Let F be any nonconstant vector field of the form F = f (x) i + g (y) j + h (z) k and let G be any nonconservative vector field of the form G = f (y, z) i + g (x, z)j + h (x, y) k. Indicate whether the following statements are true or false by placing ''T'' or ''F'' to the left of the statement. 1. G is incompressible 2. F is irrotational 3. G is irrotational 4. F is incompressible

52s is the maximum time that she can take on her last lap and still make the team.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given that he mean pace a student needs to achieve on 5 laps of the pool is 60 seconds (s).

The student swims a lap in 63 s, 62 s, 65 s, and 58 s on her first four laps.

We need to find the maximum time (in seconds) that she can take on her last lap and still make the team

Let x be the maximum time (in seconds) that she can take on her last lap

60=(63+62+65+58+x)/5

300=63+62+65+58+x

300=248+x

Subtract 248 on both sides

300-248=x

x=52s

Hence, 52s is the maximum time that she can take on her last lap and still make the team.

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Focus on Gamble B only. Multiply each winnings with their corresponding probabilities.

5100*0.50 = 2550

200*0.25 = 50

0*0.25 = 0

Add up those results: 2550+50+0 = 2600

The expected value of gamble B is $2600

The model predicts that there are approximately 0.012456 (71/5700) restaurants per capita in the year 2016

To determine the number of restaurants per capita, we need to divide the number of restaurants (R) by the population (p). Given that R = 6t + 35 and p = 200t + 4500, we can substitute these values into the equation for restaurants per capita.

Restaurants per capita = R / p

Substituting the given equations, we get:

Restaurants per capita = \((6t + 35) / (200t + 4500)\)

To find the number of restaurants per capita for the year 2016, we need to calculate the value of t for that year. Since t represents years after 2010, in 2016, t would be 6 (2016 - 2010 = 6).

Restaurants per capita (2016) = \((6 * 6 + 35) / (200 * 6 + 4500)\)

= \((36 + 35) / (1200 + 4500)\)

= 71 / 5700

This means that, on average, there is roughly one restaurant for every 80 people in the town. Please note that this prediction is based on the given growth equations and assumes a linear relationship between population and the number of restaurants.

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The money each person owes at restaurants for dinner is $1.41.

In mathematics, the tax calculation is related to the selling price and income of taxpayers. It is a charge imposed by the government on the citizens for the collection of funds for public welfare and expenditure activities. There are two types of taxes: direct tax and indirect tax.

Given that, Restaurants frequently add an​ 18% tip on the​ pre-tax bill when the party is 8 people or more.

The first step is to determine the total cost of the dinner. The total cost includes the cost of the dinner, tip and tax.

Total cost = Cost of the dinner + Tax + Tip

Tax = Cost of the meal x Percentage tax

Tax = $114.46 x 5%

Tax = $114.46 x 0.05 = $5.723

Tip = Percentage tip x Cost of the diner

Tip = 18% x $114.46

Tip = 0.18 x $114.46

Tip = $20.60

Total cost = $114.46 + $20.60 + $5.72 = $140.78

Amount each person owes = Total cost of the meal / Number of people

Amount each person owes = $140.78/10 = $1.41

Therefore, the money each person owes at restaurants for dinner is $1.41.

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"Your question is incomplete, probably the complete question/missing part is:"

Restaurants frequently add an​ 18% tip on the​ pre-tax bill when the party is 8 people or more. The tax is calculated based on the bill before the tip is included. Last​ night, 10 friends went out to dinner and decided to split the bill evenly. If the bill without tax or tip was ​$114.46 and the tax was ​5%, how much did each person​ owe?

Answer:

33.3

Step-by-step explanation:

You need to divide 200  and 150 to get you 4/3. Then you will have to _____________________________

Based on law of sine, the value of angle C is equal to 94.5 degree.

For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,

we have, by law of sines,

\(\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}\)

\(\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}\)

we have, by law of sines,

We will use the law of sines to find c as;

sin c                sin 97.5

--------------- = -------------

14.5                      13.7

(13.7)sin c= 14.5 sin 97.5

sin c =  14.5 sin 97.5 / (13.7)

sin c = - 0.1168

Angle c = 94.5

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The equation of the parabola is x² = 60y after applying the concept of the parabola.

It is defined as the graph of a quadratic function that has something bowl-shaped.

(x - h)² = 4a(y - k)

(h, k) is the vertex of the parabola:

a = √[(c-h)² + (d-k²]

(c, d) is the focus of the parabola:

It is given that:

Focus of (0, 15) and directrix y = –15.

Let (x, y) be on the parabola:

The distance between focus and (x, y):

The distance formula can be given as:

\(\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

\(\rm d=\sqrt{(x-0)^2+(y-15)^2}\)

\(\rm d=\sqrt{x^2+(y-15)^2}\)

Directrix y = -15

y + 15 = 0

\(\rm \sqrt{x^2+(y-15)^2} = |y + 5|\)

Squaring both sides:

x² + (y - 15)² =  (y + 15)²

x² + y² -30y + 225 =  y² + 30y + 225

x² -30y  = 30y

x² = 30y + 30y

x² = 60y

Thus, the equation of the parabola is x² = 60y after applying the concept of the parabola.

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Answer:

The answer is 72.49

Step-by-step explanation:

Answer:

Gary had $75.49 to begin with.

Step-by-step explanation:

63 + 12.49 = 75.49

Gary spent $63 on bananas and after buying them he had $12.49, therefor you would add his remaining $12.49 to the $63 he spent in order to get the amount of money he had before buying the bananas.

The system of equations has one solution.

To check this, we can graph the two equations of the system:

y = (-1/3)x + 7

y = -2x³ + 5x² + x - 2

On the same coordinate axis, and check how many times do the graphs intercept.

The graph can be seen in the image at the end, there you can see that there is only one intecept point. Thus, the system of equations has only one solution.

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ANSWER= the remaining piece of rope is 48 feet 9 inch long.

His total earnings for a total sale of 7,000​ could be 1450sh

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

Salary = 400

Commission = 15%

using the above as a guide, we have the following:

Total earnings = 400 + 15% * Total sales

So, we have

Total earnings = 400 + 15% * 7000

Evaluate

Total earnings = 1450

Hence, the total earnings is 1450

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Question

Simon earned 400sh weekly for goods sold and a commission of 15%

What could be his earnings for a total sale of 7,000​.

We are asked to find the real and imaginary parts of a complex number, let us study the structure of a complex number by a drawn

That is, all the complex numbers are composed by two parts: the real and the imaginary.

We can recognize the imaginary component because this is the part that multiplied the number i

In the example that was given to us, we have identifying the parts we find

Therefore, we can conclude:

* 24 is the real component,

* -3 is the imaginary component,

The graph of the given function is attached.

Given is a function for the rainfall in 5 months in inches.

We need to display the data,

So, as we can see that the data is not showing any proportion or pattern,

So, it can be displayed as a line chart.

Hence the chart is attached for the function.

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Answer:

x = -2

Step-by-step explanation:

I am not sure you typed this correctly.

the way you wrote this, it says

f(x) = (3/2)x - 3

but I suspect you mean

f(x) = 3/(2x) - 3

our even

f(x) = 3/(2x - 3)

I assume the last one.

3/(2x - 3) = 5x + 4

that is what is meant by f(x)=g(x) : find out the value(s) of x for which the y/result values of both functions are the same.

so, then we can transform

3 = (5x + 4)×(2x - 3)

3 = 10x² -15x + 8x - 12

10x² - 7x - 15 = 0

and this can be solved by the solution squared equations :

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case here

a = 10

b = -7

c = -15

so,

x = (7 ± sqrt(49 - 4×10×-15))/20 = (7 ± sqrt(49+600))/20 =

≈ (7 ± 25.48)/20

x1 = -18.48/20

x2 = 32.48/20

these are really not nice numbers for a homework or such.

so, let's try the next interpretation of what you wrote.

f(x) = 3/(2x) - 3

3/(2x) - 3 = 5x + 4

3/(2x) = 5x + 7

3 = 10x² + 14x

10x² + 14x - 3 = 0

a = 10

b = 14

c = -3

x = (-14 ± sqrt(196 - 4×10×-3))/20 =

= (-14 ± sqrt(196 + 120))/20 = (-14 ± 17.78)/20

that did not give any good numbers either.

so, next attempt :

f(x) = (3/2)x - 3 = 3x/2 - 3

3x/2 - 3 = 5x + 4

3x/2 = 5x + 7

3x = 10x + 14

7x = -14

x = -2

ok, so it seems the first, original interpretation was correct. sorry.

but just in case, please use the other 2 approaches if and as needed.

The mass, in grams, of substance Y is given the mass of substance x is 1.22 x 10^-6

Standard form is used to condense big numbers into smaller numbers. In order to write a number in standard form, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.

In order to determine the mass, multiply 6.10 by 2 and add 2 to -7

6.10 x 2 = 12.2 = 1.22 x 10^-6

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An inequality to represent the dollar amounts d in cash and prizes Regan can win is p + d ≥ 500.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Given that, Regan won the grand prize at a store giveaway. The grand prize winner is guaranteed to win at least $500 in cash and prizes.

Let d represent the amount of cash in dollars and p represent the amount of prizes.

Since the  grand prize winner is guaranteed to win at least $500,

So, p + d ≥ 500

Therefore, an inequality to represent the dollar amounts d in cash and prizes Regan can win is p + d ≥ 500.

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The probability of spinning an even number, flipping tails, then spinning an odd number is:

1/9   (as fraction) or 11.11% (as percent)

To find the probability of spinning an even number, flipping tails, then spinning an odd number. We need to consider the individual probabilities. That is:

We have only one even number in the spinner, and that is 2. Thus,

P(even number) = 1/3

For a coin, the probability of head or tail is 1/2. Thus,

P(tail) = 1/2

We have two odd number in the spinner, and that is 1 and 3. Thus,

P(odd number) = 2/3

Therefore, the probability of spinning an even number, flipping tails, then spinning an odd number will be:

P(even, tail, odd) = 1/3 * 1/2 * 2/3

                            = 2/18

                            = 1/9   (as fraction)

In percent:

P(even, tail, odd) =  1/9 * 100

                            = 11.11%

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The solution to the inequality is x >= 2.

To solve this inequality, we will first isolate the variable x on one side of the inequality.

Starting with the given inequality:

3/4x - 2/3 >= 5/6

We can simplify by adding 2/3 to both sides:

3/4x >= 5/6 + 2/3

Then, we can simplify the right-hand side:

3/4x >= 5/6 + 4/6

3/4x >= 9/6

Simplifying further, we get:

3/4x >= 3/2

Now, we can isolate the x variable by multiplying both sides by 4/3:

x >= (3/2) / (3/4)

x >= 2

Therefore, the solution to the inequality is x >= 2.

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Answer:

A. The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2.

Step-by-step explanation:
I just took the test

Answer:

36 miles

Step-by-step explanation:

Since there are 60 minutes in a hour, you can see that 20 minutes is a third of that time. To find the answer, you multiply the values by 3 to equal on hour. 20x3 = 60 and 12x3 = 36, meaning he drove 36 miles in a hour.

Using the binomial distribution, it is found that there is a 0.125 = 12.5% probability that the team goes to the championship.

The formula is:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem:

The team moves to the championship if they win all three games, hence the probability is P(X = 3), given as follows:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 3) = C_{3,3}.(0.5)^{3}.(0.5)^{0} = 0.125\)

0.125 = 12.5% probability that the team goes to the championship.

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Answer :

addition equation:

-38 + p = 26

35 + z = -72

-------------------------------

actual answer:

z = -37

p = -12

Answer: I believe that by helping or answering others you can get get questions, but I do know there is a limited amount of questions being able to ask before paying monthly. Hope this helps

Answer:

What you have to do is answer peoples question to gain more

Step-by-step explanation:

107/56 is the solution of fractions .

What do math fractions mean?

The given fractions are 5/8 and 1 2/7.

We need to find the sum of given fractions.

Now, we can write 1 2/7 as 9/7.

So, 5/8 + 9/7

Here, LCM of 8 and 7 is 56

Then, 35/56 + 72/56

=(35+72)/56

=107/56

Therefore, the sum of the two given fractions is 107/56.

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Answer:

$21.04

Step-by-step explanation:

The computation of the discount is as follows:

Discount is

= Service plan amount × discount percentage

= $123.76 × 17%

= $21.04

We simply multiplied the service plan amount with the discount percentage so that the discount amount could come

The full price when the sales price is £32.24 is £96.72

The full price when the sales price is £86.08 is  £258.24

The full price when the sales price is £105.48 is £316.44

The full price when the sales price is £230.62 is £691.86

The sales price is one third of the full price of the items. Thus, in order to determine the full price, multiply the sales price by 3.

Full price = sales price x 3

Full price when the sales price is £32.24 = 3 x £32.24 = £96.72

Full price when the sales price is £86.08 = 3 x £86.08 = £258.24

Full price when the sales price is £105.48 = 3 x £105.48 = £316.44

Full price when the sales price is £230.62 = 3 x £230.62 = £691.86

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Answer:

10.

bag a is lighter than bag b

bag b is lighter than bag c

so bag a is lighter that bag c

Step-by-step explanation:

... sorry i dont know #11, but hope this helps

Answer:

10.

Bag A is LIGHTER than Bag B

Bag B is LIGHTER than Bag C

So, Bag A is LIGHTER than Bag C

11.

pear is the heaviest, and the strawberry is the lightest

Step-by-step explanation:

This is really simple! Looking at the weight scale, the heavier object always goes lower than the lighter object. Knowing this, we can figure out which is heavier and which is lighter.

10.

Bag A is LIGHTER than Bag B

Bag B is LIGHTER than Bag C

Looking at these we can infer that bag c is heavier than both.

So, Bag A is LIGHTER than Bag C

11. The pear falls lower than the apple, meaning it is heavier. The apple falls lower, meaning is it heavier than the apple. We can infer that the pear is the heaviest, and the strawberry is the lightest

Hope this helps!!

-Ketifa

Answer:

see below

Step-by-step explanation:

The slope (gradient) is -2

Decreases by 2 events per year