Square $ABCD$ has side length 2. A semicircle with diameter $\overline{AB}$ is constructed inside the square, and the tangent to the semicircle from $C$ intersects side $\overline{AD}$ at $E$. What is the length of $\overline{CE}$

The sine function that matches the graph is given as follows:

y = 3sin(π/5(x + 0.5))

The sine function for this problem is defined as follows:

y = Asin(B(x - C)) + D.

The parameters are described as follows:

The function has a minimum value of -3 and a maximum value of 3, for a difference of 6, hence the amplitude is obtained as follows:

2A = 6

A = 3.

The function has no vertical shift, as it oscillates between -1 x 3 = -3 and 1 x 3 = 3.

The period is of 10 units, hence the coefficient B is given as follows:

2π/B = 10

10B = 2π

B = π/5.

Due to it's midline, the function was shifted 0.5 units left, hence the coefficient C is given as follows:

C = -0.5.

Hence the function is defined as follows:

y = 3sin(π/5(x + 0.5))

More can be learned about trigonometric functions at brainly.com/question/21558626

#SPJ1

The anti-derivative of g(x) is G(x) = x3 + 3x2 and the anti-derivative of f(x) is F(x) = x2 + 2x.

Part a:

The value of the integral from 0 to 6 of f(x)dx is 16. This can be calculated using the Fundamental Theorem of Calculus (FTC) which states that the integral of a function is equal to the anti-derivative of that function evaluated at the upper limit minus the anti-derivative of that function evaluated at the lower limit. This can be written as:

∫f(x)dx = F(6) - F(0)

The anti-derivative of f(x) is F(x) = x2 + 2x, so the value of the integral is:

∫f(x)dx = (62 + 2*6) - (02 + 2*0) = 36 - 0 = 16.

Part b:

The value of the integral from 4 to 9 of g(x)dx is 20. This can be calculated using the FTC which states that the integral of a function is equal to the anti-derivative of that function evaluated at the upper limit minus the anti-derivative of that function evaluated at the lower limit. This can be written as:

∫g(x)dx = G(9) - G(4)

The anti-derivative of g(x) is G(x) = x3 + 3x2, so the value of the integral is:

∫g(x)dx = (93 + 3*9) - (43 + 3*4) = 729 - 168 = 20.

Part c:

The value of the integral from 4 to 9 of 2*g(x) - f(x)dx is 68. This can be calculated using the FTC which states that the integral of a function is equal to the anti-derivative of that function evaluated at the upper limit minus the anti-derivative of that function evaluated at the lower limit. This can be written as:

∫(2*g(x) - f(x))dx = 2*G(9) - F(9) - [2*G(4) - F(4)]

The anti-derivative of g(x) is G(x) = x3 + 3x2 and the anti-derivative of f(x) is F(x) = x2 + 2x, so the value of the integral is:

∫(2*g(x) - f(x))dx = (2*(93 + 3*9) - (92 + 2*9)) - [2*(43 + 3*4) - (42 + 2*4)]

= (1854 - 19) - (544 - 16) = 1735 - 528 = 68.

Learn more about anti-derivative here:

https://brainly.com/question/21627352

#SPJ4

Discriminatory practises are those that have a disparate impact or treatment. When compared to differential treatment, which is deliberate discrimination, disparate impact is frequently referred to as inadvertent discrimination. Alternative words for this concept include adverse effect and adverse treatment.

Disparate treatment discrimination, put simply, is when a company treats a current employee or potential employee improperly due to that person's race, religion, colour, sex, national origin, etc. This type of discrimination is usually the most apparent and visible.

Disparate treatment and disparate impact are two different things; disparate treatment is purposeful discrimination, whereas disparate impact is accidental.

To know more about disparate treatment visit:

https://brainly.com/question/9811846

#SPJ4

The x-coordinates of the left edges of the rectangles are 1,5/4,6/4,7/4.

The area of this region with a Riemann Sum is 0.7595.

A specific type of approximation of an integral by a finite sum in mathematics is known as a Riemann sum. It bears the name of the German mathematician Bernhard Riemann from the nineteenth century. Approximating the area of functions or lines on a graph, as well as the length of curves and other approximations, is a highly typical use.

Given function is f(x) = 1/x on the interval [1,2] is shown.

The four rectangles of width 1/4 are present.

From the figure we can see that the x coordinate of the left edges of the rectangle are:

1,5/4,6/4,7/4

Now we plug these values in the function to find the height of rectangles.

For x=1 ,f(x) = 1

For x=5/4 ,f(x) = 4/5

For x=6/4 ,f(x) = 4/6

For x=7/4 ,f(x) = 4/7

Now, Area = length*width, and width of each rectangle is 1/4

Area of rectangle 1 = 1*1/4 = 1/4

Area of rectangle 2 = 4/5*1/4 = 1/5

Area of rectangle 3 = 4/6*1/4 = 1/6

Area of rectangle 4 = 4/7*1/4 = 1/7

Total Area is = 1/4+1/5+1/6+1/7  = 0.7595

This is an overestimation of ln(2).

To learn more about Riemann Sum visit:

https://brainly.com/question/29012686

#SPJ4

A quarter-circle with a radius of 5 has the area: 25π/4, This is where the shaded area in the figure is located.

The area of a circle’s sector is calculated as /360o (r²), where r is the radius of the circle and is the angle of the sector.

The little, subtle distinctions between words are distinguished by shades of meaning. The terms “happy” and “ecstatic,” for example, both express emotion, but one is more powerful than the other. When students study shades of meaning, they learn how to effectively articulate how they feel or think. Shade is any gloomy place where sunshine or other strong light is obstructed. A shadow is a dark form that develops on a surface when an item blocks sunlight or other light.

The shaded area in the illustration is a quarter-circle with a radius equal to 10/2, or 5 units, or half the length of the square's side.

The following formula can be used to determine a circle's area:

A = πr²

If pi is present and r is the radius (approximately equal to 3.14).

A quarter-circle with a radius of 5 has the following area:

A = (π × 5²) / 4 = (π × 25) / 4 = 25π / 4

This is where the shaded area in the figure is located.

To learn more about radius of the circle to refer:

brainly.com/question/11137975

#SPJ1

On solving the provided question, we can say that equation let x =amount of copies sold  = > 37,600is = .073  X x = 515,068.4932.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

let x =amount of copies sold to date.

37,600is = .073  X x

t x = 37,600 / .073

= 515,068.4932.

round to nearest 515,068.

To know more about equation visit:

https://brainly.com/question/649785

#SPJ4

The probability of getting a difference of 3 when two fair dice are thrown together is 1/9.

Probability is the measure of how likely it is that a certain event will occur. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that an event is certain. Probability can also be expressed as a percentage or fraction. Probability is used to describe the likelihood of an event occurring, and its calculation is based on the number of possible outcomes of the event.

This is due to the fact that there are 6 possible outcomes for each dice, and 36 possible outcomes when both dice are thrown. The only way to get a difference of 3 is for the first dice to show a 4 (1/6 probability) and the second dice to show a 1 (also 1/6 probability). This gives a combined probability of 1/6 x 1/6 = 1/36, which is 1/9.

To know more about probability click-
https://brainly.com/question/24756209
#SPJ4

The graph provided in the exercise must be used in this task, together with our statistical understanding, so that we can state: correct option is A

Statistics is a discipline of applied mathematics concerned with the gathering, description, analysis, and derivation of inferences from quantitative data. Calculus of differential and integrals, linear algebra, and probability theory are key mathematical concepts in statistics.

Statistics provide us the knowledge we need to understand how things operate. To conduct research, assess results, foster critical thinking, and make wise judgements, statistics are utilized. Almost any subject of study may benefit from the application of statistics to explore the causes, timing, and predictability of events.

The maximum points on the graph are at 21 and 31, and the sample ranges appear to be centered below 32, so we may claim so the option A is more appropriate.

To know more about statistics refer to:

https://brainly.com/question/15525560

#SPJ4

The complete question is as follows:

Answer:

Step-by-step explanation:

To find the annual tax withheld, you would need to calculate the amount of income tax that you owe based on your income and the state income tax rate.

You earn $56,000 per year and the state income tax rate is 5.5%. To find the amount of tax you owe, you would multiply your income by the tax rate.

Tax Owed = Income x Tax Rate

Tax Owed = 56,000 x 0.055

Tax Owed = 3,080

So, the annual tax withheld from your salary would be $3,080.

Answer: 6.2

Step-by-step explanation:

Using the arc length formula,

[tex]x=\frac{118}{360}(2)(3)(\pi) \approx 6.2[/tex]

Answer:

The answer is A.

Step-by-step explanation:

Lets prove the other ones wrong.

B) It is not based on a day to day prediction, rather days with simmilar conditions before the storm.

C) The United states is too broad an area.

D) It is not based on the ammount of days it snows per month, because on say December 15 it could be 60 degrees and on December 25 it could be 2 degrees. Also you could not make any predictions on a per-day basis then.

So the only clear answer is "Historically, in this area, it has snowed 10% of the time on days with similar meteorological conditions as today."

The probability that the quarterback completes his first pass on his 4th attempt is 0.44

The term probability in math is defined as the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes

Here we have given that assume a quarterback completes 44% of his passes.

Here we have to convert the percentage into decimal form, then we get,

=> 44/100

When we divide it, then we get the probability that the quarterback completes his first pass on his 4th attempt is written as,

=> 0.44

To know more about probability here.

https://brainly.com/question/11234923

#SPJ4

The equation which is graphed in this figure (see attachment) is: C. y + 2 = −3/2(x − 2)

"y plus 4 equals negative fraction 3 over 2 end fraction left parenthesis x minus 2 right parenthesis."

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

From the information provided about this graph, we have the following data points on its line:

Points on the x-axis = (0, 2).

Points on the y-axis = (1, -2).

At data point (0, 3), a linear equation of the first line can be calculated in slope-intercept form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-2) = (-2 - 1)/(2 - 0)(x - 2)

y + 2 = -3/2(x - 2)

Read more on slope here: https://brainly.com/question/11586413

#SPJ1

24 different seatings are possible when five people are to be seated around a circular table such that two seatings are considered the same if one is a rotation of the other.

What is fundamental counting principle?

A rule used to count the entire number of alternative outcomes in a circumstance is known as the fundamental counting principle. It asserts that if there are n ways to do something and then m ways to do something else, then there are nm methods to do both of these acts. The Fundamental Principle of Counting assists in determining how selection is made based on available options. The Fundamental Principle of Counting streamlines the method to choosing by taking into account all of the available options and their combinations in order to calculate the Probability.

Here,

Since there are 5 peoples,

let us fix the first person and remaining will be set according to that.

this can be arranged in,

(5-1)!=4!

=24 ways

When five persons are sitting around a circular table, 24 distinct seatings are available, with two seatings regarded the same if one is a rotation of the other.

To know more about rotation here

brainly.com/question/4747487

#SPJ4

There is no solution that satisfy the equation (1,1,1) x u = (7, -4, -3).

The term "vector" in mathematics and physics is used informally to refer to some values that cannot be stated by a single integer (a scalar) or to certain members of vector spaces. Though the components of an algebra are frequently not referred to as vectors, any algebra over a field is a vector space. They are sometimes referred to as vectors, mostly for historical reasons.

A real number is a number that can be used to represent a continuous one-dimensional quantity in mathematics, such as a temperature, duration, or distance. Continuous in this context suggests that values may vary by arbitrary little amounts. An infinite decimal expansion can nearly always represent any real number.

There is no value, not even 0, that would satisfy the equation, which is referred to as "no solution."

To learn about Vectors :

https://brainly.com/question/25705666

#SPJ4

The length of segment  is 24/√2

Given that,

Having radii of 2 and 4, respectively, and being externally tangent, are circles with centers O and P. The circle with the center at O has points A and B, while the circle with the center at P has points C and D, so that

AD and BC are frequent tangents to the outside of the circles.

To find : What is the hexagon's area?

ADPO and OPBC are congruent right trapezoids with legs 2 and 4 and with OP equal to 6. Draw an altitude from O to either DP or CP,

Creating a rectangle with width 2 and base x, and a right triangle with one leg 2, the hypotenuse 6, and the other aa Using the Pythagorean theorem,  is equal to  , and x is also equal to the height of the trapezoid. The area of the trapezoid is thus

length = 1/2 * (4+2).4√2 = 12√2

and the total length is two trapezoids, or 24/√2

To learn more about length click here:

brainly.com/question/16615236

#SPJ4

On solving the provided question, we can say that by unitary method she work rate = 24 hours x 3/120 = 72/120

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

she painter work rate i=1/40= 3/120 40 hours to complete

her assistant work rate= 1/60 = 2/120  60 hours to complete.

Combined work = 5/120

house could be painted in 24 hours each with both of them working together.

she work rate = 24 hours x 3/120 = 72/120

To know more about unitary method  visit:

https://brainly.com/question/28276953

#SPJ4

Answer:

0.850

Step-by-step explanation:

The first step is to write the number in standard form. Then, you place the decimal point in the quotient above the decimal point of the dividend. Then, divide and bring down the other digits such as hundredths, thousandth, and ect.

The perimeter of the rectangular community garden, after the size has been altered by a factor of 20, is 130 feet.

In two-dimensional shapes, a perimeter is defined to be a closed path that surrounds or outlines a shape. The perimeter of a circle or an ellipse though is called the circumference.

The perimeter P of a rectangle is equal to two times the length l plus two times the width w [P = 2(l + w)]. The length and the width of the rectangular community garden are consecutively 2,25 and 1 feet, and the scale factor is 20.

Therefore, the perimeter of the community garden is

P = 2(l + w) · 20

P = 2(2,25 + 1) · 20

P = 6.5 · 20

P = 130 feet.

This question refers to the image attached.

Learn more about an example of finding a perimeter at https://brainly.com/question/397857.

#SPJ4

Answer:

130 feet

Step-by-step explanation:

The positive and negative roots of the given quadratic graph are; -2 and 4.

We want to find the positive and negative roots of the quadratic graphs. Now, the general form of quadratic equations is expressed as;

y = ax² + bx + c

Now, for a quadratic graph, the roots are defined as the value of x where the curve crosses the x-axis.

In this given graph, we can see that the y-intercept which is the point at which the curve crosses the y-axis is at y = -8. We also see that the points at which the graph crosses the x-axis are at x = -2 and x = 4. This clearly shows that one root is positive and one root is negative.

Therefore from the two x-intercept values above as well as the y-intercept we got and when considering the type of roots that are being looked for, we can easily conclude that the positive and negative roots are as gotten above.

Read more about Quadratic Graph at; https://brainly.com/question/14477557

#SPJ1

The radius of the circle will be [tex]\sqrt{22}[/tex].

In our question, we shall first extend QRS to the circle's point T.

According to the power of a point.

[tex]QP^{2}[/tex]  =  QR*QT

[tex]6^{2}[/tex]  =  3*QT

QT = 12

Since QR = 3, RT = 9.

Since RS = 3, ST = 6.

Draw OT and OR, creating a triangle(TSO) and triangle(RSO).

OT and OR are radii, Let the radius be r.

Use the Law of Cosines on these two triangles.

OT2  =  [tex]r^{2}[/tex]  =  [tex]6^{2}[/tex] + [tex]2^{2}[/tex] - 2*6*2*cos(TSO)

OR2  =  r2  =  [tex]3^{2}[/tex] + [tex]2^{2}[/tex] - 2*3*2*cos(RSO)

Since these are equal:

[tex]6^{2}[/tex] + [tex]2^{2}[/tex] - 2*6*2*cos(TSO)  =  [tex]3^{2}[/tex] + [tex]2^{2}[/tex] - 2*3*2*cos(RSO)

40 - 24*cos(TSO)  =  13 - 12*cos(RSO)

Since angle(RSO) is supplementary to angle(TSO),  cos(RSO) = - cos(TSO)

40 - 24*cos(TSO)  =  13 + 12*cos(TSO)

27  =  36*cos(TSO)

0.75  =  cos(TSO)

Since  [tex]OT^{2}[/tex]  =  [tex]r^{2}[/tex]  =  [tex]6^{2}[/tex] + [tex]2^{2}[/tex] - 2*6*2*cos(TSO)

[tex]r^{2}[/tex]  =  40 - 24*0.75  

[tex]r^{2}[/tex]  =  22

r  =  [tex]\sqrt{22}[/tex]

Hence the radius of the given circle will be [tex]\sqrt{22}[/tex].

To learn more about Circle Properties, visit: https://brainly.com/question/29292384

#SPJ4

Answer:

yes because it's like multiplying my 1/2.

when you multiply a number with a fraction its the same as dividing.

Step-by-step explanation:

Example: 6/1 × 1/2 = 3

The system of equations to describe the condition is,

22x + 74y = 10274

48x +  61y = 10261

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

Yesterday, the organization sold 22 regular tickets and 74 VIP tickets, raising $10,274

Today, 48 regular tickets and 61 VIP tickets were sold, bringing in a total of $10,261

Cost of regular ticket = ?

Cost of VIP ticket = ?

Suppose,

Cost of regular and VIP ticket are respectively,  x & y

22x + 74y = 10274

48x +  61y = 10261

To know more about Equation check:

https://brainly.com/question/1529522

#SPJ1

Answer:

Step-by-step explanation:

width = 3x + 1

height = (24x^3 - 58x^2 + 23x + 15) / (12x^2 - 11x - 5)

Answer:

The tablecloth overhang is the amount of tablecloth that hangs over the edges of the table.

The area of the square table is 1.3m * 1.3m = 1.69m^2.

The area of the round tablecloth is pi * (diameter/2)^2 = pi * (2/2)^2 = pi * 1^2 = pi * 1 = pi m^2.

The overhang is the difference between the area of the round tablecloth and the square table.

Overhang = pi m^2 - 1.69m^2 = pi - 1.69

To find the percentage of the tablecloth that overhangs the table, we can divide the overhang by the area of the tablecloth and multiply by 100.

Overhang % = (pi - 1.69) / pi * 100 = (pi - 1.69) / pi * 100 = (3.14 - 1.69) / 3.14 * 100 = 1.45 / 3.14 * 100 = 46.14%.

So, the percentage of the tablecloth that overhangs the table is 46.14%.

The surface area of the ice is 16π square inches. At a rate of 10 cubic inches per min, the outer surface area of the ice is changing at  10/16π square inches per min.

To calculate this we have given:

The diameter of the spherical ball is 8 inches, so the radius of the ball is 8/2 = 4 inches.

The volume of a sphere is given by the formula (4/3)πr³, where r is the radius of the sphere.

The volume of the spherical ball with 2 inches of ice is (4/3)π(4³) = (4/3)π64 cubic inches.

The volume of the ice is the volume of the spherical ball with 2 inches of ice minus the volume of the spherical ball without the ice, which is (4/3)π(4³) - (4/3)π(4³ - (2³)) = (4/3)π64 - (4/3)π32 = 32π cubic inches

At a rate of 10 cubic inches per min, the thickness of the ice is decreasing at:

10 cubic inches / 32π cubic inches = 10/32π inches per min

To find the rate at which the outer surface area of the ice is changing, we can use the formula for the surface area of a sphere which is 4πr².

The surface area of the ice is 4π(4-2)³ = 4π4 = 16π square inches.

At a rate of 10 cubic inches per min, the outer surface area of the ice is changing at:

10 cubic inches / 16π square inches = 10/16π square inches per min

To learn more about the area, visit:

brainly.com/question/16151549

#SPJ4

0.1728 suburban park users bike on the park trail.

A mathematical comparison of two numbers is called a proportion.

It is an equation or statement used to depict that two ratios or fractions are equal.

According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

The proportion (p) is calculated as:

p = bike the trail/number of residents

Given that,

The number of users who bike the trail = 42

The number of residents using the park trails = 243

Thus,

p = 42/243 = 0.1728

Therefore, 0.1728 suburban park users bike on the park trail.

To know more about proportion visit: brainly.com/question/29126329

#SPJ4

Answer:

m(w) = $25+$20w

Step-by-step explanation:

Let m be the amount saved and w the weeks since the account was opened.  Greta starts with $25, so m(0) = $25.

She saves $20 each week, w.  m(1), the end of the first week, Greta would have $25 + $20 = $45.  This continues for future weeks.  We could write this as the follwoing:

 m(w) = $25+$20w

Week 5, for example, would end with m(5) = $25+$20*(5)

       m(5) = $125.

The average speed of the bus is 54.78 mph.

To find the average speed of the bus, we need to find the total distance traveled and the total time taken for the entire trip.

Distance traveled = 10 miles + 17 miles + 95 miles + 4 miles = 126 miles

To find the total time taken, we need to calculate the time taken for each segment of the trip and add them up.

Time taken for 10 miles at 25 mi/h = 10 miles / 25 mi/h = 0.4 hours

Time taken for 17 miles at 45 mi/h = 17 miles / 45 mi/h = 0.378 hours

Time taken for 95 miles at 80 mi/h = 95 miles / 80 mi/h = 1.1875 hours

Time taken for 4 miles at 12 mi/h = 4 miles / 12 mi/h = 0.333 hours

Total time taken = 0.4 hours + 0.378 hours + 1.1875 hours + 0.333 hours = 2.3 hours

Average speed = total distance / total time = 126 miles / 2.3 hours = 54.78 mph

So, the average speed of the bus is 54.78 mph.

To learn more about average speed, refer to the link:brainly.com/question/12322912

#SPJ4

The like radical to [tex]3\sqrt[4]{5x}[/tex] is given as follows:

[tex]7\sqrt[4]{5x}[/tex]

Like radicals are two radical expressions that have the same indices and radicand.

The concepts of the index and of the radicand of a radical are given as follows:

In the context of this problem, the radical expression is presented as follows:

[tex]3\sqrt[4]{5x}[/tex]

Hence the index and the radicand are given as follows:

Applying the concept of like radicals, any expression in this format is a like radical to 4 √ 5x.

n(4 √ 5x).

That is, any multiple of the term.

This means that the correct option is given by the first option, with n = 4.

More can be learned about like radicals at brainly.com/question/27497817

#SPJ1