100 points !!!!! HELP ME ASAP

Write a piecewise function represented by the graph.

Answer:

answer is 41

Step-by-step explanation:

The length of side U will be 41.2 cm. The length of side U is found by the sin law.

A triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

From the sin law;

\(\rm \frac{S}{sin \ 54^0} =\frac{U}{sin \ 68^0} \\\\ \rm \frac{36}{sin \ 54^0} =\frac{U}{sin \ 68^0} \\\\ U= \frac{36 \ sin \ 68^0}{sin \ 54^0} \\\\ U=41.2 \ cm\)

Hence, The length of side U will be 41.2 cm.

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the subjects for 10 years to see which group develops more cancer this is a Prospective study

Individuals are monitored in real-time for prospective studies, as information is gathered about them as their traits or situations evolve. Prospective studies include things like birth cohort studies.

In retrospective research, people are sampled, as details regarding their history are gathered. This could be done by asking people to recollect significant occurrences during interviews or by finding pertinent administrative data to fill in the blanks on former events and conditions.

A study sample is split into two groups in a randomized experiment: one will get the intervention under research, while the other won't.

A matched experiment is a type of research setup in which subjects are paired up according to traits they have in common before being divided into categories.

A survey involves asking a sample of people a specified set of questions.

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Answer:

C

Step-by-step explanation:

A dog has a total of 4 legs. To know how many dogs there were just by having a number of legs, we would need to divide by 4. For example, if we have 12 legs, we could divide and get 3 total dogs.

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Skew lines are lines in three-dimensional space that do not intersect and are not parallel.

Unlike parallel lines, skew lines do not lie in the same plane. Instead, they are positioned at an angle to each other, which means they are neither perpendicular nor parallel. Because they do not intersect, they never meet, no matter how far they are extended. This property makes skew lines different from parallel lines, which can be extended infinitely far and remain equidistant from each other.

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A) True. Therefore, there should be no systematic bias when probability sampling is done correctly.

When conducting a research study, it is important to ensure that the sample chosen is representative of the population. Probability sampling is a method that aims to achieve this by giving each member of the population an equal chance of being included in the sample.

When this sampling method is done correctly, it minimizes bias and ensures that the sample is truly representative. For example, let's consider a study on the average height of students in a particular school.

If we were to use probability sampling, we would assign a number to each student and then randomly select a certain number of students from that pool. This would give every student an equal chance of being chosen for the sample, eliminating any systematic bias that might arise if we were to select students based on subjective criteria.

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Alan's porch has a width of 65/72 yards.

width generally refers to the measurement of the shorter dimension of a two-dimensional object, such as a rectangle. It is usually measured perpendicular to the length, and can be calculated using the formula:

Width = Area ÷ Length

where Area is the area of the object and Length is the longer dimension.

According to the given information:

To find the width of each porch, we can use the formula for the area of a rectangle:

Area = Length x Width

For Bill's porch:

8 1/8 = 6 1/2 x Width

We can convert the mixed number 6 1/2 to an improper fraction:

8 1/8 = 13/2 x Width

To isolate Width, we can divide both sides by 13/2:

Width = (8 1/8) ÷ (13/2)

Using the division of fractions rule (invert and multiply), we get:

Width = (65/8) ÷ (13/2)

Simplifying, we get:

Width = (65/8) x (2/13) = 5/8

So Bill's porch has a width of 5/8 yards.

For Alan's porch:

8 1/8 = 3 x Width

We can isolate Width by dividing both sides by 3:

Width = (8 1/8) ÷ 3

Converting 3 to a mixed number, we get:

Width = (8 1/8) ÷ (3 0/1)

Using the division of mixed numbers rule (multiply by the reciprocal), we get:

Width = (65/8) ÷ (9/1) = 65/72

So Alan's porch has a width of 65/72 yards.

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Alan's porch has a width of 65/72 yards.

What is width?

width generally refers to the measurement of the shorter dimension of a two-dimensional object, such as a rectangle. It is usually measured perpendicular to the length, and can be calculated using the formula:

Width = Area ÷ Length

where Area is the area of the object and Length is the longer dimension.

According to the given information:

To find the width of each porch, we can use the formula for the area of a rectangle:

Area = Length x Width

For Bill's porch:

=> 8 1/8 = 6 1/2 x Width

We can convert the mixed number 6 1/2 to an improper fraction:

=> 8 1/8 = 13/2 x Width

To isolate Width, we can divide both sides by 13/2:

Width = (8 1/8) ÷ (13/2)

Using the division of fractions rule (invert and multiply), we get:

=> Width = (65/8) ÷ (13/2)

Simplifying, we get:

Width = (65/8) x (2/13) = 5/8

So Bill's porch has a width of 5/8 yards.

For Alan's porch:

8 1/8 = 3 x Width

We can isolate Width by dividing both sides by 3:

Width = (8 1/8) ÷ 3

Converting 3 to a mixed number, we get:

Width = (8 1/8) ÷ (3 0/1)

Using the division of mixed numbers rule (multiply by the reciprocal), we get:

Width = (65/8) ÷ (9/1) = 65/72

So Alan's porch has a width of 65/72 yards.

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Dan could be charged with larceny, which is a felony offense in some states.

Dan could be charged with larceny, which is the taking of another person's property without their permission or consent. In this case, Dan took money from the tip jar without the permission of the ice cream shop or its owners. In some states, this type of larceny is considered grand larceny, which is a felony offense.

Larceny is a crime of intent, meaning that the perpetrator had the intent to deprive the victim of their property permanently. In the case of Dan, he intended to take the money from the tip jar for his own use, not to return it. As such, he could be charged with larceny.

In some states, the punishment for grand larceny is prison time or fines, and the length of the sentence or amount of the fines is determined by the value of the stolen property. In this case, the stolen property was five dollar bills, so the sentence or fine could be quite severe.

It is important to note that in some states, a minor's age may be taken into account when determining the sentence for a crime such as this one. For example, if Dan was a minor, his sentence could be reduced or his charges could be dropped altogether.

In conclusion, Dan could be charged with larceny, which is a felony offense in some states. Depending on the laws of the state, the age of the perpetrator, and the value of the stolen property, Dan could face prison time, fines, or a combination of both.

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Calculate the probability of more than 1 student contacting the Advising Office during a randomly selected one-minute interval between 8:00a.m. and 9:00a.m., we can use the Poisson distribution with a mean of 2 students per minute. The probability is approximately 0.7358.

The Poisson distribution is commonly used to model the number of events that occur in a fixed interval of time or space, given a known average rate of occurrence. In this case, the mean number of students contacting the Advising Office per minute is 2.

To find the probability of more than 1 student contacting the office during a one-minute interval, we can use the Poisson probability formula:

P(X > 1) = 1 - P(X <= 1)

Using the Poisson distribution formula, we can calculate the probabilities for X = 0 and X = 1, and then subtract them from 1 to find the probability of more than 1 student.

\(P(X = 0) = (e^(-λ) * λ^0) / 0! = e^(-2) ≈ 0.1353\)

\(P(X = 1) = (e^(-λ) * λ^1) / 1! = 2 * e^(-2) ≈ 0.2707\)

P(X > 1) = 1 - (P(X = 0) + P(X = 1))

= 1 - (0.1353 + 0.2707)

≈ 0.7358

Therefore, the probability of more than 1 student contacting the Advising Office during a randomly selected one-minute interval between 8:00a.m. and 9:00a.m. is approximately 0.7358, or 73.58% rounded to four decimal places.

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The mathematical quantity of the instantaneous velocity is a derivative, specifically the derivative of the distance function d(t) with respect to time.

To find the average velocity of the rock from t = 5 to t = 5.1, we need to calculate the change in distance and time over this interval.

Change in distance = d(5.1) - d(5) = (35(5.1) - 5\((5.1)^{2}\)) - (35(5) - 5\((5)^{2}\)) ≈ -24.5 m

Change in time = 5.1 - 5 = 0.1 s

Average velocity = (change in distance) / (change in time) ≈ -245 m/s

To find the equation for the average velocity from 5 seconds to t seconds, we need to use the formula for average velocity:

average velocity = (d(t) - d(5)) / (t - 5)

Taking the limit of this expression as t approaches 5 gives us the instantaneous velocity at t = 5:

instantaneous velocity = lim (t→5) [(d(t) - d(5)) / (t - 5)]

Using the given function for d(t), we can evaluate this limit as:

instantaneous velocity = lim (t→5) [(35t - 5\(t^{2}\) - 35(5) + 5\((5)^{2}\) / (t - 5)] = -50 m/s

Since the instantaneous velocity is negative, the rock is going down at t = 5. We can tell this because the velocity is the rate of change of distance with respect to time, and the negative sign indicates that the distance is decreasing with time.

The mathematical quantity of the instantaneous velocity is a derivative, specifically the derivative of the distance function d(t) with respect to time.

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Answer:

above sea level

Step-by-step explanation:

The absolute extrema of the function y = 8cos(x) on the closed interval [0, 2π] are a maximum value of 8 at x = 0 and a minimum value of -8 at x = π.

To find the absolute extrema of the function y = 8cos(x) on the interval [0, 2π], we need to evaluate the function at the critical points and the endpoints of the interval.

First, let's look for critical points by finding where the derivative of the function is zero or undefined. Taking the derivative of y with respect to x, we have:

dy/dx = -8sin(x)

Setting this derivative equal to zero, we find that -8sin(x) = 0. Since sin(x) = 0 at x = 0 and x = π, these points are potential critical points.

Next, we evaluate the function y at the critical points and the endpoints of the interval. The function y = 8cos(x) evaluates to:

At x = 0: y = 8cos(0) = 8

At x = π: y = 8cos(π) = -8

At x = 2π: y = 8cos(2π) = 8

Comparing these values, we find that the maximum value of y = 8 is achieved at x = 0, and the minimum value of y = -8 is achieved at x = π.

Therefore, the absolute extrema of the function y = 8cos(x) on the closed interval [0, 2π] are a maximum value of 8 at x = 0 and a minimum value of -8 at x = π.

It's worth noting that since the cosine function oscillates between -1 and 1, the maximum and minimum values of y = 8cos(x) occur when cos(x) is at its extremes. In this case, the maximum occurs when cos(x) = 1 (at x = 0), and the minimum occurs when cos(x) = -1 (at x = π). The amplitude of the cosine function is 1, so multiplying it by 8 scales the function vertically, resulting in a maximum value of 8 and a minimum value of -8.

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x=root[3]{-1.500}=-1.14471

By taking a multiplication, we will see that the number of pages of the new book is 15.

We know that the first book that Joyce wrote has 6 pages on it, and the second book that she wrote has (2 + 1/2) times that number of pages.

So to find the number of pages that the second book has, we just need to take the product:

6*(2 + 1/2)

Using the distributive property of the multiplication we will get:

6*(2 + 1/2) = 6*2 + 6*(1/2)

6*2 + 6*(1/2) = 12 + 3

12 + 3 = 15

In this way, we can conclude that the second book has 15 pages.

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Answer:

If area = length * width that means the answer is 4x * 5x = 20x².

Answer:

Yepp!!

Step-by-step explanation:

\(\frac{15}{7}\) = 2\(\frac{1}{7}\)

(-4 + 7i)² = 9 + 56i ; Where x + iy is complex form.

To find the square of (-4 + 7i), we can use the formula for squaring a complex number, which states that (a + bi)² = a² + 2abi - b².

In this case, a = -4 and b = 7. Applying the formula, we have:

(-4 + 7i)² = (-4)² + 2(-4)(7i) - (7i)²

= 16 - 56i - 49i²

Since i² is equal to -1, we can substitute -1 for i²:

(-4 + 7i)² = 16 - 56i - 49(-1)

= 16 - 56i + 49

= 65 - 56i

So, (-4 + 7i)² simplifies to 65 - 56i.

If we multiply the result by 4, we get:

4(-4 + 7i)² = 4(65 - 56i)

= 260 - 224i

Therefore, 4(-4 + 7i)² is equal to 260 - 224i.

The square of (-4 + 7i) is 65 - 56i. Multiplying that result by 4 gives us 260 - 224i.

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The average return for Stock A over the 5-year period is -6.2%.

The returns for each year are 0%, -18%, -14%, 10%, and -9%. Adding these returns together gives us (-18) + (-14) + 10 + (-9) = -31%.

Next, we divide the sum by the number of years, which is 5.

∴  \(\frac{-31}{5}\)= -6.2%.

Hence, the average return for Stock A over the 5-year period is -6.2%. This means that, on average, the stock experienced a 6.2% decrease in value each year during this period.

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The solution to the equation 4x + 2y = 36 is of y = 18 - 2x, which means that the two equations are equivalent equations.

Equivalent equations are equations that are equal when both are simplified the most.

The equation in the context of this problem is defined as follows:

4x + 2y = 36

To solve the equation, we must isolate the variable y, hence:

2y = 36 - 4x.

Simplifying the entire equation by two, we have that:

y = 18 - 2x.

As y = 18 - 2x is the most simplified expression of 4x + 2y = 36, the two equations are equivalent equations.

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The simplest form of 3x + 14 – x + \(1\frac{1}{2}\) is  2x + \(15\frac{1}{2}\). Both given expressions are not equivalent.

What is an expression?

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the expression 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given expression is 3x + 14 – x + \(1\frac{1}{2}\)

Now combine like terms:

= (3x - x) + (14 + \(1\frac{1}{2}\))

= 2x +  (14 + \(1\frac{1}{2}\))

Convert mixed fraction to improper fraction:

= 2x +  (14 + 3/2)

= 2x + 31/2

= 2x + \(15\frac{1}{2}\)

The equivalent expression of 3x + 14 – x + \(1\frac{1}{2}\) is  2x + \(15\frac{1}{2}\). Therefore, 3x + 14 – x + \(1\frac{1}{2}\) is not equivalent to 4x + \(1\frac{3}{4}\).

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Check the picture below.

Answer: I am here to nswer

Step-by-step explanation: so first to this then do another thing

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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the polynomial that represents the volume of the box is is 6x^3 +5x^2 -3x-2

V=lwh

l=x+1

w=2x+1

h=3x-2

V=(x+1)(2x+1)(3x-2)

V=(x*2x+x*1+1*2x+1*1)(3x-2)

V=(2x²+x+2x+1)(3x-2)

V=(2x²+3x+1)(3x-2)

V=2x²*3x+2x²*(-2)+3x*3x+3x*(-2)+1*3x+1*(-2)

V=6x³-4x²+9x²-6x+3x-2

V=6x³+5x²-3x-2

complete question is

Find the volume of the box. Use the formula V = lwh.

Rectangular box with sides x plus 1, 2x plus 1, and 3x minus 2.

6x3 – 2

6x3+ x – 2

6x3 – 13x2 – 3x – 2

6x3 + 5x2 – 3x – 2

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False. A constant multiple of a solution of a linear, homogeneous differential equation is not necessarily a solution.

In a linear, homogeneous differential equation, the sum of any two solutions is also a solution. However, multiplying a solution by a constant does not preserve the property of being a solution. When a constant multiple is applied to a solution, the resulting function may not satisfy the differential equation.

To illustrate this, let's consider a simple example. Suppose we have a linear, homogeneous differential equation represented by the equation dy/dx = 2x. One possible solution to this equation is y = x^2. However, if we multiply this solution by a constant, say 2, we get y = 2x^2. Substituting this into the differential equation, we have d(2x^2)/dx = 4x ≠ 2x. Thus, the constant multiple of the solution is not a solution to the differential equation.

Therefore, the statement that a constant multiple of a solution of a linear, homogeneous differential equation is also a solution is false.

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The polynomial representing the perimeter of the quadrilateral is given as follows:

P = 12x - 3.

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure.

Hence the perimeter of the quadrilateral is given as follows:

P = 2x + 5x - 2 + 3x - 2 + 2x + 1.

P = 12x - 3. (combining the like terms).

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The statement "If a function f '(x) exists and is nonzero for all x, then f(8) ≠ f(0)" is not necessarily true.

If f(x) is an increasing or decreasing function on the Interval [0, 8], then it is possible that f(8) = f(0).

For example, consider the function f(x) = x, which is increasing on the interval [0, 8] and satisfies f '(x) = 1 for all x in [0, 8]. Then f(8) = 8 and f(0) = 0, so f(8) = f(0).

However, if we assume that f(x) is strictly increasing or strictly decreasing on the interval [0, 8], then the statement would be true.

This is because if f(x) is strictly increasing or decreasing, then it cannot have any repeated values in its range, and so f(8) ≠ f(0).

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Answer:

37.7 inches

Step-by-step explanation:

u have the formula so with r being radius just multiply by 2 then multiply that answer by pie and round to the nearest tenth.