For a control to reference trajectory, a robot at (5, 0) should
join a line trajectory line from (2, 3) to (8, 7). Calculate the
normalized orthogonal distance.

Answer:

We would need to know the percentage of discount offered during the sale to determine the sale price of the polo shirt. Here's an example calculation for a 25% discount:

If the discount offered is 25%, Bert will only need to pay 75% of the original price. We can calculate this as:

Sale price = (100% - 25%) x $20

Sale price = 75% x $20

Sale price = 0.75 x $20

Sale price = $15

Therefore, if the discount offered during the sale is 25%, Bert will pay $15 for the polo shirt. However, if the discount is different, the sale price will be different.

The correct symbol in the expression is 95/56 < 2 5/7

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

95/56 and 2 5/7

Convert the improper number to a mixed number

So, we have the following representation

1 39/56 and 2 5/7

By comparison;

1 39/56 is less than 2 5/7

So, the inequality symbol is a less than inequality

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Answer:

Step-by-step explanation:

1

a.  The total number of possible outcomes is 16 x 96 = 1,536.

b. She should expect to see a difference of 1 approximately 12/16 x 96 = 72 times.

c. She should expect to see a difference of 0 approximately 8/16 x 96 = 48 times.

a) There are a total of 16 possible pairs of numbers that can be rolled on the two pyramids:

(1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), and (4,4).

We can use a probability distribution to calculate the probability of each pair of numbers being rolled. Since each pyramid has four sides, there are 4 x 4 = 16 possible outcomes when both pyramids are rolled. Therefore, the probability of each outcome is 1/16.

Since Natalie is going to toss each pair of pyramids 96 times, the total number of possible outcomes is 16 x 96 = 1,536.

To calculate the difference between each pair of numbers, we can simply subtract the smaller number from the larger number.

Here is a table that shows the probability of each difference:

Difference                  Possible Pairs                           Probability

0                               (1,1), (2,2), (3,3), (4,4)                            4/16 = 1/4

1                               (1,2), (1,3), (1,4), (2,3), (2,4), (3,4),          12/16 = 3/4

                                     (2,1), (3,1), (4,1), (3,2), (4,2), (4,3)  

2                                None                                             0

3                                None                                             0

Therefore, the probability of the difference being 0 is 1/4, the probability of the difference being 1 is 3/4, and the probability of the difference being 2 or 3 is 0.

Since Natalie is going to conduct the experiment a total of 96 times, we can use these probabilities to calculate the expected number of times each difference will occur:

Difference             Probability          Expected Number of Occurrences

0                                1/4                     96 x 1/4 = 24

1                                 3/4                     96 x 3/4 = 72

2                                      0                     96 x 0 = 0

3                                 0                     96 x 0 = 0

b) we can expect the difference between each pair of numbers to be 0 about 24 times and

c) to be 1 about 72 times over the course of the experiment.

Differences 2 and 3 are not expected to occur.

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The correct question should be:

Natalie has two number pyramids each labeled 1 to 4. Natalie is going to conduct an experiment by tossing both pyramids a total of 96 times. She will find the difference of each pair of numbers rolled by subtracting the lesser number from the greater number.

a. How many possible outcomes are there? _________________

b. How many times should Natalie toss a difference of 1? ______________

c. How many times should Natalie toss a difference of 0?

The standard form for the circle x² - 10x + y² + 14y - 7 = 0 is (x - 5)² + (y + 7)² = 81. The correct answer is D.

To find the standard form of the given circle, we must complete the square by rearranging the equation and adding constants to both sides of the equation to create perfect squares. Here are the steps:

1. Rearrange the equation so that the x and y terms are together:
x² - 10x + y² + 14y = 7

2. Complete the square for the x terms by adding (10/2)² = 25 to both sides of the equation:
x² - 10x + 25 + y² + 14y = 7 + 25

3. Complete the square for the y terms by adding (14/2)² = 49 to both sides of the equation:
x² - 10x + 25 + y² + 14y + 49 = 7 + 25 + 49

4. Simplify the equation by factoring the perfect squares:
(x² - 10x + 25) + (y² + 14y + 49) = 7 + 25 + 49

(x - 5)² + (y + 7)² = 81

So, the standard form for this circle is (x - 5)² + (y + 7)² = 81, which is option D.

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The expression of one hundred twenty rupees and five paise in rupees is equals to the rupees 120.05.

We have, 120 rupees and 5 paise and we will express as rupees using decimals.

We have been given 5 paise. As we see 120 rupees so it's remain as it but we have to change 5 paise in rupees. Using the conversation factor, as we know that 100 paise = rupee 1

=> 1 paisa = Rs. 1/100

so, here conversation factor is = 1/100

The required value is obtained by multiplying the observed values by conversion factor. Therefore,

5 paise = Rs. (5×1/100)

= 5/100

= Rs. 0.05

Therefore, in decimals 5 paise = Rs. 0.05. Now, 120 rupees 5 paise = Rs. 120 + Rs. 0.05 = Rs. 120.05

Hence, required value is Rs. 120.05.

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Complete question:

Express in form of rupees

120 rupees 5 paise = — rupees.

The function in standard form of f(x)=-4 x³-10 x¹²+13 is f(x)=-10 x¹²-4 x³+13 x. The function in standard form of  f(x)=8 x²¹-5 x²+13 x )  is f(x)=8 x²¹-5 x²+13 x. The function in standard form of  ( f(x)=x^³²-10 x¹⁴ is f(x)=8 x²¹-5 x²+13 x

7.  To determine the end behavior, we look at the highest degree term, which is -10 x^{12}. As x approaches positive infinity, -10 x^{12} will approach negative infinity. As x approaches negative infinity, -10 x^{12} will approach positive infinity. Therefore, the end behavior is:
lim_{x→∞} f(x) = -∞
lim_{x→-∞} f(x) = ∞

8. The function in standard form is f(x)=8 x^{21}-5 x^{2}+13 x. To determine the end behavior, we look at the highest degree term, which is 8 x^{21}. As x approaches positive infinity, 8 x^{21} will approach positive infinity. As x approaches negative infinity, 8 x^{21} will approach negative infinity. Therefore, the end behavior is:
lim_{x→∞} f(x) = ∞
lim_{x→-∞} f(x) = -∞

9. The function in standard form is f(x)=8 x^{21}-5 x^{2}+13 x. To determine the end behavior, we look at the highest degree term, which is x^{32}. As x approaches positive infinity, x^{32} will approach positive infinity. As x approaches negative infinity, x^{32} will approach positive infinity. Therefore, the end behavior is:
limx→∞ f(x) = ∞
limx→∞f(x) = +∞

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The Cartesian equation y = 3x^2 as a polar equation can be write as r(θ) = 3 sec(θ) / (1 + tan²(θ)).

To rewrite the Cartesian equation y = 3x² as a polar equation, we need to use the conversion formulas between Cartesian coordinates (x, y) and polar coordinates (r, θ):

x = r cos(θ)
y = r sin(θ)

Substituting these formulas into the Cartesian equation gives us:

r sin(θ) = 3(r cos(θ))²

Dividing both sides by r and rearranging terms gives us:

r = 3 cos²(θ) / sin(θ)

Using the identity 1 + tan²(θ) = sec²(θ), we can rewrite the equation in terms of tan(θ) and sec(θ):

r = 3 (1 / (1 + tan²(θ))) / (1 / sec(θ))

Simplifying gives us the final polar equation:

r(θ) = 3 sec(θ) / (1 + tan²(θ))

Therefore, the Cartesian equation y = 3x²can be rewritten as the polar equation r(θ) = 3 sec(θ) / (1 + tan²(θ)).

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Answer:

Step-by-step explanation:

it's -4.89279003

The equation of a line that passes through the point (17,-12) with slope -3 is found as: y = -3x + 39.

equation of a line using point-slope form is-

y - y1 = m(x - x1)

Points: (17,-12) and  slope -3.

Put the values:

y - (-12) = -3(x - 17)

y + 12 = -3x + 51

y = -3x + 51 - 12

y = -3x + 39

Thus, the equation of a line that passes through the point (17,-12) with slope -3 is found as: y = -3x + 39.

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Mrs Sheperd was going  7.5 miles per hour

Let us assume that d represents the distance covered by Mrs Shepard, 't' represents the time required and 's' represents the speed of her bike.

Here, d = 5.25 miles

t = 0.7 hours

We know that the formula of speed is speed = distance/time

Using this formula we calculate the speed (s) of Mrs Shepard's bike.

speed = distance/time

⇒ s = d/t

⇒ s = 5.25/0.7

⇒s = 7.5 miles per hour

This means that the speed (s) of Mrs Shepard's bike was 7.5 miles per hour

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Answer:

Median is a middle number.

Step-by-step explanation:

You can use any set of number with 12 in the middle

14, 18, 12, 12, 17, 18

Middle numbers are third and forth number added together and divided by 2

The equation y^(2)-x+10=0 has no symmetry.

Symmetry is when one part of an equation is the mirror image of another part. In this case, there is no symmetry because the equation cannot be mirrored on any axis.

To check for symmetry with respect to the y-axis, we can replace x with -x and see if the equation is still true. In this case, y^(2)-(-x)+10=0 is not the same as the original equation, so there is no symmetry with respect to the y-axis.

Similarly, to check for symmetry with respect to the x-axis, we can replace y with -y and see if the equation is still true. In this case, (-y)^(2)-x+10=0 is not the same as the original equation, so there is no symmetry with respect to the x-axis.

Finally, to check for symmetry with respect to the origin, we can replace x with -x and y with -y and see if the equation is still true. In this case, (-y)^(2)-(-x)+10=0 is not the same as the original equation, so there is no symmetry with respect to the origin.

Therefore, the equation y^(2)-x+10=0 has no symmetry.

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The expression can be expanded as a sum of three logarithms:

[tex]log4(xy^5 Z^4) = log4(x) + 5 log4(y) + 4 log4(Z)[/tex]

What is the logarithms?

Logarithms are mathematical functions that help to simplify the representation of very large or very small numbers. They are the inverse functions of exponential functions.

Using the properties of logarithms, we can expand the expression as follows:

[tex]log4(xy^5 Z^4) = log4(x) + log4(y^5) + log4(Z^4)[/tex]

Now, we can simplify each logarithm using the property that log[tex](a^b[/tex]) = b log(a):

[tex]log4(x) + log4(y^5) + log4(Z^4) = log4(x) + 5 log4(y) + 4 log4(Z)[/tex]

Hence, the expression can be expanded as a sum of three logarithms:

[tex]log4(xy^5 Z^4) = log4(x) + 5 log4(y) + 4 log4(Z)[/tex]

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Answer:

G

Step-by-step explanation:

Since these triangles are similar, side lengths in one must be proportional to the other.  Segment AB is similar to DE, AC similar to DF, and BC similar to EF. With that in mind, G is the only possible answer because DE/AG correspond to one another, just as DF/AC correspond to one another.

The given permutations can be expressed as the product of the following cyclic permutations: (1 4 5 10)(2 6)(3 9 7 8).

The given permutations can be expressed as products of cyclic permutations as follows:

S10 = ([1,2,3,4,5,6,7,8,9,10],[4,6,9,5,10,2,8,3,7,1])

= (1 4 5 10)(2 6)(3 9 7 8)(7 8 3 9)

= (1 4)(4 5)(5 10)(2 6)(3 9)(9 7)(7 8)(8 3)

= (1 4 5 10)(2 6)(3 9 7 8)

Therefore, the given permutations can be expressed as the product of the following cyclic permutations: (1 4 5 10)(2 6)(3 9 7 8).

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The length of the diagonal of this square is 11 and option 4 is the correct answer.

A diagonal line is a line segment that joins two of a shape's vertices when there isn't already an edge between them. It doesn't go directly above, below, or across. The diagonals are always in the form of a straight line. In other terms, a diagonal is a line that passes through the vertex of a polygon or polyhedron and links its opposing corners.

Given that, x is the length of the diagonal of the square.

Also, x² = 132

The value of x is:

x = √132

x = 11.48

Hence, the length of the diagonal of this square is 11 and option 4 is the correct answer.

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Answer:

Step-by-step explanation:

Since tangent is negative and is equal to the ratio of opposite over adjacent, we can assume that the angle theta lies in either the third or the fourth quadrant, where the x and y coordinates have opposite signs.

In the third quadrant, sine is positive and cosine is negative. Therefore, we have:

tangent theta = opposite/adjacent = -1

sine theta = opposite/hypotenuse > 0

cosine theta = adjacent/hypotenuse < 0

Using the Pythagorean identity, we have:

sin² theta + cos² theta = 1

=> opposite²/hypotenuse² + adjacent²/hypotenuse² = 1

=> opposite² + adjacent² = hypotenuse²

Since we are given that 3π/2 < theta < 2π, we can place the triangle in the third quadrant with a reference angle of π/2. This means that the opposite side is equal to the absolute value of the adjacent side. Let's assume that the hypotenuse is equal to 1, then we have:

opposite/adjacent = -1

=> opposite = -adjacent

opposite² + adjacent² = hypotenuse²

=> adjacent² + (-adjacent)² = 1

=> 2adjacent² = 1

=> adjacent = ±1/√2

Since cosine is negative in the third quadrant, we have:

cosine theta = adjacent/hypotenuse = -1/√2

Finally, we can use the reciprocal identity to find secant:

secant theta = 1/cosine theta = -√2

Therefore, the answer is A. Negative StartRoot 2 EndRoot.

The value of tangent theta is equal to the negative 1. At this value the value of secant theta is [tex]\sqrt{2}[/tex].

The tangent theta in a triangle is the ratio of sine theta and cos theta. It can be written as,

[tex]tan\theta=\dfrac{sin\theta}{cos\theta}[/tex]

Given information-

The value of tangent theta is equal to the negative 1.

[tex]tan\theta=-1[/tex]

The tangent theta in a triangle is the ratio of sine theta and cos theta. It can be written as,

[tex]tan\theta=\dfrac{sin\theta}{cos\theta}[/tex]

The value of tangent theta is equal to the negative 1. Thus put the value in above expression as,

[tex]-1=\dfrac{sin\theta}{cos\theta}[/tex]

Simplify it further as,

[tex]-cos\theta=sin\theta[/tex]

When the value of cosine and sine theta is equal, then the angle exist in

4th quadrant with the value of [tex]\dfrac{7\pi }{4}[/tex]. Which extent to the [tex]\sqrt{2}/2[/tex] for the cosine function.

In the trigonometry cosine theta is the reciprocal of the secant theta. Thus,

[tex]\dfrac{1}{sec\theta} =\dfrac{\sqrt{2} }{}[/tex]

[tex]sec\theta=\sqrt{}\dfrac{2}{2}[/tex]

Thus the value of secant theta is [tex]\sqrt{2}[/tex]

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The period of the function is 10 and the amplitude is 4.

The period and amplitude of the function \[ y=-4 \sin \left(\frac{\pi x}{5}\right) \] can be found by examining the coefficients in the equation.

The amplitude is the absolute value of the coefficient in front of the sine function, which in this case is |-4| = 4. Therefore, the amplitude of the function is 4.

The period is found by dividing 2π by the coefficient in front of the x variable inside the sine function. In this case, the coefficient is \[\frac{\pi}{5}\]. So, the period is \[\frac{2\pi}{\frac{\pi}{5}} = 10\].

Therefore, the period of the function is 10 and the amplitude is 4.

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Answer:

a = 13.3

Step-by-step explanation:

Pythagorean theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

c^2 = a^2 + b^2

15^2 = a^2 + b^2

a^2 = 15^2 - 7^2 = 225 - 49 = 176

a = √176 = 13.26 = 13.3

The value of x is if the 8th term of the expansion of given equation is equal to 25952256 = 2. The correct answer is option a.

In order to find the value of x, we first need to find the 8th term of the expansion of [tex](x^3 + 1)^12.[/tex] Using the binomial theorem, the general term in the expansion is given by: [tex]T(k) = C(n, k-1) * (x^3)^(n-k+1) * 1^(k-1).[/tex]where T(k) is the kth term, n is the power (in this case, 12), C(n, k-1) represents the binomial coefficient [tex](n! / [(k-1)! * (n-k+1)!]),[/tex] and x^3 is the term in the expansion.

Now, we plug in the values to find the 8th term: [tex]T(8) = C(12, 7) * (x^3)^(12-7+1) * 1^7, T(8) = 792 * (x^3)^6.[/tex] We are given that the 8th term of the expansion is equal to 25952256. So, 25952256 = 792 * (x^3)^6

Now, we need to solve for [tex]x: (25952256 / 792) = (x^3)^6, 32768 = (x^3)^6[/tex]
Taking the 6th root of both sides, we get:
[tex]x^3 = 2[/tex]
Now, taking the cube root of both sides, we find the value of x:
x = 2 (option a). The correct answer is option a.

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The graph and the table show the high temperatures in a city over a 10-day period. here are the right answer:

a. 60, b. 2, 4, and 6 days

c. Yes, the high temperature is a function of the day.

The following group is shows a the high temperatures in a city for 10 -days. Where height temperature is on day 9, lowest temparature in day 7. Here the high temperature is a function of the day.            

Here we have

The graph and the table show the high temperatures in a city for 10-days    

From the table,

The high temperature on Day 7 = 60      

The high temperature 61 degrees on 2, 4, and 6 days

Since the graph shows the change in temperature as well as the change in the number of days the high temperature is a function of the day  

Therefore,

The answer are

a. 60, b. 2, 4, and 6 days

c. Yes, the high temperature is a function of the day.

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Answer:

reads 64 pages in one hour

Step-by-step explanation:

For simplicities' sake, we'll convert 1/4 of an hour into 15 minutes (60 minutes x 1/4 = 15 mins)

Since we have a ratio, of 16 pages to 15 mins, we can create the ratio by making a fraction of 16/15. Since we want to get to 1 hour, to find how many pages she read in an hour, we can multiply the top and bottom (to equalize) by 4 (because 4 x 15 = 60).

16•4/15•4

64/60

Because of this, we can see that the ratio is now 64 pages to 60 mins or one hour. Therefore, she reads 64 pages in one hour.

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Answer:

64

Step-by-step explanation:

To do this problem you have to figure out Michelle's hourly rate for reading pages. We are given that she will read 16 pages in 1/4 of an hour. This means that in 15 minutes (60 minutes in an hour / 4 for the 1/4 an hour) she will read 16 pages. We only have 15 minutes though and need 60 minutes so 60/15 gives us 4. This means that we will need 4, 15 minute periods to get to a hour. So 4*15minutes = 60 minutes or one hour and 16pages*4 = 64 pages. So in one hour she will read 64 pages.

A faster way to do this is to just multiply both sides by the recripical.

16 pages = 1/4 hour

*4/1              *4/1

64 pages = 4/4 hour

64 pages = 1 hour

The answer to 13)/(15)-:(7)/(10)  in simplest form is (26)/(21).

To divide the fractions (13)/(15) and (7)/(10), we need to multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by flipping the numerator and denominator. So, the reciprocal of (7)/(10) is (10)/(7).

Now, we can multiply the two fractions as follows:
(13)/(15) * (10)/(7) = (13*10)/(15*7) = (130)/(105)

Next, we need to simplify the fraction by finding the greatest common factor (GCF) of the numerator and denominator.The GCF of 130 and 105 is 5. So, we can divide both the numerator and denominator by 5 to get the simplest form of the fraction:
(130)/(105) = (130/5)/(105/5) = (26)/(21)

Therefore, the answer in simplest form is (26)/(21).

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Mr. Cortez is comparing the cost to join two different gyms. Gym A charges a $55 registration fee plus $24 per month. Gym B does not charge a registration fee but charges $35 per month. The cost will be the same for both gyms on the 5 months.

What is gym?

A gymnasium or gym is a place where people can exercise indoors. The word is a translation of "gymnasium," which is Greek. They are typically seen in athletic and fitness facilities, in addition to acting as activity and learning spaces in educational institutions. Gym is slang for "fitness centre," which is often a location for indoor entertainment.

Given,

Gym A charges a $55 registration fee and $24 per month

Total charges after 5 months with registration fee= (24*5+55)= $175

Gym B charges $35 per month

Total charges after 5 months= 35*5= $175

Hence the correct answer is the cost will be the same for both gyms on the 5 months.

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Answer:

   ∠e = 32°

   ∠d = 69°

   ∠f = 79°

Step-by-step explanation:

       Angle e and 32° are vertical angles, so this means that ∠e = 32° because vertical angles are congruent.

       Next, a straight line is equal to 180°, and angle e is equal to 32°, so we can write the following equation to solve for angle f:

69° + e + f = 180° ➜ 69° + 32° + f = 180° ➜ 101° + f = 180° ➜ f = 79°

       Lastly, angle d and 69° are also vertical angles, so this means that ∠d = 69° because vertical angles are congruent.

Answer:

0.38

Step-by-step explanation:

Adam should purchase the long-range weather forecast for $1. By doing so, he will have the best chance of minimizing his total expected cost for the summer.

The expected value of the sample information (EVSI) is the expected cost if Adam does not purchase the forecast and goes with the meteorological records, which is $16.6 ($15 for the season pass plus an average of $1.6 per rainy day).

The expected value of perfect information (EVPI) is the expected cost if Adam purchases the forecast and uses it to make the decision, which is $15.6 ($15 for the season pass plus an average of $0.6 per rainy day).

Thus, purchasing the long-range weather forecast is the best decision for Adam, as it will save him $1 in expected costs and allow him to minimize his total expected cost for the summer.

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