the radius of a spherical ball is increasing at a rate of . at what rate is the surface area of the ball increasing when the radius is cm?

Answer:

( − ∞ , − 5 ) ∪ ( 5 , ∞ )

Step-by-step explanation:

have a good day uwu

I think the answer is $238.

71 x $3 = $213

2 + 3 = 5

5 x $5 = $25

$213 + $25 = $238

I hope this helps.

The total cost of ticket for a group of 71 students, 3 parents, and 2 teachers to attend the museum is $360.

An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.

Now it is given that,

Cost of ticket for adult = $5.00

Cost of ticket for students = $3.00

Now, Total number of students = 71

Number of parents = 3

Number of teachers = 2

So, total adults = 3 + 2 = 5

Thus, Total cost of tickets for students = 71*5 = $355

and, Total cost of tickets for adults = 5*3 = 1$5

Therefore,

Total cost of ticket for a group of 71 students, 3 parents, and 2 teachers to attend the museum = Total cost of tickets for students + Total cost of tickets for adults

⇒ Total cost of ticket for a group = $355 + $5

⇒ Total cost of ticket for a group = $360

Thus, the total cost of ticket for a group of 71 students, 3 parents, and 2 teachers to attend the museum is $360.

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To summarize: If points a and b are in a straight line, the distance traveled and the displacement will be the same. If points a and b are not in a straight line, the distance traveled will be greater than the displacement.

The distance traveled refers to the total length covered during the journey, regardless of the direction taken. On the other hand, displacement refers to the change in position from the starting point to the ending point, taking into account the direction of travel.

Neglecting the curvature of the corners implies that the path taken is a straight line. In this case, the distance traveled and the displacement will be the same if the points a and b are in a straight line.

If points a and b are not in a straight line, then the distance traveled will be greater than the displacement. This is because the distance traveled considers the entire path covered, while displacement only considers the change in position.

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Given:

A student says that the graph of the equation \(y = 3(x + 8)\) is the same as the graph of \(y = 3x\), only translated upwards by 8 units.

To find:

Whether the student is correct or not.

Solution:

Initial equation is

\(y=3x\)

\(f(x)=3x\)

Equation of after transformation is

\(y=3(x+8)\)

\(g(x)=3(x+8)\)

Now,

\(g(x)=f(x+8)\)      ...(i)

The translation is defined as

\(g(x)=f(x+a)+b\)        ...(ii)

Where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

From (i) and (ii), we get

\(a=8\text{ and }b=0\)

Therefore, the graph of \(y=3x\) translated left by 8 units. Hence, the student is wrong.

Answer:

width = let width be w

area = 140

length = 2w-6

Area of a rectangle = l*b

⇒ 2w-6*w=140

⇒ \(2w^2-6=140\\2w^2 = 146\\w^2 = 146/2\\w^2 = 73\\w = \sqrt{73}\)

Answer:

Ok you're talking about "PI"

Area of a circle:

πr^2

What that basically means is

π <- That sign is 3.14

You wanna times that with the radius (r).

The radius is half of the diamater so divde the diameter by 2 then mutiply whatever u get with 3.14

Then the final step is do 3.14 x radias then times 2.

That's it :D

Hope this helps ~

Answer:

235.39

Step-by-step explanation:

Just subtract 50.84 from 286.23 :)

The correct option is (1) less than 10 times the original distance.The original distance was  30 cm and the new distance is 94.86 cm which is less than 10 times the original.

The force of attraction and repulsion among two charged bodies are directly proportional to a product of their charges but inversely proportional to a square of a distance between them, according to Coulomb's law.

It works along the line that connects the two charges that are called point charges.

The formula for Coulomb's law is-

\(f_{}=\frac{q_{1} q_{2}}{4 \pi \epsilon d_{}^{2}}\)

where, q₁ and q₂ are the charges;

d is the distance between them.

Now, according to the question;

Two charges that were initially separated by a particular distance are pushed closer together until force between the two is reduced by a factor of ten.

Coulomb's law of force

\(f_{1}=\frac{q_{1} q_{2}}{4 \pi \epsilon d_{1}{ }^{2}}\)

d₁ is the initial distance.

So when charges are separated further, a new force is f₂, which is represented as

\(f_{2}=\frac{q_{1} q_{2}}{4 \pi \epsilon d_{2}^{2}}\)

d₂ is the moved distance

As a result, the given force is decreased by ten times its original value.

