In a class of 25 students, there were 13 math majors, 10 were computer science majors, and 6 were dual majors in both.


How many were in math only?

How many were not majoring in computer science?

How many were not math or computer science?

The rate at which the spherical balloon's radius is increasing is

3/16π ft/min when the volume is increasing at the rate of 3 ft³/min.

Given, a spherical balloon is inflated so that its volume is increasing at the rate of 3 cubic feet per minute.

we have to find that how fast is the radius of the balloon increasing when the radius is 2 feet.

as, we know the volume of the balloon be,

V = 4/3πr³

now we have to find the rate of change of radius,

On differentiating both the sides with respect to time, we get

V' = 4/3π(3r²)dr/dt

V' = 4πr²dr/dt

as, the rate of change of volume of the balloon be, 3 ft³/min

V' = 3

3 = 4πr²dr/dt

dr/dt = 3/4πr²

Now, on putting r = 2, we get

dr/dt = 3/4π(2)²

dr/dt = 3/16π

so, the radius of the balloon increase at the rate of 3/16π.

Hence, the radius of the balloon increase at the rate of 3/16π.

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[x|-5<x<-2]

Write the inequality in set-builder notation as the set of all real numbers x such that x is greater than -5 and x is less than - 2

The quotient is  [tex]3x^2 - 7x + 10[/tex].

"Information available from the question"

In the question:

Using synthetic division,

What is the quotient for (3 x³+5 x²-18 x+39) /(x+4)

Now, According to the question:

Let's know:

Synthetic Method: The synthetic division method is a special method of dividing polynomials. This method is a special case of dividing a polynomial expression by a linear factor, in which the leading coefficient should be equal to 1.

(3 x³+5 x²-18 x+39) /(x+4)

              [tex]3x^2 - 7x + 10[/tex]

 x + 4 [tex]\sqrt{3 x^3+5 x^2-18 x+39}[/tex]

             [tex]3x^3 + 12x^2[/tex]

         -          -    

      ___________________              

                   [tex]-7x^2[/tex] - 18x

                    [tex]-7x^2[/tex] - 28x

                  +          +

     _____________________

                              10x + 39

                              10x + 40

                           -        -    

  ________________________

                                      -1

The quotient is  [tex]3x^2 - 7x + 10[/tex].

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They filled bags that total 879 and the treats that did not fit are 4

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given here, total treats = 6157, and group them in bags with 7 each

now, we can write 6157 = 879×7+4

thus, on dividing 6157 by 7 we get the remainder as 4 and the quotient as 879

Hence, the bags of treats they filled is 879, and 4  treats were given to the groomer

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Answer: 32 km (I believe)

Explanation: So, on the first day the tourists walked x/8 km.

Then the remaining distance after the first day is (x- x/8) = 7x/8 km.

On the second day, the tourists walked 4/7 of the REMAINING path, so now we multiply 4/7 by 7x/8 to get x/2 km.

So, the remaining path to travel after 2nd day is (7x/8-x/2) = 3x/8

Remember, on the third day they walked 1/3 of the remaining trail and the last 8 km.

So now, we do (3x/8 - 3x/8 x 1/3) = 8

Now, x/4 =8 ; to find x, we do 8 x 4 to get 32

So, our answer is 32

I hoped this helped!

The solution to the trigonometric equation is sin( 6x ) = 2sin(3x)cos(3x)

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the equation be represented as A

Now , the value of A is

A = sin (6x)

From the trigonometric relations ,

The value of sin( 2x ) = 2sin(x)cos(x)

Now , when x is replaced by 6x

Substituting the values in the equation , we get

sin ( 6x ) = 2 sin ( 6x/2 ) cos ( 6x/2 )

On simplifying the equation , we get

sin ( 6x ) = 2 sin ( 3x ) cos ( 3x )

So , the value of the trigonometric relation is

sin(6x) = 2sin(3x)cos(3x)

Hence , the equation is sin(6x) = 2sin(3x)cos(3x)

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Nonlinear solver method used in the slope of the objective function as the input values changes. It determines that it reached at the optimum solution when the initial value is equals to zero.

