Determine the seating capacity of an auditorium with 15 rows of seats if there are 25 seats in the first row, 29 seats in the second row, 33 seats in the third row, 37 seats in the forth row, and so on

Answer:

y-9=-4(x+2)

Step-by-step explanation:

The point-slope formula is:

y-y1=m(x-x1)

m=-4 and use the point (-2, 9)

                                       x1    y1

Plug in the information.

y-9=-4(x+2)

This is the equation written in point-slope form using the point (-2, 9).

Hope this helps!

Using a linear function, it is found that Company D would have given you the best deal for 7 hours of moving.

A linear function is modeled by:

y = mx + b

In which:

In this problem, we consider:

Hence the costs for x hours of moving from each company are given as follows:

For 7 hours, the costs are given as follows:

Due to the lower cost, Company D would have given you the best deal for 7 hours of moving.

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The equations with tangents at (0,0) are [tex]y = \frac{4}{7} x[/tex] and

[tex]y = -\frac{4}{7} x[/tex].

In this question,

The curves are x = 7 cos(t), y = 4 sin(t) cos(t)

Two tangents at (0, 0)

In this case, the parametric derivative of x and y are expressed in terms of t.

The first derivative dy/dx can be expressed as

[tex]\frac{dy}{dx}=\frac{\frac{dy}{dt} }{\frac{dx}{dt} }[/tex]

Now, dy/dt is obtained by differentiate y with respect to t,

[tex]\frac{dy}{dt}= 4[cos(t)(cos(t))+sin(t)(-sin(t))][/tex]

⇒ [tex]\frac{dy}{dt}= 4[cos^{2} (t)-sin^{2} (t)][/tex]

Now, dx/dt is obtained by differentiate x with respect to t,

[tex]\frac{dx}{dt} =7(-sin(t))[/tex]

⇒ [tex]\frac{dx}{dt} =-7sin(t)[/tex]

Thus, [tex]\frac{dy}{dx}=\frac{4[cos^{2}(t)-sin^{2}(t ) ]}{-7sin(t)}[/tex]

At (0,0) x = 0 and y = 0, Then

0 = 7 cos(t)

0 = 4 sin(t) cos(t)

and

cos(t) = 0

sin(t) cos(t) = 0

There are two values between -π and π which satisfy these equations simultaneously are

t = π/2

t = -π/2

The equation of a straight line given a point and its slope is

y-y₀ = m(x-x₀)

The two tangents lies at (0,0), so the equation becomes

y = mx

Then the two straight lines will be

y = m₁x  and

y = m₂x

For t = π/2,

[tex]m_1=\frac{dy}{dx}=\frac{4[cos^{2}(\frac{\pi }{2} )-sin^{2}(\frac{\pi }{2} ) ]}{-7sin(\frac{\pi }{2} )}[/tex]

⇒ [tex]m_1=-\frac{4[0-1]}{7(1)}[/tex]

⇒ [tex]m_1=\frac{4}{7}[/tex]

For t = -π/2,

[tex]m_2=\frac{dy}{dx}=\frac{4[cos^{2}(-\frac{\pi }{2} )-sin^{2}(-\frac{\pi }{2} ) ]}{-7sin(-\frac{\pi }{2} )}[/tex]

⇒ [tex]m_2=-\frac{4[0-1]}{-7(1)}[/tex]

⇒ [tex]m_2=-\frac{4}{7}[/tex]

Thus the equations with tangents at (0,0) are [tex]y = \frac{4}{7} x[/tex] and

[tex]y = -\frac{4}{7} x[/tex].

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The explicit formula is Tn = 18[[tex]\frac{2}{3} ^{n-1}[/tex]]

here, we have to find n.

Now, F(2) = 2/3 * f1 = 2/3 * 18 = 12

F(3) = 2/3 * f(2) = 2/3 * 12 = 8

F(4) = 2/3 * F(3) = 2/3 * 8 = 16/3

F(5) = 2/3 * 16/3 = 32/9

These equations form a pattern.

That is Tn = (2/3)^(n-1)(18)

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The first four partial sums of the sequence are S₁ = 0.3010, S₂ = 0.9999, S₃ = 2.447, S₄ = 4.8569.

In this question,

A sequence is a set of things (usually numbers) that are in order. A partial sum is the sum of part of the sequence.

The sequence is [tex]a_{n} =log(n^{n}+1 )[/tex]

The first four partial sum S₁, S₂, S₃, S₄ can be calculated by substituting n = 1,2,3,4 in the sequence.

