Function f(x) is positive, decreasing and concave up on the closed interval[a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the left sum, right sum, and trapezoidal rule approximations for the value of integral from a to b f(x)dx. Which one of the following statements is true?
a) Left sum < trapezoidal rule value < Right sumb) Left sum < Right sum < trapezoidal rule valuec) Right sum

Answer:

Dog Pogo will fetch the frisbee 12 times in 4 minutes.

Step-by-step explanation:

Given:

Number of minutes required =2 minutes.

Number of times frisbee fetch by dog = 6 times

We need to find Number of times the dog can fetch the frisbee in 4 minutes.

First we will find number of frisbee fetch in minute.

In 2 minutes = 6 times frisbee fetched by the dog

so in 1 minute = Number of times frisbee fetched by the dog in 1 minute.

By using Using Unitary method we get;

Number of times frisbee fetched by the dog in 1 minute = [tex]\frac{6}{2} =3[/tex]

Hence in 1 minutes the dog can fetch frisbee 3 times.

for 1 min = 3 times frisbee is been fetched by dog

So for 4 minutes = Number of times frisbee is been fetched by dog in 4 min.

Again by using Unitary Method we get;

Number of times frisbee is been fetched by dog in 4 min = [tex]3\times4 = 12[/tex]

Hence Dog Pogo will fetch the frisbee 12 times in 4 minutes.

Answer:12

Step-by-step explanation:

Answer:

Beneficial terms of trade or trading price between two parties are opportunity costs lower than the cost to manufacture them locally which benefits both parties. They must be less enough to cover the freight charges or additional service charges that may arise.

Answer: the number of adult tickets sold is 150

the number of student tickets sold is 210

Step-by-step explanation:

Let x represent the number of adult tickets sold.

Let y represent the number of student tickets sold.

The adult tickets cost $12 each, and the student tickets cost $8 each. The total cost of tickets sold $3,480. This means that

12x + 8y = 3480 - - - - - - - - - -1

The total number of tickets sold is 360. This means that

x + y = 360 - - - - - - - - - -2

Multiplying equation 1 by 1 and equation 2 by 12, it becomes

12x + 8y = 3480

12x + 12y = 4320

Subtracting

-4y = -840

y = -840/-4 = 210

Substituting y = 210 into equation 2, it becomes

x = 360 - y = 360 - 210

x = 150

To find the number of adult and student tickets sold, we can set up a system of equations and solve for the variables. Using the given information, we find that 150 adult tickets and 210 student tickets were sold.

To solve this problem, we can set up a system of equations. Let's let x represent the number of adult tickets and y represent the number of student tickets. From the given information, we can set up the following equations:

x + y = 360

12x + 8y = 3480

We can solve this system using the substitution method or the elimination method. Let's solve it using the substitution method:

From the first equation, we can express x in terms of y: x = 360 - y

Substituting this expression for x in the second equation, we get: 12(360 - y) + 8y = 3480

Simplifying the equation, we get: 4320 - 12y + 8y = 3480

Combining like terms, we have: -4y = -840

Dividing both sides by -4, we find: y = 210

Substituting this value of y back into the equation x + y = 360, we get: x + 210 = 360. Solving for x, we find: x = 150

Therefore, 150 adult tickets and 210 student tickets were sold.

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The 9-1-1 service fee on telecommunications bills is a type of tax such as service tax, fixed tax, business tax. Thus, the option (a), (d) and (e) is correct.

What is tax?

The term tax refers to the government charge the extra money for goods and services. The tax is also called as financial charge. The amount of tax are collect to government account as spent on public welfare. The public pay tax is compulsory. There are two types of tax such as direct tax and indirect tax.

The telecommunications bills are also included tax such as service tax, fixed tax, and business tax etc. The service tax is an indirect tax as charge on exchange of services. The fixed tax are apply on lump sum amount. The business tax is included income tax, and other expenses tax (wages, salaries etc.)

Therefore, option (a) (d) and (e) is correct.

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Answer:

Therefore the lengths of the opposite side pairs, AB and BC are 12 units and 6 units .

Step-by-step explanation:

Given:

[] ABCD is a Parallelogram.

∴ pairs of opposite sides are congruent

∴ AB = DC and

  BC = AD

To Find:

Length of AB = ?

Length of BC = ?

Solution:

[] ABCD is a Parallelogram. .............Given

∴ pairs of opposite sides are congruent

∴ AB = DC        and          BC = AD

On substituting the values we get

For 'x' i.e AB = DC  

[tex]4x=x+9\\\\4x-x=9\\\\3x=9\\\\x=\frac{9}{3}\\ \\x=3[/tex]

For 'y' i.e BC = AD

[tex]2y=6\\\\y=\frac{6}{2} \\\\y=3\\[/tex]

Now substituting 'x' and 'y' in AB and BC we get,

[tex]Length\ AB=4\times 3 =12\ units\\\\Length\ BC=2\times 3 =6\ units[/tex]

Therefore the lengths of the opposite side pairs, AB and BC are 12 units and 6 units .

C) 12, 6

Set opposite sides equal to each other and solve for x or y.

AB = DC → 4x = x + 9 → 3x = 9 → x = 3

So, AB = DC = 12

And,

AD = BC → 6 = 2y → y = 3

So, AD = BC = 6

Since in the question, there are no ordered pairs given so you can consider the below explanation to check which ordered pairs satisfies the inequality 3x-4y>12

Step-by-step explanation:

We need to identify which ordered pair(x,y) satisfies the inequality 3x-4y>12

The ordered pair (x,y) which satisfies the inequality will be the values of x and y that satisfies the inequality given 3x-4y>12

So, if x= 2 and y = 2 then the inequality will be:

3x-4y>12

3(2)-4(2)>12

6-8>12

-2>12 is false because -2 is not greater than 12

So, ordered pair (2,2) doesn't satisfy the inequality 3x-4y>12

Now if x = 10 and y = 2 then the inequality will be:

3x-4y>12

3(10)-4(2)>12

30-8>12

22>12 is true because 22 is greater than 12.

So, ordered pair (10,2) satisfies the inequality 3x-4y>12

Since in the question, there are no ordered pairs given so you can consider the above explanation to check which ordered pairs satisfies the inequality 3x-4y>12

Keywords: Solving inequalities

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To find the order pair (x,y) satisfying the inequality 3x - 4y > 12, substitute potential order pairs for x and y and evaluate. If the result is greater than 12, then the order pair satisfies the inequality.

The inequality given is 3x - 4y > 12. To find the order pair (x,y) that satisfies this inequality, let's plug in some potential solutions and see which one works.

For example, let's try the order pair (6, 1): 3(6) - 4(1) = 18 - 4 = 14, which is greater than 12, so (6,1) does satisfy the inequality.

But if we try the order pair (2, 3): 3(2) - 4(3) = 6 - 12 = -6, which is not greater than 12, so (2,3) does not satisfy the inequality.

Through these examples, you can see how we can find potential solutions to the inequality by substituting different order pairs for x and y.

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Answer:28 square shaped tiles of area 25 m^2 would be needed to cover the rectangular plot.

Step-by-step explanation:

The area of the rectangular plot is 700m^2

The area of each square tiles is 25m^2

The number of tiles needed to cover a rectangular plot would be

700/25 = 28 square shaped tiles

Answer: 73 songs

Step-by-step explanation:

The online music club has a one- time registration fee of $13.95 and charges $0.49 to buy each song. Let x represent the number of songs that a member buys. This means that the amount that a member who just joins the music club pays for x songs would be

0.49x + 13.95

If Emma has $50.00 to join the club and buy songs, the maximum number of songs she can buy would be expressed as follows

0.49x + 13.95 = 50

0.49x = 50 - 13.95 = 36.05

x = 36.05/0.49 = 73.57

the maximum number of songs she can buy is 73 since the number of songs cannot be a fraction.

50.00 - 13.95 = 36.05 (subtract the registration fee)

36.05/0.49 =  73.57 so she can buy 73 songs

The required cost of a computer Suzie will pay is $545.69.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
The original price of a computer is $599.99.
Suzie has a 15%-off coupon for the computer.
Discounted price = (1 - 0.15)×599.99

Discounted price = 0.85×599.99

A sales tax of 7% will be added to the sale price of the computer.
Price of the computer after taxes = (1 + 0.07)0.85×599.99
                                                   = $545.69

Thus, the required cost of a computer Suzie will pay is $545.69.

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Final answer:

To find how much Suzie will pay for a computer with a 15% discount and a 7% sales tax, first calculate the discount, then subtract it from the original price, calculate the sales tax on the sale price, and add it to the sale price. The total payment is the original price reduced by the discount and increased by the sales tax, rounded to the nearest cent would be approximately $545.69.

Explanation:

Calculation of Total Payment for the Computer with a Discount and Sales Tax

To calculate how much Suzie will pay for the computer after applying a 15%-off coupon and adding a 7% sales tax, you will need to perform two main calculations. First, calculate the discount amount by converting the percentage to a decimal and multiplying it by the original price. Second, calculate the sales tax on the discounted price by again converting the percentage to a decimal and multiplying it. Finally, add the sales tax to the discounted price to arrive at the total cost.

Here's a step-by-step breakdown of the calculations:

Add the sales tax to the sale price to find the total cost: $509.9915 + $35.699405 = $545.690905.

Therefore, the expression to calculate Suzie's total payment for the computer is ($599.99  times (1 - 0.15))  times (1 + 0.07). When actually performing the calculation, the total payment, rounded to the nearest cent, would be approximately $545.69.

To find the standard form of the circle's equation, one must determine the center and radius by solving a system of equations derived from the circle passing through the points (0,0), (2.8,0), and (5,2).

The question asks to write the standard form of the equation of the circle that passes through three given points, namely the origin, (2.8,0), and (5,2). The standard form for the equation of a circle is (x-h)² + (y-k)² = r², where (h,k) is the center of the circle, and r is the radius.

To find the equation, we need to determine the center and the radius. Since the circle passes through the origin, we can establish a system of equations based on the other two points which the circle passes through. We would end up with two equations:

By solving this system of equations, we can calculate the values of h, k, and r, and then plug these into the standard form equation of a circle.

Answer:

Option D) It is flawed because it is a voluntary response sample.

Step-by-step explanation:

We are given the following information in the question:

The subjects of the survey were internet users who responded to a question that was posted on a news website.

A total of 714 subjects responded to this question, answering the question, how often he or she read a book.

Option D) It is flawed because it is a voluntary response sample.

Voluntary response sample:

Answer:

15

sweatshirts were large and red.

Step-by-step explanation:

Hope this helps

Answer:the total number of sweatshirts in the shipment that were both large and red is 15

Step-by-step explanation:

The total number of sweatshirts received by Dans sporting goods is 120. Half of the sweatshirts were size large. This means that the number of sweatshirts that were size large is 120/2 = 60.

One-fourth of the large sweatshirts were red. This means that the number of large sweatshirts that were also red would be

1/4×60 = 15

Answer: There is decrease in percent of 26.47% from 2001 to 2008.

Step-by-step explanation:

Since we have given that

Number of runs that chipper had batted in 2001 = 102

Number of runs that chipper had batted in 2008 = 75

So, the year gap = 7 years

Difference in runs = 102- 75 =27

So, the percent change in runs batted from 2001 to 2008 is given by

[tex]\dfrac{27}{102}\times 100\\\\=\dfrac{2700}{102}\\\\=26.47\%[/tex]

Hence, there is decrease in percent of 26.47% from 2001 to 2008.

Yes, you are correct.

From the image, we can see 3 triangles, the large triangle and the two triangles that make the larger triangle.

All 3 of these triangles are similar since they're angle measurements are the same (can be proven by geometry).

We can gather the following information from the given information.

We know the hypotenuse to corresponding leg ratio must be equal since these two triangles are similar. Thus, we have the equation:

12/x = x/9

Using the cross product property gives us:

x² = 9 × 12

x² = 108

Taking the square root of both sides gives us:

x = √108

= 6 √3

Thus, your answer is correct. Great job!

Let me know if you need any clarifications, thanks!

Answer:

  4π -8

Step-by-step explanation:

Consider the attached diagram. The purple areas are those contained within 1 or 3 circles. The red areas are fully equivalent to the purple areas. The area of interest is the sum of the purple and red areas, or twice the red area.

Twice the red area is the area of the circle of radius 2 less the area of a square of diagonal 4.

For a circle of radius 2, its area is ...

  A = πr² = π·2² = 4π

For a square of diagonal 4, its area is ...

  A = (1/2)d² = (1/2)4² = 8

The area of interest is the difference of these, ...

  area of interest = circle area - square area

  = 4π -8

Answer:

The probability of getting a four of a kind is 29/23030 = 0.00126.  

Step-by-step explanation:

The poker deck has 52 cards, divided in 4 suits, and each suit has 13 different denominations.

In this exercise you are given that the 2 cards you are dealt have different denominations, lets call them A and B, so in order to make a 4 of a kind, you need to get from the 5 remaining community cards, 3 cards that have the denomination of one of A or B.

You cant get a four of a kind with two different denominations at the same time, because you need to reserve the majority of the community cards for just one of them. So each four of a kind is a disjoint event from the others.

Recall that, apart from the obvius four of a kind that you can get with A and B, you can still get four of a kind with any other denomination, because 4 of the community cards can still have the same denomitation.

Lets first calculate the probability to get a four of a kind with A. With B it is the same computation and the result will, therefore, be the same.

First, note that the order in which the cards are given doesnt matter, so we can calculate the probability of getting triple A in the flop (in other words, the first 3 given cards), and then multiply by all possible permutations.

Since you start with one A in your hand, there are 3 in the deck of 50 cards (remove the two cards given to you). The probability of drawing the first A is 3/50. The probability to draw the second A once you drew the first one is 2/49 (because you removed another A from the deck). The probability for the third A to be drawn is 1/48. This gives us a probability of

3/50 * 2/49 * 1/48 = 1/19600

of drawing the 3 A in the first 3 given cards. The other 2 cards can be anything.

To draw 3 aces in 5 cards we need to multiply be the total amount of ways to put 3 cards in a set of 5. That number is equivalent to the number of ways to pick places for the three A ignoring the order for them. That is, [tex] {5 \choose 3} = 10 . [/tex] So, in total, the probability to get a four of the kind A is

10 * 1/19600 = 1/1960

Similarly, the probability to get a four of a kind with B is 1/1960.

To get a four of a kind with any other kind, we need first to specify the kind; we have 13-2 = 11 possibilities to choose (we substract the 2 kinds A and B). Then we need to specify how the cards of that kind will be placed among the community cards. We have as many possibilities as the total amount of ways to pick where the other card will be, that is, 5 possibilities. Hence, we have 55 possibilities to make a four of a kind with a kind different than A or B.

We need to calculate now what is the probability of getting 4 cards of a specific kind in a specific way, for example, the first four cards. That probability is

4/50 * 3/49 * 2/48 * 1/47 = 1/230300

because we start with 50 cards on the deck with 4 cards of them being of the kind we need, and we remove them one by one.

As a result, the probability of getting a four of a kind with a different kind than A and B is 55/230300 = 11/46060.

By summing disjoint cases, We conclude that that the probability to get a four of a kind is

11/46060 + 1/1960 + 1/1960 = 29/23030 = 0.00126  

Answer:

The answer to your question is   -3x² + 29x -150

Step-by-step explanation:

                                -3x² + 29x -150

  x³ + 6x² - 3x - 5     -3x⁵ + 11x⁴ + 33x³ - 26x² - 36x - 6

                                +3x⁵ +18x⁴ -   9x³  - 15x²

                                   0     29x⁴ +24x³ - 41x² - 36x

                                         -29x⁴ - 174x³ +87x²+145x

                                            0     -150x³ +46x² +109x - 6

                                                  +150x³ +900x²-450x -750

                                                       0       946x² -341x -756

Quotient =   -3x² + 29x -150

Remainder = 946x² -341x -756

Answer:

x = -0.5.

Step-by-step explanation:

x^2 = 16^x

One way to do this is to use 2 graphs  y = x^2 and y = 16^x  .

The solution  is where the 2 graphs intersect.

The answer is x = -0.5.

========================================

Work Shown:

Let P and Q be two concentric circles

P = area of circle with radius 19

P = pi*r^2

P = pi*19^2

P = 361pi

-------

Q = area of circle with radius 29

Q = pi*r^2

Q = pi*29^2

Q = 841pi

-------

R = area of shaded region between circle P and circle Q

R = region outside circle P, but inside circle Q

R = Q - P

R = 841pi - 361pi

R = 480pi

------

S = area of circle with area equal to region R's area

S = 480pi

S = pi*r^2

pi*r^2 = 480pi

r^2 = 480

r = sqrt(480)

r = sqrt(16*30)

r = sqrt(16)*sqrt(30)

r = 4*sqrt(30)

Answer:

A) 1525

B) 4636

C) 8479

Step-by-step explanation:

Lest say that The book had been sold x copies in the period of June 1990-June 1995. And we know that the book had been sold 152*x/100 copies in the period of June 1995–June 2000. By June 2000 in total 3843 book had been sold. Therefore number of the copies that sold in the period of June 1990-June 1995 is:

[tex]252*x/100=3843\\x=1525[/tex]

number of the copies that sold in the period of June 1995-June 2000 is:

[tex]152*x/100=2318[/tex]

For the period June 2000–June 2005 2318*2=4636 book had been sold.

188 children and 155 adults were admitted that day.

Step-by-step explanation:

Given,

Cost of one children admission = $2.50

Cost of one adult admission = $5.80

Number of people entered = 343

Total admission fees collected = $1369

Let,

Number of children admission = x

Number of adult admission = y

According to given statement;

x+y=343     Eqn 1

2.50x+5.80y=1369     Eqn 2

Multiplying Eqn 1 by 2.50

[tex]2.50(x+y=343)\\2.50x+2.50y=857.50\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](2.50x+5.80y)-(2.50x+2.50y)=1369-857.50\\2.50x+5.80y-2.50x-2.50y=511.50\\3.30y=511.50[/tex]

Dividing both sides by 3.30

[tex]\frac{3.30y}{3.30}=\frac{511.50}{3.30}\\y=155[/tex]

Putting y=155 in Eqn 1

[tex]x+155=343\\x=343-155\\x=188[/tex]

188 children and 155 adults were admitted that day.

Keywords: linear equation, subtraction

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Answer:

In 9 days will the second warehouse have 1.5 times more coal than the first one

Step-by-step explanation:

The coal left in warehouses after x days can be found using the equation:

Let the second warehouse have 1.5 times more coal than the first one after n days then  

=========================

Explanation:

Let's label each pair of outcomes as an ordered pair (x,y)

x = first spinner outcome

y = second spinner outcome

We have these 12 different possible combos

(1,3),   (1,4),   (1,5),   (1,6)

(2,3),  (2,4),  (2,5),  (2,6)

(3,3),  (3,4),   (3,5),  (3,6)

Focus on the third column where y = 5 for each (x,y) pair. Of this column only (2,5) has x be an even number. The other results in that column have x be odd.

Basically (1,5) is the only possible outcome if we want the first spinner to lan on an even number, and the second spinner to land on 5.

In these conditions, there is only one outcome where the first spinner does not show an odd number and the second spinner shows a 5.

The problem involves two spinners. The first spinner has three sections labeled as 1, 2, and 3, while the second spinner has four sections labeled as 3, 4, 5, and 6. We are looking for cases where the result from the first spinner is not an odd number and the result from the second spinner is 5.

On the first spinner, the only non-odd digit is '2'. On the second spinner, the number '5' is what we seek. Therefore only one outcome will satisfy both conditions - when the first spinner lands on 2 and the second spinner on 5.

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what's the answer choices

Answer:

See explanation below

Step-by-step explanation:

In fact, the interval has to be closed (just as [a,b], for b>a). Otherwise, this is not neccesarily true. For example, consider the function f(x) = -1/x defined on the open interval (0.1). f is continuous (quotient of continuous functions) but it does not have a minimum value: it decreases infinitely near zero.

To show this result on the interval [a,b], the idea is the following:

We can use a previous theorem. If f is continuous on [a,b], there exists some N>0 such that N≤f(x) (that is, f is bounded below). Now, we take the biggest N such that N≤f(x) for all x∈[a,b] (this is known as the greatest lower bound)

The number N is the candidate for the minimum value of f. Next, we have to show that there exists some p∈[a,b] such that f(p)=N. To do this, we must use the continuty of f on [a,b]. There are many ways to do it, and usually they require the epsilon-delta definition of continuity.

This is just a description of the ideas involved, but of course, a rigorous proof would need more technical details, depending on the theorems you are allowed to use.  

Gallons of water are leaked in one year is 94.253 gallons

Given that leaky faucet drips 356,755 mL of water over the course of the year

There are approximately 3,785 mL in 1 gallon.

To find: gallons of water are leaked in one year

From given information,

Amount of water leaked in one year in ml = 356,755 mL

Also given in question that,

[tex]1 \text{ ml} = \frac{1}{3785} \text{ gallons}[/tex]

Now we can convert 356,755 mL to gallons

[tex]356,755 \text{ ml} = \frac{1}{3785} \times 356755 \text{ gallons}\\\\356,755 \text{ ml} = 94.253 \text{ gallons}[/tex]

Thus gallons of water are leaked in one year is 94.253 gallons

Answer:

d. x < 9.02 or x > 9.48 because |x − 9.25| > 0.23

Step-by-step explanation:

Given,

The standard weight of the pack = 9.25 oz,

The pack must weigh within 0.23 oz of the target weight to be accepted.

i.e. if x represents the weight of the pack,

If x > 9.25 oz

then x - 0.925 ≤ 0.23  ......(1)

if x < 9.25

then 9.25 - x ≤ 0.23

⇒ -(x-9.25) ≤ 0.23   .......(2)

From equation (1) and (2),

The accepted range of mass is,

|x-9.25| ≤ 0.23

Hence, the rejected range mass would be,

|x-9.25| > 0.23

⇒ x - 9.25 > 0.23 or -x + 9.25 < 0.23

⇒ x > 0.23 + 9.25 or -x > 0.23 - 9.25

⇒ x > 9.48 or - x > −9.02

⇒ x > 9.48 or  x < 9.02

Answer:

V (max)  = 2 ft³

and x side of the base is  x  =  0,5 feet

Step-by-step explanation:  See annex ( two different cubes)

We have a square piece of cardboard of  3 inches wide

Let  x be lenght of side to cut in each corner

Then the base of the (future cube) is    3  -  2x,  and the area is  

( 3 - 2x )²

And  the height   is x  Then volume of the cube as a function of x is:

V(x)  =  ( 3 - 2x )² *x   or       V(x)  =    ( 9 + 4x² - 12x )*x

V(x)  =  4x³  -  12x²  + 9x

Taking derivatives on both sides of the equation

V´(x)  =  12x² - 24x  + 9

V´(x)  =  0       12x² - 24x  + 9  =  0   simplifying   4x² - 8x  + 3  =  0

Second degree equation solving for x

x₁,₂ =  [ 24 ± √( 576) - 432  /24

x₁,₂ =  [24 ±√144 ]/24

x₁,₂ = ( 24 ± 12) /24         x₁  =  1.5 feet        x₂  = 0,5 feet

Of these two values we have to dismiss x₁  because if  x = 1.5 we don´t have a cube ( 0 height )

Then we take x  = 0,5  feet

And

V (max)  =  (2)²*0,5   =  4*0,5

V (max)  = 2 ft³