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marshall27 [118]

2 years ago

14

Sid is 300$ in debt. He needs to get the debt down to no more than 100$ within the next 8 months. If he pays the same amount eac

h month, what is the minimum he must pay off each month to manage this?

1 answer:

jek_recluse [69]2 years ago

7 0

He has to pay a minimum of $25 each month

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FInd the area of the circle

olchik [2.2K]

Answer:

A = 12.56 m²

General Formulas and Concepts:

<u>Pre-Alg</u>

Order of Operations: BPEMDAS

<u>Geometry</u>

Area of a Circle: A = πr²
d = 2r

Step-by-step explanation:

<u>Step 1: Define</u>

d = 4 m

<u>Step 2: Find </u><em><u>r</u></em>

Substitute: 4 = 2r
Isolate <em>r</em>: 2 = r
Rewrite: r = 2 m

<u>Step 3: Find Area</u>

Substitute: A = π(2)²
Substitute: A = (3.14)(2)²
Evaluate: A = (3.14)(4)
Multiply: A = 12.56 m²

8 0

2 years ago

For a binomial process, the probability of success is 40 percent and the number of trials is 5. Find the standard deviation.

Yakvenalex [24]

Answer:

$Sd(X) =\sqrt{1.2}=1.095$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=5, p=0.4)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

The mean for the binomial distribution is given by:

$E(X) =np=5*0.4=2$

And the variance is given by:

$Var(X) = np(1-p) =5*0.4*(1-0.4)=1.2$

And the deviation is just the square root of the variance so we got:

$Sd(X) =\sqrt{1.2}=1.095$

7 0

2 years ago

Arielle is building the wooden framework for the roof of a house. she needs the angle created by the vertical and horizontal boa

Brums [2.3K]

Answer:

Option A is correct

it is an acute triangle. about 0.8 foot needs to be removed from the 20-foot board to create a right triangle.

Step-by-step explanation:

She want to build a right angle frame

Then to proof it is right angle, we will apply Pythagoras theorem to the sides of the rectangle,

Since the vertical height of board is 12ft

And, the horizontal length of board is 15ft.

Then the beam that support the two beams which also form the hypotenuse is give as

(beam support)²=(horizontal board)²+(vertical board)²

x²=12²+15²

x²=144+225

x²=369

x=√369

x=19.2ft

Then the beam support is 19.2ft

To get the angle of the beam support to the horizontal

Applying trigonometric

Tanθ=opposite / adjacent

Tanθ= vertical / horizontal

Tanθ=12/15

Tanθ=0.8

θ=arctan(0.8)

θ=36.7°

This shows that it is an acute triangle.

We are told that the support beam is 20ft but this is not true because the support beam is calculated to be 19.2ft,

So, 0.8ft must be removed from the 20ft support beam to create the right angle.

Then, the best option is a

we need to cut the support beam by approx 0.8 feet to make right angle between vertical board and horizontal board.

5 0

3 years ago

Define fn : [0,1] --> R by the

sasho [114]

Answer:

The sequence of functions $\{x^{n}\}_{n\in \mathbb{N}}$ converges to the function

$f(x)=\begin{cases}0&0\leq x$ .

Step-by-step explanation:

The limit $\lim_{n\to \infty }c^{n}$ exists and converges to zero whenever $\lvert c \rvert$ . But, if $c=1$ the sequence $\{c^{n}\}$ is constant and all its terms are equal to $1$ , then converges to $1$ . Using this result, consider the sequence of functions $\{f_{n}\}$ defined on the interval $[0,1]$ by $f_{n}(x)=x^{n}$ . Then, for all $0\leq x$ we have that $\lim_{n\to \infty}x^{n}=0$ . Now, if $x=1$ , then $\lim_{n\to \infty }x^{n}=1$ . Therefore, the limit function of the sequence of functions is

$f(x)=\begin{cases}0&0\leq x$ .

To show that the convergence is not uniform consider $0$ . For any $n>1$ choose $x\in (0,1)$ such that $\varepsilon^{1/n}$ . Then

$\varepsilon$

This implies that the convergence is not uniform.

8 0

3 years ago

What is 4n squared plus n squared?

Nutka1998 [239]

Answer:

Step-by-step explanation:

Itś 5n²

8 0

3 years ago