Let the vector v have an initial point at (1,−1) and a terminal point at (7,2) what is the direction angle?

The number of childs plate are 201 and  adult's plate are 203.

Let's use C to represent the number of child plates and A to represent the number of adult plates.

We know that a child's plate costs $2.80 and an adult's plate costs $6.90.

Therefore, we can write two equations based on the information given:

The total number of plates served is 404

C + A = 404 ...(1)

C=404-A

The total amount collected is $1,963.50

2.8C + 6.9A = 1963.5 ..(2)

2.8(404-A)+6.9A= 1963.5

1131.2 - 2.8A +6.9A=1963.5

4.1 A =1963.5 -1131.2

4.1A=832.3

Divide both sides by 4.1

A=832.3/4.1

A=203

Now put A in equation (1)

C+203=404

C=404-203

C=201

Hence, the number of childs plate are 201 and  adult's plate are 203.

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The equation of the line that passes through the point (4, 2) and is perpendicular to the line y = 43x is y = (-1/43)x + (90/43).

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given that the line has a slope of 43.

To find the slope of the line perpendicular to it, we use the fact that the product of the slopes of two perpendicular lines is -1.

So, the slope of the perpendicular line is -1/43.

Using the point-slope form of a line, we can write the equation of the line as:

y - y1 = m(x - x1),

where (x1, y1) = (4, 2) and m = -1/43

Plugging in the values, we get:

y - 2 = (-1/43)(x - 4)

y - 2 = (-1/43)x + (4/43)

y = (-1/43)x + (4/43) + 2

y = (-1/43)x + (90/43)

Therefore, the equation of the line is y = (-1/43)x + (90/43).

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Answer:

Step-by-step explanation:

y=-2x+2

The value of row total of the column total's is 165.

The value of row total of field is 91

Column total of maple can be found by:

(46.32 /100) * y =44

Or y = (44 *100)/46.32

Or y = 94.991 =95 (approx)

Now we get value of field under maple by

Value of field under maple = (column total - value of pond under maple) = (95 - 44) = 51

Value of row total of the column total's = (column total of oak + column total of maple = (70 + 95) = 165 (total data)

Value of row total of field = ( value of field under oak + value of field under maple) = (40 + 51) = 91

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Answer:

g(1) = 1

Step-by-step explanation:

the absolute value function always gives a positive result, that is

| - a | = | a | = a

to evaluate g(1) substitute x = 1 into g(x)

g(1) = - 3| 1 - 2| + 4

    = - 3| - 1| + 4

   = - 3(1) + 4

  = - 3 + 4

  = 1

Answer:  the answer is 13 and one-half

Step-by-step explanation:

C

Step-by-step explanation:

For the function h(x) the values of h(x) when x=0,1,2,3,4,5 are 5, 9, 13,17,21,25 respectively

The given function is h(x) 4x+5

h of x equal to four times of x plus five

We have to find the values of h(x) for different values of x

x=0, h(x) = 5

x=1, h(x)=9

x=2, h(x)=13

x=3, h(x)=17

x=4, h(x)=21

x=5, h(x)=25

Hence, for the function h(x) the values of h(x) when x=0,1,2,3,4,5 are 5, 9, 13,17,21,25 respectively

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The equation that best models the data from the table after the data has been linearized is y=294755 * 1.21728^x. This equation follows an exponental model.

Looking at the data, it is very evident that it is not increasing linearly but rather exponentially.

An exponential equation has the general pattern of formula which y = ab^x, where a is the main value and b is the growth factr.

The question below is as seen in the picture, and the above answer is dependent on it.

What is the equation that best models the data from the table after the data has been linearized?

X                                 y

2                                4.4

7                               18.2

13                              120.0

19                              715.4

22                            1,768.3

26                            5,775.9

30                           10.508.5

(1 point)

logy=0.12502x+0.427231

y=1,350 76x+1,350.76

y=294755 * 1.21728^x

y=5,927 281og x-3,880 59

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The probability that a randomly selected person in the region is a woman in the 18-24 age range living alone is approximately 0.14 or 14%.

To find the probability that a randomly selected person in the region is a woman in the 18-24 age range living alone, we need to look at the intersection of the "Female" row and the "0-24" age column in the table.

The probability of selecting a woman in the 18-24 age range living alone is:

P(woman, 18-24, living alone) = (Number of women in the 18-24 age range living alone) / (Total number of people living alone)

From the table, we can see that the number of women in the 18-24 age range living alone is 20.9. The total number of people living alone is 153.6.

P(woman, 18-24, living alone) = 20.9 / 153.6

P(woman, 18-24, living alone) = 0.1362 or approximately 0.14

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The complete question:

The table shows the​ distribution, by age and​ gender, of the million people in a certain region who live alone. Use the data in the table to find the probability that a randomly selected person in the region is a woman in the 1824 age range living alone. Age |0-24|25-49|50+ |Total

Male|21.9|25.3 |28.6|75.8

Fem |20.9|26.1 |30.8|77.8

Tot |42.8|51.4 |59.4|153.6

Answer:0.5.

Step-by-step explanation:

Answer:

0.5

Step-by-step explanation:

hope this helps

There is no association between the number of fat grams and the number of calories because there are no outliers or clusters.

To make this clear, when we claim that there is no correlation between two variables, it indicates a lack of comprehensible patterns or connections. Put another way, adjustments in one factor do not seem to impact the other.

In relation to the inquiry at hand, if fat grams and calorie figures have no notable outliers or groupings, there might be an inference that these two variables are not related.

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The dimension is gioven as 69.26 feet

xy = 1836

This is the area

The cost of fence = 2x + 2y

cost of interior fencing

2x + 4y

C = 20.40(C1) + 12.00(C2)

We have to put the vakues in the formula above

C = 20.40(2x + 2y) + 12.00(2x + 4y)

= 40.80x + 40.80y + 24.00x + 48.00y

= 64.80x + 88.80y

from xy = 1836

y = 1836 / x

We have to put the value in C

C = 64.80x + 88.80(1836/x)

= 64.80x + 164236.80/x

Take the deriveative with respect to x

64.80 - 164236.80/x^2 = 0

x = √(164236.80/64.80)

=  69.26 feet

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Answer:

5

Step-by-step explanation:

use the table, when it asks f(2) that says what is the output *y) when the input is 2. Find when x=2 your answer is the y value, f(2)=5

a) The base area of the cylinder is given as follows: 78.54 ft².

b) The height of the cylinder is given as follows: 2 ft.

The volume of a cylinder of radius r and height h is given by the equation presented as follows:

V = πr²h.

The base area is given as follows:

Ab = πr².

Considering the radius of 5 ft, the base area is of:

Ab = 3.1416 x 5²

Ab = 78.54 ft².

Considering the volume of 157.08 ft³, the height of the cylinder is obtained as follows:

78.54h = 157.08

h = 157.08/78.54

h = 2 ft.

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Answer: 70 pages

Step-by-step explanation: If she read 1/7 pages on monday and the book is 490 pages, divide. 490 ÷ 1/7 = 70. 70 × 7 is 490. So use these operations in future problems. Just make sure to read carefully!

A graph of f(x) is shown in the image below.

A graph of f(x) is shown in the image below.

The vertex form equation for g(x) is g(x) = -x²

In Mathematics and Geometry, the translation a geometric figure or graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image while the translation a geometric figure or graph upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.

Since the parent function is f(x)= (x + 3)² - 2, g(x) would be created by translating f(x) three units to the right, two units up, and reflected vertically over the x-axis as follows;

f(x) = (x + 3)² - 2

g(x) = -[(x + 3 - 3)² - 2 + 2]

g(x) = -x²

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The points of the polygon are:

(1.5, 2)

(-4, 2)

(-4, -4.5)

(1.5, -4.5)

Option D is the correct answer.

We have,

From the coordinate plane,

There are 4 points that form the polygon,

The points are all in ordered pairs.

So,

(1.5, 2)

(-4, 2)

(-4, -4.5)

(1.5, -4.5)

Thus,

The points of the polygon are:

(1.5, 2)

(-4, 2)

(-4, -4.5)

(1.5, -4.5)

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Based on these factors, the polynomial that graph crosses the x-axis at only one point is A. f ⁡ ( x ) = x ³ − 7 ⁢x² + 3 ⁢x − 21

A polynomial in mathematics is a mathematical statement made up of variables (also known as indeterminates) and coefficients that only include the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

Polynomials are a fundamental algebra topic that is used in many areas of mathematics. A polynomial's degree is the largest exponent of the variable x in the expression. The correct option is A.

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Answer:

Given system of linear equations are

2x+3y+3z=5

x−2y+z=−4

3x−y−2z=3.

Represent it in matrix form

⎣

⎢

⎢

⎡

2

1

3

3

−2

−1

3

1

−2

⎦

⎥

⎥

⎤

⎣

⎢

⎢

⎡

x

y

z

⎦

⎥

⎥

⎤

=

⎣

⎢

⎢

⎡

5

−4

3

⎦

⎥

⎥

⎤

which is in the form of AX=B

A=

⎣

⎢

⎢

⎡

2

1

3

3

−2

−1

3

1

−2

⎦

⎥

⎥

⎤

∣A∣=10+15+15=40



=0

∴ A

−1

exists

To find adjoint of A

A

11

=5,A

12

=5,A

13

=5

A

21

=3,A

22

=−13,A

23

=11

A

31

=9,A

32

=1,A

33

=−7

Adj(A)=co-factor

⎣

⎢

⎢

⎡

5

3

9

5

−13

1

5

11

−7

⎦

⎥

⎥

⎤

=

⎣

⎢

⎢

⎡

5

5

5

3

−13

11

9

1

−7

⎦

⎥

⎥

⎤

A

−1

=

∣A∣

1

Adj(A)

=

40

1

⎣

⎢

⎢

⎡

5

5

5

3

−13

11

9

1

−7

⎦

⎥

⎥

⎤

X=A

−1

B

=

40

1

⎣

⎢

⎢

⎡

5

5

5

3

−13

11

9

1

−7

⎦

⎥

⎥

⎤

⎣

⎢

⎢

⎡

5

−4

3

⎦

⎥

⎥

⎤

X=

40

1

⎣

⎢

⎢

⎡

25−12+27

25+52+3

25−44−21

⎦

⎥

⎥

⎤

X=

40

1

⎣

⎢

⎢

⎡

40

80

−40

⎦

⎥

⎥

⎤

⎣

⎢

⎢

⎡

x

y

z

⎦

⎥

⎥

⎤

=

⎣

⎢

⎢

⎡

1

2

−1

⎦

⎥

⎥

⎤

Hence, x=1,y=2 and z=−1

The solution to the system of equations is

x = 3

y = 2

z = 2

To solve for x, y, and z, we can use the elimination method or substitution method. Here, we will use the elimination method.

First, we will eliminate y from the equations by multiplying the first equation by 3 and the second equation by 1, and then adding them:

(3) (2x – y + 3z = 10)

6x – 3y + 9z = 30

(1) (x + 3y – 2z = 5)

x + 3y – 2z = 5

Adding the two equations gives:

7x + 7z = 35

Simplifying, we get

x + z = 5 (Equation 1)

Next, we will eliminate y again by multiplying the second equation by 2 and the third equation by 3, and then adding them:

(2) (x + 3y – 2z = 5)

2x + 6y – 4z = 10

(3) (3x – 2y + 4z = 12)

9x – 6y + 12z = 36

Adding the two equations gives:

11x + 8z = 46

Substituting x + z = 5 from Equation 1 into the above equation, we get:

11(x + z) + 8z = 46

11x + 19z = 46

Solving for z, we get:

z = 2

Substituting z = 2 into x + z = 5 from Equation 1, we get:

x + 2 = 5

x = 3

Finally, substituting x = 3 and z = 2 into any of the original equations, we can solve for y:

2x – y + 3z = 10

2(3) – y + 3(2) = 10

6 – y + 6 = 10

y = 2

Therefore, the solution to the system of equations is:

x = 3

y = 2

z = 2

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a) The total number of balls in a bag is 9.

b) The probability that the first ball chosen is orange is 1/3.

c) The probability that the 2nd ball is also orange is 1/4.

d) The probability that both balls are orange is 1/12.

Given that:

Balls, White = 6 and Orange = 3

a) The total of ping-pong balls in the bag at the start is calculated as,

Total ball = 6 + 3

Total ball = 9

b) The probability that the first ball chosen is orange is calculated as,

P(Orange) = 3/9

P(Orange) = 1/3

c) There will be 8 balls in the bag, of which 2 are orange if the first ball selected was an orange ball. Then the probability is calculated as,

P(Orange) = 2/8

P(Orange) = 1/4

d) The product rule of probability may be used to determine the likelihood that the first and second balls are both orange:

P(Orange and Orange) = 1/3 x 1/4

P(Orange and Orange) = 1/12

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Answer:

what?

Step-by-step explanation:

The percentage of cars traveling slower than 62 mph during rush hour is 0.5 or 50%.

Since the speed of automobiles on an expressway during rush hour is normally distributed with a mean of 62 mph and a standard deviation of 5 mph, we can use the cumulative distribution function (CDF) of the normal distribution to find the percentage of cars traveling slower than 62 mph.

Let X be the speed of an automobile on the expressway during rush hour. Then, X follows a normal distribution with mean (µ) = 62 mph and standard deviation (σ) = 5 mph.

We want to find P(X < 62), which represents the probability that a car is traveling slower than 62 mph.

Using the standard normal distribution table or a calculator with built-in functions for the normal distribution, we can find the z-score corresponding to the value X = 62, using the formula;

z = (X - µ) / σ

Plugging in the given values;

z = (62 - 62) / 5 = 0

Now, we can find the cumulative distribution function (CDF) of the standard normal distribution at z = 0, denoted as Φ(0), which represents the probability that a standard normal random variable is less than or equal to 0.

Using the standard normal distribution table or a calculator with built-in functions for the normal distribution, we can find Φ(0) to be approximately 0.5.

So, P(X < 62) = Φ(0)

= 0.5

Therefore, the percentage of car is 0.5 or 50%

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Answer:

Step-by-step explanation:

Answer:

  (b)  10; 150°

Step-by-step explanation:

You want the polar coordinate equivalent of (-5√3, -5).

The polar form of (a, b) is ...

  (a, b) = (r; θ)

where ...

  r = √(a² +b²)

  θ = arctan(b/a) . . . . . with attention paid to quadrant

For the given values, the polar form is ...

  r = √((-5√3)² +5²) = √(75 +25) = 10

  θ = arctan(5/(-5√3)) = arctan(-1/√3) = 150°

The angle is a quadrant II angle with a reference angle of 30°.

The polar form is (10; 150°).

__

Additional comment

Some calculators will do the coordinate conversion based on a vector or ordered pair. Others require the coordinates of the point to be expressed as a complex number, as in the attachment. (Note the calculator mode is set to DEGrees.)

Answer:

  (d)  180° clockwise rotation

Step-by-step explanation:

Given points A(-2, -7), B(3, -2), C(2, -10) and A'(2, 7), B'(-3, 2), C'(-2, 10), you want to know the angle and direction that rotates ∆ABC to ∆A'B'C'.

We notice the signs of each of the coordinates of ABC have been reversed for the coordinates A'B'C'. For example, A(-2, -7) became A'(2, 7).

A line joining these points is a straight line through the origin. The measure of its angle at the origin is 180°. This is the angle of rotation of A'B'C' with respect to ABC.

The image is created by 180° clockwise rotation, choice D.

__

Additional comment

When rotation is 180°, the direction is immaterial. A clockwise rotation gets you to the same place as a counterclockwise rotation.

<95141404393>

The position function is s(t) = -5t³ + 3t² + 8t + 2.

We have,

To find s(t), we need to integrate the velocity function v(t) since velocity is the rate of change of position with respect to time.

To do this, we need to first find the velocity function v(t) by integrating the acceleration function a(t):

a(t) = -30t + 6

Integrating with respect to t, we get:

v(t) = -15t² + 6t + C1

We are given that v(0) = 8, so we can use this to solve for the constant C1:

v(0) = -15(0)² + 6(0) + C1 = C1

C1 = 8

Now we have the velocity function:

v(t) = -15t² + 6t + 8

To find s(t), we need to integrate v(t) with respect to t:

s(t) = -5t³ + 3t² + 8t + C2

We are given that s(0) = 2, so we can use this to solve for the constant C2:

s(0) = -5(0)³ + 3(0)² + 8(0) + C2 = C2

C2 = 2

Now we have the position function:

s(t) = -5t³ + 3t² + 8t + 2

Therefore,

The position function is s(t) = -5t³ + 3t² + 8t + 2.

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Answer:

577

Step-by-Step Explanation:

577 is right between 327 and 827.

327+827=1,154

1,154/2=577

Based on the information, the correct information regarding the graph is that C. Quantity demanded decreases as price increase.

The graph shows that for every increase of 100 units of the goods demanded, price reduces by 1 unit.

When 500 units was demanded, the price was at 1. Therefore, if 550 units are demanded, the price will reduce by half, which means the price would drop to 0.5.

The price would drop to 0.5. In this case, the the correct information regarding the graph is that Quantity demanded decreases as price increase.

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