At Frosty Freeze, 14 of the last 18 sundaes sold had nuts. What is the experimental probability that the next sundae sold will have nuts?

Answer:

[tex]\displaystyle \boxed{ \frac{dz}{du} = \frac{e^\big{\frac{u(2u + v)}{v}}}{v} \Bigg[ 4u + v \Bigg] }[/tex]

[tex]\displaystyle \boxed{ \frac{dz}{dv} = \frac{ue^\big{\frac{u(2u + v)}{v}}}{v} \Bigg[ 1 - \frac{2u + v}{v} \Bigg] }[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:
[tex]\displaystyle (cu)' = cu'[/tex]

Derivative Property [Addition/Subtraction]:
[tex]\displaystyle (u + v)' = u' + v'[/tex]

Derivative Rule [Basic Power Rule]:

Multivariable Calculus

Partial Derivatives

Partial Derivative Rule [Chain Rule]:
[tex]\displaystyle \frac{dw}{dt} = \frac{\partial w}{\partial x} \frac{\partial x}{\partial t} + \frac{\partial w}{\partial y} \frac{\partial y}{\partial t} + \frac{\partial w}{\partial z} \frac{\partial z}{\partial t}[/tex]

Step-by-step explanation:

Step 1: Define

Identify given.

[tex]\displaystyle x = 2u + v[/tex]

[tex]\displaystyle y = \frac{u}{v}[/tex]

[tex]\displaystyle z = e^{xy}[/tex]

Step 2: Find Derivatives

[tex]\displaystyle \frac{dz}{du}[/tex]:

We can find the partial derivatives by differentiating using basic differentiation rules found under "Calculus":

[tex]\displaystyle\begin{aligned}\frac{\partial z}{\partial x} & = ye^{xy} \\\frac{\partial x}{\partial u} & = 2 \\\frac{\partial z}{\partial y} & = xe^{xy} \\\frac{\partial y}{\partial u} & = \frac{1}{v} \\\end{aligned}[/tex]

Substituting in our partial derivatives and our variables x and y, we can obtain a final derivative:

[tex]\displaystyle\begin{aligned}\frac{dz}{du} & = 2ye^{xy} + \frac{xe^{xy}}{v} \\& = \frac{2ue^\big{\frac{u(2u + v)}{v}}}{v} + \frac{(2u + v)e^\big{\frac{u(2u + v)}{v}}}{v} \\& = \boxed{ \frac{e^\big{\frac{u(2u + v)}{v}}}{v} \Bigg[ 4u + v \Bigg] }\end{aligned}[/tex]

∴ we have found the derivative of z with respect to u.

[tex]\displaystyle \frac{dz}{dv}[/tex]:

We can find the partial derivatives by using the same method(s):

[tex]\displaystyle\begin{aligned}\frac{\partial z}{\partial x} & = ye^{xy} \\\frac{\partial x}{\partial v} & = 1 \\ \frac{\partial z}{\partial y} & = xe^{xy} \\\frac{\partial x}{\partial v} & = \frac{-u}{v^2} \\ \end{aligned}[/tex]

Substituting in our partial derivatives and our variables x and y, we can obtain a final derivative:

[tex]\displaystyle\begin{aligned}\frac{dz}{dv} & = ye^{xy} + \frac{-uxe^{xy}}{v^2} \\& = \frac{ue^\big{\frac{u(2u + v)}{v}}}{v} + \frac{-u(2u + v)e^\big{\frac{u(2u + v)}{v}}}{v^2} \\& = \boxed{ \frac{ue^\big{\frac{u(2u + v)}{v}}}{v} \Bigg[ 1 - \frac{2u + v}{v} \Bigg] }\end{aligned}[/tex]

∴ we have found the derivative of z with respect to v.

---

Learn more about partial derivatives: https://brainly.com/question/6212480

Learn more about multivariable calculus: https://brainly.com/question/12680404

---

Topic: Multivariable Calculus

Unit: Partial Derivatives and Applications

There is no expression that is the same as the value of 2² – 3³ + 29 which is = 2.

To simplify the expression 2² – 3³ + 29. is as follows:

2² – 3³ + 29 = 4- 9+29

= 29 -5

= 24

Therefore, there is no expression that is the same as the value of 2² – 3³ + 29. which is 2.

Learn more about maths expressions here:

https://brainly.com/question/723406

#SPJ1

The length of AB is 4.12 units, length of BC is 8.25 units and Perimeter of rectangle ABCD is 24.74 units.

The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).

Here,

A (-3, 3) and B (1, 4)

then, Length of AB = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

                               = [tex]\sqrt{(1-(-3))^2+(4-3)^2 }[/tex]

                               = [tex]\sqrt{4^2 + 1^2}[/tex]

                               = [tex]\sqrt{17}[/tex] units.

                               = 4.12 units

B (1, 4) and C (3, -4)

then, Length of BC = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
                                = [tex]\sqrt{(3 - 1)^2+(-4 - 4)^2 }[/tex]

                                = [tex]\sqrt{4 + 64}[/tex]

                                = [tex]\sqrt{68}[/tex]

                                = 8.25 units

Perimeter of Rectangle = 2 ( AB + BC )

                                        = 2 ( 4.12 + 8.25 )

                                        = 2 X 12.37

                                        = 24.74 units

Thus, the length of AB is 4.12 units, length of BC is 8.25 units and Perimeter of rectangle ABCD is 24.74 units.

Learn more about Perimeter of Rectangle from:

https://brainly.com/question/15287805

#SPJ1

Part A: The IQR for the males' data.  23

Part B: The difference between the median values of each data set. 13

Part C: The distribution of the data and if the mean or median would be a better measure of center for each Median for the males and Mean for the females

Part D:The possible reason for the outlier in the data set. The day the movie premiered

The likely missing part of the question; The Box Plots are to compare The Number of Males and The Number of Females attending the latest superhero movie every day in a given month

The known parameters

The 5 number summary in a are;

Minimum                                         0           0

FIrst Quarlite Q1                             2           5

Second Quarlite, Mediun Q2        20         7

Third Quarlite                                 25         40

Maximum                                        50         18

Outlier                                                           46

Part A:

The Inter Quartile Range, IQR = Q₃ - Q₁

For the males, we have, IQR = 25 - 2 = 23

Part B:

The difference between the median values for the males and females is given as follows;

Difference between median = Q₂ Males - Q₂ Females

∴ Difference between median = 20 - 7 = 13

The difference between the median values for the males and females = 13

Part C:

The distribution of the data for the males is skewed left, with almost all the data in the first half

The better measure of center for the skewed data is the median, given

that three quarter of the data have values that are less than half of the

range of values in the data set, and that the median is close to the third

quartile, the mean will be located further towards the minimum value of

the data than the median

The distribution of the data for the females consists of the interquartile range located approximately in the middle between the max and the min values with the median being close to the first quartile, therefore, the mean will be a better measure of center as it will be located further from the first quartile and closer midway in the IQR

Part D;

The possible reason for the outlier in the data set may be due to the first day the latest super hero movie is premiered

To know more about data sets follow

https://brainly.com/question/4219149

#SPJ1

Answer:

D

Step-by-step explanation:

1/2 is not equal to 1/2.5 is not equal to 0.5/2.25.

The correct option regarding the difference in the length of the worms is given by:

6.5 cm; this is found by determining the range which is found by finding the difference between the greatest length and the least length.

It is given by the difference of the highest value by the lowest value in the data-set.

In this problem, the difference is exactly what we want to estimate, hence we need to consider all measures(which removes the mode and the median), and find the largest lowest and the highest, which is the range, hence:

19 cm - 12.5 cm = 6.5 cm.

Which means that the correct option is given by:

6.5 cm; this is found by determining the range which is found by finding the difference between the greatest length and the least length.

More can be learned about the range of a data-set at https://brainly.com/question/24374080

#SPJ1

Answer:

the answer is letter E.

see the attachment.

Answer:

Volume in terms of pi is 24

Step-by-step explanation:

formula for volume is pi x radius squared x height

3.14 x [tex]2^{2}[/tex] x 6=

75.36 then divide by pi

75.36/3.14=24pi in[tex]^{2}[/tex]

The actual distance is: 17500mm

A map scale is used to show the relationship between the distance on the map and the distance on the earth.

Analysis:

The scale 1:500 is a reduction scale, it means every 1 mm on the map represents 500mm on the ground

So if 1mm on the map represents 500mm on the ground, then 35mm on the map would be 500 x 35 = 17500mm

In conclusion, the actual distance between the two hidden treasures is 17500mm.

Learn more about map scale reading : brainly.com/question/230911

#SPJ1

The answer is

for parallel : x-4=0

for perpendicular: y+4=0

The slope-intercept form is written as y = mx+b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis). It's usually easy to graph a line using y=mx+b.

Given line: x=-7

The slope of line x=7 is infinite

The equation of line passing through point (4,-4) and having slope infinite is

0.y+x=-7

So, 0.y= 4

hence, x=4

slope intercept form

x-4=0

Now, for perpendicular lines:

swap the coefficients on x and y with negative sign of x in x=-7

This is a vertical line, so the perpendicular line will be a horizontal line of the form y=b.

Since we are given that the line should pass through the point (4,−4), then the equation of the line is y=−4.

Learn more about intercept equation here:

brainly.com/question/13300036

#SPJ1

Answer:22

Step-by-step explanation:

23 plus 26 plus 25 plus 24 plus 23 plus 24 plus 6 plus 24 plus 23= 198 so count how many numbers there are we had to add so its 198 divided by 9 gives you the answer  22

Answer:

-4585

Step-by-step explanation:

Answer:

Francis has $1,993.46 left of his pay stub

Step-by-step explanation:

earns $3437 dollars

42% to tax (yikes! almost half of their pay)

42% of $3437 dollars: $3437 x 0.42 = 1,443.54

Francis is paying $1,443.54 in taxes

$3437 - $1,443.54 = $1,993.46

The best pairing to complete the task in the shortest amount of time is You and Aunt 1 and it would take them 30 minutes.

This represents the fastest time it takes for a person to execute a task.

The time needed for all tasks for You is:

2.5 + 5 + 1.5 = 9 hours

The time needed for all tasks for Aunt 1 is:

1.5 + 4 + 3= 8.5 hours.

9 - 8.5 = 0.5 hours

= 30 minutes

The shortest amount of time to complete all tasks is 8.5 hours by Aunt 1

Read more about the shortest amount of time here:

https://brainly.com/question/1376106

#SPJ1

The number of people out of 2000 expected to use the app will be 1300.

A survey is a research method used for collecting data from a predefined group of respondents to gain information and insights into various topics.

It is given that:-

A store employee conducted a survey of 325 randomly selected customers. According to survey 212, customers often use the app to shop.

We need to find the data for 2000 people who visited the store.

So the percentage of the people who are using the app will be calculated as:-

[tex]= \dfrac{212}{3254}=65\%[/tex]

So the number of the people out of 2000 will be:-

[tex]N\ = 2000\times \dfrac{65}{100}=1300\ \[/tex]

Hence the number of people out of 2000 expected to use the app will be 1300.

To know more about the survey follow

https://brainly.com/question/25870256

#SPJ1

Answer:

See below

Step-by-step explanation:

[tex]\displaystyle \frac{\sec x\sin x}{\tan x+\cot x}\\\\=\frac{\frac{1}{\cos x} \sin x}{\frac{\sin x}{\cos x} + \frac{\cos x}{\sin x}}\\ \\=\frac{\frac{\sin x}{\cos x} }{\frac{\sin x \sin x}{\cos x \sin x} + \frac{\cos x \cos x}{\cos x \sin x}}\\\\=\frac{\frac{\sin x}{\cos x} }{\frac{\sin^2 x}{\cos x \sin x} + \frac{\cos^2 x}{\cos x \sin x}}\\\\=\frac{\frac{\sin x}{\cos x}}{\frac{\sin^2 x+\cos^2 x}{\cos x \sin x} }\\ \\=\frac{\frac{\sin x}{\cos x} }{\frac{1}{\cos x \sin x} }[/tex]

[tex]=\frac{\sin x}{\cos x}\cdot \sin x \cos x\\ \\=\frac{\sin x \sin x \cos x}{\cos x}\\ \\=\sin^2x[/tex]

Thus, the identity is proven. Match the options up accordingly to my step-by-step process.

Answer:

the answer is for this particular problem is F

Answer:

Option C . 6 cm , 8 cm and 10 cm

Step-by-step explanation:

Question : Which three side lengths best describe the triangle in the diagram?

As we can clearly see measurement of the scale [ refer to attachment ]

In Triangle ABC

Therefore option C is Correct.

Answer:

the answer is 126 cm

sana makatulong

Step-by-step explanation:

a=60°{vertically opposite angles}

b=180°-(52+110)°=18°

c=180°-(60+18)°=102°

d=180°-102°=78°

e=180°-(78+51)°=51°

Answer:

[tex]a_n=3n-2[/tex]

Step-by-step explanation:

General form of an arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]

where:

Create expressions for the 4th and 6th terms:

[tex]\implies a_4=a+(4-1)d=a+3d[/tex]

[tex]\implies a_6=a+(6-1)d=a+5d[/tex]

The ratio of the 4th term to the 6th term is 5:8, therefore:

[tex]\implies \dfrac{a_4}{a_6}=\dfrac{5}{8}[/tex]

