MATHEMATICS COLLEGE

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Answers

Answer 1

Answer:

$y = 6x + 2$

Step-by-step explanation:

To write a linear function to represent the situation in the form of y = mx + b, we need to find,

m = slope of the graph

b = y-intercept or starting value

✔️Finding slope (m) using two points on the line, (0, 2) and (1, 8):

$slope (m) = (y_2 - y_1)/(x_2 - x_1) = (8 - 2)/(1 - 0) = (6)/(1) = 6$

y-intercept (b) = 2 (i.e the value of y when x = 0, which is the starting value oflr the point where the line intercepts the y-axis)

Substitute m = 6, and b = 2 in $y = mx + b$

$y = 6x + 2$

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Evaluate 3.2 + 6 to the second power minus 2 * 7.2 show your work will mark brainiest
Select all of the solutions to the original equation X=4X equals -16 X equals minus 4X equals 16 X equals minus 8X equals minus 1X equals one X equals eight
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out of 10 student, the favorite drink of 7 is Coke and the favorite drink of of the rest is fanta. a teacher picks a student at random. what is the probability that the favorite drink of the student is (a) Coke (b) fanta (c) neither Coke nor fanta (d) either Coke or fanta

The height distribution of NBA players follows a normal distribution with a mean of 79 inches and standard deviation of 3.5 inches. What would be the sampling distribution of the mean height of a random sample of 16 NBA players?

Answers

Answer:

The probability will be "0.0111".

Step-by-step explanation:

The given values are:

Mean,

$\mu$ = 79

Standard deviation,

$\sigma$ = 3.5

Now,

⇒ $\sigma\bar x = (\sigma)/(\sqrt n)$

$= (3.5)/(\sqrt 16)$

$=0.875$

⇒ $P(\bar x > 81) = 1 - P(\bar x < 81)$

So,

= $1 - P{((\bar x - \mu \bar x ))/( \sigma \bar x) < ((81 - 79) )/(0.875) ]$

= $1 - P(z < 2.2857)$

= $0.0111$

Which relation is not a function?

Answers

It would be 3 beacuse w=3

The distance you travel while hiking is a function of how fast you hike and how long you hike at this rate. You usually maintain a speed of three miles per hour while hiking. Write a statement that describes how the distance that you travel is determined. Then identify the independent and dependent variables of this function. a. The distance traveled is three times the number of hours I have hiked. The independent variable is hours. The dependent variable is distance.
b. The distance traveled is three times the number of hours I have hiked. The independent variable is distance. The dependent variable is hours..
c. The hours I have hiked is three times the distance. The independent variable is distance. The dependent variable is hours.
d. The hours I have hiked is three times the distance. The independent variable is hours. The dependent variable is distance.

Please select the best answer from the choices provided.

Answers

Answer:

If hours is represented as h, your distance is therefore 3*h (due to that for every hour, you walk 3 miles. For example, in one hour you'd walk 3 miles, in 2 hours you'd walk 3+3=3*2=6 miles,etc.). If distance is represented by d, we get 3*h=d. Since you have to figure out the distance from the equation (that's the purpose of it!), the distance is the dependent variable. In addition, since you can't have 2 separate variables in one equation, h is the independent variable due to that you have to put a number for h in to figure out the distance

So basically the answer is A.

An electronics firm sells four models of stereo receivers, three CD decks, and six speaker brands. When the three types of components are sold together, they form a "system." How many different systems can the electronics firm offer?A. 169
B. 72
C. 13
D. 36

Answers

Answer:

B. 72

Step-by-step explanation:

The total number of different systems that can be bundled together is the product of the possible number of ways to select 1 out of 4 stereo receivers, by 1 out of 3 CD decks and by 1 out of 6 speakers. Assuming that the order at which products are picked does not matter, the number of different systems is:

$n=(4!)/((4-1)!1!)*(3!)/((3-1)!1!)*(6!)/((6-1)!1!)\nn=4*3*6\nn=72\ systems$

The electronics firm can offer 72 different systems.