S₁ can be calculated as

S₁ = a₁

⇒ [tex]a_{1} =log(1^{1}+1 )[/tex]

⇒ [tex]a_{1} =log(1+1 )[/tex]

⇒ [tex]a_{1} =log(2 )[/tex]

⇒ [tex]a_{1} =0.3010[/tex]

Now, S₁ = 0.3010

S₂ can be calculated as

S₂ = a₁ + a₂

⇒ [tex]a_{2} =log(2^{2}+1 )[/tex]

⇒ [tex]a_{2} =log(4+1 )[/tex]

⇒ [tex]a_{2} =log(5 )[/tex]

⇒ [tex]a_{2} =0.6989[/tex]

Now, S₂ = 0.3010 + 0.6989

⇒ S₂ = 0.9999

S₃ can be calculated as

S₃ = a₁ + a₂ + a₃

⇒ [tex]a_{3} =log(3^{3}+1 )[/tex]

⇒ [tex]a_{3} =log(27+1 )[/tex]

⇒ [tex]a_{3} =log(28)[/tex]

⇒ [tex]a_{3} =1.4471[/tex]

Now, S₃ = 0.3010 + 0.6989 + 1.4471

⇒ S₃ = 2.447

S₄ can be calculated as

S₄ = a₁ + a₂ + a₃ + a₄

⇒ [tex]a_{4} =log(4^{4}+1 )[/tex]

⇒ [tex]a_{4} =log(256+1 )[/tex]

⇒ [tex]a_{4} =log(257 )[/tex]

⇒ [tex]a_{4} =2.4099[/tex]

Now, S₄ = 0.3010 + 0.6989 + 1.4471 + 2.4099

⇒ S₄ = 4.8569

Hence we can conclude that the first four partial sums of the sequence are S₁ = 0.3010, S₂ = 0.9999, S₃ = 2.447, S₄ = 4.8569.

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Answer:

s is antecedent t is consepuent

The value of each variable in the two-way table is:

a = 7

b = 31

c = 28

d = 13

e = 65

A Venn diagram uses circles that overlap each other to show logical relationships between two or more sets of items. A two-way table represents the frequency of dataset by arranging the dataset into a table made up of rows and columns.

The following have to be established:

a player can either be male or female

a player favors either the left or the right

a = females that favor the left. Looking at the Venn diagram, this number is 7.

b = total number of females : 24 + 7 = 31

c = males that favor the right = total number of males - males that favor the left

34 - 6 = 28

d = Total number of people who favor the left = 7 + 6 = 13

Total number of baseball players = 65

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Answer:

-1/2

Step-by-step explanation:

The cosine is equal to the x coordinate of the point where the terminal side of the angle intersects the unit circle.

Answer:

20 cm

Step-by-step explanation:

The volume, V, of a cone with radius r and height h is given by the formula

V = [tex](1/3) \pi r^2 h[/tex]

Since it is given that the ratio of h to r is 3/4 we have the relationship

h/r = 3/4 ==> h = (3/4)r

Substituting for h in the volume equation gives us an expression in terms of r

[tex](1/3)\pir^2h = (1/3) \pi r^2 (3/4)r\\(1/3 ) (3/4) = 1/4\\[/tex]

So the expression simplifies to[tex](1/4)\pi r^3[/tex]

We are given that this volume is 2000π cm³

So

(1/4)πr³ = 2000π

Eliminating π on both sides and multiplying by 4 on both sides gives

r³ = 8000

r = ∛8000 = 20 cm   Answer

Answer:

[tex]\boxed{\left(x+i\sqrt{\frac{2}{3}}i \right)\left(x-i\sqrt{\frac{2}{3}}i \right)}[/tex]

Step-by-step explanation:

Setting the expression equal to zero to find the roots,

[tex]3x^2 +2=0\\\\3x^2 =-2\\\\x^2 =-\frac{2}{3}\\\\x=\pm i\sqrt{\frac{2}{3}}[/tex]

This means that

[tex]3x^2 +2=\boxed{\left(x+i\sqrt{\frac{2}{3}}i \right)\left(x-i\sqrt{\frac{2}{3}}i \right)}[/tex]

The next step in the process of constructing parallel line CD is C. Set the compass width to the distance between point E and where the arc crosses line AB.

It's important to draw a line parellel to line AB. Then, on should set compasses' width to the distance where the lower arc crosses the two lines.

After that, it's vital to move the compasses to where the upper arc crosses the transverse.

In conclusion, the correct option is C.

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Answer:

The answer is A

Step-by-step explanation:

The areas of the parallelograms can be compared as: A. The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2.

A parallelogram refers to a geometrical shape and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.

Mathematically, the area of a triangle can be calculated by using this formula:

Area = ½ × b × h

Where:

Mathematically, the area of a rectangle can be calculated by using this formula;

A = LW

Where:

Next, we would determine the area of the two parallelograms as follows:

Area of parallelogram 1 = Area of red-rectangular figure - Area of triangle A - Area of triangle B - Area of triangle C - Area of triangle D.

Substituting the given parameters into the formula, we have;

Area of parallelogram 1 = (6 × 6) - (½ × 4 × 2) - (½ × 2 × 4)- (½ × 4 × 2) - (½ × 2 × 4)

Area of parallelogram 1 = 36 - 4 - 4 - 4 - 4

Area of parallelogram 1 = 36 - 16

Area of parallelogram 1 = 20 units².

For parallelogram 2, we have:

Area of parallelogram 2 = Area of blue-rectangular figure - Area of triangle P - Area of triangle Q - Area of triangle R - Area of triangle S.

Substituting the given parameters into the formula, we have;

Area of parallelogram 2 = (8 × 4) - (½ × 2 × 2) - (½ × 6 × 2)- (½ × 2 × 2) - (½ × 2 × 6)

Area of parallelogram 2 = 32 - 2 - 6 - 2 - 6

Area of parallelogram 2 = 32 - 16

Area of parallelogram 2 = 16 units².

Difference = Area of parallelogram 1 - Area of parallelogram 2

Difference = 20 - 16

Difference = 4 units².

In conclusion, we can infer and logically deduce that the area of parallelogram 1 is 4 square units greater than the area of parallelogram 2.

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The top of the escalator exists 9 feet far from the ground floor.

Let h denote the distance between the top of the escalator from the ground floor.

We have existed given that the angle of depression from the top of the escalator to the floor stands 36.84°, and the escalator exists 15 feet long.

The side h exists opposite side and 15 feet side exists hypotenuse of a right triangle.

[tex]$&\sin =\frac{\text { Opposite }}{\text { Hypotenuse }} \\[/tex]

[tex]$&\sin \left(36.84^{\circ}\right)=\frac{h}{15} \\[/tex]

[tex]$&\sin \left(36.84^{\circ}\right) * 15=\frac{h}{15} * 15 \\[/tex]

[tex]$&0.599582468446 * 15=h \\[/tex]

8.993737 = h

[tex]$&h \approx 9[/tex]

Therefore, the top of the escalator exists 9 feet far from the ground floor.

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1. The probability that a person who exists older than 35 years has a hemoglobin level between 9 and 11 exists at 0.284.

2. The probability that a person who exists older than 35 years has a hemoglobin level of 9 and above exists at 0.531.

Let the number of the person who is older than 35 years have a hemoglobin level between 9 and 11 be x.

From the given table it is clear that the total number of the person who is older than 35 years exists 162.

75+x+40 = 162

x+116 = 162

x = 162-116

x = 46

The number of people who are older than 35 years has a hemoglobin level between 9 and 11 exists at 46.

1. The probability that a person who exists older than 35 years has a hemoglobin level between 9 and 11 exists

P = Probability who is older than 35 years has a hemoglobin level                                                              

     between 9 and 11 / Person who exists older than 35

P = 46/162 = 0.284

The probability that a person who is older than 35 years has a hemoglobin level between 9 and 11 exists at 0.284.

2. Person who is older than 35 years has a hemoglobin level of 9 and above exists 46 + 40 = 86.

The probability that a person who exists older than 35 years has a hemoglobin level of 9 and above exists

P = Probability who is older than 35 years has a hemoglobin level  

       between 9 and above / Person who is older than 35

P = 86/162 = 0.531.

The probability that a person who is older than 35 years has a hemoglobin level of 9 and above exists at 0.531.

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The algebraic formula that represents the situation of the age difference between Fatimah and Nadia is x + 3 = y, where x, y > 0 and y > x.

Herein we have a situation where two people have different ages, Fatimah has an age such that she is 3 years younger than Nadia. Let be x and y variables that respesent the ages of Fatimah and Nadia, respectively. In summary, the word problem can be reduced into the following algebraic expression:

y - x = 3 (Expression that represents age difference between Fatimah and Nadia)

x + 3 = y, where x, y > 0 and y > x. (1)

The algebraic formula that represents the situation of the age difference between Fatimah and Nadia is x + 3 = y, where x, y > 0 and y > x.

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For a sample of size 300 from a population with the population proportion, the μphat and σphat are 0.0287.

A share is an equation in which ratios are set equal to each other. for example, if there may be 1 boy and three women you can write the ratio as 1 : 3 (for each boy there are 3 women) 1 / 4 are boys and three / 4 are girls.

The formula for proportion is components /complete = percent/100. This system can be used to locate the percentage of a given ratio and to locate the lacking value of an element or an entire.

A proportion is generally written as equal fractions. for example: note that the equation has a ratio on each facet of the same signal. Every ratio compares the equal units, inches, and feet, and the ratios are equivalent due to the fact the devices are regular and equal.

Given 300 2   and p 0.45

p = 0.45 Up

and Õp-sqrt(p(1-p)/n) sqrt(0.45 * 0.55/300) sqrt(0.000825) =0.0287

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If the price of one ticket of bus is $180 and the bus has 56 seats then the maximum revenue that it can earn is $5107.6

Given that the price of a bus ticket to Saskatoon is $180 and the bus has 56 seats.

We are required to find the maximum revenue that the bus company can earn.

Suppose x represents the number of seats, y represents the total amount.

Price=$156

Seats=56

When the bus is of half capacity the bus seats will be 28.

As price decreases th rider gains 2 more.

Revenue equation.

y=(156.5x)(28+2x)-------------1

Expanding the equation.

y=4368-140x+312-10[tex]x^{2}[/tex]

Differentiating with respect to x.

dy/dx=0-140+312-20x

=172-20x

Put dy/dx=0

172-20x=0

x=8.6

Substitute the value of variable x in the equation 1.

y=(156-5x)(28+2x)

=$5107.6

Hence the maximum revenue that the bus company can earn is $5107.6.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

6 > x² - 5x.

The answer for the inequality is -1 the greater than sign x greater than 6

The interval notation is ( -1,6)

Answer:

[tex]-1 < x < 6[/tex]

Step-by-step explanation:

Moving all terms to one side, we get [tex]x^2-5x-6 < 0[/tex]. Notice that we can factor the left side. Doing so, we get [tex](x-6)(x+1) < 0[/tex]. The zeroes in this equation are [tex]x-6=0 \Rightarrow x=6[/tex] and [tex]x+1=0\Rightarrow x=-1[/tex]. Now, we must create test points in the intervals: [tex]x < -1, -1 < x < 6, x > 6[/tex]. For example, we can choose [tex]x=-2,x=0,x=7[/tex]. For [tex]x=-2[/tex], we get that [tex](-2-6)(-2+1) = 8 < 0[/tex] is false, since the expression is positive. Doing the same thing for [tex]x=0[/tex] and [tex]x=7[/tex], we get that only [tex]x=0[/tex] creates a negative value. This means that the values in the interval [tex]\boxed{-1 < x < 6}[/tex] all work.

The standard form polynomial representing the volume of this shipping container is determined as: 24x^5 + 78x^4 - 147x^3 - 624x^2 - 360x.

A standard form polynomial is a polynomial expression written whereby the term with the highest degree or power on a variable is written first in the expression, followed by the least, then the constant of the polynomial comes last.

What is the Volume of a Rectangular Prism?

The Volume of a rectangular prism = (length)(width)(height).

The shipping container is a rectangular prism with the following dimensions:

Length of container = 4x² + 3x

Width of container = x² - 8

Height = 6x + 15

Plug in the values

Volume of container = (4x² + 3x)(x² - 8 )(6x + 15)

Expand

Volume of container = 24x^5 + 78x^4 - 147x^3 - 624x^2 - 360x

Thus, using the formula for the volume of a rectangular prism, the standard form polynomial representing the volume of this shipping container is determined as: 24x^5 + 78x^4 - 147x^3 - 624x^2 - 360x.

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The greatest force acting on the ball to slow it down is Gravitational force.

When ball is thrown upwards then there will be two forces on the ball opposite to the motion of ball

1. Gravitational force (mg)

2. Air friction or air drag

Both forces are opposite to the motion of the ball and it will cause the decrease in the speed of the ball.

Now here due to less value of drag coefficient on the ball we will say that ball will decrease its speed more due to gravitational force compare to friction force of air.

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The values of x are x₁ ≈ 4.8 and x₂ ≈ - 0.8.

Herein we have two circular sections of equal area, whose expressions are described by the following geometric equations:

Semicircle

A = 0.5π · x²     (1)

Half Semicircle

A = 0.25π · (x + 2)²      (2)

By equalizing (1) and (2):

0.5π · x² = 0.25π · (x + 2)²  

2 · x² = (x + 2)²  

2 · x² = x² + 4 · x + 4

x² - 4 · x - 4 = 0

x² - 4 · x + 4 = 8

(x - 2)² = 8

x - 2 = ±√8

x = 2 ± √8

x = 2 ± 2√2

x = 2 · (1 ± √2)

x = 2 · (1 ± 1.41)

x₁ = 2 · 2.41   ∨   x₂ = 2 · (- 0.41)

x₁ = 4.82   ∨   x₂ = - 0.82

The values of x are x₁ ≈ 4.8 and x₂ ≈ - 0.8.

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Answer: I believe it is 4m

Step-by-step explanation:

m+m+m+m would be equivalent to 4m which is 4 times m

Step-by-step explanation:

It's like you're adding 1+1+1+1 which equals 4 so that's what I think

Answer:

7.a) 5

7.b) 1/2

8. 1

Step-by-step explanation:

7.

a)

Read the points on the graph (0, 0) and (1, 5).

slope = (5 - 0)/(1 - 0) = 5/1 = 5

b)

read the points on the graph (0, 0) and (4, 2).

slope = (2 - 0)/(4 - 0) = 2/4 = 1/2

8.

Points (1, 4) and (5, 8)

slope = (8 - 4)/(5 - 1) = 4/4 = 1

x=-2

Step-by-step explanation:

Solution Given:

3(x-3) = 5(2x + 1)

Opening bracket we get

3x-9=10x+5

keeping common value in same side

-9-5=10x-3x

-14=7x

x=-14/7

x= -2

Answer:

-2 =x

Step-by-step explanation:

3(x-3) = 5(2x + 1)

To solve for x

Distribute

3x -9 = 10x +5

Subtract 3x from each side

3x-9-3x = 10x -3x+5

-9 = 7x+5

Subtract 5 from each side

-9-5 = 7x+5-5

-14 = 7x

Divide by 7

-14/7 = 7x/7

-2 =x

Descriptive statistics summarize numbers and inferential statistics determine whether the results are significant.

What is statistics?

The gathering, characterization, analysis, and drawing of inferences from quantitative data are all tasks that fall under the purview of statistics, a subfield of applied mathematics. Probability theory, linear algebra, and differential and integral calculus play major roles in the mathematical theories underlying statistics.

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Answer:

-93312a²

Step-by-step explanation:

1) Simplify 36³ to 46656.

-2a² × 46656

2) Simplify 2a² × 46656 to 93312a².

-93312a²

Answer:

[tex]\displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x=-\dfrac{2}{x+1}+\text{C}[/tex]

Step-by-step explanation:

Fundamental Theorem of Calculus

[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given integral:

[tex]\displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x[/tex]

Factor the denominator:

[tex]\begin{aligned}\implies x^2+2x+1 & = x^2+x+x+1\\& = x(x+1)+1(x+1)\\& = (x+1)(x+1)\\& = (x+1)^2\end{aligned}[/tex]

[tex]\implies \displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x=\int \dfrac{2}{(x+1)^2}\:\:\text{d}x[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{1}{a^n}=a^{-n}[/tex]

[tex]\implies \displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x=\int 2(x+1)^{-2}\:\:\text{d}x[/tex]

[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $ax^n$}\\\\$\displaystyle \int ax^n\:\text{d}x=\dfrac{ax^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]

Use Integration by Substitution:

[tex]\textsf{Let }u=(x+1) \implies \dfrac{\text{d}u}{\text{d}x}=1 \implies \text{d}x=\text{d}u}[/tex]

Therefore:

[tex]\begin{aligned}\displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x & = \int 2(x+1)^{-2}\:\:\text{d}x\\\\& = \int 2u^{-2}\:\:\text{d}u\\\\& = \dfrac{2}{-1}u^{-2+1}+\text{C}\\\\& = -2u^{-1}+\text{C}\\\\& = -\dfrac{2}{u}+\text{C}\\\\& = -\dfrac{2}{x+1}+\text{C}\end{aligned}[/tex]

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