The product of three less than a number and eight is nine

The line integral around the unit circle is 2π.

We can use Green's Theorem to evaluate the line integral. Green's Theorem states that for a vector field F = (P, Q) with continuous partial derivatives defined on a simply connected region R in the plane, the line integral along the boundary of R is equal to the double integral of the curl of F over R:

∮C P dx + Q dy = ∬R (∂Q/∂x - ∂P/∂y) dA

In this case, P = -y and Q = x, so ∂Q/∂x = 1 and ∂P/∂y = -1, and the curl of F is:

∂Q/∂x - ∂P/∂y = 1 - (-1) = 2

Since the unit circle is a simply connected region, we can apply Green's Theorem to find:

∮C -y dx + x dy = ∬R 2 dA

The region R is the unit disk, so we can use polar coordinates to evaluate the double integral:

∬R 2 dA = 2 ∫0^1 ∫0^2π r dr dθ = 2π

Therefore, the line integral around the unit circle is 2π.

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Answer:

\(A=2x^2+3x-5\)

Step-by-step explanation:

Given that,

Length = (2x+5) cm

Width = (x-1) cm

We need to find the area of a rectangle. The formula for the area of rectangle is given by :

A = lb

\(A=(2x+5)(x-1)\\\\=2x^2-2x+5x-5\\\\=2x^2+3x-5\)

So, the required area is equal to \(2x^2+3x-5\).

Answer:

1647

Step-by-step explanation:

1647

4

6588

4      

2 5    

2 4    

 1 8  

 1 6  

   2 8

   2 8

     0

The statement that best describes the infοrmatiοn presented in the chart is: "The number οf hurricanes was increasing but has decreased in recent years."

Hurricanes, knοwn generically as trοpical cyclοnes, are lοw-pressure systems with οrganized thunderstοrm activity that fοrm οver trοpical οr subtrοpical waters. They gain their energy frοm warm οcean waters.

The chart shοws the number οf hurricanes οf categοry 1 οr higher that οccurred during specific series οf years, and it indicates that the number οf hurricanes increased frοm 13 in 1980-1989 tο 23 in 2000-2009, and then decreased tο 10 in 2010-2017.

Therefοre, the chart suggests that the number οf hurricanes was increasing, but it has decreased in recent years. The chart dοes nοt prοvide any infοrmatiοn abοut tοrnadοes in Finleyville οr the relatiοnship between the number οf hurricanes and temperature.

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The statement that best describes the information in the graph is: "The number of hurricanes has increased but decreased in recent years." The graph shows that the number of Category 1 or greater hurricanes increased from 1980 to 2009, but decreased from 2010 to 2017.

Answer:

Date                  Account Title                                              Debit             Credit

XX-XX-XXX      Sales returns and Allowances              Rs. 5,000

                        Accounts receivable - M Center                                   Rs. 5,000  

                         Inventory                                                Rs. 5,000

                         Cost of Goods sold                                                        Rs. 5,000

Answer:

$1,539.70

Step-by-step explanation:

Given the data :

National average Teachers' salary (NATS)

YEAR:_1960 _ 1970 _ 1980 _ 1990 _ 2000 2010

NATS:4995_8626_15970_31367_41807_55202

AVEAGE SALARY INCREASE PER YEAR BETWEEN 1980 and 1990

Salary in 1980 = $15970

Salary in 1990 = $31367

Average salary increase per year:

Difference in salary / difference in years

$(31367 - 15970) / (1990 - 1980)

= $15397 / 10

= $1539.7

Step-by-step explanation:

try that hope this helps out

If the scale factor is 1, then there is no change -- all measurements remain the same.

So the image and the pre-image would be congruent.

What is the use of a Scalar Factor of Dilation?

The Scalar factor of the dilation determines how larger or smaller the image is when compared to the original object.

we can find a scalar factor of dilation by finding and measuring the center point of dillution and distance from centre point to point on the preimage and also the distance from the center point to the image point.

Expansion occurs when the absolute value of a scalar factor is greater than another one.

comparison occurs when the absolute value of the scale factor is less than another one.

The scale factor can be obtained by dividing the dimension of the new shape by the dimension of the original shape.

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The best first step in calculating an inferential statistic for the given scenario would be to calculate the mean for older siblings.

To compare the motivation to succeed between older and younger siblings, the first step is to compute descriptive statistics for each group separately. In this case, we are interested in determining if older siblings have greater motivation.

Calculating the mean for older siblings will provide an initial understanding of the central tendency of their motivation scores. By taking the average of their responses on the 1-7 scale, we can obtain a measure of their typical motivation level.

Further statistical analysis, such as hypothesis testing or calculating effect sizes, can be performed using the mean values of both older and younger siblings. However, the initial step is to calculate the mean for older siblings to establish a baseline understanding of their motivation level.

In the given scenario, the best first step in calculating an inferential statistic is to calculate the mean for older siblings. This provides a starting point to compare their motivation to succeed with that of their younger siblings.

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complete question- When should you calculate and use a "weighted average" for pooled variance in an inferential t-test? When sample sizes are equal. When sample sizes are unequal: When data is invalid. When data is unreliable: Question 17 1 pts A researcher wants to know if older siblings have greater motivation to succeed than their younger siblings. The researcher asks a group of 50 sibling pairs how motivated they are to succeed on a scale of 1-7. As discussed in lecture, what would be the best first step in calculating an inferential statistic? Calculate the standard deviation for older siblings. Calculate the mean for younger siblings. Calculate the mean for older siblings. Subtract the motivation of younger sibling from the other (older sibling).

By following these steps, you should be able to find the number of counties in Texas with childcare programs offering nighttime care for children.

To answer your question about how many of the 254 counties in Texas have child care programs that state they provide nighttime care for children, we would need to access current data on child care programs in Texas. Unfortunately, I do not have that specific data at the moment. However, I can guide you on how to find this information.
Begin by visiting the Texas Health and Human Services website (https://hhs.texas.gov) as they are responsible for overseeing child care licensing in the state. Look for information on licensed child care facilities that provide nighttime care.
Utilize websites such as Child Care Aware (https://www.childcareaware.org) or Child Care Finder (https://childcarefinder.com), where you can search for child care programs in Texas by county, and filter your search to include only programs offering nighttime care.
You may also want to check with local county websites or contact the County Clerk's office for information on child care programs within their jurisdiction, specifically those offering nighttime care.
Compile the data gathered from the above sources to determine how many of the 254 Texas counties have child care programs providing nighttime care for children.
By following these steps, you should be able to find the number of counties in Texas with child care programs offering nighttime care for children.

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The problem describes three children riding on the edge of a merry-go-round with given masses. The task is to calculate the angular momentum of the system.

To calculate the angular momentum of the system, we need to consider the angular momentum of both the merry-go-round and the children.

Calculating the moment of inertia of the merry-go-round: \((1/2) × 142 kg × (1.60 m)^2 = 181.76 kg·m^2.\)

The angular momentum of the merry-go-round is then: angular momentum = \(181.76 kg·m^2 × (21.3 rpm × 2π/60) = 766.34 kg·m^2/s.\)

For the children, we calculate their individual angular momenta using the formula: angular momentum = mass × velocity × radius. Since the children are riding on the edge of the merry-go-round, their velocities are equal to the tangential velocity of the merry-go-round.

Calculating the angular momentum for each child:

Child 1: 22.4 kg × \((1.60 m × 21.3 rpm × 2π/60) = 471.95 kg·m^2/s\)

Child 2: 29.5 kg × \((1.60 m × 21.3 rpm × 2π/60) = 622.20 kg·m^2/s\)

Child 3: 40.8 kg × (1.60 m × 21.3 rpm × 2π/60) = 855.01 kg·m^2/s

The total angular momentum of the system is the sum of the angular momenta of the merry-go-round and the children:

Total angular momentum = \(766.34 kg·m^2/s + 471.95 kg·m^2/s + 622.20 kg·m^2/s + 855.01 kg·m^2/s = 2715.50 kg·m^2/s.\)

Therefore, the total angular momentum of the system consisting of the merry-go-round and the three children is \(2715.50 kg·m^2/s.\)

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Answer:

95% decrease

Step-by-step explanation:

Subtract starting value minus final value

Divide that amount by the absolute value of the starting value

Multiply by 100 to get percent decrease

If the percentage is negative, it means there was an increase and not an decrease.

Answer:

2\(x^{2}\)+2\(y^{2}\)

Step-by-step explanation:

\((x+y)^{2}\) + (\(x^{2}\) -2xy+\(y^{2}\))

(x+y)(x+y)+(\(x^{2}\) -2xy+\(y^{2}\))

\(x^{2}\)+ xy + xy+\(y^{2}\)+\(x^{2}\)-2xy+\(y^{2}\)

\(x^{2}\)+2xy+\(y^{2}\)+\(x^{2}\)-2xy+\(y^{2}\) (cancel 2xy)

The answer is  -      2\(x^{2}\)+2\(y^{2}\)

Answer:

36

Step-by-step explanation:

the square root of any negative value results in an imaginary number, 'i'

so, \(\sqrt{-3}\) = 3i and \(\sqrt{-12}\) is 12i

'i' is equal to -1

3(-1) x 12(-1) = 36

By using the  unitary method in linear equation, the answer is 925.

We have a factory that makes 400 refrigerators every day and makes 125 more stoves per day than refrigerators is as follows:

Let's use the unitary method in linear equation to solve this problem. We can use the following equation to find x, the total number of refrigerators and stoves the factory makes in one day:

X = 400 (number of refrigerators) + (400 + 125) (number of stoves)

X = 400 + 525

X = 925

Therefore, the factory makes 925 refrigerators and stoves every day.

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Answer:

A = 90.25π

Step-by-step explanation:

Area of a circle = \(\pi r^2\)

r = 9.5

A = 90.25π

Answer:

\(\pi \times 9.5 {?}^{2} \)

The machine's expected remaining lifetime can be found using the concept of conditional probability. Specifically, we want to find the expected value of the remaining lifetime given that the machine has already been in use for 2 hours.

To find this expected value, we can use the formula:

E(X | X > 2) = ∫x*f(x | X > 2)dx

where f(x | X > 2) is the conditional probability density function of X given that X > 2.

Using Bayes' theorem, we can find that f(x | X > 2) = f(x) / P(X > 2), where P(X > 2) is the probability that X is greater than 2.

Evaluating the integral, we get:

E(X | X > 2) = ∫x*f(x) / P(X > 2) dx, with the limits of integration from 2 to infinity.

Solving for P(X > 2), we get:

P(X > 2) = ∫2 to infinity f(x) dx

Substituting the given density function into the equation, we get:

P(X > 2) = ∫2 to infinity 0.5 exp(-0.5x) dx

Solving the integral, we get:

P(X > 2) = 0.1353

Now we can use this value to solve for the expected remaining lifetime:

E(X | X > 2) = ∫2 to infinity x*f(x) / P(X > 2) dx

Solving the integral, we get:

E(X | X > 2) = 9.26 hours

Therefore, if the machine has been in use for 2 hours, we can expect it to last an additional 9.26 hours on average.

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Step-by-step explanation:

\(\large\underline{\sf{Solution-}}\)

Given that

\(\rm :\longmapsto\:\triangle ABC \: \sim \: \triangle DEF\)

\(\bf\implies \:\dfrac{AB}{DE} = \dfrac{BC}{EF} = \dfrac{AC}{DF} \)

and

\(\rm\implies \:\angle A = \angle D\)

\(\rm\implies \:\angle B = \angle E\)

\(\rm\implies \:\angle C = \angle F\)

Also, given that,

\(\rm\implies \:\dfrac{DE}{AB} = \dfrac{DF}{AC} = \dfrac{EF}{BC} = \dfrac{1}{3} \)

\(\rm :\longmapsto\:BC = 16 \: units\)

\(\rm :\longmapsto\:AC = 20 \: units\)

So, using Pythagoras Theorem, we have

\(\rm :\longmapsto\: {AC}^{2} = {AB}^{2} + {BC}^{2} \)

\(\rm :\longmapsto\: {20}^{2} = {AB}^{2} + {16}^{2} \)

\(\rm :\longmapsto\: 400 = {AB}^{2} + 256\)

\(\rm :\longmapsto\: {AB}^{2} = 400 - 256\)

\(\rm :\longmapsto\: {AB}^{2} = 144\)

\(\bf\implies \:AB = 12 \: units\)

Now,

\(\rm :\longmapsto\:sinC = \dfrac{AB}{AC} \)

\(\rm :\longmapsto\:sinC = \dfrac{12}{20} \)

\(\rm :\longmapsto\:sinC = \dfrac{3}{5} \)

Now, As we have

\(\rm :\longmapsto\:\angle C = \angle F\)

\(\rm :\longmapsto\:sin C = sin F\)

\(\bf\implies \:sinF = \dfrac{3}{5} \)

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1. Pythagoras Theorem :-

This theorem states that : In a right-angled triangle, the square of the longest side is equal to sum of the squares of remaining sides.

2. Converse of Pythagoras Theorem :-

This theorem states that : If the square of the longest side is equal to sum of the squares of remaining two sides, angle opposite to longest side is right angle.

3. Area Ratio Theorem :-

This theorem states that :- The ratio of the area of two similar triangles is equal to the ratio of the squares of corresponding sides.

4. Basic Proportionality Theorem :-

This theorem states that :- If a line is drawn parallel to one side of a triangle, intersects the other two lines in distinct points, then the other two sides are divided in the same ratio.

Using linear equations, it is 3570metre  from the post office to the

library

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

Length of each block=275 meter

let's Create a linear equation from this i.e. 275x where x=number of blocks.

No. of blocks from  post office to the library = 13 (x=13)

so, distance of  post office to the library= 275*13

                                                                    =3575meter

                                                        ≈3570 meter (round to nearest 10th)

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The average velocity from t = 2s to t = 4s would be - 48 ft/s.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that an object is thrown upward with initial velocity of 48 feet per second from a high of 120 feet. The height of the object t seconds after it is thrown is given by h(t) = - 16t² + 48t + 120.

Average rate of change of velocity with time is called average velocity. Mathematically -

v{avg.} = Δx/Δt                                                         .... Eq { 1 }

Δx = x(4) - x(2)

Δx = - 16(4)² + 48(4) + 120 - {- 16(2)² + 48(2) + 120}

Δx = - 96

Δt = 4 - 2 = 2

So -

v{avg.} = Δx/Δt = -96/2 = - 48 ft/s

Therefore, the average velocity from t = 2s to t = 4s would be - 48 ft/s.

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Answer:

  21, 29, 71, 79

Step-by-step explanation:

Only integers ending in 1, 3, 7, or 9 have powers that end in 1. For the numbers so ending, their sequences of powers mod 100 have a repeat length that is a divisor of 20. That is, raising any of these numbers to the 762nd power mod 100 is equivalent to squaring them, mod 100.

For example, the powers of 29 mod 100 are, beginning with the first power, ...

  {29, 41, 89, 81, 49, 21, 9, 61, 69, 1}

This sequence is of length 10, typical of many of the numbers ending in 1, 3, 7, or 9.

The only positive integers less than 100 whose squares end in 41 are ...

  21, 29, 71, 79 . . . . . positive integers < 100 satisfying n^762 mod 100 = 41

To determine whether there is enough evidence to reject the null hypothesis, we need to compare the computed test statistic to the critical value.

In this case, the computed test statistic is 2.50 and the critical value is 2.33. If the computed test statistic falls in the rejection region beyond the critical value, we can reject the null hypothesis. Conversely, if the computed test statistic falls within the non-rejection region, we fail to reject the null hypothesis.In this scenario, since the computed test statistic (2.50) is greater than the critical value (2.33), it falls in the rejection region. This means that the observed data is unlikely to occur if the null hypothesis were true.

Therefore, based on the given information, there is enough evidence for the emergency room nurse to reject the null hypothesis. This suggests that there is sufficient evidence to support the claim that the average number of cases of upper respiratory infections per day at the hospital is over 21 cases.

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There is enough evidence to reject the null hypothesis in this case because the computed test statistic (2.50) is higher than the critical value (2.33). This suggests the average number of daily respiratory infections exceeds 21, providing substantial evidence against the null hypothesis.

Yes, there is enough evidence for the emergency room nurse to reject the null hypothesis. The null hypothesis is typically a claim of no difference or no effect. In this case, the null hypothesis would be an average of 21 upper respiratory infections per day. The test statistic computed (2.50) exceeds the critical value (2.33). This suggests that the average daily cases indeed exceed 21, hence providing enough evidence to reject the null hypothesis.

It's crucial to understand that when the test statistic is larger than the critical value, we reject the null hypothesis because the observed sample is inconsistent with the null hypothesis. The statistical test indicated a significant difference, upheld by the test statistic value of 2.50. The significance level (alpha) of 0.05 is a commonly used threshold for significance in scientific studies. In this context, the finding suggests that the increase in respiratory infection cases is statistically significant, and the null hypothesis can be rejected.

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Answer:

its 45

Step-by-step explanation

It's right I did it on khan

The probability that Marvin teleports at least once per day is 9/25.

The probability that Marvin teleports to work in the morning is 1/5, since he has five transportation options and one of them is teleport.

The probability that he does not teleport to work is 4/5.

Similarly, the probability that Marvin teleports back home in the evening is also 1/5, and the probability that he does not is 4/5.

The probability that Marvin teleports at least once per day is the sum of the probabilities that he teleports in the morning, teleports in the evening, or teleports in both:

P(teleports at least once) = P(teleports in the morning) + P(teleports in the evening) - P(teleports both times)

P(teleports at least once) = (1/5) + (1/5) - (1/5)(1/5)

P(teleports at least once) = 9/25

Therefore, the probability that Marvin teleports at least once per day is 9/25.

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The solution to the system is x = 2 and y = 6, represented as the ordered pair (2, 6). This corresponds to option (B) in the answer choices.

To solve the system using substitution, we'll substitute the value of one variable from one equation into the other equation and solve for the remaining variable.

Given the system:

x + y = 8

y = 3x

Substituting the value of y from the second equation into the first equation, we have:

x + (3x) = 8

4x = 8

x = 2

Now, substitute the value of x into the second equation to solve for y:

y = 3(2)

y = 6

Therefore, the solution to the system is (2, 6). Option (B) is the correct answer.

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Answer:

31

Step-by-step explanation:

63-32=31

For the given triangles missing side b=2.86m and a=42.47m.

What is triangle?

A triangle is a 2-dimensional geometric shape that has three sides and three angles. It is one of the basic shapes in geometry and is commonly studied in mathematics. Triangles can be classified in different ways based on their sides and angles.

We can use the property of similar triangles that corresponding sides are in the same ratio to find the missing side lengths.

For triangle 1, we can use the fact that the angles are 45 and 35 degrees to find the ratio of the sides. Let x be the length of side b:

tan(35) = x/4.5

x = 4.5 * tan(35)

x ≈ 2.86m

So the length of side b in triangle 1 is approximately 2.86 meters.

For triangle 2, we can use the same approach to find the length of side a. Let y be the length of side a:

tan(35) = 27/y

y = 27 / tan(35)

y ≈ 42.47m

So the length of side a in triangle 2 is approximately 42.47 meters.

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Answer: this is your answer

  10

_____

6-5x

Answer:

1.7-20x OR 10/6-5x

Step-by-step explanation:

40÷(24-4x(2+3))

first you add the last set of ()

40÷(24-4x(5))

then you multiply by 4x

40÷(24-20x)

since you can't subtract those two you do this

40÷24-20x

divide 40 and 24

you get 1.66666667 then you round up

1.7-20x

you put 40/24-20x

divide the top and the bottom by 4

(40÷4)/(24÷4) -(20x÷4)

and your answer will be

10/6-5x