I need help on this I can’t figure it out

The area of the region R is 4/3 square unit, while the value of c is 2 - √3.

To find the value of c for which the two subregions have the same area, we need to first find the points of intersection of the given curves.

Setting y = 2x - x^2 = 0, we get x = 0 and x = 2. So the curves intersect at the points (0,0) and (2,0).

Now, we can set up the integral to find the area of the region R:

A = ∫[0,2] (2x - x^2) dx

A = [x^2 - (x^3/3)]|[0,2]

A = (4/3) square units

Next, we need to find the value of c for which the two subregions of R have the same area. Let (a, 2a - a^2) be the point where the line y = cx intersects the curve y = 2x - x^2.

So we have:

2a - a^2 = ca

Rearranging, we get:

a^2 - 2a + c = 0

Using the quadratic formula, we get:

a = (2 ± √(4 - 4c))/2 = 1 ± √(1 - c)

Since a > 0, we must choose the positive root.

Now, we can set up the integrals to find the areas of the two subregions of R:

A1 = ∫[0,a] (2x - x^2 - cx) dx

A2 = ∫[a,2] (2x - x^2 - cx) dx

Setting A1 = A2, we get:

∫[0,a] (2x - x^2 - cx) dx = ∫[a,2] (2x - x^2 - cx) dx

Solving for c, we get:

c = (2a - a^2)/(2a - 2)

Substituting a = 1 + √(1 - c), we get:

c = 2 - √3

Therefore, the value of c for which the two subregions of R have the same area is 2 - √3.

Learn more about area of regions here:

https://brainly.com/question/31377501

#SPJ1

This means that we can be 95% confident that the true population means examination score falls within this range based on the sample data.

The confidence interval estimate of the population means examination score can be calculated using the sample mean and the margin of error. The margin of error depends on the level of confidence and the sample size.

For example, if a sample of 100 applications provided a sample mean score of 80, and a 95% confidence level is used, the confidence interval estimate of the population mean examination score would be:

Margin of error = (critical value) x (standard error)

The critical value for a 95% confidence level with 99 degrees of freedom is 1.984. The standard error can be calculated using the formula:

Standard error = (standard deviation) / sqrt(sample size)

If the standard deviation of the examination scores is known, it can be used in the formula. If not, the sample standard deviation can be used as an estimate.

Assuming a sample standard deviation of 10, the standard error would be:

[tex]Standard\  error = \frac{10} { \sqrt{(100)}} = 1[/tex]

Therefore, the margin of error would be:

Margin of error = 1.984 x 1 = 1.984

The confidence interval estimate of the population means examination score would be:

80 ± 1.984, or between 78.016 and 81.984.

This means that we can be 95% confident that the true population means examination score falls within this range based on the sample data.

learn more about confidence intervals,

https://brainly.com/question/24131141

#SPJ11

The 95% confidence interval for the population mean examination score would be between 72.23 and 77.77, to the

nearest whole number.

To determine the confidence interval estimate of the population mean examination score based on a sample mean

provided to the nearest whole number, we need to know the sample size and the level of confidence.

Assuming a normal distribution and a level of confidence of 95%, we can use the following formula to calculate the

confidence interval estimate:

Confidence interval = sample mean +/- (critical value) x (standard error)

The critical value can be found using a t-distribution table or a calculator, based on the sample size and degrees of

freedom (n-1). For a sample size of 30 or more, we can use the z-score instead of the t-score.

The standard error is the standard deviation of the sample divided by the square root of the sample size.

For example, if a sample of 50 applications provided a sample mean of 75, and the standard deviation was 10, the

standard error would be 10/sqrt(50) = 1.41.

Assuming a level of confidence of 95%, the critical value for a sample size of 50 and degrees of freedom of 49 would be 1.96.

Therefore, the confidence interval estimate would be:

75 +/- 1.96 x 1.41 = 75 +/- 2.77

for such more question on confidence interval

https://brainly.com/question/20309162

#SPJ11

Answer: 1

Step-by-step explanation: It is the middle of the sequence, so you basically count until you find the middle

The correct option a. may.The data shown in the may histogram is more centered around a high peak.

A graph called a histogram is used to show the frequency distribution of a small number of data points for a single variable.

For the given two histograms,

May has the peak value for the frequency of day at 14.

July has the peak value for the frequency of day at 10.

Thus, The data shown in the may histogram is more centered around a high peak.

Know more about the histograms:

https://brainly.com/question/28164315

#SPJ1

Complete question-

which data set is more centered around a high peak??

a. may

b. july

c. neither

d. both

The diagram for the question is shown.

Answer:

C and D

Step-by-step explanation:

cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{4}{5}[/tex] ⇒ C

sinA = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{3}{5}[/tex] ⇒ D

Answer:

2x-13

Step-by-step explanation:

First flip the operation to be (-10x^2+2x-10) + (10x^2-3).

Then you simplify it. The 10x^2 would get canceled out. You would then get 2x-13.

To determine if each ordered pair is a point of intersection between the line x - y = 6 and the circle y² - 26 = -x², we need to substitute the values of x and y in both equations and see if they are true for both.

For the ordered pair (1, -5):

x - y = 6 becomes 1 - (-5) = 6, which is true.

y² - 26 = -x² becomes (-5)² - 26 = -(1)², which is false.

Therefore, (1, -5) is not a point of intersection.

For the ordered pair (1, 5):

x - y = 6 becomes 1 - 5 = -4, which is false.

y² - 26 = -x² becomes (5)² - 26 = -(1)², which is true.

Therefore, (1, 5) is a point of intersection.

For the ordered pair (5, -1):

x - y = 6 becomes 5 - (-1) = 6, which is true.

y² - 26 = -x² becomes (-1)² - 26 = -(5)², which is false.

Therefore, (5, -1) is not a point of intersection.

So the answer is:

(1,-5) - No

(1,5) - Yes

(5,-1) - No

to know more about equations

brainly.com/question/29657983

#SPJ1

Answer:

4028

Step-by-step explanation:

Answer:

4028

Step-by-step explanation:

You need to subtract 9,755 from 13,783 on a calculator and you get your answer.hope it helps

We have identified three parent functions that exhibit 180-degree rotational symmetry around the point (0,0): the constant function f(x) = 0, the odd power functions f(x) = x²ⁿ⁺¹ for any integer n, and the tangent function f(x) = tan(x) on the interval (-π/2, π/2).

A function f(x) exhibits 180-degree rotational symmetry around the point (0,0) if and only if f(-x) = -f(x) for all x. To see why, consider rotating the graph of f(x) by 180 degrees around the origin.

Using this criterion, we can identify the parent functions that have 180-degree rotational symmetry around the point (0,0). These functions are:

The constant function f(x) = 0. This function is symmetric about the origin, and any rotation around the origin preserves this symmetry.

The odd power functions f(x) = x²ⁿ⁺¹ for any integer n. These functions are also symmetric about the origin, and any rotation around the origin preserves this symmetry. To see why, note that f(-x) = (-x)²ⁿ⁺¹ = -x²ⁿ⁺¹ = -f(x) for all x.

The tangent function f(x) = tan(x) on the interval (-π/2, π/2). This function has vertical asymptotes at x = π/2 and x = -π/2, but these do not affect its rotational symmetry around the origin.

To see why, note that f(-x) = tan(-x) = -tan(x) = -f(x) for all x in the interval (-π/2, π/2).

To know more about function here

https://brainly.com/question/28193995

#SPJ4

Answer:

To dilate a triangle using a scale factor of 3.5, we multiply the distance between each vertex and the center of dilation (in this case, the origin) by 3.5.

Using this information, we can find the coordinates of each vertex of triangle A'B'C':

A' = (43.5, 33.5) = (14, 10.5)

B' = (33.5, -23.5) = (10.5, -7)

C' = (-33.5, 13.5) = (-10.5, 3.5)

Therefore, the vertex of point C' is (-10.5, 3.5).

So the correct answer is C′(−10.5, 3.5).

If y is proportional to the square root of x and y = 60 when x = 36, then the value of x when y = 80 is 64

We are given that y is proportional to the square root of x, or y ∝ √x.

Using the constant of proportionality k, we can write this relationship as:

y = k√x

To solve for k, we can use the values given in the problem

y = 60, x = 36

60 = k√36

60 = k × 6

k = 60 / 6

Divide the numbers

k = 10

Now that we know k, we can use the same equation to find x when y = 80

80 = 10√x

Squaring both sides, we get

6400 = 100x

x = 64

Learn more about proportional here

brainly.com/question/29765554

#SPJ4

The given question is incomplete, the complete question is:

y ∝ √x If y = 60 when x = 36, find x when y = 80​.

The answer is   X = 10

⇒ Given [tex]\frac{2x}{3} + 1 = \frac{7x}{15} + 3[/tex]

⇒  [tex]\frac{2x+3}{3} = \frac{7x+45}{15}[/tex]

⇒ 15(2x + 3) = 3(7x + 45)

⇒ 30x + 45 = 21x + 135

⇒ 30x - 21x = 135 - 45

⇒ 9x = 90

⇒ x = [tex]\frac{90}{9}[/tex]

⇒ Therefore X = 10

To know more about Solving Equations  : https://brainly.com/question/29011747

The probability of selecting no Independents is $\frac{{7 \choose 2} + {8 \choose 2}}{{20 \choose 2}} = \frac{91}{190} \approx 0.4789$.

Weight cannot be represented as a function of height.

No, the weight of Karim's friends cannot be represented as a function of their height.

To represent weight as a function of height, there should be a consistent relationship between the height and weight values.

However, from the given data, we can see that for the same height, there are different weight values, and for the same weight, there are different height values.

This indicates that there is no one-to-one relationship between height and weight, and hence weight cannot be represented as a function of height.

Read more about function at

https://brainly.com/question/28532394

#SPJ1

The probability that no more than 4 of the next 10 households that a student visits will purchase a raffle ticket is 1%.

Probability refers to the likelihood or chance of a particular event occurring, and it is usually expressed as a number between 0 and 1. An event with a probability of 0 is impossible, while an event with a probability of 1 is certain.

For example, if you toss a fair coin, the probability of getting heads is 0.5, and the probability of getting tails is also 0.5. If you roll a fair six-sided die, the probability of rolling a 6 is 1/6, and the probability of rolling any other number is also 1/6. Based on the information, the correct option is C.

Learn more about probability on

https://brainly.com/question/31306378

#SPJ1

The answer to this question is  0.077

The prompt on measurement of rooms and surface area is given below. Note that the total surface area of the room is 752 ft².

Therefore, the total surface area of the room is 96 + 96 + 160 + 160 + 120 + 120 = 752 square feet.

Learn more about Surface Area at:

https://brainly.com/question/29298005

#SPJ1

An equation that represents a function that relates the value of Ethan’s car in dollars, g(t), and the time in years since he bought the car.

[tex]g(t) = P * e^{(-rt)[/tex]

Assuming that Ethan's car depreciates in value over time, a commonly used function to model such depreciation is an exponential decay function of the form:

[tex]g(t) = P * e^{(-rt)[/tex]

where:

[tex]g(t) = P * e^{(-rt)[/tex]

where P, r, and t are specific values based on the purchase price and depreciation rate of Ethan's car, as well as the time that has passed since he bought it.

To know more about equation visit:

https://brainly.com/question/10413253

#SPJ1

The statement that is true about Evan's expression is that it represents a linear function of the amount of medicine in his bloodstream, where the initial amount is 100 milligrams and the rate of change is -0.4 milligrams per minute.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

The expression 100 - 0.4m represents the amount of medicine in Evan's bloodstream after m minutes, where the amount of medicine decreases by 0.4 milligrams each minute.

The coefficient of the variable m (-0.4) represents the rate of change of the amount of medicine in Evan's bloodstream per minute. It tells us that for every one minute that passes, the amount of medicine in his bloodstream decreases by 0.4 milligrams.

The constant term (100) represents the initial amount of medicine in Evan's bloodstream before the medicine starts to decrease.

Therefore, the statement that is true about Evan's expression is that it represents a linear function of the amount of medicine in his bloodstream, where the initial amount is 100 milligrams and the rate of change is -0.4 milligrams per minute.

To learn more about the equivalent expression visit:

https://brainly.com/question/2972832

#SPJ1

The values of a and C using Law of sines is: a = 23.2 and C = 94°

You can use the Law of Cosines, if only one of which is missing: three sides and one angle. Hence, if the known properties of the triangle is SSS(side-side-side) or SAS (side-angle-side), this law is applicable.

You can use the Law of Sines if you want to equate the ratio of the sine of an angle and its opposite side. This can be used if the known properties of the triangle is ASA(angle-side-angle) or SAS.

We are given the parameters as:

A = 39°, B = 47°, and b = 27

a/sin A = b/sin B

Thus:

a = (27 * sin 39)/sin 47

a = 23.2

Sum of angles in a triangle is 180 degrees. Thus:

C = 180 - (47 + 39)

C = 94°

Read more about Law of sine at: https://brainly.com/question/4372174

#SPJ1

The next three terms of the sequence.

(a) The sequence alternates between a run of "1"s and a run of "0"s.

Specifically, the nth term is 1 if the number of "1"s in the first n-1 terms is

odd, and 0 if the number of "1"s in the first n-1 terms is even.

(b) The nth term is[tex]\lfloor (n+1)/2\rfloor[/tex] if n is odd, and n/2 if n is even.

(c) The nth term is[tex]2^{(n-1)/2}[/tex] times the parity (i.e., 0 or 1) of n.

(d) The nth term is [tex]3\cdot 2^{n-1}[/tex].

(e) The nth term is 15-7(n-1).

(f) The nth term is the sum of the first n positive integers minus 3, i.e.,

[tex]1+2+3+\cdots+n-3.[/tex]

To determine the next three terms of each sequence, we simply apply the rule or formula given above. For example, for sequence (a), the next three terms are 0, 1, 1, since the next term is 0 (since there are an even number of 1's so far), followed by two 1's (since there are now an odd number of 1's).

For sequence (b), the next three terms are 9, 10, 10, since the next term is 9 (since the next term in the pattern is odd), followed by two 10's (since the next two terms in the pattern are even). And so on for the other sequences.

(a) The sequence alternates between a run of "1"s and a run of "0"s.

Specifically, the nth term is 1 if the number of "1"s in the first n-1 terms is

odd, and 0 if the number of "1"s in the first n-1 terms is even.

(b) The nth term is[tex]\lfloor (n+1)/2\rfloor[/tex] if n is odd, and n/2 if n is even.

(c) The nth term is[tex]2^{(n-1)/2}[/tex] times the parity (i.e., 0 or 1) of n.

(d) The nth term is [tex]3\cdot 2^{n-1}[/tex].

(e) The nth term is 15-7(n-1).

(f) The nth term is the sum of the first n positive integers minus 3, i.e.,

[tex]1+2+3+\cdots+n-3.[/tex]

for such more questions on sequence

https://brainly.com/question/7882626

#SPJ11

Answer:150°

Step-by-step explanation:

Answer:

The answer is 7 pens

Answer:

75%

Step-by-step explanation:

We are given that Sara bought a chest for $42, and then sold it for $73.50.

Recall that when finding by how much something was marked up, you should use the following formula:

(new price-original price)/(original price)

Let's substitute the values, like so:

[tex]\frac{73.50-42}{42}=\\\\ \frac{31.50}{42}[/tex]

Now, set up a proportion to find what this fraction is as a percentage:

[tex]\frac{31.5}{42} =\frac{x}{100} =\\42x=3150=\\x=75[/tex]

So, the price was marked up by 75%.

The tickets in the box model should be:
- 1 ticket with a value of $6 (representing a win)
- 4 tickets with a value of -$2 (representing a loss).

In this gambling game, you have a 4 to 1 payout and a 1 in 5 chance of winning.

To create a box model for this scenario, follow these steps:
Identify the possible outcomes:

In this game, there are two possible outcomes:

winning (with a 1 in 5 chance) and losing (with a 4 in 5 chance).
Determine the payout for each outcome:

If a player wins, they receive a 4 to 1 payout on their $2 bet, so they win $8.

However, they also lose the original $2 bet, so the net gain is $6.

If a player loses, they lose their $2 bet.
Assign tickets to the box model based on the probability of each outcome:

Since there is a 1 in 5 chance of winning, there should be 1 ticket representing a win (net gain of $6) and 4 tickets representing a loss (net loss of $2).

For similar question on tickets.

https://brainly.com/question/30468513

#SPJ11

60.8π square inches is the area of the label.

The area or region that an object’s surface occupies is known as its surface area. Volume, on the other hand, refers to how much room an object has. There are numerous shapes and dimensions in geometry, including spheres, cubes, cuboids, cones, cylinders, etc. Each form has its own volume and surface area.

We wish to find the area of the rectangle A= L x W because we know the label is a rectangle that has been folded into a cylinder form.

W is known to be 7.6 inches.

We must determine the length that encircles the can's circumference.

Radius = 4 inches,

circumference = C = 2 πr.

(In terms of π, therefore don't multiply.) C = (2) π (4)

C = 8 pi millimeters

We now have L = 8π

And W is equal to 7.6.

A = L x W

A = 60.8π square inches.

Learn more about the Surface area here:

https://brainly.com/question/29298005

#SPJ2

The formula for the general term of the arithmetic sequence is:

a) an = -10 + (n-1) * 6 and first-term = -10

b) an = -10 + (n-1) * 6 and first-term = 6

c) an = 36 + (n-1) * (-5) and first-term = 36

An arithmetic sequence is a sequence of numbers in which each term (after the first) is obtained by adding a fixed number called the common difference, d, to the preceding term. The first term of an arithmetic sequence is denoted by 'a'. The general formula for an arithmetic sequence is:

a, a + d, a + 2d, a + 3d, ...

where 'a' is the first term, 'd' is a common difference, and each term after the first is obtained by adding 'd' to the preceding term.

a) To find the common difference, we subtract any term from the term that comes after it. For example, we can subtract -10 from -4, or 2 from 8, and we get:

-4 - (-10) = 6

8 - 2 = 6

Since both of these subtractions give us the same result, we know that the common difference is d = 6. To find the first term, we can use any term and subtract the product of the common difference and its position in the sequence minus 1. For example, we can use the second term -4 and its position 2 to get:

a = -4 - (2-1) * 6 = -10

Therefore, the formula for the general term of the sequence is:

an = -10 + (n-1) * 6

b) The common difference between consecutive terms is -2 because each term is 2 less than the term before it. To find the first term, we can use any term and add the product of the common difference and its position in the sequence minus 1. For example, we can use the second term 8 and its position 2 to get:

a = 8 + (2-1) * (-2) = 6

Therefore, the formula for the general term of the sequence is:

an = 6 + (n-1) * (-2)

c) The common difference between consecutive terms is -5 because each term is 5 less than the term before it. To find the first term, we can use any term and add the product of the common difference and its position in the sequence minus 1. For example, we can use the second term 31 and its position 2 to get:

a = 31 + (2-1) * 5 = 36

Therefore, the formula for the general term of the sequence is:

an = 36 + (n-1) * (-5)

To know more about the arithmetic sequence visit:

https://brainly.com/question/15412619

#SPJ1

Answer: there is only one number

Answer:

Solo hay un número primo que se puede escribir como suma de dos números primos y también como diferencia de dos números primos.

Espero haber ayudado :D

Every day, the number of views of the video increases by 80% of the previous day's views.

Every day, the number of views of the video increases by a certain percentage. To find the daily percent change in the views, we can use the formula for percent change, which is given by:

percent change = ((new value - old value) / old value) * 100

In this case, the old value is the number of views at the start, which is 500, and the new value is the number of views after one day, which is given by:

V(1) = 500*(1.8)^1 = 900

Substituting these values into the formula, we get:

percent change = ((900 - 500) / 500) * 100 = 80%

In other words, for every day that passes, the number of views of the video is multiplied by a factor of 1.8.

To learn more about percent click on,

https://brainly.com/question/27452160

#SPJ4