A new drug to treat psoriasis has been developed and is in clinical testing. Assume that those individuals given the drug are examined before receiving the treatment and then again after receiving the treatment to determine if there was a change in their symptom status. If the initial results showed that 2.0% of individuals entered the study in remission, 77.0% of individuals entered the study with mild symptoms, 16.0% of individuals entered the study with moderate symptoms, and 5.0% entered the study with severe symptoms calculate and interpret a chi-squared test to determine if the drug was effective treating psoriasis given the information below from the final examination.

Answers

Answer:

Step-by-step explanation:

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: The distribution of severity of psoriasis cases at the end and prior are same.

Alternative hypothesis: The distribution of severity of psoriasis cases at the end and prior are different.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square goodness of fit test of the null hypothesis.

Analyze sample data. Applying the chi-square goodness of fit test to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.

DF = k - 1 = 4 - 1

D.F = 3

(Ei) = n * pi

Category observed Num expected num [(Or,c -Er,c)²/Er,c]

Remission 380 20 6480

Mild

symptoms 520 770 81.16883117

Moderate

symptoms 95 160 24.40625

Severe

symptom 5 50 40.5

Sum 1000 1000 6628.075081

Χ2 = Σ [ (Oi - Ei)2 / Ei ]

Χ2 = 6628.08

Χ2Critical = 7.81

where DF is the degrees of freedom, k is the number of levels of the categorical variable, n is the number of observations in the sample, Ei is the expected frequency count for level i, Oi is the observed frequency count for level i, and Χ2 is the chi-square test statistic.

The P-value is the probability that a chi-square statistic having 3 degrees of freedom is more extreme than 6628.08.

We use the Chi-Square Distribution Calculator to find P(Χ2 > 19.58) =less than 0.000001

Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we cannot accept the null hypothesis.

We reject H0, because 6628.08 is greater than 7.81. We have statistically significant evidence at alpha equals to 0.05 level to show that distribution of severity of psoriasis cases at the end of the clinical trial for the sample is different from the distribution of the severity of psoriasis cases prior to the administration of the drug suggesting the drug is effective.

Final answer:

The chi-square test is a statistical method that determines if there's a significant difference between observed and expected frequencies in different categories, such as symptom status in this clinical trial. Without post-treatment numbers, we can't run the exact test. However, if the test statistic exceeded the critical value, we could conclude that the drug significantly affected symptom statuses.

Explanation:

This question pertains to the use of a chi-squared test, which is a statistical method used to determine if there's a significant difference between observed frequencies and expected frequencies in one or more categories. For this case, the categories are the symptom statuses (remission, mild, moderate, and severe).

To conduct a chi-square test, you first need to know the observed frequencies (the initial percentages given in the question) and the expected frequencies (the percentages after treatment). As the question doesn't provide the numbers after treatment, I can't perform the exact chi-square test.

If the post-treatment numbers were provided, you would compare them to the pre-treatment numbers using the chi-squared formula, which involves summing the squared difference between observed and expected frequencies, divided by expected frequency, for all categories. The result is a chi-square test statistic, which you would then compare to a critical value associated with a chosen significance level (commonly 0.05) to determine if the treatment has a statistically significant effect.

To interpret a chi-square test statistic, if the calculated test statistic is larger than the critical value, it suggests that the drug made a significant difference in the distribution of symptom statuses. If not, we can't conclude the drug was effective.

Learn more about Chi-square test here:

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Write the formula for Newton's method and use the given initial approximation to compute the approximations x_1 and x_2. f(x) = x^2 + 21, x_0 = -21 x_n + 1 = x_n - (x_n)^2 + 21/2(x_n) x_n + 1 = x_n - (x_n)^2 + 21 x_n + 1 = x_n - 2(x_n)/(x_n)^2 + 21 Use the given initial approximation to compute the approximations x_1 and x_2. x_1 = (Do not round until the final answer. Then round to six decimal places as needed.)