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2 years ago

12

A woman put $580 into a saving account for one year. The rate of interest on the account was 6.5%. How much was the interest for

the year?

1 answer:

svetlana [45]2 years ago

8 0

<span>interest = $580 x 0.065 = $37.70

answer
interest for the year is </span>$37.70

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What term is 1/1024 in the geometric sequence,-1,1/4,-1/6..?

Trava [24]

Answer:

$\large\boxed{\text{sixth term is equal to}\ \dfrac{1}{1024}}$

Step-by-step explanation:

The explicit formula for a geometric sequence:

$a_n=a_1r^{n-1}$

$a_n$ - n-th term

$a_1$ - first term

$r$ - common ratio

$r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}$

We have

$a_1=-1,\ a_2=\dfrac{1}{4},\ a_3=-\dfrac{1}{6},\ ...$

The common ratio:

$r=\dfrac{\frac{1}{4}}{-1}=-\dfrac{1}{4}\\\\r=\dfrac{-\frac{1}{6}}{\frac{1}{4}}=-\dfrac{1}{6}\cdot\dfrac{4}{1}=-\dfrac{2}{3}\neq-\dfrac{1}{4}$

<h2>It's not a geometric sequence.</h2>

If $a_3=-\dfrac{1}{16}$ then the common ratio is $r=\dfrac{-\frac{1}{16}}{\frac{1}{4}}=-\dfrac{1}{16}\cdot\dfrac{4}{1}=-\dfrac{1}{4}$

Put to the explicit formula:

$a_n=-1\left(-\dfrac{1}{4}\right)^{n-1}$

Put $a_n=\dfrac{1}{1024}$ and solve for <em>n </em>:

$-1\left(-\dfrac{1}{4}\right)^{n-1}=\dfrac{1}{1024}\qquad\text{use}\ a^n:a^m=a^{n-m}\\\\-\left(-\dfrac{1}{4}\right)^n:\left(-\dfrac{1}{4}\right)^1=\dfrac{1}{1024}\\\\-\left(-\dfrac{1}{4}\right)^n\cdot(-4)=\dfrac{1}{1024}\\\\(4)\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{1024}\qquad\text{divide both sides by 4}\ \text{/multiply both sides by}\ \dfrac{1}{4}/\\\\\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{4096}\\\\\dfrac{(-1)^n}{4^n}=\dfrac{1}{4^6}\qquad n\ \text{must be even number. Therefore}\ (-1)^n=1$

$\dfrac{1}{4^n}=\dfrac{1}{4^6}\iff n=6$

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3 years ago

Brainly + 30 points!<br>Find the values of a, b, and c

torisob [31]

Answer:

23 17 31

Step-by-step explanation:

igotitright

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2 years ago

A national survey interviewed 3800 people ages 18 and older nationwide by telephone. One question asked was the amount of gasoli

NeTakaya

Answer:

For this case a parameter represent the population data and for this case the parameter would be the true mean $\mu$ who represent the amount of gasoline they used in the previous week

$\bar X= \frac{\sum_{i=1}^n X_i}{3800} =11.75$

And the sample mean is an unbiased estimator of the true mean.

Step-by-step explanation:

For this case a parameter represent the population data and for this case the parameter would be the true mean $\mu$ who represent the amount of gasoline they used in the previous week

And in order to estimate the parameter of interest we use a survey of n =3800 and the sample mean who represent an statistic is given by:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And we got:

$\bar X= \frac{\sum_{i=1}^n X_i}{3800} =11.75$

And the sample mean is an unbiased estimator of the true mean.

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2 years ago

Last year Marta invested money in two accounts. The first account had an interest rate of 3% and the second account had an inter

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The amount invested in the first account is $9,300 while the amount invested in the second account is $8,800.

<h3>How do we calculate the amount invested?</h3>

Let x represents the amount invested in the first account.

Therefore, we have:

Amount invested in the second account = x - 500

Interest income from first account = 3% * x = 0.03x

Interest income from second account = 5% * (x - 500) = 0.05x - 25

Total interest income = 0.03x + 0.05x - 25 = 719

Solving for x, we have:

0.08x = 719 + 25

x = 744 / 0.08

x = $9,300

Substituting for x, we have:

Amount invested in the second account = $9,300 - $500 = $8,800

Learn more about the amount invested here: brainly.com/question/24132106.

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Consider a t distribution with 24 degrees of freedom. Compute P(-1.27˂t˂1.27) . Round your answer to at least three decimal plac

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Answer:

Step-by-step explanation:

<em>Use the calculator provided to solve the following problems. </em>
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<em>Consider a t distribution with 24 degrees of freedom. Compute P(-1.27˂t˂1.27) . Round your answer to at least three decimal places. </em>
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<em>Consider a t distribution with 5 degrees of freedom. Find the value of c such that P(t≤c)=0.05 . Round your answer to at least three decimal places.</em>

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2 years ago