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1 year ago

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Manuela wants to have $26,000 in 18 months. About how much should she put into an 18 month CD that earns simple interest of 5.6%

a year calculated semiannually in order to reach her goal.

2 answers:

pentagon [3]1 year ago

5 0

Since it is simple interest, in 18 months it will earn 1.5*5.6 = 8.4%,

x + 0.084x = 26000

x = 2600/1.084 = $23,985.24

Leto [7]1 year ago

5 0

Answer:

Manuela should put $23,985.24 into an 18 month CD.

Step-by-step explanation:

Manuela wants to have $26,000 in 18 months CD that earns simple interest of 5.6% a year calculated semiannually.

Since it is simple interest so in 18 months (1.5 years) it will earn = 5.6 × 1.5 = 8.4%.

Formula for Simple interest

A = P( 1 + rt)

A = amount ( 26,000 )

P = Principal ( we have to find out )

r = Rate of interest in decimal 8.4% ( 0.084 )

t = time ( 1 )

Let the principal amount be x

Now we put the values in formula to find the value of x.

26,000 = x ( 1 + 0.084 × 1 )

26,000 = x ( 1.084 )

x = $\frac{26000}{1.084}$

x = 23,985.23985 rounded to 23,985.24

Manuela should put $23,985.24 into an 18 month CD.

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Answer:

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Step-by-step explanation:

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3. r^2-100=0

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4. x²-144=0

x²=144

Taking square root on both sides

$\sqrt{x^2}=\sqrt{144}\\\sqrt{x^2}=\sqrt{(12)^2}$

x=±12

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Answer:

a. 0.1647;
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c. 0.4453.

Step-by-step explanation:

By definition, if two event $A$ and $B$ are independent, then

$P(A\cap B) = P(A) \cdot P(B)$ . ( $P(A\cap B)$ is the probability that the outcome of both event $A$ and event $B$ are true.)

<h3>a.</h3>

Since the outcome of these two events are independent,

$\begin{aligned}P(\texttt{Jane} \cap \texttt{Joe}) &= P(\texttt{Jane}) \cdot P(\texttt{Joe})\\ &= 0.61 \times 0.27 \\&= 0.1647\end{aligned}$ .

<h3>b.</h3>

The logic not operator $\lnot$ or the prime superscript $^{\prime}$ denotes that an event does not happen.

$P(\texttt{Jane}^{\prime}) = 1 - P(\texttt{Jane}) = 1- 0.61 = 0.39$ .

$P(\texttt{Joe}^{\prime}) = 1 - P(\texttt{Joe}) = 1- 0.27 = 0.73$ .

Since the two events $\texttt{Jane}$ and $\texttt{Joe}$ , $\texttt{Jane}^{\prime}$ and $\texttt{Joe}^{\prime}$ are also independent. Probability that neither professor got funded:

$P(\texttt{Jane}^{\prime} \cap \texttt{Joe}^{\prime}) = P(\texttt{Jane}^{\prime}) \cdot P(\texttt{Joe}^{\prime}) = 0.39 \times 0.73 = 0.2847$ .

Probability that at least one professor got funded- in other words, it is not true that neither professor got funded:

$P((\texttt{Jane}^{\prime} \cap \texttt{Joe}^{\prime})^{\prime}) = 1- P(\texttt{Jane}^{\prime} \cap \texttt{Joe}^{\prime}) = 0.7153$ .

<h3>c.</h3>

Similarly, since the two events $\texttt{Jane}$ and $\texttt{Joe}$ , $\texttt{Jane}$ and $\texttt{Joe}^{\prime}$ are also independent. Probability that Jane but not Joe got funded:

$P(\texttt{Jane} \cap (\texttt{Joe}^{\prime})) = P(\texttt{Jane}) \cdot P(\texttt{Joe}^{\prime}) = 0.61 \times 0.73 = 0.4453$ .

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mote1985 [20]

David drove a distance (d) of 187km, to 3 significant figures. He used 28 litres of petrol (p), to 2 significant figures.
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Let number of red marbles = y

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Given that Finley has 152 yellow, red, and blue marbles in a bag.

So we get equation:

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"He has seven more red marbles than yellow marbles" means:

y=x+7...(ii)

"three times as many blue marbles as yellow marbles." means:

z=3x...(iii)

Now we just need to solve those equations to find the answer.

Plug (ii) and (iii) into (i)

x+(x+7)+(3x)=152

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Which looks similar to choice (B)

5x+7=152

5x=145

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Hence final answer is choice B.

Required equation is

x+x+7+3x=152

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