What is the equation of the following line? Be sure to scroll down first to see all answer options.

The values of x in the interval [0, 2] that satisfy the equation are 60° and 300°. These can also be written as π/3 and 5π/3 in radians.

The given equation is 6 cos(x) − 3 = 0. To find all the values of x that satisfy the equation in the interval [0,2], we shall use the following steps

Add 3 to both sides

6 cos(x) − 3 + 3 = 03 = 6 cos(x)

Divide both sides by 6cos(x) = 3/6cos(x) = 1/2

Find the value of x by using the inverse cosine of 1/2

We know that cos(60°) = 1/2 and cos(360° - 60°) = cos(300°) = 1/2.

Thus, we have two solutions within the interval [0, 2]. Therefore, the values of x in the interval [0, 2] that satisfy the equation are 60° and 300°.These can also be written as π/3 and 5π/3 in radians.

To know more about interval, click here

https://brainly.com/question/11051767

#SPJ11

The point slope equation of the line that passes through the points (-4,8) and (4,4) is x + 2y = 12   .

The point slope form of the line passing through the points (x₁,y₁) having slope as m is given by the formula .

y-y₁ = m(x-x₁)

In the question ,

it is given that

the required line passes through the points (-4,8) and (4,4) ,

So , the slope(m) is = (4-8)/(4-(-4)

= -4/8

= -1/2

the equation of the line passing through (4,4) and slope as -1/2 in the point slope form is

(y-4) = -1/2(x-4)

y - 4 = (-x + 4)/2

2y-8 = -x + 4

x + 2y = 12

Therefore , The point slope equation of the line that passes through the points (-4,8) and (4,4) is x + 2y = 12    .

The given question is incomplete , the complete question is

Write the point slope equation of the line that passes through the points (-4,8) and (4,4) .

Learn more about Point Slope Form  here

https://brainly.com/question/28895991

#SPJ1

Answer:

y - 4 = -1/2 (x-4)

Step-by-step explanation:

thats the answer on khan

a.

The mistake in this claim is that its complex conjugate is also a root of the quadratic polynomial equation.

Since the student claims the polynomial has only one imaginary fooot of -9i, this is impossible because, a polynomial with real coefficients that has a complex root also has its conjugate as a root of the quadratic polynomial equation.

So, the mistake in this claim is that its complex conjugate is also a root of the quadratic polynomial equation.

b.

One possible factored polynomial that has the correct roots is P(x) = (x + 9i)(x - 9i)

Since -9i is a root, its conjugate +9i is also a root.

So, the factors of the quadratic polynomial are x - (-9i) and x - 9i. Which are x + 9i and x - 9i.

To obtain the factored polynomial, we multiply its factors together.

So, P(x) = (x + 9i)(x - 9i)

So, one possible factored polynomial that has the correct roots is P(x) = (x + 9i)(x - 9i).

c.

The factored polynomial in standard form is x² + 81

To write the polynomial in standard form, we expand the brackets.

So,

P(x) = (x + 9i)(x - 9i)

= x² - (9i)² (difference of two squares)

=  x² - 81i²

= x² - 81 × (-1)

= x² + 81

So, the factored polynomial in standard form is x² + 81.

Learn more about quadratic polynomial equation here:

https://brainly.com/question/7784687

The 99% confidence interval estimate of the overall difference in the percentages of Democrats and Republicans that prioritize protecting the environment is (0.41, 0.53). This means we can be 99% confident that the true difference in proportions falls within this interval.

Sample size of Democrats, n1 = 750

Number of Democrats who consider the environment as a top priority, x1 = 615

Sample size of Republicans, n2 = 850

Number of Republicans who consider the environment as a top priority, x2 = 306

Calculate the sample proportions:

Sample proportion of Democrats, p1 = x1 / n1 = 615 / 750 = 0.82

Sample proportion of Republicans, p2 = x2 / n2 = 306 / 850 = 0.36

Calculate the standard error of the difference in two sample proportions:

σd = sqrt{ [P1(1-P1) / n1] + [P2(1-P2) / n2] }

σd = sqrt{ [0.82(0.18) / 750] + [0.36(0.64) / 850] }

σd = sqrt{ 0.000180 + 0.000240 }

σd = sqrt{ 0.000420 }

σd ≈ 0.0205

Determine the level of confidence:

Given level of confidence, C = 99%

Find the critical value (z-score):

The z-score corresponding to the given level of confidence can be obtained from the standard normal table. For a 99% confidence level, the critical value is approximately z = 2.576.

Calculate the margin of error:

The margin of error is given by E = z * σd

E = 2.576 * 0.0205

E ≈ 0.0528

Construct the confidence interval:

The 99% confidence interval estimate of the overall difference in the percentages of Democrats and Republicans that prioritize protecting the environment is given by (D – d, D + d), where D is the difference in sample proportions and d is the margin of error.

(0.82 – 0.36 – 0.0528, 0.82 – 0.36 + 0.0528)

(0.41, 0.53)

Interpretation:

We can be 99% confident that the true difference in the percentages of Democrats and Republicans who prioritize protecting the environment falls within the interval (0.41, 0.53).

This means that there is a significant difference between the two groups in terms of the proportion that prioritize protecting the environment. The Democrats have a higher proportion compared to the Republicans.

To learn more about confidence interval visit : https://brainly.com/question/15712887

#SPJ11

Answer:

It is the first one I am pretty sure about it gl for the results of this exam

Answer:

k = -8

Step-by-step explanation:

Given both functions, y = k - x² and y = - 6x + 1. A line tangent to the graph means that the line has one common point with the curve. Therefore, the steps to solve this problem are:

\( \displaystyle{k - {x}^{2} = - 6x + 1}\)

Arrange in quadratic terms:

\( \displaystyle{ {x}^{2} - 6x + 1 - k = 0}\)

Apply discriminant where b = -6, a = 1 and c = 1-k:

\( \displaystyle{ {b}^{2} - 4ac = 0} \\ \\ \displaystyle{ {6}^{2} - 4(1)(1 - k) = 0} \\ \\ \displaystyle{ 36 - 4(1 - k)= 0} \\ \\ \displaystyle{ 36 - 4 + 4k = 0} \\ \\ \displaystyle{ 32 + 4k = 0} \\ \\ \displaystyle{4k = - 32} \\ \\ \displaystyle{k = - 8}\)

Therefore the value of k that makes line tangent to the curve is -8.

Answer:

75.2

Step-by-step explanation:

You first multiply 7.72 by 10, which is equal to 77.2. Now it's basic math; subtract 77.2 and 2, it equals to 75.2.

Answer:

0.0772

Step-by-step explanation:

The change in profit (ΔP) when the number of units (Δx) increases by 5, based on the given marginal profit function, is -18331.50

To find the change in profit (ΔP) when the number of units (Δx) increases by 5.

we need to evaluate the marginal profit function and multiply it by Δx.

The marginal profit function is given by dP/dx = 12.1(60 - 3x).

We are given the value of x as 121, so we can substitute it into the marginal profit function to find the marginal profit at that point.

dP/dx = 12.1(60 - 3(121))

= 12.1(60 - 363)

= 12.1(-303)

= -3666.3

Now, we can calculate the change in profit (ΔP) by multiplying the marginal profit by Δx, which is 5 in this case.

ΔP = dP/dx×Δx

= -3666.3 × 5

= -18331.5

To learn more on Change in Profit click:

https://brainly.com/question/31420071

#SPJ4

Answer: The radius is about 50.2 m.

Step-by-step explanation: The formula to find the circumference of a circle is 2\(\pi\)r. We know the radius is 8 and that you need to use 3.14 as pi so: 2×3.14×8 = 50.2

Answer:

50.24

Step-by-step explanation:

circumference of a circle formula :\(\pi\)D

D=diameter

radius x 2 =diameter

8 x 2 =16

16x\(\pi\)=50.24

have a nice day!!

Answer:

number of cans Raina will be needed in court floor is 14 cans

Step-by-step explanation:

CHECK THE COMPLETE QUESTION BELOW;

Raina is staining the wooden floor of a court. The court is in the shape of a rectangle. Its length is 46 feet and its width is 35 feet. Suppose each can of wood stain covers 115 square feet. How many cans will she need to cover the court?

CALCULATION;

Given:

length of the rectangular shape =46 feet

width of the the rectangular shape = 35 feet.

The floor of the court room is having a rectangular shape, then we need to calculate the surface Area of the rectangular shape first in order to know the number of cans that Raina will be needed

Surface Area= Length × Width

= 46feet × 35 feet

=1610 square ft

Then to get the number of cans , we need to divide the surface Area by each can of wood stain covers which is 115 square feet,

number of cans Raina will be needed in court = 1610 square ft / 115 square ft = 14

number of cans Raina will be needed in court floor is 14cans

The variance of X, where X takes the values 28, 46, 73, and 73 with equal probability, is 364.5.


To find the variance of a random variable X, you need to follow these steps:
1. Calculate the mean (average) of X.
2. Calculate the squared difference between each value of X and the mean.
3. Calculate the expected value of the squared differences.
4. The result obtained in step 3 is the variance of X.
Let’s apply these steps to the given values of X: 28, 46, 73, and 73.
Step 1: Calculate the mean (average) of X.
Mean(X) = (28 + 46 + 73 + 73) / 4 = 220 / 4 = 55
Step 2: Calculate the squared difference between each value of X and the mean.
(28 – 55)^2 = 27^2 = 729
(46 – 55)^2 = 9^2 = 81
(73 – 55)^2 = 18^2 = 324
(73 – 55)^2 = 18^2 = 324
Step 3: Calculate the expected value of the squared differences.
Expected value = (729 + 81 + 324 + 324) / 4 = 1458 / 4 = 364.5
Step 4: The result obtained in step 3 is the variance of X.
Variance(X) = 364.5
Therefore, the variance of X, where X takes the values 28, 46, 73, and 73 with equal probability, is 364.5.

Learn more about Mean here: brainly.com/question/30112112
#SPJ11

Uma pay in order to replace her stuff as $1000.

According to the scenario, Uma's possessions worth $5,600 were stolen or destroyed due to the burglary. Since this amount is less than the coverage limit, Uma will be eligible for reimbursement from her insurance policy. However, she will still need to pay the deductible.

To calculate how much Uma will pay to replace her stolen items, we need to subtract the deductible from the total loss. In this case, Uma's total loss is $5,600, and her deductible is $1,000. Therefore, the amount she needs to pay out of pocket is $1,000.

To summarize, Uma's insurance policy will cover the remaining amount after she pays the deductible. In this scenario,

Uma will receive reimbursement for

=> ($5,600 - $1,000) = $4,600

from her insurance company.

She can use this amount to replace her stolen or destroyed possessions.

To know more about insurance here

https://brainly.com/question/989103

#SPJ4

Answer:

2 pounds Raspberry costs - 9.50. I pound Raspberry cost> 9.50 =4.75 2 ki 1 pound. Strawberries cost = 3.22. cost of Raspberry Jafrost of Strawberry). = 4.75.3.22 f. 53. Raspberry cost $ 1.53 more than strawberries.

Step-by-step explanation:

Answer:

You would have 10 cents.

Step-by-step explanation:

Answer: what type of math is that?

Step-by-step explanation:

Jordan would take 22 hours to drive 1,188 miles at the same speed he drove 378 miles in 7 hours.

We can use the formula:

time = distance / speed

where speed is constant, to find the time it would take Jordan to drive 1,188 miles.

The speed at which Jordan drove can be calculated as:

speed = distance / time

where distance is 378 miles and time is 7 hours.

speed = 378 / 7 = 54 miles per hour

Now, we can use the speed to find the time it would take to drive 1,188 miles:

time = distance / speed = 1,188 / 54 = 22 hours

Therefore, if Jordan can maintain the same pace, it would take him 22 hours to drive 1,188 miles.

Learn more about Constant

https://brainly.com/question/1597456?referrer=searchResults

#SPJ11

Answer:

Hello! answer: 22.96

Step-by-step explanation:

Area is base × height × 1/2 or base × height ÷ 2

Im going to use the second method.

8.2 × 5.6 = 45.92 45.92 ÷ 2 = 22.96 therefore the answer is 22.96

Answer:

I'm not sure though but this is what I got

Step-by-step explanation:

surface area of a sphere is 4 pi r square

4×22÷7×5×5

314.3

Greetings from Brasil...

Here's our problem:

\(\large{\frac{12^{16}}{12^{4}}}\)

From potentiation properties:

Mᵃ ÷ Mᵇ = Mᵃ⁻ᵇ

division of power of the same base: I repeat the base and subtract the exponents

Bringing to our problem

12¹⁶ ÷ 12⁴

12¹⁶⁻⁴

Answer:

\(12^{12}\)

Step-by-step explanation:

Answer: 1<x<5, x<1 and x>5, x<3, x>3

Step-by-step explanation:

The function is positive when it is above the x-axis.

The function is negative when it is below the x-axis.

The function is increasing when it is going "up".

The function is decreasing when it is going "down".

The function is positive when it is above the x-axis and negative when it is below the x-axis. The function is increasing when it is going "up".The function is decreasing when it is going "down".

The function is given as:

y = -x² + 6x - 56

Here, the vertex of the parabola is located at x = 3.

The behavior of the function around the vertex:

Positive or Negative:

Since the coefficient of the x² term is -1, the parabola opens downward. This means that the function is negative when x is sufficiently far away from the vertex (to the left and right).

Increasing or Decreasing:

To the left of the vertex (x < 3), the function is decreasing.

To the right of the vertex (x > 3), the function is also decreasing.

Learn more about the functions here:

brainly.com/question/12431044

#SPJ7

Based on the information provided, the appropriate population for generalizing conclusions from the study would be C. The conclusions should apply to people at that particular college.

Since the study was conducted using a random sample of 200 people from one college, the conclusions drawn from the study are most likely applicable to the population of people at that specific college. It would be incorrect to assume that the conclusions can be generalized to all people in the same country (Option A), all people within the same city as the college (Option B), people at any college (Option D), or that the conclusions apply only to the sample (Option E).

To know more about generalizing visit-

brainly.com/question/26855809

#SPJ11

Approximately 12 percent of the people in Olde Town own both a goat and a chicken.

Let's assume there are 100 people in Olde Town. According to the given information, 40 percent of people own a goat, which means there are 40 goat owners. Additionally, 35 percent of goat owners also own a chicken, which means there are 35 percent of 40, which is 14 people, who own both a goat and a chicken.

Moreover, it is mentioned that 30 percent of people own a chicken. So, there are 30 chicken owners in Olde Town. However, we have already accounted for 14 of them who also own a goat. Therefore, there are 30 minus 14, which is 16 people who own only a chicken.

To find the number of people who own both a goat and a chicken, we add the number of people who own both to the number of people who own only a chicken: 14 + 16 = 30.

To calculate the percentage, we divide the number of people who own both by the total population of Olde Town (100) and multiply by 100: (30 / 100) * 100 = 30 percent. So, approximately 30 percent of the people in Olde Town own both a goat and a chicken, which is equivalent to 12 people.

For more questions like Populations click the link below:

https://brainly.com/question/27991860

#SPJ11

A strategy canvas is a visual framework used to analyze and compare the strategic positioning of different companies or products within an industry.

It is a tool developed by W. Chan Kim and Renée Mauborgne, the creators of the Blue Ocean Strategy, to help organizations identify and create new market spaces by differentiating their offerings.

The strategy canvas consists of two axes: the horizontal axis represents the key factors that the industry competes on, and the vertical axis represents the offering level or degree of offering provided for each factor. By plotting the current state of competing products or companies on the canvas, organizations can gain insights into the competitive landscape and identify areas of opportunity for innovation and differentiation.

The strategy canvas helps visualize the competitive factors that are driving the industry and highlights areas of convergence or similarity among existing offerings. It allows organizations to identify untapped market spaces where they can create unique value propositions and redefine the competitive boundaries.

To use a strategy canvas effectively, organizations need to analyze the key factors that customers value in the industry and assess the relative performance of their offerings compared to competitors. By identifying the factors where they are underperforming and overperforming, organizations can focus on enhancing their value proposition by reallocating resources, investing in areas of differentiation, and eliminating or reducing elements that do not create significant customer value.

A strategy canvas is a powerful tool for strategic analysis and innovation. It helps organizations visualize the competitive landscape, identify areas for differentiation, and create new market spaces by providing a clear understanding of customer preferences and the competitive factors that drive industry success.

Learn more about differentiating here:

https://brainly.com/question/24898810

#SPJ11

To find the area of a triangle, we can use Heron's formula, which states that the area (A) of a triangle with side lengths a, b, and c is given by: A = √[s(s - a)(s - b)(s - c)].

where s is the semiperimeter of the triangle, calculated as: s = (a + b + c) / 2.  In this case, we have side lengths a = 16, b = 6, and c = 13. Let's calculate the semiperimeter first: s = (16 + 6 + 13) / 2

= 35 / 2

= 17.5

Now we can use Heron's formula to find the area: A = √[17.5(17.5 - 16)(17.5 - 6)(17.5 - 13)]

= √[17.5(1.5)(11.5)(4.5)]

≈ √[567.5625]

≈ 23.83.  Therefore, the area of the given triangle is approximately 23.83 (rounded to two decimal places).

To Learn more about  Heron's formula click here : brainly.com/question/29104982

#SPJ11

Parry Company's ROI for year 2 is 33.47%.

To calculate Parry Company's ROI (Return on Investment) for year 2, we need to use the formula:

ROI = (Net Operating Income / Total Assets) × 100

Given the information:

Net Operating Income for year 2 = $930,000

Total Assets at the end of year 1 = $2,775,888

Using these values in the formula, we can calculate the ROI for year 2:

ROI = (930,000 / 2,775,888) × 100

ROI = 0.3347 × 100

ROI = 33.47%

We must apply the following method to get Parry Company's ROI (Return on Investment) for year 2:

ROI is calculated as (Net Operating Income/Total Assets) / 100.

With the knowledge:

Total Assets at the end of Year 1 were $2,775,888, while Net Operating Income for Year 2 was $930,000.

We may determine the ROI for year 2 using the following numbers in the formula:

ROI = (930,000 / 2,775,888) × 100

ROI = 0.3347 × 100

ROI = 33.47%

For similar questions on ROI

https://brainly.com/question/30561521

#SPJ8