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3 years ago

10 freshmen, 9 sophomores, 8 juniors, and 9 seniors are eligible to be on a committee.

Mathematics

1 answer:

irina1246 [14]3 years ago

6 0

In how many ways can a dance committee of 15 students be chosen?
6,480 ways

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Enter an equation for the function that includes the points.Give your answer in a(b)x. In the event that a=1 , give your answer

Andrews [41]

Answer:

$f(x) = \frac{24}{25} * \frac{5}{6}^x$

Step-by-step explanation:

Given

$(x_1,y_1) = (2,\frac{2}{3})$

$(x_2,y_2) = (3,\frac{5}{9})$

Required

Write the equation of the function $f(x) = ab^x$

Express the function as:

$y = ab^x$

In: $(x_1,y_1) = (2,\frac{2}{3})$

$y = ab^x$

$\frac{2}{3} = a * b^2$ --- (1)

In $(x_2,y_2) = (3,\frac{5}{9})$

$y = ab^x$

$\frac{5}{9} = a * b^3$ --- (2)

Divide (2) by (1)

$\frac{5}{9}/\frac{2}{3} = \frac{a*b^3}{a*b^2}$

$\frac{5}{9}/\frac{2}{3} = b$

$\frac{5}{9}*\frac{3}{2} = b$

$\frac{5}{3}*\frac{1}{2} = b$

$\frac{5}{6} = b$

$b = \frac{5}{6}$

Substitute 5/6 for b in (1)

$\frac{2}{3} = a * b^2$

$\frac{2}{3} = a * \frac{5}{6}^2$

$\frac{2}{3} = a * \frac{25}{36}$

$a = \frac{2}{3} * \frac{36}{25}$

$a = \frac{2}{1} * \frac{12}{25}$

$a = \frac{24}{25}$

The function: $f(x) = ab^x$

$f(x) = \frac{24}{25} * \frac{5}{6}^x$

7 0

3 years ago

Eric is studying people's typing habits. He surveyed 525 people and asked whether they leave one space or two spaces after a per

Otrada [13]

Answer: (0.8115, 0.8645)

Step-by-step explanation:

Let p be the proportion of people who leave one space after a period.

Given: Sample size : n= 525

Number of people responded that they leave one space. =440

i.e. sample proportion: $\hat{p}=\dfrac{440}{525}\approx0.838$

z-score for 90% confidence level : 1.645

Formula to find the confidence interval :

$\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$0.838\pm (1.645)\sqrt{\dfrac{0.838(1-0.838)}{525}}\\\\=0.838\pm (1.645)\sqrt{0.00025858285}\\\\=0.838\pm (1.645)(0.01608)\\\\= 0.838\pm0.0265\\\\=(0.838-0.0265,\ 0.838+0.0265)\\\\=(0.8115,\ 0.8645)$

Hence, a 90% confidence interval for the proportion of people who leave one space after a period: (0.8115, 0.8645)

3 0

3 years ago

Our faucet is broken, and a plumber has been called. The arrival time of the plumber is uniformly distributed between 1pm and 7p

Ymorist [56]

Answer:

$E(A+B) = E(A)+E(B)=4+0.5 =4.5 hours$

$Var(A+B)= Var(A)+Var(B)=3+0.25 hours^2=3.25 hours^2$

Step-by-step explanation:

Let A the random variable that represent "The arrival time of the plumber ". And we know that the distribution of A is given by:

$A\sim Uniform(1 ,7)$

And let B the random variable that represent "The time required to fix the broken faucet". And we know the distribution of B, given by:

$B\sim Exp(\lambda=\frac{1}{30 min})$

Supposing that the two times are independent, find the expected value and the variance of the time at which the plumber completes the project.

So we are interested on the expected value of A+B, like this

$E(A +B)$

Since the two random variables are assumed independent, then we have this

$E(A+B) = E(A)+E(B)$

So we can find the individual expected values for each distribution and then we can add it.

For ths uniform distribution the expected value is given by $E(X) =\frac{a+b}{2}$ where X is the random variable, and a,b represent the limits for the distribution. If we apply this for our case we got: