match the integrals with the type of coordinates which make them the easiest to do. put the letter of the coordinate system to the left of the number of the integral. b 1. where e is: c 2. where e is: a 3. b 4. where e is: d 5. where d is: a. polar coordinates b. cartesian coordinates c. spherical coordinates d. cylindrical coordinates

The number line we can see that 1.5 is less than 1.75.

Mark two points 1.75  and 1.5 on number line  and make a number line from -1 to 2 where each point is 0.25 units away

Then compare 1.75  and 1.5 on number line

Given :

Nico wants to use a horizontal number line to compare 1 3/4 and 1.5

Lets write the fraction in decimal form to compare and mark it on number line [tex]1\frac{3}{4}[/tex] = 1.75

Now mark two points 1.75  and 1.5 on number line

Make a number line from -1 to 2 where each point is 0.25 units away

Mark a number line that are 0.25 units away using below numbers

-1, -0.75, -0.5, -0.25, 0, 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75, 2

On the number line ,

1.5 comes first

1.75 is next to 1.5

From this number line we can see that 1.5 is less than 1.75.

1.5 <       [tex]1\frac{3}{4}[/tex]

Hence the answer is the number line we can see that 1.5 is less than 1.75.

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Answer:

25%

Step-by-step explanation:

you want to figure out how many % are 55 of 220.
To get this, you do:
percentage = (55 * 100) / 220 = 25
-> so 55 are 25% of 220. 25% of the total fatal accidents were on building sites.

Greater inputs only result in the leading term becoming more and more positive if the leading coefficient is positive. The graph will incline rightward. Larger inputs will simply make the leading term more and more negative if the leading coefficient is negative. The rightward descent of the graph is planned.

The coefficient of the leading term is the leading coefficient in a polynomial. Because of the negative leading coefficient, the graph slants to the right. To ascertain the behavior, consider the function's degree and the sign of the leading coefficient.

The term with the largest power of x is the leading term in a polynomial. As an illustration, the leading word in 7+x3x2 is 3x2. A polynomial's leading coefficient is the coefficient of the leading term. The leading coefficient in the aforementioned illustration is 3.

The numbers placed in front of the variable with the largest exponent are known as leading coefficients. They can be whole numbers, fractions, or decimals, as well as positive, negative, real, or imaginary, just like regular coefficients.

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The point slope formula is [tex]y-y_1=m(x-x_1)[/tex].

The point slope form is used to calculate the equation of a straight line that is inclined to the x-axis at a certain angle and passes through a particular point.

When we know the slope of a line and a point on it, we may use the point slope formula.

Point Slope Formula:

[tex]y-y_1=m(x-x_1)[/tex]

where,

(x, y) is a point on the line at random (which should be kept as variables while applying the formula).

(x1, y1) is the line's fixed point.

slope of the line is 'm'.

Thus, the point slope formula is [tex]y-y_1=m(x-x_1)[/tex].

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The probability that the number on the second tag exceeds the number on the first tag is 0.5

A hat contains tags numbered 1, 2, 3, 4, 5, 6. two tags are selected.

The complete sample space is 6 x 6 = 36

the probability that the number on the second tag exceeds the number on the first tag...Let this event be L

when (a) the first tag is not replaced before the second tag is drawn

If the 1st tag is 1,

Then P(L) = 1/6 x 5/5

If the 1st tag is 2,

Then P(L) = 4/5 x 1/6

If the 1st tag is 3,

Then P(L) = 3/5 x 1/6

If the 1st tag is 4,

Then P(L) = 2/5 x 1/6

If the 1st tag is 5,

Then P(L) = 1/5 x 1/6

If the 1st tag is 6,

Then P(L) = 0/5 x 1/6 = 0

P(L) = 5/30 + 4/30 + 3/30 + 2/30 + 1/30

The probability that the number on the second tag exceeds the number on the first tag = (15/30) = 1/2 = 0.5

Therefore,  the probability that the number on the second tag exceeds the number on the first tag is 0.5

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If you wanted to save $30,000 you need to work 30 times .

