alan is driving west at a rate of 50 mph towards a intersection. beatrice is driving north at 60 mph away from the same intersection. at what rate is the distance them changing when alan is 0.6 mile and beatrice is 0.8 mile from the intersection?

the dimensions of each rectangle is 72.

In geometry, a shape's perimeter is referred to as its total length. The perimeter of a form is determined by adding up the lengths of all of its sides and edges. Linear measurements like centimeters, meters, inches, and feet are used to indicate its dimensions.

EXPLANATION :

The length of a rectangle is 15 cm more than its width.

L - W = 15

Compared to the first rectangle, which has a circumference of 72 cm, the second is 2 cm smaller and 5 cm wider.

2(L-2) + 2(W+5) = 72

Simplify to get 36 L + W + 3 and 36 L + W, which equals 33 by multiplying L - 2 + W + 5 by 2.

Here, combine the two equations and apply elimination.

L - W = 15 \sL + W = 33

Using the initial length, L 2L = 48 L = 24 cm, we may find W = 24 - 15 W = 9 cm, so removing W. Second rectangle width: initial width 24 - 2 = 22 cm; second rectangle length: 9 + 5 = 14 cm.

Calculate the second rectangle's perimeter using the following equation: 2(22) + 2(14) = 44 + 28 = 72

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Answer:
Midpoint = (-0.5, 1)

Step-by-step explanation:

Midpoint formula is (x1 + x2)/2, (y1 + y2)

Lets plug that into the formula.

-4 + 3 = -1

x = -1/2 or -0.5


-1 + 3 = 2

2/2 = 1

y = 1

Final Answer: (-0.5, 1) or (-1/2, 1)

Answer:

A . 6822 just divede 420 to 32 then times 562 tk 911

The answers to all the parts of the question are:

(A)  Before we begin, consider the cartesian plane, where the x-axis represents the cover charge and the y-axis represents the number of guests per night.

According to the previous information, we will find the following coordinates there: (9,165)  (10,150).

Remember that the linear equation's slope-intercept form is y=mx+b, where m is the slope and b is the intercept.

The slope can be calculated using the following formula:

In this case, the first coordinate will be (9,165) and the second will be (10,150).

The order is irrelevant.

Finally, we get the same value for m.

So,

We now have the slope and two points. Find a linear demand equation using this formula and remember that the point-slope form of a line's equation is y - y1 = m(x - x1).

Any of two coordinates can be selected.

In this case, we will select the second one.

We can choose between two coordinates.

In this case, we'll go with the second option.

Solve equation (1) for y:

We defined x as the cover charge (p) and y as the number of guests above (q).

As a result, rewrite equation 1.

Its formula depicts the number of guests per night as a function of the cover charge.

(B) The nightly revenue can be calculated by multiplying the cover charge price by the number of guests.

So we simply multiply the equation 1 by p.

(C) To calculate the nightclub's cost function, multiply the cost of two non-alcoholic drinks by the number of guests (equation 1) and add nightly overheads.

(D) To calculate the profit in terms of the cover charge, subtract the nightly costs (equation 3) from the nightly revenue (equation 2).

We will use the first derivative test (y'(x)=0) to find an extremum point to determine the entrance fee we should charge for maximum profit.

P's first derivative should be computed (p)

P'(p) = -30p + 330 = 0

30p = 330

p = 330/30

p =  $11

For maximum profit, the entrance fee should be p=$11 per guest.

Therefore, the answers to all the parts of the question are:

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The complete question is given below:

You have just opened a new nightclub, Russ' Techno Pitstop, but are unsure of how high to set the cover charge (entrance fee). One week you charged $9 per guest and averaged 165 guests per night. The next week you charged $10 per guest and averaged 150 guests per night.

(a) Find a linear demand equation showing the number of guests q per night as a function of the cover charge p. q(p) =

(b) Find the nightly revenue R as a function of the cover charge p. R(p) =

(c) The club will provide two free non-alcoholic drinks for each guest, costing the club $2 per head. In addition, the nightly overheads (rent, salaries, dancers, DJ, etc.) amount to $1,000. Find the cost C as a function of the cover charge p. C(p) =

(d) Now find the profit in terms of the cover charge p. P(p) =

Determine the entrance fee you should charge for a maximum profit. p = $ per guest.

Answer:

C

Step-by-step explanation:

Answer:

t = nRT/M + 5ab/M

Step-by-step explanation:

I'm going to assume that the t and T are seperate variables.

basically all you have to do is isolate t by dividing each side with factors that do not contain the t

We can make a 3 set venn diagram out of the given information as shown in the figure below. Based on the venn diagram, we can answer the questions.

19.  P(Dragon Ball Z or Naruto Shippuden)

This can also be written as-

1 - P(only one piece)

P(only one piece) = 2/100

Thus, P(Dragon Ball Z or Naruto Shippuden) = 1- 2/100

= 98/100

= 0.98

20. P (Naruto Shippuden/Not DBZ)

Number of people who don't like Dragon ball z = 100 - 73

= 27

Number of people who like Naruto Shippuden but not Dragon ball z = 11 + 14

= 25

Thus, P (Naruto Shippuden/Not DBZ) = 25/27

= 0.92

21. P(One piece or Naruto Shippuden)

This can also be written as-

1 - P(only DBZ)

P(only DBZ) = 22/100

Thus, P(One piece or Naruto Shippuden) = 1- 22/100

= 78/100

= 0.78

22. P(Dragon ball Z/Not One Piece)

Number of people who don't like one piece = 100 - 51

= 49

Number of people who like Naruto Shippuden but not one piece = 14 + 13

= 27

Thus, P(Dragon ball Z/Not One Piece) = 27/49

= 0.55

23.  Number of people who like both DBZ and Naruto Shippuden = 13 + 29

= 42

Thus, probability of students that like Dragon Ball Z and Naruto Shippuden = 42/100

= 0.42

24. Number of people who like one piece but not naruto = 51 - 29 - 11

= 11

Thus, the probability of students that like One Piece and do not like Naruto Shippuden = 11/100

= 0.11

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Answer:

In a election of municipality two candidates P and Q stood for the post of mayor and 35000 people were in voter list. Voters were supposed to cast for a single candidate .22000 people cast vote for P, 5500 people cast for Q and 1500 cast vote even for both. How many people didn't cast vote find it

Answer:

74x - 25.

Step-by-step explanation:

The common difference d

= 4x + 5 - (-3x + 8)

= 7x - 3

also:

11x + 2 - (4x + 5)

= 7x - 3.

First term a1 = -3x + 8

so, 12th term

= a1 + (n -1)d

= -3x + 8 + (12 - 1)(7x - 3)

= -3x + 8 + 11(7x - 3)

= -3x + 8 + 77x - 33

= 74x - 25.

Answer: The answer for question 6 is 20,  The answer for question 7 is 7,

The answer for question 9 is 72, and the answer for question 8 is 12

Step-by-step explanation: Here is how you solve question 6!

4(3+5)-3(6-2) (You multiply 4 within the parentheses and the same for 3.)

12+20-18+6

32-18+6

14+6

20

Here is how you solve question 7

6+1/4(12-8) I multiply 1/4 with 12 to get 3 and -8 to get -2

6+3-2

7

Here is how you solve question 8

8(7.3+3.7-8)/2 You multiply within the 8 parentheses

58.4+29.6-64/2

24/2

12

Here is how you solve question 9

6^2(3+5)/4 This time you do not multiply anything over!

36(8)/4 I multiplied 36 with 8 to get 288

288/4

72

Hope this Helped :D

Answer:

6.

4(3 + 5) - 3(6-2)

= 4(8) - 3(4)

= 32 - 12

= 20

7.

6 + 1/4(12 - 8)

= 6 + 1/4(4)

= 6 + 1

= 7

8.

8(7.3 + 3.7 - 8) ÷ 2

= 8(3) ÷ 2

= 24 ÷ 2

= 12

9.

(6^2(3+5)/4)

= (36(8)/4)

= 288/4

= 72

10.

8 + 5(4) - 3(2)

= 8 + 20 - 6

= 22

Answer:

14/24

Step-by-step explanation:

multiply 7 x 2 and 8 x 3

Answer:

Step-by-step explanation:

7/8 * 2/3

7 * 2 = 14

8 * 3 = 24

14/24 = 7/12

answer: 7/12

Part (a)

S1 = 1/2 since we only have one term, i.e. we aren't really summing anything here.

S2 = (1/2) + (1/4) = (2/4) + (1/4) = (2+1)/4 = 3/4

S3 = (1/2) + (1/4) + (1/8) = (4/8) + (2/8) + (1/8) = (4+2+1)/8 = 7/8

Or,

S3 = S2 + 1/8 = (3/4) + (1/8) = (6/8) + (1/8) = (6+1)/8 = 7/8

S4 = S3 + 1/16 = (7/8) + (1/16) = (14/16) + (1/16) = (14+1)/16 = 15/16

S5 = S4 + 1/32 = (15/16) + (1/32) = (30/32) + (1/32) = (30+1)/32 = 31/32

Here's the summary:

=============================================================

Part (b)

Through trial and error, the formula is

Sn = ( (2^n) -1 )/(2^n)

For example, if n = 4, then,

Sn = ( (2^n) -1 )/(2^n)

S4 = ( (2^4) -1 )/(2^4)

S4 = (16 - 1)/(16)

S4 = 15/16

=============================================================

Part (c)

u1 = first term = 1/2

r = common ratio = 1/2

Sn = u1*( 1 - r^n)/(1 - r)

Sn = (1/2)*( 1 - (1/2)^n )/(1 - 1/2)

Sn = (1/2)*( 1 - (1/2)^n )/(1/2)

Sn = 1 - (1/2)^n

Sn = 1 - 1/(2^n)

Sn = (2^n)/(2^n) - 1/(2^n)

Sn = ( (2^n) -1 )/(2^n)

This helps confirm the formula mentioned in part b

=============================================================

Part (d)

As n gets very large, Sn approaches 1

Examples:

Try out larger values of n and the Sn value should get closer to 1.

The reason why this works is because Sn = (x - 1)/x where x = 2^n

The (x-1)/x is equivalent to 1 - (1/x) and the 1/x approaches zero when x gets larger. The x gets larger as 2^n does.

The value of Sn itself will never equal 1 exactly. It simply gets closer and closer.

=============================================================

Part (e)

The diagram is missing, so I don't have enough info to be able to answer this.

The probability of color coming up the same for rolling two 20-sided dice is 129/400.

Probability is defined as how likely something is to happen. For a single dice, getting a maroon, teal, and cyan have a probability of 4/20, 7/20, and 8/20, respectively.

Before solving the probability, we must identify whether the events are considered independent or dependent. Independent events are when the probability of an event happening does not affect the other's event probability of happening. A dependent event is when the probability of an event happening affects the other event. The rolling of dice is considered an independent event.  

For events that should occur together, the multiplication rule is used. To solve for the probability of two sides coming up the same, the formula below is used.

P (A and B) = P (A) * P (B)

P (red and red) = (4/20)*(4/20) = 1/25

P (teal and teal) = (7/20)*(7/20) = 49/400

P (cyan and cyan) = (8/20)*(8/20) = 4/25

Since no specific color was stated in the problem, the sum of the probability of each color coming up the same is determined.

P (color come up the same) = P (red and red) + P (teal and teal) + P (cyan and cyan)

P (color come up the same) = 1/25 + 49/400 + 4/25

P (color come up the same) = 129/400

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Answer:hi how are you

Step-by-step explanation:

The relation between the linear and recursive functions are given as follows:

A linear function is modeled according to the following rule:

f(x) = mx + b

In which:

Considering the concepts of a linear function, the recursive function is given as follows:

The linear function with first term -1 and slope -1 is given by:

f(n) = -n.

Hence:

f(n) = -n < - > {-1,-2,-3,-4...}, where f(1) = 1 and f(n + 1) = f(n - 1) - 1 for n > 1.

The linear function with first term -1 and slope 2 is given by:

f(n) = 2n - 3

Hence:

f(n) = 2n - 3 < - > {-1,1,3,5...}, where f(1) = -1 and f(n + 1) = f(n - 1) + 2 for n > 1.

The linear function with first term 4 and slope -1 is given by:

f(n) = -n + 5

Hence:

f(n) = -n + 5 < - > {4,3,2,1...}, where f(1) = 4 and f(n + 1) = f(n - 1) - 1 for n > 1.

The linear function with first term 4 and slope 2 is given by:

f(n) = 2n + 2

Hence:

f(n) = 2n + 2 < - > {4,6,8,10...}, where f(1) = 4 and f(n + 1) = f(n - 1) + 2 for n > 1.

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Answer:

7.2

Step-by-step explanation:

The area of a rectangle is calculated by multiplying its width and length.

The length is already given as 13 cm and the area is given as 93.6 cm.

Now, to find the width we will divide the area by length:

93.6 ÷ 13 = 7.2

The time taken for the two trains to pass one another at 324 mi apart is 4 hours.

What is velocity ?

velocity is defined as rate of change of displacement d of the object with respect to rate of change in time t. In mathematics It is written as :

v = d/t

here it is given that :

Robinsport and Titusville trains are 324 mi apart on a railroad line that is distance between then is 324 mi.

also,

Trains leave each of these depots at the same time headed for the other depot and one travels at v₁ = 43 mi/h , the other at v₂ = 38 mi/h in opposite direction that is relative speed will get add-up that is :

Δv = v₁ - v₂

Δv = 43-(-38)

Δv = 81 mi/h

Now, the time taken for the two trains to pass one another is calculated :

Δv = d/t

81 = 324/t

t = 324/81

t = 4 hours

Therefore, the time taken for the two trains to pass one another is 4 hours.

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The width of the schoolyard in the drawing is 45 millimeter.

In the given statement is ,

kirk made a scale drawing of the elementary school. the scale of the drawing was 3 millimeters : 4 meters. if the actual width of the schoolyard is 60 meters.

To find the how wide is the schoolyard in the drawing

Now, According to the question:

and, Based on the given condition

Let width of the schoolyard in the drawing be x

So, 3 : 4 = x : 60

[If b/a = d/c, ad = bc]  

3/4 = x/60

3 x 60 = 4x

x = 180/4

x = 45 millimeters

Hence, The width of the schoolyard in the drawing is 45 millimeter.

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The expression that represents the age of the oldest child is x +5

Integers are whole number and can be negative or positive. For instance, 1,2, 3, -5 are al integers.

Fractions cannot be an integers. From the question, we are told that the ages of the three children are three consecutive even integer. If the  youngest child is represented by x + 3, the the others will be determine by simply adding 1 to each term

Middle child = x + 3 + 1

Middle child = x + 4

Oldest child = x + 4 + 1

Oldest child = x + 5

Hence the expression that represents the age of the oldest child is x +5

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Distance travelled in January, February and March are 348 miles, 2436 miles and 3480 miles respectively.

Ax + b = 0, where a and b are two integers, and x is a variable, is an equation expressed in the form of linear equation with one variable. This equation has only one solution.

Let the miles travelled in January be x.

Miles travelled in February = 7x.

Miles travelled in March = 10x.

Total distance covered in three months = 6,264 miles.

Hence, the linear equation formed for given data will be:

X+7x+10x = 6264

18x = 6264

X=6264/18

X=348

So,

miles travelled in January = x

miles travelled in January = 348 miles.

Miles travelled in February = 7x

Miles travelled in February = 7*348

Miles travelled in February =2436 miles

Miles travelled in March = 10x

Miles travelled in March =1 0 * 348

Miles travelled in March=3480 miles

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Answer:

(-5,4)

Step-by-step explanation:

when the coordinate is reflection it stays the same number but is change to  the opposite (-/+)

reflecting over the y-axis flip the X coordinate (-5,4)

reflecting over the x-axis flip the Y coordinate (5,-4)

The required solution of value of c is 4.

It is required to find the value of c.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.

Given:

The equation is

c=0.5q+0.5n

We have to find the value of c.

According to given question we have

By putting the value of q=3 and n=5 we have

c=0.5q+0.5n

c=0.5*3+0.5*5

By multiply with q=3 and n=5 and  simplifying we get,

c=4

The result of the equation is 4.

Therefore, the  required solution of value of c is 4.

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The given equation 3y = -12x + 6 has infinitely many solutions.

The given equation 3y = -12x + 6 can be solved using the substitution method to determine whether this equation has no solution, 1 solution or infinitely many solutions.

Given equation,

3y = -12x + 6

Rearranging the terms of the equation, we get the value of y in terms of the variable x.

=> 3y = -12x + 6

=> y = -12x/3 + 6/3

=> y = -4x + 2

Next, we substitute this value of y in terms of the variable x in the original equation,

=> 3 ( -4x + 2 ) = -12x + 6

=> -12x + 6 = -12x + 6

=> -12x + 12x = 6 - 6

=> 0 = 0

From the obtained result, we can conclude that this system has infinitely many solutions. This implies, the lines are coincident and the system is consistent and dependent.

Therefore, it can be concluded that the given equation 3y = -12x + 6 has infinitely many solutions.

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The underlined part in the given case is a statistic.

Now,

In a given sample of 12000 students, the underlined part is a statistic, because:

Hence, the underlined part is a statistic.

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3230 kilograms of the soil supplement are required for the entire vineyard;

1 km = 1000 m = 10³ m

1 km² = 1000000 m² = 10⁶ m²

1 km² = 247 acres

1 kg = 1000 g;

A vineyard has 145 acres of Chardonnay grapes.

145 acres = 145/247 km²

                = 0.587 km²

A particular soil supplement requires 5.50 grams for every square meter of vineyard.

1 km² requires = 5.5 × 10³ kg

145 acres requires = 0.587 × 5.5 × 10³ kg = 3230 kg;

An annual percentage rate is expressed as an hobby charge. It calculates what percentage of the major you will pay every year by using taking things inclusive of month-to-month bills under consideration. APR is also the annual rate of interest paid on investments without accounting for the compounding of interest within that year.

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The ending balance based on the information given will be $2000.

From the information, it was stated that there are 2 checks for $500 and 2 bills for $2000 with $5000.

It should be noted that bill is a expense and will be deducted.

This will be illustrated as:

= $5000 + (2 × $500) - (2 × $2000)

= $5000 + $1000 - $4000

= $2000

Therefore, the ending balance based on the information given will be $2000.

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The angles that are marked congruent to each other on the diagram are : angle ZVY and angle ZYV

In this question, we need to identify two angles that are marked congruent to each other on the diagram.

We know that two angles are congruent means the measure of these angles is equal to each other.

These angles are identical to each other.

In given diagram we can observe that, angle ZVY and angle ZYV are identical.

This means, angle ZVY and angle ZYV are marked congruent to each other.

Therefore, two angles that are marked congruent to each other on the diagram are : angle ZVY and angle ZYV

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Hexadecimal numbering system includes zero via nine plus letters "A'' via "F"

Before I give an explanation for what Hexadecimal is, it is ideal that we recognize what base 10 number system is. Base 10 number system which is likewise referred to as the decimal number system has 10 digits that we rely from zero all the way through 9 (zero-nine). It is the usual numerical system that is used most often. If we took the bottom 10 numerical system and combined it with six more symbols, we usually get the hexadecimal number system. Thus, this indicates hex makes use of the usual zero-nine mixed with 6 digits taken from the alphabet A-F (A, B, C, D, E, and F). So in preference to representing the numbers 10 to 15, we use A-F to symbolize the decimal values 10-15. In quick we need to get some thing like (zero 1 2 three four five 6 7 eight nine) (A B C D E F).

Therefore, Hexadecimal numbering system includes zero via nine plus letters "A'' via "F"

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In a line segment DF with point e somewhere on the line, ef = 16 and ed = 3.

We have given a line segment  DF  with a point e on the line segment

We have been informed that ef = 16 and DF = 19

We know that

⇒ DF = ed + ef

⇒ ed = DF - ef

         = 19 - 16

         = 3 units

This line segment has two ends with defined lengths, A and B. This line segment's length is equal to the distance between its ends, A and B.

A line segment is hence a section or component of a line with two endpoints. A line segment, unlike a line, has a set length.

Measuring the length of a line segment can be done using either metric measurements, such as millimeters or centimeters, or conventional measurements, such as feet or inches.

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Full question

Point e is on line segment DF given ef =16 and DF=19. Find ed.

Answer:

[tex]x=\dfrac{1}{8}, \quad x=-2[/tex]

Step-by-step explanation:

Given equation:

[tex](8x+7)(x+1)=9[/tex]

Expand the brackets:

[tex]\implies 8x^2+15x+7=9[/tex]

Subtract 9 from both sides:

[tex]\implies 8x^2+15x+7-9=9-9[/tex]

Simplify:

[tex]\implies 8x^2+15x-2=0[/tex]

To factor a quadratic equation in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]:

[tex]\implies ac=8 \cdot -2=-16[/tex]

[tex]\implies b=15[/tex]

Therefore, the two numbers are:  16 and -1.

Rewrite [tex]b[/tex] as the sum of these two numbers:

[tex]\implies 8x^2+16x-x-2=0[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies 8x(x+2)-1(x+2)=0[/tex]

Factor out the common term (x + 2):

[tex]\implies (8x-1)(x+2)=0[/tex]

Apply the zero-product property:

[tex]\implies 8x-1=0 \implies x=\dfrac{1}{8}[/tex]

[tex]\implies x+2=0 \implies x=-2[/tex]

Therefore, the solutions to the given quadratic equation are:

[tex]x=\dfrac{1}{8}, \quad x=-2[/tex]

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Answer:

x = 1/8 (or) x = -2

Step-by-step explanation:

Now we have to,

→ solve the following quadratic equation.

Let's solve for quadratic equation,

→ (8x+7)(x+1) = 9

→ 8x² + 7x + 8x + 7 - 9

→ 8x² + 15x - 2

→ 8x² + 16x - x - 2

→ 8x(x + 2) - 1(x + 2)

→ (8x - 1)(x + 2)

→ x = 1/8 (or) x = -2

Hence, the solution is x = 1/8, -2.