MATHEMATICS COLLEGE

if you are just given the two points it is the same formula. Find the midpoint between the points (4,−5) and (−4,5).

Answers

Answer 1

Answer:

Answer:

$M = (0,0)$

Step-by-step explanation:

Given

$(4,-5)$ and $(-4,5)$

Required

The midpoint (M)

This is calculated as:

$M = (1)/(2)(x_1 + x_2,y_1+y_2)$

So, we have:

$M = (1)/(2)(4-4,-5+5)$

$M = (1)/(2)(0,0)$

$M = (0,0)$

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Help me pls. Which expression shows the prime factorization of 48? 2 × 2 × 2 × 2 × 3 2 × 2 × 2 × 3 2 × 2 × 3 2 × 2 × 2 × 3 × 3

Answers

The first one which is 2 × 2 × 2 × 2 × 3

the correct one would be 2x2x2x2x3

A pharmaceutical company ran a clinical trial to test if drug X cures disease Y. A statistician named Z who is taking BIO 211 was given a task to perform a null hypothesis test. The test was perfect, and the null hypothesis was rejected at the alpha = 0.05 significance level. However, unbeknownst to Z, the company ran 39 extra clinical trials and secretly hired Z’s classmates to evaluate data obtained from each independent trial with the same null hypothesis test at the same significance level. a. What is the null hypothesis? Drug X does cure disease Y Drug X does not cure disease Y

Answers

Answer:

The null hypothesis is A) Drug X does cure disease Y

Step-by-step explanation:

Consider the provided information.

If there is no statistical significance in the test then it is know as the null which is denoted by $H_0$ , otherwise it is known as alternative hypothesis which denoted by $H_a$ .

A pharmaceutical company ran a clinical trial to test if drug X cures disease Y.

Since, claim is drug X cures disease.

Therefore, the null hypothesis is A) Drug X does cure disease Y

Solve the inequality 5y + 4 < 3y + 17

Answers

Answer:

y<13/2

Step-by-step explanation:

5y + 4 < 3y + 17

5y-3y<-4+17

2y<13

y<13/2

Answer:

y<6.5

Step-by-step explanation:

5y+4<3y+17

Subtract 3 from both sides

2y+4<17

Subtractc4 from both sides

2y<13

Divide both sides by 2

y<6.5

The amount of cream sauce on the fettuccine at Al Fred-O's follows a Normal distribution, with a mean of 3.78 ounces and a standard deviation of 0.14 ounce. A random sample of 12 plates of fettuccine is selected every day and the sauce is measured. What is the probability that the mean weight will exceed 3.81 ounces

Answers

Answer:

22.66% probability that the mean weight will exceed 3.81 ounces

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = (\sigma)/(√(n))$

In this problem, we have that:

$\mu = 3.78, \sigma = 0.14, n = 12, s = (0.14)/(√(12)) = 0.04$

What is the probability that the mean weight will exceed 3.81 ounces

This probability is 1 subtracted by the pvalue of Z when X = 3.81. So

$Z = (X - \mu)/(\sigma)$

By the Central Limit Theorem

$Z = (X - \mu)/(s)$

$Z = (3.81 - 3.78)/(0.04)$

$Z = 0.75$

$Z = 0.75$ has a pvalue of 0.7734

1 - 0.7734 = 0.2266

22.66% probability that the mean weight will exceed 3.81 ounces

Answer:

Correct answer is 0.2290

Step-by-step explanation:

Law School According to the Law School Admission Council, in the fall of 2007, 66% of law school applicants wereaccepted to some law schooL4 The training program LSATisfaction claims that 163 of the 240 students trained in 2006were admitted to law school. You can safely consider these trainees to be representative of the population of law schoolapplicants. Has LSAﬁsfaction demonstrated a real improvement over the national average?a) What are the hypotheses?b) Check the conditions and ﬁnd the P-value.c) Would you recommend this program based on what you see here? Explain.

Answers

Answer:

a) $H_(0): p = 0.66\nH_A: p > 0.66$

b) P-value = 0.2650

c) No, this programme will not be recommended as there is no real improvement over the national average.

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 240

p = 66% = 0.66

Alpha, α = 0.05

Number of students admitted to law school , x = 163

a) First, we design the null and the alternate hypothesis

$H_(0): p = 0.66\nH_A: p > 0.66$

This is a one-tailed(right) test.

Formula:

$\hat{p} = (x)/(n) = (163)/(240) = 0.6792$

$z = \frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}$

Putting the values, we get,

$z = \displaystyle\frac{0.6792-0.66}{\sqrt{(0.66(1-0.66))/(240)}} = 0.6279$

b) Now, we calculate the p-value from the table.

P-value = 0.2650

c) Since the p-value is greater than the significance level, we fail to reject the null hypothesis and accept the null hypothesis.

Thus, there is no real improvement over the national average.

No, this programme will not be recommended as there is no real improvement over the national average.

In? gambling, the chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes. For? example, if the number of successful outcomes is 2 and the number of unsuccessful outcomes is? 3, the odds of winning are 2:3(Note; if the odds of winning are 2/3, the propability of sucess is2/5)The odds of event occuring are 1:6. Find (a) the propability that the event will occur,(b) propability that the event will not occur.

(a)The propability that event will occur is....(TYPE AN INTEGER OR DECIMAL ROUNDED TO THE NEAREST THOUSANDTH AS NEEDED.)

(b)The propability thet the event will not occur is...(TYPE AN INTEGER OR DECIMAL ROUNDED TO THE NEAREST THOUSANDTH AS NEEDED)