Given:

if you wanted to save $30,000 to buy a new car. instead of focusing on saving the whole amount, you work to earn $1,000 at a time. this makes the process seem more manageable to you because you are using the heuristic.

Number of times to work = money to save / at a time money.

= $30000/$1000

= 30000/1000

= 3000/100

= 300/10

= 30 times

Therefore you need to work 30 times to earn $30,000.

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the x-intercepts of the given graph are 12n - 3 where n is 0,±1,±2...

What is equation straight line?

Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.

The given straight line is y = sin πx/6 + 1

To find the x-intercepts we have to y=0 in the function.

So the equation become, 0 = sin πx/6 + 1

sin πx/6 = - 1

πx/6=nπ+(−1) n ( -π/2)

x = 12n - 3

So, the x-intercepts of the given graph are

12n - 3 where n is 0,±1,±2...

Hence the x-intercepts of the given graph are 12n - 3 where n is 0,±1,±2...

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If a triangle has an obtuse angle which measures more than 90 degrees but less than 180 degrees it is an obtuse angled triangle.

When one of the vertex angles of a triangle is greater than 90°, it is called an obtuse angle triangle

An obtuse triangle can either be an isosceles or a scalene triangle but not an equilateral triangle.

In an obtuse angle triangle, the sum of the squares of the two sides is always less than the square of the longest side.

Therefore,  if a triangle has an obtuse angle which measures more than 90 degrees but less than 180 degrees it is an obtuse angled triangle.

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After the disk technique and the washer method, the cylindrical shell method of conducting a revolution is the third approach to determine the volume of the solid created by rotating about an axis. Technically, either of the first two approaches can find any revolution, but the cylindrical shell approach may be simpler to compute.

The cylindrical shell method's biggest drawback is that it necessitates more visualization of the regions where the cylinders are formed because you must determine both the cylinder's radius and height, whereas the other two methods only require the radius.

I'm going to start out by presuming that just the area in the first quadrant is rotating about the y-axis. Second, because the shell has a thickness of dx and the rotation revolves around a vertical axis, the integral must be expressed in terms of x. Third, the cylinder's height is and its height has a radius of [tex]36 - x^{2}[/tex]. Last but not least, the bounds are 0≤x≤6 since the area being rotated is constrained by the axes and the function. The integral can now be set up.

[tex]\int\limits {2\pi rh} \, dx = \int\limits^6_0 {2\pi x(36-x^{2} )} \, dx[/tex]                                          [Set Up the Integral]

               [tex]= 2\pi \int\limits^6_0 {36x - x^{3} } \, dx[/tex]                                                            [Distribute]                

               [tex]= 2\pi (\frac{36x^{2} }{2} - \frac{x^{4} }{4} )[/tex]  = [tex]2\pi ( (\frac{36(6)^{2} }{2} - \frac{6^{4} }{4} ) - (\frac{36(0)^{2} }{2} - \frac{0^{2} }{4} ) )[/tex]

               [tex]= 2\pi ( \frac{36(6)^{2} }{2} - \frac{6^{4} }{4} )[/tex]                                                                [Evaluate]

               [tex]= 1296\pi[/tex]                                                                                {Answer}

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The right Question is:

Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis.

[tex]y = 36 - x^{2} \\y = 0[/tex]

If the function f(x) [tex]=[/tex] x [tex]+[/tex] 3 and g(x) = x² + 2x - 3, then the value of the composite function [gof](x) is =  x² + 8x + 12  .

In the question ,

it is given that

the function f(x) is [tex]=[/tex] x [tex]+[/tex] 3

and the function g(x) is [tex]=[/tex] x² [tex]+[/tex] 2x - 3 ,

we have to find the value of composite function , (gof)(x)

(gof)(x) = g(f(x))

substituting the value of f(x) = x + 3,

we get ,

g(f(x) = g(x + 3)

Substituting the (x+3) in place of x in the function g(x) , we get

= (x+3)² + 2(x+3) - 3

= x² + 6x + 9 + 2x + 6 - 3

= x² [tex]+[/tex] 8x [tex]+[/tex] 9 + 3

= x² [tex]+[/tex] 8x + 12

Therefore , If the function f(x) = x + 3 and g(x) = x² + 2x - 3, then the value of the composite function [gof](x) is =  x² + 8x + 12  .

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The distance from (0, -4) to the line x + 5y = 10 is approximately 6 units.

To find the distance from a point to a given line, recall the following:

Step 1: Find the slope of the line, x + 5y = 10:

Rewrite the equation, x + 5y = 10 as y = mx + b, to find the value of the slope (m)

5y = -x + 10

y = -x/5 + 10/5

y = -1/5x + 2

The slope (m) = -1/5.

Step 2: Find an equation of the perpendicular line to the line x + 5y = 10 that passes through the point (0, -4):

Slope (m) = 5 [negative reciprocal of -1/5]

y-intercept (b) = -4

Substitute m = 5 and b = -4 into y = mx + b:

Equation of the line:  y = 5x - 4

Step 3:  Find the point of intersection of the lines y = 5x - 4 and y = -1/5x + 2:

Therefore, the lines intersect when 5x - 4 = -1/5x + 2

5x - 4 = -1/5x + 2

5x + x/5 = 4 + 2

26x/5 = 6

26x = 30

x = 30/26

x ≈ 1.2

Substitute x = 1.2 into y = 5x - 4:

y = 5(1.2) - 4

y = 2

Point of intersection is: (1.2, 2)

Step 4:  Find the distance between (0, -4) and (1.2, 2) using the distance formula:

d = √[(1.2 − 0)² + (2−(−4))²]

d = √[(1.2)² + (6)²]

d = √37.44

d ≈ 6 (nearest whole number)

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The total number of sides of the given polygon is 16.

What is the interior and exterior angle of a regular polygon?

In a regular polygon, all internal angles and exterior angles are equal. The formula for determining the amount of an interior angle is given:

Interior angle of a polygon = sum of interior angles/number of sides  

A polygon's exterior angles add up to 360°.

Given, each interior angle of a regular polygon = 157.5°

Then, each exterior angle of a regular polygon = 180° - 157.5° = 22.5°

the sum of the exterior angles of any n-gon = 360°

So, the total number of sides = 360°/22.5° = 16 sides

Hence, the total number of sides of the polygon is 16.

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1.Regression line is given by:

  y = 4.14 - 0.04 x

2. When explanatory variable is 0, y = 4.14

3.For each increase of 1 in explanatory variable, there can be a decrease of 0.04 in response variable.

4. The value of y is 4.28

5.  The value of r is -0.04

What is regression line?

A regression line is a line that in statistics best depicts the behavior of a set of data. It is, in other words, a line that best fits the trend of the data at hand.

Simple linear regression results:

Dependent Variable: Y

Independent Variable: X

Y = 4.1428571 - 0.035714286 X

Sample size: 7

From above equation:

1. Regression line is given by:

  y = 4.14 - 0.04 x

2. When explanatory variable is 0, y = 4.14

3. For each increase of 1 in explanatory variable, there can be a decrease of 0.04 in response variable.

4. when x = -3.5:

substitute this into the equation of regression line

y = 4.14 - 0.04*(-3.5) = 4.28

It is an example of extrapolation

5. r = -0.04

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The mean and variance of C are 200 & 1960000 respectively.

What are the mean and variance?

The mean is the average of a set of numbers, whereas the variance is the average degree to which each number deviates from the mean.

y ~ Exponential with mean of 10 hours

P. d. f of y,

[tex]f_{y} (y) = { \left \{ {{\frac{1}{10}e^{\frac{-y}{10} } } \atop {0}} \right.\\\left {{y > 0} \atop { 0 \ otherwise}} \right.[/tex]

[tex]f_{y} (y) = \int\limits^{\infty}_{-\infty} {y^{k} f_{y} (y)} \, dy[/tex]

[tex]f_{y} (y) = \int\limits^{\infty}_{0} {y^{k} \frac{1}{10} . e^{-\frac{y}{10} } \, dy[/tex]

[tex]=\frac{1}{10} \int\limits^{\infty}_{0} {y^{k+1} . e^{-\frac{y}{10} } \, dy[/tex]

[tex]= \frac{10^{k+1} }{10} \ \Gamma(k+1)[/tex] ---------(1)

E(Y³) = 10³ Γ(3+1)   [putting k = 3 in (1)]

= 10³ Γ(4)

= 10³ 3!    ..........[Γ(n) = (n-1)!]

= 6000

E(Y⁴) = 10⁴ Γ(4+1)   [putting k = 4 in (1)]

= 10⁴ Γ(5)

= 10⁴ 4!    ..........[Γ(n) = (n-1)!]

= 240000

C = 100 + 40Y + 3Y²

Mean of C,

E(C) = E(100 + 40Y + 3Y²)

E(C) = 100 + 40E(Y) + 3E(Y²)

E(Y) = 10           .......[Given]

E(Y²) = 10² Γ(2+1)   [putting k = 2 in (1)]

= 10² Γ(3)

= 10² 2!

= 200

E(C) = 100 + 40(10) + 3(200)

E(C) = 1100

The variance of C,

Var(C) = Var[100 + 40Y + 3Y²]

= 1600var(Y) + 9(Y²)

= 1600[E(Y²) - E²(Y)] + 9[E(Y⁴) - E²(Y⁴)]

= 1600[200 -(10)²] + 9[240000 - (200)²]

= 1960000

Hence, the mean and variance of C are 200 & 1960000 respectively.

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The rate of change of the functions are: I. -3 II. -1/4.

Therefore, C. Both functions are decreasing and have different rates of change.

The rate of change of any function can be calculated as = change in y / change in x.

If the rate of change is a negative number, the function is decreasing. If it is a positive number, the function is decreasing:

Rate of change of the line that passes through (3, 3) and (4, 0):

Rate of change = (0 - 3) / (4 - 3)

= -3/1

= -3 [this means the function is decreasing].

Rate of change of the function represented by the table, using two pairs of the table values, (0, -1) and (-4, 0):

Rate of change = (0 -(-1)) / (-4 - 0)

= 1/-4

= -1/4 [this shows the function is decreasing]

Therefore, the answer is: C. Both functions are decreasing and have different rates of change.

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Using compound interest  formula, the amount compounded at a rate of 3% quarterly for 5 years is $15,095.39

The compound interest is the interest-based on the initial principal amount and the interest collected over the period of time. The formula for compound interest can be derived from the formula for simple interest. The formula for simple interest is the product of the principal, time period, and rate of interest (SI = ptr/100). Before looking into to derivation of the formula for compound interest, let us understand the basic difference between simple interest, compound interest computation. The principal remains constant over a period of time, for simple internet computation, but for compound interest computation the interest is added to the principal, for compound interest computation. The compound interest formula is given below:

A = P(1 + r/n)^nt

plugging the values into the formula above

A = 13000(1 + 0.03/4)^4 * 5

A = 13000(1.0075)^20

A = $15,095.39

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(a) The demand function assuming it is linear is  P(x) = -x/3000 + 19   .

(b) The ticket price to maximize the revenue should be $9.5    .

In the question ,

it is given that ,

the number of spectators that baseball stadium can hold = 53000

the ticket price = $10

the average attendance = 27000 ,

when ticket price lowered to $8 , average attendance rose to 33000 .

So , the points are represented as

for $10 the attendance is 27000 ,

for $8 the attendance is 33000 ,

the points are (27000 , 10) and (33000 , 8) .

the slope = (change in price)/(change in attendance )

= (8-10)/(33000 - 27000)

= -2/6000

= -1/3000

So ,the equation is

(y - 10) = (-1/3000)(x - 27000)

y - 10 = -x/3000 + 27000/3000

y - 10 = -x/3000 + 9

y = -x/3000 + 19

the demand function is P(x) = -x/3000 + 19   ,

the revenue function , R(x) is x.P(x)

R(x) = x.P(x)

So , R(x) = x(-x/3000 + 19)

= -x²/3000 + 19x

to maximize the revenue function , we differentiate with respect to "x" ,

we get ,

R'(x) = 19 - 2x/3000

= 19 - x/1500

for critical value , R'(x) = 0 ,

w get ,

19 - x/1500 = 0

x/1500 = 19

x = 28500

again Differentiating R′(x) with respect to x,

R″(x) = -1/1500 < 0

So , for 28500 spectators, the revenue will be  maximum .

the ticket price for 28500 spectators will be ,

P(28500) = 19 - 28500/3000

= 19 - 9.5

= 9.5

Therefore , (a) The demand function assuming it is linear is  P(x) = -x/3000 + 19   .

