Which situation can be represented by the inequality?

Which of the following ratios are proportional? 9/12 12/15 16/20 20/24 24/35

8_murik_8 [283]

9/12 is the correct answer

6 0

3 years ago

Homemade applesauce is one of Jared's favorite foods, so he stocked up on 10 pounds of

Vanyuwa [196]

Answer:

<h2>5 quarts</h2>

Step-by-step explanation:

Let's think through this bit by bit.

10 lbs * 16 oz/lb = 160 oz. of apples.

In the proportion below, we can see we simply divide by 8, in terms of magnitude.

8 oz -> 1 cup

160 oz -> 160/8 -> 20 cup

20 cups! Is it the answer? NO! They're asking for it in units of quarts, not cups.

We must remember that 1 quart = 4 cups.

20 cups * 1/4 qt/cups = 5 quarts

8 0

3 years ago

For each given p, let ???? have a binomial distribution with parameters p and ????. Suppose that ???? is itself binomially distr

pshichka [43]

Answer:

See the proof below.

Step-by-step explanation:

Assuming this complete question: "For each given p, let Z have a binomial distribution with parameters p and N. Suppose that N is itself binomially distributed with parameters q and M. Formulate Z as a random sum and show that Z has a binomial distribution with parameters pq and M."

Solution to the problem

For this case we can assume that we have N independent variables $X_i$ with the following distribution:

$X_i Bin (1,p) = Be(p)$ bernoulli on this case with probability of success p, and all the N variables are independent distributed. We can define the random variable Z like this:

$Z = \sum_{i=1}^N X_i$

From the info given we know that $N \sim Bin (M,q)$

We need to proof that $Z \sim Bin (M, pq)$ by the definition of binomial random variable then we need to show that:

$E(Z) = Mpq$

$Var (Z) = Mpq(1-pq)$

The deduction is based on the definition of independent random variables, we can do this:

$E(Z) = E(N) E(X) = Mq (p)= Mpq$

And for the variance of Z we can do this:

$Var(Z)_ = E(N) Var(X) + Var (N) [E(X)]^2$

$Var(Z) =Mpq [p(1-p)] + Mq(1-q) p^2$

And if we take common factor $Mpq$ we got:

$Var(Z) =Mpq [(1-p) + (1-q)p]= Mpq[1-p +p-pq]= Mpq[1-pq]$

And as we can see then we can conclude that $Z \sim Bin (M, pq)$

8 0

3 years ago

What is this math problem -1/12 - (-3/4)

Ivan

Answer:

-1/12 - (-3/4)

= -1/12 + 3/4

= (-1+9)/12

= 8/12

=2/3

3 0

3 years ago

In the past, the average age of employees of a large corporation has been 40 years. Recently, the company has been hiring older

Viktor [21]

Answer:

$p_v =P(t_{(63)}>2.5)=0.0075$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can conclude that the mean age is significantly higher than 45 years at 5% of significance.

Step-by-step explanation:

1) Data given and notation

$\bar X=45$ represent the mean height for the sample

$s=16$ represent the sample standard deviation for the sample

$n=64$ sample size

$\mu_o =40$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean age is higher than 40 years, the system of hypothesis would be:

Null hypothesis: $\mu \leq 40$

Alternative hypothesis: $\mu > 40$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{45-40}{\frac{16}{\sqrt{64}}}=2.5$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=64-1=63$

Since is a one right tailed test the p value would be:

$p_v =P(t_{(63)}>2.5)=0.0075$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can conclude that the mean age is significantly higher than 45 years at 5% of significance.

6 0

3 years ago