The Earth is 1.496 × 108 km from the Sun. Express this number in standard form.

Answer:

339/100

Step-by-step explanation:

the answer is 339/100

(a) The Fourier transform of f(x) = (x² + 1)² is √(2π) exp(-2πk) / √2.

The application of Jordan's lemma is quite appropriate to find the Fourier transform of f(x) = (x² + 1)². (b) The Fourier-sine transform (assume k ≥ 0) for 1 = 2+2³ (2) (2) is 8√2 / (πk(4+k²)). Part a: The Fourier transform of f(x) = (x² + 1)² is √(2π) exp(-2πk) / √2, where exp(-2πk) represents the exponential decay of the Fourier transform in the time domain. The application of Jordan's lemma is quite appropriate in evaluating the integral for the Fourier transform. In applying Jordan's lemma, the following conditions are satisfied: i) The function f(x) is continuous and piecewise smooth .ii) The integral evaluated using the Jordan's lemma converges as k approaches infinity. iii) The complex function f(z) is analytic in the upper half-plane and approaches zero as |z| approaches infinity. The integral expression is evaluated using the residue theorem. Part b: The Fourier-sine transform (assume k ≥ 0) for 1 = 2+2³ (2) (2) is 8√2 / (πk(4+k²)). Using the definition of the Fourier-sine transform and partial fraction decomposition, the Fourier-sine transform can be evaluated. The Fourier-sine transform is used to transform a function defined on the half-line (0,∞) into a function defined on the half-line (0,∞).

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Answer: Vertical Angles are congruent

Answer:

the last one

Step-by-step explanation:

Suppose that today the exchange rate between the u.s. dollar and the chinese yuan is $1 =.12 yuan. if next week the exchange rate is $1 = .20 yuan, it is clear that yuan has depreciated relative to dollar.

What is meant by the exchange rate?

Last week: $1 = 0.12 yuan

Therefore, for exchange of $1, 0.12 yuan will be given

Today: $1 = 0.2

Therefore, for exchange of $1, 0.2 yuan will be given.

So, yuan will be given for same amount of $. Thus yuan has depreciated.

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a) The average slope or rate of change between (0, 1) and (2, 4) is 3/2.

b) The average slope or rate of change between (-2, 1/4) and (-1, 1/2) is 1/4.

c) The slope or rate of change is not constant between these two pairs of points, since the average slopes are different.

d) The function connecting these pairs of points is not a linear function.

The average slope or rate of change between two points (x1, y1) and (x2, y2) on a line is given by

average slope = (y2 - y1) / (x2 - x1)

For the points (0, 1) and (2, 4), the average slope is

average slope = (4 - 1) / (2 - 0) = 3/2

For the points (-2, 1/4) and (-1, 1/2), the average slope is

average slope = (1/2 - 1/4) / (-1 - (-2)) = 1/4

The slope or rate of change is not constant between these two pairs of points, since the average slopes are different. Therefore, the function connecting these pairs of points is not a linear function.

Note that a linear function has a constant slope, so if the slope is changing, then the function cannot be linear.

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The probability that randomly selected male student play basketball or football is 0.43   .

In the question ,

it is given that ,

total number of male students = 240

number of students that plays football = 68

number of students that plays basketball = 57

the number of students that plays both the game = 11

So , the number of student that plays only foot ball is = 68 - 11 = 57

and the number of students that plays only basketball is = 57 - 11 = 46

number of students that play basket ball or football = 57+46 = 103

So ,the probability that student plays basketball or football is

= (number of students playing football or basketball)/(total number of male students)

= 103/240

= 0.43

Therefore , the required Probability is 0.43   .

The given question is incomplete , the complete question is

At a particular school with 240 male student, 68 play football, 57 play basketball, and 11 play both. Find the probability that a randomly elected male student play basketball or football .

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a) 58^-8 is the same as 1/58^8. we can also simplify the expression by applying the rule for negative exponents to the entire fraction.

To evaluate this expression, we can use the rule that any number raised to a negative exponent is equal to the reciprocal of the same number raised to the same positive exponent. In other words, x^-n = 1/x^n.

Applying this rule to the expression 1/58^8, we get:

1/58^8 = 1/(58^8) = 58^-8

Therefore, the correct answer is 58^-8.

It is important to note that the exponentiation operator (^) has higher precedence than the division operator (/), so we need to use parentheses to indicate that the exponent should be applied to the entire denominator before the division is performed. In this case, we can also simplify the expression by applying the rule for negative exponents to the entire fraction:

1/58^8 = (1/58)^8 = 58^-8

This simplification shows that the correct answer is still 58^-8.

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Hello there, hope you are having a nice day.

This is the rule for rounding:

    - Example: 3.4 =>3

     - Example: 6.7 =>7

Using this rule, we can round 3.5:

3.5 =>4

Hope it helps. Ask me if you have any queries.

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Good luck.

Answer:

2−12x+36

Step-by-step explanation:

Answer:

(x-6)² = (x-6)(x-6) = x² - 12x + 36

Step-by-step explanation:

Answer:

Not exactly, if a possitive and a negetive are added together the number that was larger will choose its symbol. Say "k" is -3, so -3 + 2 = -1, or if "k" was -1, then -1 + 2 = 1.

Step-by-step explanation:

I hope that makes sense

Mathematical proofs are used to prove or disprove mathematical statements.

The theorems to use are:

From the question, we have: \(\triangle ABC\)

This means that, ABC is a triangle

Also, we have:

BP || AC

This means that lines BP and AC are parallel

So, the following angles are congruent by alternate angle theorem

The angles on a straight line add up to 180 degrees.

So, we have:

\(\angle 4 + \angle 1 + \angle 5 = 180\)

By substitution, the above equation becomes

\(\angle 2 + \angle 1 + \angle 3 = 180\)

Rewrite the equation as:

\(\angle 1 + \angle 2 + \angle 3 = 180\)

Hence, the statement that \(\angle 1 + \angle 2 + \angle 3 = 180\) has been proved

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Answer:

b(-10) = 6

Step-by-step explanation:

B(x)= |x+4|

Let x = -10

B(-10)= |-10+4|

            |-6|

Take the positive value

               6

Answer:

6

Step-by-step explanation:

|-10+4|

|-6|

Remove brackets

6

the decision rule for rejecting the null hypothesis is, to reject H₀ if t > 1.363.

Right-tailed test: H0µ = k H1:>k P-value = P(z>z x) This indicates the probability of obtaining a test statistic as high as or higher than z x. If the P-value is less than α, we reject H0(null hypothesis) and conclude that the data are statistically significant at the level α. We do not reject H0 if the P-value is greater than α.

H0: µ  = 5.3 , H1: µ> 5.3

it is a right-tailed test

n = 12

α = 0.10

therefore the decision rule for rejecting the null hypothesis is, Reject H0 if t> 1.363.

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Answer:

x=5 .........................................

Answer:

x=8

Step-by-step explanation:

x^2 - 48 = 2x    

x^2 - 2x - 48=0

(x+6)(x-8)=0

x+6=0     x-8=0

x= - 6         x=8

can not be negative so the answer is x=8

Answer:

hi long time no talk we need to talk on padle* i left msgs

Step-by-step explanation:

Answer:

∠IGF = 83

Step-by-step explanation:

∠IFG = ∠ IBC = 47

∠IGF = 180 - 50 - 47 = 83

Answer:

Step-by-step explanation:

Alternate exterior angles rule used for angle ABF,

1. subtract the measurement of angle FBC from 180 to find measurement for angle ABF. (180-47)= 133 degrees

Line segments EH and AD are paralell therefore angle EFB is equal to angle FBC ( they are both 47 degrees). This also means that angle ABF is equal to angle BGF. (they are both 133 degrees)

since we know the angle BFG is equal to 133 degrees we can subtract 133 from the straight line (180) to find out the measurement for angle IGF.

180-133= 47 degrees

Now we can solve for angle IGF because we know all angles in a triangle have a sum of 180 degrees. Therefore IGF will be the difference between 180 and the sum of the BFG and FIG.

Angle IGF= 180- (47+50)

Angle IGF= 180-97

Angle IGF- 83 degrees

Therefore angle IGF= 83 degrees

Liberal arts colleges have a higher median SAT score and a lower acceptance rate compared to research universities, while research universities have a higher expenditure per student and a higher percentage of top 10% high school graduates.

Descriptive statistics were calculated for liberal arts colleges and research universities based on the data given in the Excel file. The summary of descriptive statistics for each variable by school type is as  shown in the table.

Based on the results, it appears that liberal arts colleges have higher median SAT scores, lower acceptance rates, and lower expenditures per student than research universities. On the other hand, research universities have higher mean expenditures per student and higher median percentages of top 10% high school graduates than liberal arts colleges. Overall, there are differences in the characteristics of these two types of colleges.

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--The complete question is, Compute descriptive statistics for liberal arts colleges and research universities in the Excel file Colleges and Universities. Compare the two types of colleges. What can you conclude?

Colleges and Universities

School Type Med SAT Accept Rate Exp./Student Top 10% HS Grad %

Amherst Lib Arts 1315 22% $26,636 85 93

Barnard Lib Arts 1220 53% $17,653 69 80

Bates Lib Arts 1240 36% $17,554 58 88

Berkeley Univ 1176 37% $23,665 95 68

Bowdoin Lib Arts 1300 24% $25,703 78 90

Brown Univ 1281 24% $24,201 80 90

Bryn MawrLib Arts1255 56% $18,847 70 84

Cal Tech Univ 1400 31% $102,262 98 75

Carleton Lib Arts 1300 40% $15,904 75 80

Carnegie University1225 64% $33,607 52 77

Claremont Lib Arts1260 36% $20,377 68 74

Colby Lib Arts 1200 46% $18,872 52 84

Colgate Lib Arts 1258 38% $17,520 61 85

ColumbiaUniversity1268 29% $45,879 78 90

Cornell University1280 30% $37,137 85 83

DavisdsonLib Arts 1230 36% $17,721 77 89

Duke University 1310 25% $39,504 91 91

GeorgetownUniv 1278 24% $23,115 79 89

Grinnell Lib Arts 1244 67% $22,301 65 73

HamiltonLib Arts 1215 38% $20,722 51 85

Harvard Univ 1370 18% $46,918 90 90

HaverfordLib Arts 1285 35% $19,418 71 87

Johns Hop. Univ 1290 48% $45,460 69 86

MiddleburyLib Arts 1255 25% $24,718 65 92

MIT University 1357 30% $56,766 95 86

Mount Lib Arts 1200 61% $23,358 47 83

NWrn University 1230 47% $28,851 77 82

Oberlin Lib Arts 1247 54% $23,591 64 77

Occidental Lib Arts 1170 49% $20,192 54 72

Pomona Lib Arts 1320 33% $26,668 79 80

Princeton University 1340 17% $48,123 89 93

Rice University 1327 24% $26,730 85 88

Smith Lib Arts 1195 57% $25,271 65 87

Stanford University 1370 18% $61,921 92 88

Swarthnore Lib Arts 1310 24% $27,487 78 88

U of MI University 1195 60% $21,853 71 77

U of Chi University 1300 45% $38,937 74 73

U of Roc University 1155 56% $38,597 52 73

U PA University 1280 41% $30,882 87 86

U Va University 1218 37% $19,365 77 88

UCLA University 1142 43% $26,859 96 61

UNC University 1109 32% $19,684 82 73

Vassar Lib Arts 1287 43% $20,179 53 84

Wash U University 1225 54% $39,883 71 76

Wash & Lee Lib Arts 1234 29% $17,998 61 78

Wellesley Lib Arts 1250 49% $27,879 76 86

Wesleyan Lib Arts 1290 35% $19,948 73 91

Williams Lib Arts 1336 28% $23,772 86 93

Yale University 1350 19% $52,468 90 93--

1!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer:

The volume of a cylinder is calculated by multiplying the area of the base by the height. The area of the base of a cylinder is πr², where r is the radius of the cylinder. In this case, the radius is 8 centimeters, so the area of the base is 201.06 cm². The height of the cylinder is 17 centimeters, so the volume of the cylinder is 3417.02 cm³.

The volume of a rectangular prism is calculated by multiplying the length, width, and height. In this case, the length is 15 centimeters, the width is 12 centimeters, and the height is 9 centimeters. The volume of the rectangular prism is 1620 cm³.

Since the volume of the cylinder is less than the volume of the rectangular prism, the water will not overflow.

Here is an argument that can be used to defend this solution:

The volume of the cylinder is calculated by multiplying the area of the base by the height.

The area of the base of a cylinder is πr², where r is the radius of the cylinder.

In this case, the radius is 8 centimeters, so the area of the base is 201.06 cm².

The height of the cylinder is 17 centimeters, so the volume of the cylinder is 3417.02 cm³.

The volume of a rectangular prism is calculated by multiplying the length, width, and height.

In this case, the length is 15 centimeters, the width is 12 centimeters, and the height is 9 centimeters.

The volume of the rectangular prism is 1620 cm³.

Since the volume of the cylinder is less than the volume of the rectangular prism, the water will not overflow.

Step-by-step explanation:

The SOH CAO TOA identity is used to determine the acute angles of a right triangles. The terminal point of ø is (-1,0), what is tan ø is 0

Given the terminal point (-1, 0), the value of tanø is expressed as:

tanø = opposite/adjacent

tanø = y/x

From the coordinate given:

x = -1

y = 0

Substitute

tanø = 0/-1
tanø  = 0

Hence the terminal point of ø is (-1,0), what is tan ø is 0

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From the given information, the value of x in the given table is 42.5.

To find the value of x, we can use the formula for the arithmetic mean (average) of a set of numbers:

Arithmetic mean = (sum of all numbers) / (number of numbers)

Given that the average score on the test is 62, we can use this information to find the sum of all the scores.

Given that number of students is 1,2,3 and 4 with scores of 40,55,70 respectively, we can use this information to find the sum of all the scores.

Sum of all scores = (1 * 40) + (2 * 55) + (3 * 70) + (4 * x)

Now we can substitute the given average score and the number of students into the equation and solve for x.

62 = (1 * 40) + (2 * 55) + (3 * 70) + (4 * x) / 10

620 = 40 + 110 + 210 + 4x

4x = 170

x = 42.5

So, the value of x is 42.5

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The complete question is -

ten students wrote a test, and the distribution of scores is shown in the frequency table. if the average (arithmetic mean) score is 62, what is the value of x?

Score - 40, 55, 70, x

Number of students - 1, 2, 3, 4

Answer:

90-19 =71 I hope it will help you please follow me

\(\\ \Large\sf Minor\:Arc\longmapsto AOQ\)

\(\\ \Large\sf Major\:arc\longmapsto AXQ\)

Now

\(\\ \Large\sf\longmapsto m<AOQ=70°\)

\(\\ \Large\sf\longmapsto m<AXQ=2m<AOQ\)

\(\\ \Large\sf\longmapsto m<AXQ=2\times 70\)

\(\\ \Large\sf\longmapsto m<AXQ=140°\)

Answer:

The answer is eleven. 11

The rate at which the water level is rising when the water level is 6 cm is approximately 2.67 cm/s. if an inverted pyramid is filled with water at a constant rate of 55 cubic centimeters per second, the top of pyramid is in square shape with length of 8 cm and height of 14 cm.

Let's call this rate "r".

Volume of pyramid = (1/3) * base area * height

Since the pyramid has a square base, the base area is given by

Base area = (side length)^2

Substituting the given values

Base area = (8 cm)^2 = 64 cm^2

Height = 14 cm

V = (1/3) * 64 cm^2 * 14 cm = 298.67 cm^3

We know that the water is being added to the pyramid at a constant rate of 55 cm^3/s. Therefore, the rate at which the volume is increasing is

dV/dt = 55 cm^3/s

We also know that the volume of water in the pyramid at any given time is given by

V_water = (1/3) * base area * h_water

where h_water is the height of the water at that time.

To find the rate at which the water level is rising (r), we need to find dh_water/dt. We can do this by taking the derivative of both sides of the equation for V_water with respect to time

dV_water/dt = (1/3) * base area * dh_water/dt

Substituting the known values

dV_water/dt = (1/3) * (8 cm)^2 * dh_water/dt

dV_water/dt = (64/3) cm^2 * dh_water/dt

dh_water/dt = 3 * dV_water/dt / 64

dh_water/dt = 3 * 55 cm^3/s / 64 = 2.67 cm/s

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The equation in slope intercept form of the line that passes through the y-intercept (0, 1) and has a slope of 4 is y = 4x + 1

The line is passing through the y intercept = (0, 1)

Here at x = 0, the values of y = 1

Then the y intercept of the line is 1

The slope of the line = 4

The slope of the line is the change in y coordinate with respect to the change in x coordinates of the function

The slope intercept form is

y = mx + b

Where m is the slope of the line

b is the y intercept

x is the x coordinate

y is the y coordinate

Then the equation in the slope intercept form

y =4x + 1

Hence, the equation in slope intercept form of the line that passes through the y-intercept (0, 1) and has a slope of 4 is y = 4x + 1

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