In the nonlinear solver method, the initial values  used within one of the nonlinear equation.  By default the initial value chosen for all variables is zero or the lower bound. zero is in many cases is a bad initial value for a nonlinear variable. For example, if the variable appears in a product term since the initial derivative becomes zero, and it appears as if the function does not depend on the variable. When the equation is simple, the value of x can be determined analytically. This is used in the case when x can be written explicitly by applying mathematical operations or when a known formula such as the formula for solving a quadratic equation can be used to determine the exact value of x.

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Answer:

n+m+2 years

Step-by-step explanation:

m=Steve's age.

J=Jack's age.

n=Age difference between Steve and Jack

J=n+m

J+2=n+m+2 years

The median can be calculated by ordering the possible values of the random variable from smallest to largest and then finding the value for which the cumulative probability equals or exceeds 0.5.

Firstly, list out all the possible values of the random variable.Secondly, order the values from smallest to largest. Thirdly, calculate the cumulative probability for each value. Fourthly, find the value for which the cumulative probability equals or exceeds 0.5 Finally, this value is the median of the discrete random variable.The median of a discrete random variable can be found by arranging the possible values of the random variable from smallest to largest, and then calculating the cumulative probability for each value. Once the cumulative probability reaches or exceeds 0.5, the corresponding value of the random variable is the median.

Let the random variable X have values {1, 2, 3, 4, 5}.

Ordered from smallest to largest, X has the values {1, 2, 3, 4, 5}.

The cumulative probability for each value of X is calculated as follows:

P(X ≤ 1) = 0

P(X ≤ 2) = 0.2

P(X ≤ 3) = 0.6

P(X ≤ 4) = 0.9

P(X ≤ 5) = 1

The median of X is 3, since it is the smallest value for which the cumulative probability equals or exceeds 0.5.

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The answers are A) Reasonable domain to plot the growth function = [0, 9] B) y-intercept of the graph of the function f(m) represent initial length of fish = 5 cm and C) average rate of change of the function f(m) from m

is (3.84/8)

A function is defined as a relation between a set of inputs having one output each.

Given that, A marine biologist is studying the growth of a particular species of fish when the marine biologist concluded her study, the length of the fish was approximately 9.19 cm

A) For m = 0

f(0) = 5(1.07)⁰ = 5 cm

The length of the fish was approximately 9.19 cm.

m = 9

Domain = [0, 9]

Reasonable domain to plot the growth function = [0, 9]

B) y-intercept of the graph of the function f(m) represent initial length of fish = 5 cm

C) average rate of change of the function f(m) from m = 1 to m = 9

For m = 1

f(1) = 5(1.07) = 5.35 cm

For m = 9

f(9) = 5(1.07)⁹ = 9.19 cm

Change in 9 - 1 = 8 months = 9.19 - 5.35 = 3.84 cm

average rate of change of the function f(m) from m = 1 to m = 9,

= (3.84/8)

= 0.48 cm per month

Hence, The answers are A) Reasonable domain to plot the growth function = [0, 9] B) y-intercept of the graph of the function f(m) represent initial length of fish = 5 cm and C) average rate of change of the function f(m) from m is (3.84/8)

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The distance ship travelled 7.4 units between the two observations of the lighthouse.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

Given that, a ship is sailing due north. At a certain point the bearing of a lighthouse is N39.8˚E and the distance is 11.5.

P is the ship, R is the light house and Q is the bearing.

PR is the distance between the ship and the light house, PR = 11.5

∠P = 43.5°, ∠Q =39.8°

Thus, ∠R = 180° -∠P-∠Q

= 180°-43.5°-39.8°

= 96.7°

By using sin rule we get

PR/sinR =PQ/sinQ

11.5/sin96.7° =PQ/sin39.8°

11.5/0.9931 =PQ/0.6401

PQ/0.6401=11.55

PQ=7.4 units

Therefore, the distance ship travelled 7.4 units between the two observations of the lighthouse.

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Answer:

Step-by-step explanation:

as suggested,  use  SOH CAH TOA

we are given the H and O   and want an angle

use  SOH, b/c it's got the two given pieces of info

Sin(∅) = Opp / Hyp

Sin(x) = 21 / 28

arcSin ( Sin(x)) = arcSin(21/28)

x = 48.59°

cdf of U(n) = Var(Sn)=1

A standard function is one that is defined on an interval of R and is acquired by a finite series of standard operations beginning with any three fundamental functions.

f(x) = x is the identity function. f(x) = exp, an exponential function (x)

given

let U1, . . . ],

U(n) be their maximum

so cdf of U(n) =does not have a limiting distribution.

