I need help really bad ​

So, 15 and 1 is the pair of numbers whose difference is 14, with the smallest product as 15.

To find the pair of numbers with the smallest product whose difference is 14, we can start by taking the two numbers to be as close to each other as possible. This means we can take one number to be 14 less than the other. For example, we can take the numbers to be 15 and 1. The difference between these two numbers is 14, and their product is 15, which is the smallest product possible for a pair of numbers whose difference is 14.

So, 15 and 1 is the pair of numbers whose difference is 14, with the smallest product as 15.

To know more about product of numbers,

visit; brainly.com/question/24243784

#SPJ4

Using trigonometric identities and algebraic manipulations, we derive an expression for sin x and cos x in terms of cos y. The value of (sin x + cos x)(sin y + cos y) is 2.49.


1. Start with the given equations sin(x+y) = 0.9 and sin(x-y) = 0.6.
2. Rewrite the equations using trigonometric identities. For sin(x+y) = 0.9, we have sin x cos y + cos x sin y = 0.9. For sin(x-y) = 0.6, we have sin x cos y - cos x sin y = 0.6.
3. Add the two equations together to eliminate the sin x cos y term: 2 sin x cos y = 1.5.
4. Divide both sides by 2 to solve for sin x cos y: sin x cos y = 0.75.
5. Square both sides of the equation to get (sin x cos y)^2 = 0.75^2. This gives us sin^2 x cos^2 y = 0.5625.
6. Use the trigonometric identity sin^2 x + cos^2 x = 1 to rewrite sin^2 x as 1 - cos^2 x: (1 - cos^2 x) cos^2 y = 0.5625.
7. Expand and rearrange the equation: cos^2 x cos^2 y - cos^4 x = 0.5625.
8. Use the identity cos^2 x = 1 - sin^2 x to substitute for cos^2 x: (1 - sin^2 x) cos^2 y - (1 - sin^2 x)^2 = 0.5625.
9. Expand and simplify: cos^2 y - sin^2 x cos^2 y - (1 - 2sin^2 x + sin^4 x) = 0.5625.
10. Combine like terms: cos^2 y - sin^2 x cos^2 y - 1 + 2sin^2 x - sin^4 x = 0.5625.
11. Rearrange the equation to isolate sin^2 x terms: sin^4 x - sin^2 x (cos^2 y + 2) + cos^2 y - 1 + 0.5625 = 0.
12. Combine like terms: sin^4 x - sin^2 x (cos^2 y + 2) + cos^2 y - 0.4375 = 0.
13. Solve the quadratic equation for sin^2 x: sin^2 x = [(cos^2 y + 2) ± √((cos^2 y + 2)^2 - 4(cos^2 y - 0.4375))] / 2.
14. Simplify the expression: sin^2 x = [(cos^2 y + 2) ± √(cos^4 y + 4cos^2 y + 4 - 4cos^2 y + 1.75)] / 2.
15. Further simplify: sin^2 x = [(cos^2 y + 2) ± √(cos^4 y + 5.75)] / 2.
16. Since 0 ≤ y ≤ x ≤ π/2, the value of cos y is positive. Therefore, cos^2 y + 2 is positive.
17. Thus, the equation simplifies to sin^2 x = (cos^2 y + 2 + √(cos^4 y + 5.75)) / 2.
18. Take the square root of both sides: sin x = √[(cos^2 y + 2 + √(cos^4 y + 5.75)) / 2].
19. Since 0 ≤ y ≤ x ≤ π/2, the value of sin x is positive.
20. Therefore, sin x + cos x = √[(cos^2 y + 2 + √(cos^4 y + 5.75)) / 2] + √(1 - sin^2 x).
21. Substituting the values of sin x and cos x, we have sin x + cos x = √[(cos^2 y + 2 + √(cos^4 y + 5.75)) / 2] + √(1 - [(cos^2 y + 2 + √(cos^4 y + 5.75)) / 2]).
22. Simplify the expression: sin x + cos x = √[(cos^2 y + 2 + √(cos^4 y + 5.75)) / 2] + √[(2 - cos^2 y - √(cos^4 y + 5.75)) / 2].
23. Multiply the two terms: (sin x + cos x)(sin y + cos y) = √[(cos^2 y + 2 + √(cos^4 y + 5.75)) / 2] * √[(2 - cos^2 y - √(cos^4 y + 5.75)) / 2].
24. Simplify: (sin x + cos x)(sin y + cos y) = √[(cos^2 y + 2 + √(cos^4 y + 5.75))(2 - cos^2 y - √(cos^4 y + 5.75))] / 2.
25. Multiply the terms inside the square root: (sin x + cos x)(sin y + cos y) = √[4 - 2cos^2 y - 2√(cos^4 y + 5.75) + 4√(cos^2 y + 2) - 2cos^2 y + cos^4 y + 5.75] / 2.
26. Combine like terms: (sin x + cos x)(sin y + cos y) = √[5 + 2√(cos^2 y + 2) + 2cos^2 y - 2cos^2 y - 2√(cos^4 y + 5.75)] / 2.
27. Cancel out the common terms: (sin x + cos x)(sin y + cos y) = √[5 + 2√(cos^2 y + 2) - 2√(cos^4 y + 5.75)] / 2.
28. Simplify the expression: (sin x + cos x)(sin y + cos y) = √[5 - 2√(cos^4 y + 5.75) + 2√(cos^2 y + 2)] / 2.
29. The value of (sin x + cos x)(sin y + cos y) is 2.49.

Therefore, the value of (sin x + cos x)(sin y + cos y) is 2.49.

To know more about quadratic equation visit:

https://brainly.com/question/30098550

#SPJ11

In this problem, we use the product-to-sum trigonometric identities and the given information that sin(x+y) = 0.9 and sin(x-y) = 0.6 to find that the value of (sin x + cos x)(sin y + cos y) equals 1.5.

In this problem, you're asked to find the value of (sin x + cos x)(sin y + cos y). Before we solve it directly, let's take advantage of the given information: sin(x+y) = 0.9 and sin(x-y) = 0.6.

To solve this, we can use the product-to-sum trigonometric identities: sin(A)+cos(A)sin(B)+cos(B) = sin(A+B)+sin(A-B). According to the problem, sin(x+y) = 0.9 and sin(x-y)=0.6. Therefore, we have 0.9 + 0.6 which results in 1.5. Thus, the value of (sin x + cos x)(sin y + cos y) equals 1.5.

https://brainly.com/question/31896723

#SPJ12

Answer:

30°, 60° and 90°

Step-by-step explanation:

Given the expression Arccos (√3/2)=β, we can use the expression to calculate one of the acute angles in a right angled triangle.

Note that a right angled triangle is made up of two acute angles and a right angled (90°)

Let's get one of the acute angles first

If Arccos (√3/2)=β

β = cos^-1 √3/2

β = 30°

This shows that one of the acute angles is 30°

To get the third angle, we know that sum of angles in a triangle is 180° and since we already know two of the angles, i.e 90° and 30°, we can get the third angle.

90+30+x = 180

120+x = 180

x = 180-120

x = 60°

All the angle measurement for the right angled triangle are 30°, 60° and 90°

The area of a regular polygon inscribed in a circle is given by A = (1/2)nr^2sin(2π/n), where n is the number of sides and r is the radius of the circle.

For a square, n = 4, so A(square) = 2r^2.

For a regular octagon, n = 8, so A(octagon) = 2(2+√2)r^2.

The ratio of the areas is:

A(octagon)/A(square) = [2(2+√2)r^2]/(2r^2) = 2+√2 ≈ 3.83

Therefore, the octagon covers approximately 283% more of the circle's area than the square.

Learn more about Shapes here:- brainly.com/question/28820359

#SPJ11

The total number of shades of gray is given by 256 multiplied by 256 multiplied by 256, which is equal to 16,777,216.

In the RGB color system, a shade of gray is formed by setting the values for red, green, and blue to the same number. Since each color component can take on values from 0 to 255 (inclusive), we have 256 possible values for each component.

To determine the number of shades of gray, we need to find the number of unique combinations of values that can be formed. Since all three color components have the same value, we can simply count the number of unique values that can be chosen.

Since each component can take on 256 different values, there are 256 choices for the first component. For each choice of the first component, there are 256 choices for the second component, and likewise for the third component.

Therefore, the total number of shades of gray is given by 256 multiplied by 256 multiplied by 256, which is equal to 16,777,216. Hence, there are 16,777,216 shades of gray in the RGB color system, where each component is represented by a number between 0 and 255.

To know more about number refer here:

https://brainly.com/question/3589540

#SPJ11

Answer:

The correct option is;

Exponential function 2ˣ + 2

x = 0, 2, 4, 6, 8

f(x) = 3, 6, 18, 66, 258

Step-by-step explanation:

The given functions are;

f(x) = 2x + 2

x = 0, 2, 4, 6, 8

f(x) = 2, 6, 10, 14, 18

f(x) = 2ˣ + 2

x = 0, 2, 4, 6, 8

f(x) = 3, 6, 18, 66, 258

f(x) = 2·x² + 2

x = 0, 2, 4, 6, 8

f(x) = 2, 10, 34, 74, 130

f(x) = 3·x + 2

x = 0, 2, 4, 6, 8

f(x) = 2, 8, 14, 20, 26

By comparison, the function that increases at the fastest rate between x = 0 and x = 8 is Exponential function 2ˣ + 2

Answer: The answer is B on edg

Step-by-step explanation:

The region enclosed by the curves y = x, y = 3x, and y = -x + 4 needs to be sketched, and its area should be found.

To sketch the region enclosed by the curves, we need to plot the three given curves on a coordinate plane. The first curve is y = x, which represents a straight line passing through the origin (0,0) with a slope of 1. The second curve is y = 3x, which is also a straight line passing through the origin but with a steeper slope of 3. The third curve is y = -x + 4, which represents a line with a y-intercept of 4 and a negative slope of -1. By plotting these three lines on the same coordinate plane, we can see that they intersect at three points: (0,0), (1,3), and (3,1). The region enclosed by these curves is a triangular region with vertices at these three points. To find the area of this triangular region, we can use the formula for the area of a triangle: A = (1/2) * base * height. Let's draw the graph:

     |

   4 |         .  (2, 2)

     |      .

     |   .

     | .

   0 |_____________________

     0     1     2     3     4     5     6

In this graph, the first equation (y = x) is depicted by a diagonal line passing through the origin (0,0). The second equation (y = 3x) is a steeper line, while the third equation (y = -x + 4) is a downward-sloping line with a y-intercept of 4. In this case, the base of the triangle is the distance between the points (0,0) and (3,1), which is 3 units. The height of the triangle is the distance between the point (1,3) and the line y = -x + 4, which is also 3 units. Substituting these values into the area formula, we get A = (1/2) * 3 * 3 = 4.5 square units.

Learn more about triangle here:

https://brainly.com/question/31240589

#SPJ11

45 less than the product of 18 and a number written as an algebraic expression is 45 < 18x

Information from the problem include

45 less than the product of 18 and a number

Writing the problem as algebraic expression

let the number be x

The product

= 18 * x

= 18x

45 less than the product

45 < 18x

solving for x

divide through by 18

45 / 18 < 18x / 18

5 / 2 < x  as a improper fraction

x > 2 1/2 as a mixed number

Therefore the required algebraic expression for 45 less than the product of 18 and a number is 45 < 18x

Learn more on algebraic expression at:

https://brainly.com/question/4344214

#SPJ1

Answer:

y = -3/2x + 3

Step-by-step explanation:

To figure out the equation, it is very simple:

First you must find the y-int

The y-int is the point where the line touches the y-axis

The only point that touches the y-axis is (0,3)

so the y-int is 3

Next we need to find the slope, which is rise over run

we must find how far one point is from another point

so we start from the point (0,3) on the y-axis, then we go down 3 and to the right 2 and we are on the point (2,0)

so the slope is -3/2, because the line is going downwards, not upwards

now we just put the equation together, in the slope intercept form

y-int = b = 3

slope = m = -3/2

y = mx + b

y = -3/2x + 3

Answer: y = -3/2x + 3

Step-by-step explanation:

did the test  and hope this helps

Overall fraction of sold seats is 0.63333...

First we use the fact that 2/3 of the seats are located on the main floor and the number of seats on the main floor is 600, so the total number of seats can be calculated as follows:

Total number of seats = 600 / (2/3) = 900 seats

Next, we can find the number of seats in the balcony:

Balcony seats = Total number of seats - Main floor seats = 900 - 600 = 300 seats

Next, we can find the number of sold floor seats:

Sold floor seats = 4/5 * 600 = 480 seats

And the number of sold balcony seats:

Sold balcony seats = 1/2 * 300 = 150 seats

Finally, to find the overall fraction of sold seats in the theater, we add the number of sold floor seats and the number of sold balcony seats and divide by the total number of seats:

Overall fraction of sold seats = (480 + 150) / 900 = 0.63333... (rounded to the nearest hundredth)

Learn more about  overall fraction here: brainly.com/question/28699958

#SPJ1

Responder:

Teléfonos móviles :

Universo - -> {todos los teléfonos móviles} - unidad experimental

Población - -> {Samsung, tecno, LG, iPhone, Motorola, Huawei, .....} - -> valores variables de unidades experimentales

Muestra - - -> {Samsung, tecno, iPhone} - selección aleatoria de datos de población

Países europeos :

Universo - -> {todos europeos} - unidad experimental

Población - -> {Inglaterra, Noruega, Turquía, Italia, Francia, Holanda, .....} - -> valores variables de todos los países europeos

Muestra - - -> {España, Alemania, Polonia} - selección aleatoria a partir de datos de población

Explicación paso a paso:

Haciendo distinción entre universo, población y muestra. Univerae y la población se describen como sinónimos en algún texto. Sin embargo, otros textos estadísticos hicieron diferencias sutiles entre ambos; con el universo que se dice que contiene todas las unidades experimentales. ; siendo población el conjunto de valores de la variable. Sin embargo, podemos asumir de manera concluyente que ambos son sinónimos, ya que de ellos se extrae una muestra que es un subconjunto de un conjunto de datos más grande (población).

Answer:

here u go

Step-by-step explanation:

We can drag the particles in mass/grams measurement to the corresponding descriptions as follows:

1.  1.6744 × 10⁻²⁴: Two electrons and 0ne proton

2. 5.021 × 10⁻²⁴: Two protons and one neutron

3. 5.0224 × 10⁻²⁴: One proton and two neutrons

4. 3.3484  × 10⁻²⁴: One electron, one proton, and one neutron

To match the measurements to the descriptions first note that one neutron is 1.6749 × 10⁻²⁴. One proton is equal to  1.6726 × 10⁻²⁴ and one electron is equal to  9.108 × 10⁻²⁸.

To obtain the right combinations, we have to add up the particles to arrive at the constituents. So, for the figure;

1.6744 × 10⁻²⁴, we would

Add 2 electrons and one proton

= 2(9.108 × 10⁻²⁸) + 1.6726 × 10⁻²⁴

= 1.6744 × 10⁻²⁴

The same applies to the other combinations.

Learn more about electrons and protons here:

https://brainly.com/question/1481324

#SPJ1

The total number of groups in the study of one way ANOVA with the given condition of variable and levels is four different groups and number of different factors in one-way ANOVA is equal to one.

In a one-way ANOVA with one independent variable with four levels, there are four different groups in the study.

Each group represents a level of the independent variable.

There is only one factor in a one-way ANOVA.

The factor is the independent variable with the four levels, which is used to classify the groups in the study.

The factor is what the researcher is interested in studying.

And the ANOVA is used to determine if there are any statistically significant differences in the mean scores between the groups.

Learn more about groups here

brainly.com/question/23309302

#SPJ4

i. Vectors u and w are orthogonal.

ii. The two vectors orthogonal to v = √(2, -3) are u = (3, 2) and w = (-2, 3).

iii. The two unit vectors orthogonal to 7 are u = (1, -1) / √2 and w = (1, 1) / √2.

i. To show that vectors u = (a, b) and w = (-b, a) are orthogonal, we need to demonstrate that their dot product is zero.

The dot product of u and w is given by:

u · w = (a, b) · (-b, a) = a*(-b) + b*a = -ab + ab = 0

ii. To find two vectors orthogonal to vector v = √(2, -3), we can use the result from part i.

Let's denote the two orthogonal vectors as u and w.

We know that u = (a, b) is orthogonal to v, which means:

u · v = (a, b) · (2, -3) = 2a + (-3b) = 0

Simplifying the equation:

2a - 3b = 0

We can choose any values for a and solve for b. For example, let's set a = 3:

2(3) - 3b = 0

6 - 3b = 0

-3b = -6

b = 2

Therefore, one vector orthogonal to v is u = (3, 2).

To find the second orthogonal vector, we can use the result from part i:

w = (-b, a) = (-2, 3)

iii. To find two unit vectors orthogonal to 7, we need to consider the dot product between the vectors and 7, and set it equal to zero.

Let's denote the two orthogonal unit vectors as u and w.

We know that u · 7 = (a, b) · 7 = 7a + 7b = 0

Dividing by 7:

a + b = 0

We can choose any values for a and solve for b. Let's set a = 1:

1 + b = 0

b = -1

Therefore, one unit vector orthogonal to 7 is u = (1, -1) / √2.

To find the second unit vector, we can use the result from part i:

w = (-b, a) = (1, 1) / √2

To learn more about the unit vector from the given link

brainly.com/question/28028700

#SPJ11

He has eaten \(\frac{5}{8}\) pizza altogether.The total pieces of pizza was 8.Marco ate 3 for lunch and 2 for dinner.So, he ate 5 pieces of pizza out of 8.

What is fraction?

A fraction is a numerical value that is a part of whole number.In this numerator divided by denominator .In simple term both are integers.The word fraction means to break.

there are many types of fraction.Proper fraction, improper fraction,mixed fraction,whole fraction, like fraction, unlike fraction and unit fraction.

Total pieces of pizza =8

Marco ate for lunch =3

He ate for dinner =2

Total he ate =3+2

                     =5

Now remaining pieces of pizza=8-5

                       =3

To learn more about fractions visit:

https://brainly.com/question/10354322

#SPJ4

Answer:

5/8

Step-by-step explanation:

Step-by-step explanation:

Assume 80° should be 180° to have same pattern.

Use reduction formulas and solve:

As given, it simplifies to the above fraction.

If the sin was cos then the final result would be 1 as both numerator and denominator would be equal.

she would need to sell at least 37 bottles to reach her earnings goal.

Let's assume that Barbara needs to sell x bottles to earn $100. The total revenue she generates from selling water can be calculated by multiplying the number of water bottles (x) by the price per water bottle ($1.25). Similarly, the total revenue from selling iced tea can be calculated by multiplying the number of iced tea bottles (x) by the price per iced tea bottle ($1.49).

To earn $100, the total revenue from selling water and iced tea should sum up to $100. Therefore, we can set up the following equation:

(1.25 * x) + (1.49 * x) = 100

Combining like terms, the equation becomes:

2.74 * x = 100

To find the value of x, we can divide both sides of the equation by 2.74:

x = 100 / 2.74

Evaluating the right side of the equation, we find:

x ≈ 36.50

Therefore, Barbara needs to sell approximately 36.50 bottles (rounded to the nearest whole number) of water and iced tea combined to earn $100.

Learn more about equation here:

https://brainly.com/question/29538993

#SPJ11

Using the reflection concept, the function is given by:

\(g(x) = 5x - 2\)

------------------

The function given is:

\(f(x) = -5x + 2\)

The reflection over the x-axis is:

\(g(x) = -f(x)\)

\(g(x) = -(-5x + 2)\)

\(g(x) = 5x - 2\)

Which is the desired function g.

A similar problem is given at https://brainly.com/question/15196246

Surface area - The cost of medium popcorn will be $473.25.

What is surface area?

The surface area of a three-dimensional object is the space taken up by its outer surface.
For instance,
The surface area of a cube is what we need to calculate the amount of paint needed to paint it. It is consistently expressed in square units.

The surface area of the cylinder with the top open = πr(r + 2h)

we are given that,

r = 2in

h = 6in

taking π as 3.14, and substituting these vales in the above equation,

surface area = π x 2 (2 x 2 x 6)

= 3.14 x 2 (2 x 2 x 6)

= 1893in²

cost = 1893 x 0.25

= $473.25

to learn more about surface area visit:
https://brainly.com/question/16519513
#SPJ9

Lisa and Joe put $46 towards the gift

Let's call the amount of money that Sara put in "x".

Joe put in twice that amount, so he put in 2x.

Lisa put in ten dollars more than Sara, so she put in x + 10.

Together, Sara, Joe, and Lisa put in x + 2x + (x + 10) = $58.

Evaluate the like terms, so we have

4x + 10 = 58.

Subtracting 10 from both sides, we get

4x = 48.

Dividing both sides by 4, we find that

x = $12.

So Sara put in $12, Joe put in $24, and Lisa put in $22.

The total amount put by Lisa and Joe is  $24 + $22 = $46.

Read more about equations at

https://brainly.com/question/2972832

#SPJ1

Complete question

Three friends are put their money together to buy a $58 gift. Joe put in twice the amount of money as Sara. Lisa put in ten dollars more than Sara. How much money did Lisa and Joe put towards the gift?

You have not provided the contents of any of the drop-down menus, so we cannot say for certain what the answers should be--except in the case of "infinitely many solutions.

2x + 9 + 3x + x = 6x

2x + 9 + 3x + x = 15

2x + 9 + 3x + x = 6x + 9

Based on the given conditions,

(1) No solutions :

There will be no solutions when the left side is inconsistent with the right side:

2x + 9 + 3x + x =  _ x + _

We can sum of difference,

6x + 9 = 6x

Subtract 6x from both sides,

6x - 6x = -9

9 = 0

9 = 0 which is absurd and hence the equation has no solution.

(2) One solutions :

There will be one solution when the left side and right side are not inconsistent and not the same.

2x + 9 + 3x + x = 15

6x + 9 = 15

Subtract 9 from both sides.

6x = 6

Divide both sides by 6.

x = 1 and this is the only solution.

(3) Infinity solutions :

There will be an infinite number of solutions when the equation is true for any value of x. This will be the case when the left side and right side are identical.

2x + 9 + 3x + x = 6x + 9

6x + 9 = 6x + 9

Subtract 6x from both sides,

9 = 9, both sides are balanced which means, the equation has infinitely many solutions.

Therefore,

2x + 9 + 3x + x = 6x

2x + 9 + 3x + x = 15

2x + 9 + 3x + x = 6x + 9

To learn more about information visit Infinity solutions :

brainly.com/question/16797067

#SPJ1

The derivative of t^4*r1(t) is (6t^5, 9t^6, t^4 + 4t^3).

To evaluate the derivative of r1(t).r2(t) using the Product Rule, we first need to find the derivatives of r1(t) and r2(t) separately. The derivative of r1(t) is (2t, 3t^2, 1) and the derivative of r2(t) is (0, 0, e^t). Now we can apply the Product Rule, which states that the derivative of two functions multiplied together is the first function times the derivative of the second function plus the second function times the derivative of the first function. So the derivative of r1(t).r2(t) is:

d/dt (r1(t).r2(t)) = r1(t) * (0, 0, e^t) + r2(t) * (2t, 3t^2, 1)

= (0, 0, t^2*e^t) + (2t*e^3, 2t*e^2, 2t*e^t)

= (2t*e^3, 2t*e^2, t^2*e^t + 2t*e^t)

20. Similarly, to evaluate the derivative of t^4*r1(t) using the Product Rule, we first need to find the derivatives of t^4 and r1(t) separately. The derivative of t^4 is 4t^3 and the derivative of r1(t) is (2t, 3t^2, 1). Now we can apply the Product Rule:

d/dt (t^4*r1(t)) = t^4 * (2t, 3t^2, 1) + r1(t) * 4t^3

= (2t^5, 3t^6, t^4) + (4t^5, 6t^5, 4t^3)

= (6t^5, 9t^6, t^4 + 4t^3)

Know more about derivative here:

https://brainly.com/question/23819325

#SPJ11

There are 43,200 number of ways to arrange the letters in UNIVERSALLY so that no two vowels occur consecutively and the consonants appear in alphabetical order.

To find the number of ways to arrange the letters in UNIVERSALLY so that no two vowels occur consecutively and the consonants appear in alphabetical order, follow these steps:

1. Identify the vowels and consonants: Vowels are U, I, E, A, and Y; consonants are N, R, S, S, L, and L.

2. Arrange the consonants in alphabetical order: L, L, N, R, S, S.

3. Count the number of positions available for placing the vowels: There are 7 positions available for the vowels (between the consonants and at the beginning and the end of the word), which are _ L _ L _ N _ R _ S _ S _.

4. Count the permutations of the vowels: There are 5 vowels with the letters U, I, E, A, and Y occurring once. So there are 5! = 120 permutations.

5. Consider the consonants with repeating letters: Since there are two Ls and two Ss, we must divide the total permutations by the product of the repetitions (2! for L and 2! for S). Therefore, there are 6!/(2!*2!) = 360 arrangements for consonants.

6. Combine the permutations of vowels and consonants: To find the total number of ways to arrange the letters, multiply the permutations of vowels (120) by the arrangements for consonants (360).

120 * 360 = 43,200

So, there are 43,200 ways to arrange the letters in UNIVERSALLY so that no two vowels occur consecutively and the consonants appear in alphabetical order.

To learn more about number of ways, refer here:

https://brainly.com/question/29110744#

#SPJ11

The comparison test with the series ∑ 1 / n^(9/2) shows that the series converges.

To use the comparison test to determine if the series ∑ (sin^2 n) / n^(9/2) converges or diverges, we need to find a known series with terms that are greater than or equal to the terms of the given series. If the known series converges, then the given series also converges. If the known series diverges, then we cannot conclude anything about the convergence of the given series.

We can use the comparison test with the series ∑ \(1 / n^(9/2)\) to determine the convergence or divergence of the given series. Since \(sin^2\) n is always between 0 and 1, we have:

0 ≤ \((sin^2 n) / n^(9/2)\) ≤ \(1 / n^(9/2)\)

Therefore, by the comparison test, if the series ∑ \(1 / n^(9/2)\) converges, then the series ∑ \((sin^2 n) / n^(9/2)\) also converges. Conversely, if the series ∑ \(1 / n^(9/2)\) diverges, then the series ∑ \((sin^2 n) / n^(9/2)\) also diverges.

The series ∑ \(1 / n^(9/2)\) is a p-series with p = 9/2 > 1, so it converges. Therefore, by the comparison test, the given series ∑ \((sin^2 n) / n^(9/2)\) also converges.

The correct answer is B. The comparison test with the series ∑ \(1 / n^(9/2)\) shows that the series converges.

To know more about comparison test refer here:

https://brainly.com/question/31384533

#SPJ11

The sample mean variance of the continuous distribution will be 0.3428.

The population variance is equal to the sample size divided by the variance of the sampling distribution of the mean.

14 is the greatest and 1 is the smallest value in a uniform continuous distribution.

36-size samples are taken from the distribution.

Now,

Variance among the population = 14 – 2 = 12

The sample size is 36.

Given that the sample means' variance is defined as;

= Variation in the population / Sample Size

If you replace all the values, you get;

= 12 / 35

= 0.3428

As a result, the sample mean variance will be 0.3428.

Learn more about variance at

https://brainly.com/question/28984174

#SPJ4

The value of the quota if at least two-thirds of the votes are required to pass a motion is (2/3) x Total votes cast.

A quota is a number of votes required to approve an action, or in this case, a motion. It can be calculated as a fraction of the total votes cast or as a fixed number of votes.

In this case, we are given that at least two-thirds of the votes are required to pass a motion. This means that the quota is greater than or equal to two-thirds of the total votes cast.

We can calculate the value of the quota using the following formula:

Value of the quota = (2/3) x Total votes cast

For example, if the total votes cast are 100, then the value of the quota would be:

(2/3) x 100 = 66.67

Therefore, the value of the quota is (2/3) x Total votes cast.

To know more about quota refer here:

https://brainly.com/question/29072521

#SPJ11

The quadratic equation is solved and the y intercept is A ( 0 , 4 ) and the roots of the given equation are complex numbers

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

y = x² + 3x + 4

On simplifying , we get

the y-intercept of this equation, we set x = 0 and solve for y:

y = 0² + 3(0) + 4

y = 0 + 0 + 4

y = 4

So, the y-intercept of the given quadratic equation is (0, 4)

And , the roots of the equation is

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

x = (-3 ± √(3² - 4(1)(4))) / (2(1))

x = (-3 ± √(9 - 16)) / 2

x = (-3 ± √(-7)) / 2

So , the roots are complex numbers

Hence , the quadratic equation is solved

To learn more about quadratic equations click :

https://brainly.com/question/25652857

#SPJ1