find the general indefinite integral. (use c for the constant of integration.) sec(t)(4 sec(t) 3 tan(t)) dt

Set x = 0 and solve for y to find the y-intercept. The main point will be (0,y).

The point on the line where it intersects the y axis is known as the y intercept.

In analytic geometry, a y-intercept or vertical intercept is a point where the graph of a function or relation intertwines the y-axis of the coordinate system, with the horizontal axis representing a variable x and the vertical axis representing a variable y. As a result, these points satisfy the x = 0 condition.

An intercept is a point on the y-axis through which the slope of a line passes. It is the y-coordinate of a y-axis point at which a straight line or a curve interferes. This is represented by the straight line equation,

y = mx+c,

where m denotes the slope and c is the y-intercept

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Answer:

[tex]m=-\frac{2}{27}[/tex]

Step-by-step explanation:

[tex]Slope (m) =\frac{y_2-y_1}{x_2-x_1}\\(x_1,y_1)=(-18,5)\\(x_2,y_2)=(-45,7)\\m=\frac{7-5}{-45-(-18)}\\m=\frac{2}{-45+18}\\m=\frac{2}{-27}\\m=-\frac{2}{27}[/tex]

The central angle is the ratio of arc length and radius.

What is a Central Angle?

The central angle is the angle that a circle's arc occupies in its centre. The arms of the central angle are formed by the radius vectors. In other words, it's an angle whose vertex is the centre of a circle and whose arms, which have the circle's two radii as their arms, cross at two separate positions. These two points make an arc when they are combined. The angle that this arc at the circle's centre subtends is known as the central angle.

According to the central angle, we state that:

An arc's angle at the circle's centre is twice as large as its angle at any other point along the circle's circumference.

OR

The angle subtended by the arc in the opposite segment of the circle is twice as large as the angle at the centre of the circle.

Hence,

The central angle is the ratio of arc length and radius.

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If the hexagon is changed to an octagon, the area of the shaded portion will be; smaller

We are given;

Diameter of circle = 5 ft

Thus;

radius; r = 5/2 = 2.5 ft

Now, the long diagonal of the hexagon is given as 5ft and we know that if the side of the hexagon is a, then;

a = d/2

where d is the length of the long diagonal

Formula for area of hexagon is;

A = (3/2) * √3 * a²

Thus;

A =  (3/2) * √3 * 2.5²

A = 16.24 ft²

Area of circle is gotten from the formula;

A = πr²

A = π * 2.5²

A = 19.635 ft²

Thus;

Area of shaded portion = 19.635 ft² - 16.24 ft² = 3.395 ft²

If the hexagon is changed to an octagon, the formula for length of diagonal is;

L = a√(4 + 2√2)

where a is side length

Thus;

5 = a√(4 + 2√2)

a = 5/√(4 + 2√2)

Area of octagon is from the formula;

Area = 2a²(1 + √2)

Area = 2(5/√(4 + 2√2))²(1 + √2)

Area = 2(25/(4 + 2√2))(1 + √2)

Area = 17.678 ft²

Area of shaded portion = 19.635 ft² - 17.678 ft² = 1.957ft²

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The central angle states the property of the center of the circle, So It is called the central angle.

What is a Central Angle?

The central angle is the angle that a circle's arc occupies in its center. The arms of the central angle are formed by the radius vectors. In other words, it's an angle whose vertex is the center of a circle and whose arms, which have the circle's two radii as their arms, cross at two separate positions. These two points make an arc when they are combined. The angle that this arc at the circle's center subtends is known as the central angle.

An arc's angle at the circle's center is twice as large as its angle at any other point along the circle's circumference. the angle subtended by the arc in the opposite segment of the circle is twice as large as the angle at the center of the circle.

Hence,

The central angle states the property of the center of the circle, So It is called the central angle.

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Example of SMART saving goals is "Viletas de $50 each week in almone market."

SMART financial goals should be Specific, Measurable, Achievable, Relevant, Time-based.

Specific :- Your goal should be specific, not generic or vague.

Measurable :- Make your financial goal measurable by quantifying it so you can evaluate your progress and overall success.

Achievable :- The surest way to improve your financial situation is to take achievable steps.

Realistic :- Setting unrealistic goals usually leads to disappointment and surrender.

Time-based:- Give yourself a time frame to achieve the goal.

By observing all these properties of SMART financial goal the example of this goal will be "Viletas de $50 each week in almone market."

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After dividing the number, the decimal of 12/16 is 0.75.

In the given question we have to find the 12/16 as a decimal.

The division is shown by the fractional bar between the "part" and the "whole." By dividing the numerator by the denominator, any fractions can be transformed into decimals.

So when we divide 12 by 16 then the result is 0.75.

So the decimal of 12/16 is 0.75.

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The right answer is:

What is 12/16 as a decimal?

Yes, It is possible to construct a triangle whose sides measure 6 cm 5 cm and 10 cm Because the total of a triangle's two sides is bigger than the third side.

The three vertices of a triangle connect the straight lines that make up its sides. In other terms, we can state that a triangle's sides are line segments that converge at the triangle's vertices. A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question.

Given,

Sides 6 cm 5 cm and 10 cm

Sum = 6 + 5

Sum = 11

Because the total of a triangle's two sides is bigger than the third side, it is conceivable to construct a triangle with sides that measure 10 cm, 5 cm, and 6 cm.

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The margin of error for the true proportion of times the coin would land on heads on a 95% confidence level is 11.

As per the question,

⇒ Confidence interval is calculated by,

                p  ±  z(α/2) × √ ( p × q / n )   =   ( p - E, p + E )

where,     p  =  proportion in a random sample

                q  =  1 - q

                E   =  z(α/2) × √ ( p × q / n )   i.e.  margin of error

⇒  p   =   40 / 50

          =   4 / 5

∴   p   =   0.8

⇒   q  =  1 -  [tex]p^{'}[/tex]  

          =  1 - 0.8

∴    q  =  0.2

⇒  α   =   0.05

⇒ z(α/2)  =  1.94

⇒ Margin of error ( E )   =   z(α/2) × √ ( p × q / n )

                                       =   1.94 × √ ( 0.8 × 0.2 / 50 )

                                       =   1.94 × √ ( 0.16 / 50 )

                                       =   1.94 × √ ( 0.0032 )

                                       =   1.94 × 0.05656

    Margin of error ( E )   =   0.109  ≅  0.11

Therefore, 11 is the Margin of Error ( E ) for the true proportion of times the coin would land on heads at a 95% confidence level i.e option c is correct.

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The complete question is

A trick coin that was purchased at a magic shop was flipped 50 times. The coin landed on heads 40 times. Based on the results, what is the margin of error for the true proportion of times the coin would land on heads? Base your margin of error on a 95% confidence level.

a. 1

b. 10

c. 11

d. 5

The volume of the largest box that can be made is V=x(18-2x)² inches³

Volume is expressed in cubic units like m3, cm3, in3, and so on. At times, volume is also referred to as capacity.

Volume is a measurement of the amount of three-dimensional space that is occupied. It is typically quantified numerically with SI-derived units or different imperial or US customary units. The definitions of length and volume are inextricably related.

Consider the open box's height to be x inches.

The length of the box is then (18-2x) inches.

Because it is a square box, its length and width are the same.

As a result, the box's width becomes (18-2x) inches.

The volume of the open box (V)= (length)(breadth)(height)

V=(18-2x)(18-2x)(x)

V=x(18-2x)²

V=x(18-2x)² cubic inches.

Therefore, the volume of the box is V=x(18-2x)² inches³

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Answer: 6

Step-by-step explanation: n-3x6-6=6

No James' expressions for 23+3 x 9-42 are incorrect

To group numbers or variables, three common grouping symbols are used:

Parentheses are the most widely used grouping symbols.

To make the problem simpler, operations enclosed in parentheses can be carried out before any other operations.

To group the expression correctly using PEMDAS

the full meaning include

P - parenthesis

E  - exponents

M - multiplication

D - division

A - addition

S - subtraction

= 23 + 3 x 9 - 42

= 23 + (3 x 9) - 42

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The Fibonacci series in which 0 does not consider is 1,2,3,5,8,13,21,34,…

A series of numbers known as the Fibonacci sequence is one in which each succeeding number is created by adding the two numbers that came before it. The Fibonacci sequence is named for the Italian mathematician who created it.

The standard Fibonacci series

0,1,1,2,3,5,8,13,21,34,…

When 0 is not considered as Fibonacci number, the series can be rewritten as,

1,2,3,5,8,13,21,34,…

The Fibonacci series where number 0 is excluded is 1,2,3,5,8,13,21,34,…

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The parabolic equation representing the t-shirt's height is given as follows:

y = -16(x - 1)² + 24.

The equation of a quadratic function, representing a parabola, of vertex (h,k), is given by the following rule:

y = a(x - h)² + k

In which the parameters of the function are listed as follows:

Considering the maximum height, the vertex of the parabola is given by the following coordinates:

(1, 24).

Hence:

y = a(x - 1)² + 24.

When x = 0, y = 8, hence the leading coefficient of the equation is obtained as follows:

8 = a + 24

a = -16.

Thus the equation is:

y = -16(x - 1)² + 24.

The team mascot shoots a rolled T-shirt from a special T-shirt cannon to a section of people in the stands at a basketball game. The T-shirt starts at a height of 8 feet when it leaves the cannon and 1 second later reaches a maximum height of 24 feet before coming back down to a lucky winner. If the path of the T-shirt is represented by a parabola, which function could be used to represent the height of the T-shirt as a function of time, t, in seconds?

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There will be sample Z-test for mean and the confidence interval will be [119.62, 125.38] as well as we are 95% certain that sample mean will fall within the interval.

Any statistical hypothesis test called a t-test has a test statistic that, under the null hypothesis, follows a Student's t-distribution. It is most frequently used when the test statistic would have a normal distribution if the test statistic's scaling term's value were known. A statistical test called a t test is employed to compare the means of two groups. It is frequently employed in hypothesis testing to see if a procedure or treatment truly affects the population of interest or whether two groups differ from one another.

a. 0.724<p<0.752

E=(0.752-0.724)/2

=0.014

b. n=192

x=129

p=129/192=0.6719

Confidence interval=95%
Z-score= 1.96

E=Z*(√p(1-p)/n)

=1.96*√0.6719*(1-0.6719)/192

=1.96*0.0339

=0.06884

We will do a sample Z-test to determine the mean, and we can be 95% certain that the sample mean will fall within the confidence range of [119.62, 125.38].

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7.7%. is  the rate of unemployment.

According to our question-

Unemployment rate = number of unemployed people / total number of unemployed people * 100

Similarly,

Workforce = Employed + Unemployed

Unemployed = 130 million - 120 million. That's 10 million.

For this reason,

Unemployment rate = 10 / 130 * 100

Unemployment = 7.69% or about 7.7%.

Hence, 7.7%. is  the rate of unemployment.

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A rational number is a number that can be written in the form p/q where q is not equal to zero and p is an integer.

A root is a value for x that makes the function equal to zero. It is also called a solution.

Hence, a rational root is such a number that makes any polynomial function equal to zero.

let us consider a general polynomial equation-

P(x) = anxn + an− 1xn − 1 + … + a1x1 + a0

hence, the rational roots must be of the form = [tex]\pm[/tex] (factors of a0) / (factors of an).

let us now take an example,

f(x)=[tex]2 x^3-3 x^2-11 x+6[/tex]

here ao = 6, and factors of 6: 1,2,3,6

an = 2 and the factors of 2: 1,2

Hence, we have Possible Rational Roots:

[tex]$$\pm\left\{\frac{1}{1}, \frac{1}{2}, \frac{2}{1}, \frac{2}{2}, \frac{3}{1}, \frac{3}{2}, \frac{6}{1}, \frac{6}{2}\right\}$$[/tex]

removing the duplicate values we have- [tex]$$\pm\left\{1, \frac{1}{2}, 2, 3, \frac{3}{2}, 6\right\}$$[/tex]

In this way, we have the rational numbers which can be possible solutions for our function f(x).

Now we substitute each of these rational numbers one by one to check if it satisfies the equation as follows.

f(1) =[tex]2 (1)^3-3 (1)^2-11 (1)+6[/tex] = 2-3-11+6 = -6 [tex]\neq[/tex] 0.

Hence, it doesn't satisfy the equation, it means it's not the root of the equation.

