a jar of jelly beans that weigh 4.25 ounces costs 2.89. what is the cost of one ounce of jelly

Answer:

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

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Addition/Subtraction]:                                                         [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]  

Basic Power Rule:

Derivative Rule [Quotient Rule]:                                                                           [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = \frac{\cos (x - 1)}{x - 1}[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Step-by-step explanation:

We have been given that [tex]\frac{2}{3}a=16[/tex].

Since multiplicative inverse property states that any number multiplied by its reciprocal is equal to one.

[tex]\frac{2}{3}\times \frac{3}{2} =1[/tex]

To solve for a let us divide 16 by [tex]\frac{2}{3}[/tex].

[tex]a=16\div \frac{2}{3}[/tex]

Since dividing a number by fraction is same as multiplying the number by the reciprocal of fraction. So we will multiply 16 by [tex]\frac{3}{2}[/tex].

[tex]a=16\times\frac{3}{2}[/tex]

[tex]a=8\times 3[/tex]

[tex]a=24[/tex]

We can see that to solve for a we have multiplied 16 by [tex]\frac{3}{2}[/tex] and [tex]\frac{3}{2}[/tex] is reciprocal of [tex]\frac{2}{3}[/tex].

Let us verify our answer by substituting a=24 in our given equation.

[tex]\frac{2}{3}\times 24=16[/tex]

[tex]2\times 8=16[/tex]

[tex]16=16[/tex]

Hence, to find the value of a we used multiplicative inverse property.

If the 4 states have to be in a specific order say ABCD, then the total number of different possible routes is:

 43P4 = 2,961,840

So the probability is:

1 / 2,961,840 = 3.38 x 10^-7

But if the 4 states can be in any order such as DBAC, ACBD etc, then the total number of different possible routes is:

 43C4 = 123,410

So the probability is:

1 / 123,410 = 8.1 x 10^-6

No I don’t think it is practical to list all the different possible routes to select the one that is best. We can simply use mathematical models to solve for that one.

The 6 in 600 has a value one tenth the value of the 6 in 34, 761.

The question asks in which number does the 6 have a value that is one tenth the value of the 6 in 34, 761.

To find the answer, we need to compare the place value of the 6 in both numbers. In 34, 761, the 6 is in the thousands place, and its value is 6,000. To have a value that is one tenth of 6,000, the 6 would need to be in the hundreds place in the other number.

So, the number in which the 6 has a value one tenth the value of the 6 in 34, 761 would be 600.

Final answer:

The number 6 in 2,001.06 is one-tenth the value of the 6 in 34,761.

Explanation:

The number 6 in 34,761 has a value that is one-tenth the value of the 6 in the number 2,001.06.

To find this, we can compare the place values of the two 6's. The 6 in 34,761 is in the ones place, while the 6 in 2,001.06 is in the tenths place.

Since the tenths place is one place to the right of the ones place, the value of the 6 in 2,001.06 is one-tenth the value of the 6 in 34,761.

multiply 4 by 9.99 for cost of the 4 dvd's

9.99 *4 = 39.96

20% discount is: 39.96 *0.20 = 7.99

39.96 - 7.99 = 31.97

now add the sales tax:

31.97 * 1.0675 = 34.13

 total cost is $34.13

Answer:

  36

Step-by-step explanation:

36 is a factor of both numbers

_____

If the smaller divides the larger with no remainder, then the smaller number is the greatest common factor.

If there is a remainder, replace the larger number with that and repeat the process.

The data on student heights and weights suggests a strong positive correlation, implying that as a student's height increases, their weight tends to increase as well.

The data provided on student's heights and weights suggests a linear relationship. To complete the sentences based on the data:

The data seems to have a correlation coefficient close to positive one. This indicates that the weight of a student increases as the height of the student increases.

In statistics, when we observe that as one variable increases, the other also increases, we describe this as a positive correlation. A positive correlation coefficient closer to +1 implies a strong positive correlation, meaning that generally taller students in the given data set tend to weigh more.

Final answer:

The correlation coefficient for the given data is approximately 0.86, indicating a positive correlation between height and weight.

Explanation:

The data seems to have a correlation coefficient close to 0.86. This indicates that the weight of a student increases as the height of the student increases.

2A on 2A + 3B + 3C = 8 pieces

The probability:

[tex]\dfrac{2}{8}=\dfrac{2:2}{8:2}=\dfrac{1}{4}[/tex]

[tex]\dfrac{1}{4}=\dfrac{1}{4}\cdot100\%=25\%[/tex]

To write the given equation in vertex form, we need to complete the square for the x terms. The vertex form of a quadratic equation is y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola. After completing the square and rearranging the equation, we find that the equation in vertex form is y = 171(x + 7391/4) - 17113/4.

To write the given equation in vertex form, we need to complete the square for the x terms. The vertex form of a quadratic equation is given by y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.

Let's rearrange the equation to isolate the x terms on one side and the y term on the other side: 162x + 9x + y = -731 - 2

Combine like terms: 171x + y = -733

Now, we can complete the square for the x terms. Divide the coefficient of x by 2 and square the result. Add this value to both sides of the equation: 171x + y + (171/2)^2 = -733 + (171/2)^2

Simplify: 171x + y + 7391/4 = 17113/4

Finally, we can rewrite the left side as a binomial squared and simplify the right side: 171(x + 7391/4) + y = 17113/4

Therefore, the equation in vertex form is: y = 171(x + 7391/4) - 17113/4

The given equation is:

x y – 5000 = y

Rewrite this to create an explicit equation:

x y – y = 5000

y ( x – 1) = 5000

y = 5000 / (x – 1)

Derive to get dy / dx:

dy = - 5000 dx / (x – 1)^2

dy / dx = - 5000 / (x – 1)^2

So plugging in x = 6,

dy / dx = - 5000 / (6 – 1)^2

dy / dx = - 200

Answer:

[tex]\frac{dy}{dx}|_{x=6}= -200[/tex]

Step-by-step explanation:

Given : Demand equation [tex]xy − 5,000 = y[/tex]

To Find [tex]\frac{dy}{dx}|_{x=6}[/tex]

Solution :

[tex]xy- y= 5000[/tex]

[tex]y(x-1)= 5000[/tex]

[tex]y= \frac{5000}{x-1}[/tex]

Differentiating with respect to x

[tex]\frac{dy}{dx}= \frac{-5000}{(x-1)^2}[/tex]

Now substitute x = 6

[tex]\frac{dy}{dx}|_{x=6}= \frac{-5000}{(6-1)^2}[/tex]

[tex]\frac{dy}{dx}|_{x=6}= \frac{-5000}{5^2}[/tex]

[tex]\frac{dy}{dx}|_{x=6}= \frac{-5000}{25}[/tex]

[tex]\frac{dy}{dx}|_{x=6}= -200[/tex]

Hence [tex]\frac{dy}{dx}|_{x=6}= -200[/tex]  =T-shirts per dollar

If a school has 30 teachers and there is a 10% reduction, there will be 27 teachers remaining.

If a school employs 30 teachers and there is a 10% reduction, we can calculate the number of teachers after the reduction by multiplying the initial number of teachers by (100% - 10%) = 90%. So, there will be 30 * 0.90 = 27 teachers after the reduction.

https://brainly.com/question/31387045

#SPJ2

Answer:

a = -15

Step-by-step explanation:

Let's rewrite the exercise in math language.

We have to subtract a-4 from 4a+16 to get -25, that is

4a+16 - (a-4) = -25

The minus sign that is just before the parenthesis changes all the signs inside it. Therefore, if we want to delete the parenthesis, we need to change the signs before.

4a + 16 - a + 4 = -25

Now we can associate the terms with an a between them and the terms without it from the left side of the equation.

3a + 20 = -25

Let's subtract 20 on both sides.

3a + 20 - 20 = -25 - 20

3a = -45

Finally, we divide by 3 on both sides

3a/3 = -45/3

a = -15

Answer:

27 trees in each row

Step-by-step explanation:

Abe is going to plant 54 oak trees and 27 pine trees

 greatest number of trees Abe can have in each row =?

54 = 2 x 27

27 = 1 x 27

Now 27 is the common in both numbers and also is the greatest number

So, there are 2 rows of oak trees and 1 row of pine trees and all the rows have 27 number of trees.