Find the curvature ofr(t) = 9t, t2, t3at the point(9, 1, 1)

Answers

Answer 1

The curvature of the curve r(t) = (9t, t², t³) at the point (9, 1, 1) is (3/ 800)√(91/ 94).

The curvature of a curve at a given point is a measure of how much the curve is bending at that point. In order to find the curvature of a curve, we need to first find the unit tangent vector, the unit normal vector, and the unit binormal vector at the point in question.

Given r(t) = (9t, t², t³) at the point (9, 1, 1). Thus t = 1 at (9, 1, 1).

The unit tangent vector at the point (9, 1, 1) is given by the derivative of r(t) with respect to t, evaluated at t = 1

r'(t) = (9, 2t, 3t²)

so T(t) = r'(1) = (9, 2, 3)

The magnitude of T(1) = √(9² + 2² + 3²) = √(94)

The unit tangent vector at (9, 1, 1) is T(1) = (9/√(94), 2/√(94), 3/√(94))

The unit normal vector, N(1), is given by the derivative of T(1) with respect to t, evaluated at t = 1

T'(t) = (0, 2, 6t)

T'(1) = (0, 2, 6)

The magnitude of T'(1) = √(0² + 2² + 6²) = √(40)

The unit normal vector at (9, 1, 1) is N(1) = (0, 2/√(40), 6/√(40))

The unit binormal vector, B(1), is given by the cross product of T(1) and N(1)

B(1) = T(1) × N(1)

= (18/√(40×94), 6/√(40×94), -54/√(40×94))

|B| = (3/2)√(91/ 235)

Finally, the curvature, k, at the point (9, 1, 1) is given by the magnitude of T'(1)

[tex]k = \frac{|B|}{|T|^3}[/tex]

k = (3/2)√(91/ 235)/ (√40)³ = (3/ 800)√(91/ 94)

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Related Questions

The temperature in Williamstown was 38°F. Then a winter storm came through and the temperature dropped 24°F overnight. Which expression represents the change in temperature?
|−24| − |38|
|−24| + |38|
|38| − |−24|
|38| + |−24|

Answers

Answer:The temperature dropped 24°F overnight, so the change in temperature would be represented by the expression |-24|, which is the absolute value of -24.

You can also represent it by |38| - |-24| which is equal to 38 - (-24) = 38 + 24 = 62°F.

Step-by-step explanation:

Write the function of the graph in f(x)=a∙b^x form.

Answers

The exponential function graphed is given as follows:

y = 2^x.

How to model an exponential function?

The standard definition of an exponential function is given as follows:

y = ab^x.

In which the parameters are given as follows:

a is the initial value.b is the rate of change.

When x increases by one, the output is multiplied by 2, hence the parameter b is given as follows:

b = 2.

The graph crosses the y-axis at y = 1, hence the parameter a is given as follows:

a = 1.

Hence the function is defined as follows:

y = 2^x.

Missing Information

The graph is given by the image presented at the end of the answer.

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y=6\left(2\right)^{x-4}-1

Answers

y = 6(2)^(x-4)-1 is an exponential function with a base of 2 and an exponent of x-4. The coefficient of the base, 6, is called the leading coefficient. The constant term, -1, is the y-intercept, the point where the graph of the function crosses the y-axis. The function is also a shifted version of the basic exponential function y= a*b^x, where a is the leading coefficient and b is the base of the function.

Since the base of the function is 2, the graph of the function will increase or decrease at an increasing rate. The leading coefficient of 6 will affect the steepness of the graph, making it steeper than the basic exponential function y=2^x. The horizontal shift of the graph is 4 units to the left, as the exponent has x-4 instead of x.

In terms of symmetry, the graph of this function has no symmetry.

The function has no rotational symmetry because it is not repeated after any rotation around the origin.

what is the probability that 3 hearts are chosen if 7 cards are chosen from a well-shuffled deck of 52 playing cards?

Answers

The probability that 3 hearts are chosen if 7 cards are selected from a well-shuffled deck of 52 playing cards is  [tex]\\& =0.175823334\end{aligned}[/tex]

A probability simple definition is what?

The probability is a numerical representation of the possibility or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging between 0% to 100% can be used to describe probabilities.

A probability may it be negative?

Although a quasiprobability distributed enables a negative probability, called quasiprobability, for some events, the probability of the result of an experiment is never negative. These distributions may be applicable to conditional probability or unobservable occurrences.

The number of choosing  cards out of 52 is = ⁵²C₃

Number of ways of choosing 3 cards of heart out of 13 cards and 4 out of remaining 39 cards = ¹³C₅ × ³⁹C₃

Probability of choosing 5 hearts =  ¹³C₃ × ³⁹C₄ /  ⁵²C₃

[tex]\begin{aligned}\frac{13 \times 2 \times 11 \times 13 \times 19 \times 3 \times 9}{26 \times 17 \times 10 \times 7 \times 2 \times 47 \times 46} & =\frac{23523786}{133784560} \\& =0.175823334\end{aligned}[/tex]

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3/20 plus 3/5=[tex]3/20 plus3/5[/tex]

Answers

15/20 or 3/4 is the simplified answer

a standard deck of 52 cards has 13 ranks (ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king) and 4 suits ($\spadesuit$, $\heartsuit$, $\diamondsuit$, and $\clubsuit$), such that there is exactly one card for any given rank and suit. two of the suits ($\spadesuit$ and $\clubsuit$) are black and the other two suits ($\heartsuit$ and $\diamondsuit$) are red. the deck is randomly arranged. what is the probability that the top card is red and the second card is black?

Answers

The probability of the top card being red and the second card being black is P(A and B) =  0.0650.

The probability that the top card is red and the second card is black can be calculated using the formula P(A and B) = P(A) x P(B)

Let A be the event of the top card being red and B be the event of the second card being black.

The probability of the top card being red is P(A) = (26/52), since there are 26 red cards in the deck.

The probability of the second card being black is P(B) = (26/51), since there are 26 black cards left in the deck after taking away the red card from the top.

Therefore, the probability of the top card being red and the second card being black is P(A and B) = (26/52) x (26/51) = (169/2612) = 0.0650.

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lost luggage a department of transportation report about air travel found that airlines misplace about 5 bags per 1000 passengers. suppose you are traveling with a group of people who have checked 22 pieces of luggage on your flight. can you consider the fate of these bags to be bernoulli trials? explain.

Answers

The fate of the 22 checked bags can be considered the Bernoulli trials.

A Bernoulli trial is a random experiment with two possible outcomes, often referred to as a "success" or "failure." In the context of the lost luggage problem, success would be a checked bag that is not misplaced, and failure would be a checked bag that is misplaced.

For a set of trials to be considered Bernoulli trials, the following conditions must be met:

The trials must be independent, meaning that the outcome of one trial does not affect the outcome of another trial.The probability of success (a bag not being misplaced) must be constant across all trials.The trials must have only two possible outcomes: success or failure.

In this case, the fate of the 22 checked bags can be considered Bernoulli trials if the following conditions are met:

The bags are checked in separately, so the outcome of one bag does not affect the outcome of another bag, therefore they are independent trials.The probability of a bag being misplaced is given as 5 bags per 1000 passengers, which is constant across all passengers, including the group of 22 passengers.The trials have two possible outcomes: a bag is misplaced or a bag is not misplaced.

Therefore, the fate of the 22 checked bags can be considered Bernoulli trials.

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Five numbers have a median of 8, a mode of 4, a mean of 9 and a range of 11.
Find the five numbers.

Answers

Let x1, x2, x3,x4,x5 be 5 nos in increasing order.

Median of 5 nos =[(5-1)/2 +1 ] th value =

3rd value = 8

x3 = 8 ........(0)

Range = Max - Min = x5 - x1

x5 - x1 = 11

x5 = 11 + x1. .......(1)

Mean = sum of values/ no. of values

(x1+x2+x3+x4+x5)/5 = 9

x1+ x2 +8 +x4+ 11+x1 = 45 _____(using (1) and (0))

2*x1 + x2 + x4 = 45-8-11

2*x1+ x2 + x4 = 22-------------(2)

Now mode = value that occurs most number of times

Mode = 4. -------(3)

Using (3) in (2) we get

2*x1 + 4 + 4 = 22

2*x1 = 14

x1 = 7

From (1)

x5 = x1+ 11 = 7+11= 18

So

x1 = 7, x2 = 4, x3 = 8, x4 = 4, x5 = 18

work out the area of this shape​

Answers

Answer:

[tex]72cm^{2}[/tex]

Step-by-step explanation:

9/3=3

12/3=4

(4x9)+(4x6)+(4x3)=

=36+24+12

=[tex]72cm^{2}[/tex]

Keilantra has $660 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $488.20.
She buys 2 bicycle reflectors for $11.17 each and a pair of bike gloves for $19.05.
She plans to spend some or all of the money she has left to buy new biking outfits for $37.26 each.

Write and solve an inequality which can be used to determine
x
x, the number of outfits Keilantra can purchase while staying within her budget.

Answers

Answer:

We know that Keilantra has $660 to spend, she has already spent $488.20 on a bicycle, $11.17 on two reflectors and $19.05 on a pair of gloves.

We can represent the amount spent on reflectors as 2 * $11.17 = $22.34

So the total amount spent so far is:

$488.20 + $22.34 + $19.05 = $529.59

We can represent the remaining amount of money she has to spend on outfits as:

$660 - $529.59 = $130.41

We can use this remaining amount to find out the number of outfits she can purchase by dividing the remaining amount by the cost of each outfit:

$130.41 / $37.26 = 3.5

The inequality that represents this situation is:

x <= 3.5

Where x is the number of outfits Keilantra can purchase while staying within her budget.

This inequality tells us that Keilantra can purchase at most 3.5 biking outfits while staying within her budget.

However, since the number of outfits has to be a whole number, the greatest number of outfits that Keilantra can buy is 3.

(WILL GIVE BRAINIEST) A collage artist makes art out of real-life objects. She has three pieces of bamboo that measure 4 inches, 5 inches and 7 inches. If she makes a triangle out of the pieces will it be right, acute or obtuse triangle?

Answers

If the artist makes a triangle from three pieces of bamboo that measure 4 inches, 5 inches and 7 inches. The triangle will not be a right triangle because the values are not Pythagorean triple

What is Pythagorean triple?

Pythagorean triples are b² + a² = c² where b, a and c are all positive integers.

These triples are represented as (b, a, c).

Here, b is perpendicular (or right angel) to a, a is the base and the hypotenuse of the right - angled triangle is labeled .

The most known and smallest triplets are (3, 4, 5).

In the problem, the values  4 inches, 5 inches and 7 inches cannot make a Pythagorean triple since

c² = 4² + 5²

c² = 16 + 25

c² = 41

c = √41 ≠ 7

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military radar and missile detection systems are designed to warn a country of enemy attacks. a reliability question deals with the ability of the detection system to identify an attack and issue the warning. assume that a particular detection system has a 0.91 probability of detecting a missile attack. answer the following questions using the binomial probability distribution: what is the probability that one detection system will detect an attack? if required, round your answer to two decimal places. fill in the blank 1 if two detection systems are installed in the same area and operate independently, what is the probability that at least one of the systems will detect the attack? if required, round your answer to two decimal places. fill in the blank 2 if 3 systems are installed, what is the probability that at least one of the systems will detect the attack? if required, round your answer to four decimal places. fill in the blank 3 would you recommend that multiple detection systems be operated? explain. the input in the box below will not be graded, but may be reviewed and considered by your instructor.

Answers

A detection system has a probability of 0.91 to detect a missile attack. It is recommended to have multiple detection systems as it increases the overall probability of detecting an attack and allows for redundancy in case one system fails.

The probability that one detection system will detect an attack is: 0.91If two detection systems are installed in the same area and operate independently, the probability that at least one of the systems will detect the attack is: 1 - (0.09)² = 0.9801If 3 systems are installed, the probability that at least one of the systems will detect the attack is: 1 - (0.09)³ = 0.99291Yes, it is recommended to have multiple detection systems as it increases the overall probability of detecting an attack. It allows for redundancy in case one system fails and increases the chances of detecting an attack even if one system is not functioning properly.

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1) Solve for a
a+6=6 a-5= -8 a x -10= 100 (5+2a) ÷ 17 = 3

2) A rectangular field has an area of 49m. If its not a square field and the dimension is a whole number then
a) What are the dimensions of the field?
b) What is the perimeter of the field?
c) Make an equation that shows how you could find the answer to A



3) The following are the first 5 terms in a patterns: 3,5,7,9,11...
a) Make a T chart of term
b) Come up with a pattern rule relating T and V

Answers

1.

a+6=6

Solving for a:

a = 0

a-5= -8

Solving for a:

a = -13

a x -10= 100

Solving for a:

a = -10

(5+2a) ÷ 17 = 3

Solving for a:

a = -4

2.

a) The dimensions of the field are 7m by 7m.

b) The perimeter of the field is 28m.

c) To find the area of the field, you could use the equation: length x width = area. In this case, the length and width are both 7m, so the equation would be 7m x 7m = 49m^23

3.

a) T | V

1 | 3

2 | 5

3 | 7

4 | 9

5 | 11

b) The pattern rule is that the value (V) is 2 greater than the previous value.

B) El tamaño de las pantallas de televisión viene dado por la longitud en pulgadas de la diagonal de la pantalla. Si un televisor mide 40 pulgadas y tiene 95 cm de base, ¿Cuál será su altura? Recuerda que la pulgada tiene 2,54cm.

Answers

Answer: english please so I can answer it

Step-by-step explanation:

Answer:

√80 pulgada

Step-by-step explanation:

Convirtiendo 95 cm a pulgadas,

95/2,54 = 37,40 pulgadas

Ahora, la diagonal dada es de 40 pulgadas

Usando el teorema de Pitágoras, (40)²=(37,4)² + h² (Suponiendo h como altura)

h² = 40² - 37,4²

= 80

o h = √80 pulgada

A car costs £12000 when bought. It's value depreciates by 10% of the previous years value for 1 year and then at 7.2% for the next 10 years. How much will the car be worth in 5 years time?

Answers

Therefore ,on solving the provided question we can say that - Simple Interest after 5 year the car value is £7,689.6

what is interest ?

Simple interest is calculated by dividing the principal by the interest rate, the passage of time, and other elements. The formula used in marketing is simple return = principal + interest + hours. Using this approach, interest may be calculated most easily. The most common way to calculate interest is as a percentage of the principal balance. If he borrows $100 from a friend and agrees to pay it back with 5% interest, for instance, he will only pay his proportion of the 100% interest. $100 (0.05) = $5. You must pay interest when you borrow money and charge interest when you lend it.

here,

rate = 10%

Time = 1 year

Principle = 12000

=>SI = PRT/100

=> SI =  10*1*12000/100

=> SI = 1200

and

=>  After 1 year = 12000 -1200 = 10800

and

for five  years

=> SI = PRT/100

=> SI = 10800 * 7.2 * 4 / 100

=> SI = 3110.4

After 5 year = 10800 - 3110.4  = 7,689.6

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Find all the zeros of each equation.
[tex]7x^2-144=-x^4[/tex]

Answers

The equation 7x² - 144 = -x⁴ has the 4 solutions below:

x =  ±3

x =  ±4i

How to find the zeros of the equation?

Here we want to solve the equation below:

7x² - 144 = -x⁴

We can redefine the variable:

y = x²

Replacing that we will get:

7y - 144 = -y²

y² + 7y - 144 = 0

So we have a quadratic equation now, the using the quadratic formula we will get:

[tex]y = \frac{-7 \pm \sqrt{7^2 - 4*1*144} }{2} \\\\y = \frac{-7 \pm 25 }{2}[/tex]

Then the two solutions are:

y = (-7 + 25)/2 = 9

y = (-7 - 25)/2 = -16

And we know that:

y = x²

Then:

x = ±√9 = ±3

x = ±√-16 = ±4i

These are the 4 solutions.

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There are 270 students in year 7

each student studies one of french or german or spanish.

of these 270 students

2

study french

9

the number who study french : the number who study spanish = 3:7

42 boys study german

of the students who study german, what percentage are boys?

you must show your working.

Answers

Answer is 60 % is the percentage of boys studying German .

So, for this one, you must first determine the number of French students.

Simple method:

[tex]\frac{1}{9}[/tex]  is 270 divided by 9, which equals 30, hence  [tex]\frac{2}{9}[/tex]of 270 is 60. The result of multiplying [tex]\frac{1}{9}[/tex] by 2 to get [tex]\frac{2}{9}[/tex] is 60.

French is being studied by 60.

When you apply this to the French to Spanish ratio of 3:7, you get 3 and 60 on the same side. In order to get to 60, you must multiply 3 by 20. (or divide 60 by 20 to get 3).

Therefore, 20 is the number you use to apply the same formula to the other side of the ratio.

To reach 140, multiply 7 by 20 (or 7 by 10, then multiply that number by 2).

Spanish is being studied by 140.

After subtracting the French and Spanish from the overall number, you are left with 70 German speakers at 270-140-60.

42 of these 70 are males. 28 females are produced by 70-42. The percentage of males studying German is [tex]\frac{42}{70}[/tex]. This is equivalent to [tex]\frac{6}{10}[/tex], and you multiply a fraction by 10 to convert it to a percentage ([tex]\frac{60}{100}[/tex] in this case).

Additionally, 60% is equal to [tex]\frac{60}{100}[/tex]  .

Your response is thus 60%.

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A number is equal to the sum of half a second number and 3. The first number is also equal to the sum of one-quarter of
the second number and 5. The situation can be represented by using the graph below, where x represents the second
number.
46-
14-
42-
10+
8-
6
2-
2-
246
8 10 12 14 16 x
Which equations represent the situation?
Mark this and return
Save and Exit
Next
Submit

Answers

Answer:

First number 7

Step-by-step explanation:

First, let's make the first number y and the second number x

Next, we write our equations which are y=1/2x+3 and y=1/4x+5

Then, we set those two equations equal to each other and then solve for x

The first step of the equation is to add/subtract like terms, I subtracted 5 on each side of the equation, our new equation is 1/4x=1/2x-2, I then subtracted 1/2x on each side so now our equation is -1/4x=-2. We then multiply 1/4 by its reciprocal on each side. Its reciprocal is -4.

Now that we know x is equal to 8 now we can fill x into the original equations which were y=1/2x+3 and y=1/4x+5 you don't have to solve both, just one of your choosing.

Therefore your answer! .

A gas occupies 4.23 l at 2.25 atm. What is the volume at 3.46 atm?
a. 1.84 l
b. 2.75 l
c. 6.50 l
d. 32.9 l
e. 0.364 l

Answers

A gas occupies 4.23 l at 2.25 atm. 2.75 L is the volume at 3.46 atm. This can be solved using the concept of Boyle's law.

What is Boyle's law?

Boyle's law gives the relationship between pressure and volume of gas.

It states that at constant temperature pressure in inversely proportional to volume.

PV = k

where P - pressure V - volume and k - constant

P₁V₁ = P₂V₂

Given that,

initial pressure (P₁) = 2.25 atm

final pressure (P₂) = 3.46 atm

initial volume (V₁) = 4.23 L

final volume (V₂) = ?

where parameters for the first instance are on the left side and parameters for the second instance are on the right side of the equation

substituting the values in the equation

2.25 atm x 4.23 L = 3.46 atm x V

V = 2.75 L

Thus, the final volume is 2.75 L

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please help! I will give you 15 brainy point

Answers

Answer:

V = 17 m3

Step-by-step explanation:

The area of the base (triangular) is multiplied by the height, resulting in the volume

[tex]V=\frac{(2)(1)}{2} (17)=(\frac{2}{2})(17)=(1)(17)=17[/tex]

Hope this helps

a fruit stand has to decide what to charge for their produce. they need \$5.30$5.30dollar sign, 5, point, 30 for 111 apple and 111 orange. they also need \$7.30$7.30dollar sign, 7, point, 30 for 111 apple and 222 oranges. we put this information into a system of linear equations. can we find a unique price for an apple and an orange? choose 1 answer: choose 1 answer: (choice a) a yes; they should charge \$3.30$3.30dollar sign, 3, point, 30 for an apple and \$2.00$2.00dollar sign, 2, point, 00 for an orange. (choice b) b yes; they should charge \$2.00$2.00dollar sign, 2, point, 00 for an apple and \$3.30$3.30dollar sign, 3, point, 30 for an orange. (choice c) c no; the system has many solutions. (choice d) d no; the system has no solution.

Answers

The Price of an Orange is $2 and the price of an Apple is $3.3.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

Let us assume that,

Apple price =  A  $

Orange price = B  $

$5.30 for 1 apple and 1  orange

=> A + B  = 5.30    Equation 1

$7.30 for 1 apple and 2 oranges.

=> A  + 2B = 7.30   Equation 2

Equation 2 - Equation 1

=> B = 2

Thus, the Price of an Orange = $2

A + 2 = 5.30

=> A=  $3.30

Price of Apple  = $3.3

Therefore, The Price of an Orange is $2 and the price of an Apple is $3.3

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Suppose a ball was dropped from a TV tower 2120 feet high. The time it takes an object to free-fall from the top of this tower to the ground can be represented by the equation s = - 16t^2 + 2120, where s is the distance from the ground in feet and t is the time in seconds. Approximately how long would it take the object to reach the ground? Round your answer to the nearest tenth.

Answers

it would take the object approximately 11.51 seconds to reach the ground.

What is time?

Generally, Time is a concept used to describe the progression of events, or the duration of those events. It is often measured in units such as seconds, minutes, hours, days, and years.

Time can also be described as a continuum, with past events on one end and future events on the other.

Time is a fundamental aspect of the universe and is closely related to concepts such as causation, change, and entropy.

The time it would take the object to reach the ground can be found by setting the distance from the ground, s, to 0 and solving for t.

0 = -16t^2 + 2120

t^2 = (2120/16)

t = [tex]\sqrt{(2120/16)}[/tex]

t = approximately 11.51 seconds

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What is the volume of the composite solid? Use 3.14 for pie and round your answer to the nearest cm3. cylinder height is 2.5 radius : 3 inches, cone is height of 3 inches and radius of inches.

(A) 471 cm3

(B) 733 cm3

(c) 707 cm3

(D) 1099 cm3

Answers

The volume of the composite solid 28.26 cm³

What is an equation?

An equation is an expression composed of variables and numbers linked together by mathematical operations.

The volume is the space occupied for a solid figure.

For the composite:

Volume of composite = volume of cylinder + volume of cone

For cylinder:

height is 2.5, radius : 3 inches

Volume of cylinder = π * radius² * height = π * (3)² * 2.5 = 70.65 cm³

For cone:

height is 3, radius : 3 inches

Volume of cone = (1/3) * π * radius² * height = (1/3) * π * (3)² * 3 = 28.26 cm³

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The aquarium has 10 more red fish than blue fish. 60% of the fish are red. How many blue fish are in the aquarium? Show your work.

Answers

Answer:

20 blue fish

Step-by-step explanation:

r=red fish, b=blue fish. r = 10+b. 60%r=r+b. (10+b)= 0.6(r+b); 10+b = 0.6(2b+10); 10+b=1.2b+6; 4=0.2b; b=20.

PLS HELP IMMEDIATELY!!

Answers

Answer:

56 adult tickets were sold that day

Step-by-step explanation:

let a represent number of adult tickets sold and c number of child tickets sold , then

a + c = 122 → (1)

9.1a + 5.7c = 885.8 → (2)

from (1) subtract c from both sides

c = 122 - a

substitute c = 122 - a into (2)

9.1a + 5.7(122 - a) = 885.8

9.1a + 695.4 - 5.7a = 885.8

3.4a + 695.4 = 885.8 ( subtract 695.4 from both sides )

3.4a = 190.4 ( divide both sides by 3.4 )

a = 56

that is 56 adult tickets were sold that day.

What is the best approximation of the solution to the system to the nearest integer values?
A. (1, 3)
B. (3, 4)
C. (2, 3)
D. (3, 2)

Answers

The best estimate of the system solution to the nearest integer values is (2,3).

What is coordinate points?

The coordinates represent the location of a point in the 2D coordinate plane with respect to the origin. A point's x-coordinate is its perpendicular distance from the y-axis as measured along the x-axis. A point's y-coordinate is the perpendicular distance from the x-axis measured along the y-axis. A point's Cartesian coordinates (also known as rectangular coordinates) are a pair of integers (in two dimensions) or a triplet of numbers (in three dimensions) indicating signed distances from the coordinate axis. A point's coordinates are a pair of integers that define its precise location on a two-dimensional plane. Remember that the coordinate plane contains two axes that are perpendicular to each other, known as the x and y axes.

Here,

This question is asking us what the coordinates are for the point of intersection. Since the point is not directly on the grid lines, we must approximate.

The point is closest to the value "2" on the x axis.

The point is closest to the value "3" on the y axis.

This means the correct point is (2,3).

The best approximation of the solution to the system to the nearest integer values is (2,3).

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in how many ways can $8$ different people be seated around a round table with $8$ places? two sections are considered equivalent if one can be rotated to form the other.

Answers

As per the permutation, there are 5040 number of different ways are available for seating.

The term permutation in math is known as  a mathematical calculation of the number of ways a particular set can be arranged

Here we know that there are 8! ways that you can arrange 8 people.

Now here we have to imagine a specific arrangement.

Here we have consider that everyone get up and move one seat to their right.

Then in that arrangement was counted separately from the first one in the 8!

Here have to know that it’s really the same since if each person looks to their left and their right and here they’re sitting next to the same person. Then here there are 8 such “identical rotations” for each possible seating arrangement so the total number of seating's is calculated as,

=> 8! / 8

=> 7! = 5040.

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Convert a pressure of 1379 torr to atm

Answers

Conversion of pressure of 1379 torr to atm= 1.814474

What are unit Conversion ?

Unit conversion is a multi-step procedure that involves adding, subtracting, multiplying, or dividing by a conversion factor.

Additionally, choosing the right number of significant digits and rounding may be necessary during the process.

The multi-step process of unit conversion involves multiplying or dividing by a numerical factor.

Weight, distance, and temperature can all be measured in a variety of ways.

Temperature is expressed in degrees Celsius, weight is expressed in kilos, and distance is measured in kilometers.

Imagine you are on vacation in India and are informed that the two cities are 100 kilometers apart.

Hence, Conversion of pressure of 1379 torr to atm= 1.814474

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e wants a green paint that requires 3 parts blue paint to 2 parts yellow paint. if he needs a total of 10 gallons to paint the whole house, how many gallons of blue paint does he need?

Answers

The gallons of blue paint he needs to make the green paint is 6 gallons.

This is a problem in ratios. Let's look into what we know.

Volume of green paint needed = 10 gallons

Parts of blue paint needed = 3

Parts of yellow paint needed = 2

Total number of parts = parts of blue paint + parts of yellow paint

                                    3 + 2 = 5

So fraction of blue paint needed = parts of blue paint / total parts

                                                       = 3/5

Volume of blue paint needed = [tex]\frac{3}{5}[/tex] × 10

                                                 = 6 gallons

Volume of yellow paint needed = [tex]\frac{2}{5}[/tex] ×10

                                                      = 4 gallons.

So we need 6 gallons of blue paint and 4 gallons of yellow paint to make 10 gallons of green paint.

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a statistical survey shows that only 2% of secretaries know how to use the highly sophisticated word processor language tex. if a certain mathematics department prefers to hire a secretary who knows tex, what is the least number of applicants that should be interviewed so as to have at least a 50% chance of finding one such secretary? math stack

Answers

To have a 50% chance of probability finding a secretary who knows Tex, at least 50 out of 100 applicants should be interviewed.

In order to determine the least number of applicants that should be interviewed to have a 50% chance of finding one secretary who knows the word processor language Tex, we can use the binomial probability formula. This formula states that the probability of finding at least one success out of a certain number of trials is given by P(X ≥ 1) = 1 – P(X = 0). Assuming that there are 100 applicants, the probability of finding at least one secretary who knows Tex is given by 1 – (98/100)^50, which is approximately 0.5. Therefore, at least 50 out of 100 applicants should be interviewed to have a 50% chance of finding a secretary who knows the language Tex.

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