Question2: Find the area enclosed between the given curves: 1. y = x^2 - 4x, y = 2x 2. y = (x - 2)^2, y = x (Hint open (a-b)^2 = a^2-2ab+b^2)

There are number of 170 seats with folding arm tablets that are not designed for wheelchair users.

1. First we need to identify the total number of seats in the lecture hall which is 200.

2. Then we need to identify the number of seats with folding arm tablets that are designed for wheelchair users which is 30.

3. To find the number of seats with folding arm tablets that are not designed for wheelchair users, we can subtract the number of seats designed for wheelchair users from the total number of seats.

4. Therefore, 200 - 30 = 170, which means there are 170 seats with folding arm tablets that are not designed for wheelchair users.

The lecture hall in question has a total of 200 seats, with 30 of those seats having folding arm tablets that are designed for wheelchair users. To find the number of seats with folding arm tablets that are not designed for wheelchair users, we can subtract the number of seats designed for wheelchair users from the total number of seats. This means that 200 - 30 = 170, which means there are number of 170 seats with folding arm tablets that are not designed for wheelchair users.

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These are the solutions to the quadratic equation p^2 + 2p^2 - 5 * 2p + 5 = 0.

To solve the quadratic equation p^2 + 2p^2 - 5 * 2p + 5 = 0, we need to simplify and rearrange the equation to its standard form and then solve for p.

Combining like terms, the equation becomes:

3p^2 - 10p + 5 = 0

Now, we can use the quadratic formula to solve for p. The quadratic formula states:

p = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 3, b = -10, and c = 5. Substituting these values into the quadratic formula, we have:

p = (-(-10) ± √((-10)^2 - 4 * 3 * 5)) / (2 * 3)

Simplifying further:

p = (10 ± √(100 - 60)) / 6

p = (10 ± √40) / 6

p = (10 ± 2√10) / 6

Now, we can simplify and find the two possible values of p:

p₁ = (10 + 2√10) / 6

p₂ = (10 - 2√10) / 6

These are the solutions to the quadratic equation p^2 + 2p^2 - 5 * 2p + 5 = 0.

In simplified form, the solutions are:

p₁ = (5 + √10) / 3

p₂ = (5 - √10) / 3

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Answer:

p = 3 or p = 7

Step-by-step explanation:

Answer:

p²-7p-3p+21=0

p(p-7)-3(p-3)=0

(p-3)(p-7)=0

either

p=3

or

p=7

Given, the height \($h=6$, the base $b_1=9$ and $b_2=12$.\)

The area of the trapezoid is given by the formula,

\(\[A = \frac{1}{2}h(b_1+b_2)\]\)

Substitute the given values,  

\(\[A = \frac{1}{2} \times 6 \times (9+12)\]\\\)

Simplifying the above expression,

\(\[A = 45 \text{ square feet}\]\)

Therefore, the area of the trapezoid is $45$ square feet.

The perimeter of a two-dimensional geometric shape is the entire length of the boundary or outer edge. It is the sum of the lengths of all the shape's sides or edges.

The perimeter of a square, for example, is calculated by adding the lengths of all four sides of the square.

Similarly, to find the perimeter of a rectangle, sum the lengths of two adjacent sides and then double the result because there are two pairs of adjacent sides.

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To create the vectors using `seq()` and `rep()` in R:

(a) To create the vector `1;1:5;2;2:5;...;12`, we can use `seq()` and `rep()`. Here is the code:

```
vector_a <- c(1, rep(seq(1, 5), each = 2), seq(2, 5), 12)
```

- `seq(1, 5)` generates a sequence from 1 to 5.
- `rep(seq(1, 5), each = 2)` repeats each element of the sequence twice.
- `seq(2, 5)` generates a sequence from 2 to 5.
- `c()` combines all the elements into a vector.
- The resulting vector will be `1;1;2;2;3;3;4;4;5;5;2;3;4;5;12`.

The vector `1;1:5;2;2:5;...;12` can be created using `seq()` and `rep()` in R.

