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2 years ago

Please help me with this

Mathematics

1 answer:

Papessa [141]2 years ago

6 0

Answer:

see attached

Step-by-step explanation:

The grid show the non-possibilities in red, with each number corresponding to the statement that eliminates that choice. The green square (with black text) shows the one combination that is specified already (by statement 4). The lighter green numbers show possible alternatives: first period may be Schiller or English, and room 113 will be the other one. Similarly, Art may be 3rd period or Thomlinson.

These choices (light green 5, light green 6) give rise to four possibilities. Working through them, you run into inconsistencies if you choose Schiller for first period. (Art must be, but can't be, in room 112.) That leaves two possibilities.

Again, you run into inconsistencies if you choose Thomlinson as the Art teacher. (The class in 112 is 2 periods after Xavier's class, not 1.)

Hence, the only viable pair of remaining choices is Schiller in room 113 and art in 3rd period.

The final schedule is shown in the attachment.

_____

<em>Additional comment</em>

When I'm working these on paper, I use an X to mark any impossible combinations, and a circle (O) to mark a known combination. In any given 4×4 square of the grid, the remaining cells of the row and column containing a O must be Xs. Consistency must be maintained between rows and columns. This often means filling a circle in one place may result in a circle being filled in another place. Of course, once 3 of the squares in a row or column have Xs, the remaining one must be O.

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You have been hired as the quality control office of a pharmaceutical company that manufactures aspirin tablets. According to th

Firlakuza [10]

Answer:

$P(X=0)=(24C0)(0.04)^0 (1-0.04)^{24-0}=0.375413$

$P(X=1)=(24C1)(0.04)^1 (1-0.04)^{24-1}=0.$

So then the probability that the batch would be accepeted is:

$0.375413+0.375413=0.7508$

Step-by-step explanation:

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=24, p=0.04)$

On this case p=0.04 represent the probability that a random the tablet would be NOT accepted

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

They accept the batch if there is only one or no tablet that doesn’t meet the test specification, so let's find the individual probabilities for this case:

$P(X=0)=(24C0)(0.04)^0 (1-0.04)^{24-0}=0.375413$

$P(X=1)=(24C1)(0.04)^1 (1-0.04)^{24-1}=0.$

So then the probability that the batch would be accepeted is:

$0.375413+0.375413=0.7508$

3 0

2 years ago

Factor:<br> 4b2 - 12b + 9

Vikentia [17]

Answer:

(2b-3)²

Step-by-step explanation:

The square of a binomial is ...

(p - q)² = p² - 2pq + q²

The fact that the first and last terms are perfect squares suggests that you might want to look to see if the middle term matches this form. It does.

For p² = 4b², p=2b.

For q² = 9, q = 3.

Then 2pq = 2(2b)(3) = 12b.

So, the factoring is ...

4b² -12b +9 = (2b -3)²

5 0

3 years ago

Michelle is checking a division problem by doing the following: 128

MrRa [10]

899/7.....if u plug this into a calculator u will get 128.(and a bunch of decimal numbers).....but u have the whole number 128....so 128 x 7 = 896 + 3 = 899

so the answer to this problem is basically : 899/7 = 128 remainder 3

6 0

3 years ago

a construction crew built 4 1/2 miles of Road and 3 3/8 days. What is the unit rate in miles per day? Write your answer as a fra

sineoko [7]

The construction crew took $3\frac{3}{8}$ days to build $4\frac{1}{2}$ miles of road.

Therefore, in 1 day, the crew built $\frac{4\frac{1}{2} }{3\frac{3}{8} }$ miles of road

= $\frac{\frac{9}{2} }{\frac{27}{8} } =\frac{9}{2}times\frac{8}{27}=\frac{4}{3}$ miles of road

Thus, the required rate is $\frac{4}{3}$ miles or $1\frac{1}{3}$ miles per day.

5 0

3 years ago

A phone manufacturer wants to compete in the touch screen phone market. He understands that the lead product has a battery life

alisha [4.7K]

Answer:

The null hypothesis is $H_0: \mu \leq 10$

The alternative hypothesis is $H_1: \mu > 10$

b-1) The value of the test statistic is t = 1.86.

b-2) The p-value is of 0.0348.

Step-by-step explanation:

Question a:

Test if the battery life is more than twice of 5 hours:

Twice of 5 hours = 5*2 = 10 hours.

At the null hypothesis, we test if the battery life is of 10 hours or less, than is:

$H_0: \mu \leq 10$

At the alternative hypothesis, we test if the battery life is of more than 10 hours, that is:

$H_1: \mu > 10$

b-1. Calculate the value of the test statistic.

The test statistic is:

We have the standard deviation for the sample, so the t-distribution is used to solve this question

$t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.

10 is tested at the null hypothesis:

This means that $\mu = 10$

In order to test the claim, a researcher samples 45 units of the new phone and finds that the sample battery life averages 10.5 hours with a sample standard deviation of 1.8 hours.

This means that $n = 45, X = 10.5, s = 1.8$

Then

$t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}$

$t = \frac{10.5 - 10}{\frac{1.8}{\sqrt{45}}}$

$t = 1.86$

The value of the test statistic is t = 1.86.

b-2. Find the p-value.

Testing if the mean is more than a value, so a right-tailed test.

Sample of 45, so 45 - 1 = 44 degrees of freedom.

Test statistic t = 1.86.

Using a t-distribution calculator, the p-value is of 0.0348.

5 0

2 years ago