x³ + 3x² + 3x +5=0

What is the rational roots of this polynomial equation?

30 hours of use by the Washington family sprinkler and 35 hours of use by the Bennett family sprinkler.

We can find how long was each sprinkler used by substitution method.

Let W = hours of use by the Washington family

65 - W = hours of use by the Bennett family

According to the question we get

15W + 40(65 -W) = 1850

15W + 2600 - 40W = 1850

-25W = -750

W = 30

Now, put the value of W in 65 - W to calculate the hours used by the Bennett family

65 - W = 65 - 30 = 35

Thus, the amount of time used for sprinklers by the Washington family and the Bennett family is 30 hours and 35 hours, respectively.

--The given question is incomplete, the complete question is

"The Washington family and the Bennett family each used their sprinklers last summer. The water output rate for the Washington family's sprinkler was 15L per hour. The water output rate for the Bennett family's sprinkler was 40L per hour. The families used their sprinklers for a combined total of 65 hours, resulting in a total water output of 1850L. How long was each sprinkler used?"--

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Answer:

726.65 cubic inches

Step-by-step explanation:

We are going to assume that the head, middle and bottom are spheres.

The formula to get the volume of a sphere is

\(V= \frac{4}{3}\pi r^{2}\) where r is the radius of the sphere.

Now, let's proceed to apply this formula to the 3 spheres of the snowman:

The head is 12 inches wide (diameter), thus, the radius would be 6 inches:

\(V= \frac{4}{3}\pi r^{2}\\V= \frac{4}{3}\pi 6^{2}\\V= \frac{4}{3}\pi 36\\V=\frac{144\pi }{3} \\V=38\pi\) cubic inches

The middle is 16 inches wide (diameter), thus, the radius would be 8 inches.

\(V= \frac{4}{3}\pi r^{2}\\V= \frac{4}{3}\pi 8^{2}\\V= \frac{4}{3}\pi 64\\V=\frac{256\pi }{3} \\V=85.3\pi\)  cubic inches

The bottom is 18 inches wide (diameter), thus the radius would be 9 inches.

\(V= \frac{4}{3}\pi r^{2}\\V= \frac{4}{3}\pi 9^{2}\\V= \frac{4}{3}\pi 81\\V=\frac{324\pi }{3} \\V=108\pi\) cubic inches.

Now, to get the total volume of the snowman we're going to sum up the volume of all three spheres:

Total volume = \(38\pi +85.3\pi +108\pi =231.3\pi\) cubic inches.

If we take pi = 3.1416,

Total volume = \(231.3(3.1416)=726.65\) cubic inches.

Answer:

20

Step-by-step explanation:

The minimum distance the annihilation event could have occurred from the center of the machine is approximately 98.94 nanometers.

To determine the minimum distance the annihilation event could have occurred from the center of the machine, we can use the speed of light as a constant and the time difference between the collisions of the gamma rays.

The speed of light in a vacuum is approximately 299,792,458 meters per second (m/s).

Since the time difference between the collisions of the gamma rays is given as 0.33 nanoseconds, we need to convert this time to seconds. One nanosecond is equal to 1 × 10⁻⁹seconds.

0.33 nanoseconds is equal to 0.33 × 10⁻⁹ seconds.

Now, we can calculate the minimum distance using the equation:

Distance = Speed of light × Time

Distance = 299,792,458 m/s × 0.33 × 10⁻⁹ seconds

Distance ≈ 98.94 nanometers

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The exact solution and its approximation rounded to two decimal places are 2. 6213 and 2. 62 respectively.

An algebraic expression can be described as a mathematical or arithmetic expressions that is composed of arithmetic terms, factors, constants, variables, and coefficients.

These expressions are also made up of arithmetic operations which includes;

From the information given, we have that;

(2x − 1)^2 = 18

Find the square root of both sides, we have;

√(2x − 1)^2 = √18

Note that square root rules out the square, we have;

2x - 1 = 4. 24264

collect like terms

2x = 4. 24264 + 1

2x = 5. 24264

Make 'x' the subject

x = 5. 24264/2

x = 2. 6213

Hence, the value is 2. 6213

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\(a_n = a_(n-1) + a_(n-2)\)

where a_n is the number of bit strings of length n that contain a pair of consecutive 0s, a_(n-1) is the number of bit strings of length (n-1) that contain a pair of consecutive 0s, and a_(n-2) is the number of bit strings of length (n-2) that contain a pair of consecutive 0s.

To find a recurrence relation for the number of bit strings of length n that contain a pair of consecutive 0s, we can start by noting that the number of bit strings of length n that contain a pair of consecutive 0s (a_n) is dependent upon the number of bit strings of length (n-1) that contain a pair of consecutive 0s (a_(n-1)) and the number of bit strings of length (n-2) that contain a pair of consecutive 0s (a_(n-2)). This is because the last two bits of a bit string of length n can be either 00, 01, or 10. If the last two bits are 00, then the bit string of length n contains a pair of consecutive 0s and the remaining bit string must be of length (n-2). If the last two bits are 01 or 10, then the bit string of length n does not contain a pair of consecutive 0s and the remaining bit string must be of length (n-1). Therefore, we can conclude that the recurrence relation for the number of bit strings of length n that contain a pair of consecutive 0s is a_n = a_(n-1) + a_(n-2).

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Answer:

817

Step-by-step explanation:

The statements are insufficient to answer the question.

What is measurement?

Measurement is the quantification of an object's or event's attributes for comparison with other objects or events. Measurement, in other words, is the process of determining how large or small a physical quantity is in comparison to a basic reference quantity of the same kind.

So we are given 2 lists, x and y and we are given the

1.  The total number of measurements is 30. x(n) + y(n) = 30.

2. Largest measurement - Smallest Measurement = 25

But we are not told the number of measurements in either x or y. We also don't know whether the largest of smallest measurement of the combined range belongs to x or y.

We need to find the largest measurement of x and the smallest measurement of x for our answer.

1)The range for the 12 measurements in list y is 20.

Okay so we know that y has 12 measurements, therefore x has 18. And we know the y(largest) - y(smallest) = 20 INSUFFICIENT

2) List x consists of 18 measurements.

We are told that x consists of 18 elements. We already figured this out in Statement 1 as well. It again does not tell us anything further. INSUFFICIENT DATA

Hence, the statements are insufficient to answer the question.

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Answer:

B

Step-by-step explanation:

point slope uses the form y - y1 = m(x - x1)

m stand for slope. in this case it is -3

x1 is -1 and y1 is 6

when you plug it in, you get

y - 6 = -3(x - [-1])

which simplifies to your final answer: y - 6 = -3(x + 1)

Answer:

960

Step-by-step explanation:

3 * 320 = 960

Udin memiliki, secara total, 960 ikan hias

(Udin has, in total, 960 ornamental fish)

The equation to convert x feet into y miles for the walking path is y = x / 5280

To convert x feet into y miles, use the following equation:

y = x / (5280)

where y = distance in miles and x = distance in feet.

For the walking path, make sure it is 1 mile long. Therefore, set up the following equation:

distance from school to park + distance from park to school = 1 mile

Let d be the distance from the school to the park, then the distance from the park to the school is also d. Using the given requirements, set up the following two equations:

distance to first water fountain = d / 3

distance to second water fountain = 2d / 3

The total distance can be expressed as:

d + (2d/3) + (d/3) = 1 mile

Multiplying both sides by 3:

3d + 2d + d = 3 miles

Simplifying:

6d = 3

d = 1/2 mile

Now, use the equation y = x / 5280 to find the distances in miles:

Distance from school to park = (1/2) mile = (1/2) x 5280 feet = 2640 feet

Distance from park to school = (1/2) mile = (1/2) x 5280 feet = 2640 feet

Distance to first water fountain = (1/2) mile / 3 = (1/6) x 5280 feet = 880 feet

Distance to second water fountain = (2/3) x (1/2) mile = (1/3) x 5280 feet = 1760 feet

Therefore, the equation to convert x feet into y miles for the walking path is:

y = x / 5280

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Based on the given options, the linear inequality that represents the graph below is C. y ≥ -3x + 1

To determine the correct option, we need to analyze the characteristics of the graph. Looking at the graph, we observe that it represents a line with a solid boundary and shading above the line. This indicates that the region above the line is included in the solution set.

Option A, y > (-3/6)x + 1, does not accurately represent the graph because it describes a line with a slope of -1/2 and a y-intercept of 1, which does not match the given graph.

Option B, y ≥ x + 1, also does not accurately represent the graph because it describes a line with a slope of 1 and a y-intercept of 1, which is different from the given graph.

Option D, y > x + 1, is not a suitable representation because it describes a line with a slope of 1 and a y-intercept of 1, which does not match the given graph.

Only Option C. y ≥ -3x + 1.

This is because the graph appears to be a solid line (indicating inclusion) and above the line, which corresponds to the "greater than or equal to" relationship. The equation y = -3x + 1 represents the line on the graph.

Consequently, The linear inequality y -3x + 1 depicts the graph.

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Answer:

Isaac = x

Step-by-step explanation:

Erika is 3y older than Isaac

Isaac is x years old

Answer:  x+3

Work Shown:

x = Issac's age right now

x+7 = Erika's age right now

(x+7)-4 = x+3 = Erika's age four years ago

The dimensions that yield the minimum surface area of the open-top square-based, rectangular metal tank that will have a volume of 48.5 ft³ are:

The dimensions of an area, which is a two-dimensional object, refer to the length and the width.

On the other hand, the dimensions of the volume refer to the length, width, and height.

The volume of the square-based rectangular tank = 48.5ft³.

The length of each side of the surface area = 3.6468 ft (∛48.5ft)

Check:

Volume = height x length x width

= 3.6468 x 3.6468 x 3.6468

= 48.499 ft³

= 48.5 ft³

Thus, the dimensions of the surface area include the length and the width without the height.

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A function equation in slope-intercept form to model the situation are as follows;

Slope: 3.

Y-intercept: 48.

Equation: y = 3x + 48.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

Since the liquid started at a temperature of 48 degrees and drops 3 degrees per minute, an equation that model the situation is given by:

y = mx + c

y = 3x + 48

Next, we would fill in the table as follows. At x = 0, the temperature of liquid (y) is given by:

y = 3(0) + 48

y = 48.

At x = 1, the temperature of liquid (y) is given by:

y = 3(1) + 48

y = 51.

At x = 2, the temperature of liquid (y) is given by:

y = 3(2) + 48

y = 54.

At x = 3, the temperature of liquid (y) is given by:

y = 3(3) + 48

y = 57.

At x = 4, the temperature of liquid (y) is given by:

y = 3(4) + 48

y = 60.

At x = 5, the temperature of liquid (y) is given by:

y = 3(5) + 48

y = 63.

At x = 6, the temperature of liquid (y) is given by:

y = 3(6) + 48

y = 66.

At x = 7, the temperature of liquid (y) is given by:

y = 3(7) + 48

y = 69.

At x = 8, the temperature of liquid (y) is given by:

y = 3(8) + 48

y = 72.

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The equation of the plane passing through (-1, 3, 2) and perpendicular to x + 2y + 3z = 5 and 3x + 3y + z = 0 is -7x + 8y - 3z = -7.

To find the equation of the plane passing through the point (-1, 3, 2) and perpendicular to each of the planes x + 2y + 3z = 5 and 3x + 3y + z = 0, we can use the cross product of the normal vectors of the given planes. The normal vectors of the given planes are <1, 2, 3> and <3, 3, 1> respectively. Taking the cross product of these two vectors, we get <-7, 8, -3>. Therefore, the equation of the plane passing through the point (-1, 3, 2) and perpendicular to both given planes is -7x + 8y - 3z = -7.

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If rxy = 0.83, we can conclude that x and y have a relatively strong positive linear relationship or correlation.

The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables, in this case, x and y. The value of r ranges between -1 and 1. A positive value indicates a positive relationship, meaning that as one variable increases, the other variable tends to increase as well.

In this case, with rxy = 0.83, the correlation coefficient is close to 1, suggesting a strong positive linear relationship. This means that when x increases, y also tends to increase, and vice versa. The closer the value of r is to 1, the stronger the linear relationship between x and y.

It is important to note that correlation does not imply causation. While a high correlation coefficient indicates a strong linear relationship, it does not provide information about the underlying cause or direction of the relationship between the variables. Other factors and variables may influence the relationship, and further analysis may be required to understand the nature of the relationship between x and y.

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Answer:

$8.75

Step-by-step explanation:

$4.50 × 2.5 = $11.25

$20.00 - $11.25 = $8.75 change

Answer:

down below

Step-by-step explanation:

Four fifths minus three fifths is one fifth.

4/5 - 3/5 = 1/5

The way you do this is subtract the numerator and leave the denominator alone. You the place the answer from the numerator over the denominator.

Hope this helps! :)

(a) The p-value to test H0: π=0.5 against Ha: π≠0.5 using the Binomial test with the minimum likelihood method is approximately 0.109.

The p-value represents the probability of observing a test statistic as extreme as the one obtained or more extreme, assuming the null hypothesis is true. In this case, we are testing whether the probability of success (π) is different from 0.5.

Using the minimum likelihood method, we compare the observed data to the null hypothesis value and calculate the probability of obtaining results as extreme as or more extreme than the observed data. In this case, the observed data is y = 8 successes out of n = 12 trials.

To calculate the p-value, we sum the probabilities of all outcomes that are as extreme as or more extreme than the observed data. In this case, the outcomes as extreme as or more extreme than 8 successes are 0 successes, 1 success, 11 successes, and 12 successes.

By summing the probabilities of these outcomes from the Binomial distribution with n = 12 and π = 0.5, we find the p-value to be approximately 0.109.

(b) The p-value to test H0: π=0.5 against Ha: π≠0.5 using the Binomial test with the central method is approximately 0.219.

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Step-by-step explanation:

3526.49 12.64 0.21

I hope this helps

Answer:

3526.49

12.64

.21

Step-by-step explanation:

1. On the left of the decimal place, take the third number and if it is = to or higher than 5, round the second number up by 1.

3526.485 becomes 3526.49

2. If it is lower than 5, then just leave the second number alone.

12.6433 becomes 12.64

3. If it is a decimal place number, just take the third number and if it is higher than 5, increase the second number.

.2099 becomes .21

Answer:

g

Step-by-step explanation:  it is basically the same problem with the  opisate meaning

33) To graph:

3x + 4y = 12

First find the y-intercept by substituting x=0 and then solve for y

That is;

3(0) + 4y = 12

4y = 12

Divide both-side of the equation by 4

y= 3

y-intercept is (0, 3)

Similarly,

To get the x-intercept, substitute y=0 and then solve for x

3x + 4(0) = 12

3x = 12

Divide both-side by 3

x=4

The x-intercept is (4,0)

Answer:

Let's first find out how much work Ronald and Marco can do in one hour.

Ronald's rate = 1 car / 3 hours = 1/3 car per hour

Marco's rate = 1 car / 4 hours = 1/4 car per hour

Their combined rate would be the sum of their individual rates:

Combined rate = Ronald's rate + Marco's rate

= 1/3 car per hour + 1/4 car per hour

= 7/12 car per hour

This means that together, Ronald and Marco can wash and wax 7/12 of a car in one hour.

Now, let's use this combined rate to determine how long it would take them to wash and wax one car.

The formula for work is:

Work = Rate x Time

Since they want to wash and wax one car, we can plug in the values we found above and solve for time:

1 car = (7/12 car per hour) x Time

Time = 1 car / (7/12 car per hour)

Time = 12/7 hours

Therefore, it would take Ronald and Marco approximately 1 hour and 43 minutes (12/7 hours) to wash and wax one car if they worked together.

We can clearly see that the area must be more than \($\frac{8 \pi}{3}$\), and the only such answer is \(3 \pi\).

Part of what Spot can reach is \($\frac{240}{360}=\frac{2}{3}$\) of a circle with radius 2, which gives him \($\frac{8 \pi}{3}$\). He can also reach two\($\frac{60}{360}$\)parts of a unit circle, which combines to give \($\frac{\pi}{3}$\). The total area is then \($3 \pi$\).

A circle is a two-dimensional closed shape in which the set of all points in the plane is equidistant from a particular point known as the "centre."

A Sphere is a three-dimensional object, whereas a Circle is a two-dimensional figure. All points in a circle are the same distance from its center along a plane, whereas all points in a sphere are equidistant from the center along any of the axes.

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The probability that exactly one person will get out on each floor is about 0.444 or 44.4%.

There are 3 occupants, and each has 3 possible floors to get out on. Therefore, there are a total of 3^3 = 27 possible outcomes for which floor each person gets out on.

To calculate the probability that exactly one person will get out on each floor, we need to count the number of outcomes that satisfy this condition and divide by the total number of outcomes.

First, we can count the number of ways in which exactly one person gets out on the first floor. There are three people who could be the first to get out, and for each choice there are two people left who could get out on either of the remaining two floors. Therefore, there are 3 * 2^2 = 12 outcomes where exactly one person gets out on the first floor.

Similarly, there are 12 outcomes where exactly one person gets out on the second floor, and 12 outcomes where exactly one person gets out on the third floor.

Therefore, there are a total of 12 + 12 + 12 = 36 outcomes where exactly one person gets out on each floor.

Since there are 27 possible outcomes in total, the probability of exactly one person getting out on each floor is:

P(exactly one person gets out on each floor) = 36 / 27 = 4 / 3 ≈ 0.444 or approximately 44.4%.

So the probability that exactly one person will get out on each floor is about 0.444 or 44.4%.

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The value of the function c(n) = 20 + 20n at n = 5 will be 120.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that function, c is defined by the equation c(n) = 20 + 20n. It gives the monthly cost, in dollars, of visiting a gym as a function of the number of visits n.

The value of the function f(5) will be calculated as,

c(n) = 20 + 20n

c(5) = 20 + ( 20 x 5 )

c(5) = 20 + 100

c(5) = 120

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To determine the 95% energy bandwidth (B) of the signal g(t) = [0.5sinc²(0.5 t) cos(2 t)], we can apply Parseval's Theorem. Parseval's Theorem states that the total energy of a signal in the time domain is equal to the total energy of the signal in the frequency domain. Mathematically, it can be expressed as:

∫ |g(t)|² dt = ∫ |G(f)|² df

In this case, we want to find the frequency range within which 95% of the energy of the signal is concentrated. So we can rewrite the equation as: 0.95 * ∫ |g(t)|² dt = ∫ |G(f)|² df

Now, we need to evaluate the integral on both sides of the equation. Since the given signal is in the form of a product of two functions, we can separate the terms and evaluate them individually. By applying the Fourier transform properties and integrating, we can find the value of B.

For part (b), when we consider g(2t), the time domain signal is compressed by a factor of 2. This compression results in a corresponding expansion in the frequency domain. Therefore, the 95% energy bandwidth of g(2t) will be twice the value of B determined in part (a). This can be justified by considering the relationship between time and frequency domains in Fourier analysis, where time compression corresponds to frequency expansion and vice versa.

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The probability of choosing a 5 and then a 6 is 1/49

From the question, we have the following parameters that can be used in our computation:

The tiles

Where we have

Total = 7

The probability of choosing a 5 and then a 6 is

P = P(5) * P(6)

So, we have

P = 1/7 * 1/7

Evaluate

P = 1/49

Hence, the probability of choosing a 5 and then a 6 is 1/49

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Question

You randomly choose one of the tiles. Without replacing the first tile, you choose a second tile. Find the probability of the compound event. Write your answer as a fraction or percent rounded to the nearest tenth. The probability of choosing a 5 and then a 6

Answer:

200 ft

Step-by-step explanation:

area = 2500

length = 50