The average age of 5 students is 10 years. The age of one student is 6. What is the average age of the remaining 4 students?​

Answer:

  y = -10·sin(πt/5) +12

Step-by-step explanation:

You want the equation of the height of a rider of a Ferris wheel that has a radius of 10 and is 2 off the ground, with a period of 10 seconds, moving downward, starting from even with the center.

The general form of the equation will be ...

  y = A·sin(2πt/T) + B

where A is a scale factor that is based on the radius and initial direction, and B is the height of the center of the wheel above the ground.

We assume that 2 [units] off the ground means the low point of the travel is at that height. Then the middle of the wheel is those 2 [units] plus the radius of the wheel:

  B = 2 + 10 = 12

The scale factor A will be the radius of the wheel, made negative because the initial direction is downward from the initial height. That is, ...

  A = 10

The period (T) is given as 10 seconds.

Putting these parameters together gives ...

  y = -10·sin(2πt/10) +12

  y = -10·sin(πt/5) +12

__

Additional comment

We wonder if this wheel is really only 20 inches (20 in) in diameter, as that dimension seems suitable only for a model. We suspect it is probably 20 meters (20 m) in diameter.

Sometimes "m" is confused with "in" when it is written in Roman font and reproduced with poor resolution.

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The product of given two binomials which are (x-7)(x-7) is equal to x² - 14x + 49.

To multiply the binomials (x-7)(x-7), we use the distributive property of multiplication, which states that:

(a + b)(c + d) = ac + ad + bc + bd

Using this property, we can expand the expression as follows:

(x-7)(x-7) = x(x-7) - 7(x-7)

= x² - 7x - 7x + 49

= x² - 14x + 49

The distributive property of multiplication is a mathematical rule that states that when a number is multiplied by the sum of two or more numbers, it is equivalent to multiplying the number by each of the addends and then adding the products.

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The measure in radians for the central angle is approximately 0.7 radians.

To find the measure in radians for the central angle of a circle, we can use the formula:

θ = s / r

where θ is the central angle in radians, s is the intercepted arc length, and r is the radius of the circle.

In this case, the radius is given as 8 cm and the intercepted arc length is 5.6 cm.

Plugging these values into the formula, we have:

θ = 5.6 cm / 8 cm

Simplifying the expression:

θ = 0.7

We may use the following formula to get the centre angle of a circle's measurement in radians:

= s / r

s is the length of the intercepted arc, r is the circle's radius and is the centre angle in radians.

The intercepted arc length in this instance is 5.6 cm, while the radius is specified as 8 cm.

When these values are plugged into the formula, we get:

θ = 5.6 cm / 8 cm

Condensing the phrase:

θ = 0.7

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Answer:

Center: (-3, 2)

Radius: 4

Step-by-step explanation:

x2 + 6x + y2 - 4y = 3​

x² + 6x + 9 + y² - 4y + 4 = 3 + 9 + 4

(x + 3)² + (y - 2)² = 16

(x + 3)² + (y - 2)² = 4²

Center: (-3, 2)

Radius: 4

The solution of expression ∫ (0 to 10) (x + 1) dx is,

⇒ 60

We have to given that,

Expression to solve,

⇒ ∫ (0 to 10) (x + 1) dx

Now, We can simplify as,

⇒ ∫ (0 to 10) (x + 1) dx

⇒ ∫ (0 to 10) (x) dx + ∫ (0 to 10) dx  

⇒ (x² / 2)₀¹⁰ + ((x)¹⁰₀

⇒ 1/2 (10² - 0) + (10 - 0)

⇒ 1/2 × 100 + 10

⇒ 50 + 10

⇒ 60

Therefore, The solution of expression ∫ (0 to 10) (x + 1) dx is,

⇒ 60

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5. GH= 3

HI= 3x-9 and x=4

HI= 3(4)-9=

= 12-9

= 3

so, GH = HI

Do the same for GJ and JI.

6. 36=2x

18=x

So, the angles are the same.

4x-11=61

4(18)-11=61

So, the sides are also the same meaning the triangles are congruent.

Using concepts of the normal and of the uniform distribution, it is found that the correct option is:

The distribution is approximately Normal, with a mean of 8 ounces and a standard deviation of 1.2 ounces.

In an uniform distribution, all outcomes are equally as likely, thus they have the same height.

In the normal distribution,

The outcomes with the highest likelihood are those closest to the mean, thus they have the highest height.

This means that the mean of this distribution is 8.

