Suppose a robot is at the corner of a rectangular arena and needs to reach the diagonally opposite corner. If the length of the arena is 105 meters, and the width is 68 meters, find the distance that the robot needs to travel. Round your answer to the nearest whole meter.

To find an expression for the number in the nth position of the sequence 4, 7, 12, 19, we can observe a pattern in the differences between consecutive terms.

The difference between the first and second terms is 7 - 4 = 3.

The difference between the second and third terms is 12 - 7 = 5.

The difference between the third and fourth terms is 19 - 12 = 7. We can see that the differences are increasing by 2 each time. This indicates that the sequence follows a quadratic pattern.  Let's denote the position of the term as n. The expression for the nth term can be found using the formula:

nth term = (n^2) + (3n) + 1

Using this expression, we can find any term in the sequence by substituting the corresponding value for n. For example, the 5th term would be (5^2) + (3 * 5) + 1 = 25 + 15 + 1 = 41.

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Answer:

plz give me BRAINLIEST

Step-by-step explanation:

c. p >-13

Answer:

Mean = 125.136

Median = 110

Mode = 180

Step-by-step explanation:

Given the data:

75 95 180 136 89 75 110 180 100 136 180 95 180 136 75 100 110 180 180 136 75 90

Frequency distribution:

Value(X) ___freq (F) ____cumm frequency

85 _________ 4 _______ 4

89 _________ 1 _______5

90 __________1 _______6

95 __________2 ______ 8

100 _________ 2 ______10

110 __________2______ 12

136 __________4 _____ 16

180 __________6______22

2) Using the frequency distribution :

Mean = Σfx / Σf

[(85*4) + (89*1) + (90*1) + (95*2) + (100*2) + (110*2) + (136*4) + (180*6)]/ 10

= 2753 / 22

= $125.136

Median of grouped data :

Frequency + 1 / 2 = 23/2 = 11.5 th term

The median value = $110

Mode of the data:

Most frequently occurring = 180 (frequency of 6)

The mean of the frequency distribution is $125.136, the median of the frequency distribution is $110, and the mode of the frequency distribution is $180.

Given :

a) The frequency distribution is given below:

Prices              Frequency       Cumulative Frequency

85                           4                                 4

89                            1                                 5

90                            1                                  6

95                            2                                  8

100                           2                                 10

110                            2                                  12

136                            4                                 16

180                            6                                 22

b) The mean is calculated as:

\(\rm Mean = \dfrac{85\times4 + 89\times1 +90\times1 +95\times 2+100\times2 +110\times2 +136\times4 +180\times6 }{10}\)

Simplify the above expression.

Mean = $125.136

c) The median of the frequency distribution is calculated as:

\(\rm Term= Frequency + \dfrac{1}{2}=11.5\)

So, the median is $110.

The mode of the frequency distribution is $180.

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We know that the vertex form of a parabola is given.  Therefore, there is no parabola that satisfies these conditions.

y = a(x - h)^2 + k

where (h, k) is the vertex of the parabola and a is a constant that determines the shape of the parabola.

We are given the vertex (5, 25), so we can write:

y = a(x - 5)^2 + 25

We are also given two points on the parabola: (0, 0) and (10, 0). Plugging these into the equation, we get:

0 = a(0 - 5)^2 + 25 => 25 = 25a => a = 1

0 = a(10 - 5)^2 + 25 => 0 = 25a => a = 0

We get two different values for a, which means that the given points do not lie on the same parabola. Therefore, there is no unique solution to this problem.

We can also see this geometrically: the points (0, 0) and (10, 0) lie on the x-axis, which means that the parabola would have to open either upwards or downwards. However, the vertex is above the x-axis, which means that the parabola cannot intersect the x-axis. Therefore, there is no parabola that satisfies these conditions.

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Answer:

One of the most common algebraic symbols is the use of x, y or another letter of the alphabet to indicate a variable or unknown quantity. Common symbols used in algebra also include those related to equality, inequality, factorials and organization, like braces, brackets and parentheses.

Give brainiest please ;-;

Answer:

different variables represent unknown numbers.

Step-by-step explanation:

For example the equation 5x = 15

X is a variable that represents an unknown number. To get the unknown number in the example you need to divide 15 by 5 and 5 by 5 to get X alone and then X will equal 3.

So 5×3=15

I hope this helps

The cost of each lily is $3.25, and the cost of each rose is $6.50 according to the first arrangement and second arrangement.

Let's assume the cost of each lily is represented by "L" and the cost of each rose is represented by "R." Based on the given information, we can form a system of linear equations.

From the first arrangement, we know that 5 lilies and 1 rose cost $19.75. This can be written as the equation 5L + R = 19.75.

From the second arrangement, we know that 6 lilies and 3 roses cost $27.75. This can be written as the equation 6L + 3R = 27.75.

To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method.

Multiply the first equation by 3 and the second equation by -1 to eliminate the R term:

15L + 3R = 59.25

-6L - 3R = -27.75

Adding the equations, we get:

9L = 31.50

Divide both sides by 9:

L = 3.50

Now substitute the value of L back into one of the original equations. Let's use the first equation:

5(3.50) + R = 19.75

17.50 + R = 19.75

Subtract 17.50 from both sides:

R = 2.25

Therefore, the cost of each lily is $3.50, and the cost of each rose is $2.25.

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Answer:

$30.47

Step-by-step explanation:

100%-15%=85%
85%=0.85
$35.85*0.85=30.47 (to 2d.p)
Hope this helps

First, we must know the formula for solving the volume of a cylinder, which is \(V = \pi r^2 h\). Since the water is only being filled to 5 feet, we do not care about the 0.5 feet of the height.

Using the formula, we need to plug-in the numbers for the radius (20 divided by 2 is 10) and height. Doing this, the equation should now look like this: \(V = 3.14 * 10^2 * 5\). When solving, the volume of the water is 1570 feet cubed.

Answer:

1570.796 feet cubed

Step-by-step explanation:

First you find the surface area of the base of the cylinder which should look like this:

(10^2)(π)

Next you multiply that by the height (5 feet) because 3d shapes are bases stacked on each other which should look like this:

314.1592654(5)

After that arithmetic you will get 1570.796 or 1570.8 rounded as your answer!

Answer:

x=  5

Step-by-step explanation:

Your teacher should have explained it but give me points please

The upper bound of the 95% confidence interval for the average age in the U.S. is 48.29 years.

To determine the upper bound of the 95% confidence interval for the average age in the U.S., we can use the sample data from the survey. The sample size is 1072 people, randomly selected from the U.S. population, with a minimum age of 12. By calculating the average age of the respondents, we can estimate the average age of the entire U.S. population.

Using the given information that the average age of the respondents is 43.56 years, and assuming that the sample is representative of the population, we can calculate the standard error. The standard error measures the variability of the sample mean and indicates how much the sample mean might deviate from the population mean.

Using statistical methods, we can calculate the standard error and construct a confidence interval around the sample mean. The upper bound of the 95% confidence interval represents the highest plausible value for the population average age based on the sample data.

Therefore, based on the provided information and calculations, the upper bound of the 95% confidence interval for the average age in the U.S. is 48.29 years.

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Answer:

(-11, 11]

Step-by-step explanation:

The domain of a graph is the set of x-values.

An open circle means the endpoint is not included, whereas a closed circle means the endpoint is included.

We assume that with a linear relationship between two variables, for any fixed value of x, the observed residuals follows a normal distribution.

This assumption is based on the Central Limit Theorem, which states that when the sample size is large enough, the distribution of sample means will be approximately normal, regardless of the shape of the underlying population distribution.

In the case of a linear relationship between two variables, we can assume that the residuals (the difference between the observed y values and the predicted values based on the linear regression model) follow a normal distribution with mean 0 and constant variance. This assumption is important because it allows us to use statistical methods that rely on normality, such as hypothesis testing and confidence intervals.

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The equation describing the intersection of the sphere with the plane z = 9 is (x+8)^2 + (y-4)^2 = 15.

To find the equation of the sphere centered at (-8,4,8) with radius 4 and the intersection with the plane z = 9.

Step 1: Find the equation of the sphere. The general equation of a sphere is (x-a)^2 + (y-b)^2 + (z-c)^2 = r^2, where (a, b, c) is the center of the sphere and r is the radius. In this case, the center is (-8, 4, 8) and the radius is 4. So, we have:

(x+8)^2 + (y-4)^2 + (z-8)^2 = 16

Step 2: Find the intersection of the sphere with the plane z = 9. Since the plane is given by z = 9, we can substitute 9 for z in the equation of the sphere:

(x+8)^2 + (y-4)^2 + (9-8)^2 = 16

This simplifies to:

(x+8)^2 + (y-4)^2 + 1 = 16

Now, move the constant term to the other side of the equation:

(x+8)^2 + (y-4)^2 = 15

So, the equation describing the intersection of the sphere with the plane z = 9 is (x+8)^2 + (y-4)^2 = 15.

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The new standard deviation remains the same as the original standard deviation of 12.3 grams.

Option A is the correct answer.

We have,

To calculate the new standard deviation, we need to adjust the weights of the fish by adding 1.1 grams to each weight.

This adjustment affects the original data and consequently impacts the standard deviation.

Since the scale was 1.1 grams off and each fish was actually 1.1 grams heavier, this adjustment does not change the spread or variability of the data.

It only shifts the values by a constant amount.

Therefore,

The new standard deviation remains the same as the original standard deviation of 12.3 grams.

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Answer:

The values of x and y that satisfy the equation are 2 and 2, respectively.

Step-by-step explanation:

Two complex numbers are identical if and only each pair of respective coefficients are identical on both sides. Then, we need to observe the following conditions:

Real component

\(4\cdot x = 8\) (1)

Imaginary component

\(2 = y\) (2)

The solution of this system of equations is \(x = 2\) and \(y = 2\).

The values of x and y that satisfy the equation are 2 and 2, respectively.

The values of x and y that satisfy the equation is x = 2, y = 2.

Given that,

Based on the above information, the calculation is as follows:

Now

(4) (x) = 8.........real component

x = 2

And,

2 = y..... imaginery component

Therefore we can conclude that the values of x and y that satisfy the equation is x = 2, y = 2.

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No, X² is not an exponential function.

An exponential function is a function of the form f(x) = aˣ where a is a positive constant and x is a real number. The value of the function increases exponentially as x increases.

On the other hand, x² is a polynomial function, a function that can be written as the sum of a finite number of non-negative integer powers of x. The highest power of x is 2, it's called a quadratic function. And it can be represented as f(x) = ax² + bx + c where a, b, and c are real numbers and a is not 0.

Therefore, X² is not an exponential function but a polynomial function.

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The graph that does not represents a proportional relationship is: A (see image attached below).

A proportional relationship has a constant, which is uniform and is defined in the equation y = kx, as k. This means a relationship that is proportionate will have an equation in that form.

For a proportional graph, the line must pass through the point of origin which is denoted by the ordered pair, (0, 0).

Therefore, from the options given, the option B represents a proportional relationship because it contains (0, 0), while option C and D takes the form of y = kx.

Therefore, option A does not represent a proportional relationship.

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The correct choice is A. The solution to the initial value problem is y(x) = ln(8e^x).

The given differential equation is dy/dx = e^x - y, and the initial condition is y(0) = ln(8).

To solve this initial value problem, we need to determine the function y(x) that satisfies the differential equation and also satisfies the initial condition.

The given equation is separable, which means we can rearrange it to separate the variables x and y. Let's rewrite the equation:

dy = (e^x - y) dx

Next, we integrate both sides with respect to their respective variables:

∫ dy = ∫ (e^x - y) dx

Integrating, we get:

y = ∫ e^x dx - ∫ y dx

y = e^x - ∫ y dx

To solve for y, we rearrange the equation:

y + ∫ y dx = e^x

Differentiating both sides with respect to x, we have:

dy/dx + y = e^x

This is a linear first-order ordinary differential equation. Using an integrating factor, we find:

e^x * dy/dx + e^x * y = e^(2x)

Applying the integrating factor, we can rewrite the equation as:

d/dx (e^x * y) = e^(2x)

Integrating both sides, we get:

e^x * y = (1/2) * e^(2x) + C

Dividing both sides by e^x, we have:

y = (1/2) * e^x + C * e^(-x)

To find the particular solution that satisfies the initial condition y(0) = ln(8), we substitute x = 0 and y = ln(8) into the equation:

ln(8) = (1/2) * e^0 + C * e^(-0)

ln(8) = (1/2) + C

Solving for C, we find:

C = ln(8) - 1/2

Substituting the value of C back into the equation, we obtain:

y(x) = (1/2) * e^x + (ln(8) - 1/2) * e^(-x)

Simplifying, we can rewrite the equation as:

y(x) = ln(8e^x)

Therefore, the solution to the initial value problem is y(x) = ln(8e^x).

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We have to test the given series for convergence or divergence using the Alternating Series Test.The Alternating Series Test states that if an alternating series satisfies the following two conditions, then the series converges:a_n≥0 for all n.

a_n is decreasing with limit 0 as n approaches infinity.Using the above test, we have to test the series for convergence or divergence. The given series is 7-8+7/10-7/12+7/14-7/16+...On simplifying the series, we get the series as:7 - 8 + 7/10 - 7/12 + 7/14 - 7/16 +...We see that the series is alternating with a_n = (-1)^(n+1) * 7/(2n).Now we check if a_n≥0 for all n. As 7 and 2n are positive for all values of n, hence a_n is always positive for all n.

Therefore, the first condition of the Alternating Series Test is satisfied.Next, we need to check if a_n is decreasing with limit 0 as n approaches infinity.We have to evaluate the limit of a_n as n approaches infinity.Let us simplify the equation for a_n by removing the constants. We get, a_n = (-1)^(n+1) * 1/n.Using the limit definition, we have to check if the limit of a_n as n approaches infinity is 0. We have,L = lim n→∞ (-1)^(n+1) * 1/nHere, L = 0 as the denominator grows indefinitely large and the numerator is alternating between -1 and 1. Hence, the second condition of the Alternating Series Test is satisfied. Therefore, the given series converges.

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Answer:

40 pages

20% is 8 pages

1/4 is 10

22 pages for articles

Answer:

Either do 28+28+28, etc. 38 times, or follow the diagram I attached.

If you want to know more about what I did in the attachment, just ask <3

Answer:

Start by multiplying the ones: 6 times 28 is 168. Next, multiply the tens: 30 times 28 is 840. Add the products to get 1,008.

Step-by-step explanation:

Answer:

5 and 4/5

Step-by-step explanation:

Answer:

5 4/5 (5 12/15 not reduced)

Step-by-step explanation:

15 will go into 87 5 times.

15x1 = 15. 15x2 = 30. 15x3 = 45. 15x4 = 60. 15x5 = 75. 15x6 = 90. 90 can not go into 87, so you have to work with 75. 87-75=12. So, now your answer is

5 12/15. You are able to divide each of those numbers by 3, so let’s reduce. 12 divided by 3 is 4, and 15 divided by 3 is 5. So your reduced answer is 5 4/5. Hope that helped.

Answer:

x = 1

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define Equation

6x + 2 = 2(x + 4) - 2

Step 2: Solve for x

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Here we see that 8 does indeed equal 8.

∴ x = 1 is the solution to the equation.

Answer:x=7, y= 8

Step-by-step explanation: y= x+1, put in 2nd equaiton to get, -7x + 6x+6 =- 1, -x = -7, x=7. -7+y=1 ,y=8

Answer:

(x,y)=(7,8)

Step-by-step explanation:

-x + y = 1

-7x + 6y = -1

x=-1+y

-7(-1+y)+6y=-1

7+(-7y)+6y=-1

-y=-8

y=8

x=-1+8

x=7

The value of a5 is 8.

Given that,

a₁ = 4

aₙ = aₙ₋₁ + 1

So, we can find the second term a₂ using the equation of nth term,

a₂ = a₍₂₋₁₎ + 1

a₂ = a₁ + 1

Applying the value of a₁,

a₂ = 4 + 1

a₂ = 5

So, finding the value of a₃,

a₃ = a₍₃₋₁₎ + 1

a₃ = a₂ + 1

a₃ = 5 + 1

a₃ = 6

So, the value of a₄ will be,

a₄ = a₃ + 1 = 6 + 1

a₄ = 7

Therefore,

a₅ = a₄ + 1 = 7 + 1

a₅ = 8

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To produce at a point lying inside the production possibilities curve would require economic growth.

The production possibilities curve can be described as a graph  that help to display the  different combinations of output  which can be gotten from  given current resources and technology.

In this case, To produce at a point lying inside the production possibilities curve would require economic growth.

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The side lengths that form a right triangle are given as follows:

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

A right triangle is formed when the Pythagorean Theorem is respected, hence:

6² + 8² = 10²

36 + 64 = 100

100 = 100 -> right triangle with the side lengths 6, 8 and 10.

5² + 7² = [sqrt(74)]²

25 + 49 = 74

74 = 74 -> right triangle with the side lengths 5,7 and√74.

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Answer:

y=-3x-7

Step-by-step explanation:

the line is currently in standard form (ax+by=c). Let's put it into slope-intercept form (y=mx+b)

-x+3y=9

add x to both sides

3y=x+9

divide by 3

y=1/3x+3

perpendicular lines have slopes that when multiplied, equal -1.

to find the slope (m) of our new line:

1/3m=-1

multiply by 3

m=-3

the slope of the new line is -3

here's our equation so far:

y=-3x+b

we need to find b (y intecept)

since the line passes through the point (-3,2), it should be a solution in the equation (plug it in, and the result is a true statement). We can also use it to find b

so, substitute the pointt into the equation:

2=-3(-3)+b

multiply

2=9+b

subtract

-7=b

so the equation of the line is y=-3x-7

Hope this helps!

Figure C is the only angle that falls within the Range of 91 to 179 degrees.

An obtuse angle is an angle that measures between 91 and 179 degrees. Therefore, the correct answer is (c) Figure C. An obtuse angle is larger than a right angle (90 degrees) and smaller than a straight angle (180 degrees).

Figure A is a right angle measuring 90 degrees, which is smaller than an obtuse angle. Figure B is an acute angle measuring less than 90 degrees, which is also smaller than an obtuse angle. Figure D is a straight angle measuring 180 degrees, which is larger than an obtuse angle.

Figure C is the only angle that falls within the range of 91 to 179 degrees, making it the correct answer to the question.

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