MATHEMATICS COLLEGE

If the mean of 5 positive integers is 15, what is the maximum possible difference between the largest and the smallest of these 5 numbers?

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

If the mean is 15, the sum of 5 numbers is:

5*15 = 75

Minimum value for the first four numbers would be:

1, 2, 3, 4

Then the fifth number is:

75 - (1+2+3+4) = 75 - 10 = 65

So the maximum difference is:

65 - 1 = 64

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6.Valdez Construction signed a note with a payment of $5,200 per quarter for 5 years.
Find the amount they must set aside today to satisfy this capital requirement in an account earning 8% compounded quarterly.

$30,506.32

$126,346.32

$51,054.38

$85,027.44

Answers

If P = Periodic payments done quarterly (that is, four time in a year) = $5,200, n = number of years (5), R = Annual interest rate = 8% = 0.08, and A = Amount to be set aside today, then

A = P [1-(1+R/4)^4n]/(R/4) = 5200 [1-(1+0.08/4)^4*5]/(0.08/4) = $85,027.45

Therefore, Valdez construction should set aside $85,027.44 now to satisfy the capital requirement.

A rock group needs to choose 3 songs to play at the annualBattle of the Bands. How many ways can they choose their
set if they have 15 songs to pick from? /(10 pts)

Answers

Answer:

If they have 15 songs to choose from and they can only pick three, that means they might have 5 different ways of choosing those songs.

A survey of 800 students yielded the following information: 519 were seniors, 430 were commuters, and 300 of the seniors were commuters. How many of the 800 surveyed students were seniors or were commuters?

Answers

Answer:

The number is $(S \ u \ C ) = 649$

Step-by-step explanation:

From the question we are told that

The sample size is n = 800

The number of seniors is S = 519

The number of commuters is C = 430

The number of of seniors that are commuters is $(S\ n \ C )= 300$

Generally the number of 800 surveyed students who were seniors or were commuters is mathematically evaluated as

$(S \ u \ C ) = S + C - ( S \ n \ C )$

=> $(S \ u \ C ) = 519 + 430 - 300$

=> $(S \ u \ C ) = 649$

Find the solutions to x2-2x+10=0. The quadratic formula has been started for you.

Answers

Answer

The solution to the quadratic equation is

$x=1\pm3i$

EXPLANATION

Problem Statement

The question gives us the beginning of the application of the Quadratic formula on a quadratic equation. We are required to simplify the expression and get in more certain terms, the values of x.

The expression given is:

$\begin{gathered} x^2-2x+10=0 \n \n x=\frac{2\pm\sqrt[]{(-2)^2-(4)(1)(10)}}{2} \end{gathered}$

Solution

Let us begin to simplify the expression below:

$\begin{gathered} x=\frac{2\pm\sqrt[]{(-2)^2-(4)(1)(10)}}{2} \n \n x=\frac{2\pm\sqrt[]{(-2*-2)^{}-(4*1*10)}}{2} \n \n x=\frac{2\pm\sqrt[]{4-40}_{}}{2} \n \n x=\frac{2\pm\sqrt[]{-36}}{2} \n \n \text{From the laws of indices, we have:} \n \sqrt[]{a* b}=\sqrt[]{a}*\sqrt[]{b} \n \n x=\frac{2\pm\sqrt[]{-1*36}}{2} \n \n x=\frac{2\pm(\sqrt[]{-1})(\sqrt[]{36})}{2} \n \n \text{ We know that, } \n \sqrt[]{-1}=i \n \n x=(2\pm(i)(6))/(2) \n \n x=(2\pm6i)/(2) \n \n x=(2(1\pm3i))/(2) \n \n 2\text{ Crosses out} \n \n x=1\pm3i \end{gathered}$

Final Answer

The solution to the quadratic equation is

$x=1\pm3i$

How much kinetic energy does a 4 kg cats have while at 9 m/s

Answers

Answer:

162 Joules

Step-by-step explanation:

Remember, the equation for the kinetic energy of an object is:

$K=(1)/(2)mv^(2)$

where m is the mass of the object in kg (kilograms), v is the velocity of the object in m/s (meters per second), and K is the kinetic energy of the object in J (joules).

We are given that the cat's mass is 4 kg. We will use this for m. We are also given that the cat is moving at 9 m/s. This would be it's speed. We can use this for velocity, or v. Plugging in we get:

$K=(1)/(2)mv^(2)=(1)/(2)(4)(9)^(2)=(2)(81)=162$

So K, or the kinetic energy, would be 162J.

I hope you find my answer and explanation to be helpful. Happy studying.

Find the sum of the measures of the INTERIOR angles in 36-gon polygon

Answers

Answer: 6120

Step-by-step explanation:

The equation for the interior angles of a polygon is (n-2)180. So using the equation, (36-2)180=(34)180=6120.

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