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The expression in simplest form that represents the

total amount that Andrew spent would be = $8d

The simple forms of representation of expression shows that all the values of that expression are in its simplest form.

In Andrew cans of ping pong balls,

Last week he bought = 4 cans

This week he bought = 2 cans

The cost of ping pong balls = d dollars per

can..

The total amount that Andrew spent would be;

= d × ( 4+2)

= $8d

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Answer:

2. 55

3. 125

4. 125

Step-by-step explanation:

The value of the 3rd term in the expansion of (x+6) ^6 will be as follows:

540x^4

What is expansion?

Expanding brackets, also known as multiplying out, seeks to eliminate the set of brackets by multiplying each phrase inside a bracket by the term on the outside and subsequently accumulating similar phrases. When solving equations, extending brackets, which is the opposite of factorization, is frequently an essential step.

Here in the question,

We have,

(x+6) ^6

Expanding it we get:

= x^6 + 36x^5 + 540x^4 +4320x³ + 19440x² + 46656x + 46656

So, the 3rd term of the expansion is 540x^4.

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The value of the 3rd term in the expansion of \((x+6) ^6\) will be as follows: \(540x^4\). The correct answer is option (c).  \((6\ \ 4)36x^4\)

By multiplying each phrase inside a bracket by the word on the outside and then accumulating similar phrases, expanding brackets, also known as multiplying out, aims to eliminate the set of brackets. Extending brackets, which is the opposite of factorization, is frequently a crucial stage in the solution of equations.

An affine transformation termed expansion, in which the scale is expanded, is also referred to as an enlargement or dilation. It is also sometimes referred to as an enlargement and is the polar opposite of a geometric constriction.

Here in the question,

We have,

\((x+6) ^6\)

Expanding it we get:

\(= x^6 + 36x^5 + 540x^4 +4320x^3 + 19440x^2 + 46656x + 46656\)

So, the 3rd term of the expansion is \(540x^4\).

The correct answer is option (c). \((6\ \ 4)36x^4\)

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The length of the hypotenuse is 8√2 units.

According to the Pythagoras theorem, we can write -

        (hypotenuse)² = (base)² + (perpendicular)²

        (h)² = (b)² + (p)²

Given is a 45 - 45 - 90 triangle with a leg length of 8.

Equal Opp. Angles Theorem -

We can write using the Pythagoras theorem as -

x² = 8² + 8²

x² = 64 + 64

x² = 128

x = √(2 x 2 x 2 x 2 x 2 x 2 x 2)

x = √(2² x 2² x 2² x 2 )

x = 8√2

Therefore, the length of the hypotenuse is 8√2 units.

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Answer:

5x + 35 = 175

$28

Step-by-step explanation:

She paid 35 for 1 pair of skis. She paid a certain amount(x) for 5 hours (5x + 35). Therefor making the expression 5x + 35 = 175.

Then, solve the equation with inverse operations.

5x + 35 = 175

Step 1: Subtract 35 from both sides.

5x = 140

Step 2: Divide 5 from both sides.

x = 28

Therefore, Kylie paid $28 each hour of the group skiing lessons.

Answer:

147

Step-by-step explanation:

E = greatest common factor of 22 and 30 = 2

F = least common multiple of 3 and 8 = 24

G = 3 * (7 + 10) = G + 30 = 81

3 * 7 + 3 * 10 = G + 30

21 + 30 = G + 30

51 = G + 30

G = 81

H = 5 * (3 + H) = 15 + 45 = 40

5 * 3 + 5 * H = 15 + 45

15 + 5 * H = 60

20 * H = 60

H = 60 - 20

H = 40

E = 2 + F = 24 + G = 81 + H = 40

2 + 24 + 81 + 40 = 147

This was fun lol

To find \( f_{x} \) and \( f_{xy} \) for the function \( f(x, y) = x^{3} \cos(xy) \), we need to take the partial derivatives with respect to x and then with respect to y.

To find \( f_{x} \), we take the partial derivative of the function \( f(x, y) = x^{3} \cos(xy) \) with respect to x while treating y as a constant.

Taking the derivative of \( x^{3} \cos(xy) \) with respect to x, we apply the product rule. The derivative of \( x^{3} \) with respect to x is \( 3x^{2} \), and the derivative of \( \cos(xy) \) with respect to x is \( -y \sin(xy) \). Therefore, we have \( f_{x} = 3x^{2} \cos(xy) - y \sin(xy) \).

To find \( f_{xy} \), we take the partial derivative of \( f_{x} \) with respect to y while treating x as a constant.

Taking the derivative of \( f_{x} = 3x^{2} \cos(xy) - y \sin(xy) \) with respect to y, we treat x as a constant. The derivative of \( 3x^{2} \cos(xy) \) with respect to y is \( -3x^{3} \sin(xy) \), and the derivative of \( -y \sin(xy) \) with respect to y is \( -\sin(xy) - xy \cos(xy) \).

Therefore, we have \( f_{xy} = -3x^{3} \sin(xy) - \sin(xy) - xy \cos(xy) \).

Thus, \( f_{x} = 3x^{2} \cos(xy) - y \sin(xy) \) and \( f_{xy} = -3x^{3} \sin(xy) - \sin(xy) - xy \cos(xy) \).

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the work done is equal to the force applied (500 lb) multiplied by the distance (100 ft), resulting in 500 ft-lb of work done.

A force applied across a distance is what is referred to as work.

In this problem,

the force applied is the weight of the cable (5 lb/ft) multiplied by the length of the cable (100 ft).

Therefore, the work done is equal to the force applied (500 lb) multiplied by the distance (100 ft), resulting in 500 ft-lb of work done.Work is a force applied across a distance, and it is measured in a unit of energy called foot-pounds. In this problem, the force applied is the weight of the cable (5 lb/ft) multiplied by the length of the cable (100 ft). Therefore, the work done is equal to the force applied (500 lb) multiplied by the distance (100 ft), resulting in 500 ft-lb of work done. This means that 500 ft-lb of energy must be expended in order to move the cable 100 ft. This energy can be provided by a variety of sources, such as human labor, a motor, or some other mechanism.

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Answer:

22

Step-by-step explanation:

We are given that t = 5 and s = 3, so use substitution to find the answer

2t + 4s

2 (5) + 4 (3)

10 + 12

22

Answer:

Matched set

Step-by-step explanation:

The type of set created here is a matched set where each of the participants are are grouped into variables equivalent to thwor number of visits which is based in prior investigation. The set of participant classed in to each group of neutral, traumatic and happy events are similar based on the grouping condition which is the number of health visits. Hence, when we have classes formed from equivalent behavior of characteristic based on the essence of an experiment, we have matched set.

Answer:

DF

EF

DE

Step-by-step explanation:

First, we need to figure out the third angle.

Angles in a triangle add up to 180, so

180 = 61 + 59 + DEF

DEF = 180 - (61 + 59) = 180 - 120 = 60

In a triangle, the smallest angle is always opposite the shortest side, and the largest angle opposite the longest.

The three angles are 61, 60, and 59.

Since DEF(61) is the largest, DF is the longest.

Next is EDF(60), so EF is the next.

Finally, DFE(59) is the smallest angle, so DE is the shortest.

DF, EF, DE

The sum of the measures of the angle of a triangle is 180 degrees.

The given triangle is a type of triangle and the type of triangle a scalene triangle.

For a scalene triangle, the measure of the three sides are unequal and the sum of the interior angle of a triangle is 180 degrees.

Hence the measure of the angles <A, <B and <C are all less than 90 degrees since they are all acute angles.

We can therefore conclude that:

m<A + m<B + m<C = 180 degrees

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Answer:

y=3 you have to use PEMDAS

Answer:

y=3

Step-by-step explanation:

Combine multiplied terms into a single fraction

2.4y-3.2=4

12y/5 -3.2=4

Add 3.2 to both sides of the equation

12y/5- 3.2+3.2=4+3.2

Simplify

add the numbers 12y/5=7.2

Solution

y=3

Answer: D

Step-by-step explanation:

The woman slice is less than half, greater than a quarter, and just over 1/3. Since 1/3 is about 33%, I would say 35% (D).

The x -axis could be labeled from 0 to 12 with a scale of 1 , and the y -axis could be labeled from 0 to 200 with a scale of 10 .

Given that:

A beekeeper collects an average of 10 gallons of honey each month throughout the year

Where x represents the number of months since the year began, and y represents the amount of honey collected, in gallons

Since the x-axis represents the months and we have 12 months in a year. Thus, the x-axis could be labeled from 0 to 12 with a scale of 1

Since the y-axis represents the amount of honey collected, in gallons and the beekeeper collects an average of 10 gallons of honey each month. Thus, the y-axis could be labeled from 0 to 200 with a scale of 10.

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The distance between the tractor and the bale at this moment is 1 meter.

To determine the distance between the tractor and the bale at the given moment, we can use the concept of relative motion.

The distance between the tractor and the bale is the difference in their positions. Since the tractor is moving at a speed of 3 m/s and the bale is rising at a speed of 2 m/s, their relative speed is the difference between the two speeds, which is 3 m/s - 2 m/s = 1 m/s.

To find the distance, we can use the formula:

Distance = Speed × Time

In this case, the relative speed is 1 m/s. Since the tractor and the bale are moving in the same direction, we can assume that their speeds are constant over the given time. Therefore, we don't need to consider the time in this calculation.

So, the distance between the tractor and the bale at this moment is 1 meter.

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The length of the pendulum using equation is 43.56 feet.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here the given equation that represent the time of pendulum for one swing is

=> T = \(\frac{2\sqrt L}{3.3}\)

Now T = 4 sec then ,

=> 4 = \(\frac{2\sqrt L}{3.3}\)

=> 4*3.3 = 2\(\sqrt L\)

=> \(\sqrt L = 2\times3.3 = 6.6\)

=> L = 43.56 feet.
Hence the length of the pendulum using equation is 43.56 feet.

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The value of ab in the similarity transformation from triangle abc to triangle mno is 5

The given parameters are:

ab = x, bc = y, and ca = 2x

om = 5

The scale factor from abc to mno is 0.5.

So, we have:

0.5 * ca = om

Substitute om = 5

0.5 * ca = 5

Divide both sides by 0.5

ca = 10

Recall that:

ca = 2x

So, we have:

2x = 10

Divide by 2

x = 5

Recall that:

ab = x

So, we have:

ab = 5

Hence, the value of ab is 5

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Answer:

t=1

Step-by-step explanation:

2t+t−3=0

2t+t+−3=0

(2t+t)+(−3)=0(Combine Like Terms)

3t+−3=0

3t−3=0

Step 2: Add 3 to both sides.

3t−3+3=0+3

3t=3

Step 3: Divide both sides by 3.

3t

3

=

3

3

t=1

The length of side x obtained using trigonometric ratios is 5 units

Trigonometric ratios are expressions that indicate the relationship between the lengths of two of the sides of a right triangle and the interior angles of the right triangle.

The specified triangle is a right triangle, therefore, if the interior angles, and the length of one of the sides is known, the lengths of the other sides can be found.

The right triangle is a 30°-60°-90° right triangle

The length of the hypotenuse side = 10

The length of the leg with measurement x, can therefore, be found using trigonometric ratios follows;

sin(θ) = Opposite/Hypotenuse

sin(30°) = x/10

Therefore; x = 10 × sin(30°)

x = 10 × 0.5 = 5

The length of the side x in the right triangle is 5 units

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Answer:

Compared with Moldova, the income distribution in the United States in 2016 was less equal.

The GINI Index is a measure of income inequality, where a value of 0 represents perfect equality and a value of 1 represents maximum inequality. By estimating the GINI Index using the Trapezoid Rule, we can compare the income distributions.

For Moldova in 2016, the estimated GINI Index is 0.378.

For the United States in 2016, the estimated GINI Index is 0.3076.

Since the GINI Index for the United States is lower than that of Moldova, it indicates a relatively lower level of income inequality in the United States compared to Moldova. Therefore, the income distribution in the United States in 2016 was more equal than in Moldova.

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Answer:

It would equal 19 dollars

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

30-2(7+2)-1

30-2(9)-1

Then multiplication

30-18-1

Then left to right

12-1

Then again

So your answer is 11

Hope that helps!

Answer:

Archimedes

Step-by-step explanation:

Answer:

Archimedes is known as Father of Mathematics

Answer:

0.3904

Step-by-step explanation:

0.8^-3 = 0.8^1 - 0.8^4 = 0.8 - 0.4096 = 0.3904

Answer:

The best chart to show how your department's expenses compare to the total company's expenses, and hopefully save employee jobs, would be:

Pie Chart

Step-by-step explanation: