Pr. 6. Consider the set of all functions of the form y(x)=acos2x+bsin2x with arbitrary constants a and b. Is the given set of functions a vector space? If yes, find its dimension.

Answer:

One bottle of soap will hold 3/8

Step-by-step explanation:

3/4= The amount of soap she has in total

3/4= 6/8 which is the same amount but now we can divide it by 2

.75 (6/8) divided by 2= .375 (3/8)

So each soap dispenser will have 3.75 liters of soap.

Sentences: To check our work

.375x2= .75

3/4 divided by 2= 3.75

Answer: B

Step-by-step explanation:

To find the values of x, we first need to write the function into an equation. We can derive 2 equations from the problem.

Equation 1: y=2|x+6|-4

Equation 2: y=6

Now, we can substitute.

2|x+6|-4=6

Let's solve for x.

2|x+6|-4=6        [add both sides by 4]

2|x+6|=10          [divide both sides by 2]

|x+6|=5              [subtract both sides by 6]

x=-1

Now that we know x=-1 is one of the solutions, we can eliminate C and D.

We know that the absolute value makes the number inside positive always. Therefore, let's solve for x with -5 instead.

|x+6|=-5              [subtract both sides by 6]

x=-11

Therefore, we know that B is the correct answer.

Step-by-step explanation:

From both the cases we can say that √n is either a natural number or an irrational number. Hence the correct option is (d)Either a natural number or an irrational number. Note: Before solving this type of question we should have proper knowledge of natural numbers, rational numbers and irrational numbers.

Answer:

6 of each

Step-by-step explanation:

9+11=20

120 divided by 20 =6

9x6=54

11x6=66

54 + 66= 120

so six of each

Answer:

thanks for points!

Step-by-step explanation:

i rly need it merry christmas!!

Answer:

7 cm to 1 decimal place

Step-by-step explanation:

We need to know one formula in order to solve this question and it's the volume of a cylinder formula which is π × r² × h where 'r' is the radius and 'h' is the height, we want to work out the radius not the volume so we have to set up an equation to solve for the radius given the information that the volume of the cylinder is 4620 cm³ and the height is 30cm so

→ Step 1 form the equation

π × r² × h = 4620

→ Step 2, substitute in the values in this case we only need to substitute in the height

π × r² × 30 = 4620

→ Step 3, divide 30 from both sides to isolate π and r²

π × r² = 154

→ Step 4, divide both sides by π to isolate r²

r² = 154 ÷ π

r² = 49.0197224723

→ Step 5, square root both sides to isolate 'r'

r = 7.0014086063

So the radius of the cylinder is 7 cm to 1 decimal place

Answer:

7.00 cm.

Step-by-step explanation:

V = π r^2 h so

r^2  = V / π h

r = +√(V / πh)

r =  +√( 4620 / 30π)

r = 7 .00cm.

The equation of the parabola with focus (2,5) and directrix x=18 is (x - 18)² + (y - 5)² = (y - (5 + (18 - 2) / 2))².

A parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating

straight line of that surface.

The focus of a parabola is a fixed point on the interior of a parabola used in the formal definition of the curve.

The directrix is a straight line perpendicular to the axis of symmetry and placed symmetrically with respect to the focus.

The axis of symmetry is the line through the focus and perpendicular to the directrix.

The vertex of a parabola is the point where its axis of symmetry intersects the curve. It is the point where the parabola changes direction or "opens

up" or "opens down.

The directrix is a fixed straight line used in the definition of a

parabola. It is placed such that it is perpendicular to the axis of symmetry and at a distance from the vertex equal to the

distance between the vertex and focus. It is the line that is equidistant to the focus and every point on the curve.Here's

the solution to the given problem:

The distance between the directrix and the focus is equal to p = 16 (since the directrix is x = 18, the parabola opens to the left, so the distance is measured horizontally)

The vertex is (h,k) = ((18+2)/2,5) = (10,5)

Then we can use the following formula: (x - h)² = 4p(y - k)

Substitute the vertex and the value of p. (x - 10)² = 64(y - 5)

Expand and simplify. (x - 10)² + (y - 5)² = 64(y - 5)

The equation of the parabola is (x - 10)² + (y - 5)² = 64(y - 5).

for such more question on parabola

https://brainly.com/question/17987697

#SPJ11

The answer is (B) (31.56, 38.44) which means we are 95% confident that the true population mean lies between 31.56 and 38.44.

The 95% confidence interval for the population mean, µ, is given by:

CI =  ± tα/2 * (s/√n)

where  is the sample mean, s is the sample standard deviation, n is the sample size, and tα/2 is the t-value with (n-1) degrees of freedom at the α/2 level of significance.

Here,  = 35, s = 9.38, and n = 22. From the t-distribution table with (n-1) = 21 degrees of freedom and a 95% confidence level, we have tα/2 = 2.08.

Plugging in the values, we get:

CI = 35 ± 2.08 * (9.38/√22)

= (31.56, 38.44)

Know more about 95% confidence interval here:

https://brainly.com/question/15683202

#SPJ11

If the function f(x) = |x-5| + 2, then the value of f(3) is 4

The function

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

The function is defined as the mathematical statement that shows the relationship between the independent variable and the dependent variable. The function consist of different variables, numbers and mathematical operators

Here the function consist of the absolute value symbol.

|-a| = a

The absolute value of the positive and the negative number will be always positive.

The function is f(x) = |x-5| + 2

Then,

f(3) = |3-5| + 2

= |-2| + 2

= 2 + 2

= 4

Therefore, the value of f(3) is 4

I have answered the question in general, as the given question is incomplete

The complete question is:

If f(x)=|x−5| + 2, find the value of f(3).

Learn more about function here

brainly.com/question/14364803

#SPJ4

Answer:

111

Step-by-step explanation:

Answer:

111

Step-by-step explanation:

To solve the quadratic equation 3x² + x - 5 = 0, we can use the quadratic formula:

A quadratic equation is a type of equation in algebra that involves a single variable (usually x) raised to the second power, or a multiple of x². The general form of a quadratic equation is:

ax² + bx + c = 0

where a, b, and c are constants (numbers), and x is the variable.

The quadratic equation is important in mathematics and science because it appears in many real-world applications, such as physics, engineering, and economics. It is also used to model many types of natural phenomena, such as the trajectory of a ball thrown into the air, the shape of a parabolic dish, or the behavior of a vibrating string.

Solving quadratic equations involves finding the values of x that make the equation true. This can be done using a variety of methods, including factoring, completing the square, and using the quadratic formula. The solutions to a quadratic equation can be real (meaning they are numbers that can be plotted on a number line) or imaginary (meaning they involve the square root of a negative number).

x = (-b ± √(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation.

In this case, a = 3, b = 1, and c = -5, so we can substitute these values into the formula and simplify:

x = (-1 ± √(1² - 4(3)(-5))) / 2(3)

x = (-1 ± √(61)) / 6

Therefore, the solutions to the quadratic equation are:

x = (-1 + √(61)) / 6 or x = (-1 - √(61)) / 6

These are the exact solutions, but if we want to approximate them to a certain number of decimal places, we can use a calculator. For example, to approximate the solutions to two decimal places, we get:

x ≈ 0.81 or x ≈ -1.48

Therefore, the solutions to the quadratic equation 3x² + x - 5 = 0 are approximately x = 0.81 and x = -1.48.

Learn more about quadratic equation

https://brainly.com/question/1214333

#SPJ1

The theory which was first developed by Karl Marx is Conflict Theory. The legal process through which one becomes a legally recognized citizen is called naturalization.

Karl Marx was a German philosopher, economist, historian, sociologist, political theorist, journalist, and socialist revolutionary. He is known as one of the founders of social sciences. His theory was based on the conflict between the two classes of society: the proletariat (working class) and the bourgeoisie (ruling class).

The legal process through which one becomes a legally recognized citizen is called naturalization. Naturalization is the process by which foreign individuals become citizens of a new country.

To learn more about conflict theory visit:

https://brainly.com/question/30396865

#SPJ11

Answer:

5. The sum of angles in a triangle is 180° so we can write:

9x - 16 + 3x + 11 + 7x - 5 = 180

19x - 10 = 180

19x = 190

x = 10°

6. Because the measure of an exterior angle is equal to the sum of its two remote interior angles we can write:

17x - 23 = 3x + 17 + 8x - 4

17x - 23  = 11x + 13

6x = 36

x = 6°

Answer:

5. The sum of angles in a triangle is 180° so we can write:

9x - 16 + 3x + 11 + 7x - 5 = 180

19x - 10 = 180

19x = 190

x = 10°

6. Because the measure of an exterior angle is equal to the sum of its two remote interior angles we can write:

17x - 23 = 3x + 17 + 8x - 4

17x - 23  = 11x + 13

6x = 36

x = 6°

Step-by-step explanation:

hope this helps

Answer:

7776\(\pi\)

Step-by-step explanation:

Sphere Volume Formula = 4/3 times \(\pi\) times r^2

r is the radius and in this case its 18.

4/3 times \(\pi\) times 18^3

4/3 times 5832 times \(\pi\)

4 times 1944 times \(\pi\)

7776 times \(\pi\)

The volume of the sphere is 7776\(\pi\)

Answer:

the answer is down below

Step-by-step explanation:

9 to 2

Answer:

Q=L

Step-by-step explanation:

Answer:A

Step-by-step explanation:

The decimal fraction that represents the given fraction is: 0.36.

To convert the figure from the given form to the decimal fraction, you can choose to use the long division format or simply divide it with the common factors. Between, 9 and 25, there is no common factor, so the best method to use here will be long division. Thus, we can proceed as follows:

1. 25 divided by 9

This cannot go so, we put a zero and a decimal point as follows: 0.

Then we add 0 to 90

2. Now, 25 divided by 90 gives 3 remainders 15. We add 3 to the decimal: 0.3

3. 90 minus 75 is 15. we add a 0 to this and divide 150 by 25 to get 6. This is added to the decimal to give a final result of 0.36.

Learn more about decimal fractions here:

https://brainly.com/question/29404890

#SPJ1

Answer:

$12.6

Step-by-step explanation:

Amount paid ÷ number of tickets

63 ÷ 5 = 12.6

$12.6

Answer: 13 (and Sally will always be 3 years older than Jill)

Step-by-step explanation:

Let S and J stand for Sally and Jill's ages.  We are told:

If Jill is 10, how old is Sally?

 (S-5) = (J-5)+3

 (S-5) = (10-5)+3

 S-5 = 8

 S = 13

We actually don't really need an equation for solving this, other than the question asks us to write one.  It doesn't matter how many years later, since Sally is 3 years older, she will always remain 3 years older, if we ignore the likelihood that the statement doesn't hold true for the period between their actual birthdays.

In this scenario, no lurking variable is mentioned. The study found a strong correlation between SAT scores and college grades, indicating a direct relationship between the two variables.

1. Identify the variables: The variables mentioned in the scenario are SAT scores and college grades. These are the main focus of the study.

2. Determine the correlation: The study indicates that a strong correlation exists between SAT scores and college grades. This suggests that higher SAT scores tend to be associated with higher college grades.

3. Evaluate lurking variables: In this case, no additional variables are mentioned or implied. It is possible that the study accounted for other factors, such as student demographics or study habits, to ensure the correlation between SAT scores and college grades was not confounded by other variables.

4. Conclusion: Based on the information provided, there is no indication of a lurking variable. The study simply found a strong correlation between SAT scores and college grades, suggesting a direct relationship between the two variables.

Learn more about correlation:  brainly.com/question/30116167

#SPJ11

Answer:

Shape 2 and 3

Step-by-step explanation:

shape 1 is not enclosed so it cannot have area

Answer:

x = 9

Step-by-step explanation:

Take the angle of LOJ (3x) and JOK (2x+12).

LOJ + JOK = LOK.

LOK = 57.

So, 3x + 2x + 12 = 57

3x + 2x = 5x

5x + 12 = 57

57 - 12 = 45

5x = 45

x= 9

Answer:

∠ C = 100°

Step-by-step explanation:

since 2 sides of the triangle are congruent then the triangle is isosceles with base angles congruent.

consider the angle inside the triangle to the left of 140°

this angle and 140° are a linear pair and sum to 180°

angle + 140° = 180° ( subtract 140° from both sides )

angle = 40°

then the angle on the left of the triangle = 40° ( base angles congruent )

the sum of the angles in a triangle = 180° , so

∠ C + 40° + 40° = 180°

∠ C + 80° = 180° ( subtract 80° from both sides )

∠ C = 100°

Answer:

they each share the same variable which is raised to the same exponent, 1

Step-by-step explanation:

Answer:

x = 1/3

Step-by-step explanation:

12=7+15x

12-7=15x

5=15x

5/15=x

Simplify

x = 1/3

Answer:x=1/3 or x=0.3 I hope this helpful mark me brainlist if correct

Step-by-step explanation:

12=7+15x

Move the variable to the left-hand side and change its sign

12-15x=7

Then move the constant to the right-hand side and change its sign

-15x=7-12

Calculate the difference
-15x=-5

Divide both sides of the equation by -15

x=1/3 or x=0.3

Based on the provided sample output, it seems that you have a 4x4 matrix, and you want to calculate the sum of each row. Here's an example implementation in Python:

python

Copy code

def calculate_row_sums(matrix):

   row_sums = []

   for row in matrix:

       row_sum = sum(row)

       row_sums.append(row_sum)

   return row_sums

# Get the size of the matrix from the user

size = int(input("Enter the size of the matrix: "))

# Get the matrix elements from the user

matrix = []

print("Enter the matrix:")

for _ in range(size):

   row = list(map(int, input().split()))

   matrix.append(row)

# Calculate the row sums

row_sums = calculate_row_sums(matrix)

# Print the row sums

for i, row_sum in enumerate(row_sums):

   print("Sum of the", i, "row is =", row_sum)

Sample Input:

mathematica

Copy code

Enter the size of the matrix: 4

Enter the matrix:

1 1 1 1

1 1 1 1

1 1 1 1

1 1 1 1

Output:

csharp

Copy code

Sum of the 0 row is = 4

Sum of the 1 row is = 4

Sum of the 2 row is = 4

Sum of the 3 row is = 4

This implementation prompts the user to enter the size of the matrix and its elements.

It then calculates the sum of each row using the calculate_row_sums() function and prints the results.

To know more about Python, visit:

https://brainly.com/question/30391554

#SPJ11

Answer:

Breadth=8

Length=6

OR

breadth = 6

length=8

Step-by-step explanation:

Area of 4 walls = 2(l+b)h

112=2.4(l+b)

112/8=l+b

14=l+b

l=14-b

Area of base or ceiling=l x b

48=(14-b).b

48=14b-b²

b²-14b+48=0

factorize it and we get

(b-6)(b-8)=0

taking b-6=0

b=6

l=14-6

l=8

Answer:

4 9/10

Step-by-step explanation:

There are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

The multiplication principle states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.

To find the number of ways to choose 3 men from the 12 men, we can use the formula for combination, which is: ⁿCᵣ = n! / (r! (n-r)!).

where n is the total number of men and r is the number of men chosen

so, the number of ways to choose 3 men from the 12 men = ¹²C₃ = 1.

Similarly, we evaluate the number of ways to choose 2 women from the 8 women

as = ⁸C₂ = 14

Now, using the multiplication principle, we can find the total number of ways 3 men and 2 women be chosen if they are equally considered.

220 x 14 = 3080

Therefore, there are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

Know more about multiplication principle here:https://brainly.com/question/10275154

#SPJ1