Show how you got your answer, or I will mark you wrong. If correct you get the crown

Answer:

B. √2

Step-by-step explanation:

First, rationalise the fraction so that the denominator is a whole number.

10 *  √50

⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

√50 * √50

 10 √50

⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

    50

√50 can be simplified as 5√2

10 *5√2 = 50√2

50√2

⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

 50

- The 50's cancel out and you are left with √2

The solution to the differential equation dx/dt = x*sin(t), with the initial condition x(0) = 1, is x(t) = e^(-cos(t)).

To solve the differential equation:

dx/dt = x*sin(t)

We can separate the variables and integrate both sides:

1/x dx = sin(t) dt

Integrating both sides gives:

ln|x| = -cos(t) + C

Where C is a constant of integration. Solving for x, we have:

|x| = e^(-cos(t)+C) = e^C * e^(-cos(t))

Since x(0) = 1, we can substitute t=0 and x=1 into the solution to find C:

|1| = e^C * e^(-cos(0))

So e^C = 1, and C=0. Substituting this value of C back into the solution, we have:

|x| = e^(-cos(t))

Since the initial condition x(0) = 1, we take the positive value of the absolute value:

x(t) = e^(-cos(t))

Therefore, the solution to the differential equation dx/dt = x*sin(t), with the initial condition x(0) = 1, is x(t) = e^(-cos(t)).

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Answer:

Step-by-step explanation:

You want to know angles x, y, and z in the given figure where parallel lines 'a' and 'b' are crossed by a transversal. The sum of these angles is 290°.

Angles y and z are called consecutive interior angles. As such, they are supplementary, so their sum is 180°.

  x + y + z = 290°

  x + 180° = 290°

  x = 110°

Angles x and y are vertical angles, so are congruent.

  y = x = 110°

Then z is found from ...

  y + z = 180°

  110° + z = 180°

  z = 70°

The measures of x, y, and z are 110°, 110°, and 70°, respectively.

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Answer:

5 hours

Step-by-step explanation:

Time taken for trip : t + 1

Time taken for return : t

Avg. speed (trip) : 256 km/h

Avg. speed (return) : 320 km/h

The distances covered on both trips are equal.

⇒ Distance (trip) = Distance (return)

⇒ Speed (trip) × time (trip) = Speed (return) × time (return)

⇒ (256)(t + 1) = (320)(t)

⇒ 256t + 256 = 320t

⇒ 64t = 256

⇒ t = 4 hours

Time (trip) = t + 1 = 4 + 1 = 5 hours

The comparison of the linear functions to line A are given as follows:

A linear function is defined as follows:

y = mx + b.

In which the coefficients are listed as follows:

The slope determines if the lines are parallel, perpendicular, or neither, as follows:

In this problem, the function is:

y = 4x - 6.

Hence the slope is of:

m = 4.

Then the functions, relative to y = 4x - 6, are classified as follows:

The problem gives three lines with different slopes, and you have to define if they are parallel, perpendicular or neither parallel nor perpendicular.

The intercepts are not relevant and I couldn't find the problem on the internet, hence I say that they are constants.

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Answer:

(3 x 10^3) / (12 x 10^6) = 0.00025

Answer:

B.(x-y)(x+y)

Step-by-step explanation:

The factor of x² - y² can be represented by,

A.(x - y)²

INCORRECT:

Translated to (x - y)(x - y) as the exponent says it multiplied by it self

(x - y)(x - y) = x²- 2xy + y² which doesn't match

B.(x-y)(x+y)

Correct!

x times x =  x²

-y times y = -y²

x² - y²

C.(x+y)(x+y)

INCORRECT

x times x =  x²

y times y = y²

x² + y² which doesn't match as y positive here

D.2(x - y)

INCORRECT

distribute 2 so 2x - 2y which isn't the original

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Answer:

x = 12

y = 4

Step-by-step explanation:

x = 2 + 7 + 3

x = 12

y = 8 - 2 - 2

y = 4

Answer:

x = 12

y = 4 (I know you have figured this out, still including it!)

Step-by-step explanation:

[x] See attatched

        () 3 + 7 + 2 = 12

[y] 8 - 2 - 2 = 4

Have a nice day!

  I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer: TRUE

SUIIIIIIIII

The statement that "subset h of a vector space v is a subspace of v if the zero vector is in h" is true.

A subspace is a vector space that is also encompassed within another vector space.

So, while each subspace is a vector space in its own right, it is also defined with respect to another (bigger) vector space.

Three components must be demonstrated to prove that a subset is a subspace:

Additionally, demonstrate that it is closed.

Show that it is closed when scalar multiplication is used.

Show that vector 0 is a part of the subset.

As it is stated in the question;

h represents a subset of the vector space v.

The zero vector is contained in h.

This implies that h must be in the v subspace.

Hence, the statement that "subset h of a vector space v is a subspace of v if the zero vector is in h" is true.

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Answer:

The probability that Tara will select a blue marble from each bag is \(\frac{2}{27}\).

Step-by-step explanation:

Since there are 15 marbles in the first bag and 9 marbles in the second bag, that means there are a total of 135 different combinations of one marble from each bag. Since there are 5 blue marbles in the first bag and 2 blue marbles in the second bag, there are 10 different possible combinations of one blue marble from each bag. The probability that Tara will select a blue marble from each bag can be represented as \(\frac{10}{135}\) or \(\frac{2}{27}\).

Cindy should hire the 12th worker as it would result in a net increase in profit, with additional revenue exceeding the cost of hiring. Insufficient information is provided to determine the demand curve for labor or compare its elasticity. Events that would shift the factory's demand for capital include new, more efficient machines and rising wages due to a labor shortage.

a. To determine whether Cindy should hire a 12th worker, we need to compare the additional revenue generated with the additional cost incurred. Hiring the 12th worker would increase total revenue by $150 ($2,750 - $2,600) per day, but it would also increase costs by $100. Therefore, the net increase in total profit would be $50 ($150 - $100). Since the net increase in profit is positive, Cindy should hire the 12th worker.

b. By hiring the 12th worker, Cindy can increase her total revenue from $2,600 per day to $2,750 per day. The additional revenue generated by the 12th worker exceeds the cost of hiring that worker, resulting in a net increase in profit.

c. To determine the firm's demand curve for labor, we need information about the marginal product of labor (MPL) and the wage rates. Unfortunately, this information is not provided, so we cannot complete the labor demand table or derive the demand curve for labor.

Without specific data or information about changes in the quantity of labor demanded and wage rates, we cannot determine which demand curve (from part b or c) is more elastic. The elasticity of the demand curve depends on the responsiveness of the quantity of labor demanded to changes in the wage rate.

The events that would shift the factory's demand for capital are:

a. New shoemaking machines being twice as efficient as older machines would increase the productivity of capital. This would lead to an increase in the demand for capital as the factory would require more capital to produce the same quantity of shoes.

b. The wages that the factory has to pay its workers rising due to an economy-wide labor shortage would increase the cost of labor relative to capital. This would make capital relatively more attractive and lead to an increase in the demand for capital as the factory may substitute capital for labor to maintain production efficiency.

The event "Many consumers decide to walk barefoot all the time" would not directly impact the demand for capital as it is related to changes in consumer behavior rather than the production process of the shoemaking factory.

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-10/3-(-11/3)=1/3

-11/3-(-4)=1/3 also the common difference is 1/3

Answer:

The middle one unless your solving for it its the yellow one

Step-by-step explanation:

The fraction 5/10 is equivalent to 1/2.

In Maths, a fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator

To find a fraction equivalent to 5/10, we can simplify it by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 5 and 10 is 5.

Dividing both the numerator and denominator of 5/10 by 5, we get:

5/10 = (5 ÷ 5) / (10 ÷ 5) = 1/2

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Answer:

Step-by-step explanation:

To get the value of z, we need to reduce the system of equation into two and 2 unknowns;

Add 1 and 3:

y - 12y + z + 8z = 2+12

-11y + 9z = 14 ....... 4

Also Multiply equation 1 by 3 and subtract from 2

Eqn 1 * 2 will give 3x + 3y + 3z = 6

Subtract from eqn 2;

3y-(-2y)+3z-2z = 6-(-8)

5y+z = 14 ....5

Solve 4 and 5

-11y + 9z = 14 * 5

5y+z = 14 * 11

________________

-55y + 45z = 70

55y + 11z = 154

Add both

45z+11z = 70+154

56z = 224

z= 224/56

z = 4

Hence the value of z is 4

Answer:

9 is the answer

Step-by-step explanation:

You will multiply 3x3 and 9x1 it will have the least common denominator

Answer:

110 km/hour

Step-by-step explanation:

distance = 165 km

time = 1.5 hours

constant of variation = distance/time

constant of variation = 165 km / 1.5 hours = 110 km/hour

Answer:

3584

Step-by-step explanation:

\(896\)×\(4\) =\(3584\) (refer as table of 896).

hope it help :)

Answer:50 cents. $5

Step-by-step explanation: each pound of sugar costs 50 cents. you can find that out by dividing the amount of sugar you have by the cost.

The solution to the equation ƒ(x) = x + 5 is x = y - 5, where x represents the input value and y represents the output value of the function ƒ(x).

To solve the equation ƒ(x) = x + 5, we need to find the value of x that makes the equation true.

The equation is in the form of y = x + 5, where y represents the output or value of the function ƒ(x) for a given input x.

To solve for x, we need to isolate x on one side of the equation.

ƒ(x) = x + 5

Substituting y for ƒ(x), we have:

y = x + 5

Now, we want to solve for x. To isolate x, we subtract 5 from both sides of the equation:

y - 5 = x + 5 - 5

Simplifying, we get:

y - 5 = x

Therefore, the equation is equivalent to x = y - 5.

This equation tells us that the value of x is equal to the input value y minus 5.

So, if we have a specific value for y, we can find the corresponding value of x by subtracting 5 from y.

For example, if y = 10, we substitute it into the equation:

x = 10 - 5

x = 5

Thus, when y is 10, the corresponding value of x is 5.

Similarly, for any other value of y, we can find the corresponding value of x by subtracting 5 from y.

Therefore, the equation ƒ(x) = x + 5 can be solved by expressing the solution as x = y - 5, where x represents the input value and y represents the corresponding output value of the function ƒ(x).

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The question probable may be:

solve ƒ(x) = x + 5

1- SHM stands for Simple Harmonic Motion.

In SHM, an object oscillates back and forth about an equilibrium position, with a motion that can be described by a sinusoidal function. The symbols commonly used in SHM are:

y: Displacement from the equilibrium position

t: Time

k: Spring constant or restoring force constant

m: Mass of the object

c₁ and c₂: Constants determined by initial conditions

2- Hooke's law relates the force exerted by a spring to the displacement of the object attached to it. It is represented by the second-order differential equation my" + ky = 0, where m is the mass of the object and k is the spring constant. The solution to this equation is given as y = c₁ cos(√(k/m) * t) + c₂ sin(√(k/m) * t). To determine the values of c₁ and c₂, initial conditions are needed.

3- If the initial conditions are y(0) = 0 and y'(0) = 0, which means the object starts at equilibrium with zero displacement and zero velocity, we can substitute these values into the solution equation and solve for c₁ and c₂. In this case, we find that c₁ = 0 and c₂ = 0.

4- To show that the sum of the solutions c₁ cos(w₀t) and c₂ sin(w₀t) is also a solution of the SHO (Simple Harmonic Oscillator) differential equation, we substitute the sum into the differential equation and demonstrate that it satisfies the equation. By taking the derivatives and substituting, we can show that the sum of the solutions satisfies the equation, thus confirming that it is also a solution.

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The requested functions are:

a. (f+g)(x) = (3x^2-4x-14)/(x−3)

b. (f∙g)(x) = (3x+5)/(x−3)

c. (2f+3g)(x) = (6x^2+7x-21)/(x−3)

d. (3g−4f)(x) = (-12x^2+8x+57)/(x−3)

Given the functions f(x)=3x+5 and g(x)=1/(x−3), we can find the requested functions by applying the corresponding operations to the functions.

a. (f+g)(x) = f(x) + g(x) = (3x+5) + (1/(x−3)) = (3x(x−3)+5(x−3)+1)/(x−3) = (3x^2-4x-14)/(x−3)

b. (f∙g)(x) = f(x) ∙ g(x) = (3x+5) ∙ (1/(x−3)) = (3x+5)/(x−3)

c. (2f+3g)(x) = 2f(x) + 3g(x) = 2(3x+5) + 3(1/(x−3)) = (6x+10+3/(x−3)) = (6x(x−3)+10(x−3)+3)/(x−3) = (6x^2+7x-21)/(x−3)

d. (3g−4f)(x) = 3g(x) - 4f(x) = 3(1/(x−3)) - 4(3x+5) = (3-4(3x+5)(x−3))/(x−3) = (-12x^2+8x+57)/(x−3)

Therefore, the requested functions are:

a. (f+g)(x) = (3x^2-4x-14)/(x−3)

b. (f∙g)(x) = (3x+5)/(x−3)

c. (2f+3g)(x) = (6x^2+7x-21)/(x−3)

d. (3g−4f)(x) = (-12x^2+8x+57)/(x−3)

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Bianca will earn interest of $382.5 for a period of 3years.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. In simple interest, the principal amount is always the same.

Simple interest is calculated with the following formula:

S.I. = P × R × T,

where P = Principal, R = Rate of Interest in % per annum, and T = Time

Given,

Principal P = $3000

Rate of interest R = 4.25% = 4.25/100 = 0.0425

Time T = 3 years

Simple interest S.I. = P × R × T

                              = 3000 × 0.0425 × 3

                              = 127.5 × 3

                      S.I.   = $382.5

Hence, Interest Bianca will earn in 3 years = $382.5

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Answer: y=10(3)^x

Step-by-step explanation:

if you graph it it's the only one that has the matching table values to the one shown in the question.

The experimental design used in this case is a pre-post or before-after design. The response variable is the knowledge-gained score. The treatment in this experiment is the instructional intervention.

(a) The experimental design used in this case is a pre-post or before-after design. This design involves measuring the same individuals or groups before and after a treatment or intervention to assess any changes or differences. In this scenario, the pre-test and post-test are conducted to evaluate the impact of the intervention (teaching) on student learning.

(b) The response variable in this experiment is the knowledge-gained score. It represents the difference or change in test scores between the pre-test and post-test. The knowledge-gained score serves as a measure of the extent to which students' learning has improved as a result of the math course and instructional intervention.

(c) The treatment in this experiment refers to the instructional intervention implemented by the mathematics professor. It encompasses the various teaching methods, strategies, and materials employed to facilitate student learning in developmental math courses. The treatment could involve activities such as lectures, interactive discussions, practice exercises, assignments, or additional support provided to the students to enhance their math skills and knowledge.

By comparing the pre-test and post-test scores, the professor can determine the effectiveness of the treatment in improving student learning. The knowledge-gained score provides a quantitative measure of the extent to which students' knowledge and understanding have progressed over the course of the intervention. This information can be valuable for assessing the impact of the math courses and guiding future instructional practices.

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Answer:

The Answer is C: \(y > x, y < 4\)

Step-by-step explanation:

By looking at the graph the shaded area is the inequalities that you need to find.

\(y=4\) is the lines on the y-axis. Below the y-axis is shaded \(y < 4\).

From the \(y=x\) is a linear line. Above the linear line is \(y > x\)