(b) To create the vector `1;8;27;64;...;1000`, we can use `seq()` and exponentiation (`^`). Here is the code:

```
vector_b <- seq(1, 1000) ^ 3
```
- `seq(1, 1000)` generates a sequence from 1 to 1000.
- `^ 3` raises each element of the sequence to the power of 3.
- The resulting vector will be `1;8;27;64;...;1000`, as each number is cubed.

The vector `1;8;27;64;...;1000` can be created using `seq()` and exponentiation (`^`) in R.

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The amount in account is $5310.

We have given that,

$4500 is placed in an account that pays 18% interest compounded each year. And we have to find the amount in the account.

We will use the formula,

A = a(1 + r)^t

where a = initial value = $4500

           r = rate = 18% = 0.18

           t = amount of time = 1

⇒ A = 4500(1 + 0.18)^1

       = 4500(1.18)

    A = 5310

Therefore the account will have $5310 after one year.

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Binary categorical variables are typically included in multiple linear regression models using a technique called "dummy coding" or "indicator coding".

These dummy variables are then included in the multiple linear regression model as additional predictor variables, along with the continuous predictor variables. The coefficient estimates for the dummy variables represent the differences in the intercept or slope between the two categories of the binary categorical variable.

It is important to note that when using dummy coding, one of the categories of the binary categorical variable must be chosen as the reference category, and the coefficient estimates for the other categories are interpreted relative to the reference category. The choice of reference category can affect the interpretation of the coefficient estimates and should be chosen based on the research question and the goals of the analysis.

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Answer: d. No, because the study was not taken from a random sample of scholarship athletes.

Step-by-step explanation:

Since the study only focuses on basketball players, the sample may not be representative of all scholarship athletes in the university. This can cause bias in the results and make it difficult to generalize the findings to the larger population of scholarship athletes. Therefore, the university administration should not fully trust the results of this study.

It will take about 39 years for a principal of $4600 to grow to $29900 continuously compounded

Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period.

The formula to calculate compound interest is given as

A = P(1 + r/n)^nt

A = Pe^rt (Continuously compounded)

Let's substitute the values into the formula and solve

29900 = 4600e^(0.048 * t)

t = 39 years

The time it takes to compound the principal to $29900 is approximately 39 years

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Sum of 5th & 8th terms of an AP = 37

11th term = 32

A.P

We know that,

nth term of an AP – an = a + (n - 1)d

Hence,

⟹ a₅ + a₈ = 37

⟹ a + (5 - 1)d + a + (8 - 1)d = 37

⟹ 2a + 4d + 7d = 37

⟹ 2a + 11d = 37 -- equation (1)

Similarly,

⟹ a₁₁ = 32

⟹ a + (11 - 1)d = 32

⟹ a + 10d = 32

⟹ a = 32 - 10d

Substitute the value of a in equation (1).

⟹ 2(32 - 10d) + 11d = 37

⟹ 64 - 20d + 11d = 37

⟹ 64 - 37 = 20d - 11d

⟹ 27 = 9d

⟹ 27/9 = d

⟹ 3 = d

Substitute the value of d in equation (1).

⟹ 2a + 11(3) = 37

⟹ 2a + 33 = 37

⟹ 2a = 37 - 33

⟹ 2a = 4

⟹ a = 4/2

⟹ a = 2

Now,

General form of an ap = a , a + d , a + 2d...

⟶ Required AP = 2 , 2 + 3 , 2 + 2(3)...

⟶ Required AP = 2 , 5 , 2 + 6...

⟶ Required AP = 2 , 5 , 8...

I hope it will help you.

Regards.

Answer:

→ md - 2nd + 3md = 2 * [ a + (n - 1)d ]

→ 4md - 2nd = 2 * [ a + (n - 1)d ]

→ 2(2md - nd) = 2 * (a + nd - d)

→ 2md - nd - a + d = nd

→ 2md - nd - (md - 2nd) + d = nd

[ From equation (1) ]

→ 2md - nd - md + 2nd + d = nd

→ md + nd + d = nd

→ (m + n + 1)d = n * d

→ (m + n + 1) = n

Step-by-step explanation:

Answer: x=8

Step-by-step explanation: Solve for the x by simplifying both sides of the equation, then isolate the variable.

