Write an equation to represent the fraction models below

Answer:

a) The curved surface area of the frustum of the cone is given by:

= (1 + 2)

where is the slant height of the frustum, 1 is the top radius, and 2 is the bottom radius.

We can find the slant height using the Pythagorean theorem:

= √(ℎ^2 + (2 − 1)^2)

= √(28^2 + (14 − 6)^2)

= √(784 + 64)

= √848

= 29.12

Substituting the values into the formula, we get:

= × 29.12 × (6 + 14)

= 1138.5 m^2

Therefore, the curved surface area of the frustum of the cone is 1138.5 square meters.

b) The total surface area of the frustum of the cone is given by:

= 1^2 + 2^2 + (1 + 2)

Substituting the values into the formula, we get:

= × 6^2 + × 14^2 + × 29.12 × (6 + 14)

= 1138.5 + 1070.88 + 1138.5

= 3347.88 m^2

Therefore, the total surface area of the frustum of the cone is 3347.88 square meters.

c) The volume of the frustum of the cone is given by:

= 1/3 × × ℎ × (1^2 + 2^2 + 12)

Substituting the values into the formula, we get:

= 1/3 × × 28 × (6^2 + 14^2 + 6 × 14)

= 1/3 × × 28 × (36 + 196 + 84

The value of tan 2π/3 without calculator is -√3.

The value of tan 2π/3 without calculator is calculated by applying trig identities as follows;

the value of π = 180 degrees

So we can replace the value of π in the function with 180 degrees as follows;

tan ( 2π / 3) = tan (2 x 180 / 3)

tan (2 x 180 / 3) = tan (2 x 60)

tan (2 x 60) = tan (120)

tan (120) if found in the second quadrant, and the value will be negative since only sine is positive in the second quadrant.

tan (120) = - tan (180 - 120)

= - tan (60)

= -√3

Learn more about trig identities here: https://brainly.com/question/7331447

#SPJ1

The maximum number of visitors to the theme park p=14.

Given that few friends want to visit the amusement park.

They are limited to spending $325 for parking and admission.

Tickets are $39 per person, tax included, and parking is $13.

We have to find the maximum number of visitors to the amusement park p.

We can write as $13+$39p≤$325

$39p≤$325-$13

p≤14

Therefore, the maximum number of visitors to the amusement park p=14.

To learn more about inequality visit: https://brainly.com/question/30231190

#SPJ1

The results of the two-sample t-test, there does not appear to be enough evidence to support the claim that the mean FICO score of borrowers with high-interest mortgages is different than the mean FICO score of borrowers with low-interest mortgages.

To test the claim that the mean FICO score of borrowers with high-interest mortgages is different than the mean FICO score of borrowers with low-interest mortgages, we can perform a two-sample t-test.

Using the given data, we can calculate the test statistic as follows:

t = (492 - 508) / sqrt((49^2 / 19) + (38^2 / 26)) = -1.57

The degrees of freedom for this test are 19 + 26 - 2 = 43. Using a t-table or calculator and a significance level of 0.2, we can find the critical value to be approximately ±1.301.

Since the absolute value of the test statistic (1.57) is less than the critical value (1.301), we fail to reject the null hypothesis. This means that we do not have enough evidence to support the claim that the mean FICO score of high-interest mortgage borrowers is different than the mean FICO score of low-interest mortgage borrowers at the 0.2 significance level.

For such more questions on Mortgages:

https://brainly.com/question/29083801

#SPJ11

A possible coordinate pair for vertex N is (2.42, 2.58).

We have,

The area of the square is 9 square units, and each side of the square must have a length of 3 units.

Let's start by finding the coordinates of vertex P.

Since the square is a square, we know that the x-coordinate of P is the same as the y-coordinate of M, and the y-coordinate of P is the same as the x-coordinate of M.

The coordinates of P are (3, 2).

To find the coordinates of N, we can use the fact that the diagonals of a square bisect each other and are perpendicular.

The midpoint of MP is the same as the midpoint of NQ, and the slope of MP is the negative reciprocal of the slope of NQ.

The midpoint of MP.

= [(2+3)/2, (3+2)/2]

= [2.5, 2.5]

Now,

The slope of MP is (2-3)/(3-2) = -1.

We now have the coordinates of one endpoint of NQ (the midpoint) and its slope.

We can use the point-slope form of the equation of a line to find the equation of NQ:

y - 2.5 = -1(x - 2.5)

y - 2.5 = -x + 2.5

y = -x + 5

We know that N is on the line NQ and that it is a distance of 3 units from the midpoint of NQ, which is (2.5, 2.5).

We can use the distance formula to find the coordinates of N:

d = √((x2 - x1)^2 + (y2 - y1)^2)

3 = √((x - 2.5)^2 + (y - 2.5)^2)

Squaring both sides:

9 = (x - 2.5)² + (y - 2.5)^2

We also know that N is on the line y = -x + 5.

We can substitute this into the equation above to get:

9 = (x - 2.5)^2 + (-x + 2.5 - 2.5)^2

9 = (x - 2.5)^2 + (x - 5)^2

9 = x^2 - 5x + 6.25 + x^2 - 10x + 25

0 = 2x^2 - 15x + 30.75

0 = x^2 - 7.5x + 15.375

We can use the quadratic formula to solve for x:

x = (7.5 ± √(7.5² - 4(1)(15.375))) / (2(1))

x = (7.5 ± √(13.875)) / 2

x ≈ 5.08 or x ≈ 2.42

Since vertex N is to the left of vertex M, we choose the smaller value of x: x ≈ 2.42.

Now we can substitute this value of x into the equation y = -x + 5 to find the corresponding value of y:

y ≈ 2.58

Therefore,

A possible coordinate pair for vertex N is (2.42, 2.58).

Learn more about coordinates here:

https://brainly.com/question/13118993

#SPJ1

Answer: 1226.72g

Step-by-step explanation:

If 460g of flour is needed to make enough dough balls for 6 people, we can find the amount of flour needed for each person by dividing 460 by 6:

460 g / 6 = 76.67 g/person

To find the amount of flour needed for 16 people, we can multiply the amount of flour needed per person by the number of people:

76.67 g/person * 16 people = 1226.72 g

Therefore, we need 1226.72 g of flour to serve 16 people.

Answer:

We can start by dividing both sides of the equation cos(Ф) + 2sin(Ф) = 0 by sin(Ф):

cos(Ф)/sin(Ф) + 2 = 0

We can then use the identity cot(Ф) = cos(Ф)/sin(Ф) to substitute for cos(Ф)/sin(Ф):

cot(Ф) + 2 = 0

Subtracting 2 from both sides, we get:

cot(Ф) = -2

Therefore, we have shown that cos(Ф) + 2sin(Ф) = 0 can be expressed as cot(Ф) = -2.

The translated figure will be entirely within the 3rd quadrant of the graph.

We have, translation (x, y)--> (x-7,y+1).

Here, the notation (x, y) ⇒ (x-7, y+1) means that each x-coordinate has 7 subtracted from it.

Additionally, each y-coordinate has a 1 added to it because of the notation. Point B's y-coordinate is -3. It becomes -2 by adding 1.

As a result, point B's image will be at (-7, -2), 7 units to the left and 1 unit to the upper right of B.

Thus, the translated figure will be entirely within the 3rd quadrant of the graph.

Learn more about Translation here:

https://brainly.com/question/12463306

#SPJ1

The values are a = 6, b = 7 and c = 3.

Given is a quadratic equation 6x² + 7x + 3 = 0, we need to compare this with the standard form of a quadratic equation.

We know that the standard form of a quadratic equation is given by =

ax² + bx + c = 0

So,

Comparing both the equations,

ax² + bx + c = 0

6x² + 7x + 3 = 0

We see, a = 6, b = 7 and c = 3.

Hence, the values are a = 6, b = 7 and c = 3.

Learn more about quadratic equation click;

https://brainly.com/question/30098550

#SPJ1

The solution is::

a. 120 ways can they​ arrive.

b. 6 can Eduardo arrive first and Tyrone ​last

c. 0.05 is the probability that Eduardo will arrive first and Tyrone last.

Here, we have,

a) The ways Eduardo, Sarah, Maria, Jim, and Tyrone can arrive to the party is

5! = 5×4×3×2×1 = 120

The logic behind it is

5 different people can arrive first, after that

4 different people can arrive second, when first and second arrived is known,

3 different people can arrive third, then

2 different people can arrive fourth

only 1 person left to be fifth.

b) Using the same logic, when first and last arrived is known, there is

3!=3×2×1=6 ways they can arrive in this case.

c)  The probability that Eduardo will arrive first and Tyrone last is

the division of the ways Eduardo arrive first and Tyrone ​last by the ways 5 people can arrive = 6/120 = 0.05

To learn more on probability click:

brainly.com/question/11234923

#SPJ1

complete question:

Eduardo, Sarah, Maria, Jim, and Tyrone have all been invited to a dinner party. They arrive randomly and each person arrives at a different time.

a. In how many ways can they​ arrive?

b. In how many ways can Eduardo arrive first and Tyrone ​last?

c. Find the probability that Eduardo will arrive first and Tyrone last.

The least squares regression equation and the correlational figure collectively yield insightful details regarding the association among educational attainment and income in this region.

The least squares regression equation solely expresses the linear connection between two specific variables, y and x:

y = 726.4x + 14,063

A correlation coefficient of 0.7466 significantly suggests there is a moderate to strong positive association between the portion of inhabitants having at least an undergraduate degree and median returns in this area.

In conclusion, the least squares regression equation and the correlational figure collectively yield insightful details regarding the association among educational attainment and income in this region.

Learn more about regression on

https://brainly.com/question/25987747

#SPJ1

Answer:

72

Step-by-step explanation:

no

The diameter of the circle is also 7.5 units.

We have,

The radius of a circle is half of its diameter.

Given that the circle has a diameter of 7.5, we can find the radius by dividing the diameter by 2:

Radius

= diameter/2

= 7.5/2

= 3.75

The radius of the circle is 3.75 units.

The diameter of the circle is twice the radius.

Diameter = 2 x radius = 2 x 3.75 = 7.5

Thus,

The diameter of the circle is also 7.5 units.

Learn more about circle here:

https://brainly.com/question/11833983

#SPJ1

The complete question.

What is the radius and diameter of the following circle of 7.5​

The curved surface area of the frustum is approximately 1356.51m². The total surface area of the frustum is approximately 1915.09m². The volume of the frustum is approximately 12348.57m³.

To find the curved surface area of the frustum, we need to find the slant height of the frustum first. Using the Pythagorean theorem, we have

l = √(h² + (R-r)²)

where h = 28m, R = 14m, and r = 6m

l = √(28² + (14-6)²) = √(784 + 64) = √848 ≈ 29.12m

The curved surface area of the frustum can be calculated as

CSA = π(R+r)l

CSA = 22/7 × (14+6) × 29.12

CSA ≈ 1356.51m²

The total surface area of the frustum can be calculated as the sum of the curved surface area and the areas of the top and bottom circles. The area of a circle with radius r can be calculated as πr². Thus, we have

TSA = CSA + πR² + πr²

TSA ≈ 1356.51 + 22/7 × 14² + 22/7 × 6²

TSA ≈ 1915.09m²

The volume of the frustum can be calculated as

V = 1/3 × πh(R² + Rr + r²)

V = 1/3 × 22/7 × 28(14² + 14×6 + 6²)

V ≈ 12348.57m³

To know more about curved surface area:

https://brainly.com/question/30200245

#SPJ1

The equation of the line in point-slope form is given as follows:

y - 60 = 0.5(x - 40).

The point-slope equation of a line is given as follows:

y - y* = m(x - x*).

In which:

The point in this problem is given as follows:

(40, 60).

The intercept is (0, 40), meaning that when x increases by 40, y increases by 20, hence the slope m is given as follows:

m = 20/40

m = 0.5.

Thus the equation is:

y - 60 = 0.5(x - 40).

More can be learned about linear functions at https://brainly.com/question/31665185

#SPJ1

Answer:

for times it would = 34600 but for adding it would be 3,470

then subtracting would be 3,450 then dividing would be 346

Step-by-step explanation:

HOPE THIS HELPSSS

Answer:

Step-by-step explanation:

8 is the whole number

11/100 = 0.11

ANSWER: 8.11

Answer:2 hours, 15 minutes, and 0 second

2.25 hours

135 minutes

8,100 seconds

Option A. rubber, plastic and electrical insulation is the symbol of section lining.

Section lining (also referred to as cross-hatching or hatching) is an integral technique in technical drawing, engineering drafting, and architecture for representing the interior or cross-sectional view of an object. This form of sectioning uses parallel lines at 45 degree angles that fill an object's cut or sectioned areas - this helps visually differentiate solid material from empty space while emphasizing where cuts have occurred.

Complex drawings may include various methods for representing different materials, including using different thicknesses of line thicknesses or spacing or patterns in section linings to represent them

Read more on section lining here:https://brainly.com/question/28134841

#SPJ1

The 95 percent confidence interval is (0.20, 0.32).

a. We can construct a 95% confidence interval to estimate the percentage of yellow peas as follows:

Let p = proportion of yellow peas = 155/595 = 0.26

Sample size = n = 595

Standard error = SE = √(p × (1-p) / n) = √(0.26 × (1-0.26) / 595) = 0.03

95% confidence interval = p ± 1.96 × SE

= 0.26 ± 1.96 × 0.03

= 0.26 ± 0.06

So, the 95% confidence interval is (0.20, 0.32).

b. Yes, the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow, as the 95% confidence interval does not include the expected value of 0.25.

Therefore, the 95 percent confidence interval is (0.20, 0.32).

To learn more about the confidence interval visit:

https://brainly.com/question/14041846.

#SPJ1

Explanation:

A = set of odd numbers = {1,3,5}

B = set of factors of 12 = {1,2,3,4,6}

A U B = union of set A and set B

A U B = {1,3,5} union {1,2,3,4,6}

A U B = {1,3,5,       1,2,3,4,6}

A U B = {1,2,3,4,5,6}

The set union operation combines two sets into one bigger set. Duplicates are tossed out.

There are 6 elements in the set A U B = {1,2,3,4,5,6} out of 6 faces of the number cube.

Therefore, the probability event  A U B happens is 6/6 = 1 = 100%; i.e. it is guaranteed to happen. Each face of the number cube is either odd, a factor of 12, or both.

Side notes:

The surface area of the figure is 105 in².

Surface area is the sum of all the surfaces on each side of a three-dimensional shape.

To calculate the surface area of the square based pyramid, we use the formula below

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

Learn more about surface area here: https://brainly.com/question/1297098

#SPJ1

The system of equations is:

4x + 3y = 104

x = 4 + 2y

The correct options are C and D.

Let's describe the variables for our system:

x = cost of a can of paint.

y = cost of a brush.

We know that the total cost is $104, then one of the equations is:

4x + 3y = 104

And we know that the cost of a can is $4 more than the double of a brush, then the other equation is:

x = 4 + 2y

Then the correct options are C and D.

Learn moer about systems of equations at:

https://brainly.com/question/13729904

#SPJ1

Answer:

Distance between points K and L = 9 units

Distance between points M and N = √1282 or approximately 35.805 units

Step-by-step explanation:

We can find the distance, d, between a pair of points using the distance formula, which is

[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex], where (x1, y1) are set of points, and (x2, y2) are another set.

Distance between K and L:

We can allow K (5, 0) to be our (x1, y1) point and L (-4, 0) to be our (x2, y2) point.  Now we can plug in the points into the distance formula:

[tex]d=\sqrt{(5-(-4))^2+(0-0)^2}\\ d=\sqrt{9^2}\\ d=\sqrt{81}\\ d=9[/tex]

Thus, the distance between points K and L is 9 units

Distance between M and N:

Now, can allow M (-21, -29) to be our (x1, y1) point and N (0, 0) to be our (x2, y2) point.  Now we can plug in the points into the distance formula:

[tex]d=\sqrt{(-21-0)^2+(-29-0)^2}\\ d=\sqrt{(-21)^2+(-29)^2}\\ d=\sqrt{441+841}\\ d=\sqrt{1282} \\d=35.80502758\\d=35.805[/tex]

sqrt (1282) is the exact distance between the two points, while 35.805  is the approximate distance between the two points to the nearest thousandth

The surface areas are 110 in², 87.6 mm² and 49 m².

Given that are solid figure, we need to find the surface area of them,

1) Triangular prism = perimeter × length + 2 × base area

= (5 + 5 + 6) × 5 + 2(3×5) = 110 in²

2) Triangular pyramid = base area + perimeter × slant height / 2

= 1/2 × 5.2 × 6 + 3 × 6 × 8/2

= 87.6 mm²

3) Cube = 4side²

= 4 × (3 1/2)²

= 4 × 3.5²

= 49 m²

Hence the surface areas are 110 in², 87.6 mm² and 49 m².

Learn more about surface areas click;

https://brainly.com/question/29298005

#SPJ1

Answer:

  (c)  f(x) = x² +2x +3; g(x) = -x² +3

Step-by-step explanation:

You want the system of equations represented by the graph.

The parabola opening downward is one that has been reflected over the x-axis, then shifted upward by 3 units. Its equation will be ...

  y = -x² +3 . . . . . . . . the minus sign is the reflection, the +3 is the translation

Only one answer choice include this equation:

  Choice C

The relative frequency of all students surveyed who go to Cook Middle School and prefer Energy Flow is 40 %

The relative frequency of students surveyed who go to Cook Middle School and prefer Energy Flow, can be found by the formula :

= Number of students who go to Cook Middle and prefer Energy flow / Number of students surveyed

Number of students who go to Cook Middle and prefer Energy flow from the table is 20 students.

The total number of students surveyed is 50 students.

The frequency is:

= 20 / 50 x 100 %

= 40 %

Find out more on relative frequency at https://brainly.com/question/26177128

#SPJ1

The measure of the angle ABC is 84 degrees and other measures are listed below

Here, we have

8n - 38 = 5n - 8

So, we have

3n = 30

n = 10

So, we have

ABC = 8n - 38 + 5n - 8

ABC = 8(10) - 38 + 5(10) - 8

ABC = 84

So, the measure of the angle ABC is 84 degrees

Here, we have

2k + 28 = 6k - 20

So, we have

4k = 8

k = 2

So, we have

CBW = 2k + 28

CBW = 2(2) + 28

CBW = 32

So, the measure of the angle CBW is 32 degrees

The interior angle is calculated as

Angle = 180 * (n - 2)/n

Regular 18-gon

Angle = 180 * (18 - 2)/18

Angle = 160

Regular 24-gon

Angle = 180 * (24 - 2)/24

Angle = 165

Here, we have

3x - 10 = x + 8

So, we have

2x = 18

x = 9

So, we have

YA = MA = 9 + 8

YA = MA = 17

Hence, the measures of YA and MA are 17

Here, we have

4x - 15 = 2x - 3

So, we have

2x = 12

x = 6

So, we have

NY = 2(6) - 3

NY = 9

NV = 2 * 9

NV = 18

Hence, the measures of NY and NV are 9 and 18, respectively

Read more about line segments at

https://brainly.com/question/24778489

#SPJ1

The solutions for the given equation are x=−1,1,√2,−√2. Therefore, option B is the correct answer.

The given equation is x⁸-4x⁷+3x⁶+8x⁵-15x⁴+4x³+9x²-8x+2=0.

Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

Here, (x⁸-4x⁷+8x⁵+4x³)+3x⁶-15x⁴+9x²+2=0

(x-1)⁵(x³+x²-2x-2)=0

(x-1)⁵(x²-2)(x-1)=0

(x-1)⁵=0, (x²-2)=0 and (x-1)=0

x=±1 x=±√2 and x-1

Exact Form: x=−1,1,√2,−√2

Therefore, option B is the correct answer.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ1