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3 years ago

At a rate of 4% you paid $144 in interest over to year. What was the original amount of your loan

1 answer:

8 0

$\bf ~~~~~~ \textit{Simple Interest Earned}
\\\\
I = Prt\qquad 
\begin{cases}
I=\textit{interest earned}\to &\$144\\
P=\textit{original amount deposited}\\
r=rate\to 4\%\to \frac{4}{100}\to &0.04\\
t=years\to &1
\end{cases}
\\\\\\
144=P(0.04)(1)\implies \cfrac{144}{(0.04)(1)}=P\implies 3600=P$

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The probability that a randomly selected box of a certain type of cereal has a particular prize is 0.20.

MatroZZZ [7]

Answer:

a) the probability is 0.0734 (7.34%)

b) the probability is 0.7382 (73.82%)

c) 10 boxes

Step-by-step explanation:

Since each box is independent of the others and defining the random variable X= number of boxes of cereal purchased without prices until having 2 prices , then X has a negative binomial distribution . Thus

P(X=k)= C(k+r-1,k)*p^k *(1-p)^r

where

p= probability to not obtain a price when a box is purchased = 1- 0.2 = 0.8

C ( ) = combinations

k = number of boxes without prices

r= number of boxes with prices=2

P(X=k) = probability of purchasing k boxes without prices until obtaining r boxes with prices

a) for k= 8 - r = 6

P(X=6)= C(7,6)*0.8^6*0.2^2 = 7*0.8^6*0.2^2 = 0.0734 (7.34%)

b) for k≥9-2=7

P(X≥7) = 1- P(X<7)= 1- Fn(X=7)

where Fn(X) is the cumulative negative binomial distribution. We can calculate it through its relationship with the cumulative binomial distribution Fb(X) that is easily found in tables :

Fn(k=7,r=2,p=0.8) = Fb(k=7,n=k+r=9,p=0.8) = 0.2618

thus

P(X≥7) = 1- P(X<7)= 1- Fn(X=7) = 1- 0.2618 = 0.7382 (73.82%)

c) the expected value E(X) for a negative binomial distribution is

E(X)= p*r/(1-p) = 0.8*2/0.2 = 8 boxes that do not contain prices

thus

n=k+r = 8 + 2 = 10 boxes

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3 years ago

Find the measures of the missing angles.

fomenos

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<span>Angle B = 53^0
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3 years ago

The formula for the future value V (in dollars) of an investment earning simple interest is V=p+prt, where p (in dollars) is the

serious [3.7K]

Answer:

A. $p=\dfrac{V}{1+rt}$

B. $2,307.69

Step-by-step explanation:

You are given the formula

$V=p+prt,$

where V = investment earning simple interest

p = principal,

r = interest rate

t = time

So,

A. $V=p(1+rt)\\ \\p=\dfrac{V}{1+rt}$

B. r = 0.06 (or 6% as percent)

V = $3,000

t =5

so,

$3,000=p+p\cdot 0.06\cdot 5\\ \\3,000=p+0.3p\\ \\1.3p=3,000\\ \\p=\dfrac{3,000}{1.3}\approx 2,307.69$

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3 years ago

Write an expression in simplest form for the perimeter of each figure

Juli2301 [7.4K]

QUESTION 12

The given figure has five unequal sides.

The perimeter is the distance around the figure.

So we add all the lengths of the sides of the rectangle to get,

$Perimeter = 5x + 4x + 2.8y + 2x + 2.2y$

We regroup the like terms to obtain,

$Perimeter = 5x + 4x +2x + 2.8y + 2.2y$

This will simplify to give us,

$Perimeter = 11x + 5.0y$

$Perimeter = 11x + 5y$

QUESTION 13

The given figure has two pairs of sides that are equal in length and three unequal sides.

The perimeter can be found by adding all the lengths of the sides of the of the figure.

This will give us

$Perimeter = 6b + 5a + 3b + 4 + 3a + 2b + 5a$

We regroup like terms to obtain,

$Perimeter = 6b + 2b+ + 3b + 5a + 5a +3a + 4 +$

This finally simplifies to ,

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$Perimeter = 11b + 13a + 4 +$

QUESTION 14

This plane figure has four sides that are equal to 4j and two sides that are equal to 2h.

We add all the lengths of the sides of the plane figure to get,

$Perimeter =4j + 4j+ 4j+ 4j + 2h + 2h$

This will simplify to give us,

$Perimeter =16j + 4h$

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3 years ago

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Genrish500 [490]

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Step-by-step explanation:

You take A and B and put the A over the B.

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3 years ago