[tex]\implies \dfrac{a+3d}{a+5d}=\dfrac{5}{8}[/tex]

[tex]\implies 8(a+3d)=5(a+5d)[/tex]

[tex]\implies 8a+24d=5a+25d[/tex]

[tex]\implies 8a-5a=25d-24d[/tex]

[tex]\implies 3a=d \quad \leftarrow \textsf{Equation 1}[/tex]

Sum of the first n terms of an arithmetic series:

[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]

The sum of the first 7 terms of an arithmetic progression is 70:

[tex]\implies S_7=70[/tex]

[tex]\implies \dfrac{7}{2}[2a+(7-1)d]=70[/tex]

[tex]\implies 2a+6d=20[/tex]

[tex]\implies a+3d=10 \quad \leftarrow \textsf{Equation 2}[/tex]

Substitute Equation 1 into Equation 2 and solve for [tex]a[/tex]:

[tex]\implies a+3(3a)=10[/tex]

[tex]\implies a+9a=10[/tex]

[tex]\implies 10a=10[/tex]

[tex]\implies a=1[/tex]

Substitute found value of [tex]a[/tex] into Equation 1 and solve for [tex]d[/tex]:

[tex]\implies 3(1)=d[/tex]

[tex]\implies d=3[/tex]

Finally, substitute found values of [tex]a[/tex] and [tex]d[/tex] into the general form of the arithmetic sequence:

[tex]\implies a_n=1+(n-1)3[/tex]

[tex]\implies a_n=1+3n-3[/tex]

[tex]\implies a_n=3n-2[/tex]

Answer:

y = 4x - 6

Step-by-step explanation:

Hi there!

We are given the points (3,6) and (1, -2), and that a line passes through these 2 points

We want to find the equation of said line

There are 3 ways to write the equation of the line:

The  most common way is slope-intercept form, so let's write the equation of the line this way

First, we need to find the slope

The slope (m)  can be found using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] & [tex](x_2, y_2)[/tex] are points

Before we calculate, let's label the values of the points.

[tex]x_1=3\\y_1=6\\x_2=1\\y_2=-2[/tex]

Now substitute into the formula

m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m=[tex]\frac{-2-6}{1-3}[/tex]

Subtract

m=[tex]\frac{-8}{-2}[/tex]

Divide

m= 4

The slope of the line is 4

Substitute 4 as m in y=mx+b:

y = 4x + b

Now to find b

Since the equation passes through both (3,6) and (1, -2), we can use either point to help solve for b.

Taking (3,6) for example:

Substitute 3 as x and 6 as y.

6 = 4(3) + b

Multiply

6 = 12 + b

Subtract 12 from both sides

-6 = b

Substitute -6 as b into the equation

y = 4x - 6

Hope this helps!

Topic: finding the equation of the line

See more here: https://brainly.com/question/27618860

Answer:

Please clarify what you asking

Step-by-step explanation:

                      ➢◇✳︎✧✥---------------------------------------------✥✧✳︎◇⤎

[tex]Hello[/tex] [tex]There![/tex]

   We need to find the slope of the line that's parallel to 6x+5y=-5.

It's not hard, I promise! I'm going to take you through a few steps, and we'll find the answer.

Are you ready? Let's start. :)

[tex]Procedure:[/tex]

➢ First, subtract 6x from both sides:

5y=-5-6x

✦ Switch the order of the terms:

5y=-6x-5

➢ Now, divide both sides by 5:

y=-6/5x-5/5

✦ Which is the same as

[tex]\bold{y=-\displaystyle\frac{6}{5} x-1}[/tex]

➢ Part of the problem's already solved! :)

  Now, parallel lines have the same slope.

✦So the slope of the line parallel to 6x+5y=-5 is also:

◉ [tex]\bold{-\displaystyle\frac{6}{5}}[/tex] ☑︎

Problem solved! :)

[tex]Greetings ![/tex]

     ◆     •     ❖ _____________________________________❖   •. ◆

Answer:

It would be d

Step-by-step explanation:

Its d because its in a staright line

Answer:

D.

Step-by-step explanation: the rest are either non-linear , have no correlation, have a curvilinear relationship, or have no association.

Convert the cm to feet for the base and the height:

12/2 = 6 x 3 = 18 feet

9/2 = 4.5 x 3 = 13.5 feet

area = 1/2 x base x height

Area = 1/2 x 18 x 13.5

Area = 121.5 square feet

answer: 121.5 square feet

Answer:

20%

Step-by-step explanation: I took the test