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Answer:

$840.77

Step-by-step explanation:

Answer: 803.84cm3

Step-by-step explanation:
The formula for finding the volume of a cylinder is πr2h.
In other words, the area of the top face's circle times the height.

To find the circle's area, we first find the radius of the circle. Since the diameter is 8cm, we divide by 2 to get the radius, which is 4cm.

4cm squared is 4cm x 4cm, which is 16cm. 16cm times 3.14 is 50.24cm squared.

Now, we have the area of the circle. 50.24cm squared!

The height is 16cm, so to find the cylinder, we times the area of the circle by the height of the cylinder! So,

16cm x 50.24cm squared = 803.84cm cubed.

The volume of the can of soup is 803.84cm cubed.

The expression representing the perimeter of the polygon is given as follows:

7mn³/3 + 4m² + 3mn².

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

Hence the perimeter for the polygon in this problem is given as follows:

mn³(1/3 + 2) + m²(1 + 3) + mn²(1 + 2) = 7mn³/3 + 4m² + 3mn².

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Answer:

la recta

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Hello There!

So first we need to determine what the formula for area of a trapezoid is

\(A=\frac{a+b}{2} h\)

where a and b = bases and h = height

the given information is the area and the two bases

so we plug in the given information and solve for h

\(180=\frac{4+14}{2} h\\4+14=18\\\frac{18}{2} =9\\180=9h\)

divide each side by 9

\(\frac{180}{9} =20\\\frac{9h}{9} =h\)

we're left with

h=20

so we can conclude that the height is 20

Let's assume David's average speed is S km/h.

A) To find David's average speed, we can use the formula: Speed = Distance / Time.

David completed the race in 5 hours, so his speed is S km/h. Therefore, we have:

S = Distance / 5

B) Ken's average speed is 9.8 km/h less than David's average speed, which means Ken's average speed is (S - 9.8) km/h.

Ken took 7 hours to complete the race, so we have:

S - 9.8 = Distance / 7

Now, we can solve the system of equations to find the values of S and Distance.

From equation (1): S = Distance / 5

Substitute this into equation (2):

Distance / 5 - 9.8 = Distance / 7

Multiply both sides of the equation by 35 to eliminate the denominators:

7 * Distance - 35 * 9.8 = 5 * Distance

7 * Distance - 343 = 5 * Distance

Subtract 5 * Distance from both sides:

2 * Distance - 343 = 0

Add 343 to both sides:

2 * Distance = 343

Divide both sides by 2:

Distance = 343 / 2 = 171.5 km

Therefore, the distance of the cycling race is 171.5 kilometers.

To find David's average speed, substitute the distance into equation (1):

S = Distance / 5 = 171.5 / 5 = 34.3 km/h

So, David's average speed was 34.3 km/h.\(\)

Answer:

A) 34.3 km/h

B) 171.5 km

Step-by-step explanation:

Since Ken's average speed is said to be 9.8km/h less than David's average speed, and we know that Ken's average speed is dependent on him traveling for 7 hours, then we have our equation to get the distance of the cycling race:

\(\text{Ken's Avg. Speed}=\text{David's Avg. Speed}\,-\,9.8\\\\\frac{\text{Distance}}{7}=\frac{\text{Distance}}{5}-9.8\\\\\frac{5(\text{Distance})}{7}=\text{Distance}-49\\\\5(\text{Distance})=7(\text{Distance})-343\\\\-2(\text{Distance})=-343\\\\\text{Distance}=171.5\text{ km}\)

This distance for the cycling race can now be used to determine David's average speed:

\(\text{David's Avg. Speed}=\frac{\text{Distance}}{5}=\frac{171.5}{5}=34.3\text{ km/h}\)

Therefore, David's average speed was 34.3 km/h and the distance of the cycling race was 171.5 km.

The value of x is \(x=\frac{268}{3}\) = 89.33 degree.

How do you find value of x?

The algebraic expression should often take one of the following forms: addition, subtraction, multiplication, or division. Bring the variable to the left and the remaining values to the right to determine the value of x. To determine the outcome, simplify the values. The letter "x" is frequently used in mathematics to denote an unknowable amount or variable. Similar to how X-rays confounded their discoverer and Malcolm X adopted the sign to stand for the lost name of his African ancestry, x also denotes the unknown in English.

x+44+x+3+x+45=360

Group like terms

x+x+x+44+3+45=360

Add similar elements: x+x+x=3 x

3 x+44+3+45=360

Add the numbers: 44+3+45=92

3 x+92=360

Move 92 to the right side

3 x=268

Divide both sides by 3

\(\frac{3 x}{3}=\frac{268}{3}\)

Simplify

\(x=\frac{268}{3}\)

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Answer:

-8.58

Step-by-step explanation:

-3.28+4.4-9.7=-8.58

The 97% confidence interval for the mean amount of monthly mortgage payment for all homeowners in the area is between $1613.48 and $1536.52.

We shall use the following steps to find the 97% confidence interval:

First, we compute the margin of error using the formula:

Margin of error = Z * (σ / √n)

Where:

Z = the z-score

σ = standard deviation

n = sample size

Given:

Z = the z-score for a 97% confidence interval (which is 1.96 using the z-table).

σ = $215.

n = 120.

Putting the values:

Margin of error = 1.96 * (215 / √120)

= 1.96 * (215 / 10.95)

= 1.96 * 19.64

= $38.48

Next, we add and subtract the margin of error from the sample mean to find the confidence interval.

Confidence interval = $1575 +/- $38.48

= $1613.48 and $1536.52

Hence, the bank manager can be 97% confident that the average monthly mortgage payment for all homeowners in the area is between $1613.48 and $1536.52.

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Answer:

20. x = 23; 21. y = 23

Step-by-step explanation:

20. The 2 highlighted angles are congruent, meaning the angles are equal to each other;

91 = 5x-24    (add 24 to both sides)

115 = 5x    (divide both sides by 5)

x = 23

21. Opposite side exterior angles are congruent, set them equal to each other:

115 = 5y    (divide both sides by 5)

y = 23

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The length of one side of the equilateral triangle in terms of x is 6x.

To find the length of one side of the equilateral triangle in terms of x, we need to consider the perimeter of both the rectangle and the equilateral triangle.

The perimeter of a rectangle is given by the formula:

Perimeter of rectangle = 2(length + width)

In this case, the length of the rectangle is 7x cm, and the width is 2x cm. Substituting these values into the formula, we have:

Perimeter of rectangle = 2(7x + 2x) = 2(9x) = 18x

We are told that the equilateral triangle has the same perimeter as the rectangle.

Since an equilateral triangle has all sides equal, the perimeter can be calculated by multiplying the length of one side by 3.

Therefore, we have:

Perimeter of equilateral triangle = 3(side length)

Since the perimeter of the equilateral triangle is equal to the perimeter of the rectangle (18x), we can set up the equation:

3(side length) = 18x

Dividing both sides of the equation by 3, we get:

side length = 6x

Hence, the length of one side of the equilateral triangle in terms of x is 6x.

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The complete question may be like: A rectangle measures 2x cm by 7x cm. An equilateral triangle has the same perimeter as the rectangle. What is the length of one side of the triangle in terms of x?

Answer:  y-4 = 3(x - 5)

Step-by-step explanation:

The basic form for a point-slope equation is

y - b = m(x - a)

a is the x-value from the given coordinate,  b is the y-value form the given coordinate,  m is the slope. x and y are the variables in the function.

To find the slope, m, use the given coordinates. Get the difference in the y-values and divide by the difference in the x-values. This is "rise over run."

Given coordinate points: ​(4​,4​) and ​(5​,7​)   \(m=\frac{y-y_{1} } {x-x_{1 }}\) substitute values:

m= 7-4/5-4  becomes  m= 3/1   so the slope m = 3

To write the equation:  Take the basic form, substitute b and a values from either given coordinate. And use the value of m we just calculated.

y - b = m(x - a)  Using the second coordinate: (5,7)

y - 7 = 3(x - 5)

The attachment shows the graph of this equation.

(The equivalent slope-intercept form for this is y = 3x - 8 )

Answer:

Y - 4 = 3(X - 4)

Step-by-step explanation:

Y2 - Y1 / X2 - X1 = M, 7 - 4 / 5 - 4 = M, 3 / 1 = M, M = 3

Y - Y1 = M(X - X1),  

Y - 4 = 3(X - 4),

Y - 4 = 3X - 12,

+4   +4

Y = 3X - 8

Answer:

The answer is 3 miles, I had the same question

Answer:

multiple 18 x 8, then minus 6 from your answer

Answer:

1pack=6cans

18packs=x

=108canspacks=1xpack

Dividing both sides by 1 pack

X=108cans

Number of seats in each row is 51 given that a rectangular auditorium seats 2244 people and number of seats in each row exceeds the number of rows by 7. This can be obtained by assuming the value of number of seats in each row, forming quadratic equation and using quadratic formula to find root.

Here in the question it is given that,

We have to find the number of seats in each row.

Let us assume that the number of seats in each row be x.

From the given statement, number of seats in each row exceeds the number of rows by 7, we can write that,

Number of seats in one row = Number of rows + 7

x = Number of rows + 7

⇒ Number of rows = x - 7

Total number of seats in the auditorium can be written as,

⇒ (Number of seats in one row)(Number of rows) = Total number of seats

(x)(x - 7) = 2244

x² - 7x = 2244

⇒ x² - 7x - 2244 = 0

By using quadratic formula we can find the root,

x = (-b ± √b² - 4ac)/2a

here in the question, a = 1, b = -7, c = -2244

√b² - 4ac = √(-7)² - 4(1)(-2244)

√b² - 4ac = √49 + 8976

√b² - 4ac = √9025

√b² - 4ac = 95

x = (-b ± √b² - 4ac)/2a

x = (7 ± 95)/2

x = 102/2 or x = -88/2

⇒ x  = 51 or x = -44

Hence number of seats in each row is 51 given that a rectangular auditorium seats 2244 people and number of seats in each row exceeds the number of rows by 7.

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Answer:1.1.this relation is function because domains are not repeated

Step-by-step explanation:

The value of the cosine of the angle of (a - b) will be 0.80.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

It is a function that repeats itself in a particular time interval.

Suppose that sin(a) = 4/6 and cos(b) = 1/5.

Then the value of 'a' is given as,

sin(a) = 4/6

sin(a) = 2/3

a = 41.81°

Then the value of 'b' is given as,

cos(b) = 1/5

b = 78.46°

Then the value of the cosine of the angle of (a - b) will be given as,

⇒ cos(41.81° - 78.46°)

⇒ cos(-36.65°)

⇒ cos 36.65°

⇒ 0.80

The value of the cosine of the angle of (a - b) will be 0.80.

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smaller leg is the smaller side

longer leg is the longer side

hypotenuse is the longest side

triangle a example:
smaller leg: 8-5 = 3

longer leg: 2-(-8) = 10

hypotenuse: use the formula a^2 + b^2 = c^2 (not needed since the side lengths are already given)

Answer: 3 ≤ 47

Step-by-step explanation:

The inequality given is 3 ≤ 47.

To determine the solutions to this inequality, we need to find the values of x that satisfy the inequality.

Looking at the options provided:

x = 24: This is not a solution because 24 is less than 47.

x = 51: This is a solution because 51 is greater than or equal to 47.

x = 6: This is not a solution because 6 is less than 47.

x = 99: This is a solution because 99 is greater than or equal to 47.

Therefore, the solutions to the inequality 3 ≤ 47 are x = 51 and x = 99.

Answer:

< 6 = 58°

< 8 = 58°

< 5 = 122°

<7 = 122°

Step-by-step explanation:

<6 = <8 because corresponding angles are equal

5y + 13 = 7y -5  Subtract 5 y from both sides

13 = 2y -5  Add 5 to both sides

18 = 2y

9 = y

Now that we know that y = 9, we plug it back into either equation

5y + 13

5(9) + 13

45 + 13

58

<5 is supplemental to <6  so 180 - 58 = 122

<8 is supplemental to < 7 so it is 122 also

Answer:

D, dialation and rotation on edge

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

its 82

Step-by-step explanation:

The value of x is 98°. Therefore, option C is the correct answer.

In the figure, given two angles 82° and 98°.

The angles which occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.

We know that corresponding angles are congruent.

From the given figure x = 98°

The value of x is 98°. Therefore, option C is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

Lines a and b are parallel and lines e and f are parallel.

What is the value of x?  

8

82

98

172

Answer:

109

Step-by-step explanation:

Answer:

♡ hi there♡

the gradient of the graph is 5♡

have a great day or night

-madeline

✧･ﾟ: *✧･ﾟ:･ﾟ✧*:･ﾟ✧･ﾟ: *✧･ﾟ:･ﾟ✧*:･ﾟ✧

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the first three terms of the expansion of (1 +x)^n are 1 +3 +4, you want the values of x and n, and the next term.

The first few terms of the binomial expansion of (1 +x)^n are ...

  \((1+x)^n=1^n+n\cdot1^{n-1}x+\dfrac{n(n-1)}{2}1^{n-2}x^2+\dfrac{n(n-1)(n-2)}{2\cdot3}1^{n-2}x^3+\dots\)

Comparing the terms to those given, we have ...

  \(nx=3\\\\(nx)((n-1)x)/2=4\)

Expanding the second of these equations, and substituting the first, we get ...

  \((nx)(nx -x)=8\qquad\text{multiply by 2}\\\\3(3-x)=8\qquad\text{substitute $nx=3$}\\\\9-8=3x\qquad\text{add $3x-8$}\\\\\boxed{x=\dfrac{1}{3}}\qquad\text{divide by 3}\\\\\dfrac{1}{3}n=3\qquad\text{substitute for $x$ in $nx=3$}\\\\\boxed{n=9}\qquad\text{multiply by 3}\)

Then the fourth term is ...

  \(\dfrac{n(n-1)(n-2)}{6}x^3=\dfrac{9\cdot8\cdot7}{6}\cdot\left(\dfrac{1}{3}\right)^3=\boxed{\dfrac{28}{9}}\)

__

Additional comment

Then the expansion is ...

  (1 +1/3)^9 = 1 + 3 + 4 + 28/9 + 14/9 + 14/27 + ...

The n-th term is (11-n)/(3(n-1)) times the term before.

Answer:

-6.1625

Step-by-step explanation:

-1/4=-0.85

-3/4=-0.75

-0.85*8x=-6.8

-0.85*-0.75=0.6375

-6.8+0.6375=-6.1625

According to Chebyshev's Theorem, approximately 91% of the revenues are within k = 3.3 standard deviations of the mean.

What is Chebyshev's Theorem?

The minimum percentage of observations that are within a given range of standard deviations from the mean is calculated using Chebyshev's Theorem. Several other probability distributions can be applied to this theorem. Chebyshev's Inequality is another name for Chebyshev's Theorem. For a large class of probability distributions, Chebyshev's inequality ensures that no more than a specific percentage of values can deviate significantly from the mean.

According to Chebyshev's Theorem, at least 1 - 1/k² of the revenues lie within k standard deviations of the mean.

So when k = 3.3

1 -  1/k² = 1 - 1/3.3² = 1 - 0.0918 = 0.9082 = 90.82% ≈ 91%

Therefore according to Chebyshev's Theorem, approximately 91% of the revenues are within k = 3.3 standard deviations of the mean.

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Answer:

Step-by-step explanation:

none

Answer:

{x,y} = {1,1}

Step-by-step explanation:

// Solve equation [2] for the variable  x

 [2]    3x = 4y - 1

 [2]    x = 4y/3 - 1/3

// Plug this in for variable  x  in equation [1]

  [1]    3•(4y/3-1/3) + 4y = 7

  [1]    8y = 8

// Solve equation [1] for the variable  y

  [1]    8y = 8

  [1]    y = 1

// By now we know this much :

   x = 4y/3-1/3

   y = 1

// Use the  y  value to solve for  x

   x = (4/3)(1)-1/3 = 1

Solution :

{x,y} = {1,1}