The standard deviation cannot be a negative value,

So in this problem, it is 1.2,

Which means that the correct option is:

The distribution is approximately Normal, with a mean of 8 ounces and a standard deviation of 1.2 ounces.

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Answer:0

Step-by-step explanation:

so if x = -3 that means u take -3 * 2 and u get -6 because a negative * A positive is negative so -6 + 6 is 0

Answer:

0

Step-by-step explanation:

Just substitute x=-3

2x+6 =

2(-3) + 6 =

-6 + 6 = 0

The complex number in standard form is written as:

Z =  1.99 + i*0.201, so the correct option is a

Remember that a complex number can be written in standard form as:

Z = a + b*i

And in polar form the notation is (R, θ):

[tex]Z = R*e^{i*\theta} = R*cos(\theta) + i*R*sin(\theta)[/tex]

Here we have the complex number:

Z = 2(cos(11pi/6) + i*sin(11pi/6))?

So here we just need to solve these expressions, we will get:

Z = 2*(0.995 + i*0.100)

Z =  1.99 + i*0.201

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Complete question:

"Convert the polar representation of this complex number into its standard form: z = 2(cos 11pi/6+ i sin 11pi/6)? "

The height h of the cylinder is 9 meters.

A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.

The surface area of a cylinder is expressed as;

Surface Area = 2πrh + 2πr²

Given that; the surface area is 104π m² and the radius as 4 m.

We need to solve for the height (h).

Plug the values into the above formula:

Surface Area = 2πrh + 2πr²

104π = 2πrh + 2πr²

104π = 2π( rh + r² )

Divide through by 2π

52 = rh + r²

52 = ( 4 × h) + ( 4² )

52 = 4h + 16

Subtract 16 from both sides

52 - 16 = 4h + 16 - 16

52 - 16 = 4h

36 = 4h

4h = 36

h = 36/4

h = 9 meters

Therefore, the height is 9 meters.

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The x-intercepts, in order from least to greatest, are (2.46, 0) and (5.54, 0).

Use the vertex form of a quadratic function, which is [tex]y = a(x-h)^2 + k,[/tex] where (h, k) is the vertex and "a" is the coefficient of the[tex]x^2[/tex]term. Since the vertex is at (4, 8 1/3), the quadratic function's equation is y = a(x-[tex]4)^2 + 8 1/3.[/tex]

Use the y-intercept to find the value of "a".

The y-intercept is (0,3), so when x=0, y=3.

Plugging these values into the equation above, we get: [tex]3 = a(0-4)^2 + 8 1/3[/tex].

Simplifying, we get 3 = 16a + 25/3, or 9/3 = 16a. Therefore, a = 9/48 or a = 3/16.

To obtain the complete equation, enter the value of "a" into the vertex form equation: [tex]y = (3/16)(x-4)^2 + 8 1/3.[/tex]

To find the x-intercepts, set y = 0 and solve for x.

The equation becomes: [tex]0 = (3/16)(x-4)^2 + 8 1/3[/tex].

Subtracting 8 1/3 from both sides, we get: [tex]-8 1/3 = (3/16)(x-4)^2[/tex]. Multiplying both sides by -1, we get: [tex]8 1/3 = (3/16)(x-4)^2.[/tex]

Take the square root of both sides to isolate[tex]x-4: \sqrt{(8 1/3) } = \sqrt{((3/16)(x-4)^2)}[/tex] Simplifying,

we get: [tex]\sqrt{(25/3)} = (3/4)(x-4).[/tex]

Solving for x, we get two solutions: [tex]x = 4 + 4\sqrt{(3)/3 } or x = 4 - 4\sqrt{(3)/3 }[/tex]

Sort the answers in order of best to worst. The x-intercepts are (2.46, 0) and (5.54, 0) because the first answer is around 5.54 and the second solution is roughly 2.46.

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The value of angle L is 61°

Exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.

If angle A and B are interior angles and angle C is the exterior angle, what this theorem is saying is that;

A+B = C

Similarly,

angle L and angle E are the interior angles and 113 is the exterior angle, therefore;

113 = L + 52

L = 113 -52

L = 61°

Therefore angle L is 61°

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Answer:

[tex]m = \frac{1 - ( - 3)}{0 - ( - 4)} = \frac{4}{4} = 1[/tex]

In accounting, the accounting equation is a fundamental principle that describes the relationship between a company's assets, liabilities, and equity. This equation is represented as Assets = Liabilities + Equity. Every financial transaction that a company undertakes has an impact on at least two of the components of the accounting equation.

Transaction Analysis:

a. The company completed consulting work for a client and immediately collected $5,600 cash earned.

This transaction increases both cash and revenue. There is no impact on liabilities or equity.

Accounts Affected:

Cash: +$5,600

Revenue: +$5,600

b. The company completed commission work for a client and sent a bill for $4,100 to be received within 30 days.

This transaction does not impact any account initially. Revenue will increase when payment is received.

Accounts Affected:

Accounts Receivable: +$4,100

Revenue: +$0

c. The company paid an assistant $1,450 cash as wages for the period.

This transaction decreases cash and increases expenses. There is no impact on liabilities or equity.

Accounts Affected:

Cash: -$1,450

Expenses: +$1,450

d. The company collected $2,050 cash as a partial payment for the amount owed by the client in transaction b.

This transaction increases cash and decreases accounts receivable. There is no impact on liabilities or equity.

Accounts Affected:

Cash: +$2,050

Accounts Receivable: -$2,050

e. The company paid $720 cash for this period's cleaning services.

This transaction decreases cash and increases expenses. There is no impact on liabilities or equity.

Accounts Affected:

Cash: -$720

Expenses: +$720

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Complete Question

The following transactions were completed by the company

a. The company completed consulting work for a client and immediately collected $5,600 cash earned.

b. The company completed commission work for a client and sent a bill for $4,100 to be received within 30 days.

c. The company paid an assistant $1,450 cash as wages for the period.

d. The company collected $2,050 cash as a partial payment for the amount owed by the client in transaction b

e. The company paid $720 cash for this period's cleaning services  Required: Enter the impact of each transaction on individual items of the accounting equation. (Enter decreases to account balances with a minus sign.)

The equation of the line is y = x/7 - 1/7

The equation of a straight line is y=mx+c . Where m is the gradient or slope and c is the height at which the line crosses the y -axis, also known as the y -intercept.

The equation of a line can be expressed as;

y-y1 = m(x -x1)

where m is the slope

The slope = 1/7

x1 = 8 and y1 = 1

Therefore;

y -1 = 1/7( x -8)

7(y-1) = x-8

7y -7 = x-8

collecting like terms

7y = x - 8+7

7y = x -1

y = x/7 -1/7

The intercept is -1/7 and the slope is 1/7

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Using the intersecting chord theorem, we can calculate the value of x as: 12

The intersecting chord theorem states that If two chords intersect in a circle , then the products of the measures of the segments of the chords are equal.

Applying the intersecting chord theorem to the two chords of the circle, we can say that:

3x = (9 * 4)

3x = 36

x = 36/3

x = 12

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The distance between each pair of points include the following:

44. 2.8 units.

45. 5.8 units.

46. 12.0 units.

47. 16.6 units.

48. 7.1 units.

49. 4.5 units.

In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

Question 44.

By substituting the given end points into the distance formula, we have the following;

Distance = √[(3 - 1)² + (2 - 4)²]

Distance = √[(2)² + (-2)²]

Distance = √8

Distance = 2.8 units.

Question 45.

By substituting the given end points into the distance formula, we have the following;

Distance = √[(-2 + 7)² + (0 - 3)²]

Distance = √[(5)² + (-3)²]

Distance = √34

Distance = 5.8 units.

Question 46.

By substituting the given end points into the distance formula, we have the following;

Distance = √[(-6 - 2)² + (-2 - 7)²]

Distance = √[(-8)² + (-9)²]

Distance = √145

Distance = 12.0 units.

Question 47.

By substituting the given end points into the distance formula, we have the following;

Distance = √[(1 - 8)² + (-8 - 7)²]

Distance = √[(-7)² + (-15)²]

Distance = √274

Distance = 16.6 units.

Question 48.

By substituting the given end points into the distance formula, we have the following;

Distance = √[(-5 - 2)² + (-4 + 5)²]

Distance = √[(-7)² + (1)²]

Distance = √50

Distance = 7.1 units.

Question 49.

By substituting the given end points into the distance formula, we have the following;

Distance = √[(5 - 3)² + (5 - 1)²]

Distance = √[(2)² + (4)²]

Distance = √20

Distance = 4.5 units.

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The triangles are not similar

Given data ,

Let the first triangle be ΔJKL

Let the second triangle be ΔMNP

Now , the corresponding sides are

JK / JL ≠ NM / MP

where the corresponding sides of similar triangles are not in the same ratio

And , the common angle to both the triangles is ∠J = ∠M

So , ∠J = ∠M and JK / JL ≠ NM / MP

Hence , the triangles are not similar

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Answer:

Elle should buy 1 gallon of milk for $3.

