5. Which equation in point-slope form contains the points (6, 2) and (2, 4)?
O,
O
O
O
y-2=-2(x-6)
y-4=--(x-6)
y-4--2(x-2)
y-2---(x-6)

Answer:

Check below or above

Step-by-step explanation:y

Answer:

A) total area = 364ft²

B) total cost = $2,184

Step-by-step explanation:

total area of the brick paver border that surrounds the pool

= w * h = 14 * 26 = 364ft²

if brick pavers cost $6 per square foot

total cost of the brick pavers needed for this project

= 364 * 6 = $2,184

Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

The volume of the cylinder is 1538.6 units³

The volume of a cylinder can be defined as the amount of space inside the cylinder. In other words, it is the total amount of material that the cylinder can hold. To calculate the volume of a cylinder, we need to know the radius and height of the cylinder.

In your problem, the radius of the cylinder is given as 7 meters and the height is given as 10 meters. Using this information, we can calculate the volume of the cylinder as follows:

First, we need to find the area of the base of the cylinder, which is a circle. The formula for the area of a circle is A = πr², where r is the radius of the circle. So, in this case, the area of the base of the cylinder is:

A = π(7)² = 49π

Next, we can use the formula for the volume of a cylinder, which is V = Ah, where A is the area of the base and h is the height of the cylinder. So, in this case, the volume of the cylinder is:

V = 49π(10) = 490π

Apply the value of π as 3.14 then we get the volume as,

=>  V = 490  x 3.14 = 1538.6m³

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Complete Question:

What is the volume of the cylinder below?

A. 70 units³

B. 3577 units³

C. 1538.6 units³

D. 2257 units³

Answer:

y= 50

Step-by-step explanation:

y=5x+25

=> x= 25/5

=5

Therefore, x=5

y= 5x+25

=>y= 5 × 5 +25

=> y = 50

Answer:

\(f(x)=\frac{5}{6}(x+2)^2(x-1)(x-3)\)

Step-by-step explanation:

The root -2 has a multiplicity of 2, and corresponds to a factor of \((x+2)^2\).

The root 1 has a multiplicity of 1, and corresponds to a factor of \((x-1)\).

The root 3 has a multiplicity of 1, and corresponds to a factor of \((x-3)\).

So, \(f(x)=a(x+2)^2(x-1)(x-3)\).

Since \(f(0)=10\),

\(10=a(0+2)^2(0-1)(0-3) \\ \\ 10=12a \\ \\ a=\frac{5}{6} \\ \\ \therefore f(x)=\frac{5}{6}(x+2)^2(x-1)(x-3)\)

The height of package is 34 inches.

According to the statement

we have given that the perimeter of cylinderical package is 123 inches.

and we have to find the volume of this package.

So,

According to the perimeter

2(Pi)r + h = 123

and then

h = 123 - 2(Pi)r

then the volume become

V = (Pi) r^2h

V= (Pi) r^2 * [ 123 - 2(Pi)r ] = 123 (Pi) r^2  - 2(Pi)r^3

then differentiate it

dV/dr = 246(Pi) r - 6(Pi)r^2

Now take

r(246(Pi) - 6(Pi)r) = 0

then neglect r=0 and then find another value of r.

r = 246(Pi) / 6(pi)

here r=41 then

h = 123 - 2(Pi)r

h = 123 - 2(3.14)41

h = 123 - 2(Pi)r

Then put the value of r then h = 34 inches.

So, The height of package is 34 inches.

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The required polynomial with long run behavior whose only intercepts are (-5,0), (1,0), (5,0), g(x) - x4 = and (0,8) is f(x) = (8/25)(x + 5)(x - 1)(x - 5).

Given that, we need to find the equation for a polynomial with long run behavior whose only intercepts are (-5,0), (1,0), (5,0), g(x) - x4 = and (0,8).

To find the equation for the polynomial, we can make use of the following steps:

Step 1:

Determine the polynomial degree based on the number of x-intercepts and their multiplicities. In this case, there are three x-intercepts (-5, 0), (1, 0), and (5, 0), each of which has multiplicity 1. Therefore, the degree of the polynomial is 3.

Step 2:

Use the x-intercepts to construct the factored form of the polynomial,

f(x) = a(x + 5)(x - 1)(x - 5), where a is a constant to be determined.

Step 3:

The remaining information, g(x) - x4 = and (0,8), is used to determine a's value. We can plug in the value of x = 0 into the factored form of the polynomial to get

f(0) = a(5)(-1)(-5)

= 25a.

Since the y-intercept is (0, 8), we know that f(0) = 8. Therefore,

25a = 8, and

a = 8/25.

Step 4:

Substitute the value of a into the factored form of the polynomial to get

f(x) = (8/25)(x + 5)(x - 1)(x - 5).

Therefore, the required polynomial with long run behavior whose only intercepts are (-5,0), (1,0), (5,0), g(x) - x4 = and (0,8) is f(x) = (8/25)(x + 5)(x - 1)(x - 5).

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Using trigonometric identity, cos(A-B) is:

\(cos (A-B) = \frac{2\sqrt{8}\ + \sqrt{5}}{9}\)

Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

If sin A = 1/3 and A terminates in Quadrant 1. All trigonometric functions in Quadrant 1  are positive

sin A = 1/3 (sine = opposite/hypotenuse)

adjacent = √(3² - 1²)

               = √8 units

cosine = adjacent/hypotenuse. Thus,

\(cos A = \frac{\sqrt{8} }{3}\)

If cos B = 2/3 and B terminates in Quadrant 4.

opposite = √(3² - 2²)

                = √5

In  Quadrant 4, sine is negative. Thus:

\(sin B = \frac{\sqrt{5} }{3}\)

We have:

cos(A-B) = cosA CosB + sinA sinB

\(cos (A-B) = \frac{\sqrt{8} }{3} * \frac{2}{3} + \left \frac{1}{3} * \frac{\sqrt{5} }{3}\)

\(cos (A-B) = \frac{2\sqrt{8} }{9} + \left\frac{\sqrt{5} }{9}\)

\(cos (A-B) = \frac{2\sqrt{8}\ + \sqrt{5}}{9}\)

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Answer:

1. 3

2. 6.15

3. 3.976

4. 2.11

Step-by-step explanation:

Hope this helped:)) Plz mark Brainliest :))

confounding variables; the medical study did not control for other factors that could have caused the lower blood pressure in pet owners.

A confounding variable is an extraneous factor that can influence the results of a study. In this case, the medical study reported that people who owned pets had lower blood pressure than those who did not own pets. This led some doctors to believe that pet ownership had positive health benefits. However, further analysis of the data revealed that the pet owners in the study also exercised more and smoked less than those who did not own pets. This means that the pet ownership was not necessarily responsible for the lower blood pressure, but rather these other factors could have contributed to the results. Thus, the study lacked control for these confounding variables, which could have invalidated the results.

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Answer:

82 is the median

Step-by-step explanation:

Statistical guidance should perform well in situations such as clinical trials and market research where rigorous data analysis and inference are necessary. Statistical methods provide a systematic approach to control biases, handle variability, and draw reliable conclusions, ensuring accurate decision-making and predictions based on the data.

Statistical methods are crucial in determining sample sizes, designing the study, and analyzing the data to draw valid conclusions about the effectiveness and safety of the treatment.

In this situation, statistical guidance should do well because it provides a systematic framework to control for biases, random variability, and confounding factors, ensuring robust and reliable results that can be generalized to a larger population.

One example where statistical guidance should perform well is in clinical trials for new drugs or treatments.

Another example is in market research and opinion polling. Statistical techniques can be used to collect and analyze data from a representative sample of the target population, allowing for accurate estimation and prediction of consumer preferences, market trends, or election outcomes.

Statistical guidance should do well in this situation because it provides methods for random sampling, hypothesis testing, and confidence interval estimation, which help minimize sampling errors and increase the reliability of the findings.

Additionally, statistical models can capture complex relationships and make accurate predictions based on the observed data.

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Answer:

B

Step-by-step explanation:

b is the correct answer because once u combine the like terms and do all the math that is what the answer is

Answer:

I think C would be 3.25

Step-by-step explanation:

Because if you divide 65/20+3.25 sorry if i'm wrong.

Answer:

The highest number that divides each of the two or more numbers is the HCF or Highest Common Factor.

Step-by-step explanation:

Example: What is the HCF of {12,42,14}

Answer: The HCF is 2 as the biggest number they can all be divided by is 2. {12,42,14} = {2^2*3,2*3*7,2*7} The factors in each number is 2.

14. Is B

16. Is B

correct

Answer:

x = 0.5

Step-by-step explanation:

The result can be shown in multiple forms. This one is decimal form.

Option-B is correct that is the value of expression 4cos(6m)°sin(6m)° is 2sin(12m)° by using the trigonometric formula.

Given that,

We have to find the value of expression 4cos(6m)°sin(6m)° by using an trigonometric formula to write the expression as a trigonometric function of one number.

We know that,

Take the trigonometric expression,

4cos(6m)°sin(6m)°

By using the trigonometric formula we get the value of expression.

Sin2θ = 2cosθsinθ

From the expression we can say that it is similar to the formula as,

θ = 6m

Then,

= 2(2cos(6m)°sin(6m)°)

= 2(sin2(6m)°)

= 2sin(12m)°

Therefore, Option-B is correct that is the value of expression is 2sin(12m)°.

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Answer:

it's b

Step-by-step explanation:

it satifies Pythagoras theorem.

29² = 20²+21²

The price per unit that yields maximum revenue is $400.

We can start by finding the demand function for the product. Since the demand is assumed to be linear, we can use two data points to find the equation of the line:

(40, 300) and (45, 275)

Using the point-slope form of a line, we get:

(275 - 300) / (45 - 40) = -5/25 = -1/5

y - 300 = (-1/5)(x - 40)

y = (-1/5)x + 320

where y is the number of units sold per week and x is the price per unit.

The revenue function is simply the product of the price and the number of units sold:

R = xy

Substituting the demand function, we get:

R = x(-1/5)x + 320x

Simplifying, we get:

R = -1/5x^2 + 320x

To find the price per unit that yields maximum revenue, we need to take the derivative of the revenue function with respect to x and set it equal to zero:

dR/dx = -2/5x + 320 = 0

Solving for x, we get:

x = 800/2 = $400

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he get gain of rupees 1500

gain percent = Profit% = [Profit/CP] × 100

1500/5000×100 = 30%

Solution:

Given the figure;

Then;

CORRECT ANSWER: Corresponding Angles Theorem

The answer to the Equation (|b-8|=2b) is b = 8/3

Given Equation-

   |b-8|=2b

Subtract 2b from both sides

|b-8|-2b = 2b-2b

Now we will simplify it by rearranging and combining like terms

we get,

-2b + |b-8| = 0

split the problem into two cases: one positive and one negative

-2b + b-8 = 0 --eqn 1

-2b - (b-8) = 0 --eqn 2

now solve equation 1 and combine like terms

we get,

-b - 8 = 0

b= -8

equation 2

we get,

-3b=-8

b=8/3

Remove invalid solution

that is b = -8

The answer to the Equation (|b-8|=2b) is b = 8/3

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The thickness of the clay layer, which drains only from the upper surface, can be determined based on the consolidation settlement observations. With 50% of consolidation settlement occurring in 1 hour for a 25 mm thick specimen, and a total primary consolidation settlement of 35 mm occurring over many years, the thickness of the clay layer is approximately 87.5 mm.

The consolidation settlement of a clay specimen can be used to estimate the thickness of a clay layer that drains only from the upper surface. In this case, the observed settlement data provides valuable information.

Firstly, we know that 50% of the consolidation settlement occurs in 1 hour for a 25 mm thick clay specimen. This is an important parameter for calculating the coefficient of consolidation (Cv) using Terzaghi's theory. From the Cv value, we can estimate the time required for full consolidation settlement.

Secondly, we are given that the same clay settles 10 mm over 10 years and eventually settles a total of 35 mm over a longer period. This long-term settlement is known as the total primary consolidation settlement. By comparing this settlement value with the settlement data from the oedometer test, we can determine the thickness of the clay layer.

To calculate the thickness, we can use the concept of the consolidation settlement ratio. The ratio of the total primary consolidation settlement to the consolidation settlement at 50% completion is equal to the ratio of the total thickness to the thickness at 50% completion. Applying this ratio, we can determine that the thickness of the clay layer, which drains only from the upper surface, is approximately 87.5 mm.

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Answer:

n = -0.4, or n = -2/5.

Step-by-step explanation:

They are the same btw.

The mathematicians credited with developing the mathematical models that predict population growth in each of two competing species are Rosenzweig and MacArthur(OPTION A).

These two scientists developed a theory known as the "competitive exclusion principle," which states that two species competing for the same resources cannot coexist indefinitely. Instead, one species will eventually outcompete and displace the other species.
Rosenzweig and MacArthur's model is based on the Lotka-Volterra equations, which are a set of differential equations that describe the dynamics of predator-prey relationships. They extended this model to include two competing species and developed the concept of the "ecological niche" – the specific set of environmental conditions under which a species can survive and reproduce.
Their model predicts that the two species will reach a stable equilibrium, where their populations remain relatively constant over time. However, the exact outcome of the competition depends on several factors, including the initial population sizes of the two species, the relative strengths of their ecological niches, and the availability of resources.
Overall, Rosenzweig and MacArthur's mathematical model has been influential in the field of ecology, providing a framework for understanding how competing species interact and how ecosystems evolve over time.

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