Why will a pub and up be equal to zero when Y is less than and one win in is less than the other.

There isn't a standard distribution function that can match this limit everywhere.

hence  cdf of U(n) = Var(Sn)=1

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Answer:

24

Step-by-step explanation:

Perimeter are the side measures added up.

15 x 0.4 = 6

ΔLMN = 60

60 x 0.4 = 24

Answer:

Signum function

Step-by-step explanation:

Hope this helps uuuu

Answer:

x=3.

Step-by-step explanation:

[tex]way1) \ 4^x=64;\\x=log_4[64];\\x=3;\\\\way2) \ 4^x=64; \ < = > \ 4^x=4^3; \ < = > \ x=3.[/tex]

Step-by-step explanation:

Using Trigonometry

Cos ø = Adj ÷ Hyp

ø = 35°

Hyp side=15ft

A is the Adj side

Adj = Cos ø × Hyp

Adj = Cos 35° × 15

Adj = 0.8192 × 15 = 12.29

Adj = 12ft approximately

Answer: 12.3

Step-by-step explanation: Based off the quiz I did it said 12.3

If n is devisible by 3 then n^2 is devisible by 3 it easy.

n=3k so n^2=9k so 9 is devisible by 3.

In the other way, if n^2 is devisible by 3we have n^2=3k wher k is integer number which has to be devisible by 3. If k is not devisible by 3, then n=/sqrt3*r , r^2=k. So n is not integer, contradiction.

This proof show us that iff doesnt work.

If n is devisile by 4 then n^2 is also devisible by 4. But if we have that n^2 is devisibke by 4 then n hasn’t be devisible by 4. Example: n^2=36 is dev by 4 but n=6 is not dev by4.

Its allow because /sqrt 4 is 2.

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The amount of gun powder particles found around a bullet hole is directly related to the distance from which the weapon was fired.

Which two forces are acting on a bullet?

Two major forces are acting on the bullet ,the forward force of the gunshot and the downward force of gravity. The first force is called aerodynamics and the other force is called gravitational.

What does the distribution of gun powder residue around the bullet hole help to determine?

The residue exit the muzzle in a cone shaped and can land on the target objects. The size and density of the residue on the object can vary with distance allowing the fire man examiner to determine proximity of shooter to the target killing when gun is fired.

Therefore, the amount of gun powder particles found around a bullet is directly related to the distance when gun was fired.

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Answer:

Congruent

Step-by-step explanation:

If you slide the angle down the transversal, it would land perfectly on top of the corresponding angel and you would be able to see that they are congruent.

a₁ = -9

a₂ = -9 + (2 - 1) * 8 = -9 + 8 = -1

a₃ = -9 + (3 - 1) * 8 = -9 + 16 = 7

a₄ = -9 + (4 - 1) * 8 = -9 + 24 = 15

a₅ = -9 + (5 - 1) * 8 = -9 + 32 = 23

a₆ = -9 + (6 - 1) * 8 = -9 + 40 = 31

The business research project was a valuable experience that taught me about the importance of research in the business world and the various methods and techniques that can be used to conduct effective research.

One of the most useful tools or knowledge that I will be able to use in the professional world after completing this class is the ability to analyze and interpret data. This includes the ability to perform statistical analysis and draw meaningful conclusions from data sets. This skill is crucial in today's business world, as data-driven decision-making is becoming increasingly important in all industries.

In the business research project, I learned about the importance of conducting thorough research in order to make informed decisions. I also learned about the various methods of conducting research, such as primary and secondary research, and the pros and cons of each method. I also learned about the importance of using reliable sources and properly citing sources in order to ensure the credibility of my research.

It also helped me to develop my analytical skills and the ability to interpret data in order to draw meaningful conclusions. These skills will be essential in my future professional career as I work to make informed decisions and solve complex business problems.

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We can say that duties are obligations that one has, while work is an activity that is carried out and that depends on a profession.

The concepts homework and work are related because they are often linked in many contexts. Regarding these terms, we have to:

¡Hope this helped!

An integral expression that provides the solid's volume at the points y=x, y=2, and x=6 is [tex]\int\limits^{6}_{2} {y^3} \, dy[/tex]

How many areas of space are filled by an object is determined by its volume. The amount of unit cubes required to completely fill the solid serves as the measurement. By counting the solid's unit cubes, the answer can be determined.

A three-dimensional object's volume is typically thought of as its ability to accommodate matter.

According to the question,

The cross section of the solid taken perpendicular to the y- axis is a square.

Solid base equation: y=x, y=2, x=6

Square Volume = (Side3)

Since y = x in the equation and y = 2 as a result, x must equal 2.

So , Limit of x varies from 2 to 6

Volume of solid is  [tex]\int\limits^{6}_{2} {y^3} \, dy[/tex]

Hence , , an integral expression that gives the volume of the solid is [tex]\int\limits^{6}_{2} {y^3} \, dy[/tex]

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Answer:

e = mc^2

m = e/c^2

Step-by-step explanation:

Therefore ,E = xex2 + y2 + z2 dv, where e is the portion of the unit ball x2 + y2 + z2 ≤ 1 that lies in the first octant whose value is π/8

The volume of an inhabited three-dimensional space is calculated. It is commonly measured in a variety of imperial, US-standard, and SI-derived units. Volume and the notion of length are interconnected.

Here,

Given :

portion of unit ball = [tex]xe^{x^{2}+y^{2} +z^{2} }[/tex]

and x2 + y2 + z2 ≤ 1

So, using this

We find the triple integral or the volume integral of the expression  = [tex]xe^{x^{2}+y^{2} +z^{2} }[/tex]

=> [tex]\int\int\int_{e} xe^{x^{2}+y^{2} +z^{2} }[/tex]dV

=>   [tex]\int\limits^{\alpha = \pi /2}_{\alpha =0}\int\limits^{\beta = \pi /2}_{\beta =0} \int\limits^{p= 1}_{p=0}[/tex]   pcos[tex]\beta[/tex]sin[tex]\alpha[/tex][tex]e^{{p}^{2}[/tex] [tex]p^{2}[/tex]sin[tex]\alpha[/tex] dpd[tex]\alpha[/tex]d[tex]\beta[/tex]

=>[tex]\int\limits^{\alpha = \pi /2}_{\alpha =0}[/tex][tex]sin^{2}\alpha[/tex] d[tex]\alpha[/tex]  + [tex]\int\limits^{\beta = \pi /2}_{\beta =0}[/tex]cos[tex]\beta[/tex] d[tex]\beta[/tex]  +  [tex]\int\limits^{p= 1}_{p=0} p^{2} e^{p^{2}}[/tex] dp

=>π/8

Therefore ,E xex2 + y2 + z2 dv, where e is the portion of the unit ball x2 + y2 + z2 ≤ 1 that lies in the first octant whose value is π/8

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It's easier to come up with the correctness proof of the divide and conquer algorithm compared to the greedy algorithm is False statement.

It is not easier to come up with a correctness proof of the divide and conquer algorithm compared to the greedy algorithm. The correctness proof of a divide and conquer algorithm is more difficult than a greedy algorithm since it involves breaking down an algorithm into multiple sub-problems and then proving the correctness of the algorithm with respect to each sub-problem. On the other hand, the correctness proof of a greedy algorithm is relatively simple and involves determining if a given solution is optimal. Additionally, the correctness proof of a divide and conquer algorithm requires more complex mathematical analysis such as induction, recurrence relations, or complexity analysis. This makes it more difficult to come up with the correctness proof of the divide and conquer algorithm than the greedy algorithm.

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The advertising revenue models would best suit the organization needs is option (A) Bidding for ad words

Here the organization wants to buy specific keywords to accurately target the audience who would want to see these ads

The aim of the organization is to get a high effective exposure rate and engagement rate without invading consumer privacy

Bidding for ad words states that the amount of money you are willing to spend for a single click on a given keyword.

Here they will get high effective exposure rate and engagement rate without invading consumer privacy

Therefore, the best advertising revenue model is option (A) Bidding for ad words

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Answer:

Since csc 13pi/11 is undefined, it is impossible to fill in a value for angle A and B that satisfies the given restrictions. Additionally, it is impossible to find the related acute angle or the quadrant of the principle angle without a defined value for angle A and B.

Step-by-step explanation: