A bakery sells 6 rolls for $1.50. If this relationship is graphed with the number of rolls on the x-axis and the cost on the y-axis, what is the slope of the graph in dollars per roll?

Partial fractions:

[tex]\displaystyle \frac1{(n^2-1)^2} = \dfrac14 \left(\frac1{n+1} - \frac1{n-1} + \frac1{(n+1)^2} + \frac1{(n-1)^2}\right)[/tex]

Now evaluate the sums. The first two terms form a telescoping sum,

[tex]\displaystyle \sum_{n=2}^\infty \left(\frac1{n+1} - \frac1{n-1}\right) = \sum_{n=1}^\infty \left(\frac1{n+2} - \frac1n\right) \\\\ ~~~~~~~~ = \lim_{N\to\infty} \sum_{n=1}^N \left(\frac1{n+2} - \frac1n\right) \\\\ ~~~~~~~~ = \lim_{N\to\infty} \left(\frac1{N+2} + \frac1{N+1} - 1 - \frac12\right) \\\\ ~~~~~~~~= -\frac32[/tex]

The others are flavors of [tex]\zeta(2)[/tex].

[tex]\displaystyle \sum_{n=2}^\infty \frac1{(n+1)^2} = \sum_{n=3}^\infty \frac1{n^2} \\\\ ~~~~~~~~~~~~~~~~~ = \sum_{n=1}^\infty \frac1{n^2} - 1 - \frac1{2^2} \\\\ ~~~~~~~~~~~~~~~~~ = \frac{\pi^2}6 - \frac54[/tex]

[tex]\displaystyle \sum_{n=2}^\infty \frac1{(n-1)^2} = \sum_{n=1}^\infty \frac1{n^2} \\\\ ~~~~~~~~~~~~~~~~~ = \frac{\pi^2}6[/tex]

It follows that

[tex]\displaystyle \sum_{n=2}^\infty \frac1{(n^2-1)^2} = \frac14 \left(-\frac32 + \left(\frac{\pi^2}6 - \frac54\right) + \frac{\pi^2}6\right) = \boxed{\frac{\pi^2}{12} - \frac{11}{16}}[/tex]

Answer:

 does not exist

Step-by-step explanation:

You want an integer between -5 and -6.

The integers -5 and -6 are consecutive integers. There are no integers between these values. (That's what "consecutive" means.)

Answer:

Step-by-step explanation:

f(x)=-7ex

f(2)=-7e(2)

    f(2)=-10

Answer:

7(x + 4) = 70

x = 6

Step-by-step explanation:

7(x + 4) = 70  Distribute the 7.  Multiply everything inside the parentheses by 7

7x + 28 =70  Subtract 28 from both sides of the equation

7x = 42  Divide both sides by 7

x = 6

The option after high school for Jon, an active person, who is interested in higher education but who doesn't want to take out student loans is to take a reflection year.

It should be noted that based on the information, the inference has to do with the conclusion that one gets from the information or evidence that is given earlier.

In this instance, it should be mentioned that Jon, an energetic individual interested in further education but unwilling to take out student debt, has the choice to take a reflection year following high school.

In conclusion, the correct option is C.

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The probability that you will not go on to a career in physics is 0.215.

From the information, the test is so tough that anyone not going on to a career in physics has no hope of passing, whereas 55% of the seniors who do go on to a career in physics still fail the test and 75% of all senior physics majors in fact go on to a career in physics.

Therefore, the probability that you will not go on to a career in physics will be:

= (1 - 0.75) / (0.75 × 0.55) + (0.75)

= 0.25 / (1.1625)

= 0.215

Therefore, the probability that you will not go on to a career in physics is 0.215.

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It should be noted that the product of the fractions 5/2 and 2/3 will be 5/3.

It should be noted that this is a number that is expressed as a quotient, in which a numerator is divided by a denominator.

Therefore, it should be noted that the product of the fractions 5/2 and 2/3 will be illustrated as thus:

= 5/2 × 2/3

= 5/3.

Therefore, the product of the fractions 5/2 and 2/3 will be 5/3.

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Answer:

All I can think of is ¨pattern¨

The degree of the resulting polynomial, 5x^4^y² - x^3y - 12y + 8x, after subtraction is: degree 4.

Given, (10x^4y^2 - 9x^3y - 9y) - (5x^4^y2 + 10x^3y + 12y - 8x), to subtract, open the parentheses using the distributive property.

10x^4y^2 - 9x^3y - 9y - 5x^4^y² - 10x^3y - 12y + 8x

Combine like terms together

10x^4y^2 - 5x^4^y² - 9x^3y - 10x^3y - 9y - 12y + 8x

5x^4^y² - x^3y - 12y + 8x

The highest degree is 4. This determines the degree of a polynomial.

Therefore, the degree of the resulting polynomial, 5x^4^y² - x^3y - 12y + 8x, after subtraction is: degree 4.

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Answer:

True sometimes when it is stressful.

Step-by-step explanation:

Answer:

Step-by-step explanation:

your very right

From the union operation between sets, we have that the number of elements for each case will be as follows:

a) 11069.

b) 9975.

c) 11031.

The union operation between sets is the set that contains all elements that belong to at least one of the sets.

In item a, if the sets are disjoint, all the elements belong to only one set, and the number of elements in A1∪A2∪A3 is given by:

102 + 992 + 9975 = 11069.

For item b, if they are all contained into A3, the number of elements is the cardinality of A3, given by 9975.

For item c, we have that:

Hence:

n(A1∪A2∪A3) = 4 + 3 x 10 + 78 + 968 + 9951 = 11031.

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Answer:

140

Step-by-step explanation:

the square root of 16 is 4 so do that times 35

Answer:

87+(4+8)=(7+4)+x

87+12=11+x

87+12-11=x

88=x

Mark has 18 and Don has 77 number of marble to sell.

Let’s say Mark has x number of marble and Don’s marble number is y.

According to this problem we have,

Y = 4x +5

And x + y = 95

Or, x + 4x + 5 = 95

Or, 5x = 90

Or, x = 18 and y = 77  

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Answer:

8 boys and 16 girls

Step-by-step explanation:

2 boys plus 4 girls is six and six goes into 24 four times so 2 times four is eight and 4 times four is 16

Answer:

Step-by-step explanation: Since there are 24 students in total and the ratio is 2:4 then divide 24 by (2+4) which is 4. So the amount of boys is 2x4 which is 8. The amount of girls is 4x4 which is 16. 8+16=24

The required number of people that are in the US labor force is 0.0086t² + 0.087t + 25.375.

To determine the total number of people available in the US labor force.

In mathematics, it deals with numbers of operations according to the statements.

Here,
As per the data available, the number of Men in the US labor force is M = 0.0016t² + 0.315t + 19.467 and the number of women are W = 0.007t² -0.228t + 5.908.
Total people available in the US labor force,
= Number of women + number of men
= 0.0016t² + 0.315t + 19.467 + 0.007t² -0.228t + 5.908
=  0.0086t² + 0.087t + 25.375.

Thus, the required number of people that are in the US labor force is 0.0086t² + 0.087t + 25.375.

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The term of highest degree is given as 3x⁴,and it has a positive coefficient. The upper bound is +∞.

To determine the degree of a polynomial just observe the highest power of the given variable.

We have polynomial given by f(x) = 3x⁴ - 7x³  +5x -3

Here we can see that it is a polynomial in of degree 4.

We know that a polynomial of degree has n number of roots so it is obvious a polynomial of degree 4 has 4 roots.

The function that tends to infinity as x goes in both the positive and negative directions.

The term of highest degree is given as 3x⁴,and it has a positive coefficient.

The upper bound is +∞.

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The actual height of Caleb based on the ratio in the photograph and actual is 48 inches.

The ratio is the division of the two numbers.

Proportion is the relation of a variable with another. It could be direct or inverse.

Let's say Allison and Caleb's height in the photograph is A' and C' while in actuality it is A and C.

Since the ratio of height in the photograph will same as the ratio in actual life.

Thereby,

C/A = C'/A'

C/60 = 3.2/4

C = 192/4

C = 48 inches.

Hence "The actual height of Caleb based on the ratio in the photograph and actual is 48 inches".

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Given question is incomplete complete question follows ;

In a photograph, Alison stands next to her brother Caleb. Alison is 4 cm tall in the photograph. Her actual height is 60 in. Caleb is 3.2 cm tall in the photograph.

What is his actual height?

(Show your work)

The number of watts it will consume is 436.32

A light bulb consumes 2400 watts/hour

The number of watts it will consume in 5 days 12 hours can be calculated as follows

The first step is to change 5 days 12 hours to hours

120 hours + 12 hours

= 132 hours

The bulb consumes 2400 watts per hour

= 2400/132

= 18.18

The number of watts consumed in 5 days 12 hours is

= 24 × 18.18

= 436.32

Hence the light bulb will consume 436.32 watt-hour in 5 days 12 hours

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Answer:

Answer is in the picture attached

Answer:

• 5/10

• 0.5

Step-by-step explanation:

1.) if you multiply the numerator by 5 and the denominator by 5 you are left with a fraction of 5/10.

2.) the fraction line represents division. So 5 ÷ 10 = 0.5.

The confidence limits for the proportion of consumers motivated by advertising in the population, given a confidence level equal to 0.95. is; CI = (0.47, 0.77)

We are given;

Sample Size; n = 60

sample proportion; p' = 65% = 0.65

Confidence level = 0.95

Now, formula for confidence interval of proportion is;

CI = p' ± z√(p(1 - p)/n)

At CL of 95%, z = 1.96Thus;

CI = 0.65 ± 1.96√(0.65(1 - 0.65)/60)

CI = 0.65 ± 1.96√0.00379167

CI = 0.65 ± 0.12

CI = (0.65 - 0.12), (0.65 + 0.12)

CI = (0.47, 0.77)

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After the conversion, we get T² = 1/3 A

It is given that

T = [tex]A^{\frac{3}{2} }[/tex]

We have to convert the equation without rational exponents

T³ = A²

1/2 T = A³

T² = A³

T² = 1/3A

Therefore we get T² = 1/3 A without using the exponents.

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The computation shows that the tons of sugar when they'll have same price is 18 tons.

The first company charges $5500 to rent trucks plus an additional fee of $200.25. Thai will be:

= 5500 + (200.25 × s)

= 5500 + 200.25s

where s = tons of sugar

The second company charges $5041 to rent trucks plus an additional fee of $225.75 for each ton of sugar. This will be:

5041 + 225.75s

Then we will equate both of them. This will be:

5500 + 200.25s = 5041 + 225.75s

5500 - 5041 = 225.75d - 200.25s

459 = 25.5s

s = 459/25.5

s = 18

At 18 tons, they'll have same price.

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The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $5500 to rent trucks plus an additional fee of $200.25 for each ton of sugar. The second company charges $5041 to rent trucks plus an additional fee of $225.75 for each ton of sugar. For want mount if sugar do they charge the same price.

Answer:

its the first alternative

Answer: correct me if I’m wrong

Step-by-step explanation:

Answer:

6.5 kilometers per hour

Step-by-step explanation:

90 minutes is 1  1/2 hours.

to find the unit rate you would divide the distance by the time so you would divide 9.75 by 1.5 (1.5 is the decimal version of 1  1/2) which would give you 6.5 kilometers per hour

Answer:

70 squares

Step-by-step explanation:

this is my answer to your question

Answer:

Hello,

100

Step-by-step explanation:

a square 4*4 : wide=4 , lenght=4

number of rectangles= wide*(wide+1)*lenght*(lenght+1) /4 = 4*5*4*5/4=100

Proof:

1 per 1 : 16 (rectangles )

1 per 2: 3*4=12

1 per 3: 2*4=8

1 per 4: 1*4=4 so 4*(4+3+2+1)=4*10=40

2 per 1: 4*3

2 per 2: 3*3

2 per 3: 2*3

2 per 4: 1*3 so 3*(4+3+2+1)=30

3 per 1: 4*2

3 per 2: 3*2

3 per 3: 2*2

3 per 4: 1*2 so 2*(4+3+2+1)=20

4 per 1: 4

4 per 2: 3

4 per 3: 2

4 per 4: 1 so 1*(4+3+2+1)=10

Total=40+30+20+10=(4+3+2+1)*(4+3+2+1)=100