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3 years ago

Given the line y =2/3x-3

Mathematics

1 answer:

enyata [817]3 years ago

4 0

Answer:

y= -3/2x + 5

Step-by-step explanation:

You do the opposite reciprocal of the original equation's slope.

Then you use the new slope from the point (4,-1) on the graph to find the y-intercept. Which is (0,5).

That gets your answer of -3/2x + 5.

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5. A company sells small, colored binder clips in packages of 20 and offers a money-back guarantee if two or more of the clips a

SOVA2 [1]

Answer:

a) Binomial.

b) n=20, p=0.01, k≥2

The probability hat a package sold will be refunded is P=0.0169.

Step-by-step explanation:

a) We know that

the defective probability is constant and independent.
the sample size is bigger than one subject.

The most appropiate distribution to represent this random variable is the binomial.

b) The parameters are:

Sample size (amount of clips in the package): n=20
Probability of defective clips: p=0.01.
number of defective clips that trigger the money-back guarantee: k≥2

The probability of the package being refunded can be calculated as:

$P(x\geq2)=1-(P(x=0)+P(x=1))\\\\\\P(x=k) = \dbinom{n}{k} p^{k}q^{n-k}\\\\\\P(x=0) = \dbinom{20}{0} p^{0}q^{20}=1*1*0.8179=0.8179\\\\\\P(x=1) = \dbinom{20}{1} p^{1}q^{19}=20*0.01*0.8262=0.1652\\\\\\P(x\geq2)=1-(0.8179+0.1652)=1-0.9831=0.0169$

6 0

4 years ago

How to factor the gcf out of a polynomial

Ann [662]

Step-by-step explanation:

$15x^6+6x^4+9x^3\\\\\text{Find GCF of 15, 6 and 9:}\\\\15=\boxed3\cdot5\\6=\boxed3\cdot2\\9=\boxed3\cdot3\\\\GCF(15,\ 6,\ 9)=\boxed3\\\\\text{Find GCF of}\ x^6,\ x^4\ \text{and}\ x^3:\\\\\text{use}\ a^n\cdot a^m=a^{n+m}\\\\x^6=x^{3+3}=\boxed{x^3}\cdot x^3\\\\x^4=x^{3+1}=x^3\cdot x^1=\boxed{x^3}\cdot x\\\\x^3=\boxed{x^3}\cdot1\\\\GCF(x^6,\ x^4,\ x^3)=\boxed{x^3}\\\\\text{Therefore}\\\\GCF(15x^6+6x^4+9x^3)=\boxed{3}\cdot\boxed{x^3}=3x^3\\\\15x^6+6x^4+9x^3=3x^3(5x^3+2x+3)$

8 0

4 years ago

4. Meagan invests $1,200 each year in an IRA for 12 years in an account that earned 5%

Nina [5.8K]

Part A)

$\bf \qquad \qquad \textit{Future Value of an ordinary annuity}\\
\left. \qquad \qquad \right.(\textit{payments at the end of the period})
\\\\
A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]$

$\bf \qquad 
\begin{cases}
A=
\begin{array}{llll}
\textit{accumulated amount}\\
\end{array}
\begin{array}{llll}

\end{array}\\
pymnt=\textit{periodic payments}\to &1200\\
r=rate\to 5\%\to \frac{5}{100}\to &0.05\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{annually, thus once}
\end{array}\to &1\\
t=years\to &12
\end{cases}$

$\bf A=1200\left[ \cfrac{\left( 1+\frac{0.05}{1} \right)^{1\cdot 12}-1}{\frac{0.05}{1}} \right]\implies A\approx 19100.55$

part B)

so, for the next 11 years, she didn't make any deposits on it and simple let it sit and collect interest, compounded annually at 5%.

$\bf \qquad \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\ 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\to &\$19100.55\\
r=rate\to 5\%\to \frac{5}{100}\to &0.05\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{annually, thus once}
\end{array}\to &1\\
t=years\to &11
\end{cases}
\\\\\\
A=19100.55\left(1+\frac{0.05}{1}\right)^{1\cdot 11}\implies A\approx 32668.42$

part C)

well, for 12 years she deposited 1200 bucks, that means 12 * 1200, or 14,400.

now, here she is, 12+11, or 23 years later, and she's got 32,668.42 bucks?

all that came out of her pocket was 14,400, so 32,668.42 - 14,400, is how much she earned in interest.

6 0

4 years ago

Please help me solve the problem

Jlenok [28]

Answer:

Step-by-step explanation:

When you take the log of ...

b = b^1

you get ...

$\log_{b}{b}=1$

7 0

3 years ago

A random sample of 50 students at a large high school resulted in a 95 percent confidence interval for the mean number of hours

cricket20 [7]

Answer:

A . About 95% of all random samples of 50 students from this population would result in a 95% confidence interval that covered the population mean number of hours of sleep per day.

Step-by-step explanation:

x% confidence interval:

A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.

In this question:

95% CI from a sample of 50 students is (6.73, 7.67).

This means that we are 95% sure that the population mean is in this interval, that is, about 95% samples of 50 would contain the population mean, which is given by option A.

5 0

3 years ago