How many times does the rotation R(120°, P) need to be applied to a figure to map the figure to itself?

Yes, this statement is true. Because flux integral of curl vector does not depend on surface, it depends only on the boundary of the surfaces. Till we are integrating in the same boundary limits.

Given:

The image displays a paraboloid's part P, its hemisphere H, and its disk D. Assume F is a vector field on R3 with continuous partial derivatives in each of its components.

we are asked why the statement is true = ?

Yes, this claim is accurate. Because the flux integral of the curl vector is surface-independent, it only depends on the boundaries of the surfaces. till our integration is within the same boundary limitations.

Hence above given expression will hold true.

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The numerical side length of length AD is 44 units

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

AD= 4x + 8

CD = 5x - 1

Also, from the complete question (added at the end of the solution), we understand that

The lengths AD and CD are congruent

These parameters and statements above mean that

AD = CD

Substitute the known values in the above equation, so, we have the following representation

4x + 8 = 5x - 1

Collect the like terms

5x - 4x = 1 + 8

Evaluate the like terms

x = 9

Substitute x = 9 in AD= 4x + 8

AD= 4 x 9 + 8

Evaluate

AD= 44

Hence, the length is 44 units

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Complete question

Given that lengths AD and CD are congruent.

Find AD

CD = 5x-1 and AD = 4x+8

4300 km to miles:

[tex]{ \red{ \tt{2671.896}}}[/tex]

2671.896 in nearest whole number :

[tex]{ \blue{\boxed{ \tt{2672}}}}[/tex]

When the population standard deviation is much greater than 5.

What is the standard deviation?

The term "standard deviation"  refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Here, we have

The circumstance is a score that is 5 points above the mean considered a central value.

We have to find under what circumstances is a score that is 5 points above the mean considered a central value--meaning it is relatively close to the mean.

We concluded from the above statement that when the population standard deviation is much greater than 5.

Hence, when the population standard deviation is much greater than 5 then, the score that is 5 points above the mean is considered a central value.

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The probability for given conditions are a) p(4)=0.166, b) p(even)=0.5 and c) p(greater than 3)=0.5

A die is rolled, then the sample space for outcomes is {1,2,3,4,5,6}

Total number of outcomes =6

Thus, the probability for given conditions are a)p(4)=0.166, b)p(even)=0.5 and c)p(greater than 3)=0.5

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Carrying out the operations on the polynomials shows that

A + B - polynomial

A - B - polynomial

A * B - polynomial

The given polynomials are  

A = 3x²( x − 1 )

B = -3x³ + 4x² − 2x + 1

A + B

= 3x²( x − 1 ) + (-3x³ + 4x² − 2x + 1)

= 3x³ - 3x² - 3x³ + 4x² − 2x + 1

= x² − 2x + 1

This is a polynomial

A - B

= 3x²( x − 1 ) - (-3x³ + 4x² − 2x + 1)

= 3x³ - 3x² + 3x³ - 4x² + 2x - 1

= 6x³ - 7x² + 2x - 1

This is a polynomial

A * B

= 3x²( x − 1 ) * (-3x³ + 4x² − 2x + 1)

= (3x³ - 3x²) * (-3x³ + 4x² − 2x + 1)

= -9x^6 + 12x^5 - 6x⁴ + 3x³ + 9x^5 - 12x⁴ + 6x³- 3x²

= -9x^6 + 21x^5 - 18x⁴ + 9x³- 3x²

This is a polynomial

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The regression equation is y = 0.9x+ 7.5

given that

xi:  2   6    9    13    20

Yi : 7   18   9    26   23  

from the given data we have:

∑x = 2+6+9+13+20 = 50

∑y = 7+18+9+26+23 = 83

Also, we need to calculate:

∑xy = 2 × 7+ 6 × 18+ 9× 9+ 13 × 26+ 20×23 = 1001

∑[tex]x^{2}[/tex] = [tex]2^{2}[/tex] + [tex]6^{2}[/tex] + [tex]9^{2}[/tex] + [tex]13^{2}[/tex] + [tex]20^{2}[/tex] = 690

∑[tex]y^{2}[/tex]= [tex]7^{2}[/tex] +  [tex]18^{2}[/tex] + [tex]9^{2}[/tex] + [tex]26^{2}[/tex] + [tex]23^{2}[/tex] = 1659

the slope b is calculated:

b = ∑xy - ∑x × ∑y/n ÷ ∑[tex]x^{2}[/tex] - (∑x)^2 /n

now we need to substitute above values in the equation:

b = 1001 - 50×83 /5 ÷ 690 - (50)^2/5

b= 0.9

the y-intercept (a) is :

a = y - bx

where

y = ∑y/n = 83/5 = 16.6

x = ∑x/n = 50/5 = 10

now substitute these values

a = 16.5 - 0.9 × 10

a = 7.5

the regression equation:

y = bx + a

now ,

y = 0.9x+ 7.5

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The 95% confidence interval for the population proportion who claim they always buckle up is 0.0204.

a) x: 330

b) n: Number of drivers who are surveyed = 430

c) p': proportion of drivers in a sample who claimed to always buckle up = 0.7674

d) normal distribution should be used for this problem.

e) 95% confidence interval for the population proportion who claim they always buckle up.

The error margin is:

1.96 × sqrt(p(1-p) ÷ n)

1.96 × sqrt(0.7674 × 0.2326 ÷ 430) = 0.0204

(0.7674 - 0.0204,0.7674 + 0.0204) = (0.747, 0.7878)

The confidence interval is (0.747, 0.7878).

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Answer:

the correct answer is B

Step-by-step explanation:

$2.29 is the cost of a notebook.

Here, we have,

given that,

Jack bought 3 pencils and 4 notebooks and paid a total of $10.93. Sara bought 5 pencils and 2 notebooks and paid a total of $7.53.

let, the cost of a notebook = n

the cost of a pencil = p

we would solve this with simultaneous equations,

so if we write it as:

4n + 3p = 10.93

2n + 5p = 7.53

=> we get,

multiplying the equations by 5 and 3, we get,

20n + 15p = 54.65

6n + 15p = 22.59

(subtract)

14n = 32.06

divide both sides by 14,

14n ÷ 14 = 32.06÷ 14

n = 2.29

notebooks = 2.29

So the final answer is notebooks are $2.29.

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20.11 cm3/min is the rate at which the snowball's volume is decreasing.

Given,

The decreasing diameter when the spherical ball is melting = 0.2 cm/min

We have to find the rate in decrease in volume of snowball when diameter is 8 cm.

Here,

Volume of sphere, V = 4/3 π r³ = 4/3 π (D/2)³ = 1/6 π D³

Considering differences according to time,

dV/dt = d/dt (1/6 π D³) = 1/6 π × 3D² dD/dt

dV/dt = 1/2 π D² dD/dt

Substituting

D is 8 cm, and the diameter is changing at a rate of 0.2 cm/min.

dV/dt = 1/2 π D² dD/dt

dV/dt = 1/2 × π × 8² × 0.2 = 20.11 cm³/min

Therefore,

Decreasing snowball volume at a rate of 20.11 cm3/min

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Answer:

H

Step-by-step explanation:

The probability that a randomly chosen mango of this type won't be deemed to be large in size is 26.43%.

For the stated question;

The formula for the z-score is;

z = (x - μ)/σ

x < 425 gram

mean  μ = 400,

standard deviation σ = 40:

Thus,

z = (425 - 400)/40

z = 0.625

P(X < 425) = 1 - P(z = 0.625)

P(X < 425) = 1 - 0.7357

P(X < 425) = 0.2643

Thus, there is a 26.43% chance that a randomly chosen mango of this sort will not be regarded as being huge in size.

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Answer:0.8413

Step-by-step explanation:

0.8413

The mean is μ=400, and the standard deviation is σ=25.

Open Excel.  Click on an empty cell.  Type =NORMDIST(425,400,25,1) and press ENTER.

The probability, rounded to four decimal places, is P(X<425)≈0.8413.

Using proportions and ratios, the cost of 1.4lbs is $10.96

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

This is basically the process of comparing two ratios with one another.

In this problem, we will compare the two ratios and solve for the unknown cost of 1.4lbs

0.6 / 4.71 = 1.4 / x

Cross multiply both sides

x = (4.71 * 1.4) / 0.6

x = 10.96

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Answer:

see solution

Step-by-step explanation:

equation: y = 1 - 3x

when x is -2:
y = 1 -3 * -2  = y = 1+6 = y = 7
coordinates = (x,y) = (-2,7)

when x is -1:
y = 1-3*-1 = y = 1+3 = y = 4
coordinates = (x,y) = (-1,4)

when x is 0:
y = 1 - 3 * 0 = y = 1-0 = y =1
coordinates = (x,y) = (0,1)

when x is 1
y = 1-3*1 = y = 1-3 = y = -2
coordinates = (x,y) = (1,-2)

When x is 2
y = 1-3*2 = y = 1-6 = y = -5
coordinates = (x,y) = (2,-5)

when x is 3
y = 1-3*3 = y = 1-9 = y = -8
coordinates = (x,y) = (3,-8)

Plot these points on the graph and join up the dots to see the line.

bye

The summary of the percent of times each and every category appears for the entire sample is called the frequency distribution , the correct option is (d) .

In the question ,

it is asked about what is The summary of the percent of times each and every category appears for the entire sample is called ,

it is called frequency distribution ,

Frequency distribution : it lists all categories of data and number of occurrences for each data category and

it  is also the summary of percent of times each and every category appears for entire sample .

Therefore , the correct option is (d) .

The given question is incomplete , the complete question is

The summary of the percent of times each and every category appears for the entire sample is called the ,

(a) mode

(b) categorical percentage rate

(c) percentage distribution

(d) frequency distribution

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The probability that no two teams win the same number of games is 742.

The number of powers of 2 in 40! is

= (40/2) + (40/4) + (40/8) + (40/16) + (40/32)

= 20 + 10 + 5 + 2 + 1

= 38.

780-38 = 742.

Hence, the probability that no two teams win the same number of games is 742.

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There isn't a ton of information regarding exactly what you are looking for to answer this question. However, if you are trying to simply convert the following word phrase to an expression, here you go:

Hence, the final expression would be written as:

[tex](3x+4) < 4(x+1)[/tex]

Hope this helps!

The probability that a seat will be available for every person holding a reservation and planning to fly is 0.8980.

What is probability?

Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.

Given:

The probability that a person who makes reservations on a certain flight and does not show up for the flight is p=0.05.

The probability that a person who makes reservations on a certain flight and does show up for the flight is 1-p=1-0.05=0.95.

The airlines sell 160 tickets for a flight with only 155 seats.

Let X be a random variable that denotes the number of persons who show up for the flight and it follows a binomial distribution with parameters n = 160 and p = 0.95.

Hence, X~ Binom (n = 160, p = 0.95).

Here,

np=160×0.95=152>5

n(1-p)=160×0.05 = 8.1>5

Hence, both np and n(1-p) are greater than 5, the binomial distribution can be approximated to normal distribution.

The probability that a seat will be available for every person holding a reservation and planning to fly is calculated as follows:

P(X ≤ 155) = (P < 155 + 0.5)

                 [tex]=P(x < 155.5)\\\\=P(\frac{X-np}{\sqrt{np(1-p)}} < \frac{155.5 - (160 \times 0.95}{\sqrt{160\times 0.95 \times 0.05}})\\\\=P(Z < \frac{155.5-152}{2.7568})\\\\=P(Z < 1.27)\\\\=0.8980[/tex]

Hence the probability that a seat will be available for every person holding a reservation and planning to fly is 0.8980.

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Answer:

by dividing by 100

Step-by-step explanation:

630 ÷ 100 = 6.3

The coefficient of determination is 0.588 and the percentage of the total variation is 58.8%.

The coefficient of determination (r^2) refers to a measurement used to explain how much variability of one variable can be caused by its relationship to another related variable. It is the fit of goodness and measures how well a statistical model fits the observed data and is a number between 0 and 1. When the value of linear correlation coefficient r is known, the coefficient of determination can be computed simply by squaring r.

Hence if r = 0.767, then the coefficient of determination = r^2 = 0.588

As percentage of the total variation is same as the coefficient of determination (given in percentage) and is given by the R² value = 58.8%. Hence, about 58.8% of variation is explained by the linear relationship between the two variables.

Note: The question is incomplete. The complete question probably is: Use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation that can be explained by the linear relationship between the two variables. r = 0.767.

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A 95% confidence interval for the difference in mean revenue at the box office for drama and comedy movies is (7.44, 72.56).

We have given that,

Sample mean of peoples who like drama , x₁-bar = 190

Sample mean of peoples who like comedy,x₂-bar = 150

Sample size for darama sample, n₁ = 17

Sample size for comedy sample, n₂ = 14

Standard deviations, s₁ = 60

Standard deviations, s₂ = 30

Confidence level = 0.95 or 95%

Using Z-table , Z-score for 95% confidence level is 1.96..

We have to calculate a 95% confidence interval for the difference in mean revenue at the box office for drama and comedy movies.

It is given by following Confidence interval formula,

x₁-bar - x₂-bar ± Z ( √(s₁²/n₁ + s₂²/n₂))

= 190 - 150 ± 1.96(√(60²/17 + 30²/14))

= 40 ± 1.96(√3600/17 + 900/14))

= 40 ± 32.56

= (7.44, 72.56)

Hence, the required 95% confidence interval is

(7.44, 72.56) .

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Complete question:

A Hollywood studio believes that a movie that is considered a drama will draw a larger crowd on average than a movie that is considered a comedy. To test this theory. the studio randomy selects several movies that are classified as dramas and several movies that are classified as comedies and determines the box office revenue for. each movie. The results of the survey are as follows. Assurne that the population variances are approximately equal, Calculate a

95%

confidence interval for the difference in mean revenue at the box office for drama and comedy movies: Let dramas be Population-1 and comedies be Population 2. Write your answer using interval notation and round the interval endpoints to two decimal places

The best guess for the mean score for all the Georgia students would be 1050 number here.

Given that:

The mean score for a random sample of Georgia students is 1050.

Assuming,

1) X-bar = 42; µ = 44; standard deviation (sigma) = 10; N = 64. Calculate the standard error.

1) The standard error is computed as:

[tex]\sigma_{\bar X} = \frac{\sigma}{\sqrt{n}} = \frac{10}{\sqrt{64}} = 1.25[/tex]

2) You know that X-bar = 42, mu = 44, sigma-sub-X = 10, and N = 64, Calculate z-obtained.

2) The Z-value is computed as:

[tex]Z = \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{N}}} = \frac{42- 44}{\frac{10}{\sqrt{64}}} = -1.6[/tex]

3) The mean score on most IQ tests is 100 with a standard deviation of 15. If Sally has a score of 110 on an IQ test, what is her z-score.

3) The Z -score here is computed as:

[tex]Z = \frac{X -\mu}{\sigma} = \frac{110-100}{15} = 0.6667[/tex]

The best point estimate for the population mean score is equal to the sample mean which is 1050 in this case. Therefore the best guess for the mean score for all the Georgia students would be 1050 here.

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It will take 3 years for the value of the computer of initial value $1000 to reach $512.

Given, Timothy purchased a computer for $1,000.

The value of the computer depreciates by 20% every year.

we have to find the number of years value of computer will take to reach $512.

Let, the function representing this situation be,

V(t) = AB^t

where, A is the initial value of the computer and B is the depreciating rate.

So, V(t) = (1000)(1 - 20/100)^t

V(t) = (1000)(0.8)^t

Now, the value will be, 512

512 = 1000(0.8)^t

0.512 = (0.8)^t

t = 3

So, it will take 3 years for the value of the computer of initial value $1000 to reach $512.

Hence, it will take 3 years for the value of the computer of initial value $1000 to reach $512.

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The value of n should be greater than -5/2 and less than 3. So the value of n under the interval (-5/2, 3).

In the given question, n is an integer with -5<2n<6.

We have to write the value of integer.

As we know;

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. A common way to represent the set of integers in mathematical terms is z with bold.

To find the value of integer n we firstly divide the whole inequality by 2.

The given inequality is -5<2n<6.

Divide by 2, we get

-5/2<n<3

Now we can say that the value of n should be greater than -5/2 and less than 3. So the value of n under the interval (-5/2, 3).

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The given statement is false.

Given that,

The z-statistic can be used as the foundation for statistical inferences about the difference in two population means using two independent random samples if the populations are normally distributed but the population variances are unknown.

If the sample sizes are small, the populations are normally distributed, and the population variances are known, the z statistic can be used as the foundation for statistical inferences about the difference between two population means using two independent random samples.

Therefore, the above given statement can be concluded as false.

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The percent of increase on the truck was 375%.

The probability P(DD) of the letters D and D is 4/9

The letters of the alphabets used to generate the word ADD are given as

Sample space (letters) = {A, D, D}

It is assumed that when a card (i.e. letter) is selected, the card is returned to the set

This means that the selection is with replacement

These letters mean that

P(Letter D) = Count of letter D/Number of letters

So, we have the following representation

P(Letter D) = 2/3

Now, the sample space is

Sample space (letters) = {A, D, D}

These letters mean that

P(Letter D2) = 2/3

So, we have the probability equation

P(DD) = P(D) * P(D2)

This gives

P(DD) = 2/3 * 2/3

Evaluate

P(DD) = 4/9

So, the probability is 4/9

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Answer: Yes, they are proportional

Answer:

No.

Step-by-step explanation:

A proportional relationship shows that each time the amount of money would have increased/decreased in the same amount if she had payed it off constantly and it did not therfore your answer is no.

Answer:

6400

Step-by-step explanation:

-2(12-2(-4))^2

Simplify:

-2(10(-4))^2

-2(-40))^2

80^2

6400

A spherical snowball is melting and its radius decreases from 7 cm to 6.8 cm. Its approximate change in volume is 123.2 cm³.

The approximated value can be obtained using derivative approach.

The volume of the sphere is given by:

V = 4/3 πr³

dV/dr = 4 . πr²

Suppose the change of the radius is Δr, using the above derivative, the change of volume can be approximated as:

ΔV = 4 . πr² Δr

Parameters given:

r = 7 cm

Δr = 7 - 6.8 = 0.2 cm

Hence,

ΔV = 4 . π7² (0.2)

ΔV = 4 . π7² (0.2)

ΔV = 123.2 cm³

Therefore, the approximate change in volume is 123.2 cm³

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