Thus, \(f_{2}=\frac{f_{1}}{10}\)

use the expression in both forces

\(\begin{gathered} \frac{f_{1}}{10}=\frac{q_{1} q_{2}}{4 \pi \epsilon d_{2}{ }^{2}} \\\frac{q_{1} q_{2}}{4 \times 10 \pi \epsilon d_{1}{ }^{2}}=\frac{q_{1} q_{2}}{4 \pi \epsilon d_{2}{ }^{2}} \\ \frac{1}{10 \times d_{1}{ }^{2}}=\frac{1}{d_{2}{ }^{2}} \\ d_{2}=\sqrt{10} d_{1}\end{gathered}\)

Now, calculate the moved distance d₂,

\(\begin{aligned}& d_{2}=\sqrt{10} d_{1} \\ & d_{2}=\sqrt{10} \times 30 \\& d_{2}=3.162 \times 30 \\ & d_{2}=94.868 \mathrm{~cm}\end{aligned}\)

The new distance is 94.868 cm.

Therefore, the new obtained distance is less than the 10 times the original distance.

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The complete question is-

Two charges originally separated by a certain distance are moved farther apart until the force between them has decreased by a factor of 10.  Is the new distance

(1) less than 10,

(2) equal to 10, or

(3) greater than 10;

times the original distance? If the original distance was 30 cm.

Using quantifiers; a) ∀ student ∈ this class, ∃ exactly 2 mathematics classes ∈ this school that the student has taken and b) ∃ person, ∀ country ∈ the world (country ≠ Libya), the person has visited that country.

a) "Every student in this class has taken exactly two mathematics classes at this school."

In this statement, we have two main quantifiers:

Universal quantifier (∀): This quantifier denotes that we are making a statement about every individual student in the class. It indicates that the following condition applies to each and every student.

Existential quantifier (∃): This quantifier indicates the existence of something. In this case, it asserts that there exists exactly two mathematics classes at this school that each student has taken.

So, when we combine these quantifiers and their respective conditions, we get the statement: "For every student in this class, there exists exactly two mathematics classes at this school that the student has taken."

b) "Someone has visited every country in the world except Libya."

In this statement, we also have two main quantifiers:

Existential quantifier (∃): This quantifier signifies the existence of a person who satisfies a particular condition. It asserts that there is at least one person.

Universal quantifier (∀): This quantifier denotes that we are making a statement about every individual country in the world (excluding Libya). It indicates that the following condition applies to each and every country.

So, when we combine these quantifiers and their respective conditions, we get the statement: "There exists at least one person who has visited every country in the world (excluding Libya)."

In summary, quantifiers are used to express the scope of a statement and to indicate whether it applies to every element or if there is at least one element that satisfies the given condition.

Therefore, Using quantifiers; a) ∀ student ∈ this class, ∃ exactly 2 mathematics classes ∈ this school that the student has taken and b) ∃ person, ∀ country ∈ the world (country ≠ Libya), the person has visited that country.

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Answer:

25 is the same lenghth rounded

Step-by-step explanation:

aproximitly it rounded to the 10

The correct check digit for the UPC code 6-73419-23216- is "3".

The check digit is used to verify the accuracy of the UPC code when it's scanned. It's the last digit of a UPC code and is calculated using a formula based on the first 11 digits.

The formula involves adding up the digits in the odd-numbered positions and multiplying the sum by three, then adding up the digits in the even-numbered positions, and subtracting the second sum from the first sum.

The check digit is then calculated by taking the difference and finding the smallest number that, when added to the difference, is a multiple of 10. The result of this calculation is the check digit.

In this case, the correct check digit is "3".

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The solution to the system of equations is (d) (-2, 1)

From the question, we have the following parameters that can be used in our computation:

y = 2x + 5

y = -1/4x + 0.5

Substitute y = 2x + 5  in the equation y = -1/4x + 0.5

So, we have the following representation

-1/4x + 0.5 = 2x + 5

Collect the like terms

So, the equation becomes

2x + 1/4x = 0.5- 5

So, we have

2.25x = -4.5

Divide by 2.25

x = -2

Substitute x = -2 in y = 2x + 5

y = 2 x -2 + 5

y = 1

Hence, the solution is (d) (-2, 1)

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Answer:

Yes, because a rational, for example, 1, minus tt (that is supposed to be Pi Lol)

is approximately -2.14.

Answer:

x=y−6

Step-by-step explanation:

Answer:

x - y = -6

......

hope it helps!

Answer: If Rajan has \(\frac{1}{2}\) of a chocolate bar, then he has to divide it 4.

\(\frac{1}{2}\) ÷ 4 = \(\frac{1}{8}\)

Step-by-step explanation:

\(\frac{1}{2}\) ÷ 4

\(\frac{1}{2}\) × \(\frac{1}{4}\)

Multiply the numerators and denominators and you will get:    \(\frac{1}{8}\)

Hope this helped!

A preimage (the original) is the two-dimensional shape before any transformation. The image (the transferred one) is the figure after transformation.

A transformation is a process that manipulates a polygon or other two-dimensional object an a plane or coordinate system. Mathematical transformations describe how two-dimensional figures move around a plane or coordinate system.

Following are the types of transformations:-

Dilation, Reflection, Rotation, Shear, Translation.

Preimage is the set of all elements of the domain that are mapped into a given subset of the co-domain.

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.

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Answer:

Slope of the given equation is

M = 8

Answer:

7 ft ×6 ft

Step-by-step explanation:

Area of rectangle= length ×width

Let the length and width of the rectangle be L and W ft respectively.

Form 2 equations using the given information:

LW= 42 -----(1)

L= 3W -11 -----(2)

Substitute (2) into (1):

(3W -11)(W)= 42

Expand:

3W² -11W= 42

3W² -11W -42= 0

\(\boxed{x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} }\)

Applying quadratic formula:

\(W= \frac{ - ( - 11)± \sqrt{( - 11) {}^{2} - 4(3)( - 42) } }{2(3)} \)

\(W= \frac{ 11± \sqrt{625 } }{6} \)

\(W= \frac{ 11± 25}{6} \)

W= 6 or W= \( - \frac{7}{3} \) (reject)

Substitute W= 6 into (1):

L(6)= 42

L= 42 ÷6

L= 7

Thus the dimensions of the rectangle is 7 ft ×6 ft.

\(~~~~~~ \stackrel{\textit{\Large Anna}}{\textit{Simple Interest Earned Amount}} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$100\\ r=rate\to 4.5\%\to \frac{4.5}{100}\dotfill &0.045\\ t=years\dotfill &3 \end{cases} \\\\\\ A=100[1+(0.045)(3)]\implies A=100(1.135)\implies A=113.5 \\\\[-0.35em] ~\dotfill\)

\(~~~~~~ \stackrel{\textit{\Large Matt}}{\textit{Simple Interest Earned Amount}} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$100\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ t=years\dotfill &3 \end{cases} \\\\\\ A=100[1+(0.03)(3)]\implies A=100(1.09)\implies A=109 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{Anna}{113.5} - \stackrel{Matt}{109}\implies 4.5\)

The percent that the average score on the test increased during the two months is 12.5%.

It should be noted that mean simply means the average of a set of numbers that are given. In this case, the average test score of RSM students in September increased by 10%. In October it increased by another 15%..

The average of the increase will be:

= (10% + 15%) / 2

= 25% / 2

= 12.5%

The average is 12.5%.

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Answer:

y=3x+4

Step-by-step explanation:

y-y1=m(x-x1)

y-4=3(x-0)

y-4=3x

y=3x+4

The eigenvalues of the matrix A = [ 3 0 1 2 2 2 -2 1 2 ] are:

λ₁ = (5 - √17)/2 and λ₂ = (5 + √17)/2

To find the eigenvalues (A) of the matrix A = [ 3 0 1 2 2 2 -2 1 2 ], we use the following formula:

Eigenvalues (A) = |A - λI

|where λ represents the eigenvalue, I represents the identity matrix and |.| represents the determinant.

So, we have to find the determinant of the matrix A - λI.

Thus, we will substitute A = [ 3 0 1 2 2 2 -2 1 2 ] and I = [1 0 0 0 1 0 0 0 1] to get:

| A - λI | = | 3 - λ 0 1 2 2 - λ 2 -2 1 2 - λ |

To find the determinant of the matrix, we use the cofactor expansion along the first row:

| 3 - λ 0 1 2 2 - λ 2 -2 1 2 - λ | = (3 - λ) | 2 - λ 2 1 2 - λ | + 0 | 2 - λ 2 1 2 - λ | - 1 | 2 2 1 2 |

Therefore,| A - λI | = (3 - λ) [(2 - λ)(2 - λ) - 2(1)] - [(2 - λ)(2 - λ) - 2(1)] = (3 - λ) [(λ - 2)² - 2] - [(λ - 2)² - 2] = (λ - 2) [(3 - λ)(λ - 2) + λ - 4]

Now, we find the roots of the equation, which will give the eigenvalues:

λ - 2 = 0 ⇒ λ = 2λ² - 5λ + 2 = 0

The two roots of the equation λ² - 5λ + 2 = 0 are:

λ₁ = (5 - √17)/2 and λ₂ = (5 + √17)/2

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Using the normal distribution, it is found that the operating cost for the lowest 3% of the airplanes is of at most $1,630.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation are given, respectively, by:

\(\mu = 2100, \sigma = 250\).

The operating cost for the lowest 3% of the airplanes is of at most the 3rd percentile, hence at most X when Z = -1.88.

\(Z = \frac{X - \mu}{\sigma}\)

\(-1.88 = \frac{X - 2100}{250}\)

X - 2100 = -1.88(250)
X = 1630.

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Answer:

40

Step-by-step explanation:

To solve this, we can create an equation that represents this situation. Since Christopher score 7 more than twice what Mathew scored, the equation will be:

C = 2M + 7

(Variables are representative of the first letter of each name)

Seeing as Christopher scored 87, we can put that into the equation and solve for M.

So, the equation will be:

87 = 2M + 7

Subtract 7 from both sides in order to isolate variable M on the right side.

80 = 2M

Now solve for M, which is 40 (divide both sides by 2).

Answer:

19 Months :)

Step-by-step explanation:

First off 682- 55 = 627. 627/33 = 19

Answer:

19 months

Step-by-step explanation:

The limit as P approaches zero from the right of the Gompertz model, −rP×ln( K/P ), is zero.

The equilibrium solutions of a differential equation occur when the derivative of the function is equal to zero. In this case, the Gompertz ODE is given by dt/dP = −rP×ln(K/P).

To find the equilibrium solutions, we set dt/dP equal to zero and solve for P:

−rP×ln(K/P) = 0

Since ln(K/P) cannot be zero, the only solution is P = 0. Therefore, the equilibrium solution of the Gompertz ODE is P = 0.

To graph the phase plot for the Gompertz model ODE, we plot the population size P on the y-axis and the time t on the x-axis. Since the equilibrium solution is P = 0, we plot a horizontal line at P = 0 to indicate the equilibrium solution.

The phase plot will consist of a family of curves that represent different initial conditions. Each curve in the family will start at a different initial population size and evolve over time according to the Gompertz model. As time progresses, the population size decreases towards the equilibrium solution P = 0.

It's important to note that the phase plot will not intersect the equilibrium solution since it represents a stable equilibrium point. Any initial population size will eventually approach zero as time goes to infinity.

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The part of the merge sort that is accomplished with recursion is option a, where recursion is used to break the list down repeatedly until it gets to one element.

Merge sort is a divide-and-conquer algorithm, where the original list is divided into smaller sublists until each sublist contains only one element. This process is accomplished through recursive calls, where the function is called repeatedly on smaller sublists until each sublist contains only one element.

Once the sublists are reduced to single elements, the merge sort algorithm uses another recursive function to merge the sublists back together in sorted order.

Recursion is not used to find the correct order of each element, as this is accomplished during the merging phase. Similarly, recursion is not used to determine if the list needs to be sorted, as merge sort is always used to sort a list.

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Answer:

Recursion is used to break the list down repeatedly until it gets to one element.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The frame --  if it means the box on the outside which has 4 right angles, or the hexagon in the middle which has 0 right angles

The critical value for a one-tailed test at the 5% significance level with 18 degrees of freedom is 2.878.

To determine this value, the researcher can use the partial t-table above. The first row of the table contains the degrees of freedom (df) and the last column (t0.005) contains the C. To find the critical value, the researcher would look for the row with df=18 and the column with t0.005. The value at the intersection of these two values is 2.878. Therefore, the critical value for this test is 2.878.

To compare the test statistic to the critical value, the researcher would subtract the test statistic from the critical value. If the difference is greater than 0, then the test statistic is greater than the critical value and the null hypothesis can be rejected. In this case, the difference is -0.988, which is less than 0. Therefore, the test statistic is less than the critical value and the null hypothesis cannot be rejected.

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