MATHEMATICS COLLEGE

What is the circumference of the circle?1) 2 by 6 rectangle is inscribed in circle

2) 5 by 5 square is inscribed in circle

3) 5 by 6 rectangle is inscribed in circle

4)2 by 15 rectangle is inscribed in circle

5) 1 by 12 rectangle is inscribed in circle

Answers

Answer 1

Answer: I think it is 2 hope this helped you

Answer 2

Answer:

Answer:

1. 6 pi

2. 7 pi

3. 8 pi

4. 15 pi

5. 12 pi

Step-by-step explanation: Just took the USATestprep test and got them all correct, sorry I dont have a proper answer on how I got them.

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Consider the following hypothesis test:H 0: = 17H a: 17A sample of 40 provided a sample mean of 14.12. The population standard deviation is 4.a. Compute the value of the test statistic (to 2 decimals). (If answer is negative, use minus "-" sign.)b. What is the p-value (to 4 decimals)?c. Using = .05, can it be concluded that the population mean is not equal to 17? SelectYesNoItem 3Answer the next three questions using the critical value approach.d. Using = .05, what are the critical values for the test statistic (to 2 decimals)? ±e. State the rejection rule: Reject H 0 if z is Selectgreater than or equal togreater thanless than or equal toless thanequal tonot equal toItem 5 the lower critical value and is Selectgreater than or equal togreater thanless than or equal toless thanequal tonot equal toItem 6 the upper critical value.f. Can it be concluded that the population mean is not equal to 17?

Answers

Answer:

We conclude that the population mean is not equal to 17.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 17

Sample mean, $\bar{x}$ = 14.12

Sample size, n = 40

Alpha, α = 0.05

Population standard deviation, σ = 4

First, we design the null and the alternate hypothesis

$H_(0): \mu = 17\nH_A: \mu \neq 17$

We use Two-tailed z test to perform this hypothesis.

a) Formula:

$z_(stat) = \displaystyle\frac{\bar{x} - \mu}{(\sigma)/(√(n)) }$

Putting all the values, we have

$z_(stat) = \displaystyle(14.12 - 17)/((4)/(√(40)) ) = -4.5536$

b) P-value can be calculated from the standard z-table.

P-value = 0.0000

c) Since the p-value is less than the significance level, we reject the null hypothesis and accept the alternate hypothesis. Thus, the population mean is not equal to 17

d) Now, $z_(critical) \text{ at 0.05 level of significance } = \pm 1.96$

e) Rejection Rule:

We reject the null hypothesis if it is less than lower critical value and greater than the upper critical value

If the z-statistic lies outside the acceptance region which is from -1.96 to +1.96, we reject the null hypothesis.

f) Since the calculated z-stat lies outside the acceptance region, we reject the null hypothesis and accept the alternate hypothesis. Thus, the population mean is not equal to 17.

Final answer:

The test statistic is -1.78 and the p-value is 0.0761, indicating that we fail to reject the null hypothesis. Therefore, it cannot be concluded that the population mean is not equal to 17.

Explanation:

The test statistic can be calculated using the formula:

test statistic = (sample mean - population mean) / (population standard deviation / sqrt(sample size))

Plugging in the given values, we get:

test statistic = (14.12 - 17) / (4 / sqrt(40))

Calculating this gives us a test statistic value of -1.78.

The p-value can be calculated using the test statistic. We need to find the probability that a test statistic at least as extreme as -1.78 would occur assuming the null hypothesis is true. Using a standard normal distribution table or software, we find the p-value to be approximately 0.0761.

Since the p-value is greater than the significance level (alpha = 0.05), we fail to reject the null hypothesis. Therefore, we can conclude that there is not enough evidence to suggest that the population mean is not equal to 17.

Learn more about Hypothesis testing here:

brainly.com/question/34171008

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I want you to help me solve the variable equations of questions 3

Answers

Answer:

$\huge\boxed{\sf x = -24}$

Step-by-step explanation:

Given equation:

$\displaystyle -(1)/(2) x - 4 =8\n\nAdd \ 4 \ to \ both \ sides\n\n-(1)/(2) x = 8+4\n\n-(1)/(2) x = 12\n\nMultiply \ both \ sides \ by \ -2\n\n-(1)/(2) x * \ -2 = 12 * -2\n\n\boxed{x = -24}\n\n\rule[225]{225}{2}$

Answer:

$\boxed{\mathtt{1) \ x=4}}$

$\boxed{\mathtt{2) \ x=2}}$

$\boxed{\mathtt{3) \ x=-24}}$

Step-by-step explanation:

$\textsf{For these problems, we are asked to solve for x in each equation.}$

$\textsf{We should use similar steps for each of them.}$

$\large\underline{\textsf{For Number 1:}}$

$\textsf{We should first begin by adding 2 to both sides of the equation.}$

$\mathtt{8x=32}$

$\textsf{Now, divide by 8.}$

$\boxed{\mathtt{1) \ x=4}}$

$\large\underline{\textsf{For Number 2:}}$

$\textsf{Let's begin by subtracting 5 from both sides of the equation.}$

$\mathtt{-x=-2}$

$\textsf{Now, divide by -1.}$

$\boxed{\mathtt{2) \ x=2}}$

$\large\underline{\textsf{For Number 3:}}$

$\textsf{Beginning Number 3, let's multiply by -2 to both sides of the equation.}$

$\mathtt{x+8=-16}$

$\textsf{Now, subtract 8 from both sides of the equation.}$

$\boxed{\mathtt{3) \ x=-24}}$

Add: (−2x^2 + 9x − 3) + (7x^2 − 4x + 2)

Answers

Answer:

5x^2+5x-1

Step-by-step explanation:

-2x^2+9x-3+7x^2-4x+2=5x^2+5x-1

The center of the circle is located (3'8), and the circle has a radius that is 5 units long. What is the general form of the equation for the circle

Answers

9514 1404 393

Answer:

x² +y² -6x -16y +48 = 0

Step-by-step explanation:

Given:

circle center: (3, 8)
circle radius: 5

Find:

general form equation for the circle

Solution;

The standard form equation for the circle is ...

(x -h)² +(y -k)² = r² . . . . . circle with radius r centered at (h, k)

(x -3)² +(y -8)² = 5²

Subtracting 25 and expanding this will give the general form.

x² -6x +9 +y² -16y +64 -25 = 0

x² +y² -6x -16y +48 = 0

_____

Additional comment

"General form" of an equation is usually the form f(x,y) = 0, where f(x, y) is written in "standard form," with terms in lexicographical order and decreasing degree.

Slope of (10, 7) and (1, 14)

Answers

Answer:

-7/9

Step-by-step explanation:

Answer:

-7/9

Step-by-step explanation:

formula: y2-y1/x2-x1

14-7/1-10=

7/-9

We know that if the probability of an event happening is 100%, then the event is a certainty. Can it be concluded that if there is a 50% chance of contracting a communicable disease through contact with an infected person, there would be a 100% chance of contracting the disease if 2 contacts were made with the infected person