(b) The ticket price to maximize the revenue should be $9.5    .

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Answer:

B. 1 > -2, C. 4 > 1, and D. -3 < -1

Step-by-step explanation:

B. 1 is larger than -2

C. 4 is larger than 1

D. -3 is less than -1

When the negative exponent is outside the parentheses indicates that you need to take the inverse of the base number, or put it in the denominator.

Given:

when the negative exponent is outside the parentheses.

suppose (3)^-3 = 1/3^3.

Example:

(7)^-3

Take the inverse of base number and put it in denominator.

= 1/7^3

So the negative is outside the parenthesis is tells that the negative sign must be removed.

Therefore when the negative exponent is outside the parentheses indicates that you need to take the inverse of the base number, or put it in the denominator.

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The average, median and quartile of the figures 1,2,3 are:

Normal : Average= 1, median is 1 the first quartile is 1

Adjusted: Average=5.67, median is 5.62 and the quartile is 4.5

Quartile is defined as a type of quantile which divides the number of data points into four parts, Median is the middle data value, Mean is calculated by dividing the sum of the data values by the number of data values

The given figures are:

Normal 1,1,1

Adjusted: 5.82, 5.56, 5.62

Normal mean = 1+1+1 /3 = 3/3=1

Normal median= 5.56, 5.62, 5.85 =5.62

Lower quartile = [tex]n+1*\frac{1}{4}[/tex]

3+1*[tex]\frac{1}{4} =1[/tex]

Adjusted: mean [tex]\frac{5.82+5.56+5.62}{3}=\frac{17}{3}=5.67[/tex]

median: 5.56, 5.62, 5.85 = 5.62

Quartile: [tex]17+1*\frac{1}{4}[/tex]

=4.5

In the normal column, the wages remained constant but in the adjusted column, the wages were fluctuation as a sign of inflation

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It takes Ahby a total of 9.5 minutes to run a mile.

What is a total?

The sum of two or more numbers is known as the total in mathematics. It is the total of the figures added up. When we add two or more numbers, amounts, or items, the total sum is obtained. The sum can also be expressed as the total, aggregate, or tally in this example, where the sum of 3 and 7 is 10.

Solution Explained:

Given in the question,

Total time taken to run 6 miles = 57

So,

Total time taken to run 1 mile = 57/6 = 9.5 minutes

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Answer:

12 y 42

Step-by-step explanation:

Let x and y represent the two numbers:

(1)  x+y=54 and (2)  x-y=30

Solve for x:

x-y=30

x=30-y

Substitute into equation (1):

(30-y)+y=54

2y+30=54

2y=24

y=12

Substitute into equation (2):

x-12=30

x=42

Dijkstra's algorithm should be executed twice, once from s and once from u.

Given,

We have to determine an effective algorithm that, provided it's not too inconvenient, will choose the best route from s to t based on your choice for stopping at u along the way. Either the shortest path from s to t or the shortest path from s to t that includes u should be returned.

Algorithm;-

An algorithm is a process used to carry out a computation or solve a problem. In either hardware-based or software-based routines, algorithms function as a detailed sequence of instructions that carry out predetermined operations sequentially. All aspects of information technology employ algorithms extensively.

Here,

Run Dijkstra's algorithm two times, from s and u, respectively.

The shortest path from s to u and the shortest path from u to t make up the shortest path from s to t containing u.

Choose the path to return to based on their lengths by comparing this path's length to the path's length from s to t.

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The number of combinations of a president, vice president, secretary and a treasurer can be chosen from a group of 12 students is 11,880.

Given: we have group of 12 students.

we are asked to determine the number of combinations of a president, vice-president, secretary, and treasurer can be chosen from a group of 12 students.

nPr = n!/(n-r)!

12P4 = 12!/(12 - 4)!

12P4 = 12!/8!

9 × 10 × 11 × 12

= 11,880

Hence the number of combinations are 11,880.

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Median for the given data 17, 2 ,7 is  12.

What is median?

The median is that the value that’s precisely within the middle of a dataset once it's ordered. It’s a live of central tendency that separates the bottom 50% from the very best 50% of values.

Main body :

First of all to find the median data should be arranged in ascending order.

Aranging data in ascending order

2, 5 , 7 , 7 , 8 , 8 , 10 , 10 , 14 , 15 , 17 , 18 , 24 , 27 , 28 , 48

Now there are even number of terms i. e 16

So,

M1 = n / 2 and M2 = ( n / 2 ) + 1

= 16 / 2 = 8 + 1

= 8th term = 9th term

M1 = 10 M2 = 14

Median, M = ( M1 + M2 ) / 2

= ( 10 + 14 ) / 2

= 24 / 2

= 12

Hence median of observation is 12.

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you get to keep whatever 6-digit dollar amount you want as long as no one else chooses it is $809,417

you choose a random number, but don't want to make it start with 9 as everyone will be picking nine as the first digit. So instead go with the next best, 8. Then making the next digit 0 since people would be unlikely to have the second number as 0, trying to max out their money while also picking the lowest first number. Then have the rest of the digits be random to maximize the odds of no one happening to select it.

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The equation of a straight line passing through the given point and slope is y - y1 = m(x - x1).

Given:

Let the given point be (x1,y1).

slope be m.

we know that,

Line equation passing through point is:

y - y1 = m(x - x1)

where m = slope and (x1,y1) = given point.

Therefore The equation of a straight line passing through the given point and slope is  y - y1 = m(x - x1).

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Using PEMDAS rule , we can evaluate the provide expression . The required result is thirteen that's the value is L= 13.

PEMDAS order of operations: The order of operations is a rule that tells the correct sequence of steps for evaluating a given mathematical expression. We can remember the order using "PEMDAS" where

P --> Parentheses

E --> Exponents (2⁵ is 2 raised to the power of 5)

M------> Multiplication and

D---->Division (from left to right)

A--->Addition

S--->Subtraction (from left to right).

We have given that

3/4 ( 2³ + 4² )

let given expresion equal to L i.e

L = 3/4 ( 2³ + 4² )

Now, we have to solve it

Using "PEMDAS" rule ,

L = 3/4 ( 2³ + 4²)

= 3/4 ( 8 + 4²)

= 3/4 ( 8 + 16 )

= 3/4 ( 24)

= 3/4 ×24

= 24×3/4

= 72/4

L = 1 3

Hence, the given expresion is equal to 13 .

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Answer:

First, know that [tex]csc(x)=\frac{1}{sin(x)}[/tex]:

[tex]\frac{1}{sin^{2}(x)} *cos^{2}(x)=\frac{cos^{2}(x)}{sin^{2}(x)}[/tex]

Remember that cos²(x) + sin²(x) = 1, so cos²(x) = 1 - sin²(x):

[tex]\frac{cos^{2}(x)}{sin^{2}(x)} =\frac{1-sin^{2}(x)}{sin^{2}(x)} =\frac{1}{sin^{2}(x)} -\frac{sin^{2}(x)}{sin^{2}(x)} =csc^{2}(x)-1[/tex]

Step-by-step explanation:

this might be the answer

The number of ways for six ce majors and ten cs majors to stand in a line so that no two ce majors stand next to each other are 462.

We need to maintain one condition that no two ce majors stand next to each other.

So, what we can do firstly we allow ten cs majors to stand in a line as there are no restrictions on cs majors.

Total number of ways by which ten cs majors can stand=10!=3628800

Now, when 10 cs majors stand in a line then we have 11 spaces.

Now, we need to choose such  space for 6 ce majors so that no two ce majors stand next to each other.

So, it is equivalent to choose 6 spaces from 11 spaces which is given by [tex]^1^1C_6[/tex] ways =(11!)/(6!×5!)=11×2×3×8×7=462ways.

Hence, total number of ways are 462.

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