas from the first group and 453 = 135 amoebas from the second group, a total of 125+135 = 260 amoebas.

Answer 4:

Using the formula N = No eRt where N is the population, No is the initial population, R is the exponential growth rate, and t is the time in days.

N = 104 * e^(0.11714) = 1042.813 = 292.56, rounded to the nearest rabbit would be 293.

So, the population of rabbits after 14 days would be 293.

The inequality is solved to and represented in interval notation as follows

The inequality is made of two sets and can be separated as

−4 ≤ −2(y − 1)

−2(y − 1) < 2

solving the first

−4 ≤ −2(y − 1)

−4 ≤ −2y + 2

−4 - 2 ≤ −2y

-6 ≤ −2y

divide through by -2

y ≤ 3

solving the second

−2(y − 1) < 2

−2y + 2 < 2

−2y < 2 - 2

−2y < 0

divide through by -2

y > 0

the inequality in interval notation is

(-∞, 3] [0, ∞)

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When a graph is translated to the right by a units, the x-coordinate of each point on the graph increases by a units. So the equation of the transformed function will have x - a in it.

When a graph is translated down by b units, the y-coordinate of each point on the graph decreases by b units. So the equation of the transformed function will have y - b in it.

Given f(x) = |x| + 5 and the graph of f(x) is transformed into the graph of g(x) by a translation of 4 units right and a translation of 3 units down, the equation of the transformed function g(x) will be:

g(x) = f(x - 4) - 3

This is because the x-coordinate increases by 4 units and the y-coordinate decreases by 3 units.

So the equation of g(x) is:

g(x) = |x-4| + 5 - 3

g(x) = |x-4| + 2

This function g(x) will have the same shape as f(x) but shifted 4 units to the right and 3 units down.

Answer:

This function g(x) will have the same shape as f(x) but shifted 4 units to the right and 3 units down.

Step-by-step explanation: