Find the radius of a circle with an area of 90 cm^2

Answer:

Scale factor is 2

Step-by-step explanation:

A rectangle has an area of 16ft²

That is

            Length₁ x Breadth₁ =  16 ft²

Every dimension is multiplied by a scale factor, let the scale factor be s.

New dimensions are

                  Length₂ = s x Length₁

                  Breadth₂ = s x Breadth₁

New area is given by

                 Area = Length₂ x Breadth₂ = s x Length₁ x s x Breadth₁

                 Area = s² x Length₁ x Breadth₁

                 64 = s² x 16

                  s² = 4

                  s = 2

So scale factor is 2

Answer:

The absolute value of 4+7i is equal to [tex]\sqrt{4^{2}+7^{2}}[/tex].

The absolute value of the 4+7i be [tex]\sqrt{65}[/tex].

Step-by-step explanation:

The absolute value is given by .

|a + bi| = [tex]\sqrt{a^{2}+b^{2}}[/tex]

Now find the absolute value of the 4+7i.

|4+ 7i|= [tex]\sqrt{4^{2}+7^{2}}[/tex]

|4+ 7i| = [tex]\sqrt{16+49}[/tex]      

|4+ 7i| = [tex]\sqrt{65}[/tex]  

Therefore the absolute value of the 4+7i is [tex]\sqrt{65}[/tex] .  

Final answer:

Rewards program incentives are calculated by considering the alignment between the rewards offered and the needs and values of the participants. These incentives must balance the trade-off between work and compensation, adhering to principles of effort and fair compensation.

Explanation:

Understanding Rewards Program Incentives

To calculate a rewards program incentive, one must consider the various factors that influence both the likelihood and the extent to which individuals participate in the program. Such a program typically aims to increase desired behaviors - for example, increasing purchases or promoting consistent work performance - by offering some form of reward or compensation. The effectiveness of these incentives is often determined by how well they align with participants' values and needs.

In contexts where these incentives might impact work behavior, one must consider the trade-offs individuals face. If a program reduces government assistance dollar for dollar as earnings increase, this could diminish the incentive to work. Conversely, if the program allows individuals to maintain a level of government assistance even as they earn income, some might choose to work fewer hours (choice S) but still maintain or increase their total income. Others might continue to work the same number of hours (choice R) or even more, depending on how the incentives align with their personal circumstances and preferences.

There are also principles of effort and compensation to consider. Ideally, a well-designed incentive program rewards individuals according to the effort they put in and the costs they incur. However, the balance between maximizing efficiency for the program and providing adequate motivation for the participants can be complex and requires careful calibration.

To calculate a rewards program incentive, it's important to analyze the relationships among work hours, income, and effort. Changes in incentives may influence individuals to adjust their work hours to maximize benefits. The goal is to find the sweet spot where the incentive structure aligns with the desired behavior, whether that's working more, the same, or fewer hours for optimal compensation.

To calculate a rewards program incentive, you need to assess the different factors that influence choice and compensation. For instance, when a program provides financial incentives without reducing them entirely as earnings increase, individuals might alter their work hours to maximize overall income. This could mean choosing a point on the budget line, like S, where they work fewer hours but have greater income, or a point like R, maintaining the same work effort, or even increasing their hours, depending on the incentives.

The decision-making process regarding work hours and income can be complex, involving considerations of effort and compensation. These are guided by incentives and how individuals weigh the trade-offs between labor and leisure. Furthermore, such choices reflect the underlying principle that rewards should ideally align with the effort and costs involved in a person's work activity.

Changes in incentives can lead to different choices. If rewards or penalties for certain actions are adjusted, individuals may shift their decisions accordingly to maximize their benefits. For example, if a program becomes more generous without penalizing additional earnings, some may opt to work less, as they could still maintain or increase their income levels. Conversely, if the program became less generous or introduced greater penalization for earnings, individuals might be inclined to work more to achieve the same level of income.

The correct statements for this question would be:

a) The point (1, 1) is on the graph of the equation."

d) The graph of the equation is the set of all points that are solutions to the equation.

Option (a) and (d) are true.

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

The linear equation;

y = 4x - 3

Now, By option a;

To check the point (1, 1) is on the graph of the equation.

We can substitute x = 1 and y = 1 in the equation of line as;

y = 4x - 3

1 = 4 × 1 - 3

1 = 4 - 3

1 = 1

Thus, The point (1,1) is on the graph of the equation.

For option b;

Since, The point (0, 3) is not satisfy the equation y = 4x - 3.

Hence, Option b is not true.

For option c;

Since, The y - intercept of the line 4x - y = -3 and line y = 4x - 3 is not same.

Hence, Both have different graph.

Clearly, By the graph of y = 4x - 3 is is the set of all points that are solutions to the equation.

So, Option d is true.

Thus, The correct statements for this question would be:

a) The point (1, 1) is on the graph of the equation."

d) The graph of the equation is the set of all points that are solutions to the equation.

Option (a) and (d) are true.

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Answer

Find out the which line segment is a chord of circle E in the diagram below.

To prove

As given

Definition of a chord

 A chord is the striaght line  whose  endpoints are lies in the circle.

Now as shown in the diagram given in the question.

CD is the striaght line  whose endpoints lies in the circle E .

Therefore CD is a chord of circle E.

Option (d) is correct.

A rhombus becomes a square when all its angles are right angles, in addition to having equal length sides. Therefore, option B is the correct answer.

A rhombus is a type of parallelogram where all four sides are of equal length. Mind you, this doesn't automatically make it a square, which is also a kind of parallelogram but with a few extra properties. The key difference is that a square has all four angles as right angles, meaning they are 90 degrees. In a rhombus, this isn't necessarily the case.

Therefore, the correct answer to the question is 'option B) When its angles are right angles'. So a rhombus is a square only when not only all its sides are equal in length, but its angles are also all right angles.

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First, rearrange the equation so that only zero will be on the right side:

x^2 + 14x +24 = 0

Let the coefficients be:

a = 1

b = 14

c = 24

To complete the square, add (b/2)^2 to both sides of the equation:

(b/2)^2 = 49

x^2 + 14x + 49 + 24 = 49

x^2 + 14x + 49 = 25

(x+7)^2 = 25

Therefore, the solution set of the equation is {-12, -2}

The solution set of the quadratic equation x² + 14x = −24 is [-12, -2] option (a) is correct.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

We have a quadratic equation:

x² + 14x = −24

It is required to solve the equation by completing the square.

First, arrange the quadratic equation

x² + 14x + 24 = 0

x² + 14x + 7² - 7² + 24 = 0

(x + 7)² -25 = 0

(x + 7)²  = 25

x + 7 = ±5

Taking positive sign:

x + 7 = 5

x = -2

Taking negative sign:

x + 7 = -5

x = -12

The solution set is [-12, -2]

Thus, the solution set of the quadratic equation x² + 14x = −24 is [-12, -2] option (a) is correct.

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To solve 3/4 - 3/8, convert 3/4 to 6/8 and then subtract 3/8 from 6/8. The result is 3/8.

To find the answer to 3/4 - 3/8, follow these steps:

So, 3/4 - 3/8 = 3/8.

SOS

Answer:

[tex]\frac{3}{20}-\frac{1}{20}i[/tex]

Step-by-step explanation:

Find the multiplicative inverse of a complex number using the process described below:

The inverse is found by reciprocating the original complex number. The reciprocal of the complex number (6+2i) is [tex]\frac{1}{6+2i}[/tex]. Multiply the numerator and denominator of the reciprocal by conjugate of the denominator and simplify:

[tex]\frac{1}{6+2i}*\frac{6-2i}{6-2i}[/tex]

You get: [tex]\frac{3}{20}-\frac{1}{20}i[/tex]

Hope this helps!!

The probability that the rifleman will hit the target exactly 3 out of 4 shots is 0.4096, or 40.96%.

The student asked about the probability of a rifleman who averages 8 hits out of 10 shots to hit the target in 3 out of 4 shots. To solve this, we use the binomial probability formula, which is used when each shot is independent of the others.

The probability of hitting the target is given as 0.8 (8 out of 10). The probability of missing is 1 - 0.8 = 0.2. The formula for the exact outcome of 3 hits out of 4 is:
  P(X = 3) = (4 choose 3)
  (0.8)^3
  (0.2)^1

We need to calculate the binomial coefficient (4 choose 3) which is 4, multiply it by the probability of hitting the target three times (0.8)^3, and multiply the result by the probability of missing once (0.2)^1.

So, P(X = 3) = 4
  (0.512)
  (0.2) = 4
  0.1024 = 0.4096

Therefore, the probability that the rifleman will hit the target exactly 3 out of 4 shots is 0.4096, or 40.96%.

Answer:

option c

Step-by-step explanation:

because i said soooo

Final answer:

To solve for 'a' in the equation y = -1/2ax - 5 with a given slope of 5/2, we compare it to the standard linear equation format and find that 'a' is equal to -5.

Explanation:

To solve for a, we need to look at the equation y = -1/2ax - 5 given that the slope (m) is 5/2. In a linear equation of the form y = mx + b, m represents the slope. Comparing it to the given equation, we can see -1/2a is the slope in our case. Therefore, to find a, we set -1/2a equal to the given slope of 5/2 and solve:

-1/2a = 5/2

To isolate a, we first multiply both sides by -2:

a = -2(5/2)

Multiplying this out, we find:

a = -5

Thus, in the context of a linear equation and assuming the slope m provided is indeed intended to be the value of the direct variation component, the value for a is -5.

The maximum number of turns in the graph of f(x) is:

                                2

Turning Point of a graph--

The turning point of a graph is a point where the graph changes it's behavior i.e. it changes from increasing to decreasing and from decreasing to increasing.

The polynomial of degree n has atmost " n-1 " turning points.

Here we are given a polynomial f(x) as:

[tex]f(x)=2x^3-2x^2+7x-25[/tex]

The polynomial is of degree 3.

Hence, the maximum number of turning points of the function f(x) is: 3-1=2

Answer:

Statement is false .

Step-by-step explanation:

Given : The range of f(x) = [tex]log_{b}(x)[/tex] is the set of all negative real numbers.

To find : Statement is true or false.

Solution : We have given that function f(x) = [tex]log_{b}(x)[/tex].

Range :  range of logarithm function is all real numbers (-∞, ∞)

Therefore, Statement is false .

The slope of the normal line to the curve y = sqrt(8 - x^2) at the point (-2, 2) is -1/2.

The question asks for the slope of the normal line to the curve y = sqrt(8 - x^2) at the point (-2, 2). To find the slope of the normal line, we need to find the derivative of the given curve and evaluate it at the given point. The derivative of y with respect to x is d/dx [sqrt(8 - x^2)]. Using the chain rule, the derivative is -x / sqrt(8 - x^2).

To find the slope of the normal line, we take the negative reciprocal of the derivative. So the slope of the normal line is 1 / (x / sqrt(8 - x^2)). Evaluating this at x = -2, we get the slope of the normal line as -1/2.

To simplify the expression (9x^8y^3)^1/2, distribute the 1/2 exponent to the numerical coefficient and to the variables, resulting in 3x^4y^(3/2).

To simplify the expression (9x^8y^3)^1/2, we will apply the rule that states when you have an exponent (in this case the 1/2, which denotes a square root) outside the parentheses, you distribute it to both the numerical coefficient and the variables inside the parentheses. Using this rule:

Thus, the simplified form of the expression will be 3x^4y^(3/2).

The expression (9x^8y^3)^(1/2) can be simplified as 3x^4y^(3/2).

To simplify the expression, we need to understand the properties of exponents. When we have a number or variable raised to a fractional exponent, it means taking the corresponding root of the number or variable.

In this case, we are taking the square root (1/2 exponent) of each term within the parentheses: 9, x^8, and y^3.

The square root of 9 is 3 because 3^2 = 9.

The square root of x^8 is x^(8/2) = x^4 because (x^4)^2 = x^8.

The square root of y^3 is y^(3/2) because (y^(3/2))^2 = y^3.

Combining these simplified terms, we get 3x^4y^(3/2).

Therefore, the expression (9x^8y^3)^(1/2) simplifies to 3x^4y^(3/2).

Answer:

r = 1/2, -1

Step-by-step explanation:

First, you need to find the 1st and 2nd derivatives for the function y = e^rx:

y' = re^rx

y'' = r^2e^rx

Next, you substitute them into the differential equation 2y'' + y' - y = 0:

2(r^2e^rx) + re^rx - e^rx = 0

Factor e^rx out:

e^rx(2r^2 + r - 1) = 0

Divide both sides by e^rx:

2r^2 + r - 1 = 0

Factor the left side:

(2r - 1)(r + 1) = 0

Solving both of the equations, you get:

2r - 1 = 0

2r = 1

r = 1/2

r + 1 = 0

r = -1

Values: r = 1/2, -1

Answer: Hello mate! The correct answer is D.

the statement is "A number is even if the number is divisible by 6."

Here the hipotesis is "the number is divisible by 6", and this hipotesis implies the conclussion, wich is "a number is even". This is because the statement implies that te first thing we check is if the number is divisible by 6, and then we can know if the number is even or not.

this can be written as

"if a number is divisible by 6, then the number is even"

where is more easy to see wich one is the conclussion of the statement.

Then you can see that the right answer is D "the number is even"