Are the given functions y1 and y2 linearly independent or linearly dependent on the interval (0, 1) and why? Choose the correct statement below. Yi = cscº(t) - cot? (t), y2 = 9a. Since yi = - 42 on (0, 1), the functions are linearly independent on (0,1). b. Since yı = 5y2 on (0,1), the functions are linearly independent on (0,1). c. Since yı = 3y2 on (0,1), the functions are linearly dependent on (0,1). d. Since yi = - Žy2 on (0, 1), the functions are linearly dependent on (0,1).

Net rendering is a method of rendering a computer-generated animation or image on multiple computers over a network.

Net rendering is a method of rendering a computer-generated animation or image on multiple computers over a network. This technique allows a user to take advantage of the computing power of multiple computers to render a scene. To do this, the user would divide the scene into several parts, assigning each part to a different computer. The computers would then render each part of the scene independently, and then the results are combined into a single image. This process can significantly reduce the time required to render a scene, as the workload is distributed over multiple computers. For example, if it would normally take a single computer 10 minutes to render a scene, net rendering could reduce that time to 2 minutes.

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The perimeter of the figure is 16p + 10.

The whole length of a two-dimensional or three-dimensional shape's sides or edges is known as its perimeter. It is frequently referred to as the shape's perimeter or circumference. It is possible to determine the perimeter of many geometric forms with accuracy. The perimeter is a key idea in geometry and has several practical uses, such as determining the radius of a circular racetrack or determining the length of fencing required for a certain property.

The perimeter of a figure is the sum of the lengths of all its sides.

Thus,

Perimeter = (p - 9) + (7p + 5) + (p - 9) + (7p + 5)

Perimeter = 2p + 2(7p) + 2(5)

Perimeter = 16p + 10

Hence, the perimeter of the figure is 16p + 10.

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Answer:

  C, E

Step-by-step explanation:

You want the equations that represent 2 boys for every 5 girls in a class.

The number of boys is represented by x, and the number of girls is represented by y, so you have ...

  x : y = 2 : 5

As fractions, this is ...

  x/y = 2/5

Multiplying by 5y gives ...

  5x = 2y . . . . . . matches equation C

Dividing by 5, we have ...

  x = 2/5y . . . . . . matches equation E

The number of minutes she must run to reach her goal is 65.1 minutes.

The time she must run for is found by dividing the distance by the speed:

Time = Distance / Speed

We need to convert the distance from kilometers to miles before substituting values into the formula.

11.7 km = 11.7 / 1.609344 = 7.270043 miles

The formula now becomes:

Time = 7.270043 miles / 6.7 mi/h

Time = 1.085081 h

To get the time in minutes, we need to convert the time in hours to minutes. There are 60 minutes in an hour, so there are

Time = 1.085081 h x (60 minutes/1 hour)

Time = 65.104863 minutes = 65.1 minutes

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Answer: $15.25

Step-by-step explanation:

Let x be the number of apples purchased and y be the number of mangos purchased. Then we have the following constraints:

2.25x + 1.25y ≤ 20 (Jose has $20 to spend)

x + y ≥ 9 (Jose must buy at least 9 apples and mangos altogether)

x ≥ 3 (Jose must buy at least 3 apples)

y ≤ 9 (Jose can buy at most 9 mangos)

To solve this system of inequalities graphically, we can plot the relevant lines and shade the feasible region.

First, we graph the line 2.25x + 1.25y = 20 by finding its intercepts:

When x = 0, we have 1.25y = 20, so y = 16.

When y = 0, we have 2.25x = 20, so x = 8.89 (rounded to two decimal places).

Plotting these intercepts and connecting them with a line, we get:

     |       *

 16  |   *    

     |      

     |  /    

     | /      

     |/      

 0   *--------*

      0    8.89

Next, we graph the line x + y = 9 by finding its intercepts:

When x = 0, we have y = 9.

When y = 0, we have x = 9.

Plotting these intercepts and connecting them with a line, we get:

    |      

 9   |   *    

     |      

     |  /    

     | /      

     |/      

 0   *--------*

      0    9  

Finally, we shade the feasible region by considering the remaining constraints:

x ≥ 3: This means we shade to the right of the line x = 3.

y ≤ 9: This means we shade below the line y = 9.

Shading these regions and finding their intersection, we get:

   |       *

 16  |   *    |

     |       |

     |  /    |

     | /     |

     |/      |

 9   *--------*---

     |       | /

     |       |/

     |       *

 0   *--------*

      3    8.89

The feasible region is the shaded triangle bounded by the lines 2.25x + 1.25y = 20, x + y = 9, and x = 3.

To find one possible solution, we can pick any point within the feasible region. For example, the point (4, 5) satisfies all the constraints and represents buying 4 apples and 5 mangos, which costs 4(2.25) + 5(1.25) = $15.25.

Answer:

the numbers are

[tex] \sqrt{10} + 5 \\ - \sqrt{10} + 5[/tex]

Step-by-step explanation:

then there difference is

square root of 10 + 5 -(- square root of 10 +5)

=

[tex]2 \sqrt{10} [/tex]

and the cube of there sum is 15^3 = 15* 15* 15

= 3375

The total weight of the granola bars in the box is 6.7 ounces.

To calculate the total weight of the granola bars with the correct number of significant digits, we need to multiply the weight of a single bar by the number of bars in the box.

Given parameters:

Total weight of the granola bars

= Weight of a single bar x Number of bars in the box

= 0.84 ounces x 8

= 6.72 ounces

Since the weight of a single bar is given with two significant digits, and we have multiplied it by a whole number, the answer should be reported with two significant digits.

so we can say that, the total weight of the granola bars is 6.7 ounces.

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Using the mean formula we know that the new mean height of 14 people is 159.7 cm.

A mean in math is the average of a data set, calculated by adding all numbers together and then dividing the total of the numbers by the number of numbers.

For illustration, with the dataset containing: 8, 9, 5, 6, 7, the mean is 7, as 8 + 9 + 5 + 6 + 7 = 35, 35/5 = 7.

The mean height given is 159 cm.

Let, x1, x2, x3 ..... x15 be the height of 15 people.

x1+x2+x3 ..... x15/15 = 159

x1+x2+x3 ..... x15 = 159 * 15 = 2385 cm ...(1)

Let, x1 = 148 cm, who leaves the group.

148+x2+x3 ..... x15 = 2385 cm

x2+x3 ..... x15 = 2237 cm

Now, we have 14 people.

New mean = x2+x3 ..... x15/14

= 2237/14

= 159.7 cm

Therefore, using the mean formula we know that the new mean height of 14 people is 159.7 cm.

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Proved that the sum of measure of three angles of triangle is 180 using the Polygon Angle Sum Theorem

To prove that the sum of the measures of three angles of a triangle is 180 degrees, we can use the Polygon Angle Sum Theorem, which states that the sum of the measures of the interior angles of a polygon with n sides is equal to (n-2) times 180 degrees.

A triangle is a polygon with three sides, so we can apply the Polygon Angle Sum Theorem to a triangle to find the sum of its interior angles. Using n=3, we have:

Sum of measures of interior angles of triangle = (n-2) × 180 degrees

= (3-2) × 180 degrees [since we are dealing with a triangle]

= 1 × 180 degrees

= 180 degrees

Therefore, the sum of the measures of the interior angles of a triangle is 180 degrees. This means that the sum of the measures of the three angles in a triangle is always 180 degrees, regardless of the size or shape of the triangle.

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The volume of iron needed to create the rectangular prism is approximately 28650.5 cubic cm.

what is volume?

Volume is the amount of space occupied by a three-dimensional object. It is a measure of how much an object can hold or how much space it takes up. The volume of a solid object is typically measured in cubic units, such as cubic centimeters (cm³) or cubic meters (m³).

The volume of the rectangular prism without the cylinder can be calculated as:

[tex]$$V_1 = A \times h$$[/tex]

where A is the base area and h is the height

[tex]$$V_1 = 2250 \times 100$$[/tex]

[tex]$$V_1 = 225000 \ \text{cubic cm}$$[/tex]

The volume of the cylinder can be calculated as:

[tex]$$V_2 = \pi r^2 h$$[/tex]

where r is the radius and h is the height

[tex]$$V_2 = \pi \times 25^2 \times 100$$[/tex]

[tex]$$V_2 = 196349.54 \ \text{cubic cm}$$[/tex]

The volume of the rectangular prism with the cylinder missing can be calculated as:

[tex]$$V = V_1 - V_2$$[/tex]

[tex]$$V = 225000 - 196349.54$$[/tex]

[tex]$$V = 28650.46 \ \text{cubic cm}$$[/tex]

Therefore, the volume of iron needed to create the rectangular prism with a base area of 2250 square cm, a cylinder missing through the center of the prism with a radius of 25 cm, and the height of the cylinder and the prism being 100 cm, is approximately 28650.5 cubic cm (rounded to the nearest tenth of a cubic cm).

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The mean distance Jaison jogged over 9 days is 7 meters per day. This was calculated by adding up all the distances he jogged and dividing by 9.

To calculate the average distance that Jaison jogged over the 9 days, we used the formula for mean, which involves summing up all the distances he jogged and dividing by the total number of days. After adding up the distances, we found that the total distance Jaison jogged was 63 meters. Dividing this by the 9 days gives us an average distance of 7 meters per day. Therefore, Jaison jogged an average of 7 meters each day over the 9-day period.

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The height of an open cylinder of radius of 8cm given that it has a curved surface area of 1000 cm² is equals to the 159.24 cm.

The area obtained after substracting the circular area from the total area of the cylinder is called as curved surface area. Curved surface area is calculated by formula, 2πrh

where r --> radius of cylinder

h --> height of cylinder

π --> math special constant

We have an open cylinder with the following dimensions,

Radius of cylinder, r = 8 cm

Curved surface area of cylinder, A = 1000 cm². We have to calculate the height of this open cylinder. Let the height of an open cylinder be 'h cm' . Using the above formula, height of cylinder, h = curved Area/ 2πr

=> h = A/2π

=> h = 1000/2 ( 3.14)

=> h = 1000/6.28

=> h = 159.24

Hence, required value of height is 159.24 cm.

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As a result, the percentage of adults who selected math is different from the percentage of kids who did.

As a number out of 100, a percentage is a method to express a proportion or a fraction. It is symbolized by the number %. If there are 25 boys in a class of 100 pupils, for instance, then there are 25% of boys in the class. It is a helpful method to compare quantities and to express changes in values over time.

given

120 80

Total    200

Women Overall Party A Party B

70 60

Overall    130

Therefore, there are 130 ladies in the group.

b) The chart indicates that 70 women plan to support Party A.

Thus, the percentage of adults who selected English was 40% of 48, which is equal to 0.4 times 48 and 19.2 when rounded to the closest whole number.

b) Reeshma is not accurate. The percentage of adults who selected math is 35%, while for children it is 40%, according to the pie chart.

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The complete question is:-   complete the two-way table, which shows the voting intentions of a group of men and women. a How many women are in the group?

Men

Party A Party B 120

Total    200

Women   130

Total       380

b How many women intend to vote for Party A?

2 A group of 48 adults are asked what their favourite subject was at school. They can choose from

maths, English and science.

A group of 32 school children are asked the

same question.

Answer:

Step-by-step explanation:

a.  ∠ACB

b.  AC

c.  AB

d.  BC

e.  tangent, opposite, adjacent

f.  m∠ACB = tan⁻¹(34/45) = 37°

Answer:

[tex]5x {}^{3} - x + 5x + 2[/tex]

Step-by-step explanation:

Greetings!!!

So to find the sum of (f+g)(x) just simply add these two functions

Add like terms together

If you have any questions tag it on comments

Hope it helps!!!

Answer:

Step-by-step explanation:

2/5-1 2/5

Another strategy is to start by pressing a square in the middle of the grid, and then pressing the squares adjacent to it. This should help you turn off the squares in a cross pattern.

In mathematics, a sequence is an ordered list of elements, typically numbers, which may be finite or infinite. Each element in the sequence is called a term. For example, the sequence {1, 2, 3, 4, 5} is a finite sequence of integers with five terms. Sequences can be represented in several ways, such as listing out the terms, using a formula to generate the terms, or using recursive rules. For example, the sequence of even numbers can be generated using the formula 2n, where n is a positive integer. So, the first five terms of the sequence are 2, 4, 6, 8, 10. Sequences are used in many areas of mathematics, including number theory, calculus, and statistics. They are also used in real-world applications, such as modeling population growth or predicting stock prices.

Here,

One common strategy is to start by pressing one of the corner squares, and then pressing the squares adjacent to it. Then, move to the adjacent corner square and repeat the process. This should help you turn off the squares in one diagonal line.

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Answer:

The number x that is midway between x and 27, and has a midpoint of -3, is -33

midpoint = (x + 27) / 2

We also know that the midpoint is equal to -3, so we can set these two expressions equal to each other and solve for x:

-3 = (x + 27) / 2

Multiplying both sides by 2 gives:

-6 = x + 27

Subtracting 27 from both sides gives:

x = -33

Ryan makes a profit of £240.  the total sales now amount to £600. By subtracting the cost of the jumpers, i.e. £190, from the total sales, we calculate that Ryan makes a profit of £240.

Ryan spends £190 to buy 80 jumpers. He sells 50% of the jumpers, i.e. 40 jumpers, at £12 each. This brings the total sales to £480. Then, he puts the remaining 40 jumpers on a Buy one get one half price offer. He sells 20 of the remaining jumpers using this offer. Therefore, the total sales now amount to £600. By subtracting the cost of the jumpers, i.e. £190, from the total sales, we calculate that Ryan makes a profit of £240.

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None of the available options match the parabola's equation.

To determine the equation of a parabola, we can utilize the vertex form. Assuming we can read the coordinates (h,k) from the graph, the aim is to utilize the coordinates of its vertex (maximum point, or minimum point), to formulate its equation in the form y=a(xh)2+k, and then to determine the value of the coefficient a.

A parabola's vertex form is given by:

[tex]y = a(x-h)^2 + k[/tex]

where (h,k) is the parabola's vertex.

[tex]y = a(x-5)^2 - 3[/tex]

These values are substituted into the equation to produce:

[tex]-15 = a(2-5)^2 - 3[/tex]

[tex]-15 = 9a - 3[/tex]

[tex]-12 = 9a[/tex]

[tex]a = -4/3[/tex]

[tex]y = (-4/3)(x-5)^2 - 3[/tex]

This equation is expanded and simplified to produce:

[tex]y = (-4/3)x^2 + (32/3)x - 53[/tex]

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Answer:

See Below.

Step-by-step explanation:

To find the perimeter of a trapezoid, you simply add up the lengths of all four sides.

In this case, the trapezoid has sides of 8 cm, 10 cm, 16 cm, and 10 cm.

Perimeter = 8 cm + 10 cm + 16 cm + 10 cm

Perimeter = 44 cm

Therefore, the perimeter of the trapezoid is 44 cm.

Answer: 4.5

Step-by-step explanation:

A^2 +B^2 =C^2

A^2 + 6^2 =7.5^2

A^2 + 36= 56.25

A^2= 20.25

A= square root of 20.25

A= 4.5

(a) Dataset with mean substantially less than median:

9, 10, 11, 12, 90

The mean of this dataset is (9+10+11+12+90)/5 = 26.4, while the median is 11, which is substantially greater than the mean. The last data value is 90, which is a positive integer less than 100.

(b) Dataset with mean substantially more than median:

98, 99, 100, 101, 200

The mean of this dataset is (98+99+100+101+200)/5 = 119.6, while the median is 100, which is substantially less than the mean. The last data value is 200, which is a positive integer less than 100.

(c) Dataset with mean equal to median:

2, 3, 4, 4, 5

The mean of this dataset is (2+3+4+4+5)/5 = 3.6, which is equal to the median (the middle value of the dataset). The last data value is 5, which is a positive integer less than 100.

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The simplified form of the given expression as required to be determined in the task content is; 2x⁴√5.

It follows from the task content that the Simon form of the given expression √20x⁸ is required to be determined from the task content.

On this note, since the given expression is; √20x⁸.

We have that; = √ (4 × 5 × x⁸)

Therefore, since 4 and x⁸ are perfect squares; it follows that we have;

= 2x⁴ √5.

Ultimately, the simplified form of the given expression as required to be determined is; 2x⁴ √5.

Complete question; The correct expression is; √20x⁸.

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Based on the exponential decay equation, the number of employees for the company that has been decreasing yearly by 5%, will in 10 years be approximately 515.

The exponential decay equation or function gives the value in t years that has a constant ratio of decrease.

Exponential decay equation is one of the two exponential functions.  The other is the exponential growth equation.

The annual decrease in the number of employees = 5%

The current number of employees in the company = 860

The expected time = 10 years.

The exponential decay equation is as follows, y = 860 x 0.95^10.

y = 860 x 0.95^10 = 515

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Answer:

the cross is the blue color

Answer:

CP of computer = 27000 rs.

Step-by-step explanation:

D% = Dis/MP*100

We know, Dis = MP-SP

Given Profit= 1160 rs.

So,CP = 27000 rs.