I hope this help you out!

Answer:

Z

Step-by-step explanation:

The height needs to start at 96

Answer:

It's a, 4

Step-by-step explanation:

Answer:

its c

Step-by-step explanation:

Answer:

C. 2/3

Step-by-step explanation:

To solve this, we should come up with a common denominator first.

The least common denominator (LCD) of the four fractions would be 120.

So, first multiply each fraction's denominator to get 120, and multiply the numerator by the same amount.

ex. 3/4

4 x 30 = 120

3 x 30 = 90

We get 90/120.

After doing this with each fraction, we get;

13/15 = 104/120

7/8 = 105/120

2/3 = 80/120

3/4 = 90/120

Now, it is easier to see which fraction has the least value (or the one that is the smallest. Your answer is 2/3, since 80/120 is the smallest out of the four.

A metric is a single, quantifiable type of data that can be utilized for various tasks in different domains. Metrics serve as essential tools for measuring progress, assessing performance, and making informed decisions.

By converting complex information into manageable and comparable units, metrics enable individuals and organizations to monitor their objectives and drive improvement.
In business, metrics are often employed to evaluate the success of marketing campaigns, employee performance, or financial growth. They assist in identifying trends, pinpointing areas that need attention, and guiding strategic planning. Key performance indicators (KPIs) are a common type of metric used to measure the effectiveness of business processes and track progress toward organizational goals.
In scientific research, metrics provide valuable insight into the progress and impact of studies. For example, citation metrics measure the influence of a published work within a given field. Metrics also facilitate the assessment of experimental results and the development of new theories, ultimately advancing scientific knowledge.
In education, metrics serve as essential tools for gauging student performance and the quality of educational programs. They provide data on student learning outcomes, helping educators refine their teaching methods and tailor instruction to the needs of individual learners.
Overall, a metric is a versatile, quantifiable data type that plays a vital role in assessing and improving various aspects of performance across multiple domains. By offering concrete, measurable information, metrics empower decision-makers to make informed choices and drive progress.

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The number of possible ways in which we can select 3 elements from 7 elements are  given in option d. 35.

There are a total of 7 elements and we can to select 3 elements out of them.

We have to apply the permutation and combination here in order to find the answer,

The formula is ⁿCₐ

Where, C represents combination,

n is the total number of combination,

a is the number of selections that we have to do,

ⁿCₐ = n!/(n-a)!a!

Now, putting n = 7 and a = 3,

ⁿCₐ = 7!/(4)!3!

ⁿCₐ = 35

So, the total number of ways possible are 35.

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Answer:

11 pizzas, 5/7 left

Step-by-step explanation:

to find out how much pizza is needed, multiply 4/7 by 18 to get 72/7. round up to get 77/7 or 11 pizzas. 77/7 - 72/7= 5/7 so there will be 5/7 left over

Answer:

12

Step-by-step explanation:

4 x 18

6 x 1   =  72 /6

72/6 = 12

6/6 = 1

12 /1

12

Answer:

Please see the attached pictures for the full solution.

\(\boxed{ \frac{d}{dx} ( {x}^{n} ) = n {x}^{n - 1} }\)

Answer:

The answer is: F. Pyramid

The figure shown below is Pyramid.

Option F is correct.

A three-dimensional shape is a pyramid. A pyramid has a polygonal base and flat triangular faces that meet at a location known as the apex. By linking the bases to an apex, a pyramid is constructed. Each edge of the base connects to the apex, forming the triangle face known as the lateral face.

First, a cube have all faces of shape square.

second, Prism have two identical base.

Third, Polyhedron have polygonal faces.

Fourth, Polygon is a  flat or plane, two-dimensional closed shape bounded with straight sides.  

Last, Pyramid has only one identical face.

Thus, the given figure is Pyramid.

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Answer:

-4

Step-by-step explanation:

Move variables to one side and numbers on the other.

12 - 3x = -6x

+ 3x +3x

12 = -3x

/-3 /-3

-4 = x

Answer:

14 km

Step-by-step explanation:

6 km in the afternoon

x km in the morning

6= x- 25%

6= 0.75x

x= 6/0.75

x= 8 km

total 6+8= 14 km

Answer:

you add it all up and lever the sides

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

4% of 350 is 14 so he only sold 14

Answer:

both 2 and -2

Step-by-step explanation:

Substitute 4 for r(x) on the given equation.

\(4=x^2\)

\(\sqrt{4} =\sqrt{x^2}\)

\(x=2\)

\(x=-2\)

Answer:

\(5 \sqrt{5} - 2 \sqrt{5} = 3 \sqrt{5} \\ 8 \sqrt{7} + 3 \sqrt{7} = 11 \sqrt{7} \)

hope this helps.

Answer:

\(11 \sqrt{7} \)

Step-by-step explanation:

\(8 \sqrt{7} + 3 \sqrt{7} \)

\( \sqrt{7} (8 + 3) \)

\(11 \sqrt{7} \)

Answer:

mass, pressure, density is the right answer

Step-by-step explanation:

The three main characteristics that can be used to describe air are: C. mass, pressure, density.

Altitude deals with elevation of an object.

Radiation relates to transmission of energy through a medium in form of waves.

Air has mass, pressure, and density.

Therefore, the three main characteristics that can be used to describe air are: C. mass, pressure, density.

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Applying the formula for area of a rectangle, the length of the rectangle can be expressed as: 3x + 2.

Recall:

Area of a rectangle (A) = L x W

Given:

Area of rectangle (A) expressed as: 9x + 6

Width (W) = 3

Length (L) = ?

9x + 6 = L x 3

\(9x + 6 = 3L\)

\(\frac{9x}{3} + \frac{6}{3} = \frac{3L}{3}\\\\3x + 2 = L\\\\L = 3x + 2\)

Therefore, applying the formula for area of a rectangle, the length of the rectangle can be expressed as: 3x + 2.

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Parallel Lines

Given the equation of a line as:

y = mx + c

The variable m represents the slope or the gradient of the line, and c represents the y-intercept of the line.

If two lines are parallel, they have the same gradient, i.e., their value of m is equal for both and c is different. Note if c was equal also, both lines would be exactly the same, not parallel.

We are given a number of pairs of lines and we must identify which pairs are parallel lines.

a) y = 3x + 4, y = 3x - 8

Comparing the values of m (the coefficient of x) in both equations, we conclude they are parallel lines since m=3 for both and c is different.

b) y = 2x - 17 , y - 2x = 17

We must express the second equation with the y isolated at the left side:

y = 2x + 17

Both lines have the same value of m=2 and different values of c, so they are parallel.

c) y = x - 4 , y = -2x - 4

The first gradient is m=1 and the second gradient is m=-2, thus these lines are not parallel

d) 3y + 3x = 9 , y = x + 3/2

Divide the first equation by 3:

y + x = 3

And solve for y:

y = -x +3

The gradient of this line is -1 and the gradient of the other line is m=1, thus these lines are not parallel.

e) 2x = y + 8 , 2y = x + 8

Solving for y both equations:

y = 2x - 8

y = x/2 + 4

The gradients are m=2 and m=1/2 respectively, thus these lines are not parallel.

f) 3 - x = 3y , y - 3x = 5

Solving for y:

y = -x/3 + 1

y = 3x + 5

The gradients are, respectively m=-1/3 and m=3, thus these lines are not parallel.

g) 4y + 8x = 0 , y = 22 - 2x

Solving for y and rearranging:

y = -2x , y = -2x + 22

The gradients are m=-2 for both lines and the values of c are different, thus these lines are parallel.

h) y = 2x - 8 , 8y + 8x = 9

Solving the second equation for y:

y = -x + 9/8

The gradients are, respectively m=2 and m=-1, thus these lines are not parallel.

The following image summarizes the results by circling the pairs of parallel lines as required.

Answer:

There is a 11.36 pounds difference between Tray's weight on Earth and on Saturn

Step-by-step explanation:

142 × .92 = 130.64

142-130.64= 11.36