Step-by-step explanation:

In one gallon of milk, there are four quarts. So we can multiply the number of gallons by four to convert it to quarts.

(1 gallon)x(4 quarts) = 4 quarts in one gallon

4 quarts is greater than 2 quarts so 1 gallon for $3 is a better deal than 2 quarts for $3.

In Functions and Function Notation, we were introduced to the concepts of domain and range. In this section we will practice determining domains and ranges for specific functions. Keep in mind that, in determining domains and ranges, we need to consider what is physically possible or meaningful in real-world examples, such as tickets sales and year in the horror movie example above. We also need to consider what is mathematically permitted. For example, we cannot include any input value that leads us to take an even root of a negative number if the domain and range consist of real numbers. Or in a function expressed as a formula, we cannot include any input value in the domain that would lead us to divide by 0.

Diagram of how a function relates two relations.

We can visualize the domain as a “holding area” that contains “raw materials” for a “function machine” and the range as another “holding area” for the machine’s products.

We can write the domain and range in interval notation, which uses values within brackets to describe a set of numbers. In interval notation, we use a square bracket [ when the set includes the endpoint and a parenthesis ( to indicate that the endpoint is either not included or the interval is unbounded. For example, if a person has $100 to spend, he or she would need to express the interval that is more than 0 and less than or equal to 100 and write

(

0

,

100

]

. We will discuss interval notation in greater detail later.

Let’s turn our attention to finding the domain of a function whose equation is provided. Oftentimes, finding the domain of such functions involves remembering three different forms. First, if the function has no denominator or an even root, consider whether the domain could be all real numbers. Second, if there is a denominator in the function’s equation, exclude values in the domain that force the denominator to be zero. Third, if there is an even root, consider excluding values that would make the radicand negative.

Before we begin, let us review the conventions of interval notation:

The smallest term from the interval is written first.

The largest term in the interval is written second, following a comma.

Parentheses, ( or ), are used to signify that an endpoint is not included, called exclusive.

Brackets, [ or ], are used to indicate that an endpoint is included, called inclusive.

The required angles are,

∠BAC = 73 degree

∠BCA = 17 degree

∠DCF = 17 degree

∠CDF = 80 degree

∠CFD = 95 degree

Since we can see that,

In triangle ABC

The angle B is right angled

Since we know that,

Sum of interior angles of triangle = 180 degree

Therefore, in triangle ABC

⇒ (9x -8 ) + (2x-1) + 90 = 180

⇒ 11x  = 99

⇒    x  = 9

Thus,

Angle BAC =  9x - 8

                   = 9x9 - 8

                   = 73 degree

Angle BCA = 2x - 1

                   = 2x9 - 1

                    =  17 degree

Now in triangle, CDF,

Angle C is alternate angle for both the triangles,

Therefore,

Interior angle C of triangle CDF = angle DCF = 17 degree

Angle CDF = 9y  - 1

                   = 9x9 - 1

                   = 80 degree

Angle CFD = 11y + 4

                   = 11x9 - 4

                   = 95 degree

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The percentage of people with blood pressure below 133 is 78.81%.

First, we need to calculate the Z-score for the value 133 using the formula:

Z = (X - μ) / σ

where X is the value (133), μ is the mean (121), and σ is the standard deviation (15).

Z = (133 - 121) / 15

Z = 12 / 15

Z = 0.8

Next, we can use a standard normal distribution table or a calculator to find the area under the curve to the left of the Z-score 0.8.

Looking up the Z-score of 0.8 in the standard normal distribution table, we find that the area to the left of 0.8 is 0.7881.

Therefore, the percentage of people with blood pressure below 133 is 78.81%.

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Note that in this case, the missing information which is the shortest time is 27 minutes. this is computed using the knowledge of the range.

The range of a collection of data in statistics is the difference between the highest and smallest values, calculated by subtracting the sample maximum and minimum. It's measured in the same units as the data.

Thus,

Range = Longest time - Shortest time

Since

Mean: 39 minutes

Range: 26 minutes

Longest time: 53 minutes

Shortest time = Longest time - Range

⇒  Shortest time = 53 - 26

= 27 minutes.

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The simplification of the expression, ∛8x⁴y⁸ / 125 is [tex]\frac{2\sqrt[3]{x^{4}y^{8} } }{5}[/tex].

The exponential expression can be solved as follows:

Therefore, let's simplify the expression.

To simplify the expression we have to deal with the exponential by applying it laws and also the cube root.

∛8x⁴y⁸ / 125

let's solve them individually,

125 = 5³ = 5 × 5 × 5

8 = 2³ = 2 × 2 × 2

Therefore,

∛8x⁴y⁸ / 125 = [tex]\frac{2\sqrt[3]{x^{4}y^{8} } }{5}[/tex]

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The surface area of the cylinder has a radius of 8cm and a height of 10 cm is 502.4 square centimeters.

We know that,

In geometry, a cylinder is one of the basic 3d shapes with two parallel circular bases at a distance. A curving surface connects the two circular bases at a predetermined distance from the centre. The axis of the cylinder is the line segment connecting the centres of two circular bases. The height of the cylinder is defined as the distance between the two circular bases. One real-world example of a cylinder is an LPG gas-cylinder.

The surface area of this cylinder is defined as the product of the radius of the base and the height of the cylinder.

The surface area of this cylinder = (2π x r)h

We have given a radius of the base is 8 cm and the height of the cylinder is 10 cm.

The surface area of this cylinder = (2π x r)h

= (2π x 8)10

= (50.24)10

= 502.4

Thus, The surface area of the cylinder has a radius of 8cm and a height of 10 cm is 502.4 square centimeters.

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The complete question is attached below:

Thanks to the other user

To find the decimal equivalent of 2/5, you can divide the numerator (2) by the denominator (5):

2 ÷ 5 = 0.4

Therefore, the decimal equivalent to 2/5 is 0.4.

a) The area of the entire trapezoidal rear window =  882 sq.in.

b) The fractional part of a complete circle is cleared on the rear window by the 18-inch wiper = 5/12

c) The area of the part of the rear window that is cleared by the wiper = 424.12 sq. in.

d) The percent of the area of the entire rear window is cleared by the wiper =  48.09%

We know that the formula for the area of trapezoid,

A = ((a + b) / 2) × h

Here, a = 36 in., b = 48 in. and height of the trapezoid h=21 in

Using above formula, the area of the entire trapezoidal rear window would be,

A = ((36 + 48) / 2) × 21

A = 882 sq.in.

Here, the 18-inch rear window wiper clears a 150° sector of a circle on the rear window.

We know that the measure of entire circle = 360°

So, the fractional part of a complete circle is cleared on the rear window by the 18-inch wiper would be,

150° / 360° = 5/12

Now we need to find the area of the part of the rear window that is cleared by the wiper.

We know that the formula for the area of sector of a circle is:

A = (θ/360) × πr²

Here, the central angle θ = 150° and radius r = 18 in.

A = (θ/360) × πr²

A = (150/360) × π × 18²

A = 424.12 sq. in.

Now we need to find the percent of the area of the entire rear window is cleared by the wiper.

P = [(area of the part of the rear window cleared by the wiper) / (area of the entire trapezoidal rear window)] × 100

P = (424.12 / 882) × 100

P = 48.09%

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In a rectangle, the value of x is,

⇒ x = 5

We have to given that;

ABCD is a rectangle.

And, AC = 5x + 2

BD = x + 22

Since, We know that;

Diagonal of a rectangle are equal in length.

Hence, We get;

AC = BD

(5x + 2) = (x + 22)

5x - x = 22 - 2

4x = 20

x = 20/4

x = 5

Thus, the value of x is,

⇒ x = 5

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The value of x for the angle (3x + 43)° on the pair of parallel lines cut by a transversal line is equal to 3

When a transversal line intersects a pair of parallel lines, several angles are formed which includes: Corresponding angles, vertical angles, alternate angles, complementary and supplementary angles.

(2x - 13) + 123 = 180° {supplementary angles}

2x - 13 + 123 = 180°

2x + 110 = 180

2x = 180 - 110 {collect like terms}

2x = 70

x = 70/2 {divide through by 2}

x = 35

Therefore, the value of x for the angle (3x + 43)° on the pair of parallel lines cut by a transversal line is equal to 3

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Based on the information provided, it seems that you have a rectangular grid with a shaded area, and the grid contains  option D.  48 square units.

To calculate the area of the shaded part, we would need to know the dimensions of the rectangle as well as the specific location and size of the shaded region within it.

If you can provide more details about the dimensions of the rectangular grid and the shaded region, I would be happy to help you calculate the area of the shaded part. Once we have that information, we can apply the formula for calculating the area of a rectangle,

which is Area = length × width. The result will give us the area of the shaded part in square units.

The area in square units, of the shaded part of the rectangle It has 48. Therefore the correct option  D

The Question was Incomplete, Find the full content below :

The grid shown below is in the shape of a rectangle. What is the area, in square units, of the shaded part of the rectangle? a 14 b 24 c 28 d 48

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