Similarly, we can check for the rest of the numbers.

we will get f(1/2)=0, f(3)=0 and f(-2)=0

Hence, x=3,1/2 or -2 are the solutions for the equation f(x).

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Answer:

Any point with a y coordinate of -3.

Step-by-step explanation:

Because they have the same y coordinate, it is a horizontal line. So any point that has a y coordinate of -3 will be on the same line.

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If the function is on a graph and it's a straight line then its linear.

A linear function is modeled by the following rule: y = mx + b

In which m is the slope, which is the rate of change, that is, the change in y divided by the change in x.

Here b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.

If the function is on a graph and it's a straight line then its linear.

If the function is not on a graph, it will fall under a few different formulas, but as a general rule if it does not have an exponent on the x or y then it'll be linear.

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The constant of proportionality is, 8/5. And the equation that represents this relationship is, [tex]y = \frac{8}{5}x[/tex].

What is constant of proportionality?

The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.

Let, the equation  [tex]\frac{Grape juice (x)}{Apple Juice(y)}[/tex] represent the relationship between the amount of apple juice, x, and the amount of grape juice, y, in the fruit punch.

From table we can write as,

[tex]\frac{Grape Juice (x)}{(Apple Juice(y)} = \frac{8}{5} =\frac{16}{10} = \frac{8}{5} = \frac{y}{x}[/tex]

⇒  y / x = 8 / 5

From above equation,

y = ( 8 / 5 ) x

This is the equation that represent the relationship between the amount of apple juice, x, and the amount of grape juice, y, in the fruit punch.

Hence, the constant of proportionality is, 8/5.

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Answer: 310

Step-by-step explanation:

1.Find your constant difference of the sequence by subtracting from left to right which is 9

2. find your fomula by using Tn=bn+C (b is your constant difference you can find C by C=T1 -b ) which will then give us 9n-5

3. T(35)=9n-5=9(35)-5=310

The null hypothesis rejects as the significance level  α= 0.10.

What is z test?

If the data is distributed normally, a z test can be used to determine whether the means of two populations differ from one another. The z test statistic's value must be determined, together with the null hypothesis and alternative hypothesis setups, for this reason. On the z critical value, the decision criterion is based. The distribution graph is divided into acceptance and rejection zones during hypothesis testing by the z critical value. The null hypothesis can be rejected if the test statistic lies inside the rejection region; otherwise, it cannot.

First off, because the sample size is greater than 30, this is a z test rather than a t test (i.e., 59 > 30).

Z = 2.15

Currently, the p value for the given value of Z is 0.0158.

That comes out to 0.01 0.0158 0.025.

Because the significance level, alpha = 0.10, is less than 0.01 p-value 0.025, the null hypothesis should be rejected.

Hence, The null hypothesis rejects as the significance level  α= 0.10.

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The 2003rd term of the sequence of odd numbers 1, 3, 5, 7, 9,.. is 4005.

It should be noted that this is an arithmetic sequence and the formula will be written as:

a + (n - 1)d

a = first term = 1

n = number of terms = 2003

d = common difference = 3 - 1 = 2

Therefore, the 2003rd term will be:

= a + (n - 1)d

= 1 + (2003 - 1) × 2

= 1 + (2002 × 2)

= 1 + 4004

= 4005

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The following are the offered rational exponents in expression form:

• (A) the fourth root's tenth root = [tex]\sqrt[10]{4}[/tex]

A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers. The following is the structure of an expression: Expression: The following rational exponents are expressed in the expression form (Math Operator, Number/Variable, Math Operator): (A) the tenth root of four= [tex]\sqrt[10]{4}[/tex]

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No, it is not possible to construct a triangle whose sides are 3. 5 cm 9. 2 cm and 5. 3 cm. Because the sum of the triangle's two sides, 3.5 cm and 5.3 cm, is not greater than the third side, 9.2 cm, the triangle cannot exist.

A triangle has three vertices, which connect the triangle's sides, which are all straight lines. The sides of a triangle are, in other words, line segments that converge at the triangle's vertices. An "opposite" side in a right triangle is the one that is across from a specific angle, and an "adjacent" side is the one that is next to a specific angle. The hypotenuse is the longest side in a right triangle.

Given,

Sides 3.5cm, 5.3 cm and 9.2 cm

Sum = 3.5 + 5.3

Sum = 8.8

There are three sides offered, with dimensions of 3.5 cm, 5.3 cm, and 9.2 cm. The third side is always greater than the sum of any two triangle sides, as we are all aware of. Because the sum of the triangle's two sides, 3 cm and 5 cm, is not greater than the third side, 8 cm, the triangle cannot exist.

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Three angles are 36° , 36° , 180°.

Let us denote first, second, third angle by a, b, c respectively.

It is given that second angle is the same as first angle which implies that,

⇒ b = a

And third angle is three times the first which implies that,

⇒ c = 3a

We know that sum of the angle of triangle is 180°.

Therefore a + b + c = 180°

⇒ a + a + 3a = 180°

              5a = 180°

                 a = 36°

That means b = 26 °

and c = 3a = 3(36°) = 108°

Hence three angles are 36°, 36°, 108°.

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The statement that is true about the Random Variable X is P(X ≥ 4) = 0.522  , the correct option is (a) .

In the question ,

it is given that ,

the possible values of the random variable X is 1, 2, 3, 4, and 5 .

given that , 2 is twice as likely as 1 , that means

p(2) = 2p(1)

3 is one-third as likely as 2 , that means

p(3) = 1/3 p(2)

4 is four times as likely as 3 , which is

p(4) = 4/3 p(2)

and 5 is half as likely as 4 , that means

p(5) = 2/3 p(2)

We know that ,

p(1) + p(2) + p(3) + p(4) + p(5) = 1

Substituting the values in the above equation , we get

1/2 p(2) + p(2) + 1/3 p(2) + 4/3 p(2) + 2/3 p(2) = 1

So , p(2) = 6/23

hence ,

P(X ≥ 4) = P(X=4) + P(X=5)

= (4/3) × (6/23) + (2/3) × (6/23)

On simplifying further ,

we get ,

= 0.522

Therefore , the value of P(X ≥ 4) is 0.522    .

The given question is incomplete , the complete question is

Let X be a random variable with possible values 1, 2, 3, 4, and 5. Assume that 2 is twice as likely as 1, 3 is one-third as likely as 2, 4 is four times as likely as 3, and 5 is half as likely as 4. Which of the following is true (to the nearest three decimals)

(a) P(X ≥ 4) = 0.522

(b) P(X = 1 or X = 5) = 0.329

(c) P(X ≤ 2) = 0.367

(d) P(X = 2 or X = 3) = 0.293

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The expected value of your profit is -0.25 which is loss, if probability of winning is 0.001.

The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions. In everyday speech, the term "probability" refers to the likelihood that a specific event (or set of events) will take place, expressed as a number between 0 and 100% or as a linear scale from 0 (impossibility) to 1 (certainty). Statistics is the study of events that follow a probability distribution.

Given,

Probability of winning = 0.001

probability of losing = 0.999

Expected value of profit can be calculated,

E(x)

= (749 x 0.001) + (-1 x 0.999)

= -0.25

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The value of x is in the solution set of 4x - 12 ≤ 16+8x is x ≥ -7.

Given inequality:

⇒ 4x - 12 ≤ 16+8x

rearranging the like terms

4x - 8x - 12 ≤ 16

4x - 8x ≤ 16+12

-4x ≤ 16+12

-4x ≤ 28

divide by 4 on both sides

-4x/4 ≤ 28/4

-x ≤ 28/4

-x ≤ 7

x ≥ -7.

Therefore the value of x is in the solution set of 4x - 12 ≤ 16+8x is x ≥ -7.

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The area of the Earth in standard form can be expressed as [tex]5*10^8[/tex] km².

What is the area of any geometrical shape?

The area of the shape on the paper is referred to as its Area. Consider your square to be made up of smaller unit squares. The area of a figure is calculated as the number of unit squares required to cover the entire shape.

Given data:

The area of the Earth covered by water  =  361 million km²

The area of the Earth not covered by water =  149 million km²

The total area of the Earth = Area of the Earth covered by water + Area of the Earth not covered by water

                                            = 361 + 149

                                             = 510 million km²

                                              = [tex]510*10^6[/tex] km²

                                              =   [tex]510*10^8[/tex] km².

Hence, the area of the Earth in standard form can be expressed as [tex]5*10^8[/tex] km².

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